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Research Papers

Are Geometrical and Structural Variations Along the Length of the Aorta Governed by a Principle of “Optimal Mechanical Operation”?

[+] Author and Article Information
Alexander Rachev

Biomedical Engineering Program,
College of Engineering and Computing,
University of South Carolina,
Columbia, SC 29208

Stephen Greenwald

Pathology Group,
Blizard Institute,
Barts and The London School of Medicine and Dentistry,
Queen Mary University of London,
London E1 2ES, UK

Tarek Shazly

Biomedical Engineering Program,
College of Engineering and Computing,
University of South Carolina,
Columbia, SC 29208;
Mechanical Engineering Department,
College of Engineering and Computing,
University of South Carolina,
Columbia, SC 29208

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received October 18, 2012; final manuscript received May 21, 2013; accepted manuscript posted May 29, 2013; published online June 12, 2013. Assoc. Editor: Hai-Chao Han.

J Biomech Eng 135(8), 081006 (Jun 12, 2013) (9 pages) Paper No: BIO-12-1494; doi: 10.1115/1.4024664 History: Received October 18, 2012; Revised May 21, 2013; Accepted May 29, 2013

It is well-documented that the geometrical dimensions, the longitudinal stretch ratio in situ, certain structural mechanical descriptors such as compliance and pressure-diameter moduli, as well as the mass fractions of structural constituents, vary along the length of the descending aorta. The origins of and possible interrelations among these observed variations remain open questions. The central premise of this study is that having considered the variation of the deformed inner diameter, axial stretch ratio, and area compliance along the aorta to be governed by the systemic requirements for flow distribution and reduction of cardiac preload, the zero-stress state geometry and mass fractions of the basic structural constituents of aortic tissue meet a principle of optimal mechanical operation. The principle manifests as a uniform distribution of the circumferential stress in the aortic wall that ensures effective bearing of the physiological load and a favorable mechanical environment for mechanosensitive vascular smooth muscle cells. A mathematical model is proposed and inverse boundary value problems are solved for the equations that follow from finite elasticity, structure-based constitutive modeling within constrained mixture theory, and stress-induced control of aortic homeostasis, mediated by the synthetic activity of vascular smooth muscle cells. Published experimental data are used to illustrate the predictive power of the proposed model. The results obtained are in agreement with published experimental data and support the proposed principle of optimal mechanical operation for the descending aorta.

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Figures

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Fig. 1

Schematic representation of the arterial cross section (a) at the zero-stress state and (b) at a deformed state

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Fig. 2

(a) Schematic of the longitudinal segmentation of the aorta and (b) a free-body diagram of adjacent segments

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Fig. 3

Prescribed model parameters along the length of the aorta include the (a) vessel area compliance, (b) deformed inner radius, and (c) axial stretch ratio

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Fig. 4

Theoretical predictions of the zero-stress configuration along the length of the aorta include (a) the wall thickness, (b) radius of the inner arc length, and (c) opening angle. The predicted values of the opening angle show reasonable although statistically insignificant correlation with experimental data, with r = 0.74 and t-value = 1.66 (tcritical = 2.35).

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Fig. 5

Predicted and experimental values for (a) the deformed vessel thickness at physiological loading and (b) the vessel mass per unit length for each segment of the aorta. The theoretical predictions are well correlated with the experimental data, with r = 0.90 and 0.97 for the thickness and mass, respectively, and t-value > tcritical in both cases.

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Fig. 6

Predicted and experimental values for the wet mass fractions of (a) collagen, (b) elastin, and (c) smooth muscle cells along the length of the aorta. Theoretical predictions agree well with experimental data, with r = 0.85, 0.99, and 0.92 for collagen, elastin, and smooth muscle mass fractions, respectively, and t-value > tcritical in all cases.

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Fig. 7

(a) Predicted nonequilibrated axial force and (b) Peterson's modulus at physiological loading along the length of the aorta

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