Mustapha Zidi

Characterization of arterial wall mechanical behavior and stresses from human clinical data

This paper demonstrates the feasibility of material identification and wall stress computation for human common carotid arteries based on non-invasive in vivo clinical data: dynamical intraluminal pressure measured by applanation tonometry, and medial diameter and intimal-medial thickness measured by high-resolution ultrasound echotracking. The mechanical behavior was quantified assuming an axially pre-stretched, thick-walled, cylindrical artery subjected to dynamical blood pressure and perivascular constraints. The wall was further assumed to be three-dimensional and to consist of a nonlinear, hyperelastic, anisotropic, incompressible material with smooth muscle activity and residual stresses. Mechanical contributions by individual constituents--an elastin-dominated matrix, collagen fibers, and vascular smooth muscle--were accounted for using a previously proposed microstructurally motivated constitutive relation. The in vivo boundary value problem was solved semi-analytically to compute the inner pressure during a mean cardiac cycle. Using a nonlinear least-squares method, optimal model parameters were determined by minimizing differences between computed and measured inner pressures over a mean cardiac cycle. The fit-to-data from two healthy patients was very good and the predicted radial, circumferential, and axial stretch and stress fields were sensible. Hence, the proposed approach was able to identify complex geometric and material parameters directly from non-invasive in vivo human data.

Multiaxial Mechanical Characteristics of Carotid Plaque Analysis by Multiarray Echotracking System

Background and Purpose— Carotid plaque rupture depends on the various types of mechanical stresses. Our objective was to determine the multiaxial mechanical characteristics of atherosclerotic plaque and adjacent segment of the common carotid artery. Methods— A novel noninvasive echotracking system was used to measure intima-media thickness, diameter, pulsatile strain, and distensibility at 128 sites on a 4-cm long common carotid artery segment. The study included 62 patients with recent cerebrovascular ischemic event and either a plaque on the far wall of common carotid artery (n=25) or no plaque (n=37). Results— The mechanical characteristics of the carotid segment devoid of plaque did not differ between the two groups. Among patients with plaque, 16 had a larger radial strain at the level of plaque than at the level of adjacent common carotid artery (pattern A: outward-bending strain). The eight patients who had an opposite pattern (inward-bending strain) were more often dyslipidemic (100% versus 56% P=0.03) and type 2 diabetic (63% versus 12%, P=0.04) than pattern A patients. Strain gradient significantly decreased in parallel with the presence of dyslipidemia and/or type 2 diabetes. Longitudinal gradients of distensibility and Youngs elastic modulus were consistent with strain gradients. Conclusions— Type 2 diabetes and dyslipidemia were associated with a stiffer carotid at the level of the plaque than in the adjacent common carotid artery leading to an inward-bending stress. The analysis of plaque mechanics along the longitudinal axis may afford useful information, because repetitive bending strain of an atherosclerotic plaque may fatigue the wall material and result in plaque rupture.

A theoretical model of the effect of continuum damage on a bone adaptation model

Throughout life, bone is continuously turning over by the well-regulated processes of bone formation and resorption. Everyday activities damage bone, and this damage is normally repaired in a continuous remodelling process. When an imbalance in this remodelling process occurs, bones may become more susceptible to fracture. This paper is devoted to a theoretical modelling of the competition between damage and internal remodelling in bones. The general theory of adaptive damaged-elastic materials proposed here as a model for the physiological process of damaged-bone remodelling follows the general framework of continuum thermodynamics where new damaged-bone remodelling law and associated thermodynamical restrictions are stated, and specialized to the case of small strain in isothermal processes. An attempt is also made to derive: (a) the damage force (adaptive damage energy release rate ) which controls the microcracks propagation and arrest, and (b) the damage rule by introducing damage thresholds and loading/unloading conditions.

Carotid Plaque, Arterial Stiffness Gradient, and Remodeling in Hypertension

The analysis of plaque mechanics along the longitudinal axis (bending strain) may provide useful information because repetitive bending strain of an atherosclerotic plaque can fatigue the wall material and result in plaque rupture. Whether essential hypertension is associated with a specific pattern of bending strain has not yet been determined. The study included 92 patients with an atherosclerotic plaque on the common carotid artery: 66 patients with essential hypertension, either treated or not, and 26 normotensive patients. A novel noninvasive echotracking system (ArtLab; Esaote, The Netherlands) was used to measure intima-media thickness, diameter, and distensibility at 128 sites on a 4-cm-long carotid segment. Carotid plaque was either less elastic than adjacent carotid artery (inward strain) or more elastic (outward strain). Inward strain was more frequently associated with an inward plaque remodeling, whereas an outward strain was more frequently associated with an outer remodeling. In multivariate logistic regression analysis, patients with essential hypertension were more likely to exhibit an inward strain of carotid plaque (odds ratio=6.9 [1.4 to 34.9]; P<0.02), independently of 2 factors favoring inward strain: an outer remodeling (odds ratio=4.6 [1.7 to 13.4]; P<0.005) and the absence of renin-angiotensin system blockers (odds ratio=4.8 [1.1 to 20.4]; P<0.05). In conclusion, arterial wall material of hypertensive patients was less elastic at the site of the plaque than upstream, and carotid was inwardly strained in the zone affected by plaque. This may generate a high level of stress concentrations and fatigue, exposing the plaque to a greater risk of rupture.

Mechanical analysis of a prototype of small diameter vascular prosthesis: numerical simulations.

This paper concerns a mechanical analysis of a prototype of a small diameter vascular prosthesis made of a fibre reinforcement silicone material. The theoretical approach is carried out for a neoHookean strain energy function augmented with unidirectional reinforcing that is characterized by a single additional constitutive parameter for strength of reinforcement. Numerical simulations based on a finite element model compare the compliance of different grafts and predict the degree of the compliance mismatch in an anastomosis between native artery and vascular prosthesis. Furthermore, specific applied strains on the prototype, viewed as arising surgical manipulation and implying telescopic shear have been simulated. Thus, for different fibre reinforcements, the stress gradient through the wall of the tubular structure is evaluated.

Bone remodeling theory applied to the study of n unit-elements model.

The aim of this paper is to illustrate the application of mathematical tools for the analysis of non-linear dynamical systems to the study of global stability of one kind of bone remodeling scheme applied to n unit-elements model. The particular aspects analyzed here are the stationary states related to this theory and a condition of their stability. The non-linear equations governing the remodeling process are solved by finite-difference method and the well-known results on the heterogeneous spatial organizations have been retrieved and confirm the analytical study. This kind of remodeling theory is useful for investigating the effects of physiological parameters on the development, maintenance, and adaptation of bone under mechanical loading.

Finite deformations of a hyperelastic, compressible and fibre reinforced tube

Abstract Finite torsion and axial stretch of a long, hyperelastic, compressible and circular tube is studied for the design of a prototype of small diameter vascular prosthesis. The analysis is carried out in the context of the finite elasticity theory by using a class of Ogden strain energy function augmented with unidirectional reinforcing that is characterized by a single additional constitutive parameter for strength of reinforcement. The highly non-linear differential equations with variable coefficients governing the problem are solved numerically using a Runge–Kutta method. For different prestresses supported by the tube, the effects of the combined deformation on the stress distributions are presented.

Finite torsion and anti-plane shear of a compressible hyperelastic and transversely isotropic tube

Abstract In this paper, the combined finite torsion and anti-plane shear of a compressible hyperelastic and transversely isotropic hollow cylinder is studied. The analysis is carried out for a class of Blatz–Ko response augmented with unidirectional reinforcing and the governing non-linear equations are solved numerically. The transverse isotropy direction is considered helical and inhomogeneous. The results compared to the isotropic case are then presented and discussed.

Stochastic modelling of wall stresses in abdominal aortic aneurysms treated by a gene therapy

A stochastic mechanical model using the membrane theory was used to simulate the in vivo mechanical behaviour of abdominal aortic aneurysms (AAAs) in order to compute the wall stresses after stabilisation by gene therapy. For that, both length and diameter of AAAs rats were measured during their expansion. Four groups of animals, control and treated by an endovascular gene therapy during 3 or 28 days were included. The mechanical problem was solved analytically using the geometric parameters and assuming the shape of aneurysms by a ‘parabolic–exponential curve’. When compared to controls, stress variations in the wall of AAAs for treated arteries during 28 days decreased, while they were nearly constant at day 3. The measured geometric parameters of AAAs were then investigated using probability density functions (pdf) attributed to every random variable. Different trials were useful to define a reliable confidence region in which the probability to have a realisation is equal to 99%. The results demonstrated that the error in the estimation of the stresses can be greater than 28% when parameters uncertainties are not considered in the modelling. The relevance of the proposed approach for the study of AAA growth may be studied further and extended to other treatments aimed at stabilisation AAAs, using biotherapies and pharmacological approaches.

Bone remodeling regulation under unloading conditions: Numerical investigations

The present paper addresses the following question: can a simple regulatory bone remodeling model predict effects of unloading conditions on the trabecular bone morphology? In an attempt to answer this question, rat tail-suspension was chosen as a model that mimics the microgravity environment. Over 23 days, histomorphometric analysis was carried out on cross-sections of tibias of the suspended animals. The slices were digitalized and images discretized to obtain osteocyte distribution and apparent bone density. Based on these experimental data, finite element simulations were conducted to evaluate the bone loss and the change in trabecular architecture similar to those observed after a spaceflight. The numerical model is driven by a remodeling law that takes into account the nonuniform osteocyte distribution that may itself provide mechanoreception. We used the bone density rate of change from the remodeling theory and a time stepping algorithm witch are implemented in a finite element software. This approach takes into account the unloading effects on bone remodeling process and permits to confront experimental and numerical data. We showed that there is a good agreement between these data, particularly at the beginning of the simulated bone mass loss during the rat tail-suspension experiment. Indeed, we obtained a variation of 5.25% at day 7 (D7), 2.09% at day 13 (D13) and finally, 51.03% at day 23 (D23). Despite that last variation, the proposed theoretical model can be suitable to simulate the alteration of bone mineral density under the specific unloading conditions of the rat tail-suspension model.