Effects of frequency-dependent membrane capacitance on neural excitability.

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Models of excitable cells consider the membrane specific capacitance as a ubiquitous and constant parameter. However, experimental measurements show that the membrane capacitance declines with increasing frequency, i.e., exhibits dispersion. We quantified the effects of frequency-dependent membrane capacitance, c(f), on the excitability of cells and nerve fibers across the frequency range from dc to hundreds of kilohertz.


We implemented a model of c(f) using linear circuit elements, and incorporated it into several models of neurons with different channel kinetics: the Hodgkin-Huxley model of an unmyelinated axon, the McIntyre-Richardson-Grill (MRG) of a mammalian myelinated axon, and a model of a cortical neuron from prefrontal cortex (PFC). We calculated thresholds for excitation and kHz frequency conduction block, the conduction velocity, recovery cycle, strength-distance relationship and firing rate.

Main results

The impact of c(f) on activation thresholds depended on the stimulation waveform and channel kinetics. We observed no effect using rectangular pulse stimulation, and a reduction for frequencies of 10 kHz and above using sinusoidal signals only for the MRG model. c(f) had minimal impact on the recovery cycle and the strength-distance relationship, whereas the conduction velocity increased by up to 7.9% and 1.7% for myelinated and unmyelinated fibers, respectively. Block thresholds declined moderately when incorporating c(f), the effect was greater at higher frequencies, and the maximum reduction was 11.5%. Finally, c(f) marginally altered the firing pattern of a model of a PFC cell, reducing the median interspike interval by less than 2%.


This is the first comprehensive analysis of the effects of dispersive capacitance on neural excitability, and as the interest on stimulation with kHz signals gains more attention, it defines the regions over which frequency-dependent membrane capacitance, c(f), should be considered.





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Publication Info

Howell, Bryan, Leonel E Medina and Warren M Grill (2015). Effects of frequency-dependent membrane capacitance on neural excitability. Journal of neural engineering, 12(5). pp. 56015–56015. 10.1088/1741-2560/12/5/056015 Retrieved from https://hdl.handle.net/10161/23851.

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Warren M. Grill

Edmund T. Pratt, Jr. School Distinguished Professor of Biomedical Engineering

Our research employs engineering approaches to understand and control neural function. We work on fundamental questions and applied development in electrical stimulation of the nervous system to restore function to individuals with neurological impairment or injury.

Current projects include:
• understanding the mechanisms of and developing advanced approaches to deep brain stimulation to treat movement disorders,
• developing novel approaches to peripheral nerve electrical stimulation for restoration of bladder function, 
• understanding the mechanisms of and developing advanced approaches to spinal cord stimulation to treat chronic pain,
• understanding and controlling the cellular effects of transcranial magnetic stimulation, and
• design of novel electrodes and waveforms for selective stimulation of the nervous system.

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