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Small-surface-area electrodes have successfully been used to preferentially activate cutaneous nociceptors, unlike conventional large area-electrodes, which preferentially activate large non-nociceptor fibers. Assessments of the strength-duration relationship, threshold electrotonus, and slowly increasing pulse forms have displayed different perception thresholds between large and small surface electrodes, which may indicate different excitability properties of the activated cutaneous nerves. In this study, the origin of the differences in perception thresholds between the two electrodes was investigated. It was hypothesized that different perception thresholds could be explained by the varying distributions of voltage-gated ion channels and by morphological differences between peripheral nerve endings of small and large fibers. A two-part computational model was developed to study activation of peripheral nerve fibers by different cutaneous electrodes. The first part of the model was a finite-element model, which calculated the extracellular field delivered by the cutaneous electrodes. The second part of the model was a detailed multicompartment model of an Aδ-axon as well as an Aβ-axon. The axon models included a wide range of voltage-gated ion channels: Na(TTXs), Na(TTXr), Na(p), K(dr), K(M), K(A), and HCN channel. The computational model reproduced the experimentally assessed perception thresholds for the three protocols, the strength-duration relationship, the threshold electrotonus, and the slowly increasing pulse forms. The results support the hypothesis that voltage-gated ion channel distributions and morphology differences between small and large fibers were sufficient to explain the difference in perception thresholds between the two electrodes. In conclusion, assessments of perception thresholds using the three protocols may be an indirect measurement of the membrane excitability, and computational models may have the possibility to link voltage-gated ion channel activation to perception threshold measurements.

Objective. Electrical preferential activation of small nociceptive fibers may be achieved with the use of specialized small area electrodes, however, the existing electrodes are limited to low stimulation intensities. As existing electrodes have been developed empirically, the present study aimed to use computational modeling and optimization techniques to investigate if changes in electrode design parameters could improve the preferential activation of small fibers. Approach. Two finite element models; one of a planar concentric and one of an intra-epidermal electrode were combined with two multi-compartmental nerve fiber models of an Aδ-fiber and an Aβ-fiber. These two-step hybrid models were used for the optimization of four electrode parameters; anode area, anode–cathode distance, cathode area, and cathode protrusion. Optimization was performed using a gradient-free bounded Nelder–Mead algorithm, to maximize the current activation threshold ratio between the Aβ-fiber model and the Aδ-fiber model. Main results. All electrode parameters were optimal at their lower bound, except the cathode protrusion, which was optimal a few micrometers above the location of the Aδ-fiber model. A small cathode area is essential for producing a high current density in the epidermal skin layer enabling activation of small fibers, while a small anode area and anode–cathode distance are important for the minimization of current spread to deeper tissues, making it less likely to activate large fibers. Combining each of the optimized electrode parameters improved the preferential activation of small fibers in comparison to existing electrodes, by increasing the activation threshold ratio between the two nerve fiber types. The maximum increase in the activation threshold ratio was 289% and 595% for the intra-epidermal and planar concentric design, respectively. Significance. The present study showed that electrical preferential small fiber activation can be improved by electrode design. Additionally, the results may be used for the production of an electrode that could potentially be used for clinical assessment of small fiber neuropathy.

The excitability of large nerve fibers is reduced when their membrane potential is slowly depolarizing, i.e., the fibers display accommodation. The aim of this study was to assess accommodation in small (mainly Aδ) and large (Aβ) cutaneous sensory nerve fibers using the perception threshold tracking (PTT) technique. Linearly increasing ramp currents (1 ms-200 ms) were used to assess the excitability of the nerve fibers by cutaneous electrical stimulation. To investigate the PPT technique’s ability to preferentially activate different fiber types, topical application of lidocaine/prilocaine (EMLA) or a placebo cream was applied. By means of computational modeling, the underlying mechanisms governing the perception threshold in the two fiber types was studied. The axon models included the voltage-gated ion channels: transient TTX-sensitive sodium current, transient TTX-resistant sodium current (Na TTXr), persistent sodium current, delayed rectifier potassium channel (K Dr), slow potassium channel, and hyperpolarization-activated current. Large fibers displayed accommodation, whereas small fibers did not display accommodation (P < 0.05). For the pin electrode, a significant interaction was observed between cream (EMLA or placebo) and pulse duration (P< 0.05); for the patch electrode, there was no significant interaction between cream and duration, which supports the pin electrode’s preferential activation of small fibers. The results from the computational model suggested that differences in accommodation between the two fiber types may originate from selective expression of voltage-gated ion channels, particularly the transient Na TTXr and/or K Dr. The PTT technique could assess the excitability changes during accommodation in different nerve fibers. Therefore, the PTT technique may be a useful tool for studying excitability in nerve fibers in both healthy and pathological conditions. NEW & NOTEWORTHY When large nerve fibers are stimulated by long, slowly increasing electrical pulses, interactive mechanisms counteract the stimulation, which is called accommodation. The perception threshold tracking technique was able to assess accommodation in both small and large fibers. The novelty of this study is that large fibers displayed accommodation, whereas small fibers did not. Additionally, the difference in accommodation between the fiber could be linked to expression of voltage-gated ion channels by means of computational modeling.

OBJECTIVE: Over the recent years, several small area electrodes have been introduced as tools for preferential stimulation of small cutaneous nerve fibers. However, the performance of the electrodes is highly debated and have not previously been systematically compared. The electrodes have been developed empirically and little is known about the electrical potential they produce in the skin, and how this influences the nerve fiber activation. The objective of the present study was to develop and validate a computational model to compare the preferential stimulation of small fibers for electrodes of different designs.APPROACH: A finite element model of the skin was developed and coupled with an Aβ-fiber and an Aδ-fiber multi-compartmental nerve fiber model, to describe the current spread and consequent nerve fiber activation produced by five different surface electrodes; intra-epidermal, planar concentric, pin, planar array, and patch. The model was validated through experimental assessments of the strength-duration relationship, impedance, and reaction times.MAIN RESULTS: The computational model predicted the intra-epidermal electrode to be the most preferential for small fiber activation. The intra-epidermal electrode was, however, also found to be the most sensitive to positioning relative to nerve fiber location, which may limit the practical use of the electrode.SIGNIFICANCE: The present study highlights the influence of different electrode design features on the current spread and resulting activation of cutaneous nerve fibers. Additionally, the computational model may be used for the optimization of electrode design towards even better preferential stimulation of small fibers.

Following each action potential, C-fiber nociceptors undergo cyclical changes in excitability, including a period of superexcitability, before recovering their basal excitability state. The increase in superexcitability during this recovery cycle depends upon their immediate firing history of the axon, but also determines the instantaneous firing frequency that encodes pain intensity. To explore the mechanistic underpinnings of the recovery cycle phenomenon a biophysical model of a C-fiber has been developed. The model represents the spatial extent of the axon including its passive properties as well as ion channels and the Na/K-ATPase ion pump. Ionic concentrations were represented inside and outside the membrane. The model was able to replicate the typical transitions in excitability from subnormal to supernormal observed empirically following a conducted action potential. In the model, supernormality depended on the degree of conduction slowing which in turn depends upon the frequency of stimulation, in accordance with experimental findings. In particular, we show that activity-dependent conduction slowing is produced by the accumulation of intraaxonal sodium. We further show that the supernormal phase results from a reduced potassium current Kdr as a result of accumulation of periaxonal potassium in concert with a reduced influx of sodium through Nav1.7 relative to Nav1.8 current. This theoretical prediction was supported by data from an in vitro preparation of small rat dorsal root ganglion somata showing a reduction in the magnitude of tetrodotoxin-sensitive relative to tetrodotoxin -resistant whole cell current. Furthermore, our studies provide support for the role of depolarization in supernormality, as previously suggested, but we suggest that the basic mechanism depends on changes in ionic concentrations inside and outside the axon. The understanding of the mechanisms underlying repetitive discharges in recovery cycles may provide insight into mechanisms of spontaneous activity, which recently has been shown to correlate to a perceived level of pain.

Highly synchronized neural firing has been discussed in relation to learning and memory, for instance sharp-wave activity in hippocampus. We were interested to study how a postsynaptic CA1 pyramidal neuron would integrate input of different levels of synchronicity. In previous work using computational modeling we studied how the integration depends on dendritic conductances. We found that the transient A-type potassium channel K(A) was able to selectively suppress input of high synchronicity. In recent years, compartmentalization of dendritic integration has been shown. We were therefore interested to study the influence of localization and pattern of synaptic input over the dendritic tree of the CA1 pyramidal neuron. We find that the selective suppression increases when synaptic inputs are placed on oblique dendrites further out from the soma. The suppression also increases along the radial axis from the apical trunk out to the end of oblique dendrites. We also find that the K(A) channel suppresses the occurrence of dendritic spikes. Moreover, recent studies have shown interaction between synaptic inputs. We therefore studied the influence of apical tuft input on the integration studied above. We find that excitatory input provides a modulatory influence reducing the capacity of K(A) to suppress synchronized activity, thus facilitating the excitatory drive of oblique dendritic input. Conversely, inhibitory tuft input increases the suppression by K(A) providing a larger control of oblique depolarizing factors on the CA1 pyramidal neuron in terms of what constitutes the most effective level of synchronicity. Furthermore, we show that the selective suppression studied above depends on the conductance of the K(A) channel. K(A) , as several other potassium channels, is modulated by several neuromodulators, for instance acetylcholine and dopamine, both of which have been discussed in relation to learning and memory. We suggest that dendritic conductances and their modulatory systems may be part of the regulation of processing of information, in particular for how network synchronicity affects learning and memory.

The work in this thesis concerns mechanisms of excitability of neurons. Specifically, it deals with how neurons respond to input, and how their response is controlled by ion channels and other active components of the neuron. I have studied excitability in two systems of the nervous system, the hippocampus which is responsible for memory and spatial navigation, and the peripheral C–fibre which is responsible for sensing and conducting sensory information to the spinal cord.Within the work, I have studied the role of excitability mechanisms in normal function and in pathological conditions. For hippocampus the normal function includes changes in excitability linked to learning and memory. However, it also is intimately linked to pathological increases in excitability observed in epilepsy. In C–fibres, excitability controls sensitivity to responses to stimuli. When this response becomes enhanced, this can lead to pain.I have used computational modelling as a tool for studying hyperexcitability in neurons in the central nervous system in order to address mechanisms of epileptogenesis. Epilepsy is a brain disorder in which a subject has repeated seizures (convulsions) over time. Seizures are characterized by increased and highly synchronized neural activity. Therefore, mechanisms that regulate synchronized neural activity are crucial for the understanding of epileptogenesis. Such mechanisms must differentiate between synchronized and semi synchronized synaptic input. The candidate I propose for such a mechanism is the fast outward current generated by the A-type potassium channel (KA).Additionally, I have studied the propagation of action potentials in peripheral axons, denoted C–fibres. These C–fibres mediate information about harmful peripheral stimuli from limbs and organs to the central nervous system and are thereby linked to pathological pain. If a C–fibre is activated repeatedly, the excitability is altered and the mechanisms for this alteration are unknown. By computational modelling, I have proposed mechanisms which can explain this alteration in excitability.In summary, in my work I have studied roles of particular ion channels in excitability related to functions in the nervous system. Using computational modelling, I have been able to relate specific properties of ion channels to functions of the nervous system such as sensing and learning, and in particular studied the implications of mechanisms of excitability changes in diseases.

In diseases of the brain, the distribution and properties of ion channels display deviations from healthy control subjects. We studied three cases of ion channel alteration related to epileptogenesis. The first case of ion channel alteration represents an enhanced sodium current, the second case addresses the downregulation of the transient potassium current K(A), and the third case relates to kinetic properties of K(A) in a patient with temporal lobe epilepsy. Using computational modeling and optimization, we aimed at reversing the pathological characteristics and restoring normal neural function by altering ion channel properties. We identified two key aspects of neural dysfunction in epileptogenesis: an enhanced response to synaptic input in general and to highly synchronized synaptic input in particular. In previous studies, we showed that the potassium channel K(A) played a major role in neural responses to highly synchronized input. It was therefore selected as the target upon which modulators would act. In biophysical simulations, five experimentally characterized endogenous modulations on the K(A) channel were included. Relative concentrations of these modulators were controlled by a numerical optimizer that compared model output to predefined neural output, which represented a normal physiological response. Several solutions that restored the neuron function were found. In particular, distinct subtype compositions of the auxiliary proteins Kv channel-interacting proteins 1 and dipeptidyl aminopeptidase-like protein 6 were able to restore changes imposed by the enhanced sodium conductance or suppressed K(A) conductance. Moreover, particular combinations of protein kinese C, calmodulin-dependent protein kinase II, and arachidonic acid were also able to restore these changes as well as the channel pathology found in a patient with temporal lobe epilepsy. The solutions were further analyzed for sensitivity and robustness. We suggest that the optimization procedure can be used not only for neurons, but also for other organs with excitable cells, such as the heart and pancreas where channelopathies are found.