Quantification of regional differences in aortic stiffness in the aging human

Abstract

There has been a growing awareness over the past decade that stiffening of the aorta, and its attendant effects on hemodynamics, is both an indicator and initiator of diverse cardiovascular, neurovascular, and renovascular diseases. Although different clinical metrics of arterial stiffness have been proposed and found useful in particular situations, there remains a need to understand better the complex interactions between evolving aortic stiffness and the hemodynamics. Computational fluid-solid-interaction (FSI) models are amongst the most promising means to understand such interactions for one can parametrically examine effects of regional variations in material properties and arterial geometry on local and systemic blood pressure and flow. Such models will not only increase our understanding, they will also serve as important steps towards the development of fluid-solid-growth (FSG) models that can further examine interactions between the evolving wall mechanics and hemodynamics that lead to arterial adaptations or disease progression over long periods. In this paper, we present a consistent quantification and comparison of regional nonlinear biaxial mechanical properties of the human aorta based on 19 data sets available in the literature and we calculate associated values of linearized stiffness over the cardiac cycle that are useful for initial large-scale FSI and FSG simulations. It is shown, however, that there is considerable variability amongst the available data and consequently that there is a pressing need for more standardized biaxial testing of the human aorta to collect data as a function of both location and age, particularly for young healthy individuals who serve as essential controls.

Keywords: Distensibility; Elastic modulus; Fluid–solid-interaction; Material properties; Strain; Stress.

Copyright © 2013 Elsevier Ltd. All rights reserved.

Figures

Fig. 1

Schema showing the three in vivo configurations used in our calculation of blood pressure, mean wall stresses, linearized stiffness, and distensibility: an in vivo reference configuration defined near mean arterial pressure and at the in vivo axial stretch as well as configurations defined at end diastole and end systole, also at the in vivo axial stretch. Note, therefore, that the linearization is about an intermediate configuration during the cardiac cycle (cf. Baek et al., 2007). Also shown are constituent-specific natural (stress-free) configurations and the associated deposition stretches that place stressed constituents into the in vivo reference configuration, which allows it to be a useful stressed reference (Cardamone et al., 2009).

Fig. 2

Representative biaxial Cauchy stress–stretch data recreated for five different stress-controlled loading protocols (different paired symbols) and the associated best-fit (solid lines) by the four-fiber family constitutive model. These results were obtained by first generating data using previously reported nonlinear constitutive relations and associated best-fit parameters regardless of the type of experiment (e.g., uniaxial or biaxial) or constitutive relation used in the original paper. The upper two panels ((a) and (b)) show results for the 20–35 year old age group reported by García-Herrera et al. (2012) whereas the lower two panels ((c) and (d)) show results for the 57–71 year old age group reported by Labrosse et al. (2009), both for the descending thoracic aorta. The predicted loss of extensibility with aging was expected. The excellent fit by the four-fiber family model likely resulted, in part, because the data were generated from reported exponential-type constitutive relations.

Fig. 3

Cauchy stress–stretch responses during simulated equibiaxial stress-controlled loading protocols for the 19 different cases (i.e., aortic locations and age groups) studied herein (cf. Table 1). Left and right panels represent circumferential and axial behaviors, respectively, for the ascending thoracic aorta (ATA), descending thoracic aorta (DTA), and infrarenal abdominal aorta (IAA). Results were based on findings reported in the following six papers: Garcia-Herrera et al. (inverted triangle), Haskett et al. (diamond), Labrosse et al. (triangle), Martin et al. (×), Vande Geest et al. (square), and Vorp et al. (asterisk). With the exception of the single data sets from Martin et al. and Vorp et al. (shown by the × and asterisk), results for young groups are denoted by filled black symbols, results for middle aged groups by filled gray symbols, and results for older groups by open symbols. Of particular note is the biaxial stiffening of the DTA with aging that is revealed by the Garcíla-Herrera et al. (2012) data and also the excellent correspondence between the García-Herrera et al. (2012) and Labrosse et al. (2009) data for the middle aged DTA group despite the use of different experimental methods and constitutive models by these investigators. Results of Vande Geest et al. (2004) for the aging abdominal aorta similarly reveal a stiffening effect with aging as expected. Finally, note that a small black star at the top of a curve denotes those data sets that appear to be most reliable overall, consistent with those values that are found bold face in Tables 1 and 2.

Fig. 4

Calculated linearized stiffness as a function of location along the aortic tree (ATA, DTA, and IAA) and age (cf. Table 2). Top: light gray and white bars represent, respectively, the mean values of circumferential and axial stiffness (in MPa) based on all 19 results considered. Bottom: Black and dark gray bars represent values of circumferential and axial stiffness (in MPa) that appear to be most reliable based on relative comparisons of the stress–stretch results from which they were obtained (cf. Fig. 3) and their correspondence with associated calculations of distensibility (cf. Fig. 6).

Fig. 5

In vivo values of inner radius, ratio of inner radius to wall thickness, and blood pressure plotted as a function of age (cf. Table 3). Geometric data correspond to mean arterial pressure and are shown as closed black symbols: squares for the ascending thoracic aorta (ATA), circles for the proximal descending thoracic aorta (DTA), and triangles for the infrarenal abdominal aorta (IAA). Values for pressure are shown at systole, mean arterial pressure, and diastole. The lines show linear regressions of each data set. As expected, the data suggest an increase in caliber and pressure with age, but not a strong trend across the three aortic locations regarding the inner radius:wall thickness (a/h), a term that appears in both the Laplace equation for mean circumferential wall stress and the Moens–Korteweg formula for pulse wave velocity.

Fig. 6

Distensibility plotted as a function of age for the ascending thoracic aorta (top), descending thoracic aorta (middle), and the infrarenal abdominal aorta (bottom). Measured values mined from the literature are denoted by closed circles, with the solid line showing the associated linear regression of the data and the grey region the 95% confidence intervals. Calculated values based on the nonlinear constitutive model are denoted as follows: Garcia-Herrera et al. (open inverted triangle), Haskett et al. (open diamond), Labrosse et al. (open triangle), Martin et al. (×), Vande Geest et al. (open square), and Vorp et al. (asterisk). Note, in particular, the unexpected near constancy of predictions based on the Haskett et al. data, particularly for the DTA and IAA, which similar to observations based on the predicted stress–stretch responses (Fig. 3) suggests that these results must be considered suspect.

Fig. 7

Values of the mean (i.e., transmural average) circumferential (i.e., hoop) and axial Cauchy stresses calculated at mean arterial pressure (MAP) and the in vivo axial stretch shown as a function of location (ascending thoracic aorta, ATA; descending thoracic aorta, DTA; infrarenal abdominal Aorta, IAA) and age. Also shown is the associated ratio of these two components of stress. All results were determined using data in Table 1 and A1–A3