Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that are triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media and their application to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact in cardiac arrhythmias.Peer ReviewedPreprin

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

Incorporating Inductances in Tissue-Scale Models of Cardiac Electrophysiology

In standard models of cardiac electrophysiology, including the bidomain and monodomain models, local perturbations can propagate at infinite speed. We address this unrealistic property by developing a hyperbolic bidomain model that is based on a generalization of Ohm's law with a Cattaneo-type model for the fluxes. Further, we obtain a hyperbolic monodomain model in the case that the intracellular and extracellular conductivity tensors have the same anisotropy ratio. In one spatial dimension, the hyperbolic monodomain model is equivalent to a cable model that includes axial inductances, and the relaxation times of the Cattaneo fluxes are strictly related to these inductances. A purely linear analysis shows that the inductances are negligible, but models of cardiac electrophysiology are highly nonlinear, and linear predictions may not capture the fully nonlinear dynamics. In fact, contrary to the linear analysis, we show that for simple nonlinear ionic models, an increase in conduction velocity is obtained for small and moderate values of the relaxation time. A similar behavior is also demonstrated with biophysically detailed ionic models. Using the Fenton-Karma model along with a low-order finite element spatial discretization, we numerically analyze differences between the standard monodomain model and the hyperbolic monodomain model. In a simple benchmark test, we show that the propagation of the action potential is strongly influenced by the alignment of the fibers with respect to the mesh in both the parabolic and hyperbolic models when using relatively coarse spatial discretizations. Accurate predictions of the conduction velocity require computational mesh spacings on the order of a single cardiac cell. We also compare the two formulations in the case of spiral break up and atrial fibrillation in an anatomically detailed model of the left atrium, and [...].Comment: 20 pages, 12 figure

Cancer modelling: Getting to the heart of the problem

Paradoxically, improvements in healthcare that have enhanced the life expectancy of humans in the Western world have, indirectly, increased the prevalence of certain types of cancer such as prostate and breast. It remains unclear whether this phenomenon should be attributed to the ageing process itself or the cumulative effect of prolonged exposure to harmful environmental stimuli such as ultraviolet light, radiation and carcinogens (Franks and Teich, 1988). Equally, there is also compelling evidence that certain genetic abnormalities can predispose individuals to specific cancers (Ilyas et al., 1999). The variety of factors that have been implicated in the development of solid tumours stems, to a large extent, from the fact that ‘cancer’ is a generic term, often used to characterize a series of disorders that share common features. At this generic level of description, cancer may be viewed as a cellular disease in which controls that usually regulate growth and maintain homeostasis are disrupted. Cancer is typically initiated by genetic mutations that lead to enhanced mitosis of a cell lineage and the formation of an avascular tumour. Since it receives nutrients by diffusion from the surrounding tissue, the size of an avascular tumour is limited to several millimeters in diameter. Further growth relies on the tumour acquiring the ability to stimulate the ingrowth of a new, circulating blood supply from the host vasculature via a process termed angiogenesis (Folkman, 1974). Once vascularised, the tumour has access to a vast nutrient source and rapid growth ensues. Further, tumour fragments that break away from the primary tumour, on entering the vasculature, may be transported to other organs in which they may establish secondary tumours or metastases that further compromise the host. Invasion is another key feature of solid tumours whereby contact with the tissue stimulates the production of enzymes that digest the tissue, liberating space into which the tumour cells migrate. Thus, cancer is a complex, multiscale process. The spatial scales of interest range from the subcellular level, to the cellular and macroscopic (or tissue) levels while the timescales may vary from seconds (or less) for signal transduction pathways to months for tumour doubling times The variety of phenomena involved, the range of spatial and temporal scales over which they act and the complex way in which they are inter-related mean that the development of realistic theoretical models of solid tumour growth is extremely challenging. While there is now a large literature focused on modelling solid tumour growth (for a review, see, for example, Preziosi, 2003), existing models typically focus on a single spatial scale and, as a result, are unable to address the fundamental problem of how phenomena at different scales are coupled or to combine, in a systematic manner, data from the various scales. In this article, a theoretical framework will be presented that is capable of integrating a hierarchy of processes occurring at different scales into a detailed model of solid tumour growth (Alarcon et al., 2004). The model is formulated as a hybrid cellular automaton and contains interlinked elements that describe processes at each spatial scale: progress through the cell cycle and the production of proteins that stimulate angiogenesis are accounted for at the subcellular level; cell-cell interactions are treated at the cellular level; and, at the tissue scale, attention focuses on the vascular network whose structure adapts in response to blood flow and angiogenic factors produced at the subcellular level. Further coupling between the different spatial scales arises from the transport of blood-borne oxygen into the tissue and its uptake at the cellular level. Model simulations will be presented to illustrate the effect that spatial heterogeneity induced by blood flow through the vascular network has on the tumour’s growth dynamics and explain how the model may be used to compare the efficacy of different anti-cancer treatment protocols

Cardiac cell modelling: Observations from the heart of the cardiac physiome project

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field

三次元心臓モデルと不均一振動モデルによる心臓活動電位のコンピュータシミュレーション

Tohoku University西條芳文論

Novel Cardiac Mapping Approaches and Multimodal Techniques to Unravel Multidomain Dynamics of Complex Arrhythmias Towards a Framework for Translational Mechanistic-Based Therapeutic Strategies

[ES] Las arritmias cardíacas son un problema importante para los sistemas de salud en el mundo desarrollado debido a su alta incidencia y prevalencia a medida que la población envejece. La fibrilación auricular (FA) y la fibrilación ventricular (FV) se encuentran entre las arritmias más complejas observadas en la práctica clínica. Las consecuencias clínicas de tales alteraciones arrítmicas incluyen el desarrollo de eventos cardioembólicos complejos en la FA, y repercusiones dramáticas debido a procesos fibrilatorios sostenidos que amenazan la vida infringiendo daño neurológico tras paro cardíaco por FV, y que pueden provocar la muerte súbita cardíaca (MSC). Sin embargo, a pesar de los avances tecnológicos de las últimas décadas, sus mecanismos intrínsecos se comprenden de forma incompleta y, hasta la fecha, las estrategias terapéuticas carecen de una base mecanicista suficiente y poseen bajas tasas de éxito. Entre los mecanismos implicados en la inducción y perpetuación de arritmias cardíacas, como la FA, se cree que las dinámicas de las fuentes focales y reentrantes de alta frecuencia, en sus diferentes modalidades, son las fuentes primarias que mantienen la arritmia. Sin embargo, se sabe poco sobre los atractores, así como, de la dinámica espacio-temporal de tales fuentes fibrilatorias primarias, específicamente, las fuentes focales o rotacionales dominantes que mantienen la arritmia. Por ello, se ha desarrollado una plataforma computacional, para comprender los factores (activos, pasivos y estructurales) determinantes, y moduladores de dicha dinámica. Esto ha permitido establecer un marco para comprender la compleja dinámica de los rotores con énfasis en sus propiedades deterministas para desarrollar herramientas basadas en los mecanismos para ayuda diagnóstica y terapéutica. Comprender los procesos fibrilatorios es clave para desarrollar marcadores y herramientas fisiológica- y clínicamente relevantes para la ayuda de diagnóstico temprano. Específicamente, las propiedades espectrales y de tiempo-frecuencia de los procesos fibrilatorios han demostrado resaltar el comportamiento determinista principal de los mecanismos intrínsecos subyacentes a las arritmias y el impacto de tales eventos arrítmicos. Esto es especialmente relevante para determinar el pronóstico temprano de los supervivientes comatosos después de un paro cardíaco debido a fibrilación ventricular (FV). Las técnicas de mapeo electrofisiológico, el mapeo eléctrico y óptico cardíaco, han demostrado ser recursos muy valiosos para dar forma a nuevas hipótesis y desarrollar nuevos enfoques mecanicistas y estrategias terapéuticas mejoradas. Esta tecnología permite además el trabajo multidisciplinar entre clínicos y bioingenieros, para el desarrollo y validación de dispositivos y metodologías para identificar biomarcadores multi-dominio que permitan rastrear con precisión la dinámica de las arritmias identificando fuentes dominantes y atractores con alta precisión para ser dianas de estrategias terapeúticas innovadoras. Es por ello que uno de los objetivos fundamentales ha sido la implantación y validación de nuevos sistemas de mapeo en distintas configuraciones que sirvan de plataforma de desarrollo de nuevas estrategias terapeúticas. Aunque el mapeo panorámico es el método principal y más completo para rastrear simultáneamente biomarcadores electrofisiológicos, su adopción por la comunidad científica es limitada principalmente debido al coste elevado de la tecnología. Aprovechando los avances tecnológicos recientes, nos hemos enfocado en desarrollar, y validar, sistemas de mapeo óptico de alta resolución para registro panorámico cardíaco, utilizando modelos clínicamente relevantes para la investigación básica y la bioingeniería.[CA] Les arítmies cardíaques són un problema important per als sistemes de salut del món desenvolupat a causa de la seva alta incidència i prevalença a mesura que la població envelleix. La fibril·lació auricular (FA) i la fibril·lació ventricular (FV), es troben entre les arítmies més complexes observades a la pràctica clínica. Les conseqüències clíniques d'aquests trastorns arítmics inclouen el desenvolupament d'esdeveniments cardioembòlics complexos en FA i repercussions dramàtiques a causa de processos fibril·latoris sostinguts que posen en perill la vida amb danys neurològics posteriors a la FV, que condueixen a una aturada cardíaca i a la mort cardíaca sobtada (SCD). Tanmateix, malgrat els avanços tecnològics de les darreres dècades, els seus mecanismes intrínsecs s'entenen de forma incompleta i, fins a la data, les estratègies terapèutiques no tenen una base mecanicista suficient i tenen baixes taxes d'èxit. La majoria dels avenços en el desenvolupament de biomarcadors òptims i noves estratègies terapèutiques en aquest camp provenen de tècniques valuoses en la investigació de mecanismes d'arítmia. Entre els mecanismes implicats en la inducció i perpetuació de les arítmies cardíaques, es creu que les fonts primàries subjacents a l'arítmia són les fonts focals reingressants d'alta freqüència dinàmica i AF, en les seves diferents modalitats. Tot i això, se sap poc sobre els atractors i la dinàmica espaciotemporal d'aquestes fonts primàries fibril·ladores, específicament les fonts rotacionals o focals dominants que mantenen l'arítmia. Per tant, s'ha desenvolupat una plataforma computacional per entendre determinants actius, passius, estructurals i moduladors d'aquestes dinàmiques. Això va permetre establir un marc per entendre la complexa dinàmica multidomini dels rotors amb ènfasi en les seves propietats deterministes per desenvolupar enfocaments mecanicistes per a l'ajuda i la teràpia diagnòstiques. La comprensió dels processos fibril·latoris és clau per desenvolupar puntuacions i eines rellevants fisiològicament i clínicament per ajudar al diagnòstic precoç. Concretament, les propietats espectrals i de temps-freqüència dels processos fibril·latoris han demostrat destacar un comportament determinista important dels mecanismes intrínsecs subjacents a les arítmies i l'impacte d'aquests esdeveniments arítmics. Mitjançant coneixements previs, processament de senyals, tècniques d'aprenentatge automàtic i anàlisi de dades, es va desenvolupar una puntuació de risc mecanicista a la aturada cardíaca per FV. Les tècniques de cartografia òptica cardíaca i electrofisiològica han demostrat ser recursos inestimables per donar forma a noves hipòtesis i desenvolupar nous enfocaments mecanicistes i estratègies terapèutiques. Aquesta tecnologia ha permès durant molts anys provar noves estratègies terapèutiques farmacològiques o ablatives i desenvolupar mètodes multidominis per fer un seguiment precís de la dinàmica d'arrímies que identifica fonts i atractors dominants. Tot i que el mapatge panoràmic és el mètode principal per al seguiment simultani de paràmetres electrofisiològics, la seva adopció per part de la comunitat multidisciplinària d'investigació cardiovascular està limitada principalment pel cost de la tecnologia. Aprofitant els avenços tecnològics recents, ens centrem en el desenvolupament i la validació de sistemes de mapes òptics de baix cost per a imatges panoràmiques mitjançant models clínicament rellevants per a la investigació bàsica i la bioenginyeria.[EN] Cardiac arrhythmias are a major problem for health systems in the developed world due to their high incidence and prevalence as the population ages. Atrial fibrillation (AF) and ventricular fibrillation (VF), are amongst the most complex arrhythmias seen in the clinical practice. Clinical consequences of such arrhythmic disturbances include developing complex cardio-embolic events in AF, and dramatic repercussions due to sustained life-threatening fibrillatory processes with subsequent neurological damage under VF, leading to cardiac arrest and sudden cardiac death (SCD). However, despite the technological advances in the last decades, their intrinsic mechanisms are incompletely understood, and, to date, therapeutic strategies lack of sufficient mechanistic basis and have low success rates. Most of the progress for developing optimal biomarkers and novel therapeutic strategies in this field has come from valuable techniques in the research of arrhythmia mechanisms. Amongst the mechanisms involved in the induction and perpetuation of cardiac arrhythmias such AF, dynamic high-frequency re-entrant and focal sources, in its different modalities, are thought to be the primary sources underlying the arrhythmia. However, little is known about the attractors and spatiotemporal dynamics of such fibrillatory primary sources, specifically dominant rotational or focal sources maintaining the arrhythmia. Therefore, a computational platform for understanding active, passive and structural determinants, and modulators of such dynamics was developed. This allowed stablishing a framework for understanding the complex multidomain dynamics of rotors with enphasis in their deterministic properties to develop mechanistic approaches for diagnostic aid and therapy. Understanding fibrillatory processes is key to develop physiologically and clinically relevant scores and tools for early diagnostic aid. Specifically, spectral and time-frequency properties of fibrillatory processes have shown to highlight major deterministic behaviour of intrinsic mechanisms underlying the arrhythmias and the impact of such arrhythmic events. Using prior knowledge, signal processing, machine learning techniques and data analytics, we aimed at developing a reliable mechanistic risk-score for comatose survivors of cardiac arrest due to VF. Cardiac optical mapping and electrophysiological mapping techniques have shown to be unvaluable resources to shape new hypotheses and develop novel mechanistic approaches and therapeutic strategies. This technology has allowed for many years testing new pharmacological or ablative therapeutic strategies, and developing multidomain methods to accurately track arrhymia dynamics identigying dominant sources and attractors. Even though, panoramic mapping is the primary method for simultaneously tracking electrophysiological parameters, its adoption by the multidisciplinary cardiovascular research community is limited mainly due to the cost of the technology. Taking advantage of recent technological advances, we focus on developing and validating low-cost optical mapping systems for panoramic imaging using clinically relevant models for basic research and bioengineering.Calvo Saiz, CJ. (2022). Novel Cardiac Mapping Approaches and Multimodal Techniques to Unravel Multidomain Dynamics of Complex Arrhythmias Towards a Framework for Translational Mechanistic-Based Therapeutic Strategies [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/182329TESI

Modeling the Heart as a Communication System

Electrical communication between cardiomyocytes can be perturbed during arrhythmia, but these perturbations are not captured by conventional electrocardiographic metrics. We developed a theoretical framework to quantify electrical communication using information theory metrics in 2-dimensional cell lattice models of cardiac excitation propagation. The time series generated by each cell was coarse-grained to 1 when excited or 0 when resting. The Shannon entropy for each cell was calculated from the time series during four clinically important heart rhythms: normal heartbeat, anatomical reentry, spiral reentry, and multiple reentry. We also used mutual information to perform spatial profiling of communication during these cardiac arrhythmias. We found that information sharing between cells was spatially heterogeneous. In addition, cardiac arrhythmia significantly impacted information sharing within the heart. Entropy localized the path of the drifting core of spiral reentry, which could be an optimal target of therapeutic ablation. We conclude that information theory metrics can quantitatively assess electrical communication among cardiomyocytes. The traditional concept of the heart as a functional syncytium sharing electrical information cannot predict altered entropy and information sharing during complex arrhythmia. Information theory metrics may find clinical application in the identification of rhythm-specific treatments which are currently unmet by traditional electrocardiographic techniques.Comment: 26 pages (including Appendix), 6 figures, 8 videos (not uploaded due to size limitation