An analysis of deformation‐dependent electromechanical coupling in the mouse heart

The amount of force generated by heart cells is strongly influenced by feedback from the deformation of cardiac tissue, both from the changes in cell length and the rate at which cells are stretched. We analysed the effect these cellular mechanisms have on whole heart function by making a computational model of mouse heart cells, and embedding this cellular model into a representation of the heart. Unlike previous murine models, this model represents the heart at both body temperature and the high heart rates seen in these animals, allowing us to directly compare results from our computational model with experimental measurements. Results show that effects from the rate of stretch are especially important for explaining the large differences observed between force generated by isolated cells and pressure measured experimentally. The model also provides an important framework for future research focused on interpreting results from genetic manipulation experiments in mice. Abstract To investigate the effects of the coupling between excitation and contraction on whole-organ function, we have developed a novel biophysically based multiscale electromechanical model of the murine heart. Through comparison with a comprehensive in vivo experimental data set, we show good agreement with pressure and volume measurements at both physiological temperatures and physiological pacing frequencies. This whole-organ model was used to investigate the effects of material and haemodynamic properties introduced at the tissue level, as well as emergent function of our novel cell contraction model. Through a comprehensive sensitivity analysis at both the cellular and whole organ level, we demonstrate the sensitivity of the model's results to its parameters and the constraining effect of experimental data. These results demonstrate the fundamental importance of length- and velocity-dependent feedback to the cellular scale for whole-organ function, and we show that a strong velocity dependence of tension is essential for explaining the differences between measured single cell tension and whole-organ pressure transients. Tension generated by cardiac myocytes is known to be influenced by both strain and strain rate at the single cell level. These feedback mechanisms are of key importance in analysing how tension generated at the cellular level gives rise to ventricular pressure. However, the underlying mechanisms leading to these dependencies remain debated. The length dependence of cardiac cells produces an increase in tension at high sarcomere length, resulting from both a change in maximum force attributed to filament overlap, and a change in calcium sensitivity. Changes in lattice spacing, titin-based effects, and effects on sensitivity from weakly or strongly bound crossbridges have all been proposed as potential mechanisms for this length-dependent change in tension, but as of yet no full explanation is available (Campbell, 2011). The dependence of tension on velocity involves at least two different processes, known as the B process and the C process, which work on different time scales to affect the crossbridge cycle. However, the response of tension to strain rate is complex (Kawai & Brandt, 1980), and the mechanistic effects controversial, with both an increase and decrease in the rate of strongly to weakly bound crossbridges with respect to strain rate having been proposed to explain this process (Yadid & Landesberg, 2010; Palmer, 2010). These complex cellular and genetic mechanisms which determine the coupled electrical and mechanical behaviour of the heart are increasingly being investigated in experimental models which exploit the opportunities provided by genetic manipulation (Andersson et al. 2009; Lee et al. 2010). The mouse is the most commonly used species in such research, with hundreds of inbred or genetically engineered strains often being specifically developed to elucidate particular aspects of biochemistry and physiology across a wide range of functions in both normal and disease models (Skarnes et al. 2011). It is in this data-rich context that computational models provide a unique way of analysing this data by quantitatively characterising complex phenotypes and developing a rational framework for mechanistically linking measurements to function. However, even though electromechanical models have been used to investigate the mechanisms of cardiac contraction in a variety of animals (Campbell et al. 2008; Niederer & Smith, 2009; Kerckhofs et al. 2010; Keldermann et al. 2010), such a model of a mouse heart with the ability to interpret experimental data does not yet exist. Furthermore, both electrophysiological and contraction models are often based on data obtained across a range of species and temperatures. This heterogeneous source of data underpinning the parameter sets of many electromechanical models creates significant limitations in the move towards the application of models in both wet-lab and clinical settings (Niederer et al. 2009). An electromechanical model of the mouse thus provides an important opportunity in moving beyond these limitations, integrating the data which is increasingly becoming available in both normal and transgenic mice, and using it towards a better quantitative understanding of cardiac function, both specifically in this common experimental model, and ultimately in other species. The lack of species and body temperature consistent models is indicative of challenges in identifying model parameters from cell data. many contraction experiments are at temperatures et al. or in which are known to affect results et al. tension at the cellular level is seen in tissue, and of in of calcium (Campbell, which is not well These with single cell data the of length- and velocity-dependent feedback on cellular mechanisms for whole organ function, as effects be to This in to the that experimental and measurements are often focused on the of particular mechanisms as for a computational model. are also significant differences between single cell tension and ventricular as single cell tension to be with to the pressure transients. 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