Tensor field mapping with magnetostatic constraint

A non-transitory computer-readable storage medium for use in conjunction with a computer, the computer-readable storage medium configured to store program instructions that, when executed by the computer, cause the computer to perform operations comprising:

• applying, to a sample, an excitation using a source, wherein the excitation comprises an external magnetic field and a radio-frequency wave;
• measuring, using a measurement device, a response associated with the sample to the excitation;
• computing, using the measured response and information specifying the excitation as inputs to one of an inverse model and a predetermined predictive model, model parameters on a voxel-by-voxel basis in a forward model with multiple voxels that represent the sample, wherein the forward model simulates response physics occurring within the sample to the excitation, wherein the model parameters comprise magnetic susceptibilities of the multiple voxels, and wherein the forward model is a function of the excitation, the model parameters of the multiple voxels, and differential or phenomenological equations that approximates the response physics;
• determining, using a computer, an accuracy of the model parameters by comparing at least the measured response and a calculated predicted value of the response using the forward model, the model parameters and the excitation;
• and
• providing, when the accuracy exceeds a predefined value, the model parameters as an output to a user, to another electronic device, to a display or to memory.

A system configured to determine model parameters, comprising:

• a source configured to provide an excitation comprises an external magnetic field and a radio-frequency wave;
• a measurement device configured to perform measurements, wherein the measurement device comprises a magnetic-resonance apparatus;
• a processor, coupled to the source, the measurement device and memory, configured to execute program instructions;
• and
• the memory, coupled to the processor, configured to store the program instructions that, when executed by the processor, cause the system to perform operations comprising:
• applying, to a sample, the excitation using the source;
• measuring, using the measurement device, a response associated with the sample to the excitation;
• computing, using the measured response and information specifying the excitation as inputs to one of an inverse model and a predetermined predictive model, the model parameters on a voxel-by-voxel basis in a forward model with multiple voxels that represent the sample, wherein the forward model simulates response physics occurring within the sample to the excitation, wherein the model parameters comprise magnetic susceptibilities of the multiple voxels, and wherein the forward model is a function of the excitation, the model parameters of the multiple voxels, and differential or phenomenological equations that approximates the response physics;
• determining, using the processor, an accuracy of the model parameters by comparing at least the measured response and a calculated predicted value of the response using the forward model, the model parameters and the excitation;
• and
• providing, when the accuracy exceeds a predefined value, the model parameters as an output to a user, to another electronic device, to a display or to memory.