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

Abstract

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.

Optimized Hyaluronic Acid–Hydrogel Design and Culture Conditions for Preservation of Mesenchymal Stem Cell Properties

“…A rat xenograft model of AAA had previously been developed in our laboratory. 46,47 Therefore, it was important to ascertain MSC viability in dynamic culture conditions that aimed at reproducing the in vivo conditions of cells submitted to heart beat. Interestingly, Flexcell technology applied to this end revealed here that the dynamic in vitro 3D microenvironment favored MSC viability better than the static conditions.…”

The impact of personalized probabilistic wall thickness models on peak wall stress in abdominal aortic aneurysms

“…Here,̃is the correlation coefficient computed based on all adjacent tissue specimens in the dataset, and̃is an estimate for the distance between adjacent specimens. Based on the dimensions of the tensile test specimens with a length of 20 to 30 mm and a width of 8 to 10 mm, 2 estimates, 10 and 15 mm, for the average distance between 2 adjacent specimens were used to compute a correlation length according to (11). This results in 2 estimates, 20.07 and 30.10 mm for the correlation length.…”

“…In addition, many of those studies are limited to idealized geometries often in combination with elementary mathematical models for the uncertain input parameters based on random variables. Idealized arteries or aneurysm geometries in combination with parametric uncertainties such as the radius or elastic properties are studied in literature, [9][10][11][12] while Polzer et al 13 examined patient-specific AAA geometries with a random variable model for the wall thickness. To our knowledge, the study by our group 14 was the first to perform UQ in combination with 3D nonlinear patient-specific finite element models of AAAs and is also the only one considering spatially correlated uncertain quantities.…”

Parametric Stochastic Modelling of Uncertainties in the Mechanical Study of the Abdominal Aneurysm Aorta

“…Accordingly, it was assumed that the shape of aneurysms is a "parabolic-exponential" function (Elger et al, 1996;Rodriguez et al, 2008, Mohand-Kaci et al, 2011 depending on diameter and length measurements so that the mechanical problem can be solved analytically. Then, in order to investigate the influence of parametric random uncertainty on the growth of AAAs, experimental measurements performed in laboratory were used.…”