PNS simulation framework

The peripheral nerve stimulation (PNS) simulation framework has previously been described in detail (Davids et al 2017). The basic steps are outlined in figure 1. In short, the framework consists of a surface-based body model containing the major nerves of the peripheral nervous system (Step 1). Then EM field simulation determines the induced E-field distribution in the body model (Step 2). We use the low-frequency finite element method (FEM) solver of Sim4Life (Zurich MedTech AG, Switzerland) for the E-field simulation. We simulate the EM fields at a single frequency (1 kHz in this work) and then determine the field at other frequencies by simply scaling the E-field amplitude based on a linear scaling model. This allows us to quickly assess PNS in the relevant frequency range (0.46 kHz to 10.3 kHz). This simplification does not significantly affect the PNS thresholds (<3% effect). In Step 3, we project the E-field onto the nerve fibers and integrate, yielding the electric potential changes along the nerves. Finally, the response of the nerves to the coil’s E-field is computed using a model of mammalian nerve fibers, the McIntyre-Richardson-Grill (MRG) model (McIntyre et al 2002), in Step 4. In this neurodynamic model, the stimulus is the electric potential modulated by the coil waveform, e.g. a trapezoidal or sinusoidal function. PNS threshold curves are computed using the so-called ‘titration process’: The coil waveform amplitude (for a given frequency) is increased until an action potential (AP) is produced somewhere in the body model. We define the PNS onset as the creation of the first AP. As a surrogate for PNS stimulation, we also compute the neural activation function along each nerve. This activation function is the 2nd spatial derivative of the electric potential along the nerve and has been shown to be a useful scalar representation of a given diameter nerve’s threshold for AP generation (Rattay 1986).

PNS prediction workflow. Step 1: Preparation of the body model and nerve atlas. Step 2: Simulation of the electromagnetic (EM) fields in the body model. Step 3: Projection of the electric field (E-field) onto the nerve fibers and calculation of the electric potential changes. Step 4: The electric potential is modulated in time by the coil’s driving waveform and fed into a nerve model (MRG model (McIntyre et al 2002)) to simulate the nerve response, including possible action potentials.