A computational model of the coronary circulation

Nick Hill (University of Glasgow)

Friday 13th May, 2022 14:15-15:00 Maths 311B AND ZOOM


We investigate the relationship between coronary arterial and venous flow and pressure. Arterial and venous network morphometries are key haemodynamic determinants, as is the external pressure that compresses the vasculature during systole [3].

We present a computationally efficient coronary haemodynamic model using a structured tree and cross-sectionally averaged 1D flow.

This model can be implemented using only measured data. The vasculature is modelled in three compartments: large arteries, large veins, and vascular beds. The governing equations for fluid flow in large vessels are solved using a two-step LaxWendroff scheme. Large arteries and veins are joined together via a vascular bed that is modelled using a structured tree (a two-sided self-similar diverging and converging binary tree).

The structured trees provide the boundary matching condition used to join the arterial and venous sides. This choice of boundary matching condition allows for the propagation of pulse waves from the arterial to venous sides. Simulation of flow throughout a vascular network requires the specification of a network.

The networks are built using a single data set using a radius-based truncation condition. The vessel radius at which a tree is truncated governs the number of large vessels, and hence the overall network volume. Truncated trees can be thought of as sub-trees of the complete network. The impact of network morphometry on simulation results is investigated by simulating flow in several trees of varying truncation radius.

We simulate haemodynamic flows in the porcine coronary and human pulmonary circulatory systems including the external pressure imposed on the vasculature by the moving tissues. The imposition of external pressure impacts simulated flow rates.

The simulated flow changes in this model are similar to those seen in the literature, e.g. [1, 2]; that is, compressive external pressures restrict downstream flow, whereas expansive forces increase upstream flow.

By comparing simulation results from several generated coronary arterial networks, we show that network morphometry is an important determinant of overall hemodynamics. Further, we investigate the trade-off between network fidelity and flow throughout the network. Vasodilation studies are commonly used to evaluate the function of the coronary microcirculation of, and its relation to blood flow. This is of clinical interest as microcirculatory function is vital to perfusion of the myocardium.

The effect of myocardial infarction on perfusion is useful to model mathematically; as this has the potential for great impact.


This work was funded by the U.K. Engineering and Physical Sciences Research Council (Grant No. EP/N014642/1).


[1] R. B. Clipp and B. N. Steele, IEEE transactions on biomedical engineering, 56, 862–870, 2008.

[2] J. P. Mynard and P. Nithiarasu, Communications in numerical methods in engineering, 24, 367–417, 2008.

[3] T. Ramanathan and H. Skinner, Continuing Education in Anaesthesia, Critical Care and Pain, 5, 61–64, 2005.

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