An augmented iterative method for identifying a stress-free reference configuration in image-based biomechanical modeling

Abstract

augmented iterative method for identifying a stress-free reference configuration in image-based biomechanical modeling. Journal of Biomechanics, Elsevier, 2017, 58, pp.227 -231 AbstractContinuing advances in computational power and methods have enabled image-based biomechanical modeling to become a crucial tool in basic science, diagnostic and therapeutic medicine, and medical device design. One of the many challenges of this approach, however, is the identification of a stress-free reference configuration based on in vivo images of loaded and often prestressed or residually stressed soft tissues and organs. Fortunately, iterative methods have been proposed to solve this inverse problem, among them Sellier's method. This method is particularly appealing for it is easy to implement, convergences reasonably fast, and can be coupled to nearly any finite element package. However, by means of several practical examples, we demonstrate that in its original formulation Sellier's method is not optimally fast and may not converge for problems with large deformations. Fortunately, we can also show that a simple, inexpensive augmentation of Sellier's method based on Aitken's delta-squared process can not only ensure convergence but also significantly accelerate the method.

Efficient estimation of personalized biventricular mechanical function employing gradient‐based optimization

“…Among the most simplest ones is the backward displacement method that can also be used to incorporate residual stresses into the finite element models by simulating tissue growth . Nevertheless, this inverse problem (of finding the unloaded geometry) has been shown to produce nonunique solutions, especially when buckling is present, although relaxation techniques can be used to improve convergence and stability . For the case of a biventricular geometry, buckling may occur due to the thin RVFW and a high RV pressure.…”

“…55 Nevertheless, this inverse problem (of finding the unloaded geometry) has been shown to produce nonunique solutions, especially when buckling is present, 52 although relaxation techniques can be used to improve convergence and stability. 56 For the case of a biventricular geometry, buckling may occur due to the thin RVFW and a high RV pressure. For this reason, we choose a simpler approach to estimate the unloaded configuration.…”

A machine learning approach as a surrogate of finite element analysis–based inverse method to estimate the zero‐pressure geometry of human thoracic aorta

“…In the literature, several methods are available to estimate zero‐pressure organ geometries. These methods usually take as input a loaded geometry reconstructed from in vivo images and assume the material properties are known, then either (1) estimate the zero‐pressure geometry by adjusting a candidate geometry and running forward finite element (FE) simulations, or (2) estimate the prestress/prestrain field on the loaded configuration, which can be used to back out the zero‐pressure geometry (eg, by depressurizing the FE model), or (3) estimate the zero‐pressure geometry and the prestress field using an inverse FE formulation . All of these methods rely on FEA and most of them require many iterations of FE simulations, which makes these methods very time‐consuming and inefficient.…”

“…8,9 Such 3D-printed models, if built with accurate zero-pressure geometries, would enable more realistic in vitro simulation platforms for preoperative planning, such as in vitro simulation of transcatheter aortic valve replacement. 8 In the literature, several methods [10][11][12][13][14][15][16][17][18][19][20] are available to estimate zero-pressure organ geometries. These methods usually take as input a loaded geometry reconstructed from in vivo images and assume the material properties are known, then either (1) estimate the zero-pressure geometry 10,14,[16][17][18]20 by adjusting a candidate geometry and running forward finite element (FE) simulations, or (2) estimate the prestress/prestrain field on the loaded configuration, 12,13,15,19,21 which can be used to back out the zero-pressure geometry (eg, by depressurizing the FE model), or (3) estimate the zero-pressure geometry and the prestress field using an inverse FE formulation.…”

Cardiac Displacement Tracking with Data Assimilation Combining a Biomechanical Model and an Automatic Contour Detection

“…The myocardial fiber directions τ are prescribed analytically at each integration point of the volume mesh according to a rule-based criterion with the elevation angle being -60 / 60 degrees for the LV (from epicardium to endocardium) and -75/75 degrees for RV. Note that defining the reference configuration from an initial geometry can be improved by solving a static mechanical equilibrium involving the passive constitutive law and an internal ventricular pressure, see [15] and references therein.…”