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Register a new userAn orthotropic electro-viscoelastic model for the heart with stress-assisted diffusion
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Added by
Ricardo Ruiz Baier I
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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We propose and analyse the properties of a new class of models for the electromechanics of cardiac tissue. The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law (this is so for both active stress and active strain formulations of active mechanics) coupled with a four-variable phenomenological model for human cardiac cell electrophysiology, which produces an accurate description of the action potential. The conductivities in the model of electric propagation are modified according to stress, inducing an additional degree of nonlinearity and anisotropy in the coupling mechanisms; and the activation model assumes a simplified stretch-calcium interaction generating active tension or active strain. The influence of the new terms in the electromechanical model is evaluated through a sensitivity analysis, and we provide numerical validation through a set of computational tests using a novel mixed-primal finite element scheme.
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In silico models of cardiac electromechanics couple together mathematical models describing different physics. One instance is represented by the model describing the generation of active force, coupled with the one of tissue mechanics. For the numerical solution of the coupled model, partitioned schemes, that foresee the sequential solution of the two subproblems, are often used. However, this approach may be unstable. For this reason, the coupled model is commonly solved as a unique system using Newton type algorithms, at the price, however, of high computational costs. In light of this motivation, in this paper we propose a new numerical scheme, that is numerically stable and accurate, yet within a fully partitioned (i.e. segregated) framework. Specifically, we introduce, with respect to standard segregated scheme, a numerically consistent stabilization term, capable of removing the nonphysical oscillations otherwise present in the numerical solution of the commonly used segregated scheme. Our new method is derived moving from a physics-based analysis on the microscale energetics of the force generation dynamics. By considering a model problem of active mechanics we prove that the proposed scheme is unconditionally absolutely stable (i.e. it is stable for any time step size), unlike the standard segregated scheme, and we also provide an interpretation of the scheme as a fractional step method. We show, by means of several numerical tests, that the proposed stabilization term successfully removes the nonphysical numerical oscillations characterizing the non stabilized segregated scheme solution. Our numerical tests are carried out for several force generation models available in the literature, namely the Niederer-Hunter-Smith model, the model by Land and coworkers, and the mean-field force generation model that we have recently proposed. Finally, we apply the proposed scheme [...]
A method to simulate orthotropic behaviour in thin shell finite elements is proposed. The approach is based on the transformation of shape function derivatives, resulting in a new orthogonal basis aligned to a specified preferred direction for all elements. This transformation is carried out solely in the undeformed state leaving minimal additional impact on the computational effort expended to simulate orthotropic materials compared to isotropic, resulting in a straightforward and highly efficient implementation. This method is implemented for rotation-free triangular shells using the finite element framework built on the Kirchhoff--Love theory employing subdivision surfaces. The accuracy of this approach is demonstrated using the deformation of a pinched hemispherical shell (with a 18{deg} hole) standard benchmark. To showcase the efficiency of this implementation, the wrinkling of orthotropic sheets under shear displacement is analyzed. It is found that orthotropic subdivision shells are able to capture the wrinkling behavior of sheets accurately for coarse meshes without the use of an additional wrinkling model.
This paper presents an extended Galerkin analysis for various Galerkin methods of the linear elasticity problem. The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor $boldsymbol sigma_h$, displacement $u_h$ inside each element and the modifications of these two variables $check boldsymbol sigma_h$ and $check u_h$ on elementary boundaries. Motivated by many relevant methods in literature, this formulation can be used to derive most existing discontinuous, nonconforming and conforming Galerkin methods for linear elasticity problem and especially to develop a number of new discontinuous Galerkin methods. Many special cases of this four-field formulation are proved to be hybridizable and can be reduced to some known hybridizable discontinuous Galerkin, weak Galerkin and local discontinuous Galerkin methods by eliminating one or two of the four fields. As certain stabilization parameter tends to infinity, this four-field formulation is proved to converge to some conforming and nonconforming mixed methods for linear elasticity problem. Two families of inf-sup conditions, one known as $H^1$-philic and another known as H(div)-phillic, are proved to be uniformly valid with respect to different choices of discrete spaces and parameters. These inf-sup conditions guarantee the well-posedness of the new proposed formulations and also offer a new and unified analysis for many existing methods in literature as a by-product.
Recent advances in imaging techniques have enabled us to visualize lung tumors or nodules in early-stage cancer. However, the positions of nodules can change because of intraoperative lung deflation, and the modeling of pneumothorax-associated deformation remains a challenging issue for intraoperative tumor localization. In this study, we introduce spatial and geometric analysis methods for inflated/deflated lungs and discuss heterogeneity in pneumothorax-associated deformation. Contrast-enhanced CT images simulating intraoperative conditions were acquired from live Beagle dogs. Deformable mesh registration techniques were designed to map the surface and subsurface tissues of lung lobes. The developed framework addressed local mismatches of bronchial tree structures and achieved stable registration with a Hausdorff distance of less than 1 mm and a target registration error of less than 5 mm. Our results show that the strain of lung parenchyma was 35% higher than that of bronchi, and that subsurface deformation in the deflated lung is heterogeneous.
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