Systems and methods for determining volume of activation for deep brain stimulation

A computer system comprising a processor that comprises:

• a finite element model (FEM) circuit, configured to determine a FEM that models an implanted electrode and a tissue medium in which the electrode is implanted;
• a Fourier FEM solver circuit communicatively coupled to the FEM circuit and configured to calculate a potential distribution in the tissue medium using information from the FEM circuit and a capacitive component of at least one of the electrode and the tissue medium, wherein the calculating includes:
• separating a stimulus waveform into frequency components;
• obtaining a solution of a Poisson equation at at least one frequency component with a stiffness matrix (σ+iω), wherein the stiffness matrix is representative of the capacitive component of the at least one of the electrode and the tissue medium;
• and
• using the solution to reassemble the stimulus waveform;
• and
• a volume of activation (VOA) circuit, communicatively coupled to the Fourier FEM solver circuit, configured to provide a predicted VOA using the potential distribution and a neuron model.

A non-transitory computer-readable storage medium, including instructions that, when performed by a computer, cause the computer to:

• determine a finite element model (FEM) of an implanted electrode and a tissue medium in which the electrode is implanted;
• calculate a potential distribution in the tissue medium using a Fourier FEM solver and a capacitive component of at least one of the electrode and the tissue medium, wherein the calculating includes:
• separating a stimulus waveform into frequency components;
• obtaining a solution of a Poisson equation at at least one frequency component with a stiffness matrix (σ+iω), wherein the stiffness matrix is representative of the capacitive component of the at least one of the electrode and the tissue medium;
• and
• using the solution to reassemble the stimulus waveform;
• and
• predict a volume of activation (VOA) using the potential distribution and a neuron model.

A computer system comprising a processor that is programmed to perform steps comprising:

• determining a finite element model (FEM) of an implanted electrode and a tissue medium in which the electrode is implanted;
• calculating a potential distribution in the tissue medium using a Fourier FEM solver and a capacitive component of at least one of the electrode and the tissue medium, wherein the calculating includes:
• separating a stimulus waveform into frequency components;
• obtaining a solution of a Poisson equation at at least one frequency component with a stiffness matrix (σ+iω), wherein the stiffness matrix is representative of the capacitive component of the at least one of the electrode and the tissue medium;
• and
• using the solution to reassemble the stimulus waveform;
• and
• predicting a volume of activation (VOA) using the potential distribution and a neuron model.

A computer-assisted method comprising:

• determining a finite element model (FEM) of an implanted electrode, a tissue medium in the electrode is implanted, and an electrode-tissue interface;
• calculating a potential distribution in the tissue medium using a Fourier FEM solver and a capacitive component of at least one of the electrode, the tissue medium, and the electrode-tissue interface, wherein the calculating the potential distribution in the tissue medium includes:
• separating a stimulus waveform into frequency components;
• obtaining a solution of a Poisson equation at at least one frequency component with a stiffness matrix (σ+iω), wherein the stiffness matrix is representative of the capacitive component of the at least one of the electrode, the tissue medium, and the electrode-tissue interface;
• and
• using the solution to reassemble the stimulus waveform;
• and
• predicting a volume of activation (VOA) using the potential distribution and a neuron model.

A computer-assisted method comprising:

• determining a finite element model (FEM) of an implanted electrode and a tissue medium in which the electrode is implanted;
• calculating a potential distribution in the tissue medium using a Fourier FEM solver and a capacitive component of at least one of the electrode and the tissue medium, wherein the calculating the potential distribution includes:
• separating a stimulus waveform into frequency components;
• obtaining a solution of a Poisson equation at at least one frequency component with a stiffness matrix (σ+iω), wherein the stiffness matrix is representative of the capacitive component of the at least one of the electrode and the tissue medium;
• and
• using the solution to reassemble the stimulus waveform;
• and
• predicting a volume of activation (VOA) using the potential distribution and a neuron model.

A method comprising:

• determining a finite element model (FEM) of an implanted electrode, a tissue medium in which the electrode is implanted, and an electrode-tissue interface;
• calculating an impedance by dividing a stimulation voltage by an integrated current density along an active electrode contact;
• calculating a potential distribution in the tissue medium in both time and space using a Fourier FEM solver, using a capacitive component of at least one of the electrode, the tissue medium, and the electrode-tissue interface, and using the calculated impedance, wherein the calculating the potential distribution includes:
• separating a stimulus waveform into frequency components;
• obtaining a solution of a Poisson equation at at least one frequency component with a stiffness matrix (σ+iω), wherein the stiffness matrix is representative of a capacitive component of at least one of the electrode and the tissue medium;
• and
• using the solution to reassemble the stimulus waveform;
• and
• predicting a volume of activation (VOA) using multiple stimulation waveforms;
• using the potential distribution, and using a neuron model;
• wherein the predicting the VOA includes interpolating the potential distribution onto a plurality of model axons.