Multiscale Finite Element Modeling of Active Contraction in Striated Muscle

Greater than one in three American adults have at least one type of cardiovascular disease, a major cause of morbidity. Computational cardiac mechanics has become an important part of the research effort to understand the heart’s response to mechanical stimuli and as an extension, disease progression and potential therapies. To this end, the present work aims to extend these efforts by implementing a cell level contractile model in which active stress generation in muscle tissue is driven by half-sarcomere mechanics. This is accomplished by enhancing the MyoSim model of actin and myosin in order to produce a multiscale model. This contraction model simulates cross-bridge dynamics and captures key components of contraction such as length-dependent activation, Ca2+ activation and sensitivity, and filament cooperativity. Embedding this physiologically motivated contraction model allows for the testing of hypotheses and predictions regarding the interplay between molecular mechanisms and organ level function, while capturing spatial heterogeneity. This multiscale approach has been used to predict an increase in the end-systolic pressure-volume relationship due to the inclusion of a recently discovered super-relaxed state in left-ventricle simulations. It has also been used to predict a decrease in stress generation and efficiency in skeletal muscles due to myofibril misalignment. Finally, the foundation for cardiac growth and remodeling simulations has been implemented

The Virtual Physiological Human: Ten Years After

Biomedical research and clinical practice are struggling to cope with the growing complexity that the progress of health care involves. The most challenging diseases, those with the largest socioeconomic impact (cardiovascular conditions; musculoskeletal conditions; cancer; metabolic, immunity, and neurodegenerative conditions), are all characterized by a complex genotype–phenotype interaction and by a “systemic” nature that poses a challenge to the traditional reductionist approach. In 2005 a small group of researchers discussed how the vision of computational physiology promoted by the Physiome Project could be translated into clinical practice and formally proposed the term Virtual Physiological Human. Our knowledge about these diseases is fragmentary, as it is associated with molecular and cellular processes on the one hand and with tissue and organ phenotype changes (related to clinical symptoms of disease conditions) on the other. The problem could be solved if we could capture all these fragments of knowledge into predictive models and then compose them into hypermodels that help us tame the complexity that such systemic behavior involves. In 2005 this was simply not possible—the necessary methods and technologies were not available. Now, 10 years later, it seems the right time to reflect on the original vision, the results achieved so far, and what remains to be done

Multi-scale computer models of lymphatic pumping

The lymphatic system maintains fluid homeostasis by returning interstitial fluid to the veins. Lymphatics pump fluid locally with contracting segments of the vessel (lymphangions) bounded by valves. Contractions are generated by specialized muscle exhibiting phasic and tonic contractions. Deficient pumping can result in accumulation of interstitial fluid, called lymphoedema. Lymphoedema treatments have limited effectiveness, partially attributable to a lack of understanding of contractions. A lumped parameter computational model of lymphangion pumping has previously been developed in the group. In this thesis I detail development of two multiscale models of lymphatic pumping to facilitate improved treatments for lymphoedema. The first model captures subcellular mechanisms of lymphatic muscle contraction. This model is based on the sliding filament model and its smooth muscle adaptation. Contractile elements are combined with passive viscoelastic elements to model a cell. Many arrangements were trialled but only one behaved physiologically. The muscle model was then combined with the lymphangion model for comparison with experiments. This model captures mechanical and energetic aspects of both contraction types. I show that the model provides results similar to published experiments from rat mesenteric lymphatics. The model predicted a peak efficiency of 35%, in the upper range from other muscle types. In the range of frequencies and amplitudes simulated, the direct effect of calcium oscillations can increase lymphangion outflow by up to 40% of the flow in their absence. The second model aims to improve our understanding of lymphangion interaction in large networks through computational homogenisation. In this model we do not directly simulate all lymphangions but sample lymphangions at evenly spaced intervals to reduce the computational intensity. We show through this model that increased external pressure at the network inlet collapses lymphangions and that this disruption of pumping for a few lymphangions reduces the outflow from the entire network.Open Acces

Integrated Heart - Coupling multiscale and multiphysics models for the simulation of the cardiac function

Mathematical modelling of the human heart and its function can expand our understanding of various cardiac diseases, which remain the most common cause of death in the developed world. Like other physiological systems, the heart can be understood as a complex multiscale system involving interacting phenomena at the molecular, cellular, tissue, and organ levels. This article addresses the numerical modelling of many aspects of heart function, including the interaction of the cardiac electrophysiology system with contractile muscle tissue, the sub-cellular activation-contraction mechanisms, as well as the hemodynamics inside the heart chambers. Resolution of each of these sub-systems requires separate mathematical analysis and specially developed numerical algorithms, which we review in detail. By using specific sub-systems as examples, we also look at systemic stability, and explain for example how physiological concepts such as microscopic force generation in cardiac muscle cells, translate to coupled systems of differential equations, and how their stability properties influence the choice of numerical coupling algorithms. Several numerical examples illustrate three fundamental challenges of developing multiphysics and multiscale numerical models for simulating heart function, namely: (i) the correct upscaling from single-cell models to the entire cardiac muscle, (ii) the proper coupling of electrophysiology and tissue mechanics to simulate electromechanical feedback, and (iii) the stable simulation of ventricular hemodynamics during rapid valve opening and closure

Spatial heterogeneity enhances and modulates excitability in a mathematical model of the myometrium

The muscular layer of the uterus (myometrium) undergoes profound changes in global excitability prior to parturition. Here, a mathematical model of the myocyte network is developed to investigate the hypothesis that spatial heterogeneity is essential to the transition from local to global excitation which the myometrium undergoes just prior to birth. Each myometrial smooth muscle cell is represented by an element with FitzHugh–Nagumo dynamics. The cells are coupled through resistors that represent gap junctions. Spatial heterogeneity is introduced by means of stochastic variation in coupling strengths, with parameters derived from physiological data. Numerical simulations indicate that even modest increases in the heterogeneity of the system can amplify the ability of locally applied stimuli to elicit global excitation. Moreover, in networks driven by a pacemaker cell, global oscillations of excitation are impeded in fully connected and strongly coupled networks. The ability of a locally stimulated cell or pacemaker cell to excite the network is shown to be strongly dependent on the local spatial correlation structure of the couplings. In summary, spatial heterogeneity is a key factor in enhancing and modulating global excitability

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

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