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WIREs Syst Biol Med
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Measurement and modeling of coronary blood flow

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Ischemic heart disease that comprises both coronary artery disease and microvascular disease is the single greatest cause of death globally. In this context, enhancing our understanding of the interaction of coronary structure and function is not only fundamental for advancing basic physiology but also crucial for identifying new targets for treating these diseases. A central challenge for understanding coronary blood flow is that coronary structure and function exhibit different behaviors across a range of spatial and temporal scales. While experimental studies have sought to understand this feature by isolating specific mechanisms, in tandem, computational modeling is increasingly also providing a unique framework to integrate mechanistic behaviors across different scales. In addition, clinical methods for assessing coronary disease severity are continuously being informed and updated by findings in basic physiology. Coupling these technologies, computational modeling of the coronary circulation is emerging as a bridge between the experimental and clinical domains, providing a framework to integrate imaging and measurements from multiple sources with mathematical descriptions of governing physical laws. State‐of‐the‐art computational modeling is being used to combine mechanistic models with data to provide new insight into coronary physiology, optimization of medical technologies, and new applications to guide clinical practice. WIREs Syst Biol Med 2015, 7:335–356. doi: 10.1002/wsbm.1309 This article is categorized under: Analytical and Computational Methods > Computational Methods Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models
Pressure and velocity signals averaged over nine heart beats (top) acquired from a healthy human subject. The six major forward and backward waves associated with changes in coronary pressure are highlighted, where compression and expansion waves are due to an increase and a decrease in pressure, respectively. The filled waves reflect flow acceleration whereas the empty waves represent flow deceleration. Note also that the first wave is often undetectable due to its low amplitude. AV = aortic valve; LV = left ventricle.
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Coronary computed tomography angiography (CCTA) (upper right) and quantitative coronary angiography (lower right) demonstrate a >50% stenosis and 62% stenosis, respectively. Computed FFR (FFRCT) produces a nonfunctionally significant value of 0.87, confirmed by a measured fractional flow reserve (FFR) of 0.86. (Reprinted with permission from Ref under the terms of the Creative Commons Attribution Noncommercial License. Copyright 2013 Wiley)
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The coupled one‐dimensional (1D) poroelastic model of Lee et al., with vasculature reconstructed from a porcine arterial network imaged using a cryomicrotome. The epicardial vessels branch into transmural vessels which are seen penetrating the left ventricle (LV) myocardium, the domain of which is represented by a hexahedral finite‐element mesh (faint white lines). The terminating arterioles are coupled with a hyperporoelastic domain within the LV mesh, which during systolic contraction causes physiological flow reversal in the explicit arterioles.
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Image (a) shows a cross section of a porcine heart imaged with a cryomicrotome including a segmentation of the left coronary artery (LCA) tree (red), microspheres (green), and LCA myocardial boundary (gray). Image (b) shows the fed volume territories assigned to each of the terminal vessels in the network, used to define outlet boundary conditions in a Poiseuille model which was compared to microsphere distribution. There is a noticeably higher density of vessels and corresponding fed volume territories in the subendocardium compared to the subepicardium. Note that the colors in the right image do not represent values and are intended only to distinguish neighboring fed volume territories (Reprinted with permission from Ref . Copyright 2015 Springer).
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Illustration of the multiscale homogenization process for anatomical vascular data. (a) Porcine left coronary artery network as extracted from cryomicrotome images. This network is partitioned into a discrete proximal portion (b) and three distinct compartmental sets of vessels of varying scale (c). Each set of vessels is processed to produce spatially varying and scale‐dependent continuum model parameter fields (d).
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On the left is a simulation of contrast agent (CA) transport in a porcine left ventricle using a flow field derived from the multicompartment Darcy model. The CA concentration is sampled in the three‐slice protocol typical of clinical perfusion imaging, as marked on the cross‐section below. In the upper‐left region of the top two slices is an area of very low concentration, indicating the presence of a regional perfusion defect. On the right are two simulated time series for CA concentration for both a blood‐bound and a freely diffusive CA, with total signal (black), fluid signal (light gray) and tissue signal (dark gray) shown. The freely diffusive CA signal is asymmetric and has a much longer tail due to the storage of CA in the tissue, which only slowly diffuses back into the fluid, consistent with physiological signals.
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An example of quantitative analysis of transmural perfusion gradients (TPGs) from short‐axis perfusion magnetic resonance (MR) images. Apical, midventricular, and basal perfusion images are shown left‐to‐right (top) at peak enhancement during first pass of gadolinium. The asterisks indicate a subendocardial perfusion defect in the inferior segments (no ischemia was seen on the apical slice in this case). Data are sampled in the radial direction starting from the 0° position, clockwise. Gradientogram plots (bottom) segmented on a 15% threshold showing green areas of inducible TPG corresponding to areas of subendocardial ischemia in the corresponding to the above MR images. The angular position is represented on the y‐axis. The time axis represents the evolution of the TPG from the signal intensity upslope in the left ventricle (T‐onset) to the 15 following dynamic images (T‐onset + 5 second). (Reprinted with permission from Ref . Copyright 2013 Elsevier)
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Physiology > Mammalian Physiology in Health and Disease
Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models
Analytical and Computational Methods > Computational Methods

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