Finite element and finite volume-element simulation of pseudo-ECGs and cardiac alternans

In this paper, we are interested in the spatio-temporal dynamics of the transmembrane potential in paced isotropic and anisotropic cardiac tissues. In particular, we observe a specific precursor of cardiac arrhythmias that is the presence of alternans in the action potential duration. The underlying mathematical model consists of a reaction–diffusion system describing the propagation of the electric potential and the nonlinear interaction with ionic gating variables. Either conforming piecewise continuous finite elements or a finite volume-element scheme are employed for the spatial discretization of all fields, whereas operator splitting strategies of first and second order are used for the time integration. We also describe an efficient mechanism to compute pseudo-ECG signals, and we analyze restitution curves and alternans patterns for physiological and pathological cardiac rhythms

Four Ways to Fit an Ion Channel Model

© 2019 Biophysical Society Mathematical models of ionic currents are used to study the electrophysiology of the heart, brain, gut, and several other organs. Increasingly, these models are being used predictively in the clinic, for example, to predict the risks and results of genetic mutations, pharmacological treatments, or surgical procedures. These safety-critical applications depend on accurate characterization of the underlying ionic currents. Four different methods can be found in the literature to fit voltage-sensitive ion channel models to whole-cell current measurements: method 1, fitting model equations directly to time-constant, steady-state, and I-V summary curves; method 2, fitting by comparing simulated versions of these summary curves to their experimental counterparts; method 3, fitting to the current traces themselves from a range of protocols; and method 4, fitting to a single current trace from a short and rapidly fluctuating voltage-clamp protocol. We compare these methods using a set of experiments in which hERG1a current was measured in nine Chinese hamster ovary cells. In each cell, the same sequence of fitting protocols was applied, as well as an independent validation protocol. We show that methods 3 and 4 provide the best predictions on the independent validation set and that short, rapidly fluctuating protocols like that used in method 4 can replace much longer conventional protocols without loss of predictive ability. Although data for method 2 are most readily available from the literature, we find it performs poorly compared to methods 3 and 4 both in accuracy of predictions and computational efficiency. Our results demonstrate how novel experimental and computational approaches can improve the quality of model predictions in safety-critical applications

Verification and Validation of Numerical Modelling Approaches Pertinent to Stomach Modelling

The digestive system is vital to the human body. Over many decades, scientists have been investigating the food breakdown mechanisms inside the stomach through in vivo human and animal studies and in vitro experiments. Due to recent improvements in computing speed and algorithm development, computational modelling has become a viable option to investigate in-body processes. Such in silico models are more easily controlled to investigate individual variables, do not require invasive physical experiments, and can provide valuable insights into the local physics of gastric flow. There is a huge potential for numerical approaches in stomach modelling as they can provide a comprehensive understanding of the complex flow and chemistry in the stomach. However, to make sure the numerical methods are accurate and reliable, rigorous verification and validation are essential as part of model development. A significant focus of this thesis was on verifying and validating the numerical modelling approaches pertinent to stomach modellin

Analysis and modelling of the PY complex in the pyloric circuit of the crab stomatogastric ganglion

PhD ThesisCentral pattern generators (CPGs) are neural circuits that control rhythmic motor patterns such as walking running and swallowing. Injuries can sever the spinal cord or conditions such as Huntington's disease and Parkinson's disease can damage nerves from the brain that control CPGs. Understanding the connectivity of neural circuits has proved insu cient to understand the dynamics of such circuits. Neuromodulators and neurohormones can di erentially a ect every connection in neural circuits and di erent circuits are a ected in very di erent ways. The resulting complexity of such systems make them very di cult to study but research is greatly facilitated by the use of model organisms and computational models. The crustacean stomatogastric ganglion (STG) has been used as a model system for many years. Its relative simplicity and accessibility to neurons makes it an ideal system for the study of neural interaction, CPGs and the e ect of neuromodulators on neural systems. The e ect of dopamine on the pyloric CPG of the crab STG was recorded using voltage sensitive dye imaging and electrophysiological techniques. To analyse voltage sensitive dye (VSD) imaging data a heuristic method was devised that uses the timing of the activity plateaus of neurons for the estimation of the dynamics of the temporal relationship of the neurons' activities. MATLABR was used to create a Hodgkin-Huxley based model of the pyloric constrictor pyloric dilator neurons (PDs) with parameters that could capture the dynamics of neuromodulation. The MATLABR model includes two compartments, the soma and the axon, for the anterior burster neuron, the lateral pyloric neurons (LPs), two PDs and ve individual pyloric constrictor neurons (PYs). By di erentially changing the values of the model synapses, the model is able to reproduce the de-synchronisation of the pyloric constrictor neurons as was observed experimentally i on the dea erented stomatogastric nervous system. Existing models model PYs and PDs as single neurons. These models are unable to show the desynchronising e ect of dopamine on multiple neurons of the same type. The model created for this research is able to re ect the e ect of neuromodulation on the complete circuit by allowing parameters of synapses between neurons of the same type to be adjusted di erentially, re ecting the biological system more accurately

Finite element simulations: computations and applications to aerodynamics and biomedicine.

171 p.Las ecuaciones en derivadas parciales describen muchos fenómenos de interés práctico y sus solucionessuelen necesitar correr simulaciones muy costosas en clústers de cálculo.En el ámbito de los flujos turbulentos, en particular, el coste de las simulaciones es demasiado grande sise utilizan métodos básicos, por eso es necesario modelizar el sistema.Esta tesis doctoral trata principalmente de dos temas en Cálculo Científico.Por un lado, estudiamos nuevos desarrollos en la modelización y simulación de flujos turbulentos;utilizamos un Método de Elementos Finitos adaptativo y un modelo de ¿número de Reynolds infinito¿para reducir el coste computacional de simulaciones que, sin estas modificaciones, serían demasiadocostosas.De esta manera conseguimos lograr simulaciones evolutivas de flujos turbulentos con número deReynolds muy grande, lo cual se considera uno de los mayores retos en aerodinámica.El otro pilar de esta tesis es una aplicación biomédica.Desarrollamos un modelo computacional de Ablación (Cardiaca) por Radiofrecuencia, una terapiacomún para tratar varias enfermedades, por ejemplo algunas arritmias.Nuestro modelo mejora los modelos existentes en varias maneras, y en particular en tratar de obteneruna aproximación fiel de la geometría del sistema, lo cual se descubre ser crítico para simularcorrectamente la física del fenómeno

Proactive esophageal cooling protects against thermal insults during high-power short-duration radiofrequency cardiac ablation

[EN] Background Proactive cooling with a novel cooling device has been shown to reduce endoscopically identified thermal injury during radiofrequency (RF) ablation for the treatment of atrial fibrillation using medium power settings. We aimed to evaluate the effects of proactive cooling during high-power short-duration (HPSD) ablation. Methods A computer model accounting for the left atrium (1.5 mm thickness) and esophagus including the active cooling device was created. We used the Arrhenius equation to estimate the esophageal thermal damage during 50 W/ 10 s and 90 W/ 4 s RF ablations. Results With proactive esophageal cooling in place, temperatures in the esophageal tissue were significantly reduced from control conditions without cooling, and the resulting percentage of damage to the esophageal wall was reduced around 50%, restricting damage to the epi-esophageal region and consequently sparing the remainder of the esophageal tissue, including the mucosal surface. Lesions in the atrial wall remained transmural despite cooling, and maximum width barely changed (<0.8 mm). Conclusions Proactive esophageal cooling significantly reduces temperatures and the resulting fraction of damage in the esophagus during HPSD ablation. These findings offer a mechanistic rationale explaining the high degree of safety encountered to date using proactive esophageal cooling, and further underscore the fact that temperature monitoring is inadequate to avoid thermal damage to the esophagus.Research reported in this publication was supported by the National Heart, Lung, And Blood Institute of the National Institutes of Health under Award Number R44HL158375 (the content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health) and by the Spanish Ministerio de Ciencia, Innovacion y Universidades/Agencia Estatal de Investigacion (MCIN/AEI/10.13039/501100011033 under grant RTI2018-094357-B-C21).Mercado Montoya, M.; Gomez Bustamante, T.; Berjano, E.; Mickelsen, SR.; Daniels, JD.; Hernández Arango, P.; Schieber, J.... (2022). Proactive esophageal cooling protects against thermal insults during high-power short-duration radiofrequency cardiac ablation. International Journal of Hyperthermia. 39(1):1202-1212. https://doi.org/10.1080/02656736.2022.21218601202121239

Design of novel drug delivery polymeric complexes via innovative crosslinking reactions

A thesis submitted to the Faculty of Health Sciences, University of the Witwatersrand, in fulfilment of the requirements for the Degree of Master of Science in Medicine (Pharmacy), JohannesburgThis thesis presents a multifaceted approach which comprehensively describes the design of novel drug delivery polymeric complexes through the application of innovative crosslinking reactions. These reactions have been built on the statistical and mathematical principles governing the technique of Design of Experiments. At the outset, pertinent aspects covering the importance of rate-controlled drug delivery in achieving superior therapeutics is presented. In addition, the fundamental mechanisms which regulate the complex behaviour of polymeric materials are outlined, placing emphasis on the mathematical models which demonstrate the critical need to be able to synchronize the processes of matrix hydration, relaxation, disentanglement, erosion and dissolution. Initially, the Plackett-Burman Design was evaluated to develop a crosslinked polymeric oilisphere device for the in vitro site-specific delivery of Mentha piperita oil. This design proved to be highly successful in rapidly identifying the appropriate release rate-modifying variables through the application of stepwise regression optimization and Artificial Neural Networks.IT201

The Role of Plasma Membrane ATPase Pumps in the Regulation of Rhythmic Activity in Electrically Excitable Cells

Membrane bound ion pumps have long been studied in a housekeeping role, and it is well known that they play a major part in creating the ionic gradients which determine the electrical excitability in a cell. Recent work has begun to highlight other, more direct roles for ion pumps in rhythm generation and information processing. As many pumps obtain energy for active ion transport from adenosine triphosphate (ATP) hydrolysis, they can exchange ions in an electrically asymmetric manner, generating an outward current, which along with ion channel currents, drives the membrane potential of the cell. Membrane potential is a major determining characteristic for how information is transferred between neurons, and so in persistently active excitable cells, pumps can provide a considerable contribution to neuron dynamics. Specialized networks of neurons and non-neural cells which drive rhythmic behaviors such as breathing and locomotion, must robustly produce useful patterns for the animal under dynamic behavioral goals in a highly variable environment. Here we will focus on two well-studied classes of ATPase pumps (the plasma membrane calcium ATPase pump (PMCA) and the sodium-potassium ATPase pump (Na+/K+ pump)) and investigate the role of these pumps in two rhythm generating biological subsystems with a combination of modeling and experimental approaches. In a model of a leech heartbeat central pattern generator, we demonstrate how the neuromodulator myomodulin can regulate the temporal properties of rhythm generation through effects on the hyperpolarization-activated current and the Na+/K+ pump current, and discuss the benefits of modulators which target multiple currents. With this model, we also show how synaptic inhibition can support a functional pattern when pump current is downregulated. Then, in a model of interstitial cells of Cajal (ICC) in the muscular syncytium of the intestinal walls, we demonstrate that due to the importance of complex intracellular calcium oscillations in the generation of ICC rhythms, the PMCA pump can play a major role in regulating the temporal properties of rhythm generation. We discuss rhythm generation mechanisms in both systems and predict parameter domains of multistability which correspond to both functional and pathological states of rhythm generation

Nonlinear effects in finite elements analysis of colorectal surgical clamping

Minimal Invasive Surgery (MIS) is a procedure that has increased its applications in past few years in different types of surgeries. As number of application fields are increasing day by day, new issues have been arising. In particular, instruments must be inserted through a trocar to access the abdominal cavity without capability of direct manipulation of tissues, so a loss of sensitivity occurs. Generally speaking, the student of medicine or junior surgeons need a lot of practice hours before starting any surgical procedure, since they have to difficulty in acquiring specific skills (hand–eye coordination among others) for this type of surgery. Here is what the surgical simulator present a promising training method using an approach based on Finite Element Method (FEM). The use of continuum mechanics, especially Finite Element Analysis (FEA) has gained an extensive application in medical field in order to simulate soft tissues. In particular, colorectal simulations can be used to understand the interaction between colon and the surrounding tissues and also between colon and instruments. Although several works have been introduced considering small displacements, FEA applied to colorectal surgical procedures with large displacements is a topic that asks for more investigations. This work aims to investigate how FEA can describe non-linear effects induced by material properties and different approximating geometries, focusing as test-case application colorectal surgery. More in detail, it shows a comparison between simulations that are performed using both linear and hyperelastic models. These different mechanical behaviours are applied on different geometrical models (planar, cylindrical, 3D-SS and a real model from digital acquisitions 3D-S) with the aim of evaluating the effects of geometric non-linearity. Final aim of the research is to provide a preliminary contribution to the simulation of the interaction between surgical instrument and colon tissues with multi-purpose FEA in order to help the preliminary set-up of different bioengineering tasks like force-contact evaluation or approximated modelling for virtual reality (surgical simulations). In particular, the contribution of this work is focused on the sensitivity analysis of the nonlinearities by FEA in the tissue-tool interaction through an explicit FEA solver. By doing in this way, we aim to demonstrate that the set-up of FEA computational surgical tools may be simplified in order to provide assistance to non-expert FEA engineers or medicians in more precise way of using FEA tools