Human nerve fibers exhibit a distinct pattern of threshold fluctuation following a single action potential known as the recovery cycle. We developed geometrically and electrically accurate models of mammalian motor nerve fibers to gain insight into the biophysical mechanisms that underlie the changes in axonal excitability and regulate the recovery cycle. The models developed in this study incorporated a double cable structure, with explicit representation of the nodes of Ranvier, paranodal, and internodal sections of the axon as well as a finite impedance myelin sheath. These models were able to reproduce a wide range of experimental data on the excitation properties of mammalian myelinated nerve fibers. The combination of an accurate representation of the ion channels at the node (based on experimental studies of human, cat, and rat) and matching the geometry of the paranode, internode, and myelin to measured morphology (necessitating the double cable representation) were needed to match the model behavior to the experimental data. Following an action potential, the models generated both depolarizing (DAP) and hyperpolarizing (AHP) afterpotentials. The model results support the hypothesis that both active (persistent Na(+) channel activation) and passive (discharging of the internodal axolemma through the paranodal seal) mechanisms contributed to the DAP, while the AHP was generated solely through active (slow K(+) channel activation) mechanisms. The recovery cycle of the fiber was dependent on the DAP and AHP, as well as the time constant of activation and inactivation of the fast Na(+) conductance. We propose that experimentally documented differences in the action potential shape, strength-duration relationship, and the recovery cycle of motor and sensory nerve fibers can be attributed to kinetic differences in their nodal Na(+) conductances.

McIntyre, Cameron C., Warren M. Grill, David L. Sherman, and Nitish V. Thakor. Cellular effects of deep brain stimulation: model-based analysis of activation and inhibition. J Neurophysiol 91: 1457-1469, 2004. First published December 10, 2003 10.1152/jn.00989.2003. Deep brain stimulation (DBS) is an effective therapy for medically refractory movement disorders. However, fundamental questions remain about the effects of DBS on neurons surrounding the electrode. Experimental studies have produced apparently contradictory results showing suppression of activity in the stimulated nucleus, but increased inputs to projection nuclei. We hypothesized that cell body firing does not accurately reflect the efferent output of neurons stimulated with high-frequency extracellular pulses, and that this decoupling of somatic and axonal activity explains the paradoxical experimental results. We studied stimulation using the combination of a finite-element model of the clinical DBS electrode and a multicompartment cable model of a thalamocortical (TC) relay neuron. Both the electric potentials generated by the electrode and a distribution of excitatory and inhibitory trans-synaptic inputs induced by stimulation of presynaptic terminals were applied to the TC relay neuron. The response of the neuron to DBS was primarily dependent on the position and orientation of the axon with respect to the electrode and the stimulation parameters. Stimulation subthreshold for direct activation of TC relay neurons caused suppression of intrinsic firing (tonic or burst) activity during the stimulus train mediated by activation of presynaptic terminals. Suprathreshold stimulation caused suppression of intrinsic firing in the soma, but generated efferent output at the stimulus frequency in the axon. This independence of firing in the cell body and axon resolves the apparently contradictory experimental results on the effects of DBS. In turn, the results of this study support the hypothesis of stimulation-induced modulation of pathological network activity as a therapeutic mechanism of DBS. Because of the similarity in therapeutic outcomes achieved with DBS and lesions, it has been argued that high-frequency electrical stimulation (HFS) inactivates the structures being stimulated. Recordings made in the stimulated nucleus show inhibition and/or decreased activity during and after the stimulus train (Benazzouz et al. 1995Boraud et al. 1996;Dostrovsky et al. 2000). However, recordings made in efferent nuclei of the stimulated nucleus indicate that the output of the stimulated nucleus is increased during DBS (Anderson et al. 2003;Hashimoto et al. 2003;Maurice et al. 2003;Windels et al. 2000Windels et al. , 2003. These results appear to be contradictory, with the former indicating that DBS inhibits the stimulated nucleus and the latter indicating that DBS excites the nucleus.A significant obstacle in interpreting experimental results of DBS and developing a clear mechanism of action is the lack of quantitative understanding of the influence of HFS on ...

Competing interestsJ. K. K. is a consultant for Medtronic and Boston Scientific. P. B. is a consultant for Medtronic. W. M. G. is the Director, Chief Scientific Officer and share owner of Deep Brain Innovations, LLC. He also receives royalty payments for licensed patents on temporal patterns of deep brain stimulation. M. I. H. has received travel expenses and honoraria from Boston Scientific for speaking at meetings. A. H. was supported by the German Research Council (DFG grant 410169619) and reports lecture fees from Medtronic and Boston Scientific unrelated to the present work. P. A. T. works as a consultant for Boston Scientific Neuromodulation. J. V. works as a consultant to Boston Scientific, Medtronic, and Newronika and has received honoraria for lectures from Boston Scientific and Medtronic as well as research grants from Boston Scientific and Medtronic. A. M. L. has served as a consultant for Boston Scientific, Medtronic, Aleva, and Abbott and is a co-founder of Functional Neuromodulation. All other authors declare no competing interests. Peer review informationNature Reviews Neurology thanks V. Visser-Vandewalle and Y. Temel for their contribution to the peer review of this work. Publisher's noteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The objective of this project was to examine the influence of stimulus waveform and frequency on extracellular stimulation of neurons with their cell bodies near the electrode (local cells) and fibers of passage in the CNS. Detailed computer-based models of CNS cells and axons were developed that accurately reproduced the dynamic firing properties of mammalian motoneurons including afterpotential shape, spike-frequency adaptation, and firing frequency as a function of stimulus amplitude. The neuron models were coupled to a three-dimensional finite element model of the spinal cord that solved for the potentials generated in the tissue medium by an extracellular electrode. Extracellular stimulation of the CNS with symmetrical charge balanced biphasic stimuli resulted in activation of fibers of passage, axon terminals, and local cells around the electrode at similar thresholds. While high stimulus frequencies enhanced activation of fibers of passage, a much more robust technique to achieve selective activation of targeted neuronal populations was via alterations in the stimulus waveform. Asymmetrical charge-balanced biphasic stimuli, consisting of a long-duration low-amplitude cathodic prepulse phase followed by a short-duration high-amplitude anodic stimulus phase, enabled selective activation of local cells. Conversely, an anodic prepulse phase followed by a cathodic stimulus phase enabled selective activation of fibers of passage. The threshold for activation of axon terminals in the vicinity of the electrode was lower than the threshold for direct activation of local cells, independent of the stimulus waveform. As a result, stimulation induced trans-synaptic influences (indirect depolarization/hyperpolarization) on local cells altered their neural output, and this indirect effect was dependent on stimulus frequency. If the indirect activation of local cells was inhibitory, there was little effect on the stimulation induced neural output of the local cells. However, if the indirect activation of the local cells was excitatory, attempts to activate selectively fibers of passage over local cells was limited. These outcomes provide a biophysical basis for understanding frequency-dependent outputs during CNS stimulation and provide useful tools for selective stimulation of the CNS.

Background: Transcranial magnetic stimulation (TMS) enables non-invasive modulation of brain activity with both clinical and research applications, but fundamental questions remain about the neural types and elements TMS activates and how stimulation parameters affect the neural response. Objective: To develop a multi-scale computational model to quantify the effect of TMS parameters on the direct response of individual neurons. Methods: We integrated morphologically-realistic neuronal models with TMS-induced electric fields computed in a finite element model of a human head to quantify the cortical response to TMS with several combinations of pulse waveforms and current directions. Results: TMS activated with lowest intensity intracortical axonal terminations in the superficial gyral crown and lip regions. Layer 5 pyramidal cells had the lowest thresholds, but layer 2/3 pyramidal cells and inhibitory basket cells were also activated at most intensities. Direct activation of layers 1 and 6 was unlikely. Neural activation was largely driven by the field magnitude, rather than the field component normal to the cortical surface. Varying the induced current direction caused a waveform-dependent shift in the activation site and provided a potential mechanism for experimentally observed differences in thresholds and latencies of muscle responses. Conclusions: This biophysically-based simulation provides a novel method to elucidate mechanisms and inform parameter selection of TMS and other cortical stimulation modalities. It also serves as a foundation for more detailed network models of the response to TMS, which may include endogenous activity, synaptic connectivity, inputs from intrinsic and extrinsic axonal projections, and corticofugal axons in white matter.

The excitation and conduction properties of computer-based cable models of mammalian motor nerve fibres, incorporating three different myelin representations, are compared. The three myelin representations are a perfectly insulating single cable (model A), a finite impedance single cable (model B) and a finite impedance double cable (model C). Extracellular stimulation of the three models is used to study their strength-duration and current-distance (I-X) relationships, conduction velocity (CV) and action potential shape. All three models have a chronaxie time that is within the experimental range. Models B and C have increased threshold currents compared with model A, but each model has slope to the I-X relationship that matches experimental results. Model B has a CV that matches experimental data, whereas the CV of models A and C are above and below the experimental range, respectively. Model C is able to produce a depolarising afterpotential (DAP), whereas models A and B exhibit hyperpolarising afterpotentials. Models A and B are determined to be the preferred models when low-frequency stimulation (< approximately 25 Hz) is used, owing to their efficiency and accurate excitation and conduction properties. For high frequency stimulation (approximately 25 Hz and greater), model C, with its ability to produce a DAP, is necessary accurately to simulate excitation behaviour.

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is an effective treatment for the motor symptoms of Parkinson’s disease (PD). The effects of DBS depend strongly on stimulation frequency: high frequencies (>90Hz) improve motor symptoms, while low frequencies (<50Hz) are either ineffective or exacerbate symptoms. The neuronal basis for these frequency-dependent effects of DBS is unclear. The effects of different frequencies of STN-DBS on behavior and single-unit neuronal activity in the basal ganglia were studied in the unilateral 6-hydroxydopamine lesioned rat model of PD. Only high frequency DBS reversed motor symptoms and the effectiveness of DBS depended strongly on stimulation frequency in a manner reminiscent of its clinical effects in persons with PD. Quantification of single-unit activity in the globus pallidus externa (GPe) and substantia nigra reticulata (SNr) revealed that high frequency DBS, but not low frequency DBS, reduced pathological low frequency oscillations (~9Hz) and entrained neurons to fire at the stimulation frequency. Similarly, the coherence between simultaneously recorded pairs of neurons within and across GPe and SNr shifted from the pathological low frequency band to the stimulation frequency during high frequency DBS, but not during low frequency DBS. The changes in firing patterns in basal ganglia neurons were not correlated with changes in firing rate. These results indicate that high frequency DBS is more effective than low frequency DBS, not as a result of changes in firing rate, but rather due to its ability to replace pathological low frequency network oscillations with a regularized pattern of neuronal firing.

We have developed a method to predict excitation of axons based on the response of passive models. An expression describing the transmembrane potential induced in passive models to an applied electric field is presented. Two terms were found to drive the polarization of each node. The first was a source term described by the activating function at the node, and the other was an ohmic term resulting from redistribution of current from sources at other nodes. A total equivalent driving function including both terms was then defined. We found that the total equivalent driving function can be used to provide accurate predictions of excitation thresholds for any applied field. The method requires only knowledge of the intracellular strength-duration relationship of the axon, the passive step response of the axon to an intracellular current, and the values of the extracellular potentials. Excitation thresholds for any given applied field can then be calculated using a simple algebraic expression. This method eliminates the errors associated with use of the activating function alone, and greatly reduces the computation required to determine fiber response to applied extracellular fields.