title: Mathematical modelling of the electrical and mechanical properties of cardiac cells coupled with non-muscle cells
Creators: name: Mortensen, Peter Bliss
Publisher: name: University of Glasgow
Year: 2021
Subjects: subject: Cardiac cells, electrophysiology, myocytes, fibroblasts, HEK cells, hiPSC cells, muscle contraction, intercell connections.

description: The heart is arguably the most important organ in the body. It works tirelessly every minute of our lifespan, supplying blood throughout the body, with maximum efficiency. The heart is composed of a large number of distinct cell phenotypes that are coupled together and interacting via a complex system of electrical and mechanical processes. The work in this thesis explores the interactions between cardiac cells, and how these interactions and connections impact both the mechanical and electrical behaviour of the heart. Specifically, novel results on three distinct research projects are presented. Firstly, a mathematical model of contractile units, coupled in series and suspended between two springs, is constructed. This was done to investigate a problem posed by experiments, in which monolayers of cardiomyocytes were cultured onto substrates with a range of stiffnesses. It was discovered that the stiffness of the substrate impacts the nature of the contraction in the cells. In particular, on soft substrates, like a flexible hydrogel, the cells can contract freely with a regular motion. However, if the substrate is stiff, like glass or plastic, multi-peaked behaviour in the recorded motion of the cells appears. The mathematical model of this system confirms that the substrate stiffness is in fact the cause of the multiple peaks in the contraction profiles, but also highlights that when many contractile units are coupled in a chain the contraction of the unit is dependent on its position within the chain. The second piece of research presented coupled electrophysiology models of cardiomyocytes and fibroblasts. This work explores action potential propagation as a function of the fundamental patterns of fibroblast density that appear in fibrotic regions, and how these patterns and the fibroblast density can result in the failure of the action potential propagation. Primary action potential biomarkers including: conduction velocity, peak potential and triangulation index are estimated from direct numerical simulations. Through these simulations, it is shown that the action potential propagation is blocked by the fibroblast density and the pattern of their distribution. This work also investigates how these results are affected by the differentiation between fibroblasts and myofibroblasts. Furthermore, the asymptotic separation of fast and slow time scales, that are typical in electrophysiological models, is exploited to estimate the threshold number of fibroblasts per myocyte that will allow propagation. The final research project explores a problem presented by experiments which co-cultured human induced pluripotent stem cell derived cardiomyocytes (hiPSC-CM) with human embryonic kidney cells (HEK cells). In particular, this work addresses the question of, if the cells were cultured together and the HEK cells were expressing the inward rectifying current, can the spontaneous activity of the hiPSC-CM be suppressed? To this end, a novel model of the HEK cellelectrophysiology was coupled with an electrophysiology model of the hiPSC-CMs. This workshows that the coupling of the cells can cause the spontaneous nature of the hiPSC-CM to fail ashypothesised in the original experiments. Specifically, coupling the cardiomyocytes with HEK cells that are expressing the inward rectifying current, IK1, increases the time between individual action potentials, known as the cycle length, in comparison to the system with wild type HEK cells coupled with the cardiomyocytes. Also, the spontaneous activity is stopped entirely when sodium current of the cardiomyocytes is adjusted. The ultimate aim of this work is to outline the significance of intercell interactions that ap-pear in cardiac tissue and that these interactions must be considered to properly model cardiacbehaviour. As well as elucidating significant details of cell behaviour, all three pieces of workshow that if these interactions are imbalanced, the primary function of action potential propaga-tion or muscle contraction can be affected to the extent of failing to perform.