Towards a Patient Specific Computational Model of Coronary Flow, Myocardial Perfusion, and Ventricular Mechanics

Abstract

Coronary artery diseases (CAD) constitute a global burden in terms of both health and economic impact. With significantly higher spatio-temporal resolution, contrast agent (CA) enhanced magnetic resonance imaging (MRI) of myocardial perfusion is a safe technique for diagnosing CAD such as coronary arteries stenosis and microvascular disease. In clinical practice, interpretation of coronary perfusion MRI is mostly qualitative, relying on an experienced operator to identify true perfusion defects. In this thesis, a new computational framework is created towards a feasible patient-specific quantitative analysis of myocardial blood flow in MR myocardial perfusion imaging.
This framework consists of three parts. The principal mechanics model is developed based on the poromechanics theory considering the porous medium (myocardium) as the superposition of two continua (tissue and blood) that move with distinct kinematics, coupled with the scalar transport (advection and diffusion) of CA. The Lagrangian formulations are derived and applied to all the constitutive equations. The mechanics model is solved by finite element method within FEniCS Python library. Moreover, an iterative regularisation algorithm is developed to inversely estimate the permeability of a porous medium based on the observed CA concentration. It employs the adjoint equation to efficiently compute the gradient of the objective function that has a large degrees of freedom within Python library dolfin-adjoint. Finally, a modified MRI simulator MRXCAT is integrated into the framework to generate synthetic MR perfusion images, which transfers the CA concentration field into the MR signal intensity.
The results of the iterative regularisation algorithm tested on a 2D Darcy’s flow show that this algorithm can estimate the heterogeneous permeability with acceptable error. Also, its sensitivity study indicates that this method works for different Peclet number without requiring high observation frequency of CA concentration. Secondly, the mechanics model is implemented on a cuboid geometry to study the effect on active contraction, passive swelling and the corresponding porosity change. Its sensitivity study suggests that the CA parameters such as Damkohler number and Peclet number have to be chosen to avoid the range that produces non-monotonic behaviour. Additionally, the max upslope of the concentration is a better choice than peak value for quantifying perfusion capability. In the end, the model is implemented on an ellipsoid geometry with realistic myo-fibre orientation and boundary conditions. The results show that the coronary arteries stenosis and microvascular disease can be simulated in terms of both CA concentration and synthetic MRI signal, although the parameter study suggests a slightly different monotonicity. In general, this new pipeline, which generates synthetic MR perfusion images based on physiological parameters and poromechanics theory, with the aid of the inverse method for estimating patient-specific parameters, can provide a novel approach to quantifying MR perfusion images.

Date of Award	18 Feb 2026
Original language	English
Awarding Institution	University of Bath
Supervisor	Andrew Cookson (Supervisor), Katharine Fraser (Supervisor) & Richie Gill (Supervisor)