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.

Keywords:

• abdominal aortic aneurysm
• stochastic model
• membrane stress variation
• confidence region