Maxwell parallel imaging

A computer system, comprising:

• an interface circuit configured to communicate with an electronic device;
• memory configured to store program instructions;
• and
• a processor configured to execute the program instructions, wherein, when executed by the processor, the program instructions cause the computer system to determine coefficients in a representation of coil sensitivities and magnetic-resonance 5 (MR) information associated with a sample by performing operations comprising:
• acquiring, from a measurement device or memory, MR signals associated with the sample;
• accessing a predetermined set of coil magnetic field basis vectors associated with a surface surrounding the sample, wherein the coil sensitivities of coils in the measurement device are represented by weighted superpositions of the predetermined set of coil magnetic field basis vectors using the coefficients, and wherein the predetermined coil magnetic field basis vectors are solutions to Maxwell's equations;
• and
• solving, on a voxel-by-voxel basis for voxels associated with the sample, a nonlinear optimization problem for MR information associated with the sample and the coefficients in the representation of coil sensitivities based at least in part on:
• a forward model that uses the MR information as inputs and simulates response physics of the sample to output computed MR signals corresponding to the MR signals, the coefficients and the predetermined set of coil magnetic field basis vectors, wherein the MR information comprises quantitative values of one or more MR parameters in the voxels;
• wherein a given coil sensitivity for a given voxel is represented by a linear superposition of products of the coefficients and predetermined coil magnetic field basis vectors on the surface in the predetermined set of coil magnetic field basis vectors;
• and
• wherein the MR parameters comprise one or more of:
• a nuclei density, a spin-lattice relaxation time along a direction of an external magnetic field, a spin-spin relaxation time perpendicular to the direction of the external magnetic field, an adjusted spin-spin relaxation time, components in a diffusion tensor, a velocity, a temperature, an off-resonance frequency, an electrical conductivity, a dielectric constant, a magnetic susceptibility, or a permittivity.

A non-transitory computer-readable storage medium for use in conjunction with a computer system, the computer-readable storage medium configured to store program instructions that, when executed by the computer system, cause the computer system to determine coefficients in a representation of coil sensitivities and magnetic-resonance (MR) information associated with a sample by performing operations comprising:

• acquiring, from a measurement device or memory, MR signals associated with the sample;
• accessing a predetermined set of coil magnetic field basis vectors associated with a surface surrounding the sample, wherein the coil sensitivities of coils in the measurement device are represented by weighted superpositions of the predetermined set of coil magnetic field basis vectors using the coefficients, and wherein the predetermined coil magnetic field basis vectors are solutions to Maxwell's equations;
• and
• solving, on a voxel-by-voxel basis for voxels associated with the sample, a nonlinear optimization problem for MR information associated with the sample and the coefficients in the representation of coil sensitivities based at least in part on:
• a forward model that uses the MR information as inputs and simulates response physics of the sample to output computed MR signals corresponding to the MR signals, the coefficients and the predetermined set of coil magnetic field basis vectors, wherein the MR information comprises quantitative values of one or more MR parameters in the voxels;
• wherein a given coil sensitivity for a given voxel is represented by a linear superposition of products of the coefficients and predetermined coil magnetic field basis vectors on the surface in the predetermined set of coil magnetic field basis vectors;
• and
• wherein the MR parameters comprise one or more of:
• a nuclei density, a spin-lattice relaxation time along a direction of an external magnetic field, a spin-spin relaxation time perpendicular to the direction of the external magnetic field, an adjusted spin-spin relaxation time, components in a diffusion tensor, a velocity, a temperature, an off-resonance frequency, an electrical conductivity, a dielectric constant, a magnetic susceptibility, or a permittivity.