Fiber Threshold Accommodation as a Mechanism of Burst and High-Frequency Spinal Cord Stimulation.

OBJECTIVES: Burst and high-frequency spinal cord stimulation (SCS), in contrast to low-frequency stimulation (LFS, < 200 Hz), reduce neuropathic pain without the side effect of paresthesia, yet it is unknown whether these methods' mechanisms of action (MoA) overlap. We used empirically based computational models of fiber threshold accommodation to examine the three MoA. MATERIALS AND METHODS: Waveforms used in SCS are composed of cathodic, anodic, and rest phases. Empirical studies of human peripheral sensory nerve fibers show different accommodation effects occurring in each phase. Notably, larger diameter fibers accommodate more than smaller fibers. We augmented our computational axon model to replicate fiber threshold accommodation behavior for diameters from 5 to 15 µm in each phase. We used the model to predict threshold change in variations of burst, high frequency, and LFS. RESULTS: The accommodation model showed that 1) inversion of larger and smaller diameter fiber thresholds produce a therapeutic window in which smaller fibers fire while larger ones do not and 2) the anodic pulses increase accommodation and perpetuate threshold inversion from burst to burst and between cathodic pulses in burst, high frequency, and variations, resulting in an amplitude "window" in which larger fibers are inactivated while smaller fibers fire. No threshold inversion was found for traditional LFS. CONCLUSIONS: The model, based on empirical data, predicts that, at clinical amplitudes, burst and high-frequency SCS do not activate large-diameter fibers that produce paresthesia while driving medium-diameter fibers, likely different from LFS, which produce analgesia via different populations of dorsal horn neural circuits.

Dynamic Computational Model of the Human Spinal Cord Connectome.

Connectomes abound, but few for the human spinal cord. Using anatomical data in the literature, we constructed a draft connectivity map of the human spinal cord connectome, providing a template for the many calibrations of specialized behavior to be overlaid on it and the basis for an initial computational model. A thorough literature review gleaned cell types, connectivity, and connection strength indications. Where human data were not available, we selected species that have been studied. Cadaveric spinal cord measurements, cross-sectional histology images, and cytoarchitectural data regarding cell size and density served as the starting point for estimating numbers of neurons. Simulations were run using neural circuitry simulation software. The model contains the neural circuitry in all ten Rexed laminae with intralaminar, interlaminar, and intersegmental connections, as well as ascending and descending brain connections and estimated neuron counts for various cell types in every lamina of all 31 segments. We noted the presence of highly interconnected complex networks exhibiting several orders of recurrence. The model was used to perform a detailed study of spinal cord stimulation for analgesia. This model is a starting point for workers to develop and test hypotheses across an array of biomedical applications focused on the spinal cord. Each such model requires additional calibrations to constrain its output to verifiable predictions. Future work will include simulating additional segments and expanding the research uses of the model.

Theoretical Effect of DBS on Axonal Fibers of Passage: Firing Rates, Entropy, and Information Content.

BACKGROUND: Deep brain stimulation (DBS) has effects on axons that originate and terminate outside the DBS target area. OBJECTIVE: We hypothesized that DBS generates action potentials (APs) in both directions in "axons of passage," altering their information content and that of all downstream cells and circuits, and sought to quantify the change in fiber information content. METHODS: We incorporated DBS parameters (fiber firing frequency and refractory time, and AP initiation location along the fiber and propagation velocity) in a filtering function determining the AP frequency reaching the postsynaptic cell. Using neural circuitry simulation software, we investigated the ability of the filtering function to predict the firing frequency of APs reaching neurons targeted by axons of passage. We calculated their entropy with and without DBS, and with the electrode applied at various distances from the cell body. RESULTS: The predictability of the filtering function exceeded 98%. Entropy calculations showed that the entropy ratio "without DBS" to "with DBS" was always >1.0, thus DBS reduces fiber entropy. CONCLUSIONS: (1) The results imply that DBS effects are due to entropy reduction within fibers, i.e., a reduction in their information. (2) Where fibers of passage do not terminate in target regions, DBS may have side effects on nontargeted circuitry.

High-Frequency Stimulation of Dorsal Column Axons: Potential Underlying Mechanism of Paresthesia-Free Neuropathic Pain Relief.

OBJECTIVE: Spinal cord stimulation (SCS) treats neuropathic pain through retrograde stimulation of dorsal column axons and their inhibitory effects on wide dynamic range (WDR) neurons. Typical SCS uses frequencies from 50-100 Hz. Newer stimulation paradigms use high-frequency stimulation (HFS) up to 10 kHz and produce pain relief but without paresthesia. Our hypothesis is that HFS preferentially blocks larger diameter axons (12-15 µm) based on dynamics of ion channel gates and the electric potential gradient seen along the axon, resulting in inhibition of WDR cells without paresthesia. METHODS: We input field potential values from a finite element model of SCS into an active axon model with ion channel subcomponents for fiber diameters 1-20 µm and simulated dynamics on a 0.001 msec time scale. RESULTS: Assuming some degree of wave rectification seen at the axon, action potential (AP) blockade occurs as hypothesized, preferentially in larger over smaller diameters with blockade in most medium and large diameters occurring between 4.5 and 10 kHz. Simulations show both ion channel gate and virtual anode dynamics are necessary. CONCLUSION: At clinical HFS frequencies and pulse widths, HFS preferentially blocks larger-diameter fibers and concomitantly recruits medium and smaller fibers. These effects are a result of interaction between ion gate dynamics and the "activating function" (AF) deriving from current distribution over the axon. The larger fibers that cause paresthesia in low-frequency simulation are blocked, while medium and smaller fibers are recruited, leading to paresthesia-free neuropathic pain relief by inhibiting WDR cells.

Modeling effects of scar on patterns of dorsal column stimulation.

OBJECTIVE: The purpose of this study was to examine how scar formation may affect electrical current distribution in the spinal cord when using paddle leads placed in the epidural space during treatment with spinal cord stimulation. MATERIALS AND METHODS: A finite element model of the spinal cord was used to examine changes in stimulation using a guarded cathode configuration with and without scar. Additionally, two potential "compensatory" programming patterns were examined in order to understand how the three-dimensional electrical field may be affected by scar. Direct comparisons with prior studies in the literature and use of known anatomy of dorsal column fiber distributions also enabled a computational estimate of the number of fibers likely reaching threshold with each stimulus pattern. RESULTS: Notable potential and current distribution changes were found related to the modeled scar. Compensatory stimulation patterns (both in spatial and in amplitude dimensions) affect the fiber activation patterns in complex ways that may not be easily predetermined by a programming specialist. CONCLUSIONS: This study is one of the first to examine the effects of scar tissue on dorsal column stimulation and the only one using a detailed computational approach toward that end. It appears that different thickness and location of scar between electrode contacts and the dura may likely lead to a significant number and location of complex changes in the activated fibers. It is likely that a more complete assessment of scarring and its effect on the electrical environment of any given paddle lead would allow more accurate and predictable reprogramming of patients with commercially available systems in place.

Mechanism of dorsal column stimulation to treat neuropathic but not nociceptive pain: analysis with a computational model.

OBJECTIVE: Stimulation of axons within the dorsal columns of the human spinal cord has become a widely used therapy to treat refractory neuropathic pain. The mechanisms have yet to be fully elucidated and may even be contrary to standard "gate control theory." Our hypothesis is that a computational model provides a plausible description of the mechanism by which dorsal column stimulation (DCS) inhibits wide dynamic range (WDR) cell output in a neuropathic model but not in a nociceptive pain model. MATERIALS AND METHODS: We created a computational model of the human spinal cord involving approximately 360,000 individual neurons and dendritic processing of some 60 million synapses--the most elaborate dynamic computational model of the human spinal cord to date. Neuropathic and nociceptive "pain" signals were created by activating topographically isolated regions of excitatory interneurons and high-threshold nociceptive fiber inputs, driving analogous regions of WDR neurons. Dorsal column fiber activity was then added at clinically relevant levels (e.g., Aß firing rate between 0 and 110 Hz by using a 210-µsec pulse width, 50-150 Hz frequency, at 1-3 V amplitude). RESULTS: Analysis of the nociceptive pain, neuropathic pain, and modulated circuits shows that, in contradiction to gate control theory, 1) nociceptive and neuropathic pain signaling must be distinct, and 2) DCS neuromodulation predominantly affects the neuropathic signal only, inhibiting centrally sensitized pathological neuron groups and ultimately the WDR pain transmission cells. CONCLUSION: We offer a different set of necessary premises than gate control theory to explain neuropathic pain inhibition and the relative lack of nociceptive pain inhibition by using retrograde DCS. Hypotheses regarding not only the pain relief mechanisms of DCS were made but also regarding the circuitry of pain itself, both nociceptive and neuropathic. These hypotheses and further use of the model may lead to novel stimulation paradigms.

Investigation of mechanisms of vagus nerve stimulation for seizure using finite element modeling.

OBJECTIVE: While the efficacy of vagus nerve stimulation (VNS) to reduce seizures in pharmaco-resistant patients is clinically proven, its efficacy and side effects mechanisms are not fully understood. Our goals were 1) to use a finite element model (FEM) and axon models to examine different fiber activation and blocking thresholds and 2) examine fiber activation and blocking in three fiber groups likely to be responsible for efficacy and side effects. METHODS: Using FEM, we examined the field potential along axons within a vagus nerve model with fascicles. These data were input to a computational fiber model to estimate numbers of axons activated across all diameters. We estimated numbers of activated and blocked fibers by diameter. RESULTS: 1) At the low end of VNS amplitudes, little efficacy for seizure control is appreciated while large Aß fibers associated with the recurrent laryngeal nerve are recruited. As amplitudes are increased, Aß fibers can produce hoarseness, and next recruited are fast B fibers associated with the aortic fascicle. We hypothesize these B fibers are the source of efficacy in treating seizure. As amplitudes are further increased, coughing may occur, possibly due to recruitment of smaller and deeper pulmonary fibers. 2) Clinical parameters are in a range that could cause inadvertent blocking at the cathode and activation at the anode. Conversely, innovative approaches to field shape and charge-balancing can allow controlled fiber activation at the cathode for maximum activation of the fibers responsible for efficacy, and possibly blocking at the anode to minimize side effects and expand therapeutic range. In design and operation, the cathode and anode can each be approached as a band pass filter. SIGNIFICANCE: The B fiber group is necessary and possibly sufficient to produce VNS efficacy in epilepsy. This group may emanate from aortic baroreceptors that, via synapses in the solitary tract nucleus, stimulate the locus coeruleus, hypothalamus and other influential targets such as the hippocampus. Responder rates may be increased with a lead that fully encircles the nerve. With better identification of the fiber groups involved in VNS, efficacy, side effects, therapeutic range and responder rates can be optimized.