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C Michler,
A N Cookson, R Chabiniok,
E Hyde,
J Lee,
M Sinclair,
T Sochi,
A Goyal,
G Vigueras,
D A Nordsletten,
N P Smith
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ABSTRACT: We present a method to efficiently simulate coronary perfusion in subject-specific models of the heart within clinically relevant time frames. Perfusion is modelled as a Darcy porous-media flow, where the permeability tensor is derived from homogenization of an explicit anatomical representation of the vasculature. To account for the disparity in length scales present in the vascular network, in this study, this approach is further refined through the implementation of a multi-compartment medium where each compartment encapsulates the spatial scales in a certain range by using an effective permeability tensor. Neighbouring compartments then communicate through distributed sources and sinks, acting as volume fluxes. Although elegant from a modelling perspective, the full multi-compartment Darcy system is computationally expensive to solve. We therefore enhance computational efficiency of this model by reducing the N-compartment system of Darcy equations to N pressure equations, and N subsequent projection problems to recover the Darcy velocity. The resulting 'reduced' Darcy formulation leads to a dramatic reduction in algebraic-system size and is therefore computationally cheaper to solve than the full multi-compartment Darcy system. A comparison of the reduced and the full formulation in terms of solution time and memory usage clearly highlights the superior performance of the reduced formulation. Moreover, the implementation of flux and, specifically, impermeable boundary conditions on arbitrarily curved boundaries such as epicardium and endocardium is straightforward in contrast to the full Darcy formulation. Finally, to demonstrate the applicability of our methodology to a personalized model and its solvability in clinically relevant time frames, we simulate perfusion in a subject-specific model of the left ventricle. Copyright © 2012 John Wiley & Sons, Ltd.
International journal for numerical methods in biomedical engineering. 10/2012;
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ABSTRACT: The strong coupling between the flow in coronary vessels and the mechanical deformation of the myocardial tissue is a central feature of cardiac physiology and must therefore be accounted for by models of coronary perfusion. Currently available geometrically explicit vascular models fail to capture this interaction satisfactorily, are numerically intractable for whole organ simulations, and are difficult to parameterise in human contexts. To address these issues, in this study, a finite element formulation of an incompressible, poroelastic model of myocardial perfusion is presented. Using high-resolution ex vivo imaging data of the coronary tree, the permeability tensors of the porous medium were mapped onto a mesh of the corresponding left ventricular geometry. The resultant tensor field characterises not only the distinct perfusion regions that are observed in experimental data, but also the wide range of vascular length scales present in the coronary tree, through a multi-compartment porous model. Finite deformation mechanics are solved using a macroscopic constitutive law that defines the coupling between the fluid and solid phases of the porous medium. Results are presented for the perfusion of the left ventricle under passive inflation that show wall-stiffening associated with perfusion, and that show the significance of a non-hierarchical multi-compartment model within a particular perfusion territory.
Journal of biomechanics 12/2011; 45(5):850-5. · 2.66 Impact Factor
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ABSTRACT: The objective of this paper is to propose and assess an estimation procedure-based on data assimilation principles-well suited to obtain some regional values of key biophysical parameters in a beating heart model, using actual Cine-MR images. The motivation is twofold: (1) to provide an automatic tool for personalizing the characteristics of a cardiac model in order to achieve predictivity in patient-specific modeling and (2) to obtain some useful information for diagnosis purposes in the estimated quantities themselves. In order to assess the global methodology, we specifically devised an animal experiment in which a controlled infarct was produced and data acquired before and after infarction, with an estimation of regional tissue contractility-a key parameter directly affected by the pathology-performed for every measured stage. After performing a preliminary assessment of our proposed methodology using synthetic data, we then demonstrate a full-scale application by first estimating contractility values associated with 6 regions based on the AHA subdivision, before running a more detailed estimation using the actual AHA segments. The estimation results are assessed by comparison with the medical knowledge of the specific infarct, and with late enhancement MR images. We discuss their accuracy at the various subdivision levels, in the light of the inherent modeling limitations and of the intrinsic information contents featured in the data.
Biomechanics and Modeling in Mechanobiology 07/2011; 11(5):609-30. · 3.19 Impact Factor
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ABSTRACT: In this paper we apply specific data assimilation methods in order to estimate regional contractility parameters in a biomechanical
heart model, using as measurements real Cine MR images obtained in an animal experiment. We assess the effectiveness of this estimation based on independent knowledge
of the controlled infarcted condition, and on late enhancement images. Moreover, we show that the estimated contractility
values can improve the model behavior in itself, and that they can serve as an indicator of the local heart function, namely,
to assist medical diagnosis for the post-infarct detection of hypokinetic or akinetic regions in the myocardial tissue.
05/2011: pages 304-312;
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ABSTRACT: We propose a methodology for performing the estimation of a key constitutive parameter in a biomechanical heart model –namely,
the tissue contractility –using tagged-MRI data. We adopt a sequential data assimilation strategy, and the image data is
assumed to be processed in the form of deforming tag planes, which we employ to obtain a discrepancy between the model and
the data by computing distances to these surfaces. We assess our procedure using synthetic measurements produced with a model
representing an infarcted heart as observed in an animal experiment, and the estimation results are found to be of superior
accuracy compared to assimilation based on segmented endo- and epicardium surfaces.
01/1970: pages 409-417;
