Structural strain energy function applied to the ageing of the human aorta

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.

Arterial remodeling using a constituent-based approach

Alkiviadis Tsamis

This thesis is intended to contribute to the field of biomechanics of growth and remodeling of arteries. The work focuses particularly on growth and remodeling caused by sustained hypertension, increased blood flow, and ageing. A structure-based constitutive law is employed, which accounts for the elastic and structural properties of the components of the vascular tissue. Analysis of the biomechanical properties of the arterial wall allows for quantification of the developed wall stresses and strains. The dynamics of arterial growth and remodeling is described by appropriate remodeling rate equations. The corner-stone of this theoretical project is, of course, the development of physiologically relevant evolution laws describing the shear stress- and wall stress-induced growth and remodeling of the arterial wall. The model predictions are presented in the form of an introduction, four chapters (four papers) and a conclusion. The introduction begins with the motivation for this project. The link between mechanical load and remodeling in blood vessels follows. The state of the art on theoretical models of arterial remodeling in response to hypertension, changed flow, and ageing is also presented. The first paper presents a novel theoretical model of hypertension-induced arterial remodeling using a structure-based constitutive law. Arterial remodeling in response to sustained hypertension has been previously modeled using 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. by applying similar evolution laws to a constituent-based SEF, which includes a statistical description for collagen recruitment in load bearing. Remodeling affects the material properties only through changes in the probability density function of collagen engagement. The model simulates the remodeling of a rabbit thoracic aorta and predicts that, at the final adapted hypertensive state, the wall thickness is increased to conserve the baseline value of hoop stress and the lumen radius remains unchanged to preserve the normotensive levels of intimal shear stress. Furthermore, the remodeling of material properties serves to restore the arterial compliance to control levels. The material at the final adapted state is softer than its normotensive counterpart as indicated by the average circumferential stress-strain curves. Model predictions 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. The second paper addresses a predictive model of arterial remodeling in response to increased flow using a constituent-based SEF. Prior theoretical models of arterial remodeling in response to changes in blood flow were based on the assumption that material properties of the vascular tissue remain unchanged during the remodeling process. Experimental findings show, however, that increased flow causes structural alterations in the elastin resulting in a decrease in its effective elastic stiffness. To account for these effects, we propose a predictive model of arterial remodeling in response to increased flow hypothesizing that the deviation of the intimal shear stress from its baseline value initiates and drives the variation in the mechanical properties of elastin. The mismatch in wall stresses with respect to baseline values drives the changes in the geometrical parameters of the stress-free configuration. A constrained mixture approach is followed and the artery is modeled as a thick-walled cylindrical tube made of nonlinear, elastic, anisotropic and incompressible material. We make use of literature data for a rabbit thoracic aorta. The model predicts that, at the final adapted state, the arterial compliance depends non-monotonically on the magnitude of the flow, which is in agreement with available experimental data in the literature. The third paper expands the model of the first paper in order to include another major aspect of remodeling in a healthy matured vessel: the new mass that is produced during remodeling results from an increase in the mass of smooth muscle cells and collagen fibers. The model also takes into consideration the effect of the average pulsatile strain on collagen fiber engagement in load bearing. Remodeling of a human thoracic aorta was simulated by the model and the results agree well with published model predictions and experimental data. According to the model, the total arterial mass increases fast in the early stages of remodeling and does not vary thereafter, despite any further geometrical changes as well as structural reorganization of the collagen fibers. Furthermore, the perfect or incomplete restoration of the average pulsatile strain at the end of the remodeling process has an impact on the time course of certain parameters of the model such as the opening angle. Future experimental studies on the time variation of compliance, opening angle and mass fractions will validate and improve the introduced hypotheses of the model. In the fourth paper we perform a theoretical study of aortic remodeling in ageing using a constituent-based modeling approach. The model is based on two major hypotheses. First, mechanical fatigue failure in the elastin structure is caused by the pulsatile wall strain and the number of cardiac cycles. The fragmentation of elastin results in an increase in the inner radius at the zero-load state. Second, the accumulation of advanced glycation end products (AGEs) over time increases the cross-linking of collagen fibers making the recruitment of the fibers occur at lower strains and more abruptly. This raises the stiffness of the collagen fiber network. Furthermore, the geometrical remodeling follows the increase in the lumen radius at the load-free configuration and preserves the baseline level of circumferential stress at the inner and outer surface under mean pressure. Additionally, the geometrical changes lead to an increase in the content of collagen fibers, affecting accordingly the mass fractions of elastin and smooth muscle cells. We employ the constituent-based SEF of Zulliger and Stergiopulos in order to verify the results of their curve-fitting study on the elastic and structural properties of the human thoracic aorta. We further monitor the time variation of certain geometrical characteristics. Model results agree well with published experimental data. According to the model, the fragmentation of elastin only affects the geometrical remodeling, with the total arterial mass being increased with increased damage of elastin. With progressed age, elastin contributes less in bearing load, allowing the stiff collagen to lower the arterial compliance and cause a monotonic decrease in the pulsatile strain. Also, the accumulation of AGEs over time impacts on both the material and the geometrical parameters, with the latter being affected at high ages. The net effect is a decrease in the arterial dimensions and mass at high ages due to an increased accumulation of AGEs. Surprisingly, the time course of the mass fractions of the wall components is not affected by the increase or decrease of AGEs, indicating that the geometrical and structural reorganization of the vascular tissue is done in such a way in order to preserve the relative content of the wall constituents. There is a need for more experimental data to support the conclusions of the parametric analysis. The concluding section summarizes the main results of the thesis, presents the improvements made over previous theoretical investigations, emphasizes the need for more experimental data in order to validate and improve the models, and proposes future extensions of the work.

EPFL2010

Pressure and Flow Wave Propagation in Patient-Specific Models of the Arterial Tree

Philippe Reymond

Blood flow in the arterial circulation induces hemodynamic forces that play an important role in various forms of vascular diseases. Temporal variation of the wall shear stress seems to play a significant role in atherogenesis and plaque stability. Flow induced wall shear stress has been linked to growth and possibly rupture of the aneurysm wall. Hemodynamic forces are patient-specific and difficult to assess in the clinic. At present, there is no in vivo measurement technique that enables measurement of hemodynamic forces to the degree of precision needed. However, when imaging modalities used frequently in clinical routine re-create high-definition, patient geometric quantification of the blood vessel, they can be employed as a base for creating predictive hemodynamic models. Which in the case of understanding healthy vs. pathologic blood flow within the cerebral or systemic circulation, renders this an interesting approach. First, we developed a "generic 1D" distributed model of the human arterial tree including the primary systemic arteries and coupled this to a heart model. The fluid mechanics equations were solved numerically to obtain pressure and flow throughout the arterial tree. A nonlinear viscoelastic constitutive law for the arterial wall was considered while distal vessels were terminated with a three-element Windkessel model. The coronary arteries were modeled assuming a systolic flow impediment proportional to ventricular varying elastance. The model predictions were validated with noninvasive measurements of pressure and flow performed in young volunteers. Flow in the large arteries was visualized with magnetic resonance imaging, cerebral flow detected with ultrasound Doppler and blood pressure measured with applanation tonometry. Model predictions at different arterial locations compared well to measured flow and pressure waves at the same anatomical points. Thus, the generic 1D model reflected the flow and pressure measurements of the "average subject" of our volunteer population. Following the same approach as the generic 1D model, we built and validated a patient-specific model. In this case, geometric data, flow and pressure measurements were obtained for one person. The model predicted pressure and flow waveforms in good agreement with the in-vivo measurements with regards to wave shape and features. Comparison with a generic 1-D model has shown that the patient-specific model better predicted pressure and flow at specific arterial sites. Overall, the patient-specific 1-D model was able to predict pressure and flow waveforms in the main systemic circulation, whereas this was not always the case for a generic 1-D model. The inherent underestimation of energy losses of the 1-D wave propagation model, due to bifurcations, non-planarity and complex geometry, were examined. The 1-D model was compared to a rigid wall 3-D computational fluid dynamic model. Newtonian and non-Newtonian blood properties were studied and the longitudinal pressure distribution along the arteries was compared with the 1-D patient-specific model mean pressure prediction. The results indicated that pressure drop is significant only in small diameter vessels such as the precerebral and cerebral arteries. In these vessels the 1-D model in comparison to 3-D models consistently underestimated pressure drop. The complex flow patterns resulting from asymmetry and bifurcation yield shear stresses in the 3-D model that were greater than the 1-D model. A 3-D unsteady fluid structure interaction simulation in a patient-specific model was performed to simultaneously capture the flow details, given by the 3-D model, and wave propagation phenomena, provided by the 1-D model. The 3-D unsteady fluid structure interaction approach is the most computationally intense and cumbersome, but it allows physiological simulations with a high level of detail and accuracy. For instance, this approach could be relevant to obtain blood flow details in regions that are prone to atherosclerotic plaques or development of aneurysms. The 3-D fluid structure interaction simulation was performed for a patient-specific aorta. Important clinical parameters such as wall shear stress were quantified and significant differences were found in comparison to the rigid wall 3-D simulation indicating the relevance of a fluid structure interaction approach. A comparison of the fluid structure interaction to an equivalent 1-D model resulted in good reproduction of the pressure and flow waveforms. The effect of a decreased compliance of the arterial tree on hemodynamical parameters has been assessed with the use of a 1-D model. Local, proximal aorta and global stiffening of the arterial tree were modeled and led to two different mechanisms that contribute to the increase in central pulse pressure. They probably both contribute to systolic hypertension and their relative contribution depends on the topology of arterial stiffening and geometrical alterations taking place in aging or in disease. All these patient-specific models are about to being in use in a clinical environment and will be useful for providing better diagnostics and treatment planning in a near future.

EPFL2011

Novel non-invasive techniques for hemodynamic monitoring

Orestis Vardoulis

The monitoring of hemodynamic parameters is crucial for optimal patient management and treatment. However, established methods are often invasive and possibly inapplicable to sensitive age groups. Novel, non-invasive techniques have the potential to transform cardiovascular (CV) assessment, offering reduced hospitalization periods, lower infection risk and decreased staff-to-patient ratio. Cardiac output (CO) monitoring provides valuable insight on global tissue perfusion. To overcome limitations of traditional methods, a novel technique was proposed. Taking into account the basic principles of CV physiology we derived an equation where the required variables can be extracted non-invasively. The novel technique was validated in a controlled, in silico, environment against previously established wave analysis methods. Subsequent data analysis showed that the new method yielded superior accuracy and precision. The new method was further evaluated in vivo using a 2D transthoracic echocardiography protocol for CO estimation. The corresponding comparison showed that the SVB method provides highly reproducible and accurate estimates of CO when compared to ultrasound. The estimation of pulse transit time (PTT) affects critically the accuracy and precision of pulse wave velocity (PWV) measurements. We proposed the "Diastole-Patching" method (DPm), which estimates PTT based on a signal region in the diastolic foot of the wave and is more robust against noisy arterial waveforms. DPm and previously established techniques were tested with a computational model of the arterial tree where the "real" values of PWV are known. The novel method yielded the highest agreement, accuracy and precision even when the waves were distorted with noise. The technique was further evaluated against the corresponding â"reference" algorithm of a commercially available device with in vivo acquired waves. DPm yielded more precise and reproducible measurements of PWV. Total Systemic Compliance (CT) expresses the ability of the arterial system to dilate and store blood during cardiac ejection. Our aim was to develop a relationship between aPWV and CT. The proposed, generalized Bramwell-Hill model of the systemic arterial tree estimates CT by a single non-invasive measurement of PWV. The proposed scheme was found to accurately estimate CT from aPWV. The mechanical properties of woven Dacron grafts differ significantly from the human aorta. As a result, aortic graft implantation changes the aortic geometry and mechanical properties, thus affecting blood pressure and wave reflections. A dedicated cardiovascular model was developed to include graft geometry and in vitro measured Dacron properties. It was found that aortic reconstruction affected aortic hemodynamics. For the proximal graft, the primary reason for pulse pressure rise is augmentation of the forward wave. For the distal graft, the pulse pressure rise is associated with augmented wave reflections resulting from the compliance mismatch between the aorta and the distal graft. To conclude, this body of work has shown that given the current computational tools and biosensors, it is possible to design and validate a set of non-invasive techniques that will provide valuable clinical insight for a wide gamut of cardiovascular diseases.

EPFL2014