Excitation properties of computational models of unmyelinated peripheral axons

Abstract

Biophysically-based computational models of nerve fibers are important tools for designing electrical stimulation therapies, investigating drugs that affect ion channels, and studying diseases that affect neurons. Although peripheral nerves are primarily composed of unmyelinated axons (i.e., C-fibers), most modeling efforts focused on myelinated axons. We implemented the single-compartment model of vagal afferents from Schild et al. 1994 and extended the model into a multi-compartment axon, presenting the first cable model of a C-fiber vagal afferent. We also implemented the updated parameters from Schild and Kunze 1997. We compared the responses of these novel models to three published models of unmyelinated axons (Rattay and Aberham 1993; Sundt et al. 2015; Tigerholm et al. 2014) and to experimental data from single fiber recordings. Comparing Schild et al. 1994 and 1997 revealed that differences in rest potential and action potential shape were driven by changes in maximum conductances rather than changes in sodium channel dynamics. Comparing the five model axons, the conduction speeds and strength-duration responses were largely within expected ranges, but none of the models captured the experimental threshold recovery cycle-including a complete absence of late subnormality in the models-and their action potential shapes varied dramatically. The Tigerholm et al. 2014 model best reproduced the experimental data, but these modeling efforts make clear that additional data are needed to parameterize and validate future models of autonomic C-fibers.

kHz-frequency electrical stimulation selectively activates small, unmyelinated vagus afferents

“…Neuro-electric computational models of nerve fibers can reveal how single channel biophysics and anatomical properties of axons can account for the effects of electrical stimuli on fiber activity and excitability [ 55 ]. To gain mechanistic insight into fiber selectivity at the level of the cell membrane, we simulated voltage responses to kHz trains in larger, myelinated fibers (2.6 μm axonal diameter, 5 μm myelin diameter) and in smaller, unmyelinated fibers (1.3 μm axonal diameter).…”

“…Other ion channels may also be involved, including delayed rectifier potassium and T-type low-voltage-activated calcium channels, all of which play significant roles in the responses of retinal ganglion neurons to kHz stimuli [ 44 ], with the caveat that retinal neurons have different biophysical properties than all other neurons. Because of the limited data on the intrinsic ion channel diversity of functionally distinct vagal fibers [ 55 , 92 ], our study modeled nerve fibers equipped with a minimal set of ion channels, the universally present sodium channels, to gain insight into how morphological differences between fibers could explain part of the experimental effect. In addition, our model only simulated the nerve fibers with a homogeneous surrounding environment as saline solution.…”

Computational models of compound nerve action potentials: Efficient filter-based methods to quantify effects of tissue conductivities, conduction distance, and nerve fiber parameters

“…The two fiber types are based on two distinct fiber models and it is not surprising that they differ in their ability to match the in vivo data. Available models of unmyelinated fibers, including the model that we used [ 46 ], produce action potentials with CV and strength-duration responses consistent with experimental measurements, but other characteristics such as recovery cycle and action potential shape do not match well with experimental measurements [ 89 ]. There is a need for models of unmyelinated fibers that reproduce experimental measurements, including in vivo CNAP recordings.…”

Intermittent KHz-frequency electrical stimulation selectively engages small unmyelinated vagal afferents

“…In addition, our model only incorporated basic ionic channel and membrane properties. Newly-reported ionic currents in vagus nerves 81 along with frequency-dependent membrane capacitance 69 may also influence the KES-induced selectivity. Additional in silico studies will include nerve-specific ion channel properties to elucidate the mechanisms underlying recorded variances, as well incorporating physiologically relevant experimental designs for further model validation.…”