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 ...

The clinical use of deep brain stimulation (DBS) is among the most important advances in the clinical neurosciences in the past two decades. As a surgical tool, DBS can directly measure pathological brain activity and can deliver adjustable stimulation for therapeutic effect in neurological and psychiatric disorders correlated with dysfunctional circuitry. The development of DBS has opened new opportunities to access and interrogate malfunctioning brain circuits and to test the therapeutic potential of regulating the output of these circuits in a broad range of disorders. Despite the success and rapid adoption of DBS, crucial questions remain, including which brain areas should be targeted and in which patients. This Review considers how DBS has facilitated advances in our understanding of how circuit malfunction can lead to brain disorders and outlines the key unmet challenges and future directions in the DBS field. Determining the next steps in DBS science will help to define the future role of this technology in the development of novel therapeutics for the most challenging disorders affecting the human brain.

Despite the clinical success of deep brain stimulation (DBS) for the treatment of movement disorders, many questions remain about its effects on the nervous system. We have developed a methodology to predict the volume of tissue activated (VTA) by DBS on a patient-specific basis. Our goals are to identify the intersection between the VTA and surrounding anatomical structures and to compare activation of these structures with clinical outcomes. The model system consists of three fundamental components: 1) a 3D anatomical model of the subcortical nuclei and DBS electrode position in the brain, each derived from magnetic resonance imaging (MRI); 2) a finite element model of the DBS electrode and electric field transmitted to the brain, with tissue conductivity properties derived from diffusion tensor MRI; 3) VTA prediction derived from the response of myelinated axons to the applied electric field, which is a function of the stimulation parameters (contact, impedance, voltage, pulse width, frequency). We used this model system to analyze the effects of subthalamic nucleus (STN) DBS in a patient with Parkinson's disease. Quantitative measurements of bradykinesia, rigidity, and corticospinal tract (CST) motor thresholds were evaluated over a range of stimulation parameter settings. Our model predictions showed good agreement with CST thresholds. Additionally, stimulation through electrode contacts that improved bradykinesia and rigidity generated VTAs that overlapped the zona incerta / fields of Forel (ZI/H2). Application of DBS technology to various neurological disorders has preceded scientific characterization of the volume of tissue directly affected by the stimulation. Synergistic integration of clinical analysis, neuroimaging, neuroanatomy, and neurostimulation modeling provides the opportunity to address wide ranging questions on the factors linked with the therapeutic benefits and side effects of DBS.

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DBS has rapidly emerged as an effective treatment for movement disorders; however, little is known about the VTA during therapeutic stimulation. In addition, the influence of tissue and electrode capacitance has been largely ignored in previous models of neural stimulation. The results and methodology of this study provide the foundation for the quantitative analysis of the VTA during clinical neurostimulation.

Background Deep brain stimulation (DBS) of subcallosal cingulate white matter (SCC) is an evolving investigational treatment for major depression. Mechanisms of action are hypothesized to involve modulation of activity within a structurally defined network of brain regions involved in mood regulation. Diffusion tensor imaging (DTI) was used to model white matter connections within this network to identify those critical for successful antidepressant response to SCC DBS. Methods Pre-operative high-resolution MRI data, including DTI, were acquired in 16 patients with treatment-resistant depression who then received SCC DBS. Computerized tomography was used post-operatively to locate DBS contacts. The activation volume around the active contacts used for chronic stimulation was modeled for each patient retrospectively. Probabilistic tractography was used to delineate the white matter tracts that traveled through each activation volume. Patient-specific tract maps were calculated using whole-brain analysis. Clinical evaluations of therapeutic outcome from SCC DBS were defined at 6 months and 2 years. Results Whole brain activation volume tractography (AVT) demonstrated that all DBS responders at six months (n=6) and 2 years (n=12) shared bilateral pathways from their activation volumes to (1) medial frontal cortex via forceps minor and uncinate fasciculus, (2) rostral and dorsal cingulate cortex via the cingulum bundle, and (3) subcortical nuclei. Non-responders did not consistently show these connections. Specific anatomical coordinates of the active contacts did not discriminate responders from non-responders. Conclusions Patient-specific AVT modeling may identify critical tracts that mediate SCC DBS antidepressant response. This suggests a novel method for patient-specific target and stimulation parameter selection.