Mathematical models in physiology

Computational modelling of biological processes and systems has witnessed a remarkable development in recent years. The search-term (modelling OR modeling) yields over 58000 entries in PubMed, with more than 34000 since the year 2000: thus, almost two-thirds of papers appeared in the last 5–6 years, compared to only about one-third in the preceding 5–6 decades.\ud \ud The development is fuelled both by the continuously improving tools and techniques available for bio-mathematical modelling and by the increasing demand in quantitative assessment of element inter-relations in complex biological systems. This has given rise to a worldwide public domain effort to build a computational framework that provides a comprehensive theoretical representation of integrated biological function—the Physiome.\ud \ud The current and next issues of this journal are devoted to a small sub-set of this initiative and address biocomputation and modelling in physiology, illustrating the breadth and depth of experimental data-based model development in biological research from sub-cellular events to whole organ simulations

Computational probabilistic quantification of pro-arrhythmic risk from scar and left-to-right heterogeneity in the human ventricles

Both scar and left-to-right ventricular (LV/RV) differences in repolarization properties have been implicated as risk factors for lethal arrhythmias. As a possible mechanism for the initiation of re-entry, a recent study has indicated that LV/RV heterogeneities in action potential duration (APD) adaptation can cause a transient increase in APD dispersion following rate acceleration, promoting unidirectional block of conduction at the LV/RV junction. In the presence of an ischemic region and ectopic stimulation, a pathological dispersion in repolarization has been suggested to increase the risk of electrical re-entry. However, the exact location and timing of the ectopic activation play a crucial role in initiation of re-entry, and certain combinations may lead to re-entry even under normal LV/RV dispersion in repolarization. This suggests that the phenomenon needs to be investigated in a quantitative way. In this study we employ a computationally efficient, phenomenological model in order to investigate the proarrhythmic properties of a range of combinations of position and timing of an ectopic activation. This allows us to probabilistically study how increasing interventricular dispersion of repolarization increases arrhythmic risk. Results indicate that a larger LV/RV dispersion in repolarization allows ectopic beats to initiate re-entry during a significantly larger time window and from a greater number of locations compared to the case of smaller LV/RV dispersion

A comparative study fourth order runge kutta-tvd Scheme and fluent software case of inlet flow problems

Inlet as part of aircraft engine plays important role in controlling the rate of airflow entering to the engine. The shape of inlet has to be designed in such away to make the rate of airflow does not change too much with angle of attack and also not much pressure losses at the time, the airflow entering to the compressor section. It is therefore understanding on the flow pattern inside the inlet is important. The present work presents on the use of the Fourth Order Runge Kutta – Harten Yee TVD scheme for the flow analysis inside inlet. The flow is assumed as an inviscid quasi two dimensional compressible flow. As an initial stage of computer code development, here uses three generic inlet models. The first inlet model to allow the problem in hand solved as the case of inlet with expansion wave case. The second inlet model will relate to the case of expansion compression wave. The last inlet model concerns with the inlet which produce series of weak shock wave and end up with a normal shock wave. The comparison result for the same test case with Fluent Software [1, 2] indicates that the developed computer code based on the Fourth Order Runge Kutta – Harten – Yee TVD scheme are very close to each other. However for complex inlet geometry, the problem is in the way how to provide an appropriate mesh model

Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity

It has become widely accepted that the most dangerous cardiac arrhythmias are due to re- entrant waves, i.e., electrical wave(s) that re-circulate repeatedly throughout the tissue at a higher frequency than the waves produced by the heart's natural pacemaker (sinoatrial node). However, the complicated structure of cardiac tissue, as well as the complex ionic currents in the cell, has made it extremely difficult to pinpoint the detailed mechanisms of these life-threatening reentrant arrhythmias. A simplified ionic model of the cardiac action potential (AP), which can be fitted to a wide variety of experimentally and numerically obtained mesoscopic characteristics of cardiac tissue such as AP shape and restitution of AP duration and conduction velocity, is used to explain many different mechanisms of spiral wave breakup which in principle can occur in cardiac tissue. Some, but not all, of these mechanisms have been observed before using other models; therefore, the purpose of this paper is to demonstrate them using just one framework model and to explain the different parameter regimes or physiological properties necessary for each mechanism (such as high or low excitability, corresponding to normal or ischemic tissue, spiral tip trajectory types, and tissue structures such as rotational anisotropy and periodic boundary conditions). Each mechanism is compared with data from other ionic models or experiments to illustrate that they are not model-specific phenomena. The fact that many different breakup mechanisms exist has important implications for antiarrhythmic drug design and for comparisons of fibrillation experiments using different species, electromechanical uncoupling drugs, and initiation protocols.Comment: 128 pages, 42 figures (29 color, 13 b&w

Directed graph mapping exceeds phase mapping in discriminating true and false rotors detected with a basket catheter in a complex in-silico excitation pattern

[EN] Atrial fibrillation (AF) is the most frequently encountered arrhythmia in clinical practise. One of the major problems in the management of AF is the difficulty in identifying the arrhythmia sources from clinical recordings. That difficulty occurs because it is currently impossible to verify algorithms which determine these sources in clinical data, as high resolution true excitation patterns cannot be recorded in patients. Therefore, alternative approaches, like computer modelling are of great interest. In a recent published study such an approach was applied for the verification of one of the most commonly used algorithms, phase mapping (PM). A meandering rotor was simulated in the right atrium and a basket catheter was placed at 3 different locations: at the Superior Vena Cava (SVC), the Crista Terminalis (CT) and at the Coronary Sinus (CS). It was shown that although PM can identify the true source, it also finds several false sources due to the far-field effects and interpolation errors in all three positions. In addition, the detection efficiency strongly depended on the basket location. Recently, a novel tool was developed to analyse any arrhythmia called Directed Graph Mapping (DGM). DGM is based on network theory and creates a directed graph of the excitation pattern, from which the location and the source of the arrhythmia can be detected. Therefore, the objective of the current study was to compare the efficiency of DGM with PM on the basket dataset of this meandering rotor. The DGM-tool was applied for a wide variety of conduction velocities (minimal and maximal), which are input parameters of DGM. Overall we found that DGM was able to distinguish between the true rotor and false rotors for both the SVC and CT basket positions. For example, for the SVC position with a CVmin = 0.01 cmms, DGM detected the true core with a prevalence of 82% versus 94% for PM. Three false rotors where detected for 39.16% (DGM) versus 100% (PM); 22.64% (DGM) versus 100% (PM); and 0% (DGM) versus 57% (PM). Increasing CVmin to 0.02 cmms had a stronger effect on the false rotors than on the true rotor. This led to a detection rate of 56.6% for the true rotor, while all the other false rotors disappeared. A similar trend was observed for the CT position. For the CS position, DGM already had a low performance for the true rotor for CVmin = 0.01 cmms (14.7%). For CVmin= 0.02 cmms the false and the true rotors could therefore not be distinguished. We can conclude that DGM can overcome some of the limitations of PM by varying one of its input parameters (CVmin). The true rotor is less dependent on this parameter than the false rotors, which disappear at a CVmin = 0.02 cmms. In order to increase to detection rate of the true rotor, one can decrease CVmin and discard the new rotors which also appear at lower values of CVmin.Supported in part by Direccion General de Politica Cientifica de la Generalitat Valenciana (grant ID PROMETEU 2020/043) , Valencia, Spain. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 900008) , Brussels, Belgium. Research at Sechenov University was financed by the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of WorldClass Research Centers "Digital biodesign and personalized healthcare" (grant ID 075152020926) , Russia.Nieuwenhuyse, EV.; Martínez-Mateu, L.; Saiz Rodríguez, FJ.; Panfilov, AV.; Vandersickel, N. (2021). Directed graph mapping exceeds phase mapping in discriminating true and false rotors detected with a basket catheter in a complex in-silico excitation pattern. Computers in Biology and Medicine. 133:1-11. https://doi.org/10.1016/j.compbiomed.2021.104381S11113

Assessing the ability of substrate mapping techniques to guide ventricular tachycardia ablation using computational modelling

BACKGROUND: Identification of targets for ablation of post-infarction ventricular tachycardias (VTs) remains challenging, often requiring arrhythmia induction to delineate the reentrant circuit. This carries a risk for the patient and may not be feasible. Substrate mapping has emerged as a safer strategy to uncover arrhythmogenic regions. However, VT recurrence remains common. GOAL: To use computer simulations to assess the ability of different substrate mapping approaches to identify VT exit sites. METHODS: A 3D computational model of the porcine post-infarction heart was constructed to simulate VT and paced rhythm. Electroanatomical maps were constructed based on endocardial electrogram features and the reentry vulnerability index (RVI - a metric combining activation (AT) and repolarization timings to identify tissue susceptibility to reentry). Since scar transmurality in our model was not homogeneous, parameters derived from all signals (including dense scar regions) were used in the analysis. Potential ablation targets obtained from each electroanatomical map during pacing were compared to the exit site detected during VT mapping. RESULTS: Simulation data showed that voltage cut-offs applied to bipolar electrograms could delineate the scar, but not the VT circuit. Electrogram fractionation had the highest correlation with scar transmurality. The RVI identified regions closest to VT exit site but was outperformed by AT gradients combined with voltage cut-offs. The performance of all metrics was affected by pacing location. CONCLUSIONS: Substrate mapping could provide information about the infarct, but the directional dependency on activation should be considered. Activation-repolarization metrics have utility in safely identifying VT targets, even with non-transmural scars

Chaste: an open source C++ library for computational physiology and biology

Chaste - Cancer, Heart And Soft Tissue Environment - is an open source C++ library for the computational simulation of mathematical models developed for physiology and biology. Code development has been driven by two initial applications: cardiac electrophysiology and cancer development. A large number of cardiac electrophysiology studies have been enabled and performed, including high performance computational investigations of defibrillation on realistic human cardiac geometries. New models for the initiation and growth of tumours have been developed. In particular, cell-based simulations have provided novel insight into the role of stem cells in the colorectal crypt. Chaste is constantly evolving and is now being applied to a far wider range of problems. The code provides modules for handling common scientific computing components, such as meshes and solvers for ordinary and partial differential equations (ODEs/PDEs). Re-use of these components avoids the need for researchers to "re-invent the wheel" with each new project, accelerating the rate of progress in new applications. Chaste is developed using industrially-derived techniques, in particular test-driven development, to ensure code quality, re-use and reliability. In this article we provide examples that illustrate the types of problems Chaste can be used to solve, which can be run on a desktop computer. We highlight some scientific studies that have used or are using Chaste, and the insights they have provided. The source code, both for specific releases and the development version, is available to download under an open source Berkeley Software Distribution (BSD) licence at http://www.cs.ox.ac.uk/chaste, together with details of a mailing list and links to documentation and tutorials

A multiscale model for collagen alignment in wound healing

It is thought that collagen alignment plays a significant part in scar tissue formation during dermal wound healing. We present a multiscale model for collagen deposition and alignment during this process. We consider fibroblasts as discrete units moving within an extracellular matrix of collagen and fibrin modelled as continua. Our model includes flux induced alignment of collagen by fibroblasts, and contact guidance of fibroblasts by collagen fibres. We can use the model to predict the effects of certain manipulations, such as varying fibroblast speed, or placing an aligned piece of tissue in the wound. We also simulate experiments which alter the TGF-β concentrations in a healing dermal wound and use the model to offer an explanation of the observed influence of this growth factor on scarring