Abstract:

Regular activation of the heart originates from cyclic spontaneous depolarisations of sinoatrial node cells (SANCs). Variations in electrolyte levels, commonly observed in haemodialysis (HD) patients, and the autonomic nervous system (ANS) profoundly affect the SANC function. Thus we investigated the effects of hypocalcaemia and sympathetic stimulation on the SANC beating rate (BR). The β-adrenergic receptor (β-AR) signalling cascade, as described by Behar et al., was incorporated into the SANC models of Severi et al. (rabbit) and Fabbri et al. (human). Simulations were conducted across various extracellular calcium ([Ca]) (0.6-1.8 mM) and isoprenaline concentrations [ISO] (0-1000 nM) for a sufficient period of time to allow transient oscillations to equilibrate and reach a limit cycle. The β-AR cell response of the extended models was validated against new Langendorff-perfused rabbit heart experiments and literature data. The extended models revealed that decreased [Ca] necessitated an exponential-like increase in [ISO] to restore the basal BR. Specifically at 1.2 mM [Ca], the Severi and Fabbri models required 28.0 and 9.6 nM [ISO], respectively, to restore the initial BR. Further reduction in [Ca] to 0.6 mM required 170.0 and 43.6 nM [ISO] to compensate for hypocalcaemia. A sudden loss of sympathetic tone at low [Ca] resulted in a loss of automaticity within seconds. These findings suggest that hypocalcaemic bradycardia can be compensated for by an elevated sympathetic tone. The integration of the β-AR pathways led to a logarithmic BR increase and offers insights into potential pathomechanisms underlying sudden cardiac death (SCD) in HD patients. KEY POINTS: We extended the sinoatrial node cell (SANC) models of Severi et al. (rabbit) and Fabbri et al. (human) using the β-adrenergic receptor (β-AR) signalling cascade Behar et al. described. Simulations were conducted across various extracellular calcium ([Ca]) (0.6-1.8 mM) and isoprenaline concentrations [ISO] (0-1000 nM) to reflect conditions in haemodialysis (HD) patients. An exponential-like increase in [ISO] compensated for hypocalcaemia-induced bradycardia in both models, whereas interspecies differences increased the sensitivity of the extended Fabbri model towards hypocalcaemia and increased sympathetic tone. The extended models may help to further understand the pathomechanisms of several cardiovascular diseases affecting pacemaking, such as the high occurrence of sudden cardiac death (SCD) in chronic kidney disease (CKD) patients.

Abstract:

Since the turn of the millennium, computational modelling of biological systems has evolved remarkably and sees matured use spanning basic and clinical research. While the topic of the peri-millennial debate about the virtues and limitations of 'reductionism and integrationism' seems less controversial today, a new apparent dichotomy dominates discussions: mechanistic vs. data-driven modelling. In light of this distinction, we provide an overview of recent achievements and new challenges with a focus on the cardiovascular system. Attention has shifted from generating a universal model of the human to either models of individual humans (digital twins) or entire cohorts of models representative of clinical populations to enable in silico clinical trials. Disease-specific parameterisation, inter-individual and intra-individual variability, uncertainty quantification as well as interoperable, standardised, and quality-controlled data are important issues today, which call for open tools, data and metadata standards, as well as strong community interactions. The quantitative, biophysical, and highly controlled approach provided by in silico methods has become an integral part of physiological and medical research. In silico methods have the potential to accelerate future progress also in the fields of integrated multi-physics modelling, multi-scale models, virtual cohort studies, and machine learning beyond what is feasible today. In fact, mechanistic and data-driven modelling can complement each other synergistically and fuel tomorrow's artificial intelligence applications to further our understanding of physiology and disease mechanisms, to generate new hypotheses and assess their plausibility, and thus to contribute to the evolution of preventive, diagnostic, and therapeutic approaches.

Abstract:

Background: Computer models for simulating cardiac electrophysiology are valuable tools for research and clinical applications. Traditional reaction-diffusion (RD) models used for these purposes are computationally expensive. While eikonal models offer a faster alternative, they are not well-suited to study cardiac arrhythmias driven by reentrant activity. The present work extends the diffusion-reaction eikonal alternant model (DREAM), incorporating conduction velocity (CV) restitution for simulating complex cardiac arrhythmias. Methods: The DREAM modifies the fast iterative method to model cyclical behavior, dynamic boundary conditions, and frequency-dependent anisotropic CV. Additionally, the model alternates with an approximated RD model, using a detailed ionic model for the reaction term and a triple-Gaussian to approximate the diffusion term. The DREAM and monodomain models were compared, simulating reentries in 2D manifolds with different resolutions. Results: The DREAM produced similar results across all resolutions, while experiments with the monodomain model failed at lower resolutions. CV restitution curves obtained using the DREAM closely approximated those produced by the monodomain simulations. Reentry in 2D slabs yielded similar results in vulnerable window and mean reentry duration for low CV in both models. In the left atrium, most inducing points identified by the DREAM were also present in the high-resolution monodomain model. DREAM's reentry simulations on meshes with an average edge length of 1600$\mu$m were 40x faster than monodomain simulations at 200$\mu$m. Conclusion: This work establishes the mathematical foundation for using the accelerated DREAM simulation method for cardiac electrophysiology. Cardiac research applications are enabled by a publicly available implementation in the openCARP simulator.