Hydrokinetic approach to large-scale cardiovascular blood flow
Introduction
The human cardiovascular system is a very complex physiological network: blood is pumped by the heart through the large arteries to the smaller diameter arterioles, then through capillaries and eventually to the venules, where the deoxygenated blood is passed through veins back to the heart, imposing a circular pattern through the whole body. Atherosclerosis is the most common cardiovascular disease, primarily affecting the arterial blood vessels; the resulting coronary heart disease is the most common cause of mortality and morbidity in developed countries, responsible for ∼35% of annual deaths, about half of which occur suddenly and with no prior symptoms [1]. Although the development of atherosclerosis depends on the presence of systemic risk factors, such as high cholesterol, diabetes and high blood pressure, the clinical manifestations of the disease – heart attack, sudden coronary death and angina pectoris – are focal, resulting from the accumulation of lipid molecules and inflammatory cells at specific locations within the wall of the coronary arteries. Prior research, observational in vitro and in vivo, has found that the foci of atherosclerosis appear in regions of disturbed blood flow, where the local endothelial shear stress (ESS) is low (<1.0 Pa) or of alternating direction [2]. Therefore, atherosclerotic lesions frequently form near arterial branches and bifurcations, where flow is always disturbed as compared to un-branched regions [3], [4]. In those sites, the endothelial cell morphology is modified in a way to favor the adhesion of leukocytes on the surface wall and the uptake of lipoproteins.
The evidence for the key role of low average ESS in the localization and progression of atherosclerosis is compelling and widely accepted [2], [3], [5], [6], although steady low ESS and oscillatory ESS with a mean close to zero seem to elicit somewhat different biological responses [7]. To date however, there is no direct method to predict the occurrence of atherosclerosis and no non-invasive method for measuring ESS in human coronary arteries in vivo. Therefore, predictions of where disease is likely to develop and what form it would take (that is, stable vs. unstable) in coronary arteries were previously limited. As previous work dating back about a decade has demonstrated [6], [8], [9], a viable alternative is offered by the combined use of 3D reconstruction techniques and fluid-dynamics simulation methods.
This work is part of a systematic effort aimed at simulating coronary endothelial shear stress using Multi-Detector Computed Tomography (MDCT). Coronary CT angiography is an emerging, non-invasive imaging modality to assess the coronary artery lumen anatomy. This technique also gives information regarding coronary wall and plaque morphology; the spatial and temporal resolution of current systems have improved from earlier technologies. Newest MDCT systems with 320-detector rows [10], [11] enable 3D acquisition of the entire coronary arterial tree in a single heart beat with radiation doses comparable to coronary catheterization.
The main objective of the computational approach to hemodynamics described below is to develop and deploy a general purpose, non-invasive, methodology to routinely study blood flow patterns in vivo in human coronary arteries. Another crucial goal is to design a non-invasive, practical tool capable of eventually determining which regions within the coronary arteries might be at risk of rapid progression to thin cap fibroatheromas and possible plaque rupture. A direct benefit of this approach would be the enhanced biomedical understanding of the causes and evolution of plaques in the body arteries, with important implications for predicting the course of atherosclerosis and possibly preventing or mediating its effects.
In a previous companion paper [12], we have discussed the main features of the code MUPHY, a general-purpose software for the simulation of complex flows. In this work, we present a major extension which allows MUPHY to incorporate the full sequence of steps entailed by a complete cardiovascular analysis of real-life patients, namely, medical data acquisition, geometry import and mesh generation, flow simulation, data analysis and visualization. The capabilities of the resulting computational tool are demonstrated through a set of large-scale simulations (performed on grids with ∼two hundred million computational cells) of the arterial tree of a real patient, involving a complex, multi-branched, geometry.
Our simulations of blood flow are based on the Lattice Boltzmann (LB) method, which is particularly efficient and flexible in handling complex arterial geometries. In the past, the LB method has been applied to a broad range of fluid-dynamic problems, including turbulence [13] and multiphase flows [14], as well as in blood-flow simulations with elastic boundaries [15], steady and pulsatile flows [16], [17], [18], [19], [20], [21] and flows with complex boundaries [22]. The joint use of simulation and imaging techniques presented here could allow to non-invasively and inexpensively screen large numbers of patients for incipient coronary disease, and to intervene at clinical level prior to the occurrence of a catastrophic event.
The rest of the paper is organized as follows: Section 2 presents the LB method as implemented here for complex flows; Section 3 discusses some details of our MUPHY code; Section 4 presents results for a real arterial tree of a patient; the final Section 5 contains some concluding remarks.
Section snippets
Lattice Boltzmann for hemodynamic flows
In the last decade, the Lattice Boltzmann (LB) method has captured increasing attention from the fluid-dynamics community as a competitive computational alternative to the discretization of the Navier–Stokes equations of continuum mechanics. LB is a minimal form of the Boltzmann kinetic equation, based on the collective dynamics of fictitious particles on the nodes of a regular lattice. The dynamics of these particles is designed in such a way as to obey the basic conservation laws ensuring
The MUPHY software
The simulation of real-life blood flows involves five basic steps:
- (1)
Acquisition of MDCT data;
- (2)
Data segmentation into a stack of slices;
- (3)
Mesh generation from the segmented slices;
- (4)
Flow simulation;
- (5)
Data analysis and visualization.
Test application
We have investigated the left and right human coronary artery systems of a number of patients. In the following, we focus on a particular left coronary system composed of a left main/LAD vessel branching into six primary vessels, labeled according to standard nomenclature as LM/LAD, LCX, RAMUS, D1, D2, D3 and D4. LM/LAD represents the longest vessel, named LM in the proximal region and LAD after the bifurcation with LCX. The LCX vessel further branches into OM1, while RAMUS further branches
Conclusions
We have presented the main aspects of the lattice kinetic approach to the computational study of large-scale cardiovascular blood flow, through the detailed illustration of the specific features of the multi-scale/physics code MUPHY. We discussed the full sequence of steps involved by the analysis of blood flow in a real-life cardiovascular case, including medical data acquisition, geometry and mesh generation, flow simulation and data analysis and visualization. We have described the design,
Acknowledgements
This work was supported by Harvard's Initiative in Innovative Computing and by the Cyber Infrastructure Laboratory of the Harvard School of Engineering and Applied Sciences. We wish to thank Michelle Borkin, Joy Sircar, Peter H. Stone, Michael Steigner for useful discussions.
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