# US 12,007,455 B2 · Tensor field mapping with magnetostatic constraint > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 12,007,455 B2 - Document ID: US12007455B2 - Status: Granted - Kind: B2 - Application number: 17/832,200 - Filed: 2022-06-03 - Published: 2022-09-29 - Granted: 2024-06-11 - Earliest claimed: 2019-02-15 - Assignees: Q Bio, Inc. - Applicants: Q Bio, Inc. - Inventors: Doruk Tayli; Stamatis Lefkimmiatis; Athanasios Polymeridis - Web page: https://patentgrep.com/patent/US12007455B2 ## CPC - G01R 33/30: Sample handling arrangements, e.g. sample cells, spinning mechanisms - G01R 33/5608: {Data processing and visualization specially adapted for MR, e.g. for feature analysis and pattern recognition on the basis of measured MR data, segmentation of measured MR data, edge contour detection on the basis of measured MR data, for enhancing measured MR data in terms of signal-to-noise ratio by means of noise filtering or apodization, for enhancing measured MR data in terms of resolution by means for deblurring, windowing, zero filling, or generation of gray-scaled images, colour-coded images or images displaying vectors instead of pixels (image data processing or generation, in general G06T)} - G01R 33/36: Electrical details, e.g. matching or coupling of the coil to the receiver - G01R 33/443: {Assessment of an electric or a magnetic field, e.g. spatial mapping, determination of a B0 drift or dosimetry} - G01R 33/54: Signal processing systems, e.g. using pulse sequences {; Generation or control of pulse sequences; Operator console} - G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12) ## Abstract A system may measure a response associated with a sample to an excitation. The system may compute, using the measured response and the excitation as inputs to an inverse model or a predetermined predictive model, model parameters on a voxel-by-voxel basis in a forward model with multiple voxels that represent the sample. The predetermined predictive model was trained using training data for different excitation strengths, different measurement conditions, or both. The forward model may simulate response physics occurring within the sample to a given excitation, and the model parameters may include magnetic susceptibilities of the multiple voxels. Moreover, the system may determine 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. When the accuracy exceeds a predefined value, the system may provide the model parameters as an output. ## Claims ### Claim 1 A method for determining model parameters associated with a sample, comprising operations of: applying, to the sample, an excitation using a source, wherein the excitation comprises or corresponds to one or more of: electromagnetic radiation, a radio-frequency wave, a particle beam, a sound wave, an external magnetic field, or an electric field; measuring, using a measurement device, a response associated with the sample to the excitation; computing, using an inverse model or a predetermined predictive model, which has the measured response and information specifying the excitation as inputs, the model parameters on a voxel-by-voxel basis in a forward model with multiple voxels that represent the sample, wherein the predetermined predictive model was trained, prior to the applying and the measuring, using training data for different excitation strengths, different measurement conditions or both, wherein the model parameters comprise magnetic susceptibilities of the multiple voxels, wherein the forward model simulates response physics occurring within the sample to the excitation, 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 to an electronic device, to a display or to memory. ### Claim 2 (depends on 1) The method of claim 1, wherein the excitation has at least a wavelength and an intensity or a flux. ### Claim 3 (depends on 1) The method of claim 1, wherein the forward model simulates the response physics occurring within the sample to a given wavelength and a given intensity or a given flux that are selected from a range of measurement conditions that comprise the excitation. ### Claim 4 (depends on 1) The method of claim 1, wherein the predetermined predictive model comprises one of: a machine-learning model, or a neural network. ### Claim 5 (depends on 1) The method of claim 1, wherein, when the accuracy exceeds the predefined value, the model parameters are computed in a single pass without further iteration. ### Claim 6 (depends on 1) The method of claim 1, wherein, when the computing uses the inverse model, the computing comprises iteratively repeating the applying, measuring, computing and determining operations with at least a second excitation instead of the excitation and that is different from the excitation. ### Claim 7 (depends on 1) The method of claim 1, wherein, when the accuracy is less than the predefined value, the method comprises: adding the excitation and the measured response to a training dataset; and determining, using the training dataset, a revised instance of the predictive model. ### Claim 8 (depends on 1) The method of claim 1, wherein the method comprises training the predictive model using a simulated dataset computed using the forward model, a range of model parameters and a range of excitations. ### Claim 9 (depends on 1) The method of claim 1, wherein the forward model comprise a magneto-static simulator configured to simulate perturbations to the external magnetic field associated with the magnetic susceptibilities of the multiple voxels. ### Claim 10 (depends on 9) The method of claim 9, wherein the magneto-static simulator computes a solution to an integral equation. ### Claim 11 (depends on 10) The method of claim 10, wherein the magneto-static simulator is configured to compute the solution using a method of moments. ### Claim 12 (depends on 10) The method of claim 10, wherein the magnetic susceptibilities of the multiple voxels are initially assumed to have a constant value and the magneto-static simulator is configured to compute the solution using a Fourier transform. ### Claim 13 (depends on 1) The method of claim 1, wherein the magnetic susceptibilities of the multiple voxels comprise absolute susceptibilities that are computed without use of a reference material. ### Claim 14 (depends on 1) The method of claim 1, wherein a subset of the model parameters is associated with spin dynamics and the magnetic susceptibilities of the multiple voxels are used to regularize the spin dynamics in the computing operation. ### Claim 15 (depends on 1) The method of claim 1, wherein the magnetic susceptibilities of the multiple voxels reduce or eliminate artifacts in a remainder of the model parameters that are associated with the magnetic susceptibilities. ### Claim 16 (depends on 1) The method of claim 1, wherein the measured response comprises a time-domain response of the sample and is other than an image. ### Claim 17 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 perform operations comprising: applying, to a sample, an excitation using a source, wherein the excitation comprises or corresponds to one or more of: electromagnetic radiation, a radio-frequency wave, a particle beam, a sound wave, a magnetic field, or an electric field; measuring, using a measurement device, a response associated with the sample to the excitation; computing, using an inverse model or a predetermined predictive model, which has the measured response and information specifying the excitation as inputs, model parameters on a voxel-by-voxel basis in a forward model with multiple voxels that represent the sample, wherein the predetermined predictive model was trained, prior to the applying and the measuring, using training data for different excitation strengths, different measurement conditions or both, wherein the model parameters comprise magnetic susceptibilities of the multiple voxels, wherein the forward model simulates response physics occurring within the sample to the excitation, 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 to an electronic device, to a display or to memory. ### Claim 18 (depends on 17) The non-transitory computer-readable storage medium of claim 17, wherein the predetermined predictive model comprises one of: a machine-learning model, or a neural network. ### Claim 19 A system, comprising: a source configured to provide an excitation, wherein the excitation comprises or corresponds to: electromagnetic radiation, a radio-frequency wave, a particle beam, a sound wave, a magnetic field, or an electric field; a measurement device configured to perform measurements; a computation device, coupled to the source, the measurement device and memory, configured to execute program instructions; and the memory, coupled to the computation device, configured to store the program instructions that, when executed by the computation device, 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 an inverse model or a predetermined predictive model, which has the measured response and information specifying the excitation as inputs, model parameters on a voxel-by-voxel basis in a forward model with multiple voxels that represent the sample, wherein the predetermined predictive model was trained, prior to the applying and the measuring, using training data for different excitation strengths, different measurement conditions or both, wherein the model parameters comprise magnetic susceptibilities of the multiple voxels, wherein the forward model simulates response physics occurring within the sample to the excitation, 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 computation device, 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 to an electronic device, to a display or to the memory. ### Claim 20 (depends on 19) The system of claim 19, wherein the predetermined predictive model comprises one of: a machine-learning model, or a neural network.