Special issue on reduced order modelling for cardiovascular problems

Abstract

Reduced-order models of blood flow in the cardiovascular system are simplified versions of three-dimensional models in which the simulated haemodynamic quantities are not a function of three spatial dimensions, but only one (onedimensional models) or none (zero-dimensional or lumped parameter models). 1 Such models produce considerable reductions in computational cost, often without a significant loss of accuracy. This special issue contains seven invited papers on the application of reduced-order modelling to several cardiovascular conditions: coronary heart disease, hypertension, pregnancy complications, and respiratory function. With these clinically relevant applications, the collection shows the ability of reduced-order modelling to complement in vivo experiments by overcoming their practical and/or ethical limitations, providing a platform for in silico experimentation and a tool with great potential for diagnostic purposes and clinical decision making.A major strength of reduced-order modelling is its usefulness in gaining insights into complex processes and interactions in the cardiovascular system, where such insights would be difficult or impossible to obtain (practically and/or ethically) with in vivo experiments. Several papers in this special issue provide examples of such investigations. Abdullateef et al. 2 explored the impact of arterial tapering on wave reflection, which has relevance to the ageing aorta that dilates unequally along its length (leading to an approximate doubling of tapering angle from ages 20 to 70 years). It was concluded that wave reflections arising from tapering augment peak and pulse pressure, thus forming another deleterious effect of aortic dilation due to fragmentation of elastic fibres, aside from reduced arterial compliance. Zhang et al. 3 investigated complex haemodynamic interactions in the setting of dextro-transposition of the great arteries (d-TGA). Using a reduced-order model of the foetal circulation, they investigated the effects of ductus arteriosus constriction and restrictive foramen ovale on pulmonary arterial pressures and pulmonary/mitral valve function, which may play a role in poor outcomes in a subset of d-TGA cases.Aside from the complexity of blood flow dynamics from a biomechanical point of view, another layer of important physiological complexity arises from regulatory processes. In this regard, Fernandes et al. 4 provided major enhancements to a lumped parameter cardiovascular model by incorporating gas transport and cardiorespiratory regulation. The major receptors and afferent pathways were modelled, including the arterial baroreflex, pulmonary stretch receptors, and central and peripheral chemoreceptors, where the latter was linked to O 2 and CO 2 saturations arising from the haemodynamic and gas transport parts of the model. These drove sympathetic and parasympathetic activation, which in turn regulated key aspects of cardiovascular state (unstressed venous volume, cardiac contractility, heart rate, and peripheral resistance, including regional...