Optimizing selective stimulation of peripheral nerves with arrays of coils or surface electrodes using a linear peripheral nerve stimulation metric

Abstract

Objective. We present a PNS oracle, which solves these computation time and linearity problems and is, therefore, well-suited for fast optimization of voltage distributions in contact electrode arrays and current drive patterns in non-contact magnetic coil arrays. Approach. The PNS oracle metric for a nerve fiber is computed from an electric field map using only linear operations (projection, differentiation, convolution, scaling). Due to its linearity, this PNS metric can be precomputed for a set of coil or electrode segments, allowing rapid PNS prediction and comparison of any possible coil or electrode stimulation configuration constructed from this set. The PNS oracle is closely related to the classical activating function and modified driving functions but is adjusted to better correlate with full neurodynamic modeling of myelinated mammalian nerves. Main results. We validated the PNS oracle in three MRI gradient coils and two body models and found good correlation between the PNS oracle and the full neurodynamic modeling approach (R2 > 0.995). Finally, we demonstrated its potential utility by optimizing the driving currents and voltages of arrays of 108 magnetic coils or 108 contact electrodes to selectively stimulate target nerves in the lower leg. Significance. Peripheral nerve stimulation (PNS) by electromagnetic fields can be accurately simulated using coupled electromagnetic and neurodynamic modeling. Such simulations are slow and non-linear in the electric field, which makes it difficult to iteratively optimize coil and electrode configurations or drive patterns aiming to avoid PNS or to initiate it for therapeutic purposes.

Optimization of MRI Gradient Coils With Explicit Peripheral Nerve Stimulation Constraints

“…The representation of the PNS model in matrix form (the P-matrix) allows the winding optimizer to quickly assess and compare thousands of candidate coil designs and iteratively approach an optimal design. The convexity of the optimization guarantees convergence to an optimal solution and stems from the linearity of the PNS oracle [23,24] with respect to the current applied to individual coil segments (basis elements). Although formulation of the P-matrix for a given coil basis set requires considerable precomputation, it can be applied to multiple design problems for that geometry.…”

“…The P-matrix formulation involves a few important approximations. First, the response of a nerve to the induced E-field is modeled by a linear predictor (the PNS oracle), that has a PNS threshold accuracy of ~7% compared to the reference thresholds obtained using full non-linear neurodynamic models [23,24]. Other factors of uncertainty arise from typical limitations of the electromagnetic body models itself (such as the topology of conductive tissues and dielectric tissue properties) and the limited number of nerve segments included in our nerve atlases (~1900 segments per model).…”

“…The electric potentials for the remaining ~90% of basis elements are obtained using a barycentric interpolation scheme. We then predict the response of each nerve fiber using either a full nonlinear neurodynamic model [32,33,34] or our linear PNS oracle [24].…”

“…While the electromagnetic fields naturally obey superposition, it is important to find a linear expression for the nerve responses so that each nerve's response can be represented as a weighted sum of precomputed responses from each basis function (wire segment). To achieve this, we developed the "PNS oracle", a generalized linear version of the neurodynamic response function that correlates well with PNS thresholds computed from the full neurodynamic modeling [23,24]. Armed with a pre-computation of how each basis function contributes to the PNS threshold of each nerve segment, the full response from the candidate winding pattern is obtained from a simple "P-matrix" multiplication with the stream function basis weights.…”

Electric field calculation and peripheral nerve stimulation prediction for head and body gradient coils

“…Our work demonstrates an important capability for predicting population-mean PNS thresholds with sufficient accuracy to be useful for a number of important applications in head gradient design and development. Recent work by Davids et al and others 25,34,[46][47][48] has used anatomically and compositionally realistic body models together with physiologically realistic neuronal activation models to predict PNS thresholds for individual body models. The use of realistic body and neuronal activation models is clearly important for understanding PNS fundamentals and for prediction of both threshold and location of PNS at the level of the individual human subject.…”