Determining tremor characteristics from deep brain local field potential recordings

Abstract

Disclosed herein is a system and method to predict the tremor amplitude of patients with neurological movement disorders from DBS data in addition to, or in lieu of determining other characteristics such a tremor frequency. The disclosed system and method provide an interactive and quantitative measure of the tremor amplitude (and frequency) based on DBS LFP data. Specifically, in some implementations, the disclosed system and methods can be integrated into a closed-loop system for DBS stimulation programming and / or adjustment. The same or a different machine learning model can be incorporated into a DBS system to provide feedback for setting and / or adjusting DBS to be applied to a patient, for example.

Description

Atty. Dkt. No.103361-596WO1 DETERMINING TREMOR CHARACTERISTICS FROM DEEP BRAIN LOCAL FIELD POTENTIAL RECORDINGS CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. provisional patent application no. 63 / 582,275, filed on September 13, 2023, and titled “DETERMINING TREMOR CHARACTERISTICS FROM DEEP BRAIN LOCAL FIELD POTENTIAL RECORDINGS,” the disclosure of which is expressly incorporated herein by reference in its entirety. BACKGROUND

[0002] With the commercial availability of neurostimulators capable of recording deep brain Local Field Potentials (LFPs), there is growing interest in analyzing the spectrum of the LFPs recorded from patients with various neurological movement disorders, such as Parkinson’s disease (PD), essential tremors (ET), and the like. SUMMARY

[0003] Disclosed herein is a system and method to predict the tremor amplitude of patients with neurological movement disorders from DBS data in addition to, or in lieu of determining other characteristics such as tremor frequency. Currently, neurologists and neurosurgeons assess the amplitude of a tremor using subjective and qualitative methods, such as judging hand-drawn spirals by patients or estimating the severity of a tremor based on tasks the patient is asked to perform. The disclosed system and methods provide an interactive and quantitative measure of the tremor amplitude (and frequency) based on DBS LFP data. Specifically, in some implementations, the disclosed system and methods can be integrated into a closed-loop system for DBS stimulation programming and / or adjustment. The same or a different machine learning model can be incorporated into a DBS system to provide feedback for setting and / or adjusting DBS to be applied to a patient, for example.

[0004] In some embodiments, a method of determining tremor frequency in a patient is disclosed. The method includes recording a deep brain local field potential (LFP) signal using a directional deep brain stimulation (DBS) lead implanted in the brain of the patient;Atty. Dkt. No.103361-596WO1 generating a frequency spectrum representation of the LFP signal; identifying a pair of dominant peaks in a beta-band of the frequency spectrum representation of the LFP signal; and calculating the tremor frequency as a difference between the pair of dominant peaks.

[0005] In some embodiments, the frequency spectrum representation of the LFP signal is generated using a Fast Fourier Transform (FFT).

[0006] In some embodiments, the method further includes applying a digital filter to the frequency spectrum representation of the LFP signal to remove noise prior to identifying the pair of dominant peaks. In some embodiments, the digital filter is a Savitzky-Golay filter.

[0007] In some embodiments, the method further includes filtering the LFP signal with at least one low-pass filter and at least one high-pass filter prior to generating the frequency spectrum representation of the LFP signal. In some embodiments, the at least one low-pass filter includes two 100 Hz low-pass filters. In some embodiments, the at least one high-pass filter includes two 1 Hz high-pass filters.

[0008] In some embodiments, the method further includes providing an indication of the tremor frequency to a user. In some embodiments, providing the indication includes displaying the tremor frequency via a user interface.

[0009] In some embodiments, an annular DBS lead of directional DBS lead includes an elongate body and a plurality of annular electrodes spaced apart along a length of the elongate body.

[0010] In some embodiments, the method further includes calculating a tremor amplitude prediction as an average of a magnitude of the pair of dominant peaks; and predicting, from a trained machine learning model, a tremor amplitude. In some embodiments, the trained machine learning model is a nonlinear regression model.

[0011] In some embodiments, the method further includes adjusting a stimulation input based on the tremor amplitude and tremor frequency. In some embodiments, the step of adjusting is performed by a clinician. In some embodiments, the step of adjusting is performed by a feedback algorithm.

[0012] In some embodiments, a system for tremor assessment is disclosed. The system includes a deep brain stimulation component, wherein the dee deep brain stimulation component includes one or more leads and a stimulator; and one or more computing devices,Atty. Dkt. No.103361-596WO1 wherein one of the one or more computing devices is configured to calculate tremor frequencies.

[0013] In some embodiments, one of the one or more computing devices is configured to predict tremor amplitude.

[0014] In some embodiments, the one or more computing devices include a component for a user interaction.

[0015] In some embodiments, the system further includes a feedback component, wherein the feedback component includes a clinician feedback or an algorithmic feedback.

[0016] In some embodiments, the feedback component is configured to adjust a stimulation input.

[0017] In some embodiments, the system is a closed loop system. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] FIG.1 is a diagram of directional leads. There are four levels of electrodes along the length of the lead. The top and bottom electrodes are continuously conducting full rings, while the middle-level electrodes are split into three isolated conducting segments. These leads allow stimulation and recording between levels (parallel to the leads) and between segments of a multi-segment level (lateral direction to the leads).

[0019] FIG.2 is a diagram of an LFP signal measured by channel 7 vs. time. The sampling rate is 250 Hz. There are 5288 time samples with a recording duration of 21.148 seconds.

[0020] FIG.3 is a diagram of an FFT Magnitude spectrum of the signal obtained from channel 17. This is a “regular” plot and not a stem (or lollipop) plot. The red dashed lines show the bounds of the alpha, beta, and gamma spectral bands at 8 Hz, 13 Hz, and 31 Hz respectively. The presence of noise is because no filtering has been applied to the FFT signal in this figure.

[0021] FIG.4 includes CWT scalograms of beta-band LFP signal power obtained from channel 17. The beta-band signal is obtained by passing the time signal through a 13-31 Hz, 5th-order discrete Butterworth band-pass filter. The top and bottom dashed red horizontal lines are the edges of the beta band. The middle solid red horizontal line is at the carrier frequency illustrated in FIG.9. The top plot contains 21.148 seconds of LFP activity. It shows that beta bursts appear in burst groups with a burst group duration of around 3 sec.Atty. Dkt. No.103361-596WO1 (enclosed in white rectangles of 3 seconds width). The significance of 3 seconds duration is explained later where it is shown that the duration can be calculated from the width of the measured power spectrum tremor peak of the patient’s limbs from a video recording of the patient, FIG.16. The bottom plot shows the first 4 seconds of LFP activity to zoom-in on one burst group to focus on a burst train in the group. The white rectangle encompassing 13 numbered semi-periodic bursts is 2.5sec wide indicating an approximate mean burst frequency of ~5.2 Hz.

[0022] FIG.5 is an FFT Magnitude spectrum of the signal obtained from channel 17. A Savitzky-Golay filter has been applied to the raw FFT shown in FIG.3 to reduce noise and unveil the salient features of the spectrum, such as the two dominant peaks at frequencies ^^^1^= 23.35 Hz and ^^^2^ = 18.43 Hz.

[0023] FIG.6 is a diagram Magnitude Spectrum of the Idealized Twin Peak Model. This model consists of only two frequencies ^^^1^= 23.35 Hz and ^^^2^ =18.43 Hz obtained from FIG.5. It also carries over the peak magnitude ratio of 0.7 from FIG.5.

[0024] FIG.7 is an illustration of beating in the Idealized Twin Peak model. The top plot shows beating or amplitude modulation, illustrating how constructive and destructive superpositions of ^^^1^ and ^^^2^ signals produce beating phenomena. The middle plot shows the power in the signal (square of the magnitude). This plot shows bursts with frequency equal to the beat frequency, ^^^The bottom plot shows the CWT scalogram of the signal power in the Idealized Twin Peak model showing the periodic bursts located in the beta band with a frequency equal to the beat frequency.

[0025] FIG.8 includes CWT scalograms of the LFP signal power from FIG.4 and the Idealized Twin Peak Model from FIG.7, plotted together for ease of comparison.

[0026] FIG.9 is an FFT Magnitude spectrum of the signal obtained from channel 17. Association of the two beta-band dominant peaks in the LFP Spectrum with two frequencies ^^^1^ and ^^^2^ which beat against each other to produce a tremor frequency, ^^^^^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^. The carrier frequency, ^^^^^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^, of the beats (bursts), as well asand ^^^2^ are located in the beta band while ^^^^^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^= 4.92 Hz is a much lower frequency.

[0027] FIG.10 is an illustration of beating phenomena in the beta band LFT obtained from channel 17. The top plot shows beating or amplitude modulation. The middle plot shows the power in the signal (square of the magnitude). This plot shows bursts with a mean frequencyAtty. Dkt. No.103361-596WO1 equal to the tremor frequency, ^^^^^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^= ^^^^^^^^ ^^^^ ^^^^ ^^^^. The bottom plot shows the CWT scalogram of the beta band power in the LFT (same as in FIG.4) showing the almost periodic bursts located in the beta band with a frequency equal to the tremor frequency ^^^^^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^= ^^^^^^^^ ^^^^ ^^^^ ^^^^.

[0028] FIG.11 is a chart illustrating the distribution of energy of the LFP spectrum among the alpha, beta, and gamma bands for all the 15 channels in the left lead. The histograms in this figure and the next figure (FIG.12) are drawn to the same scale so they can all be compared with each other. Channels marked with the letters TP exhibit dominant twin peaks which can be identified by our peak-finding algorithm.

[0029] FIG.12 is a chart illustrating the distribution of energy of the LFP spectrum among the alpha, beta, and gamma bands for all the 15 channels in the right lead. The histograms in this figure and the previous figure (FIG.11) are drawn to the same scale so they can all be compared with each other. Channels marked with the letters TP exhibit dominant twin peaks which can be identified by our peak-finding algorithm.

[0030] FIG.13 is a chart of mean tremor frequencies, ^^^^^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^, from all the eight channels that show Dominant Twin Peak activity (marked by TP in FIGS.11 and 12). The frequencies have a mean value of 5.26 Hz and a standard deviation of 0.31 Hz; from which a mean tremor frequency for the PD patient is predicted as 5.26 ± 0.31 Hz.

[0031] FIG.14 is a diagram of key location points on a human body that can be identified by a “Pose Landmark Detection” model. The right and left wrists, knees, and heels were used as key locations to determine the PD patient's corresponding x and y coordinates from the patient’s video. The figure is for illustrative purposes and is not generated from the PD patient’s video. The illustration in the figure is generated by Google’s MediaPipe from a video licensed from Adobe Stock.

[0032] FIG.15 is a measured CWT scalogram (Adison 2020) of the patient’s right-hand wrist tremor obtained from the video of the patient. The scalogram shows that the tremor has a fluctuating intensity in time of approximately ^^^^tremor_fluctuation= 3.0 sec durations, which are indicated by white rectangles of 3.0-sec width.

[0033] FIG.16 is a chart of measured (from the patient’s video) Power Spectrum (blue curve) of the patient’s right hand’s wrist movement showing a right wrist tremor peak with a mean value of 5.22 Hz and an HWHM of 0.32 Hz. The tremor frequency prediction based on Dominant Twin Peaks (FIG.13) is shown in green. The figure demonstrates that the tremorAtty. Dkt. No.103361-596WO1 frequencies from the LFP Dominant Twin Peaks closely match both the mean value of the measured tremor frequency and the width of the measured tremor frequency peak.

[0034] FIG.17 is a chart of measured tremor frequencies from the x and y coordinates corresponding to the right and left wrists, knees, and heels of the PD patient. Red lines show the prediction, 5.26 ± 0.31 Hz (Fig.13), obtained from the LFP Dominant Twin Peaks via. Eq. (5). The solid red line is at the predicted mean, 5.26Hz, while the pair of horizontal red dashed lines show the upper and lower bounds, ± 0.31 Hz of the prediction. The vertical error bars on the data points show the widths of the measured tremor peaks.

[0035] FIG.18 is an FFT Magnitude spectrum of the signal obtained from channel 1 showing the twin peak frequency magnitude, h1and h2, and associated tremor amplitude prediction.

[0036] FIGs.19A-19D are various embodiments of the system.

[0037] FIGs.20A-20D are various embodiments of the method.

[0038] Various objects, aspects, features, and advantages of the disclosure will become more apparent and better understood by referring to the detailed description taken in conjunction with the accompanying drawings, in which similar reference characters identify corresponding elements throughout. In the drawings, similar reference numbers generally indicate identical, functionally similar, and / or structurally similar elements. DETAILED DESCRIPTION

[0039] Disclosed herein are systems and methods for determining native tremor characteristics, such as frequency and amplitude, from deep brain LFP recordings, according to various implementations. Determining native tremor characteristics can be useful in diagnostic, clinical, and / or treatment settings. In one aspect, for example, the disclosed systems and methods can be used in a feedback loop to set or adjust treatment parameters (e.g., applied stimulation) based on the determined tremor characteristics. It should be appreciated that the disclosed systems and methods may be used in applications for various neurological movement disorders, such as PD, ET, and the like. Thus, while PD patients are referred to herein for discussion, the present disclosure is not intended to be limiting in this regard.Atty. Dkt. No.103361-596WO1

[0040] It has been hypothesized that the beta burst trains found in the subthalamic nucleus local field potential of a PD patient, for example, could be linked to the phenomena known as “beating” in the field of signal processing. It is demonstrated herein that burst trains arise from the beating of two dominant peaks in the beta band, and quantitively determine the mean resting tremor frequency of the PD patient as the difference between the two dominant twin frequencies observed in the beta-band. It was found that these beta-band dominant twin peaks are observed only in the lateral channels of an example deep brain stimulation (DBS) directional (1-3-3-1) electrode leads; these are channels that measure potentials between segments of multi-segment electrodes in a direction lateral to the lead’s length.

[0041] Referring now to Figs.19A-19D, a system for calculating tremor frequencies is disclosed. The system includes a deep brain stimulator 1920 and one or more computing devices 1940. The deep brain stimulator 1920 includes one or more leads 1922 and a stimulator 1924, where the one or more leads 1922 are implanted in the patient along a right and a left side of the patient’s brain, and the stimulator 1924 is implanted in another area of the patient, for example, in the chest or abdominal region. In some embodiments, the stimulator 1924 and the one or more leads 1922 are electrically connected so that the stimulator can transmit electrical stimulation to the leads and can receive a deep brain local field potential (LFP). In some embodiments, the system further includes a computing device 1940, wherein the computing device 1940 is one or more computing devices communicatively coupled to one another and to the deep brain stimulator 1920.

[0042] In one embodiment, the computing device 1940 the system for calculating tremor frequencies includes (see Fig.19A) a display 1942 and a Tremor Analysis module 1944, wherein the Tremor Analysis module 1944 is stored in a storage device (e.g., memory) and is executed on one or more processors. The system further includes a user interaction computing device 1932, such as a mobile computing device.

[0043] In one embodiment, the computing device 1940 of the system for calculating tremor frequencies includes (see Fig.19B) a display 1942, and a Tremor Analysis module 1944, wherein the Tremor Analysis module 1944 is stored in a storage device (e.g., memory) and is executed on one or more processors. The computing device 1940 further includes a user interaction module 1934.

[0044] In one embodiment, the system for calculating tremor frequencies further includes a feedback component, thereby forming a closed loop system. In one example, the feedbackAtty. Dkt. No.103361-596WO1 component is a clinician feedback 1950 (see Fig.19C), wherein a clinician interacts with the user interaction component 1930 to adjust a stimulation input to the stimulator 1924. In another example, the feedback component is a feedback module 1960 (see Fig.19D), wherein the feedback module 1960 adjusts the stimulation input to the stimulator 1924.

[0045] Referring now to Fig.20A, an embodiment of the method of determining tremor frequency in a patient is shown. The method comprises recording a deep brain local field potential (LFP) signal using a directional deep brain stimulation (DBS) lead implanted in the brain of the patient 2010; generating a frequency spectrum representation of the LFP signal 2020; identifying a pair of dominant peaks in a beta-band of the frequency spectrum representation of the LFP signal 2030; and calculating the tremor frequency as a difference between the pair of dominant peaks 2040.

[0046] In some embodiments, the frequency spectrum representation of the LFP signal is generated using a Fast Fourier Transform (FFT).

[0047] In some embodiments, the method further includes applying a digital filter to the frequency spectrum representation of the LFP signal to remove noise prior to identifying the pair of dominant peaks, for example, a Savitzky-Golay filter.

[0048] In some embodiments, the method further includes filtering the LFP signal with at least one low-pass filter and at least one high-pass filter prior to generating the frequency spectrum representation of the LFP signal. For example, the at least one low-pass filter includes two 100 Hz low-pass filters, two 90 Hz high-pass filters, two 80 Hz high-pass filters, two 70 Hz high-pass filters, two 60 Hz high-pass filters, two 50 Hz high-pass filters, two 40 Hz high-pass filters, two 30 Hz high-pass filters, two 20 Hz high-pass filters, two 10 Hz high- pass filters, two 5 Hz high-pass filters, or two 1 Hz high-pass filters.

[0049] In some embodiments, the method further includes providing an indication of the tremor frequency to a user, wherein providing the indication includes displaying the tremor frequency via a user interface.

[0050] In some embodiments, an annular DBS lead of directional DBS lead includes an elongate body and a plurality of annular electrodes spaced apart along a length of the elongate body.

[0051] Referring now to Fig.20B, an embodiment of the method of determining tremor frequency in a patient is shown. The method comprises recording a deep brain local fieldAtty. Dkt. No.103361-596WO1 potential (LFP) signal using a directional deep brain stimulation (DBS) lead implanted in the brain of the patient 2010; generating a frequency spectrum representation of the LFP signal 2020; identifying a pair of dominant peaks in a beta-band of the frequency spectrum representation of the LFP signal 2030; calculating a tremor amplitude prediction as an average of a magnitude of the pair of dominant peaks 2050; and predicting, from a trained machine learning model, a tremor amplitude 2060.

[0052] Referring now to Fig.20C, an embodiment of the method of determining tremor frequency in a patient is shown. The method comprises recording a deep brain local field potential (LFP) signal using a directional deep brain stimulation (DBS) lead implanted in the brain of the patient 2010; generating a frequency spectrum representation of the LFP signal 2020; identifying a pair of dominant peaks in a beta-band of the frequency spectrum representation of the LFP signal 2030; calculating the tremor frequency as a difference between the pair of dominant peaks 2040; calculating a tremor amplitude prediction as an average of a magnitude of the pair of dominant peaks 2050; and predicting, from a trained machine learning model, a tremor amplitude 2060.

[0053] Referring now to Fig.20D, an embodiment of the method of determining tremor frequency in a patient is shown. The method comprises recording a deep brain local field potential (LFP) signal using a directional deep brain stimulation (DBS) lead implanted in the brain of the patient 2010; generating a frequency spectrum representation of the LFP signal 2020; identifying a pair of dominant peaks in a beta-band of the frequency spectrum representation of the LFP signal 2030; calculating the tremor frequency as a difference between the pair of dominant peaks 2040; calculating a tremor amplitude prediction as an average of a magnitude of the pair of dominant peaks 2050; predicting, from a trained machine learning model, a tremor amplitude 2060, for example, the trained machine learning model is a nonlinear regression model; adjusting a stimulation input based on tremor amplitude and tremor frequency 2070; and repeating the method at step 2010. In some examples, the step of adjusting is performed by a clinician. In some examples, the step of adjusting is performed by a feedback algorithm.

[0054] In summary, it was found that the beta band peaks accurately predict the measured mean tremor frequency of the patient and the width of the frequency peak in the measured spectrum of the limbs’ coordinates obtained from the video. Additionally, as discussedAtty. Dkt. No.103361-596WO1 below, the time duration of the burst groups in the LFP can be determined from the distribution of tremor frequencies obtained from the different channels of the leads. Closed Loop System with Tremor Amplitude Prediction

[0055] The work outlined above demonstrates that the LFP beta band spectrum fully encoded the patient’s tremor. In other words, it accurately predicted the measured mean tremor frequency of the patient and the width of the frequency peak in the measured spectrum of the limbs’ coordinates. Furthermore, the observed duration of the burst groups in the LFP was obtained from the standard deviation of the tremor frequencies obtained from the LFP data. Since it encoded the patient’s tremor information, the LFP beta band spectrum also contained information about the tremor amplitude.

[0056] Thus, a Tremor Amplitude Predictor (TAP) is defined as:where h1and h2are the heights of dominant twin peaks. Unlike the tremor frequency, which is the same for each channel of leads in a DBS system, TAP values vary from channel to channel. TAP values represent the measured energy in the Dominant Twin Peaks and are related to the strength (amplitude) of the tremor. TAP values from all the lateral channels can be used as features in a machine learning model, as discussed below, to predict the amplitude (severity) of the tremor in patients with neurological movement disorders.

[0057] Thus, the disclosed system and methods can be used to predict the tremor amplitude of patients with neurological movement disorders from DBS data in addition to, or in lieu of determining other characteristics such a tremor frequency. Currently, neurologists and neurosurgeons assess the amplitude of a tremor using subjective and qualitative methods, such as judging hand-drawn spirals by patients or estimating the severity of a tremor based on tasks the patient is asked to perform. The disclosed system and methods provide an interactive and quantitative measure of the tremor amplitude (and frequency) based on DBS LFP data. Specifically, in some implementations, the disclosed system and methods can be integrated into a closed-loop system for DBS stimulation programming and / or adjustment. The same or a different machine learning model can be incorporated into a DBS system to provide feedback for setting and / or adjusting DBS to be applied to a patient, for example.Atty. Dkt. No.103361-596WO1

[0058] In some implementations, the disclosed techniques (e.g., the identification of TAP values) are realized as part of a machine learning model (e.g., a non-linear regression model) which is designed and trained to predict tremor amplitude in patients. Specifically, in some such implementations, the above-described “Tremor Amplitude Predictor” can be used to generate tremor amplitude predictor values based on LFP data for a patient, which are in turn used as features in the machine learning model. The target data for the machine learning model can be obtained by either using a multi-camera motion detection setup or an inertial sensor-based motion capture system, among other techniques. The tremor amplitude data is used as target variables for training the machine learning model using “Tremor Amplitude Predictors” as the feature set. EXAMPLE

[0059] With the commercial availability of Deep Brain Stimulation (DBS) neurostimulators and sensing leads capable of recording deep brain Local Field Potentials (LFPs), researchers now commonly study the spectral characteristics of LFPs recorded from the subthalamic nucleus (STN) of patients with Parkinson’s disease (PD). Exaggerated basal ganglia activity in the beta band is commonly found in patients with PD.

[0060] Recently, the peaks in the beta band power spectrum have gained attention in connection with using the peaks as biological feedback signals for closed-loop DBS in patients suffering from PD [Feldmann et al., 2022; Koeglsperger et al., 2021; Plate et al., 2021; Vissani et al., 2020). Extensive work has also been published to correlate subthalamic synchronized oscillatory activity with motor impairment in patients with PD ( Neumann et al., 2016; Neumann et al., 2017; Telkes et al., 2018; Beudel et al., 2015]. Bursts of LFP power in the beta band, known as beta bursts, have also been observed and studied recently Tinkhauser et al., 2017; Tinkhauser et al., 2017; Tinkhauser et al., 2018; Torrecillos et al., 2018).

[0061] In some respects, the present disclosure focuses on the tremor dominant (TD) subtype of PD and the related beta burst trains. In some respects, the central problem that is addressed by the present study is that if the frequency spectrum of the limb motions of a PD patient are measured, for example by evaluating the video of the patient or using motion capture cameras, a strong peak is found in the measured spectrum. This peak is centered around the tremor frequency of the patient, ^^^^tremor_measured; the finite width of this peak,Atty. Dkt. No.103361-596WO1 Δ ^^^^tremor_measured, is related to the time duration of the tremor fluctuations, ^^^^tremor_fluctuation, i.e., the time interval over which the tremor’s intensity fluctuates, i.e., repeatedly waxes and wanes over time. Since the statistical population of PD patients has an average tremor frequency in the range 4 – 8 Hz (Bain 2002) ^^^^tremor_measured lies in this interval. In contrast, he LFP spectrum includes the beta band frequencies, 13 to 31 Hz, which are much larger than ^^^^tremor_measured. Furthermore, the widths of the various peaks in the beta band seem to have no obvious connection to Δ ^^^^tremor_measured. There seems to be no clear relationship between the features of the LFP spectrum in the beta band and the measured tremor spectrum ( ^^^^tremor_measured, Δ ^^^^tremor_measured). This study explores a hypothesis that makes a direct connection between the features of the (higher frequency) LFP beta band spectrum and (lower frequency) measured tremor spectrum features, ^^^^tremor_measured, Δ ^^^^tremor_measured, and ^^^^tremor_fluctuation. To support the hypothesis, the patient’s limb coordinates we independently measured time-series obtained from a video of the patient. Google®'s MediaPipe1 framework is used to obtain the limb coordinates corresponding to the patient's left and right wrists, knees, and heels.

[0062] In addition, the study also presents a theoretical foundation on which the hypothesis is based, by noting that the LFP spectrum of the PD patient when appropriately smoothed, shows two dominant frequency peaks close to each other in the beta band. Unlike earlier works, the beta burst trains found in the STM local field potentials of a PD patient are explicitly linked to the phenomena known as “beating” (or amplitude-modulation) in the field of communications. In amplitude modulation two frequencies close to each other, when superimposed, give rise to a power burst train which has a frequency equal to the difference of the two superimposed frequencies. This resulting burst train has a lower frequency than the original two frequencies. It was shown that the lower-frequency burst trains seen in the time- frequency visualization of the patient’s LFP data arise from the beating of the two higher- frequency dominant peaks observed in the beta band.

[0063] It was found that the beta-band dominant twin peaks were observed in the lateral channels of the aforementioned DBS directional (1-3-3-1) electrode leads, e.g., channels that measure LFPs between segments of multi-segment levels (lateral direction to the lead) and not parallel to the lead. Additionally, noise in the LFP spectrum can be removed appropriately to reveal the dominant twin peaks. In some implementations, as discussed below, a Savitzky-Golay filter is applied to the raw LFP spectrum for this purpose. It wasAtty. Dkt. No.103361-596WO1 found that the beta band peaks not only accurately predict the measured mean tremor frequency of the patient, but also the width of the frequency peak in the measured spectrum of the limbs’ coordinates obtained from the video. It is also demonstrated below that the time duration of the burst groups in the LFP can be determined from the distribution of LFP tremor frequencies obtained from the various channels of the 1-3-3-1 leads. Materials and Methods

[0064] The LFP signal recordings were obtained from a 71-year-old female patient suffering from PD. Medtronic’s SenSight™ directional (1-3-3-1) electrode leads2, Model 3389™, were implanted into the dorsolateral aspect of the STN on both the left and right hemispheres. A Medtronic Model B35200 Percept™ PC neurostimulator with BrainSense™ technology was implanted on March 2023 to deliver DBS. The neurostimulator (in conjunction with directional leads) is capable of recording intracranial LFPs through one or two leads implanted in the brain. This implanted neurotransmitter was used with stimulation turned off to make the LFP signal recordings on March 2023.

[0065] LFP Recordings from 1-3-3-1 Leads: The 1-3-3-1 leads, shown in FIG.1, are known as directional leads2. All the available measurement directions are grouped into channels. There are 15 channels per lead, leading to a total of 30 channels if leads are implanted in both hemispheres (as is the case for the recordings described herein). As explained in Figure 1, these leads allow stimulation and recording between levels (parallel to the leads) and between segments of a multi-segment level (lateral direction to the leads). The recordings were made with stimulation turned off. The LFP time series were downloaded as a JSON file from the tablet that is used to communicate with the neurostimulator. The time series for each of the 30 channels consists of 21-second LFP recordings sampled at 250 Hz. Medtronic also applies two 100 Hz low-pass and two 1 Hz high-pass filters to the signal, and these LFP signals were used for all the analyses in this study.

[0066] There are four levels (0, 1, 2, and 3) of electrodes arranged along the length of a lead. The top (level-0) and bottom (level-2) electrodes are continuously conducting full rings, while the middle-level electrodes (levels-2 and 3) are split into three isolated “directional” conducting segments (a, b, and c). These leads allow stimulation and recording between levels (parallel to the leads) and between segments of a multi-segment level (lateral direction to the leads).Atty. Dkt. No.103361-596WO1

[0067] A computing device (e.g., a mobile computing device such as a tablet) is used to communicate with the neurostimulator for stimulation programming and LFP signal recording. In some implementations, the computing device includes a display that provides a broad spatial overview of LFP signals measured from both hemispheres of the patient with stimulation turned off. The survey information was stored in a JSON data file on the computing device. As part of the survey, an approximately 21-second LFP recording was made, sampled at 250 Hz, for each of the 30 channels and stored in the JSON data file. The signal also underwent two 100 Hz low-pass and two 1 Hz high-pass filters. This information is summarized in Table 1. Table 1. Information about the raw recordings

[0068] Beating of two higher frequencies to produce a lower frequency power burst. Here the phenomena of beating or amplitude modulation is illustrated by using simple mathematical reasoning. Consider the superposition of two sinusoids with frequencies ^^^^1and ^^^^2(which lie close to each other) by using the identity,which shows that the superposition of two waves with similar frequencies ^^^1^ and ^^^2^ and produces a carrier wave which oscillates with the mean frequency:Atty. Dkt. No.103361-596WO1 ^^^^^^^1^ + ^^^2^^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ =2(2) and whose amplitude is modulated with a lower frequency wave with frequency:

[0069] The beat frequency is defined as the frequency of modulation of the power in the signal (square of the magnitude of the signal), ^^^^^^^^ ^^^^ ^^^^ ^^^^= ^^^1^ − ^^^2^ (4)

[0070] It is noted that the beat frequency ^^^^beatis much lower than the frequencies ^^^^1and ^^^^2, particularly when these frequencies are close to each other.

[0071] Tools used for Signal Processing and Analysis. In this study, Python v3.2.10 and its scientific packages are used for all signal processing and analysis of the signals. Fast Fourier Transforms (FFT) algorithm (McClellan et al., 2016) evaluated by using the “scipy.fft.rfft” function, is used to calculate the frequency spectra of the LFP signals as well as the limb tremor spectra obtained from the video of the patient. Frequency-bin sizes of 0.047 Hz for LFPs, and 0.05 Hz for the video recordings are employed. The square of the magnitude spectrum from the FFT only shows power at a particular frequency without any information about when a frequency event is happening in time. To get that information, the phase spectrum of the FFT is also needed. However, it is not possible to visualize time events by just looking at the magnitude and phase FFT spectra together. To visualize beta power bursts in detail, the signal’s power both in the frequency and the time domains need to be shown simultaneously while also obeying the time-frequency uncertainty principle (Addison 2020; Mallat 2008). The Continuous Wavelet Transform (CWT) scalogram of the LFPs time series were use for this visualization of the LFP signal and also the measured tremor time series. To concentrate on the beta band, the LFP signal is passed through a 13-31 Hz 5th-order discrete Butterworth band-pass filter. Butterworth filters are also known as maximally flat magnitude filters since they are designed to give a frequency response as flat as possible in the passband. Python’s function named “cw” with “gaus8” wavelet from the “pywt” package was used to obtain the scalograms. A frequency of 8 and 50 Hz were used for the upper and lower frequencies of the LFP scalograms; for the measured limb tremor scalograms, 1 and 10 Hz were used.Atty. Dkt. No.103361-596WO1

[0072] Automatic (programmatic) detection of the Dominant Twin Peaks in the LFP spectrum. To make the detection of the dominant twin peak in the LFP spectrum objective, software was used to detect the peaks in the spectrum automatically with a desired prominence (quality) from all the 30 channels. The “find_peaks” function of Python’s “scipy.signal” package was used with the prominence parameter set to 0.04. Before detecting the peaks programmatically, the FFT of the signal needs to be smoothed appropriately to reveal the dominant peaks. Note that the FFT spectrum is smoothed in the frequency domain to specifically observe and detect the peaks in the FFT. A low pass filter that is designed to give a flat passband when used on a time series, such as the Butterworth filter, is not appropriate for this purpose since it potentially destroys the spectrum’s tenacity and smears the peaks, making it difficult to use software tools to detect the peaks. Instead, we use the Savitzky-Golay filter popularized by Whittaker (Whittaker, Robinson 1924) and Guest (Guest 2012) for smoothing the spectrum. This filter, popular in the signal processing community, works by fitting subsets (windows) of adjacent data points with low-degree (order) polynomials by using the least square fit method3 (Riordon et al., 2000). A window size of 51 and polynomial order of 3 is used in this paper. When it is noted that a twin peak was detected in the spectrum of a channel, it is implied that the software has detected twin peaks with a permanence equal to or greater than 0.04.

[0073] Measuring Limb Tremor Frequencies from a Video of the Patient. Google®'s MediaPipe is a framework based on AI for developers to build multimodal (e.g., video or audio) machine learning pipelines. Its primary use case is to provide machine learning models that can run live on smartphones or other edge devices. It can be used to rapidly analyze videos of patients taken by mobile phones or tablets. In this paper, we make use of MediaPipe’s “Pose Landmark Detection”. It uses its internal AI models to automatically identify key location points on a human body in a video or an image. These points are located at major connections to limbs and torso, such as wrists, heels, and knees. The possible location points are illustrated in Fig.14 on a human body. The framework also automatically evaluates a time series of the x and y coordinates of the key location points from a video. This information is sufficient to measure the patient’s tremor frequency, ^^^^tremor_measured; either the x or y coordinate time-series can be used, and both give the same frequency characteristics. Since measuring the amplitude of the tremor is not of interested for this study, it was not required to collect a time series for the z coordinates to account for the total motion trajectory of the limb. The limb tremor measurements are all obtained from a patient’s videoAtty. Dkt. No.103361-596WO1 made on December 15, 2022. A basic consumer-grade hand-held Sony HDR-CX440 Handycam video camera is used. The framework is used on this 854 by 480-pixel video, sampled at 30 fps (frames per second) to determine the x and y coordinates of the right and left wrists, knees, and heels of the PD patient.

[0074] Results and Discussion

[0075] For the following discussion, the LFP signal measured by channel 17 was selected. This channel was associated with a lateral measurement of the LFP between level-2 segments, a and c, of the left lead, denoted as “(17) 2a-2c left”. This channel was chosen because it shows strong beta band activity. This channel is denoted as “(17) 2a-2c left”. This channel was chosen to illustrate the points because it shows the strongest beta band energy compared with the other channels. This will be discussed in detail in the section Energy Distribution of LFPs from Different Channels below where we calculate the energy in the alpha, beta, and gamma bands for all the 30 channels from the LFP spectrum. It is noted that all the 30 channels, and not just channel number 17, were used to calculate the relevant statistical parameters which enabled us to reach the conclusions in this paper. Local Field Potential Spectrum and Scalogram In this paper, we use 21.15 seconds of channel 17’s LFP recorded signal with 5288 time-samples. The sampling rate is 250 Hz. Figure 3 shows the magnitude spectrum of this signal obtained by using the Fast Fourier Transforms (FFT) algorithm (McClellan et al.2016). The bounds of the alpha, beta, and gamma spectral bands are shown by red dashed lines. For the boundaries of the spectral bands, we use 8 Hz, 13 Hz, and 31 Hz for the alpha, beta, and gamma bands respectively. Note that it is hard to detect dominant peaks in the signal, especially by software tools, because of the lack of smoothness.

[0076] Local Field Potential Signal and Spectrum: FIG.2 shows 21.148 seconds of channel 17’s signal vs. time with 5288-time samples. FIG.3 shows the magnitude spectrum of this signal obtained using a Fast Fourier Transforms (FFT) algorithm. The frequency-bin size was 0.047 Hz. It is noted that this figure is known as a “regular” plot in MATLAB or Python and is not a stem (or lollipop) plot. The bounds of the alpha, beta, and gamma spectral bands are shown by vertical dashed lines. For the boundaries of the spectral bands, 8 Hz, 13 Hz, and 31 Hz were selected for the alpha, beta, and gamma bands respectively. As shown, enhanced activity in the beta band for this PD patient was recorded as expected. Note the appreciable noise level as no filtering has been applied to the FFT signal in this figure. Python’s “rfft” function from the “scipy.fft” package was used to evaluate the FFT.Atty. Dkt. No.103361-596WO1

[0077] Tremor Frequency’s Relationship with the LPF Scalogram. FIG.4 shows the Continuous Wavelet Transform (CWT) scalogram of channel 17’s beta-band LFP signal power. To obtain the beta-band signal, the full-band LFP signal was passed through a 13-31 Hz, 5th-order discrete Butterworth band-pass filter. The advantage of a CWT scalogram is that it displays the signal energy both in the frequency and the time domains consistent with the uncertainty principle for time and frequency. Python’s function named “cw” with the “gaus8” wavelet from the “pywt” package was used to obtain the scalogram.

[0078] The scalogram in FIG.4 shows that the beta band signal power was composed of groups of bursts of LFP energy (enclosed in the rectangles in the top plot), with each group composed of semi-periodic trains of bursts (enclosed in the rectangle in the bottom plot). The top plot contains 21.15 seconds of LFP activity. It shows that the burst groups (enclosed in rectangles) have an approximate duration of around three seconds. This burst group duration of the LFP data is one of the features we are interested in this paper and use ^^^^lfp_groupsto denote this time. As will be discussed below, The LFP feature, ^^^^lfp_groups, will be connected with the measured tremor flotation time ^^^^tremor_fluctuation from the video of the patient, FIG. 14.

[0079] The bottom plot zooms in on one semi-periodic burst train within a group by displaying the scalogram of the first four seconds of LFP activity. The rectangle encompassing 12 numbered semi-periodic bursts is 2.5 seconds wide; a quick division shows that these energy bursts have an approximate periodicity of 5.2 Hz. It has been reported in the literature that the statistical population of PD patients has an average measured rest tremor frequency of 5.3 Hz ± 1.2 Hz, therefore the beta-band burst activity of 5.2 Hz is in the probable region of the tremor frequencies of the statistical PD patient population. This suggests a plausible link between the frequency of the beta bursts with the tremor frequency of a PD patient.

[0080] The frequency axis of the scalogram shows that the frequencies making up the bursts (~20 Hz) lie in the beta-band; however, as found by counting the number of bursts along the time axis, the burst trains occurred with an approximate frequency of 5.2 Hz. This is indicative of the phenomena known as beating or amplitude modulation in signal processing when two superimposed waves of similar frequencies beat against each other to produce lower frequency modulated bursts.Atty. Dkt. No.103361-596WO1

[0081] Dominant Twin Peaks in the filtered LPF Scalogram: The noise in the FFT of the LFP shown in FIG.3 makes it difficult to identify dominant peaks in the spectrum. To reveal the salient features of the spectrum a Savitzky-Golay filter (with a window size of 51 and polynomial order of 3) is applied to the FFT signal (Whittaker, Robinsonto 1924; Guest 2012; Riordon et al.2000), which then clearly reveals two dominant twin peaks in the beta band as shown in FIG.5. After the filter was applied, it was possible to programmatically detect prominent peaks in the spectrum. In some studies, the peaks were automatically detected using the “find_peaks” function of Python’s “scipy.signal” package (with parameter “prominence” set to 0.04). The dominant beta-band twin peaks in FIG.5 are detected to be ^^^1^ = 23.35 Hz and ^^^2^ = 18.43 Hz.

[0082] Idealized Twin Peaks Model. To support the claim that the beta burst trains in the LFP scalogram in Figure 4 are originating from the beating of the two dominant peak frequencies, we first construct an idealized model for illustrative purposes with contains only two frequencies which beat against each other. Specifically, we use this model to observe and recognize the signature of the beating of two frequencies in a CWT scalogram. This model, shown in FIG.6, consists of only two frequencies, ^^^^0= 3.35 Hz and ^^^^1= 18.43 Hz, obtained from the peaks in FIG.5.

[0083] The corresponding time domain signal consists of a superposition of the two sinusoidal waves with frequencies ^^^^0and ^^^^1. This superposition that gives us the amplitude- modulated wave, Eq. (1), is shown in the top plot of FIG.7, illustrating how constructive and destructive superpositions of the two sinusoidal signals produce the beating phenomena. The square of the magnitude of this signal which has a periodicity of the beat frequency, Eq. (4), is shown in the middle plot of FIG.7. Finally, the bottom plot of FIG.7 shows the CWT scalogram (Addison 2020) of the Idealized Twin Peak model which shows the characteristic signature of a burst train caused by the beating of two waves with frequencies ^^^^0and ^^^^1. The bursts in the idealized model occur periodically at the beat frequency of ^^^^0 − ^^^^1 = 4.92 Hz.

[0084] For a comparison of the CWT scalogram of the beta-band LFP and the Ideal Twin Peak Model, the corresponding scalograms of the two signals are drawn together in FIG.8. As pointed out earlier, to concentrate on the beta band, the LFP signal is passed through a 13- 31 Hz 5th-order discrete Butterworth band-pass filter. Notice that the scalogram of the beta- band LFP signal (FIG.4) has the same signature of beta burst trains as exhibited in the scalogram of the Idealized Model which originated from the beating of two frequencies.Atty. Dkt. No.103361-596WO1 Furthermore, the burst in the beta-band LFP scalogram also occurs periodically at the same beat frequency of ^^^^0− ^^^^1= 4.92 Hz. Figure 9 illustrates the association of the two beta-band dominant peaks in the LFP Spectrum. The two frequencies ^^^^0and ^^^^1beat against each other to produce the beat frequency, ^^^^beat= 4.92 Hz of the burst trains. The carrier frequency, ^^^^carrier, of the beats, as well as ^^^^0and ^^^^1are in the beta band while ^^^^beatis at a much lower frequency.

[0085] Dominant Twin Peaks in the LFP Signal: Based on the discussion above, it would be ideal to associate the Dominant Twin Peaks, ^^^1^ and ^^^2^ , in the LFP Spectrum (Fig.5) with the two frequencies ^^^1^ and ^^^2^ which beat against each other to produce the tremor frequency, ^^^1^ – ^^^^2. However, in practice, the limb tremor of a patient is not composed of a single frequency. Instead, the measured spectrum consists of a peak with a mean value and a non- zero width, as illustrated by the measured results (FIG.16) from a video of the patient. These measurements of tremor frequencies from the patient’s video are discussed below. With the non-zero width in mind, the limb tremor frequency, ^^^^^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^, is defined as the mean value of the tremor frequency associated with a PD patient:

[0086] Equation 5 forms a basis of the disclosed system and methods, providing a quantitative procedure (e.g., illustrated in FIG.9) to calculate the mean limb tremor frequency of a patient from the magnitude spectrum of the LFP for a given channel.

[0087] Beating in the beta-band LFP signal is illustrated in FIG.10. The top plot shows the beta-band signal vs. time, and the middle plot shows its power vs. time. The beating of the two frequencies ^^^1^ and ^^^2^ to produce semi-periodic beta bursts is apparent in these plots. Finally, the third plot of FIG.10 shows the beta-band scalogram (same as in FIG.4) for ease of comparison. It is instructive to compare FIG.10 with FIG.7, the equivalent figure for the Idealized Twin Peak model.

[0088] Statement of the Hypothesis

[0089] Having laid the theoretical background, the central problem mentioned at the beginning of this study is addressed and connected to the LFP spectrum to the spectrum of tremor by formally forming a hypothesis in three parts. A) the frequency of the power burst trains, in the LFP scalogram (which we have shown to be ^^^^1– ^^^^2, is equal to the tremor frequency ^^^^tremor_measured. In fact, the limb tremor of a patient is not composed of a single frequency, instead, the tremor spectrum consists of a peak located at ^^^^tremor_measured withAtty. Dkt. No.103361-596WO1 a non-zero width Δ ^^^^tremor_measured. Therefore, ^^^^1– ^^^^2is calculated over all the channels exhibiting dominant twin peaks to evaluate the mean ( ^^^^1– ^^^^2)mean. The hypothesis associates this mean value with ^^^^tremor_measured: ^^^^^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^_ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^= ( ^^^1^ − ^^^2^ )^^^^ ^^^^ ^^^^ ^^^^(5a)

[0090] B) The second part of the hypothesis links Δ ^^^^tremor_measuredto the LFP spectrum. Then, ^^^^1– ^^^^2is evaluated over all the channels exhibiting dominant twin peaks and calculate the standard deviation ( ^^^^1– ^^^^2)std dev. The hypothesis associates the standard deviation with Δ ^^^^tremor_measured:

[0091] C) It is shown later that the tremor fluctuation time, ^^^^tremor_fluctuation, can be evaluated from Δ ^^^^tremor_measured.The third part of the hypothesis states that ^^^^tremor_fluctuationis equal to the time duration, ^^^^lfp_groups, of groups of beta-band trains seen in the scalograms of the LFP (top plot, FIG.4):

[0092] In summary, the hypothesis connects (predicts) three defining features of the measured tremor spectrum, ^^^^tremor_measured,and ^^^^tremor_fluctuation, to three independent features, ( ^^^^1– ^^^^2)mean, ( ^^^^1– ^^^^2)std dev, and ^^^^lfp_groups seen in the LFP signals.

[0093] Energy Distribution in the Bands: Now, the distribution of energy of the LFP spectrum among the alpha, beta, and gamma bands for all 30 channels is investigated. First, the LFP energy in a band is defined as the integrated power of the spectrum over the frequency range of that band. FIG.11 shows the distribution of the energy for all 15 channels of the left lead, and FIG.12 shows the same results for the 15 channels of the right lead. The histograms are drawn to the same scale for all the 30 channels. Note that the LFP energy in the bands is much higher in the left channels than in the right channels, indicating a stronger right-side tremor of the PD patient compared with the left-side.

[0094] Automatically Picking Channels with Dominant Twin Peaks: The peak-finding algorithm discussed above can be used on the LFP Magnitude Spectrums (with Savitzky- Golay filtering) originating from all the 15 left channels in FIG.11 to automatically identify six channels that exhibit clear Dominant Twin Peaks; these channels have been marked by the letters TP (Twin Peaks) in the figure. It is interesting to note that these six channelsAtty. Dkt. No.103361-596WO1 comprise all the left lateral channels, i.e., channels that make lateral measurements between segments within the same level electrode of the 1-3-3-1 lead. Dominant Twin Peaks are weak or non-existent in measurements associated with all the other left channels, i.e., those that make left measurements along the length of the 1-3-3-1 lead.

[0095] Since the LFP activity is lower in the right hemisphere, the automatic peak finding algorithm is able to identify only two channels in the right lead which exhibit clear Dominant Twin Peaks, marked by TP in FIG.12. It should be noted that both these channels are also lateral channels, i.e., they measure the LFP signal between segments belonging to the same level of the 1-3-3-1 right lead. In summary, none of the left or right channels that make measurements along the length of the leads show Dominant Twin Peak activity that could be automatically detected by our software. This is emphasized so that to replicate the results of this study, other researchers may need to ensure that lateral channels for DBS recordings are also selected.

[0096] Distribution of LFP Tremor Frequencies Obtained from Different Channels: Now we evaluate the mean ( ^^^^1– ^^^^2)meanand the standard deviation ( ^^^^1– ^^^^2)std devby using all the eight channels that show Dominant Twin Peak activity (marked by TP in FIGS.11 and 12). The results are shown in FIG 13, with a mean ( ^^^^1– ^^^^2)meanof 5.26 Hz, and a standard deviation of deviation ( ^^^^1– ^^^^2)std devof 0.31 Hz. Hence, based on eqs. (5a) and (5b), the hypothesis predicts a tremor frequency for the PD patient to be 5.26 ± 0.31 Hz. It is noted that this width, 0.31 Hz, has no obvious relationship with the width of the peaks in the beta band of the LFP spectrum.

[0097] Measurements of Tremor Frequency from a Video of the Patient: Google®'s MediaPipe framework was used to obtain a time series consisting of 550 time-samples (18.33 seconds) of the x and y coordinates of the limbs from a video of the patient. Figure 16 shows the tremor power spectrum (square of magnitude FFT) obtained from the time series of the PD patient’s right hand’s wrist movement. The spectrum shows a right wrist tremor peak located at ^^^^tremor_measured= 5.26 Hz, and a Half Width at Half Max (HWHM) width Δ ^^^^tremor_measured= 32Hz. Predictions made by the hypothesis, Eqs. (5a) and (5b), are noted in the inset. Note that the measured quantities ^^^^tremor_measured= 5.26 Hz, and Δ ^^^^tremor_measured= 32Hz, show a close match with the predictions of our hypothesis 5.26 ± 0.31 Hz obtained from the LFP (FIG.13).Atty. Dkt. No.103361-596WO1

[0098] Measured Tremor Frequencies from the Wrists, Knees, and Heels. Figure 17 shows the measured (from the video) tremor frequencies, ^^^^tremor_measured, from the x and y coordinates of the right and left wrists, knees, and heels of the PD patient, and compares these measurements with the hypothesis predictions, 5.26 ± 0.31 Hz (FIG.13), obtained from the LFP Dominant Twin Peaks. The vertical error bars show the widths of the measured tremor peaks, Δ ^^^^tremor_measured. The agreement between the two is excellent; all eight measurements lie within the margins of the hypothesis predictions based on the LFP spectrum. These results lend strong credence to our hypothesis predictions, eq, (5a) and (5b), by demonstrating that the tremor frequencies based on the beta-band Dominant Twin Peaks not only match, ^^^^tremor_measured, the location of the measured tremor frequencies, but also the measured widths, Δ ^^^^tremor_measured, of the tremor frequency peaks.

[0099] Determining the Tremor Fluctuation Time from the Video

[0100] Implication of the Finite Width of the Tremor Frequency Peak: Next, the implication of the third part of the hypothesis, Eq. (5c), are discussed. First, Δ ^^^^tremor_measuredis determined from the video data and the tremor fluctuation time is calculated, ^^^^tremor_fluctuation from it. Based on Fourier Transform theory, a non-zero spectral width implies that the signal has a corresponding finite duration σ! (Mallat 2008). This is a result of the frequency-time uncertainty principle:

[0101] where, ^^^^^^^^is the sigma value (or standard deviation) of the frequency peak, and ^^^^^^^^is the sigma value (or standard deviation) of the time peak. In the following, Δ ^^^^tremor_measuredis defined as the Half Width at Half Max (HWHM) of the tremor peak. For a Gaussian, HWHM = Δ ^^^^tremor_measured= 1.2σt. A 5-sigma half width is used for the duration Δ ^^^^tremor_measured, which gives:

[0102] A finite Δ ^^^^tremor_measuredimplies that the tremor intensity is fluctuating (waxing and waning) over this interval, i.e., it gives us the measured tremor fluctuation time (from the video),Atty. Dkt. No.103361-596WO1 ^^^^^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^_fluctuation= ∆ ^^^^^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^_ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^(8)

[0103] Using Δ ^^^^tremor_measured= 0.32 Hz from FIG.16, Eqs. (7) and (8) give ^^^^tremor_fluctuation = 3.0 sec.

[0104] Measured Scalogram from the Patient’s Video. To visualize tremor fluctuations in the measured tremor signal from the video of the patient, the signal’s CWT scalogram was evaluated (Addison 2020). Figure 15 shows the scalogram for the PD patient’s right wrist movement. It can be seen that the patient’s tremor burst trains (enclosed in white rectangles) are located at a frequency of 5.22 Hz (the horizontal red line at 5.22 Hz is the measured tremor frequency from Figure 13). A rough estimate of the tremor frequency is determined by counting the number of maxima (dark red features) in a white rectangle to be approximately 30 features per 3.0 seconds. Dividing this by 3.0 seconds and further dividing by 2 (since the scalogram is a power spectrum) gives ~5 Hz, a close approximation to the measured tremor frequency. We note that the scalogram shows ^^^^tremor_fluctuation = 3.0 sec. fluctuations in the intensity of the tremor (enclosed in white rectangles). Scalograms from the other limbs for x and y coordinates also show the same behavior. We compare this to the LFP signal power scalogram in Figure 4 (top plot), which shows that the LFP burst groups also have durations, ^^^^lfp_groups, of approximately 3.0 seconds, lending support for the third part of the hypothesis, Eq. (5c). Conclusions

[0105] In summary, this study provides strong support for the hypothesis comprising Eqs. (5a), (5b) and (5c). Specifically, for the first time in the literature, features of the beta band spectrum with the defining features associated with the tremor dynamics measured from the patient’s video, such as tremor frequency and tremor fluctuation time, are connected. This connection is between two spectra that lie in different frequency bands; beta-band STN LFPs lie in the 13-31 Hz range while the physical tremors of PD patients lie in the 4-8 Hz (Bain 2002) range. Furthermore, beyond the hypothesis itself, communication theory was used to theoretically explain this connection between the two spectra by asserting that the tremor frequency oscillations are due to the beating of two dominant frequencies in the beta band of the STN LFPs. To summarize, properties of a PD patient’s tremor such as frequency and tremor duration can be obtained from the patient’s subthalamic nucleus beta-band spectrum.

[0106] The revelation that beta burst trains in the STN LFPs are linked to the phenomena known as “beating” sheds light on new possibilities for interpreting and utilizing DBSAtty. Dkt. No.103361-596WO1 recordings of PD patients. Furthermore, the identification of beta-band dominant twin peaks specifically in the lateral channels of directional leads may suggest new directions in electrode design and application. This specificity may pave the way for enhanced precision in signal reading, possibly leading to more effective treatment delivery. Configuration of Certain Implementations

[0107] The construction and arrangement of the systems and methods shown in the various implementations are only for illustration. Although only a few implementations have been described in detail in this disclosure, many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes, and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.). For example, the position of elements may be reversed or otherwise varied, and the nature or number of discrete elements or positions may be altered or varied. Accordingly, all such modifications are intended to be included within the scope of the present disclosure. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative implementations. Other substitutions, modifications, changes, and omissions may be made in the design, operating conditions, and arrangement of the implementations without departing from the scope of the present disclosure.

[0108] The present disclosure contemplates methods, systems, and program products on any machine-readable media for accomplishing various operations. The implementations of the present disclosure may be implemented using existing computer processors, or by a special purpose computer processor for an appropriate system, incorporated for this or another purpose, or by a hardwired system. Implementations within the scope of the present disclosure include program products including machine-readable media for carrying or having machine-executable instructions or data structures stored thereon. Such machine- readable media can be any available media that can be accessed by a general purpose or special purpose computer or other machine with a processor. By way of example, such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store desired program code in the form of machine- executable instructions or data structures, and which can be accessed by a general purpose or special purpose computer or other machine with a processor.Atty. Dkt. No.103361-596WO1

[0109] When information is transferred or provided over a network or another communications connection (either hardwired, wireless, or a combination of hardwired or wireless) to a machine, the machine properly views the connection as a machine-readable medium. Thus, any such connection is properly termed a machine-readable medium. Combinations of the above are also included within the scope of machine-readable media. Machine-executable instructions include, for example, instructions and data which cause a general-purpose computer, special purpose computer, or special purpose processing machines to perform a certain function or group of functions.

[0110] Although the figures show a specific order of method steps, the order of the steps may differ from what is depicted. Also, two or more steps may be performed concurrently or with partial concurrence. Such variation will depend on the software and hardware systems chosen and on designer choice. All such variations are within the scope of the disclosure. Likewise, software implementations could be accomplished with standard programming techniques with rule-based logic and other logic to accomplish the various connection steps, processing steps, comparison steps and decision steps.

[0111] It is to be understood that the methods and systems are not limited to specific synthetic methods, specific components, or to particular compositions. It is also to be understood that the terminology used herein is for the purpose of describing particular implementations only and is not intended to be limiting.

[0112] As used in the specification and the appended claims, the singular forms “a,” “an” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another implementation includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another implementation. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

[0113] “Optional” or “optionally” means that the subsequently described event or circumstance may or may not occur, and that the description includes instances where said event or circumstance occurs and instances where it does not.Atty. Dkt. No.103361-596WO1

[0114] Throughout the description and claims of this specification, the word “comprise” and variations of the word, such as “comprising” and “comprises,” means “including but not limited to,” and is not intended to exclude, for example, other additives, components, integers or steps. “Exemplary” means “an example of” and is not intended to convey an indication of a preferred or ideal implementation. “Such as” is not used in a restrictive sense, but for explanatory purposes.

[0115] Disclosed are components that can be used to perform the disclosed methods and systems. These and other components are disclosed herein, and it is understood that when combinations, subsets, interactions, groups, etc. of these components are disclosed that while specific reference of each various individual and collective combinations and permutation of these may not be explicitly disclosed, each is specifically contemplated and described herein, for all methods and systems. This applies to all aspects of this application including, but not limited to, steps in disclosed methods. Thus, if there are a variety of additional steps that can be performed it is understood that each of these additional steps can be performed with any specific implementation or combination of implementations of the disclosed methods. REFERENCES 1. Feldmann LK., Lofredi R., Neumann W-J, Al-Fatly B, Roediger J, Bahners BH, Nikolov P, Denison T, Saryyeva A, Krauss J., Faust K, Florin E, Schnitzler A, Schneider G-H, and Kühn AA. Toward therapeutic electrophysiology: beta-band suppression as a biomarker in chronic local field potential recordings. npj Parkinsons Dis.2022;8(44) 2. Koeglsperger T, Mehrkens JH, and Bötzel K. Bilateral double beta peaks in a PD patient with STN electrodes. Acta Neurochir.2021;163:205-209 3. Plate A, Hell F, Mehrkens JH, Koeglsperger T, Bovet A, Stanslaski S, and Bötzel K. Peaks in the beta band of the human subthalamic nucleus: a case for low beta and high beta activity. J. Neurosurg.2021;136(3):672-680. 4. Vissani M, Usaias IU, and Mazzoni, A. Deep brain stimulation: a review of the open neural engineering challenges. J. Neural Eng.2020;17,051002 5. Neumann WJ, Degen K, Schneider GH, Brücke C, Huebl J, Brown P, and Kühn AA. Subthalamic synchronized oscillatory activity correlates with motor impairment in patients with Parkinson’s disease. Mov Disord.2016; 31(11):1748–1751.Atty. Dkt. No.103361-596WO1 Neumann WJ, Staub-Bartelt F, Horn A, Schanda J, Schneider G-H, Brown P, and Kühn AA. Long term correlation of subthalamic beta band activity with motor impairment in patients with Parkinson’s disease. Clin Neurophysiol.2017;128(11):2286–2291. Telkes I, Viswanathan A, Jimenez-Shahed J, Abosch A, Ozturk M, Gupte A, Jankovic J, Ince NF. Local field potentials of subthalamic nucleus contain electrophysiological footprints of motor subtypes of Parkinson’s disease. ProcNatl Acad Sci USA. 2018;115(36): E8567–E8576 Beudel, M., Little, S., Pogosyan A., Ashkan K., Foltynie, T., Limousin P., Zrinzo L., Hariz, M., Bogdanovic, M., Cheeran, B., Green, A. L., Aziz, T., Thevathasan, W., and Brown, P. Tremor Reduction by Deep Brain Stimulation Is Associated With Gamma Power Suppression in Parkinson's Disease. Neuromodulation (2015); 18(5): 349-54. Tinkhauser G, Pogosyan A, Little S, Beudel M, Herz DM, Tan H, and Brown P. The modulatory effect of adaptive deep brain stimulation on beta bursts in Parkinson's disease. Brain.2017;140:1053–1067. Tinkhauser G, Pogosyan A, Tan H,, Herz DM, Kühn AA, and Brown P. Beta burst dynamics in Parkinson's disease OFF and ON dopaminergic medication. Brain. 2017;140:2968–2981. Tinkhauser G, Torrecillos F, Duclos Y, Tan H, Pogosyan A, Fischer P, Carron R, Welter M-L, Karachi C, Vandenberghe W, Nuttin B, Witjas T, Régis J, Azulay J-P, Eusebio A, and Brown P. Beta burst coupling across the motor circuit in Parkinson's disease. Neurobiol. Dis.2018;117:217–225. Torrecillos F, Tinkhauser G, Fischer P, Green AL, Aziz TZ, Foltynie T, Limousin P, Zrinzo L, Ashkan K, Brown P, and Tan H. Modulation of Beta bursts in the subthalamic nucleus predicts motor performance. J. Neurosci.2018;38:8905–8917. Medtronic SenSight™ directional leads. https: / / www.medtronic.com / us-en / healthcare- professionals / products / neurological / deep-brain-stimulation-systems / sensight-lead.html Google MediaPipe Pose Landmark Detection Guide. https: / / developers.google.com / mediapipe / solutions / vision / pose_landmarker McClellan JH, Schafer RW, and Yoder MA. DSP First, 2nd Ed. Pearson, 2016, p.334.Atty. Dkt. No.103361-596WO1 Addison PS. The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance, 2nd Ed. CRC Press, 2020, pp.7–. Mallat S. A Wavelet Tour of Signal Processing: The Sparse Way, 3rd Ed. Academic Press, 2008, pp.15– Cichaczewski E, Munhoz RP, Maia JM, Nohama P, Nóvak EM, and Teive HA. Electrophysiologic characteristics of tremor in Parkinson’s disease and essential tremor. Arq. Neuro-Psiquiatr.2014;72(4) Whittaker ET, and Robinson G. Graduation Formulae obtained by fitting a Polynomial. The Calculus of Observations. Blackie & Son.1924. pp.291–6. OCLC 1187948. Guest PG. Ch.7: Estimation of Polynomial Coefficients. Numerical Methods of Curve Fitting. Cambridge University Press.2012

[1961] . pp.147–. ISBN 978-1-107-64695-7

Claims

Atty. Dkt. No.103361-596WO1 WHAT IS CLAIMED IS:

1. A method of determining tremor frequency in a patient, the method comprising: recording a deep brain local field potential (LFP) signal using a directional deep brain stimulation (DBS) lead implanted in the brain of the patient; generating a frequency spectrum representation of the LFP signal; identifying a pair of dominant peaks in a beta-band of the frequency spectrum representation of the LFP signal; and calculating the tremor frequency as a difference between the pair of dominant peaks.

2. The method of claim 1, further comprising applying a digital filter to the frequency spectrum representation of the LFP signal to remove noise prior to identifying the pair of dominant peaks.

3. The method of claim 2, wherein the digital filter is a Savitzky-Golay filter.

4. The method of claim 1, further comprising filtering the LFP signal with at least one low-pass filter and at least one high-pass filter prior to generating the frequency spectrum representation of the LFP signal.

5. The method of claim 4, wherein the at least one low-pass filter comprises two 100 Hz low-pass filters.

6. The method of claim 4, wherein the at least one high-pass filter comprises two 1 Hz high-pass filters.

7. The method of claim 1, further comprising providing an indication of the tremor frequency to a user.

8. The method of claim 7, wherein providing the indication comprises displaying the tremor frequency via a user interface.

9. The method of claim 1, wherein the frequency spectrum representation of the LFP signal is generated using a Fast Fourier Transform (FFT).Atty. Dkt. No.103361-596WO1 10. The method of claim 1, wherein an annular DBS lead of directional DBS lead comprises an elongate body and a plurality of annular electrodes spaced apart along a length of the elongate body.

11. The method of claim 1, further comprising: calculating a tremor amplitude prediction as an average of a magnitude of the pair of dominant peaks; and predicting, from a trained machine learning model, a tremor amplitude.

12. The method of claim 11, wherein the trained machine learning model is a nonlinear regression model.

13. The method of claim 11, further comprising adjusting a stimulation input based on the tremor amplitude and tremor frequency.

14. The method of claim 13, wherein the step of adjusting is performed by a clinician.

15. The method of claim 13, wherein the step of adjusting is performed by a feedback algorithm.

16. A system for tremor assessment, the system comprising: a deep brain stimulation component, wherein the deep brain stimulation component comprises one or more leads and a stimulator; and one or more computing devices, wherein one of the one or more computing devices is configured to calculate tremor frequencies.

17. The system of claim 16, wherein one of the one or more computing devices is configured to predict tremor amplitude.

18. The system of claim 16, wherein the one or more computing devices comprise a component for a user interaction.

19. The system of claim 16, further comprising a feedback component, wherein the feedback component comprises a clinician feedback or an algorithmic feedback.Atty. Dkt. No.103361-596WO1 20. The system of claim 19, wherein the feedback component is configured to adjust a stimulation input.

21. The system of claim 20, wherein the system is a closed loop system.

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