Pulsatile blood flow in the entire coronary arterial tree: theory and experiment

Huo, Yunlong; Kassab, Ghassan S.

doi:10.1152/ajpheart.00200.2006

Cited by 81 publications

(70 citation statements)

References 34 publications

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“…The coronary wall thickness for every order was adopted from data of Guo and Kassab (3). The static Young's modulus was calculated as ϳ7.0 ϫ 10 6 dyn/cm 2 , as described in a previous publication (7).…”

Section: Mathematical Modelmentioning

confidence: 99%

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A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree

Huo

Kassab²

2007

American Journal of Physiology-Heart and Circulatory Physiology

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Huo Y, Kassab GS. A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree. Am J Physiol Heart Circ Physiol 292: H2623-H2633, 2007. First published January 5, 2007; doi:10.1152/ajpheart.00987.2006.-Using a frequency-domain Womersley-type model, we previously simulated pulsatile blood flow throughout the coronary arterial tree. Although this model represents a good approximation for the smaller vessels, it does not take into account the nonlinear convective energy losses in larger vessels. Here, using Womersley's theory, we present a hybrid model that considers the nonlinear effects for the larger epicardial arteries while simulating the distal vessels (down to the 1st capillary segments) with the use of Womersley's Theory. The main trunk and primary branches were discretized and modeled with one-dimensional Navier-Stokes equations, while the smaller-diameter vessels were treated as Womersley-type vessels. Energy losses associated with vessel bifurcations were incorporated in the present analysis. The formulation enables prediction of impedance and pressure and pulsatile flow distribution throughout the entire coronary arterial tree down to the first capillary segments in the arrested, vasodilated state. We found that the nonlinear convective term is negligible and the loss of energy at a bifurcation is small in the larger epicardial vessels of an arrested heart. Furthermore, we found that the flow waves along the trunk or at the primary branches tend to scale (normalized with respect to their mean values) to a single curve, except for a small phase angle difference. Finally, the model predictions for the inlet pressure and flow waves are in excellent agreement with previously published experimental results. This hybrid one-dimensional/Womersley model is an efficient approach that captures the essence of the hemodynamics of a complex large-scale vascular network. The present model has numerous applications to understanding the dynamics of coronary circulation. coronary flow; pulse wave; admittance; impedance THE FLUID DYNAMIC APPROACH uses the geometry and mechanical properties of the vasculature and the principles of conservation of mass and momentum to obtain the blood flow-pressure relation. The solution of such equations yields information on instantaneous velocity and pressure distributions. The fluid dynamic approach was first formulated in 1755 by Euler. Womersley (32,33) and McDonald [as reported by Nichols and O'Rourke (22)] linearized Euler's equation and presented the theory and solution in great detail. Because of the complexity of the vascular architecture, however, this approach recognizes that it is necessary to idealize the geometry of the vasculature.The frequency-domain Womersley-type approach was recently applied to the entire coronary arterial tree down to the first segment of (arterial) capillaries in a vasodilated, potassiumarrested heart (7). Inasmuch as this approach represents a linearization of the fluid dynamic (time-domain) approach, it ign...

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Section: Mathematical Modelmentioning

confidence: 99%

“…The frequency-domain Womersley-type approach was recently applied to the entire coronary arterial tree down to the first segment of (arterial) capillaries in a vasodilated, potassiumarrested heart (7). Inasmuch as this approach represents a linearization of the fluid dynamic (time-domain) approach, it ignores higher-order nonlinear terms.…”

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confidence: 99%

A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree

Huo

Kassab²

2007

American Journal of Physiology-Heart and Circulatory Physiology

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“…Here, the flow rates were calculated based on a full coronary arterial tree haemodynamic analysis [19]. Briefly, the entire LAD, LCX and RCA trees down to the first capillary bifurcations have been reconstructed [20], based on pig morphometric data [21].…”

Section: Structure and Flow Analysismentioning

confidence: 99%

“…A search was then made to find a vessel whose diameter was the closest to the diameter of each terminal of the epicardial coronary arterial trees for animals in both high-fat diet and control groups so that the crown resistance can be pasted to the corresponding terminal. Given the resistance distal to each terminal, we computed the flow rate in each vessel of epicardial coronary arterial trees [19] and determined coefficients and exponents of function -structure scaling power laws for animals in both groups. The basic assumption is that the microvasculature distal to terminal vessels of the epicardial coronary arterial tree is anatomically unchanged in the high-fat diet group.…”

Section: Structure and Flow Analysismentioning

confidence: 99%

Computed tomography-based diagnosis of diffuse compensatory enlargement of coronary arteries using scaling power laws

Huo

Choy

Wischgoll

et al. 2013

J. R. Soc. Interface.

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Glagov's positive remodelling in the early stages of coronary atherosclerosis often results in plaque rupture and acute events. Because positive remodelling is generally diffused along the epicardial coronary arterial tree, it is difficult to diagnose non-invasively. Hence, the objective of the study is to assess the use of scaling power law for the diagnosis of positive remodelling of coronary arteries based on computed tomography (CT) images. Epicardial coronary arterial trees were reconstructed from CT scans of six Ossabaw pigs fed on a high-fat, high-cholesterol, atherogenic diet for eight months as well as the same number of body-weight-matched farm pigs fed on a lean chow (101.9 + 16.1 versus 91.5 + 13.1 kg). The high-fat diet Ossabaw pig model showed diffuse positive remodelling of epicardial coronary arteries. Good fit of measured coronary data to the length-volume scaling power lawc ; where L c and V c are crown length and volume) were found for both the high-fat and control groups (R 2 ¼ 0.95 + 0.04 and 0.99 + 0.01, respectively). The coefficient, K LV , decreased significantly in the high-fat diet group when compared with the control (14.6 + 2.6 versus 40.9 + 5.6). The flow-length scaling power law, however, was nearly unaffected by the positive remodelling. The length-volume and flow-length scaling power laws were preserved in epicardial coronary arterial trees after positive remodelling. K LV , 18 in the length-volume scaling relation is a good index of positive remodelling of coronary arteries. These findings provide a clinical rationale for simple, accurate and non-invasive diagnosis of positive remodelling of coronary arteries, using conventional CT scans.

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“…We thank the authors for their kind appraisal of our study (1) and appreciate the opportunity to clear up some of the misunderstandings. The model is unlike any other in that it is based on the anatomy (diameters and lengths) of the entire coronary arterial tree to the capillaries.…”

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Editorial Commentary on Pulsatile Blood Flow in the Entire Coronary Arterial Tree: Theory and Experiment

Kassab¹

2006

American Journal of Physiology-Heart and Circulatory Physiology

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.-The pulsatility of coronary circulation can be accurately simulated on the basis of the measured branching pattern, vascular geometry, and material properties of the coronary vasculature. A Womersley-type mathematical model is developed to analyze pulsatile blood flow in diastole in the absence of vessel tone in the entire coronary arterial tree on the basis of previously measured morphometric data. The model incorporates a constitutive equation of pressure and cross-section area relation based on our previous experimental data. The formulation enables the prediction of the impedance, the pressure distribution, and the pulsatile flow distribution throughout the entire coronary arterial tree. The model is validated by experimental measurements in six diastolic arrested, vasodilated porcine hearts. The agreement between theory and experiment is excellent. Furthermore, the present pulse wave results at low frequency agree very well with previously published steady-state model. Finally, the phase angle of flow is seen to decrease along the trunk of the major coronary artery and primary branches toward the capillary vessels. This study represents the first, most extensive validated analysis of Womersley-type pulse wave transmission in the entire coronary arterial tree down to the first segment of capillaries. The present model will serve to quantitatively test various hypotheses in the coronary circulation under pulsatile flow conditions. Editorial Commentary on Pulsatile Blood Flow in the Entire Coronary Arterial Tree: Theory and ExperimentTo the Editor: Rogers et al. (2) provided an editorial commentary titled "Is there a need for another model on the pulsatile nature of coronary blood flow?" We thank the authors for their kind appraisal of our study (1) and appreciate the opportunity to clear up some of the misunderstandings. The model is unlike any other in that it is based on the anatomy (diameters and lengths) of the entire coronary arterial tree to the capillaries. The authors are correct that the literature is replete with lumped models of pulsatile analysis of coronary circulation. This is not "another" model, however, in that it is a distributive model anchored on vascular geometry and branching pattern unlike the previously published lumped models of pulsatile flow analysis. Regrettably, the extensive structural basis of the model went unnoticed in this commentary.In the commentary, Rogers et al. (2) prompted, "the question that we have about such model information is the discrepancy from published results." They raise three major issues that are perceived limitations of the model that will be addressed in turn:1) For example, two studies report significant pressure losses in vessels greater than 100 -140 m in diameter, whereas one reports minimal pressure dissipation in vessels of this size. Yet the model predicts minimal pressure losses in vessels down to ϳ70 m in diameter, which is at odds with two reports.To interpret a model prediction, one must understand the context. Figure 12 of our paper (1) sho...

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Pulsatile blood flow in the entire coronary arterial tree: theory and experiment

Cited by 81 publications

References 34 publications

A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree

A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree

Computed tomography-based diagnosis of diffuse compensatory enlargement of coronary arteries using scaling power laws

Editorial Commentary on Pulsatile Blood Flow in the Entire Coronary Arterial Tree: Theory and Experiment

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