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

BACKGROUND

Peripheral nerve recordings can enhance the efficacy of neurostimulation therapies by providing a feedback signal to adjust stimulation settings for greater efficacy or reduced side effects. Computational models can accelerate the development of interfaces with high signal-to-noise ratio and selective recording. However, validation and tuning of model outputs against in vivo recordings remains computationally prohibitive due to the large number of fibers in a nerve.

METHODS

We designed and implemented highly efficient modeling methods for simulating electrically evoked compound nerve action potential (CNAP) signals. The method simulated a subset of fiber diameters present in the nerve using NEURON, interpolated action potential templates across fiber diameters, and filtered the templates with a weighting function derived from fiber-specific conduction velocity and electromagnetic reciprocity outputs of a volume conductor model. We applied the methods to simulate CNAPs from rat cervical vagus nerve.

RESULTS

Brute force simulation of a rat vagal CNAP with all 1,759 myelinated and 13,283 unmyelinated fibers in NEURON required 286 and 15,860 CPU hours, respectively, while filtering interpolated templates required 30 and 38 seconds on a desktop computer while maintaining accuracy. Modeled CNAP amplitude could vary by over two orders of magnitude depending on tissue conductivities and cuff opening within experimentally relevant ranges. Conduction distance and fiber diameter distribution also strongly influenced the modeled CNAP amplitude, shape, and latency. Modeled and in vivo signals had comparable shape, amplitude, and latency for myelinated fibers but not for unmyelinated fibers.

CONCLUSIONS

Highly efficient methods of modeling neural recordings quantified the large impact that tissue properties, conduction distance, and nerve fiber parameters have on CNAPs. These methods expand the computational accessibility of neural recording models, enable efficient model tuning for validation, and facilitate the design of novel recording interfaces for neurostimulation feedback and understanding physiological systems.

Assessment of the Factors Influencing the Recording Performance of Circumneural Electrodes

The quality of recorded peripheral nerve signals is decisive for their application in therapies. The electroneurogram can be recorded via implantable circumeural electrodes that are wrapped around the peripheral nerve. The shape and amplitude of the signal recorded by the electrode are influenced by the design and contact configuration of the electrode. In this paper, the impact of the number of contacts, contact size and electrical insulation to the outside is investigated to predict the single fiber action potential based on the measured impedance data.

Determination of electrode to nerve fiber distance and nerve conduction velocity through spectral analysis of the extracellular action potentials recorded from earthworm giant fibers

Microneurography and the use of selective microelectrodes that can resolve single-unit nerve activity have become a tool to understand the coding within the nervous system and a clinical diagnostic tool to assess peripheral neural pathologies. Central to these techniques is the use of the differences in the shape of the extracellular action potential (AP) waveform to identify and discriminate units from one another. Theoretical modeling of the origins of these shape differences has shown that the position of the nerve fiber relative to the electrode and the conduction velocity of the unit contribute to these differences giving rise to the hypothesis that more information about the fiber and its relationship to the electrode could be extracted given further analysis of the AP waveform. This paper addresses this question by exploring the electrical coupling between the electrode and nerve fiber. Idealized models and the literature indicate that two parameters, the electrode-fiber distance and the unit conduction velocity, contribute to the amplitude of the extracellular AP detected by the electrode, which confounds the quantification of coupling using the spike amplitude alone. To resolve this, we develop a method that enables differential quantification of these two parameters using spectral analysis of the single-unit AP waveform and demonstrate that the two parameters could be effectively decoupled in an in vitro earthworm model. The method could open the way forward toward micro-scale in situ monitoring of the interaction of nerve fiber and neural interface.

Influence of unit distance and conduction velocity on the spectra of extracellular action potentials recorded with intrafascicular electrodes

The use of highly selective penetrating electrodes yields multi-unit extracellular action potential (AP) recordings of the nerve fibers in the vicinity of the electrode. Accessing the information carried within the neural data stream further requires discrimination and separation of the multi-unit recording into their constituent multiple single unit spike trains. Shape differences in the single fiber action potentials (SFAPs) are typically used as the criteria for unit separation. The present paper explores the origins of the shape differences through analysis of the SFAP in the frequency domain. We present the derivation and computational model predictions of a method to quantitatively analyse changes in the spectral components of SFAPs with an axially located intrafascicular electrode with non-radially symmetrical sensitivity function. A spatial tissue filter relationship was derived using reciprocity equations in the spatial frequency domain and transformed to time frequency. A three dimensional bioelectrical volume conductor finite element model of a recording electrode residing in a nerve fascicle was developed to explore the potential distribution in the nerve fascicle and further derive the electrode-fiber coupling function in the time-frequency domain. It was found that the spectral distribution of the SFAP was multimodal in nature, similar to empirical reported earlier, and could be predicted by taking the single fiber action currents (SFACs) filtered by the electrode-fiber coupling function. This function manifested itself as a low-pass filter of the SFAC, dependent upon the fiber's location relative to the electrode and conduction velocity. Analysis of the spectral distribution revealed that changes in the landmarks of the distribution could be related to the fiber location and conduction velocity. Moreover, a consistent relationship was found when exploring the distribution of fibers located off the one axis of symmetry.