Mathematical Model Investigating the Effects of Neurostimulation Therapies on Neural Functioning: Comparing the Effects of Neuromodulation Techniques on Ion Channel Gating and Ionic Flux Using Finite Element Analysis

Neurostimulation therapies demonstrate success as a medical intervention for individuals with neurodegenerative diseases, such as Parkinson’s and Alzheimer’s disease. Despite promising results from these treatments, the influence of an electric current on ion concentrations and subsequent transmembrane voltage is unclear. This project focuses on developing a unique cellular-level mathematical model of neurostimulation to better understand its e↵ects on neuronal electrodynamics. The mathematical model presented here integrates the Poisson-Nernst-Planck system of PDEs and Hodgkin-Huxley based ODEs to model the e↵ects of this neurotherapy on transmembrane voltage, ion channel gating, and ionic mobility. This system is decoupled using the Gauss-Seidel method and then the equations are solved using the finite element method on a biologically-inspired discretized domain. Results demonstrate the influence of transcranial electrical stimulation on membrane voltage, ion channel gating, and transmembrane flux. Simulations also compare the e↵ects of two di↵erent types of neurostimulation (transcranial electrical stimulation and deep brain stimulation) showcasing cellular-level di↵erences resulting from these distinct forms of electrical therapy. Hopefully this work will ultimately help elucidate the principles by which neurostimulation alleviates disease symptoms

Effect of phase separation and supercooling on the storage capacity in a commercial latent heat thermal energy storage: Experimental cycling of a salt hydrate PCM

Latent heat storage technologies offer process benefits like daily peak shaving. In this work a commercial storage design for storing cold thermal energy has been studied using a laboratory prototype containing 168 kg of a commercial salt-hydrate phase change material (PCM). The storage was charged and discharged with subsequent cycles at different mass flow rates over a fixed temperature range and duration. It was found that the PCM TES design exhibits phase separation and increased supercooling with continuous cycling. Both phenomena lead to a gradual decrease of the effective storage capacity. With later cycles only the bottom part stores latent heat, while the top and middle parts of the storage remain liquid. The results were repeatable and are consistent with T-History measurements of samples from the PCM TES before and after cycling. It is likely that the PCM itself does not suffer from incongruent melting. Instead, the phase separation is likely to occur due to a segregation of different liquid phases across the height of the storage. It was found that T-History measurements alone are not able to predict this behavior. Moreover, it is shown that phase separation in the storage can be reversed by increasing the PCM temperature and mechanical mixing of the liquid phase. This phase separation has to be prevented in future work in order to achieve stable performance with the studied storage design

Location specificity of transcranial electrical stimulation on neuronal electrodynamics: A mathematical model of ion channel gating dynamics and ionic flux due to neurostimulation

Transcranial Electrical Stimulation (TES) continues to demonstrate success as a medical intervention for individuals with neurodegenerative diseases. Despite promising results from these neuromodulation modalities, the cellular level mechanisms by which this neurotherapy operates are not fully comprehended. In particular, the effects of TES on ion channel gating and ion transport are not known. Using the Poisson-Nernst-Planck model of electrodiffusion, coupled with a Hodgkin-Huxley based model of cellular ion transport, we present a model of TES that, for the first time, integrates electric potential energy, individualized ion species, voltage-gated ion channels, and transmembrane ionic flux during TES administration. Computational simulations are executed on a biologically-inspired domain with medically-based TES treatment parameters and quantify neuron-level electrical processes resulting from this form of neurostimulation. Results confirm prior findings that show that TES polarizes the cell membrane, however, these are extended as simulations in this paper show that polarization occurs in a location specific manner, where the type and degree of polarization depends on the position on the membrane within a node of Ranvier. In addition, results demonstrate that TES causes ion channel gating variables to change in a location specific fashion and, as a result, transmembrane current from distinct ion species depends on both time and membrane location. Another simulation finding is that intracellular calcium concentrations increase significantly due to a TES-induced calcium influx. As cytosolic calcium is critical in intracellular signaling pathways that govern proper neurotransmitter secretion as well as support cell viability, this alteration in calcium homeostasis suggests a possible mechanism by which TES operates at the neuronal level to achieve neurotherapeutic success

A Computation Based Approach for Modeling the Efficacy of Neurostimulation Therapies on Neural Functioning

Neurostimulation demonstrates success as a medical treatment for patients suffering from neurodegenerative diseases and psychiatric disorders. Despite promising clinical results, the cellular-level processes by which they achieve these favorable outcomes are not completely understood. Specifically, the neuronal mechanisms by which neurostimulation impacts ion channel gating and transmembrane ionic flux are unknown. To help elucidate these mechanisms, we have developed a novel mathematical model that integrates the Poisson-Nernst-Planck system of PDEs and Hodgkin-Huxley based ODEs to model the effects of this neurotherapy on transmembrane voltage, ion channel gating, and ionic mobility. Using a biologically-inspired domain, in silico simulations are used to assess the impact of TES and DBS on neuronal electrodynamics. Results show that an instantaneous polarization of the membrane\u27s resting potential occurs in a location specific manner, where the type and degree of polarization depends on the position on the membrane. This polarization in turn leads ion channel gating and transmembrane ionic flux to change in a site specific fashion. In addition, results show differences in polarization, membrane voltage, and transmembrane ion mobility resulting from highly distinct forms of neurostimulation, namely tran-scranial electrical stimulation and deep brain stimulation

Thermal energy storage using phase change materials: Techno-economic evaluation of a cold storage installation in an office building

Utilizing the latent heat of solidification and melting of so-called phase change materials (PCMs) allows higher storage densities and increased process flexibility within energy systems. However, there is an existing gap in the current literature studying simultaneously the technical and economic performance of these thermal energy storages within an actual application. Thus, in this work a comprehensive techno-economic analysis of a full-scale storage with 7000 L salt-hydrate surrounding a polypropylene capillary tube heat exchanger is presented. The storage is located in a multi-story office building in Gothenburg, Sweden and is used for daily peak shaving of the building’s cooling energy demands. The daily utilizable storage capacity for the installation was determined to be 99kWh, which is 36% of the installed capacity given by the storage manufacturer. The major limiting factor were found to be 60–75% smaller charging rates than what was designed by the manufacturer. Using a mixed integer linear programming model (MILP) to yield optimum scheduling, the storage investment cost limit for a 5\ua0year payback time can be estimated as 9804 SEK ( 921 EUR). These developed key performance indicators can be readily compared against alternative storage technologies and designs in order to select the optimal storage design for equivalent applications. Future work is needed to investigate reasons behind the lower than expected storage capacity