Abstract: Previous theoretical models of arterial remodeling in response to changes in blood flow were based on the assumption that material properties of the arterial wall remain unchanged during the remodeling process. According to experimental findings, however, remodeling due to increased flow is accompanied by alteration in the structural properties of elastin, which results in a decrease in its effective elastic stiffness. To account for these effects, we propose a predictive model of arterial remodeling hypothesizing that the variation in mechanical properties of elastin is initiated and driven by the deviation of the intimal shear stress from its baseline value. Geometrical remodeling restores the wall stress distribution as it was under normal flow conditions. A constrained mixture approach is followed. Artery is modeled as a thick-walled cylindrical tube made of non-linear, elastic, anisotropic and incompressible material. Data for a rabbit thoracic aorta have been employed. At the final adapted state, the model predicts a non-monotonic dependence of arterial compliance on the magnitude of flow. This result is in agreement with available experimental data in the literature.

Abstract: Aim: It was the aim of this study to investigate the long- term effects of reduced aortic compliance on cardiovascular hemodynamics and cardiac remodeling. Method: Sixteen swine, divided into 2 groups, a control and a banding group, were instrumented for pressure and flow measurement in the ascending aorta. Teflon prosthesis was wrapped around the aortic arch in order to limit wall compliance in the banding group. Hemodynamic parameters were recorded throughout a 60-day period. After sacrifice, the mean cell surface of the left ventricle was documented. Results: Banding decreased aortic compliance by 49 +/- 9, 44 +/- 16 and 42 +/- 7% on the 2nd, 30th and 60th postoperative day, respectively (p < 0.05), while systolic pressure increased by 41 +/- 11, 30 +/- 11 and 35 +/- 12% (p < 0.05), and pulse pressure by 86 +/- 27, 76 +/- 21 and 88 +/- 23%, respectively (p < 0.01). Aortic characteristic impedance increased significantly in the banding group. Diastolic pressure, cardiac output and peripheral resistance remained unaltered. The mean left ventricular cell surface area increased significantly in the banding group. Conclusions: Acute reduction in aortic compliance results in a significant increase in characteristic and input impedance, a significant decrease in systemic arterial compliance and a subsequent increase in systolic and pulse pressures leading to left ventricular hypertrophy.

Abstract: Despite extensive attention to abdominal aortic aneurysm (AAA) in the biomedical engineering community, its effect on aortic hemodynamics and arterial wave reflection has not been addressed before. We used experimental and numerical methods, relying on a realistic AAA geometry constructed from patient computer tomography scans (CT-scans), to study this issue. Pressure and flow waves were measured and simulated before and after AAA repair, and wave reflections were analyzed using linear wave separation and wave intensity analysis. With AAA, pronounced reflections were present in the pressure and flow waveforms. The reflection coefficient measured experimentally in the upper aorta was negative with AAA (-0.10) versus 0.47 without AAA. Wave intensity analysis confirmed the presence of a backward expansion wave caused by sudden expansion of the aorta; this was absent without AAA. These results were confirmed using a 1-D numerical model. A parameter study using this model demonstrated that dominant factors are diameter and compliance of the aneurysm, with larger diameters and more compliant AAA generating more negative reflections. Finally, a preliminary noninvasive study in three patients before and after AAA repair demonstrated that AAA-repair increased the reflection coefficient. In conclusion, the presence of AAA significantly alters wave reflection and hemodynamics in the aorta, with apparently measurable effects in humans.

Abstract: BACKGROUND: With advancing age arteries stiffen, reducing arterial compliance and leading to the development of systolic hypertension and to a substantial increase in pulse pressure. An augmented pulse pressure can be a predictor of the development of hypertension, which has been linked to several cardiovascular diseases including atherosclerosis, and to pathologies such as diabetes and renal dysfunction. In this study, we tested the hypothesis that reduced wall compliance induces pulse-pressure-mediated changes in arterial wall metabolism and remodeling. METHODS: Porcine carotid arteries were perfused for 24 h using an ex vivo arterial support system. Control arteries were exposed to a pulse shear stress (6 +/- 3 dynes/cm(2)) combined with a pulse pressure of 80 +/- 10 mm Hg, yielding a physiological cyclic stretch of 4-5%. A reduced compliance group was also studied, in which arteries were wrapped with an external band, thereby decreasing cyclic stretch to levels <1%. RESULTS: The experimentally reduced compliance caused a decreased contraction capacity induced by norepinephrine(NE), and this was associated with lower levels of alpha-smooth muscle cell-actin (alpha-SMC-actin) and desmin protein expressions. Arteries that were exposed to a reduced cyclic stretch exhibited a higher level of matrix metalloproteinase-2 (MMP-2) expression activity as well as an increase in Ki67 expression, thereby suggesting that matrix degradation and cellular proliferation had been initiated. Furthermore, the expression of plasminogen activator inhibitor-1 (PAI-1) in stiffened arteries was lower than in the control arteries. CONCLUSIONS: These findings underline the importance of cyclic stretch in the maintenance of a differentiated and fully functional phenotype of vascular SMCs, as well as in the regulation of migratory properties, proliferation, and matrix turnover.

Abstract: Earlier experimental work on decellularized arteries revealed the existence of significant residual stresses within the arterial wall, which are released upon chemical removal of vascular smooth muscle in normal arteries causing substantial radial expansion. Hence, the often-used Hill's model describing active and passive stresses within the wall does not hold true, because the existence of prestresses precludes the fundamental assumption of zero active stress when the vascular smooth muscle is inactive. We have, therefore, developed a new mathematical model based on a modified Hill's model, where the total wall elastin is partitioned in two parts: one in-parallel to vascular smooth muscle and collagen and one connected in-series with vascular smooth muscle. Based on experimental evidences, compressive prestresses were assumed to exist on the parallel elastic component and tensile prestresses on the series elastic component. Further, we assumed that the elastic constants of elastin and collagen and the statistical description of collagen engagement are not affected by decellularization. Excellent fits of the pressure-diameter curves of normal and decellularized arteries were obtained. The model predicts that the majority of elastin is in-series with the vascular smooth muscle (74 +/-8%) and thus only about one-fourth of elastin acts in parallel to the vascular smooth muscle. We conclude that correct biomechanical modeling of the arterial wall requires the knowledge of the zero stress state of both the series and parallel elastic components.

Abstract: The three-dimensional biomechanical behavior of the vascular wall is best described by means of strain energy functions. Significant effort has been devoted lately in the development of structure-based models of the vascular wall, which account for the individual contribution of each major structural component (elastin, collagen, and vascular smooth muscle). However, none of the currently proposed structural models succeeded in simultaneously and accurately describing both the pressure-radius and pressure-longitudinal force curves. We have hypothesized that shortcomings of the current models are, in part, due to unaccounted anisotropic properties of elastin. We extended our previously developed biomechanical model to account for elastin anisotropy. The experimental data were obtained from inflation-extension tests on facial veins of five young white New Zealand rabbits. Tests have been carried out under a fully relaxed state of smooth muscle cells for longitudinal stretch ratios ranging from 100% to 130% of the in vivo length. The experimental data (pressure-radius, pressure-force, and zero-stress-state geometries) provided a complete biaxial mechanical characterization of rabbit facial vein and served as the basis for validating the applicability and accuracy of the new biomechanical model of the venous wall. When only the pressure-radius curves were fitted, both the anisotropic and the isotropic models gave excellent results. However, when both pressure-radius and pressure-force curves are simultaneously fitted, the model with isotropic elastin shows an average weighted residual sum of squares of 8.94 and 23.9 in the outer radius and axial force, respectively, as compared to averages of 6.07 and 4.00, when anisotropic elastin is considered. Both the Alkaike information criterion and Schwartz criterion show that the model with the anisotropic elastin is more successful in predicting the data for a wide range of longitudinal stretch ratios. We conclude that anisotropic description of elastin is required for a full 3D characterization of the biomechanics of the venous wall.

Abstract: Lumped-parameter models are used to estimate the global arterial properties by fitting the model to measured (aortic) pressure and flow. Different model configurations coexist, and it is still an open question as to which model optimally reflects the arterial tree and leads to correct estimates of arterial properties. An assessment was made of the performance of (a) the three-element Windkessel model (WK3) consisting of vascular resistance R, total arterial compliance C, and characteristic impedance Zc; (b) a four-element model with an inertance element L placed in parallel with Zc (WK4-p); and (c) a four-element model with L placed in series with Zc (WK4-s). Models were fitted to data measured non-invasively in 2404 healthy subjects, aged between 35 and 55 years. It was found that model performance segregated into two groups. In a group containing 20 per cent of the dataset (characterized by low blood pressure and wave reflection) the WK4-p model outperformed the other models, with model behaviour as envisioned by its promoters. In these cases, the WK3 and WK4-s models led to increased overestimation of total arterial compliance and underestimation of characteristic impedance. However, in about 80 per cent of the cases, the WK4-p model showed a behaviour that was very similar to that of the WK3 and WK4-s models. Here, the WK4-s model yielded the best quality of fit, although model parameters reached physically impossible values for L in about 12 per cent of all cases. The debate about which lumped-parameter model is the better approximation of the arterial tree is therefore still not fully resolved.

Abstract: Central aortic pressure gives better insight into ventriculo-arterial coupling and better prognosis of cardiovascular complications than peripheral pressures. Therefore transfer functions (TF), reconstructing aortic pressure from peripheral pressures, are of great interest. Generalized TFs (GTF) give useful results, especially in larger study populations, but detailed information on aortic pressure might be improved by individualization of the TF. We found earlier that the time delay, representing the travel time of the pressure wave between measurement site and aorta is the main determinant of the TF. Therefore, we hypothesized that the TF might be individualized (ITF) using this time delay. In a group of 50 patients at rest, aged 28-66 yr (43 men), undergoing diagnostic angiography, ascending aortic pressure was 119 +/- 20/70 +/- 9 mmHg (systolic/diastolic). Brachial pressure, almost simultaneously measured using catheter pullback, was 131 +/- 18/67 +/- 9 mmHg. We obtained brachial-to-aorta ITFs using time delays optimized for the individual and a GTF using averaged delay. With the use of ITFs, reconstructed aortic pressure was 121 +/- 19/69 +/- 9 mmHg and the root mean square error (RMSE), as measure of difference in wave shape, was 4.1 +/- 2.0 mmHg. With the use of the GTF, reconstructed pressure was 122 +/- 19/69 +/- 9 mmHg and RMSE 4.4 +/- 2.0 mmHg. The augmentation index (AI) of the measured aortic pressure was 26 +/- 13%, and with ITF and GTF the AIs were 28 +/- 12% and 30 +/- 11%, respectively. Details of the wave shape were reproduced slightly better with ITF but not significantly, thus individualization of pressure transfer is not effective in resting patients.

Abstract: Stiffening of the aorta with progressing age leads to decrease of aortic compliance and thus to an increase of pulse pressure amplitude. Using a strain energy function (SEF) which takes into account the composition of the arterial wall, we have studied the evolution of key structural components of the human thoracic aorta using data obtained from the literature. The SEF takes into account the wavy nature of collagen, which upon gradual inflation of the blood vessel is assumed to straighten out and become engaged in bearing load. The engagement of the individual fibers is assumed to be distributed log-logistically. The use of a SEF enables the consideration of axial stretch (lambda(z)) and residual strain (opening angle) in the biomechanical analysis. Both lambda(z) and opening angle are known to change with age. Results obtained from applying the SEF to the measurements of aortic pressure-diameter curves indicate that the changes in aortic biomechanics with progressing age are not to be sought in the elastic constants of elastin and collagen or their volume fractions of the aortic wall but moreover in alterations of the collagen mesh arrangement and the waviness of the collagen fibers. In old subjects, the collagen fiber ensemble engages in load bearing much more abruptly than in young subjects. Reasons for this change in collagen fiber dynamics may include fiber waviness remodeling or cross-linkage by advanced glycation end-products (AGE). The abruptness of collagen fiber engagement is also the model parameter that is most responsible for the decreased compliance at progressed ages.

Abstract: Hypertension-induced arterial remodeling has been previously modeled using stress-driven remodeling rate equations in terms of global geometrical adaptation (Rachev A, Stergiopulos N, Meister JJ. Theoretical study of dynamics of arterial wall remodeling in response to changes in blood pressure. J Biomech 29: 635-642, 1996) and was extended later to include adaptation of material properties (Rachev A, Stergiopulos N, Meister JJ. A model for geometric and mechanical adaptation of arteries to sustained hypertension. J Biomech Eng 120: 9-17, 1998). These models, however, used a phenomenological strain energy function (SEF), the parameters of which do not bear a clear physiological meaning. Here, we extend the work of Rachev et al. (1998) by applying similar remodeling rate equations to a constituent-based SEF. The new SEF includes a statistical description for collagen engagement, and remodeling now affects material properties only through changes in the collagen engagement probability density function. The model predicts asymptotic wall thickening and unchanged deformed inner radius as to conserve hoop stress and intimal shear stress, respectively, at the final adapted hypertensive state. Mechanical adaptation serves to restore arterial compliance to control levels. Average circumferential stress-strain curves show that the material at the final adapted hypertensive state is softer than its normotensive counterpart. These findings as well as the predicted pressure-diameter curves are in good qualitative agreement with experimental data. The novelty in our findings is that biomechanical adaptation leading to maintenance of compliance at the hypertensive state can be perfectly achieved by appropriate readjustment of the collagen engagement profile alone.