What can modelling provide to cardiac physiology?

Indicative perhaps of the fundamentally integrative nature of physiological research is that, as an academic subject, it is inherently interdisciplinary. This interdisciplinarity and the scientific collaboration that it necessitates spans a wide range of multi-modal experimental techniques that are now deployed with the goal of providing mechanistic insight into physiological systems. One of these approaches, and arguably most promising for gaining a comprehensive understanding of the cardiovascular system, is mechanistic multi-scale computational modelling. The Journal of Physiology has a long history of publishing studies by innovators who have successfully used mathematical and computational models to provide new quantitative and mechanistic interpretations of physiological measurements. Seminal examples of modelling frameworks that remain in use today are the oxygen diffusion models proposed by Krogh (1919) and the nerve impulse model of Hodgkin & Huxley (1952), a framework which has been subsequently pioneered by Noble and co-workers (2012) to understand cardiac repolarisation. However, as both the measurement and modelling techniques have progressed in sophistication it is becoming increasingly challenging for single research groups, let alone individuals, to apply both approaches to complex biomedical problems. This situation thus requires not only technical collaboration, but also a scientific appreciation of the opportunities and limitations of both experimental measurement and numerical modelling techniques by the authors, reviewers and readers of scientific publications. The experimental wet lab community has an established culture of critiquing physiological data and the methods used to acquire them. Similarly, the academic branch of numerical analysis has a significant history in applying techniques to test if sets of mathematical equations are indeed being solved correctly. However, in part due to the relative novelty of computational physiology, a key challenge at the experimental–modelling interface is validating and justifying embedded parameters that are used to predict complex physiological behaviour. Key to addressing these issues are a number of important and largely complementary priorities that are now receiving the attention of the modelling community. These include the clear articulation of methods used to extract parameters from data so that the model provides a framework whereby parameter values and initial and boundary conditions predict a physiological response. In similar fashion, this is the same way a parameter extraction process (which is in turn also a model although it is rarely framed as such) uses data to predict a parameter value. Understanding the sensitivity and robustness of this process and the relevance of the information (e.g. species, temperature, measurement method) for the resulting model is key to understanding the potential limitations of the final predictions. Related to this issue of parameterisation is the development and application of methods to test if the complexity of a model can be justified by the available data – key information for assessing the predictive capacity of a modelling framework. Finally, and of particular importance for the modelling work within this journal, is the development and focusing of models that can facilitate our understanding of complex behaviour by giving mechanistic insight, and in so doing generate new hypotheses that can be experimentally validated. The genesis of this special issue of The Journal of Physiology was at the Cardiac Physiome Workshop held in Oxford in July 2011, where many of these issues were discussed and research across the modelling–experimental spectrum presented. The studies within this special issue collectively provide a summary of a number of the research highlights presented at this meeting, which spanned spatial, temporal and functional scales of the heart. Furthermore, and of particular importance for their publication within The Journal of Physiology, they also provide an exciting set of examples of the current state-of-the-art of physiologically driven modelling. Key to this work is that, rather than developing models as ends in themselves, each of these studies uses modelling as a tool to enhance our understanding of physiological data. It is this approach, supported by robust data driven parameterisations, that will be essential to the on-going success of research that integrates experimental and modelling techniques. At the subcellular level Hake et al. (2012) have developed a detailed computational framework of a cardiac calcium spark based on a three-dimensional reconstruction of electron tomography data. In a related study also analysing calcium handing Livshitz et al. (2012) use a computational model, together with experimental data, to define the subcellular T-space compartment and provide a theoretical basis for estimating dynamic calcium concentration in this compartment under different conditions of calcium loading. Investigating the effects of individual L-type calcium channels, Ryu et al. (2012) and Morotti et al. (2012) both integrate channel models into whole cell electrophysiological frameworks in the rabbit and human respectively. Continuing this progression in scale, whole cellular models are also developed and applied, again in the rabbit and human, respectively, by Severi et al. (2012) and Kharche et al. (2012) who focus on understanding integrated electrophysiologically driven cardiac pacemaking. These types of cellular frameworks are further applied at the whole organ scale by both Bishop & Plank (2012) and Rantner et al. (2012) to predict the effects of whole organ structure in arrhythmia and defibrillation. Land et al. (2012) combine this type of activation model with cellular and whole organ mechanics models fitted at multiple scales to a specific mouse strains. Working on rat mechanics Valdez-Jasso et al. (2012) perform a series of biaxial mechanical experiments to determine the, often overlooked, constitutive properties of the right ventricular myocardium. Rouillard et al. (2012) integrate mechanical effects from a different perspective developing and validating against data an agent-based computational model of infarct healing. Focusing on addressing issues surrounding metabolic function Han et al. (2012) report on an integrated experimental-modelling approach to analysing the coupling between mechanics and heat generated during contraction. Finally, the study from Rolandi et al. (2012) completes this issue by distinguishing the combined effects of metabolic vascular control and extravascular compression on coronary resistance in the human heart. We thank the authors for their exemplars that have illustrated this approach.