Age dependency of the biaxial biomechanical behavior of human abdominal aorta

BACKGROUND: The biomechanical behavior of the human abdominal aorta has been studied with great interest primarily due to its propensity to develop such maladies as atherosclerotic occlusive disease, dissections, and aneurysms. The purpose of this study was to investigate the age-related biaxial biomechanical behavior of human infrarenal aortic tissue. METHODS OF APPROACH: A total of 18 samples (13 autopsy, 5 organ donor) were harvested from patients in each of three age groups: Group 1 (<30 years old, n=5), Group 2 (between 30 and 60 years old, n=7), and Group 3 (>60 years old, n=6). Each specimen was tested biaxially using a tension-controlled protocol which spanned a large portion of the strain plane. Response functions fit to experimental data were used as a tool to guide the appropriate choice of the strain energy function W. RESULTS: Under an equibiaxial tension of 120 N/m, the average peak stretch values in the circumferential direction for Groups 1, 2, and 3 were (mean +/-SD) 1.46 +/- 0.07, 1.15 +/- 0.07, and 1.11 +/- 0.06, respectively, while the peak stretch values in the longitudinal direction were 1.41 +/- 0.03, 1.19 +/- 0.11, and 1.10 +/- 0.04, respectively. There were no significant differences between the average longitudinal and circumferential peak stretch within each group (p > 0.1), but both of these values were significantly less (p < 0.001) for Groups 2 and 3 when compared to Group 1. Patients in Group 1 were modeled using a polynomial strain energy function W, while patients in Groups 2 and 3 were modeled using an exponential form of W, suggesting an age-dependent shift in the mechanical response of this tissue. CONCLUSION: The biaxial tensile testing results reported here are, to our knowledge, the first given for the human infrarenal aorta and reinforce the importance of determining the functional form of W from experimental data. Such information may be useful for the clinician or researcher in identifying key changes in the biomechanical response of abdominal aorta in the presence of an aneurysm.     

The biaxial mechanical behaviour of abdominal aortic aneurysm intraluminal thrombus: Classification of morphology and the determination of layer and region specific properties

Intraluminal thrombus (ILT) is present in 75% of clinically-relevant abdominal aortic aneurysms (AAAs) yet, despite much research effort, its role in AAA biomechanics remains unclear. The aim of this work is to further evaluate the biomechanics of ILT and determine if different ILT morphologies have varying mechanical properties.     

Time-dependent biaxial mechanical behavior of the aortic heart valve leaflet

Despite continued progress in the treatment of aortic valve (AV) disease, current treatments continue to be challenged to consistently restore AV function for extended durations. Improved approaches for AV repair and replacement rests upon our ability to more fully comprehend and simulate AV function. While the elastic behavior the AV leaflet (AVL) has been previously investigated, time-dependent behaviors under physiological biaxial loading states have yet to be quantified. In the current study, we performed strain rate, creep, and stress-relaxation experiments using porcine AVL under planar biaxial stretch and loaded to physiological levels (60 N/m equi-biaxial tension), with strain rates ranging from quasi-static to physiologic. The resulting stress-strain responses were found to be independent of strain rate, as was the observed low level of hysteresis ( approximately 17%). Stress relaxation and creep results indicated that while the AVL exhibited significant stress relaxation, it exhibited negligible creep over the 3h test duration. These results are all in accordance with our previous findings for the mitral valve anterior leaflet (MVAL) [Grashow, J.S., Sacks, M.S., Liao, J., Yoganathan, A.P., 2006a. Planar biaxial creep and stress relaxatin of the mitral valve anterior leaflet. Annals of Biomedical Engineering 34 (10), 1509-1518; Grashow, J.S., Yoganathan, A.P., Sacks, M.S., 2006b. Biaxial stress-stretch behavior of the mitral valve anterior leaflet at physiologic strain rates. Annals of Biomedical Engineering 34 (2), 315-325], and support our observations that valvular tissues are functionally anisotropic, quasi-elastic biological materials. These results appear to be unique to valvular tissues, and indicate an ability to withstand loading without time-dependent effects under physiologic loading conditions. Based on a recent study that suggested valvular collagen fibrils are not intrinsically viscoelastic [Liao, J., Yang, L., Grashow, J., Sacks, M.S., 2007. The relation between collagen fibril kinematics and mechanical properties in the mitral valve anterior leaflet. Journal of Biomechanical Engineering 129 (1), 78-87], we speculate that the mechanisms underlying this quasi-elastic behavior may be attributed to inter-fibrillar structures unique to valvular tissues. These mechanisms are an important functional aspect of native valvular tissues, and are likely critical to improve our understanding of valvular disease and help guide the development of valvular tissue engineering and surgical repair.     

On parameter estimation for biaxial mechanical behavior of arteries

This article considers the parameter estimation of multi-fiber family models for biaxial mechanical behavior of passive arteries in the presence of the measurement errors. First, the uncertainty propagation due to the errors in variables has been carefully characterized using the constitutive model. Then, the parameter estimation of the artery model has been formulated into nonlinear least squares optimization with an appropriately chosen weight from the uncertainty model. The proposed technique is evaluated using multiple sets of synthesized data with fictitious measurement noises. The results of the estimation are compared with those of the conventional nonlinear least squares optimization without a proper weight factor. The proposed method significantly improves the quality of parameter estimation as the amplitude of the errors in variables becomes larger. We also investigate model selection criteria to decide the optimal number of fiber families in the multi-fiber family model with respect to the experimental data balancing between variance and bias errors.     

Altered mechanical behavior of epicardium under isothermal biaxial loading

Most soft tissues that are treated clinically via heating experience multiaxial states of stress and strain in vivo and are subject to complex constraints during treatment. Remarkably, however, there are no prior data on changes in the multiaxial mechanical behavior of a collagenous tissue subjected to isometric constraints during heating. This paper presents the first biaxial stress-stretch data on a collagenous membrane (epicardium) before and after heating while subjected to various biaxial isometric constraints. It was found that isometric heating does not allow the increase in stiffness at low strains that occurs following isotonic heating. Moreover increasing the degree of stretch prior to heating increased the thermal stability of the tissue consistent with the concept that mechanical loading primarily affects the activation entropy, not the activation energy.     

Non-linear viscoelastic behavior of abdominal aortic aneurysm thrombus

The objective of this work was to determine the linear and non-linear viscoelastic behavior of abdominal aortic aneurysm thrombus and to study the changes in mechanical properties throughout the thickness of the thrombus. Samples are gathered from thrombi of seven patients. Linear viscoelastic data from oscillatory shear experiments show that the change of properties throughout the thrombus is different for each thrombus. Furthermore the variations found within one thrombus are of the same order of magnitude as the variation between patients. To study the non-linear regime, stress relaxation experiments are performed. To describe the phenomena observed experimentally, a non-linear multimode model is presented. The parameters for this model are obtained by fitting this model successfully to the experiments. The model cannot only describe the average stress response for all thrombus samples but also the highest and lowest stress responses. To determine the influence on the wall stress of the behavior observed the model proposed needs to implemented in the finite element wall stress analysis.     

Evolving mechanical properties of a model of abdominal aortic aneurysm

The novel three-dimensional (3D) mathematical model for the development of abdominal aortic aneurysm (AAA) of Watton et al. Biomech Model Mechanobiol 3(2): 98–113, (2004) describes how changes in the micro-structure of the arterial wall lead to the development of AAA, during which collagen remodels to compensate for loss of elastin. In this paper, we examine the influence of several of the model’s material and remodelling parameters on growth rates of the AAA and compare with clinical data. Furthermore, we calculate the dynamic properties of the AAA at different stages in its development and examine the evolution of clinically measurable mechanical properties. The model predicts that the maximum diameter of the aneurysm increases exponentially and that the ratio of systolic to diastolic diameter decreases from 1.13 to 1.02 as the aneurysm develops; these predictions are consistent with physiological observations of Vardulaki et al. Br J Surg 85:1674–1680 (1998) and Lanne et al. Eur J Vasc Surg 6:178–184 (1992), respectively. We conclude that mathematical models of aneurysm growth have the potential to be useful, noninvasive diagnostic tools and thus merit further development.     

Respiratory mechanical effects of abdominal distension

We develop a theory to predict the partitioning of a change in volume of the abdominal contents into the end-expiratory volume changes of the lung, rib cage, and anterior abdominal wall. First, we calculate the distribution of such a volume change using the relative compliances of the three compartments. We then consider the inspiratory influence of abdominal pressure on the rib cage and its effect on the distribution of this volume. We test our theory by inducing gastric distension in three experienced laboratory personnel. We instilled and subsequently withdrew 1 liter of water from a gastric balloon and examined the effects of this change in gastric volume on the relaxation characteristics of the respiratory system. The distribution of the volume change that would be expected from the observed relative compliances of the three compartments would be approximately 66% into change in lung volume, 25% into change in rib cage volume, and 9% into change in abdominal volume. Instead, in line with our predictions for acute gastric distension, approximately 33% went into decrease in lung volume, 40% into increase in rib cage volume, and 26% into increase in abdominal volume. These results suggest that the interactions among the rib cage, abdomen, and diaphragm are such as to defend against large changes in end-expiratory lung volume in the face of abdominal distension.     

Mesoscopic simulations of systolic flow in the human abdominal aorta

The complex nature of blood flow in the human arterial system is still gaining more attention, as it has become clear that cardiovascular diseases localize in regions of complex geometry and complex flow fields. In this article, we demonstrate that the lattice Boltzmann method can serve as a mesoscopic computational hemodynamic solver. We argue that it may have benefits over the traditional Navier-Stokes techniques. The accuracy of the method is tested by studying time-dependent systolic flow in a 3D straight rigid tube at typical hemodynamic Reynolds and Womersley numbers as an unsteady flow benchmark. Simulation results of steady and unsteady flow in a model of the human aortic bifurcation reconstructed from magnetic resonance angiography, are presented as a typical hemodynamic application.     

Effects of hindlimb unweighting on the mechanical and structure properties of the rat abdominal aorta.

Previous studies have shown that hindlimb unweighting of rats, a model of microgravity, reduces evoked contractile tension of peripheral conduit arteries. It has been hypothesized that this diminished contractile tension is the result of alterations in the mechanical properties of these arteries (e.g., active and passive mechanics). Therefore, the purpose of this study was to determine whether the reduced contractile force of the abdominal aorta from 2-wk hindlimb-unweighted (HU) rats results from a mechanical function deficit resulting from structural vascular alterations or material property changes. Aortas were isolated from control (C) and HU rats, and vasoconstrictor responses to norepinephrine (10(-9)-10(-4) M) and AVP (10(-9)-10(-5) M) were tested in vitro. In a second series of tests, the active and passive Cauchy stress-stretch relations were determined by incrementally increasing the uniaxial displacement of the aortic rings. Maximal Cauchy stress in response to norepinephrine and AVP were less in aortic rings from HU rats. The active Cauchy stress-stretch response indicated that, although maximum stress was lower in aortas from HU rats (C, 8.1 +/- 0.2 kPa; HU, 7.0 +/- 0.4 kPa), it was achieved at a similar hoop stretch. There were also no differences in the passive Cauchy stress-stretch response or the gross vascular morphology (e.g., medial cross-sectional area: C, 0.30 +/- 0.02 mm(2); HU, 0.32 +/- 0.01 mm(2)) between groups and no differences in resting or basal vascular tone at the displacement that elicits peak developed tension between groups (resting tension: C, 1.71 +/- 0.06 g; HU, 1.78 +/- 0.14 g). These results indicate that HU does not alter the functional mechanical properties of conduit arteries. However, the significantly lower active Cauchy stress of aortas from HU rats demonstrates a true contractile deficit in these arteries.     

Determination of linear viscoelastic behavior of abdominal aortic aneurysm thrombus

The objective of this study is to determine whether the linear viscoelastic properties of an abdominal aortic aneurysm thrombus can be determined by rheometry. Although large strains occur in the in vivo situation, in this work only linear behavior is studied to show the applicability of the described methods. A thrombus exists of several layers that vary in composition, structure and mechanical properties. Two types of thrombus are described. In discrete transition thrombi the layers are not or at most weakly attached to each other and the structure of each layer is different. Continuous transition thrombi consist of strongly attached layers whose structure changes gradually throughout the thickness of the thrombus. Shear experiments are performed on samples from both types of thrombus on a rotational rheometer using a parallel plate geometry. In the discrete type the storage modulus G' cannot be assumed equal for the different layers. In the continuous thrombus, G', changes gradually throughout the layered structure. In both types the loss modulus, G', does not vary throughout the thrombus. Furthermore, it was found that Time-Temperature Superposition is applicable to thrombus tissue. Since results were reproducible it can be concluded that the method we used to determine the viscoelastic properties is applicable to thrombus tissue.     

Identification of in vivo material and geometric parameters of a human aorta: toward patient-specific modeling of abdominal aortic aneurysm

Recent advances in computational modeling of vascular adaptations and the need for their extension to patient-specific modeling have introduced new challenges to the path toward abdominal aortic aneurysm modeling. First, the fundamental assumption in adaptation models, namely the existence of vascular homeostasis in normal vessels, is not easy to implement in a vessel model built from medical images. Second, subjecting the vessel wall model to the normal pressure often makes the configuration deviate from the original geometry obtained from medical images. To address those technical challenges, in this work, we propose a two-step optimization approach; first, we estimate constitutive parameters of a healthy human aorta intrinsic to the material by using biaxial test data and a weighted nonlinear least-squares parameter estimation method; second, we estimate the distributions of wall thickness and anisotropy using a 2-D parameterization of the vessel wall surface and a global approximation scheme integrated within an optimization routine. A direct search method is implemented to solve the optimization problem. The numerical optimization method results in a considerable improvement in both satisfying homeostatic condition and minimizing the deviation of geometry from the original shape based on in vivo images. Finally, the utility of the proposed technique for patient-specific modeling is demonstrated in a simulation of an abdominal aortic aneurysm enlargement.     

Altered mechanical behavior of epicardium due to isothermal heating under biaxial isotonic loads

Recent isothermal biaxial isotonic tests suggest that increasing the temperature hastens the rate of denaturation of epicardium whereas increasing the mechanical load during heating delays this process, findings that are consistent with prior uniaxial tests on tendons. Yet, contrary to uniaxial reports, a clear time-temperature-load equivalency was not found in this multiaxial setting. There is, therefore, a need to delineate multiaxial thermomechanical behavior in greater detail, and ultimately, to correlate changes therein with the underlying microstructure. Toward this end, we describe a new experimental approach for quantifying heating-induced changes in the multiaxial mechanical response of thin sheet-like specimens. Illustrative results are presented for bovine epicardium subjected to nine different thermomechanical loading protocols. Among other results, it is shown that thermal damage tends to increase the stiffness at low strains and that overall changes in extensibility correlate well with the degree of thermal damage independent of the specific thermomechanical protocol. Multiaxial changes in behavior are nevertheless complex, and there is a need for significantly more testing before constitutive relations can be formulated.