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

A memristive circuit for self-organized network topology formation based on guided axon growth

Circuit implementations of neuronal networks so far have been focusing on synaptic weight changes as network growth principles. Besides these weight changes, however, it is also useful to incorporate additional network growth principles such as guided axon growth and pruning. These allow for dynamical signal delays and a higher degree of self-organization, and can thus lead to novel circuit design principles. In this work we develop an ideal, bio-inspired electrical circuit mimicking growth and pruning controlled by guidance cues. The circuit is based on memristively coupled neuronal oscillators. As coupling element, we use memsensors consisting of a general sensor, two gradient sensors, and two memristors. The oscillators and memsensors are arranged in a grid structure, where oscillators and memsensors realize nodes and edges, respectively. This allows for arbitrary 2D growth scenarios with axon growth controlled by guidance cues. Simulation results show that the circuit successfully mimics a biological example in which two neurons initially grow towards two target neurons, where undesired connections are pruned later on.

Bioelectronic Medicine: a multidisciplinary roadmap from biophysics to precision therapies

Bioelectronic Medicine stands as an emerging field that rapidly evolves and offers distinctive clinical benefits, alongside unique challenges. It consists of the modulation of the nervous system by precise delivery of electrical current for the treatment of clinical conditions, such as post-stroke movement recovery or drug-resistant disorders. The unquestionable clinical impact of Bioelectronic Medicine is underscored by the successful translation to humans in the last decades, and the long list of preclinical studies. Given the emergency of accelerating the progress in new neuromodulation treatments (i.e., drug-resistant hypertension, autoimmune and degenerative diseases), collaboration between multiple fields is imperative. This work intends to foster multidisciplinary work and bring together different fields to provide the fundamental basis underlying Bioelectronic Medicine. In this review we will go from the biophysics of the cell membrane, which we consider the inner core of neuromodulation, to patient care. We will discuss the recently discovered mechanism of neurotransmission switching and how it will impact neuromodulation design, and we will provide an update on neuronal and glial basis in health and disease. The advances in biomedical technology have facilitated the collection of large amounts of data, thereby introducing new challenges in data analysis. We will discuss the current approaches and challenges in high throughput data analysis, encompassing big data, networks, artificial intelligence, and internet of things. Emphasis will be placed on understanding the electrochemical properties of neural interfaces, along with the integration of biocompatible and reliable materials and compliance with biomedical regulations for translational applications. Preclinical validation is foundational to the translational process, and we will discuss the critical aspects of such animal studies. Finally, we will focus on the patient point-of-care and challenges in neuromodulation as the ultimate goal of bioelectronic medicine. This review is a call to scientists from different fields to work together with a common endeavor: accelerate the decoding and modulation of the nervous system in a new era of therapeutic possibilities.

A physiological model of phrenic nerve excitation by electrical stimulation

Mechanical ventilation is essential in intensive care treatment but leads to diaphragmatic atrophy, which in turn contributes to prolonged weaning and increased mortality. One approach to prevent diaphragmatic atrophy while achieving pulmonary ventilation is electrical stimulation of the phrenic nerve. To automize phrenic nerve stimulation resulting in lung protective tidal volumes with lowest possible currents, mathematical models are required. Nerve stimulation models are often complex, so many parameters have to be identified prior to implementation. This paper presents a novel, simplified approach to model phrenic nerve excitation to obtain an individualized patient model using a few data points. The latter is based on the idea that nerve fibers are excited when the electric field exceeds a threshold. The effect of the geometry parameter on the model output was analyzed, and the model was validated with measurement data from a pig trial (RMSE in between 0.44 × 10-2and 1.64 × 10-2for parameterized models). The modeled phrenic nerve excitation behaved similarly to the measured tidal volumes, and thus could be used to develop automated phrenic nerve stimulation systems for lung protective ventilation.

Modeling the excitation of nerve axons under transcutaneous stimulation

Computational models enable a safe and convenient way to study the excitation of nerve fibers under external stimulation. Contemporary models calculate the electric field distribution from transcutaneous stimulation and the resulting neuronal response separately. This study uses finite element methods to develop a multi-scale model that couples electric fields within macroscopic tissue layers and microscopic nerve fibers in a single-stage computational framework. The model included a triaxial myelinated nerve fiber bundle embedded within a volume conductor of tissue layers to represent the median nerve innervating the forearm muscles. The model captured the excitability of nerve fibers under transcutaneous stimulation and their nerve-tissue interactions to a transient external stimulus. The determinants of the strength-duration curve, rheobase, and chronaxie for the proposed model had close correlations with in-vivo experimentation on human participants. Additionally, the excitability indices for the triaxial myelinated nerve fiber implemented using the finite element method agreed well with experimental data from the literature. The validity of the proposed model encourages its use for applications involving transcutaneous stimulation. Capable of capturing field distribution across realistic morphologies, the model can serve as a testbed to improve stimulation protocols and electrode designs with subject-level specificity.

Integrating Finite Element Method for Multiscale Modeling and Simulation of Retinal Ganglion Cell Stimulation Strategies

The finite element method (FEM) has become an increasingly popular tool for the computational modeling of multiscale biological systems, including the electrode-tissue interface and the behavior of individual neural cells. However, a significant challenge in these studies is integrating multiple levels of complexity, each with its biophysical properties. This paper presents a single platform solution for modeling these multiscale systems using the finite element method. The proposed method combines different finite element formulations tailored to the specific biophysical properties of each scale into a single unified simulation platform. The results of this method are compared to experimental data to demonstrate the accuracy and efficacy of the proposed approach. With the goal of eliciting the most significant possible response from the retinal ganglion cell's (RGC) multiple components, we devised an electrical stimulation strategy and electrode placement setup that took into account both the RGC's horizontal and vertical location. We found that the activity in a single RGC model could be elicited by a cathodic pulse of amplitude 34 µA. We observed that the optimum electrode placement for a neural response is around the initial axon segment, 30 μm from the soma, and 10 μm above the RGC. Our results show that the proposed method can accurately capture the complex behavior of these multiscale systems and provide a valuable tool for further research in retinal prostheses.Clinical Relevance- To develop efficient electrical stimulation schemes for retinal prosthesis applications, this research can shed light on the behavior of the electrode-tissue interface and individual neural cells. Electrical stimulation of RGCs has shown promise in the application of retinal prostheses. Still, a thorough understanding of the electrode-induced electric field is essential for the design of effective and safe stimulation protocols. Electrical stimulation's side effects may require knowledge of multiple physics disciplines (such as thermal or structural deformation owing to implant placement inside the eye). Finding a solution to diseases that cause vision impairment could be aided by a finite element method (FEM) framework that simulates the neuronal response to extracellular electrical stimulation for realistic 3D cell and electrode geometries.

Multiscale approach for tFUS neurocomputational modelling

Among the non-invasive methods employed for brain stimulation, trans cranial Focused Ultrasound Stimulation (tFUS) is the technique with the best penetration into the tissues and spatial resolution. The development of computational models of US propagation in brain tissue can be useful for estimating the behaviour of neural cells subjected to mechanical stimulus due to US. This paper aims at studying the neural cell response of a cortical Regular Spiking point neuron model, for different values of stimulus Duty Cycle (DC). The main goal is to use a multiscale approach to couple the results obtained from a macroscale simulation on wave propagation in tissue, with neuron model described by Hodgkin-Huxley equations to study latency and firing rate of the RS model. The obtained results showed that latency and firing rate have slight variations along the propagation direction of the US beam, in the focal region under the skull model, for different stimulus DC.

Identification of the Tidal Volume Response to Pulse Amplitudes of Phrenic Nerve Stimulation Using Gaussian Process Regression

While mechanical ventilation (MV) can lead to ventilator-induced diaphragmatic atrophy due to diaphragm inactivity, electrical phrenic nerve stimulation (PNS) can keep the diaphragm active and therefore prevent diaphragmatic weakness. To quantify the effectivity of PNS, an identification experiment during PNS is presented, and its data is used in Gaussian process regression (GPR) of the tidal volume based on the constant voltage amplitude of the stimulation pulses. The measurements were split into training data of variable size and test data for cross validation. For variable training sizes and different PNS settings, the GPR had a root mean square deviation (RMSD) between 0.39 and 0.91 mL/kg. An identification experiment as short as one and a half minutes was able to characteristically capture the relationship between tidal volume and voltage amplitude. The proposed method needs to be validated in further experiments.