System and method for digital modeling of cardiac cell membrane electrophysiology

Abstract

A computational system and method for digital modeling of cardiac cell membrane electrophysiology is disclosed. The system generates a digital model representing the cell membrane as a dielectric lipid bilayer comprising a capacitor element and a resistor element, where the resistor element is emulated by a plurality of ion channels. The system calculates cell membrane potential based on intracellular and extracellular concentrations of key ions, such as Na+, K+, Ca2+, and Cl-, using the Goldman-Hodgkin-Katz equation. Generation of cellular membrane action potentials is simulated by modeling the opening and closing of voltage-gated ion channels in response to triggering events. The model provides dynamic visualizations of the distinct phases of the action potential, including depolarization and repolarization, offering a high-fidelity tool for research and for enhancing the realism of training simulations in electrophysiology procedures.

Description

[0001] SYSTEM AND METHOD FOR DIGITAL MODELING OF CARDIAC CELL MEMBRANE ELECTROPHYSIOLOGY FIELD OF THE INVENTION

[0002] The present invention relates generally to the field of computational cell modeling and more specifically to a system and method for the digital simulation of membrane structure and electrophysiological functions of a cardiac cell.

[0003] BACKGROUND OF THE INVENTION

[0004] Cell membrane modeling involves creating digital representations of cell membranes to better understand their structure and functions. In cardiology, these models are crucial for research into cardiac electrophysiology, understanding the mechanisms of arrhythmias, and predicting the effects of novel pharmaceutical compounds. These models can be used for simulations and studies in fields like biology and biochemistry. Various approaches include coarse-grained molecular dynamics simulations, where simplified representations of molecules are used to study membrane dynamics over time. Additionally, there are continuum models that describe membrane behavior using differential equations. These models aid researchers in exploring membrane properties, such as fluidity, permeability, and interactions with other cellular components.

[0005] The development of cell membrane models involves integrating experimental data, computational methods, and theoretical frameworks. Researchers use a variety of techniques to create these models:

[0006] 1. Molecular Dynamics Simulations: This involves simulating the motion of atoms and molecules over time. Researchers use force fields to calculate interactions between atoms, allowing them to study the dynamics and properties of cell membranes at the molecular level.

[0007] 2. Coarse-Grained Models: These models simplify the representation of molecules, grouping atoms into larger units. Coarse-grained simulations are computationally less expensive and can provide insights into membrane behavior over longer timescales 3. Continuum Models: These models use differential equations to describe the macroscopic properties of membranes, such as elasticity and bending. They provide a more abstract view of membrane behavior and are useful for studying larger-scale phenomena.

[0008] 4. Hybrid Models: Some researchers use a combination of atomistic and coarse-grained models to balance accuracy and computational efficiency. This allows them to simulate specific regions of interest at a finer level of detail.

[0009] In the specific field of cardiac modeling, these foundational techniques have been used to create landmark models, such as the Luo-Rudy model for guinea pig ventricular cells and the ten Tusscher-Panfilov model for human ventricular cells. These state-of-the-art models typically rely on complex systems of ordinary differential equations, a form of continuum modeling, to describe the dynamics of numerous individual ion currents and reconstruct the cardiac action potential with high biophysical fidelity.

[0010] Increasing computational power allows researchers to perform more complex and realistic simulations. High-performance computing enables simulations at higher resolutions and longer timescales, enhancing the accuracy and applicability of membrane models. However, while these detailed models provide a high degree of biophysical accuracy, their complexity presents significant drawbacks. First, their computational intensity often requires specialized high-performance computing resources, limiting their accessibility and precluding real-time interactive simulations on standard computer systems. A user cannot easily modify a parameter, such as the extracellular potassium concentration, and immediately see the resulting change in the action potential waveform without significant processing time. Second, the intricate system of equations can make it difficult for students and trainees in electrophysiology to intuitively grasp the direct relationship between changes in core ion concentrations and the resulting action potential morphology. The fundamental principles can be obscured by the large number of interdependent variables.

[0011] The choice of the most suitable model depends on the research question and the level of detail required. In many cases, researchers use a combination of models or refine existing ones. Advances in computational power and techniques continue to enhance the fidelity of digital cell membrane models, yet a trade-off between biophysical completeness and computational efficiency has created a gap in the available tools, particularly for educational and training applications. Therefore, there remains a specific, unmet need for an interactive and computationally efficient model that accurately simulates the distinct phases of the cardiac action potential, for instance by directly utilizing the Goldman-Hodgkin-Katz (GHK) equation for membrane potential calculation, and provides clear, intuitive visualization of ion channel states. Such a model is needed to serve as an effective educational and training tool for medical students, residents, and professionals in electrophysiology, allowing them to explore fundamental principles in a dynamic and hands-on manner without the need for supercomputing resources.

[0012] SUMMARY OF THE INVENTION

[0013] The present invention provides a solution to the aforementioned problems by disclosing a computationally efficient and highly interactive system and method for the digital modeling of cardiac cell membrane structure and electrophysiological functions. The invention is particularly suited to serve as an effective educational and training tool, enabling users to intuitively understand the relationship between ion concentrations and the cardiac action potential without requiring high-performance computing resources.

[0014] In one aspect, the present invention provides a computational system for digital modeling. The system comprises at least one computer system with a processor and memory storing computer-readable instructions. These instructions configure the system to generate a digital model of a cardiac cell membrane, wherein the membrane is fundamentally represented as a dielectric lipid bilayer. This model comprises a capacitor element, representing the membrane's ability to accumulate charge, and a resistor element, which is dynamically emulated by a plurality of ion channels that regulate the flow of ions.

[0015] Functionally, the system is configured to receive or access stored data representing intracellular and extracellular ion concentrations for key ions, including sodium (Na+), potassium (K+), calcium (Ca2+), and chloride (Cl⁻). Using this data, the system calculates the cell membrane potential based on the Goldman-Hodgkin-Katz (GHK) equation, which accounts for the permeability and concentration gradients of multiple ion species. The core of the simulation involves triggering and modeling the generation of cellular action potentials. This is achieved by simulating the dynamic opening and closing of voltage-gated ion channels in response to triggering events, such as a simulated electric discharge or changes in ion concentrations. The system simulates and outputs the resulting action potentials and resting potentials over time. In certain embodiments, the system further comprises a graphical user interface (GUI) that allows users to input and modify ion concentration values and other parameters, providing an interactive experience. The system can provide visualizations of the changes in membrane potential over time, clearly illustrating the distinct phases of depolarization and repolarization. The model may also simulate the function of the ATPase pump in maintaining ion gradients and generating cellular energy.

[0016] In another aspect, the invention provides a method for digital modeling of membrane structure and functions in cardiac cells. The method comprises the steps of setting a dielectric in a cell membrane model with capacitor and resistor elements; calculating a cell membrane charge using the Goldman-Hodgkin-Katz equation based on ion concentrations; triggering the generation of an action potential by simulating the opening and closing of voltage-gated ion channels; simulating the resulting action potential and ion transport across the membrane; and recording or displaying the simulated results for analysis.

[0017] By simplifying the underlying computational framework while maintaining physiological accuracy in the representation of the action potential, the present invention offers a valuable and accessible tool for education, training, and research in the field of cardiac electrophysiology.

[0018] In one aspect of the invention, a computational system for digital modeling of cardiac cell membrane function, the system comprising:

[0019] a. a processor; and

[0020] b. a memory storing computer-readable instructions that, when executed by the processor, cause the system to:

[0021] i. maintain a data repository of biological data related to cardiac cell membranes and a plurality of ion channels;

[0022] ii. generate a digital model of a cardiac cell membrane, wherein the membrane is represented as a lipid bilayer having a capacitor element and a resistor element, the resistor element being emulated by the plurality of ion channels; iii. receive intracellular and extracellular ion concentration data for a plurality of ion types;

[0023] iv. calculate a cell membrane potential based on the intracellular and extracellular ion concentration data using the Goldman- Hodgkin-Katz equation;

[0024] v. simulate the generation of a cellular membrane action potential by modeling the opening and closing of voltage-gated ion channels from the plurality of ion channels in response to a triggering event; and

[0025] vi. output data representing the simulated action potential over time.

[0026] In another aspect of the invention, the system above is provided, wherein the triggering event is a simulated electric discharge of a specified value over a predetermined peri od of time.

[0027] In another aspect of the invention, the system as defined in any of above is provided, wherein the plurality of ion types includes sodium (Na+), potassium (K+), calcium (Ca2+), and chloride (Cl−) ions.

[0028] In another aspect of the invention, the system as defined in any of above is provided, wherein the instructions further cause the system to generate a graphical user interface (GUI) configured to allow a user to input the ion concentration data and to display a visualization of the simulated action potential.

[0029] In another aspect of the invention, the system as defined in any of above is provided, wherein the visualization illustrates the processes of depolarization and repolarization corresponding to distinct phases of the cardiac action potential.

[0030] In another aspect of the invention, the system as defined in any of above is provided, wherein the instructions further cause the system to simulate an energy generation function of an ATPase pump in maintaining ion gradients.

[0031] In another aspect of the invention, the system as defined in any of above is provided, further comprising a data export module configured to export the output data for use in another computational platform.

[0032] In one aspect of the invention, a method for digital modeling of cardiac cell membrane function, the method comprising the steps of

[0033] a. maintaining, in a data repository of a computer system, biological data related to cardiac cell membranes and a plurality of ion channels, b. generating, by the computer system, a digital model of a cardiac ceil membrane, wherein the membrane is represented as a lipid bilayer having a capacitor element and a resistor element, the resistor element being emulated by the plurality of ion channels;

[0034] c. receiving, by the computer system, intracellular and extracellular ion concentration data for a plurality' of ion types;

[0035] d. calculating, by the computer system, a cell membrane potential based on the intracellular and extracellular ion concentration data using the Goldman-Hodgkin-Katz equation;

[0036] e. simulating, by the computer system, the generation of a cellular membrane action potential by modeling the opening and closing of voltage-gated ion channels from the plurality of ion channels in response to a triggering event; and

[0037] f. outputting, from the computer system, data representing the simulated action potential over time.

[0038] In another aspect of the invention, the method above is provided, wherein the triggering event is a simulated electric discharge of a specified value over a predetermined period of time.

[0039] In another aspect of the invention, the method as defined in any of above is provided, wherein the plurality of ion types includes sodium (Na+), potassium (K+), calcium (Ca2+), and chloride (Cl−) ions.

[0040] In another aspect of the invention, the method as defined in any of above is provided, further comprising generating a graphical user interface (GUI) to display a visualization of the simulated action potential, wherein the visualization illustrates the processes of depolarization and repolarization.

[0041] In another aspect of the invention, the method as defined in any of above is provided, further comprising simulating an energy generation function of an ATPase pump in maintaining ion gradients.

[0042] BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a schematic block diagram illustrating the architecture of the computational system for digital modeling of cardiac cell membrane function, in accordance with an embodiment of the present invention. Figure 2 presents the bio-electrical properties of the cell membrane as an electric circuit, in accordance with an embodiment of the present disclosure.

[0044] Figure 3 presents the bio-electrical properties of the cell membrane in the digital model of the present invention, in accordance with an embodiment of the present disclosure.

[0045] Figure 4 presents resting potential and overshot value in the digital model of the present invention, in accordance with an embodiment of the present disclosure.

[0046] Figure 5 provides a traditional schematic representation of different phases of a ventricular Action Potential (AP) generation (A) and a voltage-time-based depiction of AP in cardiac contractile cells (B), in accordance with an embodiment of the present disclosure.

[0047] Figure 6 provides Action Potential (AP) graph built by the digital model of the present invention, in accordance with an embodiment of the present disclosure.

[0048] Figure 7 presents direct correspondence between the ”0” phase generated AP (dark gray screens) of the digital model of the present invention compared to the traditional schematic representation of voltage-time-based depiction of AP in cardiac contractile cells provided in Fig.4, in accordance with an embodiment of the present disclosure.

[0049] Figure 8 presents direct correspondence between the ”1” phase of the AP generated by the digital model of the present invention compared to the one provided in Fig.4, in accordance with an embodiment of the present disclosure.

[0050] Figure 9 presents direct correspondence between the ”2” phase of the AP generated by the digital model of the present invention compared to the one provided in Fig.4, in accordance with an embodiment of the present disclosure.

[0051] Figure 10 presents direct correspondence between the ”3” phase of the AP generated by the digital model of the present invention compared to the one provided in Fig.4, in accordance with an embodiment of the present disclosure.

[0052] Figure 11 presents direct correspondence between the ”4” phase of the AP generated by the digital model of the present invention compared to the one provided in Fig.4, in accordance with an embodiment of the present disclosure.

[0053] Figure 12 presents the dynamic movement of a number of types of ions, in accordance with an embodiment of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS For the purposes of promoting an understanding of the principles of the invention, reference will now be made to the embodiments illustrated in the figures and specific language will be used to describe the same. While examples and features of disclosed principles are described herein, modifications, adaptations, and other implementations are possible without limitation of the scope of the disclosed embodiments. Any further applications of the principles as described herein are contemplated as would normally occur to one skilled in the art.

[0054] This disclosure employs open-ended permissive language, indicating for example, that some embodiments “may” employ, involve, or include specific features. The use of the term “may”, and other open-ended terminology is intended to indicate that although not every embodiment may employ the specific disclosed feature, at least one embodiment employs the specific disclosed feature.

[0055] In the following description, it is to be understood that the present disclosure may be practiced without one or more of the following details. Reference will now be made in detail to non-limiting examples of this disclosure, examples of which are illustrated in the accompanying figures. The examples are described below by referring to the figures, wherein like reference numerals refer to like elements. When similar reference numerals are shown, corresponding description(s) are not repeated, and the interested reader is referred to the previously discussed figure(s) for a description of the like element(s).

[0056] Various embodiments are described herein with reference to a system(s) and method(s). It is intended that the disclosure of one is a disclosure of all. For example, it is to be understood that disclosure of a system described herein also constitutes a disclosure of the method implemented by the system, via, for example, one or more processors. It is to be understood that this form of disclosure is for ease of discussion only, and one or more aspects of one embodiment herein may be combined with one or more aspects of other embodiments herein, within the intended scope of this disclosure.

[0057] To provide a more thorough understanding of the present invention, the following description is organized into sections. First, the overall system architecture is described. Subsequently, the detailed implementation of the digital model, its calculation methods, and simulation processes are discussed.

[0058] 1. System architecture and operating environment

[0059] Referring now to the drawings, wherein like reference numerals designate identical or corresponding parts throughout the several views, Figure 1 is a schematic block diagram illustrating the architecture of a computational system 100 in accordance with an embodiment of the present invention.

[0060] The system 100 comprises at least one computer system, which may be a personal computer, a server, or a distributed computing environment. The computer system includes a processor 110 and a non-transitory computer-readable memory 120. The memory 120 stores computer-readable instructions that, when executed by the processor 110, configure the system to perform the digital modeling of cardiac cell membrane function.

[0061] The memory 120 stores several functional modules, including a data input module 130, a modeling engine 140, a data repository 150, a graphical user interface (GUI) module 160, and a data export module 170.

[0062] The data input module 130 is configured to receive intracellular and extracellular ion concentration data. This data may be input by a user via the GUI module 160 or retrieved from the data repository 150. The data repository 150 is configured to maintain biological data related to cell membrane structures, ion channel properties, and predefined ion concentrations for various cardiac cell types.

[0063] The modeling engine 140 is the core computational component, configured to execute the instructions for generating the digital model, calculating membrane potentials, and simulating the action potentials as described in detail below.

[0064] The GUI module 160 is configured to generate an interactive interface for display on a user device. The GUI allows users to input parameters, initiate simulations, and view the output. The output includes, for example, visualizations of changes in membrane potential over time. The data export module 170 is configured to format and export simulation data, such as time-series data of membrane potential or ion flux, for use in other computational platforms for further analysis.

[0065] 2. Digital model of the cell membrane

[0066] The modeling engine 140 generates a digital model of a cardiac cell membrane based on established biophysical principles. As illustrated in the electrical circuit equivalent of Figure 2, a biological cell membrane possesses both capacitive and conductive properties. In the digital model of the present invention, shown in Figure 3, the cellular membrane is represented as a dielectric lipid bilayer. This model comprises two primary electrical elements:

[0067] a) A capacitor element 210, representing the lipid bilayer's ability to accumulate and separate charge across its approximately 5 nm thickness. The lipid layer consists of fatty acids, such as palmitic and arachidonic acids. In a preferred embodiment, the membrane's specific capacitance is set to approximately 1 μF / cm2.

[0068] b) A resistor element 220, which is emulated by a plurality of digitally represented ion channels. These channels are configured in the model to allow ions to move across the membrane at different rates and with varying permeability, thus creating electrical resistance and conductance that dictate ion flow.

[0069] 3. Membrane potential calculation

[0070] A key function of the modeling engine 140 is the calculation of the cell membrane potential based on the intracellular and extracellular ion concentration data received via the data input module 130. The calculations are based on established biophysical principles for modeling ion flux across a dielectric membrane.

[0071] For determining the equilibrium potential of a single ion, the model can reference the Nernst equation, which is expressed as follows:

[0072]

[0073] Where:

[0074] ® Em is the membrane equilibrium potential;

[0075] « R is the universal gas constant (e.g., 8.314 J·K−1·mol−1); « T is the absolute temperature in Kelvin;

[0076] » z is the valence (charge) of the ion;

[0077] « F is the Faraday's constant (e.g., 9.65 x 104C mol ’);

[0078] ® in is the natural logarithm;

[0079] « Paois the concentration of the ion (e.g., potassium) outside the cell; and ® Pa; is the concentration of the ion inside the cell.

[0080] As a specific example of this calculation, the modeling engine 140 can determine the potassium equilibrium potential. At normal body temperature (37 °C), substituting for the constants (R, T, and F) and converting to the common logarithm (1g), the equation simplifies. Using exemplary concentrations for potassium, the potential is calculated to be approximately –86 mV:

[0081] 4

[0082] Em= 61.5 × lg—= −86 mV

[0083] 100

[0084] However, the modeling engine 140 is configured to generate a more accurate representation of the overall membrane potential, as the Nernst equation is limited to a single ion type. As stated in the present invention, the membrane charge values do not meet calculations performed with the help of the Nernst equation where such are done for one ion only, and the simulator summarizes charges of all cations and anions in the cell.

[0085] Therefore, in the preferred embodiment, the modeling engine 140 utilizes the more comprehensive Goldman-Hodgkin-Katz (GHK) equation. The GHK equation is significantly more applicable as it accounts for the relative membrane permeabilities and activities (or concentrations) of multiple key ion types simultaneously. The GHK equation as implemented by the system is:

[0086]

[0087] Where:

[0088] « Em is the overall membrane potential;

[0089] ® R, T, and F are the universal gas constant, absolute temperature, and Faraday's constant, respectively; « P_K, P_Na, and P CI are the selective permeabilities of the membrane to potassium, sodium, and chloride ions, respectively;

[0090] ® The terms aK0, aNa0, aCl0represent the activities or concentrations of the respective ions in the extracellular space; and

[0091] ® The terms aK-., aNa.i, aCh represent the activities or concentrations of the respective ions in the intracellular space.

[0092] By executing this GHK calculation, the system 100 generates a resting membrane potential that accurately reflects the combined influence of all relevant ions. As shown in Figure 4, an exemplary simulation run generated by the system yields a resting potential 310 of approximately -90.0 mV and an overshot value 320 of approximately +22.8 mV, which are consistent with physiological values for ventricular cardiomyocytes. This demonstrates the higher fidelity of the multi-ion GHK model over a single-ion Nernst calculation for simulating the cell's actual electrical state.

[0093] 4. Action potential simulation and visualization

[0094] The system 100 is further configured to simulate the generation of cellular membrane action potentials (APs). The simulation is triggered by an event, such as a simulated electric discharge of a specified value or a modeled stimulus from an adjacent cell. The core of the AP simulation involves modeling the dynamic opening and closing of various voltage-gated ion channels.

[0095] The simulation accurately reproduces the five distinct phases of a ventricular AP, as conventionally illustrated in Figure 5. The output data from the simulation can be visualized via the GUI 160 as an AP graph over time, an exampl e of which is shown in Figure 6.

[0096] Referring now' to Figures 7-11, the correspondence between the simulation generated by the present invention and the conventionally understood phases of the cardiac AP is described.

[0097] Phase 0 (Depolarization): As shown in Figure 7, upon a triggering event, the modeling engine 140 simulates the rapid opening of voltage-gated sodium channels (INa). The GUI 160 visually indicates this, for example, by showing the status of INa channels 610 and indicating the percentage of open channels (e.g., 96%). This results in a rapid influx of Na+ions, causing the sharp upstroke of the AP graph 620.

[0098] Phase 1 (Initial repolarization): As shown in Figure 8, following the peak of depolarization, the modeling engine 140 simulates the inactivation of the INa channels 710. This cessation of sodium influx, combined with the transient outward flux of K’ ions, causes the initial dip in the membrane potential, as seen in the corresponding portion of the AP graph 720.

[0099] Phase 2 (Plateau): As shown in Figure 9, this phase is characterized by a balance of ion flows. The modeling engine 140 simulates the opening of L-type voltage-gated calcium channels (ICa) 810, leading to an influx of Ca2+ions. This inward current is balanced by an outward current of K+ions, creating the characteristic plateau phase 820 of the cardiac AP. The dynamic movement of multiple ion types during this and other phases is complex, as illustrated in the schematic of Figure 12.

[0100] Phase 3 (Repolarization): As shown in Figure 10, the modeling engine 140 simulates the closing of the ICa channels and the continued, dominant opening of potassium channels (IK, IK1). This results in a significant outward flux of K+ions, causing the membrane potential to return towards its resting state, as shown in the repolarization curve 910.

[0101] Phase 4 (Resting potential): As shown in Figure 11, the system simulates the restoration of the resting membrane potential. The modeling engine 140 models the activity of ion pumps, such as the Na+ / K+-ATPase pump. This pump utilizes cellular energy in the form of ATP to actively transport Na+ions out of the cell and K+ions into the cell, against their concentration gradients, re-establishing the pre-AP ionic balance and the resting potential 1010.

[0102] 5. Exemplary software implementation

[0103] In a preferred embodiment of the invention, the functionalities of the modeling engine 140 are implemented using an object-oriented programming paradigm. The following is a description of exemplary software classes and functions used to achieve the simulation described above. This description is intended to be illustrative and not limiting.

[0104] 1. PotMyo This class contains the cardiomyocytes membrane channels. It is there that the generation of action potentials is brought about as an integral functional complex. The class provides electrical connections across the heart departments: from the sinus node to the Bachmann’s bundle and left atrium; from the sinus node to the Torel’s bundle; from the sinus node to the right atrium; from the AV node to the His bundle and the Purkinje fibers. The result is contractions of both the atria and ventricles. This class utilizes the classes PotMembranlonesMembran and ThePsevdoPD.

[0105] 2. PotMembranlonesMembran

[0106] This class represents membrane channels of cardiomyocytes.

[0107] 3. ThePsevdoPDPsevdoPD

[0108] This class represents cell membrane action potential.

[0109] 4. PotMembranlones

[0110] The PotMembranlones function loads the initial parameters.

[0111] 5. Potlones

[0112] The Potlones function initializes the initial parameters of the dGrln and dGrOut ions, controlling the movement of one gram of ions into and out of the cell.

[0113] 6. PotlonCa

[0114] The PotlonCa function performs electrochemical reactions for calcium ions; it is descended from Potlones function.

[0115] 7. PotlonK

[0116] The PotlonK function performs electrochemical reactions for potassium; it is descended from Potlones function.

[0117] 8. PotlonKCa

[0118] The PotlonKCa function performs electrochemical reactions for potassium ions in relation to calcium ions; it is descended from Potlones. 9. PotlonNa

[0119] The function PotlonNa performs electrochemical reactions for sodium; it is descended from Potlones.

[0120] 10. PotlonNas

[0121] The function PotlonNas performs electrochemical reactions for potassium ions in the slow current channels; it is descended from Potlones.

[0122] 11. PotMembranlones

[0123] This class encompasses all the ions for the synchronous processing. It provides the membrane structures to separate the cytoplasm from the extracellular environment. The class contains the ATP pumps maintaining the ion concentration gradient on either side of the membrane. The class features the aerobic and anaerobic mechanism of providing energy to the heart cells. It forms the pacemaker cells of the sinus node and pacemaker cells for pacemakers of codependent elements of the cardiac conduction system. The class utilizes the Goldman-Hodgkin-Katz equation for calculation of the resting potential and action potential.

[0124] 12. LoadMembranlones

[0125] The LoadMembranlones function loads the original parameters.

[0126] 13. MembranPotencial

[0127] The MembranPotencial function calculates the membrane potential.

[0128] 14. PD

[0129] The PD function calculates all action potentials. Parameters: uOtdel - the zone of the myocardium part.

[0130] 15. Pitanie

[0131] The Pitanie function describes the transformation of ADP into ATP in the cytosol of a myocyte. Parameters uOtdel - the zone of part of the myocardium.

[0132] 16. PorogMV

[0133] The PorogMV function cuts off the mV value if it goes beyond a certain threshold value. Parameters: dMV - mVolt threshold. 17. PotMembranlones

[0134] The PotMembranlones function loads the initial parameters.

[0135] 18. SubstratToATP

[0136] The SubstratToATP function converts the substrate to ATP.

[0137] 19. PotStep

[0138] This class provides the electrochemical reactions. The class serves as the basis for Potlones. Subclassed by Potlones.

[0139] 20. Close

[0140] The Close function describes attempts to close a specific channel. Parameters dMV -mv count, *puNumerCurCanal - current channel number, *pdBeginCloseMV - the beginning of channel closure in MV, *pdCloseMV - closed channel in MV.

[0141] 21. CloseAll

[0142] The CloseAll function describes attempts to close all channels. Parameters dMV -number of MV, *pdBeginCloseMV - the beginning of channel closure in MV, *pdCloseMV - closed channel in MV.

[0143] 22. Deactiv

[0144] The Deactiv function closes the ion channel, which releases a certain mass of ions in grams when the electrochemical gradient is at its maximum. Parameters *puNumerCurCanal - current channel number, *pcEptPlasma - transfer to the specified plasma, *pcPlasma - plasma for substance transfer, dBeginSuspTimeKaliy - potassium ion transfer start time, dEndSuspTimeKaliy - potassium ion transfer end time, uSpidOpenNaCanal - Sodium channel opening rate, *puTimePD - repolarization phase time, bOpenCaCanal - open Calcium channel, *pbCaFromPeysmeker - calcium channel for pacemaker.

[0145] 23. GetGradientCx

[0146] The GetGradientCx function calculates the change in concentration on both sides of the membrane. Parameters *pcEptPlasma - transfer to the specified plasma, *pcPlasma -plasma for transfer of substances. 24. GetState

[0147] The GetState function calculates the number of closed or open channels. uSet Parameters - The option to open or close a channel.

[0148] 25. IonECSet

[0149] The IonECSet function sets the base plasma concentration on the outer surface of the membrane. Parameters dMols - molarity, *pcEptPlasma - transfer to the specified plasma, *pcPlasma - plasma for the transfer of substances.

[0150] 26. IonECSet2

[0151] The IonECSet2 function sets the base plasma concentration. Parameters dMols -molarity, *pcEptPlasma - transfer to the specified plasma, *pcPlasma - plasma for the transfer of substances.

[0152] 27. IonesOpen

[0153] The IonesOpen function calculates the number of open channels. Parameters dCx -concentration, dCurdCx - current concentration of ions, *puTimePD - channel opening time, *puSpidOpenNaCanal - sodium channel opening rate.

[0154] 28. korelacia

[0155] The korelacia function determines the number of channels required to set the voltage. Parameters SourceOt - initial voltage, SourceDo - final voltage, ValueOt - initial number of channels, ValueDo - finite number of channels, Value - total number of channels, to set the voltage.

[0156] 29. Nasos

[0157] The Nasos function describes a transport system that allows an ion to be moved with direct energy expenditure against concentration and electrochemical gradients; in the repolarization stage, the pump uses ATP energy in an amount determined by the degradation of fatty acids during beta-oxidation. Parameters dGr - grams of ion, *pcEptPlasma - transfer to the specified plasma, *pcPlasma - plasma for the transfer of substances. 30. Open

[0158] The Open function opens a certain number of channels (counts how many of them). Parameters *pdMV - number of MV when opening a channel, *puTimePD - channel opening start time, *puSpidOpenNaCanal - sodium channel opening speed, uTemp -temperature.

[0159] 31. PotStep

[0160] The PotStep function initializes variables that control the kinetics of ions and the closure of all membrane channels.

[0161] 32. Returnion

[0162] The Returnion function describes a grammatical calculation of the mass of ions involved in the repolarization phase, parameters dDelenie - adjustment by coefficient, dMV - mb count, *puNumerCurCanal - current channel number, *pcEptPlasma -transfer to the specified plasma, *pcPlasma - plasma for substance transfer, *pdAutoPorogMV - automatic MV threshold in the channel, *pdBeginCloseMV - the beginning of channel closure in mb, *pdCloseMV - channel closure in MV, *puTimePD - repolarization phase time, *puSpidOpenNaCanal - Sodium channel opening rate.

[0163] 33. SetCurrentState

[0164] The SetCurrentState function opens or closes the current (by this calculation) membrane channels. Parameters *puNumer - channel number, uSet - option to open or close the channel.

[0165] 34. UtilAtpNasosa

[0166] The UtilAtpNasosa function uses ATP energy to power the pump function to move ions. Parameters pdGr - mass of ions, dDelenie - correction by co-factor, *pcEptPlasma - transfer to the specified plasma, *pcPlasma - plasma for transfer of substances.

[0167] The following functions bridge the Cellular and Electrophysiology models. uCountCells

[0168] UINT uCountCells - number of cells for minimum antegrade momentum calculation. PotMyo The PotMyo function sets the clock speed of the sine node.

Claims

CLAIMS1. A computational system for digital modeling of cardiac cell membrane function, the system comprising:a. a processor, andb. a memory storing computer-readable instructions that, when executed by the processor, cause the system to:i. maintain a data repository' of biological data related to cardiac cell membranes and a plurality of ion channels;ii. generate a digital model of a cardiac cell membrane, wherein the membrane is represented as a lipid bilayer having a capacitor element and a resistor element, the resistor element being emulated by the plurality of ion channels;iii. receive intracellular and extracellular ion concentration data for a plurality of ion types;iv. calculate a cell membrane potential based on the intracellular and extracellular ion concentration data using the Goldman- Hodgkin-Katz equation;v. simulate the generation of a cellular membrane action potential by modeling the opening and cl osing of voltage-gated ion channels from the plurality of ion channels in response to a tri ggering event; andvi. output data representing the simulated action potential over time.

2. The sy stem of claim 1, wherein the triggering event is a simulated electric discharge of a specified value over a predetermined period of time.

3. The system of claim 1, wherein the plurality of ion types includes sodium (Na+), potassium (K+), calcium (Ca2’), and chloride (<' I ) ions.

4. The system of claim 1, wherein the instructions further cause the system to generate a graphical user interface (GUI) configured to allow a user to input the ion concentration data and to display a visualization of the simulated action potential.

5. The system of claim 4, wherein the visualization illustrates the processes of depolarization and repolarization corresponding to distinct phases of the cardiac action potential.

6. The system of claim 1, wherein the instructions further cause the system to simulate an energy generation function of an ATPase pump in maintaining ion gradients.

7. The system of claim 1, further comprising a data export module configured to export the output data for use in another computational platform.

8. A method for digital modeling of cardiac cell membrane function, the method comprising the steps of:a. maintaining, in a data repository of a computer system, biological data related to cardiac cell membranes and a plurality of ion channels, b. generating, by the computer system, a digital model of a cardiac cell membrane, wherein the membrane is represented as a lipid bilayer having a capacitor element and a resistor element, the resistor element being emulated by the plurality of ion channels;c. receiving, by the computer system, intracellular and extracellular ion concentration data for a plurality of ion types;d. calculating, by the computer system, a cell membrane potential based on the intracellular and extracellular ion concentration data using the Goldman-Hodgkin-Katz equation,e. simulating, by the computer system, the generation of a cellular membrane action potential by modeling the opening and closing of voltage-gated ion channels from the plurality of ion channels in response to a triggering event; andf. outputting, from the computer system, data representing the simulated action potential over time.

9. The method of claim 8, wherein the triggering event is a simulated electric discharge of a specified value over a predetermined period of time.

10. The method of claim 8, wherein the plurality of ion types includes sodium (Na+), potassium (K+), calcium (Ca2’), and chloride (Cl−) ions.

11. The method of claim 8, further comprising generating a graphical user interface (GUI) to display a visualization of the simulated action potential,wherein the visualization illustrates the processes of depolarization and repolarization.

12. The method of claim 8, further comprising simulating an energy generation function of an ATPase pump in maintaining ion gradients.

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