Apparatus and methods for neural stimulation using polynomial distortion algorithm

Abstract

Exemplary embodiments of the present disclosure include apparatus, methods and systems for therapeutic neuromodulation of neurons and circuits utilizing a polynomial distortion algorithm (PDA). Exemplary embodiments provide for selective activation of specific model neurons by PDA tuning of the stimulating waveform to the intrinsic biophysical properties of the neuron. Furthermore, exemplary embodiments provide energy optimization of the waveform that can minimize off-target effects. Selective activation of specific model neurons can be achieved by PDA tuning of the stimulating waveform to the intrinsic biophysical properties of the neuron. Furthermore, energy optimization of the waveform can minimize off-target effects. Apparatus and methods utilizing a polynomial distortion algorithm to stimulate neurons with different channel activation properties, channel conductance properties, and diameters are provided.

Description

[0001] APPARATUS AND METHODS FOR NEURAL STIMULATION USING POLYNOMIAL DISTORTION ALGORITHM CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims provisional priority to application number 63 / 764,093 filed February 27, 2025. the entire contents of which is incorporated herein by reference.

[0003] BACKGROUND

[0004] Therapeutic electrical stimulation of neurons is typically accomplished using rectangular pulses. Under this paradigm, the excitability of neurons can be evaluated, and certain intrinsic neuronal properties are known to be associated with greater excitability. For instance, neurons with larger diameters [1-3] or larger leak channel conductances [4,5] have lower thresholds for activation by an exogenous step current. As such, activating less excitable neurons automatically activates more excitable neurons. Therapeutic exogenous stimulation using rectangular pulse waveforms is unable to fully mimic normal physiological recruitment behavior (e.g., small fibers before larger fibers as described by Henneman’s size principle [6]) or selectively stimulate less excitable neurons without unintentionally activating nearby neuronal structures that are more excitable. The rectangular waveform is an unnatural stimulus shape. Electrical inputs that excite neurons in vivo have complex waveform shapes. How these shapes provide selective excitation related to the intrinsic electrophysiological properties of the neuron per se is of interest in computational neuroscience and neuro therapeutics.

[0005] Excitation is traditionally evaluated using strength-duration curves where the amplitude and width of a rectangular pulse are used as the basis. A previous study, however, showed that multiple mechanisms can elicit an action potential in a neuron. An action potential generated using a standard depolarizing pulse uses a mechanism different from one generated through anodal break using a hyperpolarizing pulse. In the Hodgkin-Huxley model of the neuron [7], these mechanisms are reflected as having different trajectories through the state space [8], The multi-dimensional nature of the neuronal state space (e.g., V, m, n, and h, in the Hodgkin-Huxley model) raises aninteresting question regarding whether stimulus waveform shapes can be tuned to recast excitability from a different lens where the shape of the stimulus is a parameter.

[0006] Phrenic nerve stimulators are used to restore breathing following spinal cord injury; however, clinical complications and failures persist. Diaphragmatic dysfunction associated with high cervical spinal cord injury (SCI) or central hypoventilation syndromes frequently results in chronic respiratory insufficiency and long-term dependence on mechanical ventilation. Although phrenic nerve stimulation has been demonstrated as a viable approach for restoring independent respiration, and cervical implantation techniques are well documented, existing technologies remain limited. FDA-approved diaphragmatic pacing systems are implanted via a cervical approach in both adult and pediatric SCI populations, and their long-term safety has enabled clinical adoption. Nevertheless, stimulation parameters in current systems are not optimized, and ventilator dependence commonly persists following implantation. Commercially available systems, including those marketed by Avery Biomedical, generally employ static stimulation parameters and lack real-time, patient-specific control. The absence of adaptive modulation limits the ability to accommodate physiological variability, including diaphragmatic fatigue and changing ventilatory demands. Further, existing phrenic nerve stimulators fail to replicate physiological motor unit recruitment, in which small, low-force motor units are activated prior to progressive recruitment of larger units. Clearly, there is a need for improved methods for nerve stimulation.

[0007] SUMMARY

[0008] Briefly, the present disclosure provides apparatus, methods, and systems for therapeutic neuromodulation of neurons and circuits utilizing a polynomial distortion algorithm (PDA). Exemplary embodiments provide for selective activation of specific model neurons by PDA tuning of the stimulating waveform to the intrinsic biophysical properties of the neuron. Furthermore, exemplary embodiments provide energy optimization of the waveform that can minimize off-target effects. As shown with data provided herein (e.g., FIGS. 1-14), PDA can be utilized in systems to provide a non-square-wave or complex electrical stimulation to selectively stimulate neurons based on the type or class of excitability the neuron exhibits e.g. Type 1, Type 2, Type 3 also called class 1, 2, 3 respectively, as originally defined by Hodgkin)

[0120] and other domains

[0009] 2

[0010] 4931-6275-7522, v. 1of selectivity (e.g. neuron channel composition). Type 1 neurons, so called integrators can encode input strength, whereas Type 2 neurons, so-called resonators, cannot. However, Type 2 neurons can exhibit subthreshold oscillations, whereas Type 1 neurons generally do not. Computational power and efficiency can be surprising and unexpectedly improved by PDA as compared to previous methods; for example, by implementing the assumption of a polynomial fraction for electrical pulses, the search space is limited by an order or magnitude, avoiding the curse of dimensionality observed with other methods such as EDA. PDA preferably does not interpolate between the extrema. If desired, multiple complex electrical stimulations can be generated by PDA to first stimulate neurons or nerve fibers with smaller diameter, followed by stimulating neurons or nerve fibers with larger diameters. This stimulation pattern can be particularly useful for mimicking natural nerve stimulation causing contraction of muscles, such as for example the phrenic nerve causing a contraction of the diaphragm. Systems utilizing PDA include systems comprising an electrode including, e.g., phrenic nerve stimulation.

[0011] As shown in the below examples, systems and methods are provided that utilize PDA to optimize electrical stimulation waveforms both in vitro and in vivo, including in phrenic nerve stimulators. In vitro experiments using dissociated rat hippocampal cells in culture and fluorescent calcium imaging for continuous monitoring of individual neuron activity demonstrated improvements in optimization of signals for neuron stimulation. PDA was used to facilitate selective stimulation of neuronal subgroups within heterogenous populations, allowing for targeted activation of individual neurons or neuron types based on specific ion channel properties or spatial coordinates. These methodologies were also applied in vivo to the central nervous system (CNS), e.g., to optimize neuronal firing patterns and achieve selective targeting within the CAI hippocampal region and the ventral tegmental area region of a murine model. PDA methodologies provided herein were also utilized in vivo in the peripheral nervous system (PNS) to optimize stimulation parameters for phrenic nerve activation in a rat model, optogenetic monitoring in vivo, and in a rat sciatic nerve model. Data for such approaches are provided in the figures and examples. These results demonstrate that methods and systems provided herein can be used to provide in vivo modulation of and therapies to neurons in both the CNS and PNS. For example, these approaches can be applied to benefit phrenic nerve breathing stimulators, which may improve breathing smoothness (e.g., recruiting small, low-force motor nerve bundles first, unlike

[0012] 3

[0013] 4931-6275-7522, v. 1current phrenic pacemakers), decrease muscle fatigue, thus reducing clinical failures and mortality / morbidity associated with these approaches.

[0014] Systems and methods that utilize PDA provided herein can be used to decrease off-target stimulation of neurons in a variety of different clinical approaches. For example, PDA can be utilized in the stimulation of the phrenic nerve for treating central respiratory failure in order to decrease stimulation of larger (10-20 pm) diameter nerve fibers that can adversely cause overstimulation and muscle fatigue that is often observed when using square-wave type electrical stimulation. PDA can similarly be used to decrease off-target stimulation of nerve fibers including: the vagus nerve, sciatic nerve, spinal cord, dorsal root ganglion, and / or thalamus / sub-thalamus area of the brain. PDA can be used to generate electrical waveforms to initially stimulate smaller diameter nerve fibers, while reducing or minimizing stimulation of larger diameter nerve fibers having a diameter of 6-12 pm, 10-20 pm, 13-20 pm, or at least 5, 6, 7, 8, 9, 10. 11. 12, 13, 14, 15, 16, 17, 18, 19, or 20 pm, or any range derivable therein.

[0015] Exemplary embodiments of the present disclosure include an apparatus for applying a therapeutic treatment to a mammalian subject. In certain embodiments the apparatus comprises a stimulation electrode and a programmable arbitrary waveform generator, where the programmable arbitrary waveform generator is configured to: receive a detected signal from the subject; transmit a first stimulation signal waveform to the subject via the stimulation electrode; receive a response signal from the subject; and transmit a second stimulation signal waveform to the subject via the stimulation electrode, wherein the second stimulation signal waveform is generated using a polynomial distortion algorithm (PDA). Nerve cuff stimulators may have, e.g., 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 or more electrodes. A variety of nerve cuff electrodes are commercially available that can be used with the PDA methods and systems provided herein, including a nerve cuff electrode comprising concentric electrodes with multiple contacts around a single portion of the nerve that allows recording and / or stimulation at different locations around the same point. The stimulation may occur be between two at least two sites or electrodes, but the PDA modulation of an electrical stimulation can be extended to make use of more complex geometries resulting from additional electrodes.

[0016] 4

[0017] 4931-6275-7522, v. 1The polynomial distortion algorithm (PDA) may distort the roots of a polynomial function that mimics the first stimulation signal waveform. In some embodiments the apparatus is configured to provide for selective activation of a neuron by polynomial distortion algorithm (PDA) tuning of the first stimulation signal waveform to an intrinsic biophysical property of the neuron. In specific embodiments the intrinsic biophysical property comprises an axonal diameter, a channel conductance, and / or a channel activation curve.

[0018] In certain embodiments the apparatus is configured to provide energy optimization of the second stimulation signal waveform. In particular embodiments the energy optimization is configured to minimize off-target effects of the subject. In some embodiments the programmable arbitrary waveform generator is configured to receive a second response signal from the subject where the second response signal is in response to the second stimulation signal waveform, and transmit a third stimulation signal waveform via the stimulation electrode where the third stimulation signal waveform is generated using the polynomial distortion algorithm (PDA).

[0019] In specific embodiments the programmable arbitrary waveform generator is configured to apply subsequent stimulation signal waveforms and receive subsequent response signals in an iterative process. The waveform generator may preferably be in either constant voltage or current mode. In certain embodiments the iterative process allows for selective stimulation of nerve fibers of reduced diameter. In particular embodiments the reduced diameter is less than about 10 pm or less than about 5 pm. In certain embodiments the apparatus is configured to transmit the first stimulation signal waveform to a peripheral nerve bundle in the subject. In some embodiments the peripheral nerve bundle is the phrenic nerve of the subject. In specific embodiments the stimulation signals are configured for treatment of central respiratory failure.

[0020] In certain embodiments the peripheral nerve bundle is the vagus nerve of the subject. In particular embodiments the stimulation signals are configured for treatment of epilepsy, hypertension, or depression. In some embodiments the peripheral nerve bundle is the sciatic nerve of the subject. In specific embodiments the stimulation signals are configured for treatment of urinary incontinence. In certain embodiments the peripheral nerve bundle is a spinal cord nerve or dorsal root ganglion of the subject. In particular embodiments the stimulation signals are configured for treatment of pain or chronic pain. In some embodiments the pain results from failed

[0021] 5

[0022] 4931-6275-7522, v. 1back surgery syndrome (FBSS), complex regional pain syndrome (CRPS), peripheral neuropathy (including diabetic neuropathy), post-herpetic neuralgia, phantom limb pain, visceral pain, or cancer-related pain. In specific embodiments the apparatus is configured to transmit the first stimulation signal waveform to a central nerve or the brain of the subject.

[0023] In certain embodiments the apparatus is configured to transmit the first stimulation signal waveform to the ventral tegmental area (VTA), thalamus, or subthalamus. In particular embodiments the first stimulation signal and the second stimulation signal are deep brain stimulation signals. In some embodiments the deep brain stimulation signals are directional deep brain stimulation (DBS) signals. In specific embodiments the deep brain stimulation signals are configured for treatment of Parkinson’s disease, epilepsy, or a seizure disorder. In certain embodiments the deep brain stimulation signals are configured for treatment of absence seizures, tonic seizures, atonic seizures, clonic seizures, myoclonic seizures, or tonic-clonic seizures. In particular embodiments the first stimulation signal waveform and the second stimulation signal waveform are transcranial magnetic stimulation (TMS) signals. In some embodiments the first stimulation signal waveform and the second stimulation signal waveform are transcranial direct current stimulation (TDCS) signals.

[0024] In specific embodiments the first stimulation signal waveform and the second stimulation signal waveform are configured to treat at least one of central respiratory failure, hypertension, urinary incontinence, pain or chronic pain, parkinsonian tremor, movement disorder, epilepsy, depression, coma, cognitive impairment, obsessive compulsive disorder, depression, migraine, pain, addiction, or stroke rehabilitation. PDA approaches may be used in cardiac applications, such as systolic dysfunction, heart failure, ischemic heart disease, or ventricular arrhythmia. In certain embodiments the response signal from the subject comprises muscle contraction, one or more nerve signals affecting muscle contraction, pain perception by the subject, or performance of a motor skill by the subject.

[0025] In particular embodiments the PDA algorithm is configured to iteratively perform the steps of: fitting a first polynomial function to the response signal; differentiating the polynomial function to generate a derivative; identifying roots of the derivative; distorting the roots of the derivative;

[0026] 6

[0027] 4931-6275-7522, v. 1integrating the derivative; and scaling and offsetting the derivative to create a second polynomial function to generate the second stimulation signal waveform.

[0028] Exemplary embodiments include a method of treating a condition in a mammalian subject, where the method comprises: receiving an oscillating electrical signal from a subject; applying a first stimulation signal waveform to the subject, wherein the first stimulation signal waveform modifies the oscillating electrical signal from the subject to produce a response signal; receiving the response signal from the subject; and applying a second stimulation signal waveform to the subject, wherein the second stimulation signal is generated using a polynomial distortion algorithm (PDA).

[0029] In certain embodiments the method further comprises: applying a third stimulation signal waveform to the subject, where the third stimulation signal waveform is generated using a polynomial distortion algorithm (PDA), and the third stimulation signal waveform modifies the oscillating electrical signal from the subject to produce a second response signal; receiving the second response signal from the subject; and applying a fourth stimulation signal waveform to the subject, where the fourth stimulation signal waveform is generated using a polynomial distortion algorithm (PDA), and the fourth stimulation signal waveform is configured to optimize the second response signal without regard to the phase window of the oscillating electrical signal.

[0030] Some embodiments further comprise applying subsequent stimulation signal waveforms and receiving subsequent response signals in an iterative process. In specific embodiments the signal waveforms are administered to a peripheral nerve bundle in the subject. In certain embodiments the peripheral nerve is the phrenic nerve. In some embodiments the condition comprises central respiratory failure. In specific embodiments the peripheral nerve is the vagus nerve. In certain embodiments the condition comprises epilepsy, hypertension, or depression. In particular embodiments the peripheral nerve is the sciatic nerve. In some embodiments the condition is urinary incontinence. In specific embodiments the peripheral nerve is a spinal nerve or a dorsal root ganglion. In certain embodiments the condition is pain or chronic pain. In certain embodiments the pain results from ailed back surgery syndrome (FBSS), complex regional pain syndrome (CRPS). peripheral neuropathy (including diabetic neuropathy), post-herpetic neuralgia, phantom limb pain, visceral pain, or cancer-related pain.

[0031] 7

[0032] 4931-6275-7522, v. 1In particular embodiments the signal waveforms are administered to a central nervous system region or neuron or a peripheral nervous system neuron or nerve of the subject. In some embodiments the signal waveforms are administered to the ventral tegmental area (VTA), thalamus, or subthalamus. In specific embodiments the condition comprises essential tremor or Parkinsonian tremor. In certain embodiments the condition is a epilepsy or a seizure disorder. In particular embodiments the seizure disorder is characterized by absence seizures, tonic seizures, atonic seizures, clonic seizures, myoclonic seizures, or tonic-clonic seizures. In some embodiments the condition is movement disorder, epilepsy, depression, coma, cognitive impairment, obsessive compulsive disorder, depression, migraine pain, addiction, or stroke. In specific embodiments the subject is a human.

[0033] Certain embodiments further comprise providing for selective activation of a neuron by polynomial distortion algorithm (PDA) tuning of the first stimulation signal waveform to an intrinsic biophysical property of the neuron. In particular embodiments the intrinsic biophysical property comprises an axonal diameter. In some embodiments the intrinsic biophysical property comprises a channel conductance. In specific embodiments the intrinsic biophysical property comprises a channel activation curve. In certain embodiments the response signal is neuronal transmission by a nerve fiber having a diameter of less than about 10 pm or less than about 5 pm.

[0034] In particular embodiments the method comprises selectively inducing action potentials in nerve bundles having a diameter of less than about 5 pm, while causing reduced stimulation of action potentials in nerve bundles having a diameter of greater than about 5 pm. In some embodiments the method comprises selectively inducing action potentials in nerve bundles having a diameter of less than about 10 pm, while causing reduced stimulation of action potentials in nerve bundles having a diameter of greater than or equal to about 10 pm or about 13 pm.

[0035] An aspect of the present disclosure relates to a method of non-therapeutic stimulation of nerve fibers in a mammalian subject, the method comprising: receiving an oscillating electrical signal from a subject; applying a first stimulation signal waveform to the subject, wherein the first stimulation signal waveform modifies the oscillating electrical signal from the subject to produce a response signal; receiving the response signal from the subject; and applying a second stimulation signal waveform to the subject, wherein the second stimulation signal is generated

[0036] 8

[0037] 4931-6275-7522, v. 1using a polynomial distortion algorithm (PDA). Based on detecting the response to the second stimulation signal waveform in the subject (e.g., based on the physical response of the subject for a physical movement, such as for example breathing, physiological response, or electrical brain activity such as for example frequency of a seizure response or activity of neurons in the subject) the process can be repeated over time to alter, improve, or optimize the response in the subject. The method may further comprise: applying a third stimulation signal waveform to the subject, wherein: the third stimulation signal waveform is generated using a polynomial distortion algorithm (PDA); and the third stimulation signal waveform modifies the oscillating electrical signal from the subject to produce a second response signal; receiving the second response signal from the subject; and applying a fourth stimulation signal waveform to the subject, wherein: the fourth stimulation signal waveform is generated using a polynomial distortion algorithm (PDA); and the fourth stimulation signal waveform is configured to optimize the second response signal without regard to the phase window of the oscillating electrical signal. The method may further comprise applying subsequent stimulation signal waveforms and receiving subsequent response signals in an iterative process. The signal waveforms may be administered to a peripheral nerve bundle in the subject. The peripheral nerve may be the phrenic nerve, the vagus nerve, the sciatic nerve, a spinal nerve or a dorsal root ganglion. The signal waveforms may be administered to a central nervous system neuron or region or a peripheral nervous system neuron or nerve of the subject, preferably wherein the signal waveforms are administered to the ventral tegmental area (VTA), thalamus, or subthalamus. The mammalian subject may be a human. The method may further comprise providing for selective activation of a neuron by polynomial distortion algorithm (PDA) tuning of the first stimulation signal waveform to an intrinsic biophysical property of the neuron, preferably wherein the intrinsic biophysical property comprises an axonal diameter and / or wherein the intrinsic biophysical property comprises a channel conductance and / or wherein the intrinsic biophysical property comprises a channel activation curve. The response signal may be neuronal transmission by a nerve fiber having a diameter of less than about 10 pm or less than about 5 pm. The method may comprise selectively inducing action potentials in nerve bundles having a diameter of less than about 5 pm, while causing reduced stimulation of action potentials in nerve bundles having a diameter of greater than about 5 pm. preferably wherein the method comprises selectively inducing action potentials in nerve bundles having a diameter of less than about 10 pm, while causing reduced stimulation of action potentials in nerve bundles having a

[0038] 9

[0039] 4931-6275-7522, v. 1diameter of greater than or equal to about 10 pm or about 13 pm. The stimulation may lead to muscle relaxation and / or stress reduction by stimulation of the vagus nerve. The stimulation may lead to an increase of the tidal volume by stimulation of the phrenic nerve. The stimulation may lead to an increase of muscle strength or muscle coordination by stimulation of the sciatic nerve. The stimulation may lead to an increase of blood flow by stimulation of the spinal nerve. The stimulation may lead to a modulation of sensory signal transmission by stimulation of the dorsal root ganglion. The method may be performed by programmable circuitry. The method may comprise: selecting a field of view that includes a plurality of neurons disposed between stimulation electrodes; applying an initial biphasic stimulus; determining, for each neuron, a change in firing frequency relative to a predetermined baseline firing frequency; and adding one or more neurons to a region of interest when a ratio of the change in firing frequency to the predetermined baseline firing frequency exceeds a threshold. The method may comprise: determining whether an exposure time associated with imaging the field of view exceeds a time limit in response to when the ratio does not exceed the threshold; selecting a different field of view when the exposure time does not exceed the time limit; and replacing a neuronal sample when the exposure time exceeds the time limit. The method may comprise delivering the generated waveform for a plurality of trials; determining whether multicell selectivity is present based on trial results; applying the polynomial distortion algorithm, upon determining that multicell selectivity is present, to generate distorted waveforms; adding candidate waveforms to a library when a target neuron is activated without activation of a non-target neuron; testing candidate waveforms for robustness over a plurality of additional trials; and selecting, as a new parent seed, a robust candidate waveform having a lower energy metric than a current parent seed. The method may include configurations wherein the second stimulation signal waveform is applied to a phrenic nerve of the subject. The method, in some embodiments, may further comprise receiving ventilator-derived respiratory data including at least one of tidal volume, respiratory phase timing, or capnography data, wherein the polynomial distortion algorithm (PDA) updates one or more stimulation parameters based on the ventilator-derived respiratory data. The method may include configurations wherein the polynomial distortion algorithm iteratively adjusts at least one of stimulation timing, waveform shape, or stimulation energy across successive respiratory cycles to improve consistency of tidal volume generated by phrenic nerve stimulation.

[0040] 10

[0041] 4931-6275-7522, v. 1Other objects, features and advantages of the present invention will become apparent from the following detailed description. It should be understood, however, that the detailed description and the specific examples, while indicating certain embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description.

[0042] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood to one of ordinary skill in the art to which this invention belongs. Although any methods, devices and materials similar or equivalent to those described herein can be used in the practice or testing of the invention, the exemplified methods, devices and materials are now described.

[0043] Although the invention has been described with respect to specific embodiments thereof, these embodiments are merely illustrative, and not restrictive of the invention. The description herein of illustrated embodiments of the invention, including the description in the Abstract and Summary, is not intended to be exhaustive or to limit the invention to the precise forms disclosed herein (and in particular, the inclusion of any particular embodiment, feature or function within the Abstract or Summary is not intended to limit the scope of the invention to such embodiment, feature or function). Rather, the description is intended to describe illustrative embodiments, features and functions in order to provide a person of ordinary skill in the art context to understand the invention without limiting the invention to any particularly described embodiment, feature or function, including any such embodiment feature or function described in the Abstract or Summary. While specific embodiments of, and examples for, the invention are described herein for illustrative purposes only, various equivalent modifications are possible within the spirit and scope of the invention, as those skilled in the relevant art will recognize and appreciate. As indicated, these modifications may be made to the invention in light of the foregoing description of illustrated embodiments of the invention and are to be included within the spirit and scope of the invention. Thus, while the invention has been described herein with reference to particular embodiments thereof, a latitude of modification, various changes and substitutions are intended in the foregoing disclosures, and it will be appreciated that in some instances some features of embodiments of the invention will be employed without a corresponding use of other features without departing from the scope and spirit of the invention as set forth. Therefore, many 11

[0044] 4931-6275-7522, v. 1modifications may be made to adapt a particular situation or material to the essential scope and spirit of the invention. The disclosures of all patents, patent applications and publications cited herein are hereby incorporated herein by reference in their entireties, to the extent that they are consistent with the present disclosure set forth herein.

[0045] Reference throughout this specification to "one embodiment", "an embodiment", or "a specific embodiment" or similar terminology means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment and may not necessarily be present in all embodiments. Thus, respective appearances of the phrases "in one embodiment", "in an embodiment", or "in a specific embodiment" or similar terminology in various places throughout this specification are not necessarily referring to the same embodiment. Furthermore, the particular features, structures, or characteristics of any particular embodiment may be combined in any suitable manner with one or more other embodiments. It is to be understood that other variations and modifications of the embodiments described and illustrated herein are possible in light of the teachings herein and are to be considered as part of the spirit and scope of the invention.

[0046] In the description herein, numerous specific details are provided, such as examples of components and / or methods, to provide a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that an embodiment may be able to be practiced without one or more of the specific details, or with other apparatus, systems, assemblies, methods, components, materials, parts, and / or the like. In other instances, well-known structures, components, systems, materials, or operations are not specifically shown or described in detail to avoid obscuring aspects of embodiments of the invention. While the invention may be illustrated by using a particular embodiment, this is not and does not limit the invention to any particular embodiment and a person of ordinary skill in the art will recognize that additional embodiments are readily understandable and are a part of this invention.

[0047] At least a portion of embodiments discussed herein can be implemented using a computer communicatively coupled to a network (for example, the Internet), another computer, or in a standalone computer. As is known to those skilled in the art. a suitable computer can include a processor or central processing unit (“CPU”), at least one read-only memory (“ROM”), at least

[0048] 12

[0049] 4931-6275-7522, v. 1one random access memory (“RAM”), at least one hard drive (“HD”), and one or more input / output (“I / O”) device(s). The I / O devices can include a keyboard, monitor, printer, electronic pointing device (for example, mouse, trackball, stylist, touch pad, etc.), or the like.

[0050] ROM, RAM, and HD are computer memories for storing computer-executable instructions executable by the CPU or capable of being complied or interpreted to be executable by the CPU. Suitable computer-executable instructions may reside on a computer readable medium (e.g., ROM, RAM, and / or HD), hardware circuitry or the like, or any combination thereof. Within this disclosure, the term “computer readable medium” or is not limited to ROM, RAM, and HD and can include any type of data storage medium that can be read by a processor. For example, a computer-readable medium may refer to a data cartridge, a data backup magnetic tape, a floppy diskette, a flash memory module or drive, an optical data storage drive, a CD-ROM, ROM, RAM, HD, or the like. Software implementing some embodiments disclosed herein can include computer-executable instructions that may reside on a non-transitory computer readable medium (for example, a disk, CD-ROM, a memory, etc.). Alternatively, the computer-executable instructions may be stored as software code components on a direct access storage device array, magnetic tape, floppy diskette, optical storage device, or other appropriate computer-readable medium or storage device.

[0051] Any suitable programming language can be used to implement the routines, methods or programs of embodiments of the invention described herein, including the custom script. Other software / hardware / network architectures may be used. For example, the software tools and the custom script may be implemented on one computer or shared / distributed among two or more computers in or across a network. Matlab and python were used to generate such software tools. Communications between computers implementing embodiments can be accomplished using any electronic, optical, radio frequency signals, or other suitable methods and tools of communication in compliance with known network protocols. Additionally, any signal arrows in the drawings / figures should be considered only as exemplary, and not limiting, unless otherwise specifically noted. Based on the disclosure and teachings provided herein, a person of ordinary skill in the art will appreciate other ways and / or methods to implement the invention.

[0052] 13

[0053] 4931-6275-7522, v. 1A “seizure” as used herein refers to a disease characterized by a paroxysmal alteration of neurologic function, or characterized by an excessive, hypersynchronous discharge of neurons in the brain. “Epileptic seizure” is used to distinguish a seizure caused by abnormal neuronal firing from a nonepileptic event, such as a psychogenic nonepileptic seizure (PNES). “Epilepsy” is the condition of recurrent, unprovoked seizures. Epilepsy can result from a variety of numerous causes, each reflecting underlying brain dysfunction

[0121] , A seizure provoked solely by a reversible insult (e.g., fever, hypoglycemia) does not fall under the definition of epilepsy because it is a short-lived secondary condition, not a chronic state. “Seizure disorder” refers to a disease characterized by seizures. In some embodiments, the seizure disorder may be an “epilepsy syndrome,” which refers to a group of clinical characteristics that consistently occur together, with similar seizure type(s), age of onset, EEG findings, triggering factors, genetics, natural history, prognosis, and / or response to antiepileptic drags (AEDs).

[0054] The methods described herein may be computerized. They may be performed by a computer as mentioned above, or, in general, by programmable circuitry that comprises one or more processors and / or one or more Field Programmable Gate Arrays (“FPGA”) and / or controllers and / or other electronics.

[0055] Parkinson's disease (PD) is a progressive nervous system disorder. PD is the second most common progressive neurodegenerative disorder affecting older American adults. PD results from a pathophysiologic loss or degeneration of dopaminergic neurons in the substantia nigra of the midbrain and is typically characterized by the development of neuronal Lewy Bodies. Idiopathic Parkinson's Disease has been associated with a variety of risk factors (e.g., Beitz, 2014). PD typically includes both motor and non-motor symptoms. For example, PD patients may exhibit a tremor (e.g., at rest), muscle rigidity, bradykinesia, and / or stooping posture. PD has occasionally been associated with other neurobehavioral symptoms, such as depression, anxiety, cognitive impairment, or autonomic dysfunction (e.g., orthostasis and hyperhidrosis).

[0056] Deep brain stimulation (DBS) can be used to treat diseases such as epilepsy and PD. DBS involves the therapeutic use of repeated or chronic electrical stimulation of the brain, e.g., via an implanted electrode. It can be used to treat the motor symptoms of Parkinson's disease (PD), essential tremor, and dystonia. A variety of brain regions can be targeted for electrical stimulation

[0057] 14

[0058] 4931-6275-7522, v. 1via the implanted electrode. For example, to treat epilepsy, the brain region that is targeted can be the anterior thalamic nucleus (ATN), cerebellum, caudate nucleus (CN), subthalamic nucleus (STN), hippocampus, centromedian nucleus of the thalamus (CM), corpus callosum (CC). locus coeruleus (LoC), or mammillary bodies (MB). In some embodiments, the seizure focus can be targeted (e.g., using an RNS® device, Neuropace, Inc., CA, USA) for detection and stimulation at the seizure focus, and this approach is normally customized for each patient. To treat PD, DBS can be used to target the globus pallidus intemus (GPi), STN, or pedunculopontine nucleus (PPN) in the brain of a subject. Additional details regarding these approaches are described, e.g., in Herrington et al., 2016.

[0059] The systems and methods provided herein that utilize PDA may utilize a phrenic nerve stimulator. A variety of phrenic nerve stimulators can be used, including traditional implanted phrenic nerve cuff systems with external transmitters, intradiaphragmatic muscle-electrode systems, fully implanted transvenous phrenic stimulators, and external stimulation. The conventional phrenic nerve pacers may include a nerve cuff and RF receiver. For intradiaphragmatic (direct muscle) pacing systems, instead of cuffing the nerve, multiple small electrodes are implanted laparoscopically into the diaphragm near the intramuscular branches of the phrenic nerve, and a separate grounding electrode is placed subcutaneously, preferably wherein all leads exit the abdomen and connect to an external pulse generator via a percutaneous connector. Fully implanted transvenous phrenic nerve stimulators use a pacing lead that is implanted in a thoracic vein adjacent to the phrenic nerve, such as the left pericardiophrenic or right brachiocephalic vein. External stimulation approaches may use surface or belt electrodes over the lower thorax / abdomen to activate the diaphragm; these approaches may be used to prevent ventilator-induced diaphragm dysfunction or aid weaning rather than to fully replace ventilation.

[0060] Any embodiment of any of the present methods, composition, kit, and systems may consist of or consist essentially of - rather than comprise / include / contain / have - the described steps and / or features. Thus, in any of the claims, the term “consisting of’ or “consisting essentially of’ may be substituted for any of the open-ended linking verbs recited above, in order to change the scope of a given claim from what it would otherwise be using the open-ended linking verb.

[0061] 15

[0062] 4931-6275-7522, v. 1The use of the term “or” in the claims is used to mean “and / or” unless explicitly indicated to refer to alternatives only or the alternatives are mutually exclusive, although the disclosure supports a definition that refers to only alternatives and “and / or.”

[0063] Throughout this application, the term “about” or “approximately” is used to indicate that a value includes the standard deviation of error for the device or method being employed to determine the value.

[0064] Following long-standing patent law. the words “a” and “an,” when used in conjunction with the word “comprising” in the claims or specification, denotes one or more, unless specifically noted.

[0065] As used herein, the terms “comprises,” “comprising,” "includes," "including," "has," "having," or any other variation thereof, are intended to cover a non-exclusive inclusion. For example, a process, product, article, or apparatus that comprises a list of elements is not necessarily limited only those elements but may include other elements not expressly listed or inherent to such process, process, article, or apparatus.

[0066] Furthermore, the term "or" as used herein is generally intended to mean "and / or" unless otherwise indicated. For example, a condition A or B is satisfied by any one of the following: A is true (or present) and B is false (or not present), A is false (or not present) and B is true (or present), and both A and B are true (or present). As used herein, including the claims that follow, a term preceded by "a" or "an" (and "the" when antecedent basis is "a" or "an") includes both singular and plural of such term, unless clearly indicated within the claim otherwise (i.e., that the reference "a" or "an" clearly indicates only the singular or only the plural). Also, as used in the description herein, the meaning of "in" includes "in" and "on" unless the context clearly dictates otherwise.

[0067] As used herein, "patient" or "subject" includes mammalian organisms, such as human and non-human mammals, for example, but not limited to, rodents, mice, rats, non-human primates, companion animals such as dogs and cats as well as livestock, e.g„ sheep, cow, horse, etc. Therefore, for example, although the described embodiments illustrate use of the present methods on humans, those of skill in the art would readily recognize that these methods and compositions could also be applied to veterinary medicine as well as on other animals.

[0068] 16

[0069] 4931-6275-7522, v. 1BRIEF DESCRIPTION OF THE DRAWINGS

[0070] The following drawings form part of the present specification and are included to further demonstrate certain aspects of the present invention. The invention may be better understood by reference to one or more of these drawings in combination with the detailed description of specific embodiments presented herein. The patent or application file may contain at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

[0071] FIG. 1 illustrates a depiction of nerve fiber recruitment patterns in endogenous physiological conditions and square wave exogenous electrical stimulation.

[0072] FIG. 2 illustrates neural responses to endogenous versus exogenous stimulation while varying fiber diameter and stimulation amplitude.

[0073] FIG. 3 illustrates a depiction of electrical waveforms used for selectively stimulating small diameter fibers.

[0074] FIG. 4 illustrates an outline of the polynomial distortion algorithm.

[0075] FIG. 5 illustrates L2-norm values of both EDA (orange / grey) and PDA (blue / black) runs. Pale lines show the results of each individual run, while the bold lines show the result of the average across 20 runs.

[0076] FIG. 6 illustrates Optimal stimulus waveforms (top panels) for selectively stimulating both traditional (blue / black) and modified (orange / grey) Hodgkin-Huxley as seen in the system responses (bottom panels).

[0077] FIG. 7 illustrates the upper envelope of both traditional (blue / black) and Clay variant (orange / grey) neuronal response (middle panel) to the ZAP function (top panel) shows the different resonant frequencies for each type.

[0078] 17

[0079] 4931-6275-7522, v. 1FIG. 8 illustrates Stimulus-duration curve plotted on log-log scale for the traditional Hodgkin-Huxley (blue / black) and increasing sodium persistent conductances: lightest blue / black (gNaP = 0) to darkest blue / black (gNaP = 0.05).

[0080] FIG. 9 illustrates the optimal stimulus waveform showing selective activation of the traditional Hodgkin-Huxley (higher blue / black peak trajectories) against Hodgkin-Huxley with persistent sodium channels (lower orange / grey peak).

[0081] FIG. 10 illustrates graphs showing a narrow window exists for the size of the intermediate pulse segment such that only the traditional Hodgkin-Huxley neuron fires while the version with a persistent sodium channel (gNaP = 0.02) does not fire.

[0082] FIG. 11 illustrates that by changing the stimulus waveform shape, one can selectively stimulate the smaller neuron without activating the larger neuron, and vice versa.

[0083] FIG. 12 illustrates that although both selective stimulus waveforms generate an action potential for the 15-um neuron (right) versus the 25 -um neuron (left), the mechanism of depolarization is different.

[0084] FIG. 13 illustrates that by modifying the stimulus waveform shape (top row), one is able to orderly recruit small to large fibers (left to right).

[0085] FIG. 14 illustrates success (out of 100) for stimulus optimized to activate only the traditional Hodgkin-Huxley (upper graph results) when under increasingly noisy environments.

[0086] FIG. 15 illustrates a programmable arbitrary wave generator block diagram according to an exemplary embodiment of the present disclosure.

[0087] FIG. 16 illustrates a programmable arbitrary wave generator flow diagram according to an exemplary embodiment of the present disclosure.

[0088] FIG. 17 illustrates a programmable arbitrary wave generator circuit diagram according to an exemplary embodiment of the present disclosure.

[0089] 18

[0090] 4931-6275-7522, v. 1FIG. 18 In vitro application of PDA to optimize waveforms in neurons. Reduction in energy consumption was observed compared to other stimulation waveforms

[0091] FIG. 19 In vitro application of PDA to optimize waveforms in neurons. Current (mA) over time is shown.

[0092] FIG. 20 illustrates a schematic detailing the experimental configuration for the Polynomial Distortion Algorithm (PDA). The in vitro preparation consists of dissociated mouse hippocampal cells in culture and fluorescent calcium imaging was used for continuous monitoring of individual neuron activity.

[0093] FIG. 21 illustrates the system architecture and operational logic flowchart for PDA.

[0094] FIGS. 22A-22C PDA alteration of stimulus waveforms to target individual neurons.

[0095] FIG. 23: PDA stimulation of the CNS in vivo, observed using optogenetic monitoring. Across five experimental trials, the PDA consistently outperformed standard square-pulse stimulation, achieving robust activation responses while utilizing significantly lower energy levels.

[0096] FIG. 24: PDA stimulation to optimize phrenic nerve activation in vivo. PDA waveforms outperformed standard square-pulse stimulation by achieving robust acceleration outputs with significantly lower energy requirements.

[0097] FIG. 25: PDA stimulation to optimize phrenic nerve activation in vivo. PDA waveforms outperformed standard square-pulse stimulation.

[0098] FIG. 26: Example schematic for system for phrenic nerve stimulation using PDA. Clinical workflow and data integration between the patient, the ventilator, and the PDA control system is shown.

[0099] FIG. 27: Continuous analysis of incoming ventilatory data and dynamically updating of stimulation parameters by PDA is shown. The signal can thus be repeatedly modulated or further improved over time and transmitted to an electrical stimulator (e.g., Ripple stimulator).

[0100] 19

[0101] 4931-6275-7522, v. 1FIG. 28: The temporal relationship between mechanical ventilation and stimulated pacing is shown.

[0102] DETAILED DESCRIPTION

[0103] Exemplary embodiments provide therapeutic neuromodulation of neurons and circuits utilizing a polynomial distortion algorithm (PDA). Particular embodiments provide for selective activation of specific model neurons by PDA tuning of the stimulating waveform to the intrinsic biophysical properties of the neuron. Furthermore, specific embodiments provide energy optimization of the waveform that can minimize off-target effects. Exemplary embodiments of the present disclosure include apparatus and methods utilizing a polynomial distortion algorithm to stimulate neurons with different channel activation properties, channel conductance properties, and diameters. In some aspects, PDA can be used to generate a complex or non-square electrical wave to first stimulate smaller diameter nerve fibers, which can avoid initial stimulation of larger diameter nerve fibers that can cause adverse clinical consequences, in systems for stimulation of nerves including the phrenic nerve (e.g., to treat central respiratory failure), vagus nerve (e.g., to treat epilepsy hypertension, or depression), sciatic nerve (e.g., to treat urinary incontinence), spinal cord (e.g., to treat pain), dorsal root ganglion (e.g., to treat pain), and / or the thalamus I subthalamus regions (e.g., to treat essential tremor or Parkinsonism). In this way, PDA can provide the surprising technical effect of avoiding the adverse preferential initial stimulation of larger diameter nerve fibers that have been associated with the application of square wave type electrical stimulation. PDA was shown to more quickly arrive at solutions and utilize less computing power, as compared to other methods including EDA. Additional methods and systems are provided.

[0104] Previous studies examined how waveform shapes can be used to minimize stimulation energy while maintaining the same desired outcomes [9], In those studies, the focus was on energy efficiency and not selectivity. Exemplary embodiments of the present disclosure demonstrate how waveform shapes can change the order of excitation, allowing one to selectively stimulate neurons that are considered relatively unexcitable, i.e., with a high rheobase, without co-activating neurons that are considered highly excitable. Three separate experiments utilizing embodiments of the present disclosure compare excitability in neurons that differ in one key parameter and identify distinct stimulus waveforms that can selectively activate each type. Using a polynomial distortion 20

[0105] 4931-6275-7522, v. 1algorithm, the inventors examined excitability in neurons with different channel activation properties, channel conductance properties, and diameters. The inventors demonstrate that the properties of excitability can be reversed and explore the ionic mechanisms underlying these reversals to gain insight into how these non-traditional waveforms are taking advantage of the specific differences between neurons to achieve these results.

[0106] In examining excitability, the inventors constructed three sets of model neurons. Each set consists of neurons that differ in one key feature: channel activation curves, channel conductance, and axonal diameter.

[0107] Neurons with different channel activation curves

[0108] The first case study is based on the traditional Hodgkin-Huxley model [7], stated as follows:

[0109] CV̇ = -120m3h(V - 115) - 36n4(V + 12) - 0.3(V - 10.613) - It- u

[0110] ṁ = —m(am(V) + βm(V)) + am(V)

[0111] ṅ = —n(an(V) + βn(V)) + an(V)

[0112]

[0113] ḣ = -h(ah(V) + βh(V)) + ah(V)

[0114] where

[0115] = “SM- faW = 0.125. M-'7"

[0116] (KI = 0.07^e-'' / 2“. / ?„( / ) =>01,

[0117]

[0118] The inventors adjusted the Hodgkin-Huxley model neuron’s potassium activation subunit such thatn(V) is:

[0119] αn(V) = 0.125 e-V / 80

[0120] 21

[0121] 4931-6275-7522, v. 1This model change described by Clay and colleagues alters the traditional Hodgkin-Huxley from exhibiting Type 2 behavior, in which sustained repetitive firing of action potentials occurs for as long as a suprathreshold depolarizing current pulse is applied, to Type 3 behavior, where the neuron only fires once at the beginning of the pulse

[0010] . These two types of neurons, the traditional Hodgkin-Huxley model, showing Type 2 behavior, and the Clay variant, showing Type 3 behavior, provide important contrasting examples of two neurons that differ slightly in their activation curves yet display different dynamics.

[0122] Neurons with different channel conductance

[0123] In the second case study, the inventors introduced a persistent sodium channel into the traditional Hodgkin-Huxley neuron model, as seen by adding —gNaL(V - 115) to CV̇

[0124] CV̇ = -120m3h(V - 115) - 36n4(V + 12) - 0.3(V - 10.613) - gNaL(V - 115) - u

[0125] where is the conductance of the sodium persistent channel. The inventors studied neurons over a range of conductances from 0.01 mS / cm2to 0.05 mS / cm2. These channels are known to produce subthreshold depolarizing currents that drive the neuron towards its threshold, and thus increase their excitability. While this is a simplified model, the presence of persistent sodium channels is known to change the behaviors of neurons, affecting the frequency and pattern of firing in many neurons [11,12], These channels are known to produce sub threshold depolarizing currents that help drive the neuron towards its threshold, and thus push it towards excitability.

[0126] Because of the persistent sodium channel, these neurons do not start from the same resting membrane potential, and do not have the same thresholds. To visualize these thresholds more clearly, the inventors dimensionally reduce the four-dimensional Hodgkin-Huxley model down to a two-dimensional version by making assumptions described previously by Krinskii & Kokoz

[0013] , and implemented by Izhikevich

[0014] ,

[0127] First, given that the sodium activation subunit has a time constant much faster than the sodium inactivation subunit and the potassium activation subunit, the inventors can assume an instantaneous transition to the sodium activation steady state, m∞

[0128] 22

[0129] 4931-6275-7522, v. 1G-m

[0130] m∞= — m

[0131]

[0132] “b

[0133] Second, the potassium activation subunit appears to be inversely proportional to the sodium inactivation subunit. As such, the inventors can set:

[0134] h(t) = 1 — crn(t),

[0135] where a = 1.27 as determined when plotting the Hodgkin-Huxley neuron at its resting state. This value fluctuates as the action potential arises, but during the subthreshold region prior to the action potential, the value of a is more stable.

[0136] Neurons with different axonal diameters

[0137] Exogenous electrical stimulation of peripheral nerves preferentially activates large fibers due to their lower activation thresholds and greater susceptibility to external electrical fields, compared to smaller fibers. However, selectivity in stimulating small fibers, sparing large fibers, can play an important role in clinical applications.

[0138] Electrical stimulation is increasingly employed in clinical interventions to address neurological disorders and functional deficits in both the central and peripheral nervous systems. While electrical stimulation devices are widely available, their clinical effectiveness is limited by the difficulty of accurately mimicking natural recruitment patterns. In biological systems, neuronal recruitment is guided by complex pathways that optimize signal transmission and ensure efficient network communication. However, external electrical stimuli tend to activate large-diameter axons preferentially, which is the reverse of the ideal recruitment order in certain therapeutic applications. A well-studied example is the recruitment order of motor units. According to Henneman’s size principle, motor neurons are naturally activated in a sequence based on ascending axonal diameter — from smallest to largest [28,29]. This principle extends beyond the motor system, impacting how small fibers are independently recruited in other systems as well. FIG. 1 demonstrates the contrasting recruitment patterns: the classical recruitment hierarchy of Henneman’s size principle driven by physiological signals versus the reversed order imposed by

[0139] 23

[0140] 4931-6275-7522, v. 1exogenous electrical stimulation. This reversal poses a significant challenge to the efficacy of various clinical applications of electrical stimulation.

[0141] Exogenous electrical stimulation often results in non-selective recruitment patterns, activating a broader range of neurons than intended. This lack of specificity reduces the precision and effectiveness of stimulation, limiting its therapeutic potential. Understanding and replicating physiological recruitment patterns is crucial for developing more effective electrical stimulation techniques. More specifically, one limiting factor is the challenge of selectively targeting smalldiameter neurons without activating larger ones simultaneously. The ability of electrical signals to distinguish between neuron sizes is essential for tailored treatment. Achieving this specificity requires understanding targeted therapeutics, physiological mechanisms behind size-specific recruitment, and mechanisms of exogenous stimulation. Exemplary embodiments of the present disclosure provide applications and advancements in size-specific recruitment in peripheral nerves, primarily focusing on direct neural stimulation. Reference

[0030] provides a review of skeletal muscle electrical stimulation and recruitment patterns.

[0142] Targeted Therapeutics: Clinical Significance

[0143] Small-diameter nerve axons play a crucial role in biological regulation and in the transmission of sensory modalities. Their slower conduction velocities allow for energy-efficient and precise temporal summation of information, influencing neural signal processing and modulation within various nerve fiber bundles

[0031] , Disabling neurological syndromes result in pathological signaling of small-diameter fibers due to inflammation, degeneration, traumatic injury, and other lesions

[0032] ,

[0144] Bioelectronic stimulators commonly use rectangular-wave pulses that increase intensity from the rheobase, the minimum exogenous step current for inducing an action potential. Nevertheless, this nonselective supramaximal method tends to neglect the precise targeting of small-fiber neurons linked to different diseases. Existing electrode technologies also have inadequate insulation, leaking current and stimulating nearby large fiber neurons, resulting in clinically adverse side effects related to large fiber stimulation

[0033] , Table 1 provides a summary

[0145] 24

[0146] 4931-6275-7522, v. 1of clinical use cases that highlight the adverse effects associated with preferential activation of large fibers by exogenous nerve stimulation.

[0147] Biophysics

[0148] To understand the physiological mechanisms of these clinical observations more fully, experimental and computational studies have revealed the biophysical mechanisms of preferential excitation of large neuronal fibers by exogenous electrical fields. This neuronal size effect is the inverse of the effect of endogenously generated potential, in which neurons are recruited in order from smallest to largest, for example as described by the Henneman size principle for motor fibers and units. FIG. 2 illustrates the cellular biophysical distinction between endogenous and exogenous excitation. The initiation of an action potential in an axon through electrical stimulation from an exogenous source requires the depolarization of the axonal membrane potential until a threshold is reached for voltage-gated sodium channels. When an axon is exposed to an external electric field, its resting membrane potential undergoes changes that depend on the polarity and strength of the electric field and the transmembrane resistance and capacitance of the axon. Axonal diameter comes into play here because the membrane resistance varies as the inverse of the axon diameter squared, while capacitance varies as the product of the diameter squared, i.e., large diameter axons have lower membrane resistance and higher membrane capacitance than small diameter axons. This makes it easier for electrical fields to generate the transmembrane currents (mostly capacitive) necessary to reach the threshold in large vs small diameter axons. Once the threshold is reached, the action potential will propagate from node to node down the axon.

[0149] In FIG. 2, exogenous stimulation is depicted in blue / black, and endogenous stimulation in orange / grey. Results are generated from the Chiu-Ritchie-Rogart-Stagg-Sweeney (CRRSS) Model for nodal and internodal regions with potassium, sodium, and leak channels

[0063] , While sodium channels dominate nodal region dynamics, potassium channels are included for completeness.

[0150] FIG. 2 panel A shows equivalent electrical circuitry diagrams for myelinated nerve fibers stimulated either endogenously or exogenously. In the diagrams, Venrepresents the potential at node n, GNa, GK, and Gl denote the sodium, potassium, and leak conductances, respectively, at a node of Ranvier.

[0151]

[0152] indicates the capacitance at compartment n, and Ra is the axial resistance.

[0153] 25

[0154] 4931-6275-7522, v. 1For endogenous stimulation, Vendo denote the endogenous input current at a node, whereas I xo represents the exogenous field current at compartment n.

[0155] FIG. 2 panel B shows threshold current at downstream node n = 21 as a function of fiber diameter, with step electrical stimulation applied either endogenously at node n = 11 or exogenously as a field originating at node n = 11. Node numbers are included for figure reproducibility. The recruitment pattern for exogenous stimulation shows an inverse correlation between threshold current and fiber diameter. In contrast, endogenous stimulation exhibits linear growth with increasing diameter. This results in inversely correlated threshold-diameter curves between the two stimulation types. The numbered dots correspond to the specific diameter and rheobase current used to generate the subplot in C.

[0156] FIG. 2 panel C shows differential neuron responses to equivalent endogenous and exogenous stimulation. Depolarizing step currents are applied at 0.5 ms. Graphs 1 and 2 show the responses of neurons with diameters 15 pm and 20 pm, respectively, to a 0.15 mA step current. Graphs 3 and 4 show the responses of neurons with diameters 15 pm and 20 pm, respectively, to a 0.0015 mA step current. Electrical stimulation is applied both endogenously and exogenously in all cases.

[0157] Square waves from standard electrodes exploit these properties of large axons. When applied as a stimulus, square waves induce a rapid change in the membrane potential. The lower input resistance and the higher input capacitance of larger axons result in more pronounced depolarization of the membrane potential and more effective action potential generation and propagation. The result is that larger-diameter axons are activated first at lower stimulus thresholds than smaller-diameter axons.

[0158] The pattern of recruitment generated by exogenous stimulation is the inverse of naturally occurring endogenous stimulation. Neurons are activated endogenously by graded synaptic inputs, which converge and summate near the axon hillock. The generation of an action potential occurs when this summation surpasses the neuron’s threshold potential. As first explained for motor unit recruitment [28,29] and later seen in other systems, the impact of this synaptic input is controlled by the neuron’s input resistance [33,34], Small neurons, characterized by their reduced surface

[0159] 26

[0160] 4931-6275-7522, v. 1area, possess a higher input resistance. This high input resistance results in a larger voltage change for a given synaptic input compared to larger neurons, which have lower input resistance due to their larger surface area. Consequently, smaller neurons can reach the threshold for action potential generation with a lower level of synaptic input. Exogenous stimulation does not rely on this physiological integration of synaptic input. Instead, electric fields directly applied to the neurons result in more uniform and widespread depolarization. The mechanisms of this activation are further described in the section below.

[0161] Mechanisms of Exogenous Stimulation: Insights on Targeting Small Fibers

[0162] Researchers have delved into the selective activation of small fibers in an attempt to restore physiological recruitment patterns, using computational models and in vivo experiments. The focus has been on minimizing energy consumption, selectively blocking large fibers, and reducing invasiveness in system design. However, the transition to in vivo studies has brought about notable challenges, particularly concerning charge per protocol duration (the total charge accumulated in a session) and charge density. These factors play a role in neural damage due to electrode corrosion and the generation of electrochemical toxins

[0036] , Electrode design can be miniaturized, and a variety of material modification, and stimulation strategies, highlighting techniques to address the challenges of crosstalk and electrode failure are available

[0036] , These techniques include modifications of electrode designs and stimulation methodologies enabled by material development and computer simulation.

[0163] Various approaches have been employed to achieve targeted stimulation of small neural fibers.

[0164] Inhibition of Large Diameter Fibers

[0165] Modulating the properties of stimulating waveforms allows for selective stimulation by attempting to inhibit the excitation of large fibers. These methods work by suppressing nerve fiber excitability by leveraging ion channel activation properties.

[0166] Pulse Shape

[0167] 27

[0168] 4931-6275-7522, v. 1The shape of a single depolarizing pulse has been utilized to differentially modulate the resting state of axons. Various waveform shapes, as illustrated in FIG. 3 panel A and FIG. 3 panel B, have demonstrated some degree of success in preferentially targeting small fibers [37-41] in experimental preparations.

[0169] Fiber selectivity using pulse shape changes has not been achieved in clinical settings in part because of technical limitations that reduce both effectiveness and patient tolerance. Fiber selectivity is strongly influenced by passive current spread in the tissue, which is affected by the anatomical configuration of the nerve fibers, electrode geometry and design, and the electrical properties of the interstitial compartments surrounding the electrodes. Discovery of pulse waveform shapes that preferentially stimulate a small-diameter fiber might be demonstrated in computational models such as illustrated in FIG. 2 and in controlled experimental preparations. However, in clinical practice it is impossible to know the localization of targeted small fibers and the ambient interstitial electrical properties relative to the electrodes, and spatial and electrical parameters can change over time. Paths with lower resistance will have a disproportionately larger share of the current. Therefore, nearby large fibers - closer to the electrode with lower resistance -will receive a disproportionately larger share of the current. Another important factor is current spread that activates afferent nerve endings with specialized mechanoreceptors, nociceptors, or chemoreceptors. While most nerve endings are located outside the nerve bundle, current spread to adjacent tissues with afferent nerve endings can result their co-activation and trigger painful sensations and reflex arcs. Further, muscle is electrically active and susceptible to artifactual electrical stimulation, and nearby muscle can also be at risk from current spread. Pulse shape tuning research has not fully addressed these challenges. Additionally, monophasic rectangular and quasi-trapezoidal blocking techniques rely on pulse widths exceeding 500 microseconds, often leading to electrode erosion from excessive electrical stimulation and dissolution of chemical components [42,43],

[0170] Pulse Duration

[0171] The charge distribution along an axon during electrical stimulation is influenced by pulse duration, resulting in different threshold amplitudes for large and small fibers

[0044] , Large fibers are optimized for brief intense pulses, while longer, gradually increasing pulses (FIG. 3 panel C)

[0172] 28

[0173] 4931-6275-7522, v. 1decrease their responsiveness

[0045] , In response to such long-duration pulses that increase gradually, large fibers adapt by lowering their excitability through a process called accommodation, which opposes the effect of stimulation. [46,47], This rapid adaptation to slow signals means that large-diameter neurons require higher currents to activate. Small fibers, on the other hand, have larger chronaxie (the minimum amount of time to reach two times the rheobase) and are better suited for prolonged pulses. The gradual buildup of depolarization over time through temporal summation allows small fibers to respond at a lower current intensity. Compared to large fibers, small fibers retain excitability from long-duration pulses due to this temporal summation.

[0174] [48,44], Unlike large fibers, small fibers, either did not display any accommodation or did so at a significantly slower rate

[0049] , While long-duration increasing pulses can effectively block large fibers, they are energetically inefficient and pose risks of tissue damage. Also, the effectiveness of this method depends heavily on the distance between the neuron and the electrode

[0050] . To prevent the unintended activation of nearby large fibers concurrent inhibition methods are often necessary.

[0175] As shown in FIG. 3 panel D, biphasic pulse stimulation aims to address these challenges. This method employs a long cathodal pulse slightly exceeding the blocking threshold for large fibers, suppressing their excitability. The (often shorter) anodal pulse allows the smaller fibers, which have different recovery dynamics, to be selectively activated. This reversal of the typical recruitment order helps achieve selective stimulation of smaller fibers. By alternating an anode pulse and cathode pulse to block large fibers before stimulating small ones, net charge accumulation and potential tissue damage is minimized

[0054] , Prior experimental studies in animal models have reported that high-frequency electrical stimulation of the vagus nerve, including stimulation in the kilohertz range (e.g., greater than approximately 5 kHz), can result in preferential activation of vagal C-fiber afferents while reducing or blocking activation of larger-diameter, myelinated fibers. Computational modeling efforts accompanying these studies have suggested that myelin structure and nodal-internodal organization may influence how externally applied high-frequency fields interact with voltage-gated sodium channel dynamics, contributing to differential excitation or conduction block across fiber classes. These observations highlight that stimulation frequency and waveform characteristics can influence fiber-specific responses and provide useful context for understanding mechanisms of selective neural activation observed in various neuromodulation paradigms.

[0054] ,

[0176] 29

[0177] 4931-6275-7522, v. 1The rapid switching between anodal and cathodal phases causes ions to shift that intensifies the difference in the ion concentration gradient across the neuron’s membrane in a manner that favors initiation of depolarization above threshold

[0051] . Using a single electrode may make it difficult to stimulate small neurons effectively, and factors like distance and temperature play a significant role in optimizing waveform parameters

[0052] , While multiple electrodes slightly improve these challenges, achieving reliable results remains difficult.

[0178] Pulse Frequency

[0179] Higher frequency. kHz. pulse trains have been explored as means to recruit small fiber neurons and inhibit large neurons at a suprathreshold level. In varying the current amplitude and pulse width, short-duration pulses evoke subthreshold depolarization of an axon membrane which temporally summates to an action potential. kHz stimulation in models of the deep brain, vagus nerve, and peripheral receptors yielded asynchronous firing [53-55]. However, practical results have yielded inconclusive outcomes with unknown mechanisms of action and potential long-term effects

[0056] .

[0180] Pulse Sequencing

[0181] Preliminary stimulation, prior to a suprathreshold pulse, can be used to alter the states of the neuronal membrane, ionic channel gating variables, and subsequent activation threshold of a specific nerve. More specifically, deliberately adjusting stimulus amplitudes can preferentially alter the excitability of nerve fibers. This initial pre-pulse (FIG. 3, panel E) or burst of high frequency pre-pulsing (FIG. 3, panel F) can be used to selectively target small neurons by increasing the activation energy requirements of large fibers and increasing the excitability of small ones. In applying a subthreshold pre-pulse, one increases the activation threshold of large fibers more than smaller ones [57-59], This observation has been shown through quantifiable changes in the initial conditions of sodium and potassium channels on the membrane.

[0182] Cathodal (depolarizing) subthreshold pre-pulses can lead to the inactivation of sodium channels and the activation of potassium channels, thereby decreasing neuronal excitability. Conversely, anodal (hyperpolarizing) pre-pulses act differently

[0060] , effectively lowering the activation threshold of unmyelinated C-fibers compared to larger myelinated Ab fibers. This is 30

[0183] 4931-6275-7522, v. 1achieved by reducing potassium ion current in C-fibers, making them more excitable than their larger counterparts, which are more resistant to anodal hyperpolarization.

[0184] When using suprathreshold stimulation, if the pulse is sufficiently strong and long, the membrane potential closest to the anode is likely depolarized at the onset, resulting in activation instead of inhibition. In contrast, a subthreshold anodal pulse will act near the anode and hyperpolarize it, forming an initial blocking region. This differential response between fibers of different sizes and distances from the stimulating electrode results in distinct activation profiles. Notably, this geometry-based variation can make it challenging to consistently achieve selective activation of small fibers alone

[0059] , However, this differential excitability is central to anodal blocking [61,62], Anodal blocking is a technique for small fiber stimulation that works by inducing hyperpolarization near the anode (positive electrode), preventing action potentials in neurons within the hyperpolarized region. Under standard conditions, this hyperpolarization effect selectively blocks activation of the larger, more myelinated fibers. However, when the pre-pulse intensity is sufficiently high, anodal blocking is overcome allowing large fibers to also depolarize. Thus, the intensity and duration of the pre-pulse are crucial for selective stimulation. While this method may achieve large fiber inhibition with extensive parameter optimization and off-target effects, it falls short of selectively stimulating a precise window of small fiber neurons in isolation

[0060] . Additionally, it requires a large amplitude of monophasic current, which may induce irreversible processes at the electrodes, leading to electrode corrosion [63,64],

[0185] Integrated Approaches

[0186] Recent studies have reported new methods for deep brain electrical stimulation using surface electrodes. Delivery of pulse trains noninvasively through two or more electrodes can result in interfering electric fields that produce localized deep brain stimulation [DBS]

[0065] , The potential application of interfering fields for peripheral nerve stimulation also has been explored

[0066] , The biophysical mechanisms of optimizing these signals for minimizing off target effects and achieving selective stimulation, based on active and passive ionic properties of the cell, may provide further insights into clinical translation of interfering electric fields for neuromodulation

[0067] . For small fibers deep within a nerve bundle, it may be possible to tune the interference frequency to match the optimal responsive frequency of small fibers. Tuning of the beat frequency

[0187] 31

[0188] 4931-6275-7522, v. 1might enable selective alteration of small fibers signaling, for example entrainment at specified burst frequencies.

[0189] Experimental results suggest the feasibility of deep peripheral nerve stimulation at stimulation frequencies of approximately 0.5-4 Hz using temporally interfering electrical fields. Reported methods include the use of two pairs of cutaneous electrodes that emit high-frequency sinusoidal carrier signals (e.g., on the order of ~3 kHz), where a relative offset between the carrier frequencies produces a beat frequency corresponding to the desired stimulation frequency.

[0067] ,

[0190] Spatial Selectivity of Small Fibers

[0191] Despite research on novel electrical properties of the stimulating waveform, spatial distribution of fibers highly affects efficacy in practice. As a result, electrode design could lead to selective small fiber stimulation. Researchers aim to fine-tune the electric field distribution generated by waveform properties by altering electrode parameters. Precise positioning of electrodes contributes to the targeted stimulation of small neural fibers.

[0192] Reducing Electrode Size

[0193] Researchers have observed that reducing electrode size enables selective stimulation of non-overlapping, spatially isolated small-diameter neuronal fibers. However, in determining an optimal electrode size, there is a tradeoff between precision and impedance

[0068] , Smaller cathode areas create higher current densities that can be focused on specific fibers, but they also result in greater impedance. Although smaller electrodes improve spatial resolution and reduce cross-talk between fibers, more confounding factors — such as electrode placement accuracy, tissue properties, and variability in neuron response — can still affect the overall effectiveness of stimulation

[0069] , The spatial orientation and intemodal distribution of small-diameter neurons play a crucial role in determining the effect of fine spatial changes in the voltage field and subsequent behavior of targeted stimulation

[0070] ,

[0194] 32

[0195] 4931-6275-7522, v. 1Increasing Contact Points / Number of Electrodes

[0196] Investigators have enhanced spatial resolution by increasing the number of contact points along the targeted nerve segment [71-73], By increasing the number of electrodes, spatial resolution is improved, enabling more localized stimulation that can selectively activate small fibers while minimizing the activation of larger fibers. Additionally, multi-electrode configurations allow for the use of more complex waveforms tailored to the unique properties of small-diameter fibers. However, it is important to note that this method requires a comprehensive understanding of the geometry of the targeted neural fibers. Moreover, its applicability may be limited, as it primarily provides spatial selectivity and may not be feasible in all systems

[0074] , Nevertheless, the future of multi-electrode arrays holds promise, particularly with the potential for closed-loop feedback systems, which could adapt stimulation in real-time based on neural responses.

[0197] Electrode Geometry

[0198] Recent novel methodologies have explored the impact of electrode placement relative to targeted regions

[0075] , In general, chronaxie times measured relative to extracellular stimulation are dependent on the electrode position relative to the neural structure, due to dispersion factors as the waveform propagates

[0076] , However, the shortest chronaxie times were found closest to the electrode, where the rate of change in the current-distance relationship is smaller in large fibers than in small-diameter neurons. Studies focusing on peripheral neuropathy use this phenomenon to provide valuable insights into the optimal depth of pin electrodes. Recently, intraepidermal electrical stimulation has used pin electrodes with terminals at the same epidermis level to establish selective stimulation [77,78], Even in these simplified experiments, the majority of participants did not yield selective recruitment to a single pulse. These results illustrated the difficulties of finding optimal parameters, given that the method relies on spatial distributions relative to fiber size, and the significant variation among individuals that limits applicability

[0078] , Computational models have also shown promising results regarding the potential for small -diameter targeting in vivo through the use of intrafascicular electrodes. To validate these computational findings, further biophysical analysis and increased complexity of the model are necessary. In this context, human studies using intraepidermal electrodes have further examined how electrode placement and

[0199] 33

[0200] 4931-6275-7522, v. 1stimulation parameters influence afferent fiber selectivity. Tn one such study, perception thresholds and response latencies to pulse trains were used to infer preferential activation of A3 versus C fibers, providing an empirical framework for assessing size-dependent recruitment under constrained spatial conditions. A computational model was additionally employed to explore how variations in stimulus parameters may contribute to differences in perceived pain responses, highlighting the interplay between electrode geometry, stimulus timing, and fiber-specific activation in practical stimulation settings.

[0077] ,

[0201] Outlook

[0202] Size-specific fiber recruitment by exogenous stimulation remains a significant challenge in the implementation of minimally invasive devices to treat medical conditions with electrical impulses. Understanding of the principles of selective size activation and implementation for electroceuticals is incomplete. As advancements in neurostimulation and recording technologies continue to unfold, the potential for precise and targeted modulation of neuronal circuits holds immense promise for improving patient outcomes and advancing our understanding of neural function

[0079] , Key questions remain in methods of isolating electric fields, development of biocompatible materials, classifications of peripheral sensory nerve subtypes, and studies on longterm implications for neuronal structure

[0038] , Based on limitations to existing methodologies the study of orderly recruitment based on cell size is confounded by other factors affecting exogenous field effects, for example, the effects of distance between the cell target and the electric field source, the configuration of the source, and the temporal dynamics of propagating fields. An understanding of the classical Henneman size principle as well as the inverse size principle related to exogenous stimulation is essential for future research on restoration of neural function with bioelectronic devices that selectively target small-diameter fibers that are near large fibers. Several areas of future investigation may overcome some of these challenges. Related modeling efforts have also explored predictive approaches to understanding fiber recruitment under specific stimulation protocols. In one such study, a regressor model was used to predict the firing rates of stimulated nerve fibers based on defined stimulation parameters. The model was validated using a simplified optic nerve model, where it was able to reproduce firing rates and certain patterns associated with perceived images. While these results demonstrated reasonable predictive capability, the study also highlighted limitations in capturing the full variability of biological

[0203] 34

[0204] 4931-6275-7522, v. 1neural systems, underscoring ongoing challenges in translating simplified models to complex in vivo conditions.

[0079] , Methods and systems provided herein can address many of these challenges. For exogenous electrical stimulation, the use of customized complex waveforms [80-83] that exploit the differential intrinsic characteristics of small-diameter fibers has not been fully explored. It may be possible to selectively activate or inhibit small fibers while avoiding off target stimulation of larger fibers. This approach, which focuses on the intrinsic properties of the target fibers, could enable more precise control over neural activation. Moreover, integrating closed-loop stimulation systems that dynamically adjust waveforms based on real-time feedback from the neural activity could further enhance the selectivity and effectiveness of stimulation

[0084] , Such systems would allow for personalized and adaptable stimulation patterns, enabling more targeted and efficient activation of small fibers.

[0205] Beyond electrical stimulation, future research on chemogenetic and optogenetic methods hold great promise [85-87]. These methods have yielded important insights into central nervous system function in experimental animal preparations. Clinical applications have been limited in part by the invasiveness and other safety considerations related to delivery of light and ligands into the central nervous system. Peripheral nerves may be more accessible for therapeutic neuromodulation by light or chemicals. In optogenetics, the selective targeting of opsins to release inhibitory neurotransmitters can selectively modulate small fiber neurons allowing for noninvasive and minimally damaging stimulation, although the potential for immunogenicity driven by expression of a foreign protein in the peripheral nervous system may limit clinical utility. Another promising method is the use of focused ultrasound neuromodulation [88,89] for targeting of neurons and nerve fibers, with significant progress on localizing the neuromodulating field.

[0206] Neurons with different axonal diameters

[0207] In the third case study, the inventors built out axons with different diameters. Unlike the previous two case studies, the inventors included a spatial component to modeling neuronal behavior using the Chiu-Ritchie-Rogart-Stagg-Sweeney (CRRSS) model [15,16] instead of the Hodgkin-Huxley model. The CRRSS model constructs a series of compartments that alternate between node of Ranvier and internode. The internode compartments are wrapped with myelin,

[0208] 35

[0209] 4931-6275-7522, v. 1but unlike the earlier McNeal model [1] the myelin is not treated as a perfect insulator and the capacitance is included.

[0210] The membrane voltage potential can be modeled by incorporating both membrane currents as well as axial currents for the node compartments as well as internode compartments:

[0211] dNodesi =rmembrane, node T axial, node)- node

[0212] dlnternodesir(jmembrane, internode T 1 axial, internode) • '■'Internode

[0213] The node currents are defined as follows:

[0214] ^membrane, node 9Na™- h(nodeSi ^Na) "b ffifnodeSi Vj)

[0215] / 'internodei_-l— node i ^e, internode ^e.nodei

[0216] ' i axial, node =? l I _D— i - _ n z_

[0217] ' Kin ' KnRin +Rn internode^ — node i ^e, internodei ^e.nodet

[0218]

[0219] Rin +RnRin +Rn

[0220] while the internode currents are defined as follows:

[0221] I membrane, internode = gminternodesi

[0222] > tnodei internodei ^e.nodei ^e, internodei ‘axial, internode ^ 1 n i n ' o _i_ D

[0223] ' “in “n “in “n (nodei+y— internode: Ve,nodei+1^e, internodei

[0224] + 2 - - - - -

[0225]

[0226] 'Rin +Rn Rin+ Rn

[0227] The membrane currents for the node incorporate the active elements of the voltage-gated sodium channels, which are described as such:

[0228] d

[0229]

[0230] mt= —(am+ * m + am

[0231] dht= — (ah+ ^) * h + ah

[0232] 36

[0233] 4931-6275-7522, v. 1where

[0234] 97+0.363*nodes; „ amCL

[0235] m= - - B = - — -

[0236]

[0237] 1+exp ((31-nodes;) / 5.3)’ 'mexp ((nodes;-238) / 4.17)’

[0238] =156a =Ph

[0239] ' 1+exp (C24-nodes;) / 10)’ exp ((nodes;-55) / 5)’

[0240] The inventors constructed a 21 -node neuron with internodal regions between each one. The stimulus was modeled as a point source right outside the membrane at the 11thnode. For this simulation, the goal was not to activate just the subunit where the stimulus is closest but to cause downstream propagation of the action potential. Thus, while the stimulus was given at node 11, the metric for success was whether or not an action potential was seen at node 21.

[0241] Extrema Distortion Algorithm

[0242] To find the optimal stimulus waveform for all these different experiments, the inventors had previously developed the extrema distortion algorithm (EDA). EDA is a stochastic hillclimbing approach that focuses on the extrema features of a stimulus waveform. It treats the targeted system in question as a black box and iteratively finds better solutions. This approach works by taking a randomly generated starting waveform and iteratively distorting the waveform by incorporating noise to both the amplitude of both minima and maxima as well as the interval between these points. After this distortion process, each new waveform is applied to the system and evaluated for its ability to cause the desired outcome (e.g., firing an action potential) and energy requirements (e.g., L2-norm). This distortion process occurs several times with the same starting seed, and the best solution is chosen from the group. This best solution becomes the starting seed for the next iteration. We had previously demonstrated that this method achieved results similar to those of gradient-based techniques, as applied to both the Hodgkin-Huxley and the FitzHugh-Nagumo [9].

[0243] Polynomial Distortion Algorithm

[0244] While EDA has successfully found optimized waveforms, this approach required significant computational power and time. Because each stimulus was treated as a vector of 300 elements, the ODE solvers needed to interpolate the spaces between the known 300 points, increasing simulation time. Given that the inventors’ previous studies have shown stimuli to be 37

[0245] 4931-6275-7522, v. 1smooth and continuous [1, 2], the inventors assumed that the stimulus could be modeled as a polynomial function and conducted two experiments using the same starting seeds for the extrema distortion algorithm (EDA) and PDA. PDA represents the stimulus as a set of polynomial roots. With EDA, the search space may span as large as 300 dimensions, making this approach vulnerable to the curse of dimensionality, or the complications that arise when analyzing and organizing data in high-dimensional spaces. Using the assumption of a polynomial function, this approach can restrict the search space to an order of magnitude smaller number of degrees of freedom. In the studies provided herein, the inventors were able to successfully use a 20-degree polynomial function. This PDA approach can not only drastically reduce the search space, but it can also remove any need to interpolate between the extrema, allowing for faster computation and simulation. Each algorithm was tested 20 times on a single Hodgkin-Huxley neuron, each run consisting of 1000 iterations. Instead of distorting the extrema of the signal, the new algorithm distorts the roots of the polynomial function that mimics the signal, allowing for faster computation and simulation.

[0246] Referring now to FIG. 4, an overview of this approach is illustrated providing an outline of the polynomial distortion algorithm. More specifically, the polynomial distortion algorithm can be outlined as follows:

[0247] 1. Let the function represent the system in question. Thus, (|i) is the response of the system to a given stimulus.

[0248] 2. Let jipre= (jJ.pre[1], [J.pre[2],...,.pre[M]), M being the product of the number of samples per unit time and the duration of the stimulus, TstimLength. This vector is initially randomly generated using a uniform random number generator at each time point.

[0249] 3. Fit fipreto a polynomial function with predetermined degree, d, which is designated / r0where

[0250] Ho = aQ+ a t + a2t2+ + adtd. where 0 < t < TstimLength.

[0251] 4. Identify the real roots of the first derivative of / r0: {r1(r2,..., rd}.

[0252] 5. Create a set of intervals, I, to be defined as rn— rn-, for n = 2,..., d. Multiply each of these intervals by a random number generated from a Gaussian distribution:

[0253] 38

[0254] 4931-6275-7522, v. 1

[0255]

[0256] If enip, n

[0257] 6. Rescale the new time intervals such that the total duration matches the original duration:

[0258] In Itemp.n * ' Itemp

[0259]

[0260] 7. Use these new intervals to redefine a new set of real roots. Combine them with their original complex roots if needed to create a new polynomial dp0'.

[0261] 8. Integrate dp0' to construct a “neighboring stimulus” / r0'. To address the constants and potential excessive scaling due to integration, apply two constraints:

[0262] a. ^stlmLengthp0'(t)dt = 0

[0263] b. ^stiinLengtK ^2dt =J^stimLength ^2 ^

[0264]

[0265] 9. Apply this new stimulus, p0', to the system and measure its system response.

[0266] 10. Calculate the performance metric (e.g.,

[0267]

[0268] fi0' t)2dt) of this neighboring stimulus, penalizing the performance metric if the stimulus does not successfully cause a state transition. As an example, the inventors used L2-norm:

[0269] C^stimLength

[0270] J = I Po(t)2dt + penalty

[0271]

[0272] Jo

[0273] 11. If the system successfully causes a state transition, multiply the stimulus by a scaling down factor of 1% and calculate a new performance metric. Continue this process until the scaled down stimulus is no longer able to cause a state transition. The performance metric will be the scaled polynomial that successfully caused a state transition.

[0274] 12. Repeat steps 5-11 ten (10) times to produce 10 neighboring stimuli based on the starting stimulus.

[0275] 13. Compare the original starting stimulus with the neighboring stimuli to find the solution with the best performance.

[0276] 14. Repeat steps 4-13 for a predetermined number of iterations, L. using the best performing stimulus found from the previous iteration as the new starting seed in step 4.

[0277] 39

[0278] 4931-6275-7522, v. 115. After L iterations, output the stimulus with the best performance metric as the optimized stimulus.

[0279] The inventors observed that when polynomial coefficients were randomly selected during the initialization phase (Step 2), the resulting waveforms were too large and no longer within the normal physiological range. As such, one modification made was to randomly generate a bounded vector-based stimulation and then fit a polynomial to it. This helped to restrict the polynomial waveform to stay within specific bounds. Alternative techniques may also be used to restrict the polynomial form to a bounded family (e.g., Chebyshev polynomials).

[0280] The two constraints we have imposed in Step 8 are (a) that the stimulus is always chargeneutral and (b) that the L2-norm of the stimulus generated is the same as the L2-norm of the original stimulus. The L2-norm of the stimulus is titrated down in Step 11 to find the solution that barely causes the desired outcome. In some instances, the inventors modified the additive constant and the multiplicative scale by identifying the two free parameters that minimized the difference between the original stimulus and the candidate stimulus. While this took a little longer to converge, it was a smoother and more efficient convergence in the long ran. Similar to the inventors’ previous work, the inventors have used the L2-norm as our optimization metric to reduce the energy of the stimulus. Other metrics can also be used in its place depending on the application.

[0281] As such, the inventors have had to separate out the selectivity component from the energy reduction component of the algorithm utilized in exemplary embodiments of the present disclosure. In this particular case, because the selectivity was a binary question (e.g., did it selectively activate the desired neuron without activating the other neurons), the inventors would feed it many test stimuli regardless of the L2-norm until a library of successfully selective starting seeds was collected. If the inventors had a more graded question, the optimization metric for PDA could be constructed to not include L2-norm and focus first on achieving the desired outcomes, slowly improving itself towards that optimality. Then a second PDA could be used to reduce the L2-norm while maintaining the desired selectivity.

[0282] Results

[0283] Comparison of polynomial distortion algorithm versus extrema distortion algorithm

[0284] 40

[0285] 4931-6275-7522, v. 1Using the timeit function in MATLAB, EDA took around 1500 seconds to run for 100 iterations, while PDA took 168 seconds. In terms of the number of iterations needed to converge towards an efficient L2-norm, FIG. 5 shows the average L2-norm value at each iteration for the first 1000 iterations. As the figure shows, PDA produces a very fast convergence in the first few iterations compared to EDA. FIG. 5 shows the L2-norm values of both EDA (orange / grey) and PDA (blue / black) runs. Pale lines show the results of each individual run, while the bold lines show the result of the average across 20 runs each.

[0286] Table 1 below shows several summary statistics at iteration 100 and iteration 1000 for the two different algorithms.

[0287] Table 1.

[0288] Extrema Distortion Polynomial Distortion Algorithm Algorithm Mean L2-norm at 100 iterations 27.7027 19.0073 Mean L2-norm at 1000 iterations 26.6154 18.2108 Median L2-norm at 100 iterations 17.0007 18.3669 Median L2-norm at 1000 iterations 15.9819 17.0429 Min L2-norm at 100 iterations 15.6858 15.9426 Min L2-norm at 1000 iterations 15.5142 15.9342

[0289]

[0290] Table 1: Summary statistics comparing extrema distortion algorithm against polynomial distortion algorithm.

[0291] As can be seen in Table 1, the best solution for EDA is ultimately better than PDA, which is to be expected given the number of degrees of freedom available for EDA to tune. However, PDA results are very close, while both converge faster in terms of the number of iterations required while using less computational time relative to EDA per iteration.

[0292] Selectively stimulating neurons with different subunit activation curves.

[0293] 4931-6275-7522, v. 1Referring now to FIG. 6, using the polynomial distortion algorithm, the inventors found efficient selective stimulus waveforms for the traditional Hodgkin-Huxley (Type 2 behavior) and the Clay variant (Type 3 behavior). FIG. 3: illustrates optimal stimulus waveforms (top panels) for selectively stimulating both traditional (blue / black) and modified (orange / grey) Hodgkin-Huxley as seen in the system responses (bottom panels).

[0294] The inventors note that both stimulus waveforms have the hyperpolarizing pre-pulse that the inventors had found in their previous work for efficient stimulation of the traditional Hodgkin-Huxley neuron

[0012] , Between the two Types of neurons though, the inventors note that the stimulus waveform for selectively stimulating the Type 3 excitable neurons

[0010] is narrower compared to the stimulus waveform for selectively stimulating the traditional Type 2 excitable neuron. The inventors hypothesized that the narrower stimulus could be activating the Type 3 neuron selectively due to a difference between the resonant frequencies of the two neurons. In order to test this, the inventors used a ZAP function as an input waveform for both the traditional Hodgkin-Huxley as well as the Clay variant in order to gain insight into their subthreshold resonant frequencies

[0018] ,

[0295] The inventors defined the ZAP function as follows:

[0296] / (t) - sin(— \

[0297]

[0298] V J\5000Z

[0299] such that the frequency at time, t milliseconds, is (t 15) Hz. FIG. 7 shows the response of both neurons to the ZAP function as well as a convolution of the two selective stimuli with the ZAP function. In FIG. 7, the upper envelope of both traditional (blue / black) and Clay variant (orange / grey) neuronal response (middle panel) to the ZAP function (top panel) shows the different resonant frequencies for each type. The upper envelope of the convolution of the two selective stimuli (bottom) shows how the resonant frequencies peak close to their specific neuron’s resonant frequencies.

[0300] Here, the traditional Hodgkin-Huxley, or Type 2 neuron, has a subthreshold resonant frequency around 33 Hz, while the Clay variant, or Type 3 excitable neuron, has a subthreshold resonant frequency around 41 Hz. The inventors convolved the stimulus against the ZAP function

[0301] 42

[0302] 4931-6275-7522, v. 1to identify where the two selective stimuli match closely with the frequencies and found that the stimulus selective for the Type 2 excitable neuron had a peak around 34 Hz compared to the stimulus selective for the Type 3 excitable neuron which peaked around 44 Hz. As such, the stimulus waveforms retain the same fundamental shape of a hyperpolarizing phase followed by a depolarizing portion, and the stimulus selectivity is based on the subthreshold resonant properties of the neurons that are being targeted.

[0303] Selectively stimulating neurons with different channels

[0304] In the second case study, the inventors found that the addition of the persistent sodium leak channel to the Hodgkin-Huxley model led to an increase in the resting membrane threshold. Furthermore, progressively increasing the conductance of the persistent sodium leak channel led to progressive increases in the resting membrane potential. A strength-duration curve using simple pulses shows that the curves do not overlap and are steadily decreasing as conductance increases. FIG. 8 illustrates a stimulus-duration curve plotted on log-log scale for the traditional Hodgkin-Huxley (blue / black) and increasing sodium persistent conductances: lightest blue / black (gNaP = 0) to darkest blue / black (gNaP = 0.05).

[0305] As such, it would be impossible to activate the traditional Hodgkin-Huxley neuron using only a depolarizing rectangular pulse without causing action potentials in the neurons with the persistent sodium channel included. By changing the waveforms however, the inventors were able to find solutions that were able to selectively stimulate the neurons with a persistent sodium channel without activating the traditional Hodgkin-Huxley neuron as seen in the upper portion of FIG. 6 in panel (A). Because the neurons have different resting membrane potentials and thresholds, the inventors also used the two-dimensional Hodgkin-Huxley to better visualize the different state variables.

[0306] FIG. 9. illustrates the optimal stimulus waveform showing selective activation of the traditional Hodgkin-Huxley (blue / black trajectories) against Hodgkin-Huxley with persistent sodium channels (orange / grey). Each vertical set represents increasing levels of sodium persistent conductance for the modified Hodgkin-Huxley from 0.01 (left) to 0.05 (right). The 2D Hodgkin-Huxley could not get separation when the conductance was at 0.04 and 0.05. The original four-

[0307] 43

[0308] 4931-6275-7522, v. 1dimensional Hodgkin-Huxley’s results and the two-dimensionally reduced Hodgkin-Huxley are shown here.

[0309] In this dimensionally reduced version of the Hodgkin-Huxley model, the efficient waveforms are similar. While there are some discrepancies between the 2D and the original model, similar selectively stimulating waveforms can be seen in FIG. 9 panel (B). One could divide up the stimulus waveform into a hyperpolarizing pre-pulse, a secondary waveform segment, and a depolarizing pulse. The inventors explored this secondary waveform segment even further to better understand the dynamics of this stimulus.

[0310] In order to do this, the inventors tested different variations of the optimized stimulus (gNaP = 0.02), with varying lengths of this secondary waveform segment. This was done by shrinking and stretching this portion using linear interpolation. As can be seen from the figure below, when the secondary waveform segment is very small, or near non-existent, the stimulus is sufficient to cause both the traditional as well as the modified neuron to fire an action potential. As the secondary waveform segment increases in length, however, there is an increasing amount of hyperpolarizing stimulus, and a brief window appears in which the neuron with the persistent sodium channel is no longer activated, but the traditional neuron is still activated. As the segment increases further, however, both neurons are no longer able to fire an action potential. This phenomenon was observed when gNaP = 0.01 and gNaP = 0.03 with little changes to the size of the brief window.

[0311] FIG. 10 illustrates a narrow window exists for the size of the intermediate pulse segment such that only the traditional Hodgkin-Huxley neuron fires while the version with a persistent sodium channel (gNaP = 0.02) does not fire. Top panel shows for different scaled lengths of the intermediate pulse segment, which neuron activates an action potential. Example stimuli and phase plot response curves are drawn below. In the phase plot, the traditional Hodgkin-Huxley (blue / black solid) and the modified version with persistent sodium (orange / grey solid) are plotted with their respective separatrices (dashed lines).

[0312] When viewing the trajectories in the phase plane, a few more observations can be made. First, it is important to note that although the neuron with the persistent sodium channel sits at a

[0313] 44

[0314] 4931-6275-7522, v. 1higher voltage resting membrane potential and is therefore closer to the threshold as seen by the dashed lines, this neuron also sits at a higher level of potassium subunit activation. Given that the potassium channel is a key component of the hyperpolarizing current in the neuron, the increased potassium activation creates a counter-balancing force on the neuron, negating the depolarizing nature of the action potential.

[0315] What one can observe from this process is that when using a traditional waveform pulse, the energy is given quickly, and thus there is an immediate step in the V state variable, leading to an action potential. When measuring only along the V-axis, the distance between the resting state for the modified neuron is smaller than that in the traditional neuron. As such, the modified neuron will always fire whenever the traditional neuron fires. Although potassium activation is higher for the modified neuron, the time scale for potassium to respond, thus countering the action potential is too slow.

[0316] However, this experiment demonstrates that if more time is given to allow the potassium current to rise, a narrow window can be achieved in which the traditional neuron is able to fire an action potential, while the modified, and normally more excitable, neuron does not.

[0317] Selectively stimulating neurons with different diameters

[0318] The inventors’ last case study explored ways to counteract the traditional finding that with exogenous stimulation, small fibers are less excitable than large axon diameter fibers. As stated previously, the objective of this experiment is not to activate just the node at which the stimulus is being given, but to create action potential propagation downstream of the site of activation. As seen in FIG. 11, by changing the size and shape of the waveform, one can selectively cause propagation of an action potential for either 15 um or 25 um neurons.

[0319] Specifically, FIG. 11 illustrates that by changing the stimulus waveform shape, one can selectively stimulate the smaller neuron without activating the larger neuron, and vice versa. Each column shows a stimulus (top) and the response of both 15 um (middle) and 25 um neurons (bottom) to that stimulus. The neuronal response shows not only the voltage membrane response closest to the point of exogenous stimulation, but also at several nodes downstream. As can be seen, the left column’s stimulus is able to selectively cause propagating action potentials in the 15- 45

[0320] 4931-6275-7522, v. 1um neuron, but not the 25-um neuron, while the right column’s stimulus is able to selectively do the opposite.

[0321] In trying to understand the mechanism underlying how the small fiber neurons were activated without the activation of the larger fibers, the inventors examined the current flow within each of the nodes. Compared to membrane-only models that focus only on current flow across the membrane, these axon models include current flow longitudinally down the axon as well as across the membrane. This trans- and intra-compartment dynamic leads to an interesting phenomenon captured between these two waveforms as seen in FIG. 12. While both stimulus waveforms cause depolarization at the closest node, the mechanism of depolarization is different. For the 25-um neuron, the depolarization follows a more traditional mechanism with an influx of current across the membrane. For the 15-um neuron, however, the depolarization of the node is heavily driven by an axial influx of current along the fiber as opposed to across the membrane. The direction of current across the membrane is outwards as opposed to inwards.

[0322] As seen in FIG. 12, although both selective stimulus waveforms generate an action potential for the 25-um neuron (orange / grey) versus the 15-um neuron (blue / black), the mechanism of depolarization is different. While there is an initial inward current across the membrane depolarizing the 15-um neuron, the membrane current switches to an outward flow, pulling into the compartment an axial current. In contrast, the 25-um neuron’s depolarization occurs mainly from an inward current. Using the polynomial distortion algorithm, the inventors were also able to identify waveforms that selectively stimulate neurons at different sizes such that the inventors can mimic orderly recruitment from small to large fibers as seen in FIG. 13. Specifically, FIG.

[0323] 13 illustrates that by modifying the stimulus waveform shape (top row), we can orderly recruit small to large fibers (left to right). Each plot shows the response at each node compartment, aligned by when the action potential peaks at the last compartment.

[0324] Examining Robustness

[0325] While waveforms can be identified that selectively target traditionally less excitable neurons, a question arises as to how robust are these solutions. The inventors added white noise to the stimulus waveforms at different amplitudes to test this, and examined how successful these

[0326] 46

[0327] 4931-6275-7522, v. 1waveforms were at activating the less excitable neuron while leaving the more excitable neuron quiescent. FIG. 11 shows that this setup can tolerate a small amount of noise in many cases, but the success rate drops as the noise grows. Interestingly, the stimulus's failure is not due to the activation of the more traditionally excitable neurons but instead the failure of the targeted neuron to activate. FIG. 14 illustrates (out of 100) for stimulus optimized to activate only the traditional Hodgkin-Huxley (blue / black) when under increasingly noisy environments. The same stimulus and noise profiles are applied also to Hodgkin-Huxley models with persistent sodium conductance. As noise increases, the stimulus begins to activate the Hodgkin-Huxley model with gNaP = 0.01 (orange / grey). Increasing levels of gNaP, which are traditionally more excitable, do not activate even under larger amounts of noise.

[0328] Referring now to FIG. 15, a schematic of a programmable arbitrary waveform generator (pAWG) according to the present disclosure is shown. It is understood that the example shown in FIG. 15 is merely one embodiment configured to apply a therapeutic treatment to a subject via nerve stimulation.

[0329] In this embodiment, a programmable arbitrary waveform generator is coupled to one or more electrodes. The programmable arbitrary waveform generator includes a sensing subsystem. The sensing subsystem is configured to receive an analog electroencephalogram (EEG) signal from the electrodes. The sensing subsystem may, for example, perform current isolation, signal amplification and level shifting, and conversion of the analog EEG signal to a digital signal. The sensing subsystem may then transmit a filtered digital EEG signal to a programmable central processing unit.

[0330] The programmable central processing unit includes a polynomial distortion algorithm (PDA). The polynomial distortion algorithm may be implemented as a software program and may be stored in a memory. The polynomial distortion algorithm may be executed by a processor.

[0331] The processor may initialize stimulation, generate distortion processes, and compute one or more performance metrics. The polynomial distortion algorithm may be repeated or iterated for a predetermined number of iterations. In some embodiments, the polynomial distortion algorithm

[0332] 47

[0333] 4931-6275-7522, v. 1may utilize parameters stored in memory that define an initial stimulation prior to initiating the distortion process.

[0334] The programmable central processing unit may transmit a digital stimulus to a stimulating subsystem. The stimulating subsystem may include a digital-to-analog conversion process. The stimulating subsystem includes a summing amplifier and a resistor (Rl). The stimulating subsystem may convert the digital stimulus into an analog stimulus, as depicted in FIG. 15, and deliver the analog stimulus to an electrode.

[0335] The stimulating subsystem may further transmit the analog stimulus to a current sensing subsystem. The current sensing subsystem may detect a voltage difference across an amplifier and convert the analog signal to a digital signal using an analog-to-digital converter. The current sensing subsystem may store the resulting digital signal in memory as a current measurement.

[0336] In this embodiment, the programmable arbitrary waveform generator (pAWG) is capable of producing biphasic waveforms with amplitudes of ±1V and a resolution of 488|1V at a maximum frequency of 1kHz. FIG. 15 illustrates a pAWG block diagram and the major components of the pAWG and their interactions. This pAWG can produce waveforms of any shape within the specified ranges. In contrast, many commercially available neurostimulators used to treat neurological conditions utilize only rectangular pulses

[0109] , In the illustrated embodiment, the pAWG comprises a Raspberry Pi 3B+ microcontroller

[0110] , one 12-bit analog-to-digital converter (ADC) and 12-bit digital-to-analog converter (DAC) hardware attached on top (HAT), and Analog Devices OP07CPZ operational amplifiers[lll]. The PDA is stored on an SD card on the microcontroller and can be executed using Python 3. The microcontroller has internet capabilities, allowing for remote access via secure shell (SSH) protocol. With the microcontroller’ s 1.4GHz 64-bit quad-core processor, multiple processes can be performed simultaneously. These processes can be broken down into outputs and inputs of the PDA on the microcontroller as shown in FIG. 16. FIG. 16 illustrates a pAWG flow diagram. In panel A, the PDA-generated stimulus is converted to an analog signal by a 12-bit digital to analog converter (DAC). The stimulus is shifted down so its amplitude falls between + / - IV. The adjusted stimulus flows across a resistor to the target system. In panel B, the current being injected into the black-box system is measured and scaled to fall within the 0-2V constraint of the analog to digital converter (ADC). The analog

[0337] 48

[0338] 4931-6275-7522, v. 1current signal is stored for future use in the PDA. In panel C, the black-box system is isolated from the pAWG by using a voltage follower. The system response signal may then be shifted or amplified to fall within the ADC 0-2V constraint.

[0339] Output

[0340] Once the PDA generates a stimulus, the microcontroller passes the stimulus to a DAC output channel on the ADC-DAC HAT at a rate of 1kHz. The DAC converts each 12-bit digital value in the stimulus to an analog voltage value between 0V-2V. An operational amplifier configured as a summing amplifier shifts the voltage stimulus so that its amplitude is now between +1V. Resistor values of the summing amplifier may be adjusted to additionally scale the stimulus, if necessary, depending upon the target system. The final, adjusted stimulus Vstimulusadjusted) isdefined in Equation (1) below, where Vstimulusis the PDA-generated stimulus and resistors are those shown in FIG. 16, which illustrates the programmable AWG Circuit Diagram. In FIG. 17, the "input" and "output" labels refer to the input and output of the pAWG. The ADC_IN and DAC_OUT labels refer to the ADC-DAC HAT on the Raspberry Pi 3B+. The final stimulus then generates current as it flows across a resistor (Rz) to the system of interest.

[0341] «3 Tv7 stimulus — 1x• (1) ^stimulus_ad justed

[0342]

[0343] . 2.

[0344] Inputs

[0345] The amplitude of the current associated with the voltage stimulus is measured and can be used as a performance metric in the EDA. As the stimulus is output from the DAC, the microcontroller simultaneously reads the current across R, between the DAC output and the system of interest. The current (7) is measured using an operational amplifier configured as a difference amplifier. The negative and positive inputs to the amplifier are connected on either side of Rz, and resistor values are chosen such that the signal is amplified by a factor, G, to be in range of the ADC input (0V-2V). The output of this difference amplifier (Vout) is connected to a channel of the ADC and is defined in Equation (2). The voltage difference across Rz(AC) is read at a sample rate of 1kHz. The EDA calculates the current associated with the given stimulus using Ohm’s Law, as defined in Equation (3). Resistor labels refer to those in FIG.17.

[0346] 49

[0347] 4931-6275-7522, v. 1R7(2)

[0348] Vout = -^(Ay) = G * (AV)

[0349] _ Vout (3)

[0350]

[0351] At the same time, the system’s response to the PDA stimulus is read by the microcontroller at a sampling rate of 1kHz. The output voltage of the system (

[0352]

[0353] ^ysresponse) is first connected to an operational amplifier configured as a unity-gain amplifier to isolate the system of interest from the pAWG hardware. The output voltage from this amplifier must be in the ADC range of OV to 2V, so another amplifier may be used to set a DC voltage offset (i.e. shift the voltage range) and scale the amplitude. The values of the DC offset and gain are dependent on the target system’s output voltage range. The final voltage read from the system (Vsys_response_adj is described by Equation (4) below. Resistor labels refer to those in FIG. 17.

[0354] + DC_0ffset (4) Vsys_response_ad j

[0355]

[0356] 2

[0357] In summary, the pAWG described here can be used to interface with a variety of black-box systems. The pAWG provides a closed-looped system in which the analog response of a blackbox system is recorded during stimulation and is used to inform the generation of a more optimal stimulus. Stimulation consists of a single-channel, biphasic waveform with an amplitude of ±1V and a resolution of 488p, V at a maximum frequency of 1kHz. The simultaneous recording of the black-box system response as well as the current output of the AWG during stimulation is a vital aspect of this device. These measurements can be used to optimize stimuli for a desired outcome while monitoring the amount of current injected into the system. In addition, the user can easily modify the software program simply by uploading the program to the SD card either remotely or directly.

[0358] 50

[0359] 4931-6275-7522, v. 1The advantages of the pAWG are abundant. This device is designed to optimize waveforms to elicit a desired outcome in a system. This type of system has many applications, including deep brain stimulation (DBS). The black-box system in this case would represent a network of neurons in a section of brain tissue. The current-monitoring feature of the pAWG is important for use in human subjects because injecting too much current into biological tissue is known to cause harmful side effects in DB S [112-114],

[0360] The quad-core processor on the microcontroller gives the AWG the ability to read and write simultaneously, providing accurate response information from the black-box system. Using the EDA program stored on board the microcontroller, the pAWG can generate any type of waveform within the voltage range of the DAC with a high resolution. It is not limited to pulses or square waves that are common among AWGs

[0109] , Using the SSH capabilities of the microcontroller, the user can upload customized versions of the EDA and adjust parameters of the algorithm remotely. This allows for simple adjustments to be made while adapting the device to a specific black-box system, or patient in the case of DBS.

[0361] Discussion

[0362] Bioelectronic stimulators typically deliver rectangular-wave pulses, and graded increases in the intensity of the stimulation initially activate neurons with the lowest rheobase, i.e., the lowest threshold for an action potential in response to a depolarizing step current. For example, cells or axons initially activated are those with the largest diameter, with greater depolarizing leak currents, and with other intrinsic channel properties that increase membrane excitability. This order of graded activation limits therapeutic efficacy when it is desirable to selectively activate a subgroup of less excitable neurons in a population exposed to the exogenous stimulus.

[0363] Embodiments of the present disclosure demonstrate that model neurons with higher rheobase - less excitation to a traditional step current - can be selectively activated using novel waveforms that reverse the classical order of neuronal activation by exogenous stimulation. Embodiments of the present disclosure comprise computational methods for optimizing the waveforms that enable selective activation of the target subpopulations of neurons. Analysis of the ionic mechanisms for this selectivity reveals a rich repertoire of activation trajectories that are not

[0364] 51

[0365] 4931-6275-7522, v. 1accessed using traditional rectangular-wave stimuli. Results from exemplary embodiments suggest that bioelectronic devices with a programmable waveform interface can target cells that are less excitability relative to neighboring cells that are closer to threshold.

[0366] Advances in electrode technology have increased the spatial precision for localizing stimulus currents to smaller tissue volumes [19,20], While these advances are enabling improved clinical outcomes in some applications, there are many different types of neurons that can collocate well within the spatial resolution of the electrode system and would activate simultaneously leading to unintended consequences [21,22], While electrode size and configurations can steer current to smaller zones of excitation, the spatial selectivity is often insufficient for targeted stimulation of neuronal subtypes that are in close proximity. The inventors have sought to explore whether changes in the stimulus waveform shape can aid in the selective stimulation of neurons with different intrinsic biophysical properties. While a previous study examined the role of hyperpolarizing and depolarizing pre-pulses on selectivity

[0023] , the inventors chose to relax the constraints of rectangular waveforms completely, allowing for arbitrary waveforms. In the embodiments disclosed herein, the inventors explored selectivity across three distinct neuronal properties: subunit activation, channel conductances, and axonal diameter.

[0367] The results from these studies demonstrate that stimulus waveforms can be shaped to modify the order of excitation. The use of stimulus waveform optimization approaches not only provides new avenues for stimulus protocols, but also gives insights into the underlying mechanisms that can be exploited to selectively stimulate different neuronal populations. For example, given that Hodgkin-Huxley neurons are known to have resonant properties

[0024] , some stimulus waveform properties can be tuned to take advantage of these differences as seen in results from exemplary embodiments of the present disclosure. While in other cases, efficient stimulus waveforms could be structured to navigate hyperpolarizing and depolarizing channel subunits to selectively stimulate one group and not another. One of the fascinating findings from this study has been regarding the selective stimulation of different diameter neurons. Traditional understanding of depolarization is built around the Hodgkin-Huxley model of the neuronal membrane, with depolarizing membrane voltage associated with an inward current. By examining the different current components using our computational models, the inventors find that the stimulus that activates small fibers selectively without activating larger fibers is able to do this by 52

[0368] 4931-6275-7522, v. 1pulling current axially from neighboring nodes. The larger stimulus that is given here predominantly causes an outward current which pulls axial current from neighboring nodes. This essentially creates a retrograde current which negates the propagation of action potentials which normally follows after depolarization. Previous studies have noted a hyperpolarization of neighboring nodes after prepulse stimulation which supports this idea2, although this mechanism reveals that hyperpolarization may not be necessary. As long as the retrograde axial current generated is strong enough to reduce the propagating current, downstream action potentials will not occur. This mechanism favors larger fibers because a stronger retrograde axial current relative to the propagating current can be generated compared to small fibers. As such, small fibers can be selectively activated. By adjusting this stimulus, the retrograde axial current can be adjusted in order to determine the size of the threshold for small fibers versus large fibers.

[0369] When looking at spatial stimulation, waveforms that exploit the magnitude and direction of axial versus membrane currents also opens possibilities for mechanisms that can enhance excitation in ways that diverge from using rectangular waveforms that are directed toward traditional mechanisms of excitation that govern the membrane’s rheobase threshold.

[0370] As seen in the results discussed herein, dimensional reduction was used to better understand the dynamics of the ionic mechanisms relating to sodium persistent current. While studying Type 2 and Type 3 excitability, the inventors considered doing a similar experiment using Prescott’s models of excitability for all three types

[0025] , Prescott et al. not only developed a simplified 2D model that exhibits the different types of excitability, but they expanded the ionic bases to a 3D model as well, splitting Isiowinto a delayed rectifier K+current and a subthreshold current Isub. The inventors’ analysis was able to find solutions that were capable of selectively stimulating the different types of neurons when using the 3D model, but their algorithms were unable to find any stimulus waveforms capable of selectively stimulating the different types of neurons in the dimensionally reduced 2D model. This finding reinforces what has been noted previously regarding dimensional reduction, that the dimensional reduction process preserves dynamics and behaviors in certain areas of the state-space

[0026] , This means that there are certain areas, including potentially the trajectories between stable points or limit cycles, that are not well represented. As such, while dimensional reduction can be useful in specific cases, certain behaviors or trajectories may be lost at lower dimensions. Notably, in the dimensional reduction 53

[0371] 4931-6275-7522, v. 1of the sodium persistent current analysis, the inventors were able to maintain similar behaviors in the selective stimulation of neurons with different conductances.

[0372] The three examples disclosed herein were chosen as well studied intrinsic mechanisms that modify excitation in healthy neurons and diseases states. Many inherited mutations of ion channels in neurological diseases, or channelopathies, are due to changes in the conductance of a neuron or the channel’s activation curves

[0027] , The ability to selectively target neurons with the mutated channelopathy allows for precise activation or inhibition of those pathological neurons.

[0373] Exemplary embodiments of the present disclosure can be used in various applications, including for example, deep brain stimulation (DBS), transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (TDCS). Exemplary embodiments of the present disclosure can be used to treat various conditions in subjects, including for example, movement disorders, epilepsy, depression, coma, cognitive impairment, obsessive compulsive disorder, depression, migraine pain, addiction, and stroke rehabilitation.

[0374] Exemplary Systems for Nerve Stimulation using PDA

[0375] PDA can be utilized in systems for stimulating nerve bundles in a mammalian subject, to treat a variety of diseases or injuries. As shown herein, PDA can be utilized to decrease the amount of computing power required to provide solutions for targeted electrical stimulation of neurons and / or selectively stimulate smaller nerve fiber (e.g., see FIG. 14). By utilizing less computing power, optimization of electrical waveforms can be performed by PDA to arrive at clinically therapeutic electrical waveforms for treating a disease, decreasing the duration of time needed to test modifications to electrical stimulation parameters after implanting a device in a subject in order to improve or optimize the therapy, thus decreasing associated risks associated with this period of time needed to optimize or personalize the therapy.

[0376] Stimulating smaller nerve fibers can provide significant clinical therapeutic advantages for treating disease or injuries. PDA can be utilized to selectively target smaller diameter (e.g., less than about 10, 9, 8, 7, 6, or 5 pm in diameter) or larger diameter neurons or nerve fibers (e.g., greater than about 5, 6, 7, 8, 9, or preferably larger than 10 pm in diameter). Select examples of nerves and therapeutic applications of targeting smaller nerves are provided in Table 2.

[0377] 54

[0378] 4931-6275-7522, v. 1Table 2

[0379] Therapeutic Fiber-specific target Off-target fiber type (diameter); side

[0380] Stimulated Structure Application (diameter) effects Reference 1 Small-to-large motor fibers (2- Large fibers (10-20ym); overstinnuiation muscle I Phrenic Nerve Central respiratory failure 15pm) fatigue [64-6S] i

[0381] Vagus Nerve Epilepsy Ab fibers (1-5pm) Acs fibers (13- 20pm); hoarseness, cough, apnea [67,68] i Hypertension A-5 (1-5prn) and C (1pm) fibers AS fibers (6- 12pm); bradycardia, syncope [§9,70] i Depression Ab (1-5pm) and C (1pm) fibers Ao fibers {13-20pmi: hoarseness, cough, apnea [§7.68,71] i

[0382] Motor fibers ( 1C-20pm); painful limb muscle I Sciatic Nerve Urinary incontinence Parasympathetic fibers (2-4ym) contraction [72,73] i

[0383] Spina! Cord Pain A / S. Ab, C fibers Spinal cord sensory fibers (13-20pm>: paresthesia [74-76] i

[0384] Motor fibers (l0-20ym); painful limb muscle i Dorsal Root Ganglion Pain Ap:fibers contraction [77-7S] I

[0385] Thalamus / Sub-Thalamic Essential, ’Parkinsonian Small neurons (1-5pm) near i Area Tremor electrode Large neurons (>5pm): dysarthria, confusion [80-81] I

[0386]

[0387] PDA can be utilized in systems for electrical stimulation of the phrenic nerve, e.g., to treat central respiratory failure. Phrenic nerve stimulation systems generally include an electrode (e.g., a small, implantable electrode designed to directly contact the phrenic nerve, optionally with multiple poles for stimulation), lead wires (insulated wires connecting the electrode to the implanted receiver), a receiver or stimulator (e.g., a small device implanted under the skin that receives radiofrequency signals from the external transmitter and delivers electrical pulses to the electrode), and an external transmitter (e.g., a handheld device that can send radiofrequency signals to the implanted receiver and allows for control of stimulation parameters including pulse frequency, shape, and amplitude). Example phrenic nerve systems that are commercially available and may potentially be modified to utilize PDA include the NeuRx® Diaphragm Pacing System (Synapse Biomedical Inc.) and diaphragm pacing systems available from Avery Biomedical Devices™.. Electrodes for a phrenic nerve stimulation system can utilize cervical, thoracic, or transvenous placement of one or more electrodes. Cervical placement involves placing the electrode(s) near the phrenic nerve in the neck of a patient. Thoracic placement involves positioning electrodes near the phrenic nerve within the chest cavity. With transvenous placement, electrodes are delivered via a catheter inserted into a large vein (e.g., the jugular vein) to access the phrenic nerve. Phrenic nerve stimulation can be used to stimulate breathing after a spinal injury or partial or complete central respiratory failure. Stimulation of the phrenic nerve can also be used to treat sleep apnea (e.g., central sleep apnea due to a neurological condition or disease), diaphragm paralysis (e.g., to assist with respiration in individuals with high spinal cord injuries causing diaphragm paralysis), or diaphragmatic weakness (e.g., to support breathing in patients with a weakened diaphragm due to a neuromuscular disease). Examples systems that may potentially be modified to utilize PDA for phrenic nerve stimulation for sleep apnea include the remede® System (Zoll®). By using PDA to generate electrical waveforms, small to large diameter motor fibers (about 2-15 pm in diameter) can be stimulated, preferably by stimulating the smaller diameter nerve fibers before the larger diameter nerve fiber, with reduced stimulation of large fibers (about 10-20 pm in diameter). In this way, PDA can be utilized to reduce overstimulation of diaphragm muscles and the related risks associated with muscle fatigue.PDA can be used to generate electrical waveforms in vagus nerve stimulation systems. Vagus nerve stimulation systems can be utilized, e.g., to treat epilepsy, hypertension, or depression. For these applications target neurons of about 1-5 pm in diameter can be selectively stimulated, while reducing stimulation of larger nerve fibers of about 6-12 pm or 12-20 pm in diameter. The vagus nerve stimulation system may use electrodes that have a helical or substantially flat shape (e.g., Deininger et al. “Breath-by-breath comparison of a novel percutaneous phrenic nerve stimulation approach with mechanical ventilation in juvenile pigs: a pilot study.” Sci Rep 14, 10252 (2024)).

[0388] Sciatic nerve stimulation systems can utilize PDA to improve targeting to relevant nerve fibers to treat urinary incontinence. Using PDA to selectively stimulate parasympathetic nerve fibers (about 2-4 pm in diameter) while reducing stimulation of motor fibers (about 10-20 pm in diameter) can be used to reduce or eliminate painful muscle contractions associated with the use of square- wave type electrical stimulation.

[0389] Spinal cord stimulation systems can utilize PDA to improve targeting of nerve fibers for the treatment of pain. Nerve fibers affecting sensory information for painful stimuli (including Ap, A5, and C pain fibers) can be selectively targeted to treat pain using PDA, while reducing stimulation of larger spinal cord fibers (about 13-20 pm in diameter) involved in processing sensory information and / or paresthesia (numbness of a portion of the skin) side effects. Spinal cord stimulation to treat pain can be effective, although the mechanism for spinal cord stimulation treating pain is still not fully understood.

[0390] Dorsal root ganglion stimulation systems can utilize PDA to improve targeting of nerve fibers for the treatment of pain. Nerve fibers affecting sensory information for painful stimuli (including A pain fibers) can be selectively targeted to treat pain using PDA, while reducing stimulation of larger motor control nerve fibers (about 10-20 pm in diameter) that can cause painful limb muscle contractions.

[0391] PDA can utilized in deep brain stimulation (DBS) systems to target nerve bundles of smaller diameters. For example, thalamus / subthalamus stimulation systems can utilize PDA to improve targeting of nerve fibers for the treatment of essential tremor or Parkinsonian tremor (e.g.,

[0392] E>7

[0393] 4931-6275-7522, v. 1resulting from Parkinson’s disease “PD” or Parkinson-plus syndrome). Smaller diameter (about 1-5 pm) nerve fibers can be targeted, while decreasing stimulation of larger (>5 pm) diameter nerve fibers that can contribute to dysarthria or confusion. Commercially available systems for thalamus / subthalamus nerve stimulation that may be modified to utilize PDA include. DBS systems may include a lead wire or electrode implanted into the thalamus, wherein the lead is connected to an implantable pulse generator (IPG), and the IPG is inserted under the skin of the chest wall. By selectively stimulating regions of the central nervous system, including, tremors and movement problems can be treated. DBS may involve the placement of electrodes in the thalamus, pallidum, and subthalamic nucleus (STN) to treat the specific symptoms of PD.

[0394] Stimulation of the ventral tegmental area (VTA) can be performed using a DBS system utilizing PDA to treat depression

[0115] , The VTA is composed of an admixed and heterogenous population of neurons that receive broad inputs from multiple brain areas and project widely across the brain. The VTA acts as the originating node in a brain network that underlies motivation and salience and a pathological impairment in these systems is closely associated with core symptoms of depression. Fibers connecting the VTA to cortical and subcortical structures, such as the superolateral and inferomedial branches of the median forebrain bundle (MFB), are thought to exhibit hypoconnectivity in depression, and their electrical manipulation is a promising therapeutic avenue

[0116] . Commercially available systems for MFB stimulation include Medtronic model 3389 and Boston Scientific Cartesia. Nerve fibers of the MFB can be selectively targeted with PDA, while avoiding nearby larger (about 5-12 um in diameter)

[0118] fibers of the oculomotor nerve that cause involuntary movements of the eye and vision impairment, which if not occurring with initial lead placement

[0117] , sometimes occurs later with implantable pulse generator replacement

[0119] or after a period of DBS system inactivity. Alternatively, unmyelinated efferent dopaminergic fibers or even their cell bodies originating from the VTA that are admixed with afferent fibers from the cortex and subcortex

[0119] may be directly recruited, either in addition to or independent of myelinated ones. In addition to selecting fiber specific fiber tracts based on axon diameter, there are additional routes to treat depression with cell-type electrical manipulation (e.g. decreasing activity of lateral habenula [LHb]).

[0395] 58

[0396] 4931-6275-7522, v. 1Human Application and Devices

[0397] Systems for nerve stimulation can include the PDA methods provided herein. Such methods and systems can be incorporated into a variety of neural interface technology, including as the Ripple Neuromed Explorer Summit System, to enable closed-loop, feedback-driven stimulation.

[0398] Phrenic nerve stimulators may be modified to utilize PDA methods. Adaptive platforms can be used dynamically adjust stimulation parameters in real-time based on ventilator-derived metrics, such as tidal volume. PDA can be implemented within an intraoperative environment to optimize phrenic nerve stimulation in real-time. By integrating the algorithm with current-controlled stimulation hardware, diaphragmatic activation patterns can be refined during surgical procedures. Schematics discussed below provide examples for clinical workflow and data integration between the patient, the ventilator, and the PDA control system.

[0399] As illustrated in FIG. 26, the PDA can receive real-time physiological input(s) directly from a ventilator system (e.g., the Draeger Perseus A500) in the operating room. This integration can achieved by leveraging a communication protocol (e.g., Draeger MEDIBUS. X) to extract serial data through a programmed interface (e.g., Lantronix interface). The device preferably captures high-fidelity ventilator telemetry and archives it within a local database (e.g., PostgreSQL) on the host computer or research workstation. Utilizing custom scripts, the system can perform real-time analysis of the ventilatory data, preferably executing bulk data retrieval at a frequency of 2 Hz to ensure temporal synchronization with the stimulation algorithm (see FIG.

[0400] 27).

[0401] FIG. 26 illustrates an exemplary closed-loop respiratory neuromodulation system. A subject is intubated and coupled to a ventilatory support system (e.g., Perseus A500, Dragerwerk AG & Co. KGaA, Lubeck, Germany). The ventilatory system provides time-resolved output, including respiratory phase timing and delivered volume. Ventilator output is communicated to a programmable central processing unit (CPU). The programmable CPU includes an optimization algorithm, such as a Polynomial Distortion Algorithm (PDA). The PDA is stored in memory and executed by a processor. Following each stimulation event, the programmable CPU receives ventilator output, respiration metrics, and capnography data. The PDA evaluates the physiological 59

[0402] 4931-6275-7522, v. 1response. The PDA iteratively updates stimulation parameters across successive iterations. The stimulation parameters are calibrated based on ventilator-derived feedback. The programmable CPU transmits a digital stimulation signal to a stimulating subsystem (e.g., Ripple Neuro, Salt Lake City, Utah, USA). The stimulating subsystem converts the digital signal into an analog stimulation waveform. The analog waveform is delivered via an electrode operatively coupled to a phrenic nerve. Electrical stimulation of the phrenic nerve induces diaphragmatic contraction. Ventilator telemetry is continuously analyzed to identify respiratory phase transitions. Stimulation timing and waveform characteristics are iteratively refined. This closed-loop operation provides improved synchronization between mechanical ventilation and diaphragmatic activation. Additional advantages include reduced stimulation energy, adaptation to physiological variability, and improved respiratory efficiency. Through the continuous analysis of incoming ventilatory data, the PDA may dynamically updates stimulation parameters and transmits them to the stimulator (e.g., Ripple stimulator), establishing a robust closed-loop environment. To ensure patient safety throughout this process, the ventilator can be configured to Pressure-Controlled Continuous Mandatory Ventilation (PC-CMV) mode. The proprietary script utilizes the ventilator telemetry to identify the termination of mechanical support phases, subsequently triggering electrical stimulation to achieve synchronized diaphragmatic activation. The temporal relationship between mechanical ventilation and stimulated pacing is illustrated in FIG. 28.

[0403] FIG. 28 depicts a graph illustrating tidal volume as a function of time. The graph includes periods of mechanical ventilatory support separated by a period of phrenic nerve stimulation support. Electrical stimulation is delivered following an initial calibration phase and prior to optimization by the Polynomial Distortion Algorithm (PDA). During the stimulation support period, activation of the phrenic nerve induces diaphragmatic contraction, resulting in the onset of tidal volume. In the illustrated embodiment, stimulation is delivered for approximately three seconds per respiratory cycle at a rate of approximately 20 breaths per minute. Ventilator output corresponding to tidal volume and timing is preferably continuously monitored. The ventilator-derived measurements are provided to a programmable central processing unit. The PDA evaluates the measured tidal volume response following each stimulation event. Based on this evaluation, stimulation parameters are iteratively adjusted across successive cycles. The iterative process calibrates stimulation timing and waveform characteristics to improve consistency of tidal volume generation during the stimulation support period. Accordingly, FIG.

[0404] 60

[0405] 4931-6275-7522, v. 128 illustrates the use of ventilator-derived tidal volume measurements to iteratively refine phrenic nerve stimulation under closed-loop control. The electrical stimulation events designed using PDA can be administered in an alternating pattern with a standard breathing stimulation. For example, the PDA waveform may be administered once every 6, 5, 4, 3, 2, or 1 breaths administered using a standard phrenic nerve stimulating impulse. The frequency of PDA waveforms can be increased over time as the electrical waveform continues to improve for the response generated in the subject or human patient. Once the waveform has been sufficiently or completely optimized to generate the desired response in the patient (e.g., a smooth inhalation of air), one may optionally proceed with stimulating the patient at a sufficient duration using only the PDA generated waveform, with or without further modification(s) by additional application of PDA to the waveform.

[0406] Upon the successful acquisition of definitive experimental results, the apparatus and system can be miniaturized, preferably wherein the architecture is included in a self-contained, implantable medical device. This next-generation stimulator will feature an embedded PDA capable of autonomous, real-time modulation based on integrated physiological feedback loops. The PDA approaches can be included in an adaptive, implantable phrenic nerve stimulation system.

[0407] EXAMPLES

[0408] The following examples are included to demonstrate preferred embodiments of the invention. It should be appreciated by those of skill in the art that the techniques disclosed in the examples which follow represent techniques discovered by the inventor to function well in the practice of the invention, and thus can be considered to constitute preferred modes for its practice. However, those of skill in the art should, in light of the present disclosure, appreciate that many changes can be made in the specific embodiments which are disclosed and still obtain a like or similar result without departing from the spirit and scope of the invention.

[0409] Example 1 - Stimulation Optimization of Subgroups of Neurons In Vitro and in Vivo

[0410] The research described below has advanced across three primary domains: experimental validation of the Polynomial Distortion Algorithm (PDA) in neuronal cell cultures, the transition 61

[0411] 4931-6275-7522, v. 1to in-vivo preparations, and the strategic expansion toward clinical applications via the establishment of infrastructure for hospital-based testing.

[0412] Experimental application in vitro

[0413] It has been demonstrated herein that the PDA effectively and rapidly optimizes electrical stimulation waveforms; notably, it achieves results using significantly less energy than a standard optimized square pulse. On average, the PDA achieved a 47% reduction in energy consumption compared to the optimized rectangular pulse. Based on a total sample size of n=34, the results are detailed in Table 3 below and FIGS. 18-19.

[0414] Table.3.

[0415] Square Seed PostFinal

[0416] Wave (L2- Search Post-PDA Truncation Stimulus

[0417] norm) (L2-norm) (L2-norm) (L2-norm) Length (ms)

[0418] Average 1 1.180 0.525 0.495 0.948

[0419] Std Dev 0 0.055 0.187 0.185 0.086

[0420] Min 1 1.019 0.131 0.088 0.613

[0421] Median 1 1.201 0.501 0.487 0.983

[0422]

[0423] A schematic detailing the experimental configuration is provided in FIG. 20. The in vitro preparation consists of dissociated mouse hippocampal cells in culture and fluorescent calcium imaging was used for continuous monitoring of individual neuron activity.

[0424] The schematic includes a microscope. The microscope is imaging a sample. Electrodes are coupled to the sample. The electrodes are receiving an analog output is controlled with a stimulating subsystem (as depicted in FIG. 15). The stimulating subsystem converts the analog signal to digital. The stimulating subsystem receives a digital output from a programable. The programable includes an optimization algorithm. The optimization algorithm may, for example, include the PDA.

[0425] Furthermore, prior computational analyses indicated that the PDA facilitates selective stimulation of neuronal subgroups within heterogenous populations enabled by sculpting the waveform to match selective thresholds of the targeted neuron. This capability enables the targeted

[0426] 62

[0427] 4931-6275-7522, v. 1activation of individual neurons based on either specific ion channel properties or spatial coordinates. In the second phase of the in-vitro studies, PDA was deployed to achieve selective targeting activation across distinct cell populations. The system architecture and operational logic are illustrated in FIG. 21.

[0428] FIG. 21 depicts an exemplary flowchart. A user of the system may identify a selective stimulus and neurons of interest. The user may place a coverslip containing neurons into a chamber and identify a field of view (FoV) between stimulation electrodes that includes healthy neurons.

[0429] As depicted in FIG. 21, the user may check neural responses during an initial stimulus check. The user may deliver a biphasic stimulus, which may include, for example, a 4 ms, 15 mA electrical pulse. The user may analyze the change in firing frequency relative to a predetermined baseline frequency for individual neurons. The user may determine whether the ratio of the change in frequency divided by the predetermined frequency exceeds 3 percent for neurons within the FoV when stimulated. If the ratio exceeds 3 percent, the user may add healthy cells to regions of interest (RO I). The system may then perform a current sweep to identify firing thresholds for each cell in the RO1. The current sweep may range from 1.0 mA to 19 mA using a biphasic square wave (4 ms pulse). The user may calculate the mean firing threshold and the percent variance across cells. The user may then calculate the square-wave L2 norm (L2N) based on the mean firing threshold. A random waveform may be generated, for example using MATLAB or a similar programming environment such as Python, with an L2N equal to the square-wave energy plus or minus the percent variance. If the ratio of the change in frequency divided by the predetermined frequency is less than 3 percent, the user may determine whether the cell exposure time on the microscope exceeds 10 minutes. If the exposure time is less than 10 minutes, the user may select a new FoV and repeat the initial stimulus check. If the exposure time exceeds 10 minutes, the user may replace the coverslip with new neurons and repeat the initial stimulus check. After generating the random waveform, the user may deliver the stimulus five times (5 / 5 trials). The user may then determine whether there is evidence of multicell selectivity. If evidence of multicell selectivity is present, the user may capture video footage showing alternating firing between cells and proceed to PDA-based energy reduction of the selective stimulus. If no evidence of multicell selectivity is observed, the user may determine whether a tenth trial has been reached. If fewer than ten trials have occurred, the user may generate a new random waveform. If the tenth trial has been reached,

[0430] 63

[0431] 4931-6275-7522, v. 1the user may return to the initial stimulus check. Upon reaching the energy-reduction step, the user may determine whether a stimulus (the parent seed) fires a target primary cell without firing a secondary cell. The user may then execute the Polynomial Distortion Algorithm (PDA) for a predetermined number of iterations (e.g., 10 iterations, as shown in FIG. 21). The current parent seed may be used to generate distorted waveforms. The user may determine whether to inject a distortion based on whether the change in firing frequency divided by the predetermined frequency, averaged over two of two stimulations, indicates activation of the target cell without activation of the secondary cell.

[0432] If the criterion is met, the stimulus may be added to a library of candidate seeds, and the user may proceed to the next distortion iteration. If the criterion is not met, the user may continue to the next distortion until the tenth distortion iteration is reached.

[0433] After completing the tenth distortion iteration, the user may evaluate the robustness of each stimulation added to the library during that iteration. Each candidate seed may be tested for consistent activation across five of five trials. Seeds that meet this robustness criterion may be retained and the process may proceed to the next iteration.

[0434] Next, the user may determine whether any seed in the library is both robust and has a lower L2N than the current parent seed. If so, that seed may be selected as the new parent seed and the PDA process may continue for an additional set of iterations. If not, the process may continue until completion of the tenth iteration.

[0435] After completing the tenth iteration, the user may finalize a post-PDA waveform that selectively activates the primary cell without activating secondary cells. The user may then determine whether two PDA cycles, each focusing on one of the two cells, have been completed. If not, the user may switch the roles of the primary and secondary cells and repeat the PDA process. If both PDA cycles have been completed, the user may capture video footage showing alternating firing between cells and proceed to a state of confirmed selectivity with PDA optimization completed.

[0436] The method may include: performing a current sweep over a plurality of stimulus amplitudes to determine a firing threshold for each neuron in a region of interest. The method, in

[0437] 64

[0438] 4931-6275-7522, v. 1some embodiments, may include: computing a mean firing threshold and a variance metric across the firing thresholds; computing an energy metric for a square-wave stimulus based on the mean firing threshold. The method, in some embodiments, may include: generating a waveform having an energy that is within a range defined by the energy metric adjusted by the variance metric, wherein the generated waveform is used as the first stimulation signal waveform or the second stimulation signal waveform.

[0439] An example of these experiments is shown in FIGS. 22A-22C, with multiple experiments exhibiting similar findings. Here we show that two distinct stimulus waveforms, having the same L2 norm, elicit an action potential specifically in one cell or the other, both in close proximity. These results provide proof-of-concept of the major premise of our original claim, viz, PDA can discover stimulus waveforms that target individual neurons. In the figures show, tracings show fluorescence activation of a single cell induced by the stimulus waveform. The color of the tracings for stimulus and response are matched for two cells (blue / black and red / black tracings).

[0440] Experimental application in vivo

[0441] Following the conclusion of the in-vitro studies, it was sought to replicate these findings via an in-vivo preparations. Two parallel research avenues were pursued: first, applying the methodology to the central nervous system (CNS) to optimize neuronal firing patterns and achieve selective targeting within the CAI hippocampal region and the ventral tegmental area region of a murine model; and second, applying the PDA methodology in the peripheral nervous system (PNS) to optimize stimulation parameters for phrenic nerve activation in a rat model.

[0442] To investigate the behavioral applications of the PDA within the CNS, a custom fiber photometry system was implemented. Bespoke fiber cannulas were engineered capable of simultaneous optogenetic monitoring and electrical stimulation, utilizing a neurophotometrics platform for data acquisition. Across five experimental trials, the PDA consistently outperformed standard square-pulse stimulation, achieving robust activation responses while utilizing significantly lower energy levels. A representative example of these results is provided in FIG. 23.

[0443] Furthermore, a platform for calcium imaging in murine models was established, integrating Miniscope technology with modified Gradient-Index (GRIN) lenses and field stimulation

[0444] 65

[0445] 4931-6275-7522, v. 1electrodes. This setup allows for the real-time optical monitoring of neuronal responses during electrical stimulation.

[0446] In the PNS research, the PDA was applied to optimize phrenic nerve stimulation, aiming to enhance diaphragmatic activation. Prior computational modeling indicates that the PDA can facilitate a physiological recruitment order — activating small-diameter fibers before larger ones. This approach addresses a significant limitation of current commercial devices, which typically exhibit 'reversed recruitment,' preferentially activating large-diameter fibers first and resulting in a less naturalistic response, with the adverse outcome of inducing large fiber fatigue resulting in pacemaker failure.

[0447] As a foundational step, the rat sciatic nerve model was initially utilized, which offered a more accessible surgical preparation for establishing the experimental framework. For these procedures, a cuff electrode was employed for nerve stimulation, while distal accelerometers secured to the hindlimb recorded mechanical responses. Consistent with previous findings, PDA waveforms outperformed standard square-pulse stimulation by achieving robust acceleration outputs with significantly lower energy requirements. A representative example of this comparative performance is illustrated in FIGS. 24-25.

[0448] Phrenic nerve experiments using rat models have been initiated. In this phase, respiration and capnography metrics obtained via a small-animal ventilator serve as physiological inputs for the PDA optimization loop. Procedural protocols can be generated based on these approaches, and full-scale experimental trials will be performed. The results shown in these in vivo animal models will extend to similar advantages in human patients.

[0449] All of the devices, systems and / or methods disclosed and claimed herein can be made and executed without undue experimentation in light of the present disclosure. While the devices, systems and methods of this invention have been described in terms of particular embodiments, it will be apparent to those of skill in the art that variations may be applied to the devices, systems and / or methods in the steps or in the sequence of steps of the method described herein without departing from the concept, spirit and scope of the invention. All such similar substitutes and

[0450] 66

[0451] 4931-6275-7522, v. 1modifications apparent to those skilled in the art are deemed to be within the spirit, scope and concept of the invention as defined by the appended claims.

[0452] 67

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Claims

CLAIMS:

1. An apparatus for applying a therapeutic treatment to a mammalian subject, the apparatus comprising:a stimulation electrode; anda programmable arbitrary waveform generator, wherein the programmable arbitrary waveform generator is configured to:receive a detected signal from the subject;transmit a first stimulation signal waveform to the subject via the stimulation electrode;receive a response signal from the subject; andtransmit a second stimulation signal waveform to the subject via the stimulation electrode, wherein the second stimulation signal waveform is generated using a polynomial distortion algorithm (PDA).

2. The apparatus of claim 1 wherein the polynomial distortion algorithm (PDA) distorts the roots of a polynomial function that mimics the first stimulation signal waveform.

3. The apparatus of claim 1 or claim 2 wherein the apparatus is configured to provide for selective activation of a neuron by polynomial distortion algorithm (PDA) tuning of the first stimulation signal waveform to an intrinsic biophysical property of the neuron.

4. The apparatus of claim 3 wherein the intrinsic biophysical property comprises an axonal diameter.

5. The apparatus of claim 3 or claim 4 wherein the intrinsic biophysical property comprises a channel conductance.

6. The apparatus of any one of claims 3-5 wherein the intrinsic biophysical property comprises a channel activation curve.

7. The apparatus of any one of claims 1-6 wherein the apparatus is configured provide energy optimization of the second stimulation signal waveform.

8. The apparatus of claim 7 wherein the energy optimization is configured to minimize off-target effects of the subject.

9. The apparatus of any one of claims 1-8 wherein the programmable arbitrary waveform generator is configured to:receive a second response signal from the subject, wherein the second response signal is in response to the second stimulation signal waveform; andtransmit a third stimulation signal waveform via the stimulation electrode, wherein the third stimulation signal waveform is generated using the polynomial distortion algorithm (PDA).

10. The apparatus of claim 9 wherein the programmable arbitrary waveform generator is configured to apply subsequent stimulation signal waveforms and receive subsequent response signals in an iterative process.

11. The apparatus of claim 9, wherein the iterative process allows for selective stimulation of nerve fibers of reduced diameter.

12. The apparatus of claim 11, wherein the reduced diameter is less than about 10 pm or less than about 5 pm.

13. The apparatus of any one of claims 1-10 wherein the apparatus is configured to transmit the first stimulation signal waveform to a peripheral nerve bundle in the subject.

14. The apparatus of claim 13, wherein the peripheral nerve bundle is the phrenic nerve of the subject.

15. The apparatus of claim 14, wherein the stimulation signals are configured for treatment of central respiratory failure.

16. The apparatus of claim 13, wherein the peripheral nerve bundle is the vagus nerve of the subject.

17. The apparatus of claim 16, wherein the stimulation signals are configured for treatment of epilepsy, hypertension, or depression.

18. The apparatus of claim 13, wherein the peripheral nerve bundle is the sciatic nerve of the subject.

19. The apparatus of claim 18, wherein the stimulation signals are configured for treatment of urinary incontinence.

20. The apparatus of claim 13, wherein the peripheral nerve bundle is a spinal cord nerve or dorsal root ganglion of the subject.

21. The apparatus of claim 20, wherein the stimulation signals are configured for treatment of pain or chronic pain.

22. The method of claim 21, wherein the pain results from failed back surgery syndrome (FBSS), complex regional pain syndrome (CRPS), peripheral neuropathy (including diabetic neuropathy), post-herpetic neuralgia, phantom limb pain, visceral pain, or cancer-related pain.

23. The apparatus of any one of claims 1-10 wherein the apparatus is configured to transmit the first stimulation signal wavefomi to a central nerve or the brain of the subject.

24. The apparatus of any one of claims 1-10, wherein the apparatus is configured to transmit the first stimulation signal wavefomi to the ventral tegmental area (VTA), thalamus, or subthalamus.

25. The apparatus of any one of claims 1-10 wherein the first stimulation signal and the second stimulation signal are deep brain stimulation signals.

26. The apparatus of claim 25 wherein the deep brain stimulation signals are directional deep brain stimulation (DBS) signals.

27. The apparatus of claim 25 wherein the deep brain stimulation signals are configured for treatment of Parkinson’s disease, epilepsy, or a seizure disorder.

28. The apparatus of claim 27, wherein the deep brain stimulation signals are configured for treatment of absence seizures, tonic seizures, atonic seizures, clonic seizures, myoclonic seizures, or tonic-clonic seizures.

29. The apparatus of any one of claims 1-10 wherein the first stimulation signal waveform and the second stimulation signal waveform are transcranial magnetic stimulation (TMS) signals.

30. The apparatus of any one of claims 1-10 wherein the first stimulation signal waveform and the second stimulation signal waveform are transcranial direct current stimulation (TDCS) signals.

31. The apparatus of any one of claims 1-10 wherein the first stimulation signal waveform and the second stimulation signal waveform are configured to treat at least one of central respiratory failure, hypertension, urinary incontinence, pain or chronic pain, parkinsonian tremor, movement disorder, epilepsy, depression, coma, cognitive impairment, obsessive compulsive disorder, depression, migraine, pain, addiction, or stroke rehabilitation.

32. The apparatus of any one of claims 1-31, wherein the response signal from the subject comprises muscle contraction, one or more nerve signals affecting muscle contraction, pain perception by the subject, or performance of a motor skill by the subject.

33. The apparatus of any one of claims 1-31, wherein the PDA algorithm is configured to iteratively perform the steps of:fitting a first polynomial function to the response signal:differentiating the polynomial function to generate a derivative;identifying roots of the derivative;distorting the roots of the derivative;integrating the derivative; andscaling and offsetting the derivative to create a second polynomial function to generate the second stimulation signal waveform.

34. A method of treating a condition in a mammalian subject, the method comprising: receiving an oscillating electrical signal from a subject;applying a first stimulation signal waveform to the subject, wherein the first stimulation signal waveform modifies the oscillating electrical signal from the subject to produce a response signal;receiving the response signal from the subject; andapplying a second stimulation signal waveform to the subject, wherein the second stimulation signal is generated using a polynomial distortion algorithm (PDA).

35. The method of claim 34 further comprising:applying a third stimulation signal waveform to the subject, wherein:the third stimulation signal waveform is generated using a polynomial distortion algorithm (PDA); andthe third stimulation signal waveform modifies the oscillating electrical signal from the subject to produce a second response signal;receiving the second response signal from the subject; andapplying a fourth stimulation signal waveform to the subject, wherein:the fourth stimulation signal waveform is generated using a polynomial distortion algorithm (PDA); andthe fourth stimulation signal waveform is configured to optimize the second response signal without regard to the phase window of the oscillating electrical signal.

36. The method of claim 35 further comprising applying subsequent stimulation signal waveforms and receiving subsequent response signals in an iterative process.

37. The method of claim 34, wherein the signal waveforms are administered to a peripheral nerve bundle in the subject.

38. The method of claim 37, wherein the peripheral nerve is the phrenic nerve.

39. The method of claim 38, wherein the condition comprises central respiratory failure.

40. The method of claim 37, wherein the peripheral nerve is the vagus nerve.

41. The method of claim 40, wherein the condition comprises epilepsy, hypertension, or depression.

42. The method of claim 37, wherein the peripheral nerve is the sciatic nerve.

43. The method of claim 42, wherein the condition is urinary incontinence.

44. The method of claim 37, wherein the peripheral nerve is a spinal nerve or a dorsal root ganglion.

45. The method of claim 42, wherein the condition is pain or chronic pain.

46. The method of claim 45, wherein the pain results from ailed back surgery syndrome (FBSS), complex regional pain syndrome (CRPS), peripheral neuropathy (including diabetic neuropathy), post-herpetic neuralgia, phantom limb pain, visceral pain, or cancer-related pain.

47. The method of claim 34, wherein the signal waveforms are administered to a central nervous system neuron or region or a peripheral nervous system neuron or nerve of the subject.

48. The method of claim 47, wherein the signal waveforms are administered to the ventral tegmental area (VTA), thalamus, or subthalamus.

49. The method of claim 48, wherein the condition comprises essential tremor or Parkinsonian tremor.

50. The method of claim 49, wherein the condition is a epilepsy or a seizure disorder.

51. The method of claim 50, wherein the seizure disorder is characterized by absence seizures, tonic seizures, atonic seizures, clonic seizures, myoclonic seizures, or tonic- clonic seizures.

52. The method of claim 48, wherein the condition is movement disorder, epilepsy, depression, coma, cognitive impairment, obsessive compulsive disorder, depression, migraine pain, addiction, or stroke.

53. The method of claim 34, wherein the subject is a human.

54. The method of any one of claims 34-53 further comprising providing for selective activation of a neuron by polynomial distortion algorithm (PDA) tuning of the first stimulation signal waveform to an intrinsic biophysical property of the neuron.

55. The method of claim 54 wherein the intrinsic biophysical property comprises an axonal diameter.

56. The method of claim 54 or claim 55 wherein the intrinsic biophysical property comprises a channel conductance.

57. The method of any one of claims 54-56 wherein the intrinsic biophysical property comprises a channel activation curve.

58. The method of any one of claims 54-57, wherein the response signal is neuronal transmission by a nerve fiber having a diameter of less than about 10 pm or less than about 5 pm.

59. The method of any one of claims 54-57, wherein the method comprises selectively inducing action potentials in nerve bundles having a diameter of less than about 5 pm, while causing reduced stimulation of action potentials in nerve bundles having a diameter of greater than about 5 pm.

60. The method of any one of claims 54-57, wherein the method comprises selectively inducing action potentials in nerve bundles having a diameter of less than about 10 pm, while causing reduced stimulation of action potentials in nerve bundles having a diameter of greater than or equal to about 10 pm or about 13 pm.

61. The method of any one of claims 34-60, further comprising:selecting a field of view that includes a plurality of neurons disposed between stimulation electrodes; applying an initial biphasic stimulus;determining, for each neuron, a change in firing frequency relative to a predetermined baseline firing frequency; andadding one or more neurons to a region of interest when a ratio of the change in firing frequency to the predetermined baseline firing frequency exceeds a threshold.

62. The method of claim 34-60, further comprising:determining whether the exposure time associated with imaging the field of view exceeds a time limit in response to when the ratio does not exceed the threshold; selecting a different field of view when the exposure time does not exceed the time limit; andreplacing a neuronal sample when the exposure time exceeds the time limit.

63. The method of any one of claims 34-60, further comprising:delivering the generated waveform for a plurality of trials;determining whether multicell selectivity is present based on trial results; applying the polynomial distortion algorithm, upon determining that multi cell selectivity is present, to generate distorted waveforms;adding candidate waveforms to a library when a target neuron is activated without activation of a non-target neuron;testing candidate waveforms for robustness over a plurality of additional trials; and selecting as a new parent seed a robust candidate waveform having a lower energy metric than a current parent seed.

64. The method of any one of claims 34-60, wherein the second stimulation signal waveform is applied to a phrenic nerve of the subject.

65. The method of claim 64, wherein the method further comprises:receiving ventilator-derived respiratory data including at least one of tidal volume, respiratory phase timing, or capnography data, wherein the polynomialdistortion algorithm (PDA) updates one or more stimulation parameters based on the ventilator-derived respiratory data.

66. The method of claim 65, wherein the polynomial distortion algorithm iteratively adjusts at least one of stimulation timing, waveform shape, or stimulation energy across successive respiratory cycles to improve consistency of tidal volume generated by phrenic nerve stimulation.

67. A method of non-thcrapcutic stimulation of nerve fibers in a mammalian subject, the method comprising:receiving an oscillating electrical signal from a subject;applying a first stimulation signal waveform to the subject, wherein the first stimulation signal waveform modifies the oscillating electrical signal from the subject to produce a response signal;receiving the response signal from the subject; andapplying a second stimulation signal waveform to the subject, wherein the second stimulation signal is generated using a polynomial distortion algorithm (PDA).

68. The method of claim 67 further comprising:applying a third stimulation signal waveform to the subject, wherein:the third stimulation signal waveform is generated using a polynomial distortion algorithm (PDA); andthe third stimulation signal waveform modifies the oscillating electrical signal from the subject to produce a second response signal;receiving the second response signal from the subject; andapplying a fourth stimulation signal waveform to the subject, wherein:the fourth stimulation signal waveform is generated using a polynomial distortion algorithm (PDA); andthe fourth stimulation signal waveform is configured to optimize the second response signal without regard to the phase window of the oscillating electrical signal.

69. The method of claim 68, further comprising applying subsequent stimulation signal waveforms and receiving subsequent response signals in an iterative process.

70. The method of claim 67, wherein the signal waveforms are administered to a peripheral nerve bundle in the subject.

71. The method of claim 70, wherein the peripheral nerve is the phrenic nerve, the vagus nerve, the sciatic nerve, a spinal nerve or a dorsal root ganglion.

72. The method of claim 71, wherein the signal waveforms are administered to a central nervous system neuron or region or a peripheral nervous system neuron or nerve of the subject, preferably wherein the signal waveforms are administered to the ventral tegmental area (VTA), thalamus, or subthalamus.

73. The method of claim 67, wherein the subject is a human.

74. The method of any one of claims 67-73 further comprising providing for selective activation of a neuron by polynomial distortion algorithm (PDA) tuning of the first stimulation signal waveform to an intrinsic biophysical property of the neuron, preferablywherein the intrinsic biophysical property comprises an axonal diameter and / or wherein the intrinsic biophysical property comprises a channel conductance and / or wherein the intrinsic biophysical property comprises a channel activation curve.

75. The method of any one of claims 67-74, wherein the response signal is neuronal transmission by a nerve fiber having a diameter of less than about 10 pm or less than about 5 pm.

76. The method of any one of claims 67-75, wherein the method comprises selectively inducing action potentials in nerve bundles having a diameter of less than about 5 pm, while causing reduced stimulation of action potentials in nerve bundles having a diameter of greater than about 5 pm. preferably wherein the method comprisesselectively inducing action potentials in nerve bundles having a diameter of less than about 10 pm, while causing reduced stimulation of action potentials in nerve bundles having a diameter of greater than or equal to about 10 pm or about 13 pm.

77. The method of any one of claims 67-76, wherein the stimulation leads to muscle relaxation and / or stress reduction by stimulation of the vagus nerve.

78. The method of any one of claims 67-76, wherein the stimulation leads to an increase of the tidal volume by stimulation of the phrenic nerve.

79. The method of any one of claims 67-76, wherein the stimulation leads to an increase of muscle strength or muscle coordination by stimulation of the sciatic nerve.

80. The method of any one of claims 67-76, wherein the stimulation leads to an increase of blood flow by stimulation of the spinal nerve.

81. The method of any one of claims 67-76, wherein the stimulation leads to a modulation of sensory signal transmission by stimulation of the dorsal root ganglion.

82. The method according to any of claims 34 to 81, performed by programmable circuitry.

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