Rapid PNS Threshold Prediction for MRI Gradient Coil Design

The patent creates a simplified linear PNS predictor model that copies the essential functionality of the full neurodynamic model but uses linear operations instead of complex nonlinear simulations. This surrogate model reproduces PNS threshold predictions with sufficient accuracy for optimization purposes while reducing computation time from hours/days to milliseconds.

The patent precomputes a P-matrix that contains pre-calculated influence coefficients for each coil element and nerve segment combination. This preliminary computation allows rapid PNS assessment during optimization by simply multiplying the P-matrix with coil currents, eliminating the need for repeated full neurodynamic simulations.

The patent extracts only the essential linear components needed for PNS threshold prediction from the full neurodynamic model. By taking out the critical electric field-to-PNS threshold relationship and representing it through a linear P-matrix, the complex nonlinear neurodynamic simulations are eliminated while retaining sufficient prediction accuracy for coil optimization.

The patent substitutes the complex biological neurodynamic system with a simplified linear mathematical model. The nonlinear ion channel dynamics and action potential generation processes are replaced with a linear P-matrix formulation that uses simple matrix multiplication and convolution operations, making the system tractable for numerical optimization.

The patent uses a simplified linear PNS predictor as a copy of the full neurodynamic model's prediction capability. This surrogate model enables repeated evaluations during numerical optimization with millisecond computation time, allowing hundreds or thousands of iterations to complete in minutes rather than weeks, while maintaining sufficient accuracy for finding optimal coil designs.

The patent performs preliminary computation of the P-matrix before the optimization process. This precomputation stores all the necessary influence coefficients that will be needed during repeated assessments, allowing the optimization algorithm to rapidly evaluate different coil configurations by simple matrix operations without repeating the full simulation setup and computation each time.