A Multiscale Approach to Axon and Nerve Stimulation Modeling: A Review.

Electrical nerve fiber stimulation is a technique widely used in prosthetics and rehabilitation, and its study from a computational point of view can be a useful instrument to support experimental tests. In the last years, there was an increasing interest in computational modeling of neural cells and numerical simulations on nerve fibers stimulation because of its usefulness in forecasting the effect of electrical current stimuli delivered to tissues through implanted electrodes, in the design of optimal stimulus waveforms based on the specific application (i.e., inducing limb movements, sensory feedback or physiological function restoring), and in the evaluation of the current stimuli properties according to the characteristics of the nerves surrounding tissue. Therefore, a review study on the main modeling and computational frameworks adopted to investigate peripheral nerve stimulation is an important instrument to support and drive future research works. To this aim, this paper deals with mathematical models of neural cells with a detailed description of ion channels and numerical simulations using finite element methods to describe the dynamics of electrical stimulation by implanted electrodes in peripheral nerve fibers. In particular, we evaluate different nerve cell models considering different ion channels present in neurons and provide a guideline on multiscale numerical simulations of electrical nerve fibers stimulation.

Biophysical modeling of ß-cells networks: Realistic architectures and heterogeneity effects.

The ß-cells dynamics is the regulator of insulin secretion in the pancreas, and its investigation is a central aspect in designing effective treatment strategies for diabetes. Despite great efforts, much is still unknown about the complex organization of such endocrine cells and realistic mathematical modeling represents a useful tool to elucidate key aspects of glucose control in humans. In this contribution, we study the human ß-cells collective behaviour, by modeling their electric and metabolic coupling in a cluster, of size and architecture similar to human islets of Langerhans. We focus on the effect of coupling on various dynamics regimes observed in the islets, that are spiking and bursting on multiple timescales. In particular, we test the effect of hubs, that are highly glucose-sensitive ß-cells, on the overall network dynamics, observing different modulation depending on the timescale of the dynamics. By properly taking into account the role of cells heterogeneity, recently emerged, our model effectively describes the effect of hubs on the synchronization of the islet response and the correlation of ß-cells activity.

Nonlinear diffusion and thermo-electric coupling in a two-variable model of cardiac action potential.

This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q10 and Moore factors are used to describe thermo-electric feedback in a 10° range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra, and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis.

Multi-band decomposition analysis: application to cardiac alternans as a function of temperature.

OBJECTIVE: It has long been known that variations in temperature can facilitate the development of cardiac arrhythmias. Here, we aim to quantify the effects of temperature on cardiac alternans properties. APPROACH: in this work, we use optical mapping recordings of canine ventricular epicardial preparations to demonstrate that hypothermia can promote the formation of alternans, which is an important precursor to potentially lethal arrhythmias like fibrillation. We then present a novel quantification of alternans properties for a broad range of cycle lengths under different thermal states. Specifically, we apply the recently developed multi-band-decomposition analysis (MBDA) in the context of cardiac action potential dynamics. MAIN RESULTS: We show that the MBDA offers several advantages compared with traditional analysis of action potential durations. First, MBDA allows a depiction and quantification of the magnitude of alternans at all threshold values simultaneously and thus offers more information about how alternans relates to the action potential morphology while also removing the necessity of choosing a single threshold value. Second, the MBDA technique offers simple ways for assessing action potential amplitude alternans. Finally, MBDA provides a quantification of signal quality without any additional processing. SIGNIFICANCE: We find that the MBDA technique shows promise in leading to a deeper understanding of cardiac alternans properties.

Gap-junction coupling and ATP-sensitive potassium channels in human ß-cell clusters: Effects on emergent dynamics.

The importance of gap-junction coupling between ß cells in pancreatic islets is well established in mouse. Such ultrastructural connections synchronize cellular activity, confine biological heterogeneity, and enhance insulin pulsatility. Dysfunction of coupling has been associated with diabetes and altered ß-cell function. However, the role of gap junctions between human ß cells is still largely unexplored. By using patch-clamp recordings of ß cells from human donors, we previously estimated electrical properties of these channels by mathematical modeling of pairs of human ß cells. In this work we revise our estimate by modeling triplet configurations and larger heterogeneous clusters. We find that a coupling conductance in the range 0.005-0.020 nS/pF can reproduce experiments in almost all the simulated arrangements. We finally explore the consequence of gap-junction coupling of this magnitude between ß cells with mutant variants of the ATP-sensitive potassium channels involved in some metabolic disorders and diabetic conditions, translating studies performed on rodents to the human case. Our results are finally discussed from the perspective of therapeutic strategies. In summary, modeling of more realistic clusters with more than two ß cells slightly lowers our previous estimate of gap-junction conductance and gives rise to patterns that more closely resemble experimental traces.

Experimental evidence and mathematical modeling of thermal effects on human colonic smooth muscle contractility.

It has been shown, in animal models, that gastrointestinal tract (GIT) motility is influenced by temperature; nevertheless, the basic mechanism governing thermal GIT smooth muscle responses has not been fully investigated. Studies based on physiologically tuned mathematical models have predicted that thermal inhomogeneity may induce an electrochemical destabilization of peristaltic activity. In the present study, the effect of thermal cooling on human colonic muscle strip (HCMS) contractility was studied. HCMSs were obtained from disease-free margins of resected segments for cancer. After removal of the mucosa and serosa layers, strips were mounted in separate chambers. After 30 min, spontaneous contractions developed, which were measured using force displacement transducers. Temperature was changed every hour (37, 34, and 31°C). The effect of cooling was analyzed on mean contractile activity, oscillation amplitude, frequency, and contraction to ACh (10(-5) M). At 37°C, HCMSs developed a stable phasic contraction (~0.02 Hz) with a significant ACh-elicited mean contractile response (31% and 22% compared with baseline in the circular and longitudinal axis, respectively). At a lower bath temperature, higher mean contractile amplitude was observed, and it increased in the presence of ACh (78% and 43% higher than the basal tone in the circular and longitudinal axis, respectively, at 31°C). A simplified thermochemomechanical model was tuned on experimental data characterizing the stress state coupling the intracellular Ca(2+) concentration to tissue temperature. In conclusion, acute thermal cooling affects colonic muscular function. Further studies are needed to establish the exact mechanisms involved to better understand clinical consequences of hypothermia on intestinal contractile activity.