Inverse modelling of image-based patient-specific blood vessels: zero-pressure geometry andin vivostress incorporation

Abstract

Abstract.In vivo visualization of cardiovascular structures is possible using medical images. However, one has to realize that the resulting 3D geometries correspond to in vivo conditions. This entails an internal stress state to be present in the in vivo measured geometry of e.g. a blood vessel due to the presence of the blood pressure. In order to correct for this in vivo stress, this paper presents an inverse method to restore the original zero-pressure geometry of a structure, and to recover the in vivo stress field of the final, loaded structure. The proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations, but can be significantly accelerated by a quasiNewton technique in which a least-squares model is used to approximate the inverse of the Jacobian. The here proposed backward displacement method allows for a straightforward implementation of the algorithm in combination with existing structural solvers, even if the structural solver is a black box, as only an update of the coordinates of the mesh needs to be performed.Mathematics Subject Classification. 65D18, 74L15, 49Q10, 65N21, 90C53.

An Animal-Specific FSI Model of the Abdominal Aorta in Anesthetized Mice

“…Solid mechanics could provide another approach to explain branch-related ruptures as the mechanical tension exerted on the tunica media is expected to be elevated near branch bifurcations. Both CFD (Computational Fluid Dynamics to simulate the flow field in a model with rigid walls) and CSM (Computational Solid Mechanics to simulate the wall stress without accounting for the fluid domain) have been used to study arterial fluid dynamics [5][6][7][8][9][10][11][12][13] and solid mechanics [14][15][16] in normal [7][8][9][10][11][12][14][15][16] and aneurysmatic [5,6,13] mice. However, the appropriate pressure and shear distribution as a function of time are essential inputs for a correct CSM simulation, while the inclusion of distending walls has been shown to significantly influence the calculated flow field with CFD [17].…”

An Inverse Finite Element u/p-Formulation to Predict the Unloaded State of In Vivo Biological Soft Tissues

“…11,19,22,43 The method is fully implicit thus achieving quadratic convergence, while simulations require very few load steps to reach final solution compared to explicit solvers, 17 and it can run quickly since no mesh updating is required during the analysis. 2,11 Additionally, the present algorithm ensures convergence using a combination of residual and energy criterion checks. In contrast to this, existing backward incremental methods or pull-back iterative inverse approaches 7,9,33,34 are limited with respect to nodal spatial-location convergence checks.…”

“…5a and 5b, it is clearly demonstrated that the presence of the ILT layer can give different aortic-wall reference configuration predictions, hence, significantly affecting subsequent studies in rupture risk assessment and haemodynamic analysis, as also reported by various other investigators. 2,26,40 Breast Deformation…”

“…Their numerical approach was subsequently utilised for the stress analysis of patient-specific cerebral aneurysms. 43 More recently, Bols et al 2 formulated an iterative backward displacement method to recover the zero-pressure configuration of human blood vessel geometries and predict the in vivo stress distribution through a fixed-point algorithm.…”

“…42 The proposed full-implicit inverse algorithm can achieve very fast convergence-in comparison to explicit codes 17 -while simultaneously being very efficient in enforcing material incompressibility, as opposed to pure displacement based inverse formulations. 2,9,12 The proposed methodology is founded on the concept of re-parametrisation of the balance equation in the current (deformed) setting. 14 The numerical procedure assumes a non-specific constitutive description of the isochoric term, seamlessly incorporates anisotropic constitutive models, and circumvents the simplification assumptions made in previous works of discontinuous pressure across the element boundaries.…”