Meshfree and Particle Methods in Biomechanics: Prospects and Challenges

The use of meshfree and particle methods in the field of bioengineering and biomechanics has significantly increased. This may be attributed to their unique abilities to overcome most of the inherent limitations of mesh-based methods in dealing with problems involving large deformation and complex geometry that are common in bioengineering and computational biomechanics in particular. This review article is intended to identify, highlight and summarize research works on topics that are of substantial interest in the field of computational biomechanics in which meshfree or particle methods have been employed for analysis, simulation or/and modeling of biological systems such as soft matters, cells, biological soft and hard tissues and organs. We also anticipate that this review will serve as a useful resource and guide to researchers who intend to extend their work into these research areas. This review article includes 333 references

From medical images to individualized cardiac mechanics: A Physiome approach

Cardiac mechanics is a branch of science that deals with forces, kinematics, and material properties of the heart, which is valuable for clinical applications and physiological studies. Although anatomical and biomechanical experiments are necessary to provide the fundamental knowledge of cardiac mechanics, the invasive nature of the procedures limits their further applicability. In consequence, noninvasive alternatives are required, and cardiac images provide an excellent source of subject-specific and in vivo information. Noninvasive and individualized cardiac mechanical studies can be achieved through coupling general physiological models derived from invasive experiments with subject-specific information extracted from medical images. Nevertheless, as data extracted from images are gross, sparse, or noisy, and do not directly provide the information of interest in general, the couplings between models and measurements are complicated inverse problems with numerous issues need to be carefully considered. The goal of this research is to develop a noninvasive framework for studying individualized cardiac mechanics through systematic coupling between cardiac physiological models and medical images according to their respective merits. More specifically, nonlinear state-space filtering frameworks for recovering individualized cardiac deformation and local material parameters of realistic nonlinear constitutive laws have been proposed. To ensure the physiological meaningfulness, clinical relevance, and computational feasibility of the frameworks, five key issues have to be properly addressed, including the cardiac physiological model, the heart representation in the computational environment, the information extraction from cardiac images, the coupling between models and image information, and also the computational complexity. For the cardiac physiological model, a cardiac physiome model tailored for cardiac image analysis has been proposed to provide a macroscopic physiological foundation for the study. For the heart representation, a meshfree method has been adopted to facilitate implementations and spatial accuracy refinements. For the information extraction from cardiac images, a registration method based on free-form deformation has been adopted for robust motion tracking. For the coupling between models and images, state-space filtering has been applied to systematically couple the models with the measurements. For the computational complexity, a mode superposition approach has been adopted to project the system into an equivalent mathematical space with much fewer dimensions for computationally feasible filtering. Experiments were performed on both synthetic and clinical data to verify the proposed frameworks

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

A contact formulation based on a volumetric potential: Application to isogeometric simulations of atrioventricular valves

This work formulates frictionless contact between solid bodies in terms of a repulsive potential energy term and illustrates how numerical integration of the resulting forces is computationally similar to the “pinball algorithm” proposed and studied by Belytschko and collaborators in the 1990s. We thereby arrive at a numerical approach that has both the theoretical advantages of a potential-based formulation and the algorithmic simplicity, computational efficiency, and geometrical versatility of pinball contact. The singular nature of the contact potential requires a specialized nonlinear solver and an adaptive time stepping scheme to ensure reliable convergence of implicit dynamic calculations. We illustrate the effectiveness of this numerical method by simulating several benchmark problems and the structural mechanics of the right atrioventricular (tricuspid) heart valve. Atrioventricular valve closure involves contact between every combination of shell surfaces, edges of shells, and cables, but our formulation handles all contact scenarios in a unified manner. We take advantage of this versatility to demonstrate the effects of chordal rupture on tricuspid valve coaptation behavior

Računalna mehanika u znanosti i inženjerstvu – Quo vadis

Computational Mechanics has many applications in science and engineering. Its range of application has been enlarged widely in the recent decades. Hence, nowadays areas such as biomechanics and additive manufacturing are among the new research topics, in which computational mechanics helps solve complex problems and processes. In this contribution, these emerging areas will be discussed together with new discretization schemes, e. g. virtual element method and particle methods, whereby the latter need high performance computing facilities in order to solve problems such as mixing in an accurate way. Failure analysis of structures and components is another topic that is developing fast. Here, modern computational approaches rely on the phase field method that simplifies discretizations schemes. All these approaches and methods are discussed and evaluated by means of examples.Računalna mehanika ima široku primjenu u znanosti i inženjerstvu. Njeno područje primjene se znatno povećalo u zadnjim desetljećima. Danas polja kao biomehanika i aditivna proizvodnja nova su područja istraživanja u kojima računalna mehanika pomaže rješavati složene probleme i procese. U radu se razmatraju ova granična područja zajedno s novim diskretizacijskim postupcima kao što su metoda virtualnih elemenata i metoda čestica, gdje potonja zahtijeva moćnu računalnu opremu da bi se mogli točno riješiti problemi kao što je miješanje. Analiza oštećenja konstrukcija i njenih komponenata je drugo područje koje se brzo razvija, pa se ovdje moderni računalni postupci odnose na metodu faznih polja koja pojednostavljuje diskretizacijske sheme. Svi navedeni postupci i metode su razmatrani i vrednovani u numeričkim primjerima

Topology Optimization and 3D printing of Large Deformation Compliant Mechanisms for Straining Biological Tissues

This paper presents a synthesis approach in a density-based topology optimization setting to design large deformation compliant mechanisms for inducing desired strains in biological tissues. The modelling is based on geometrical nonlinearity together with a suitably chosen hypereleastic material model, wherein the mechanical equilibrium equations are solved using the total Lagrangian finite element formulation. An objective based on least-square error with respect to target strains is formulated and minimized with the given set of constraints and the appropriate surroundings of the tissues. To circumvent numerical instabilities arising due to large deformation in low stiffness design regions during topology optimization, a strain-energy based interpolation scheme is employed. The approach uses an extended robust formulation i.e. the eroded, intermediate and dilated projections for the design description as well as variation in tissue stiffness. Efficacy of the synthesis approach is demonstrated by designing various compliant mechanisms for providing different target strains in biological tissue constructs. Optimized compliant mechanisms are 3D-printed and their performances are recorded in a simplified experiment and compared with simulation results obtained by a commercial software.Comment: 23 pages, 14 figure

Atomistic and continuum scale models for flexoelectric nanostructures and composites

This work explores the phenomenon of flexoelectricity in nanomaterials and nanostructures by molecular dynamics models and continuum models. Flexoelectricity is an electromechanical phenomenon describing the coupling between electric polarization and strain gradient in a material. Thanks to the strain gradient term, flexoelectricity exhibits an universal existence and size-dependent behavior, enabling strong electromechanical coupling at micro/nanoscale, leading to ideal application in micro/nano-devices, such as Nanogenerator. However, it is difficult to measure or estimate the intrinsic flexoelectric coefficients of a material due to the interference from the piezoelectric effect, representing the coupling between electric polarization and strain. Additionally, the standard continuum model, such as the finite element model, cannot accommodate flexoelectricity due to the higher-order continuity requirement (C1 continuity) imposed by the strain gradient term, requiring the development of novel continuum approaches for the design guidance of flexoelectric devices. These difficulties limit our understanding and potential engineering utilization of flexoelectricity. In the framework of molecular dynamics, this work develops a core-shell and charge-dipole model for extracting flexoelectric coefficients of a traditional electromechanical material (BaTiO3) and newly emerged two-dimensional (2D) materials (in total 21 materials), respectively. Specially designed mechanical loading schemes are employed within the core-shell and charge-dipole model to eliminate the interference from piezoelectricity, enabling direct measurement of the materials’ flexoelectric response. The core-shell models’ results show that the size/surface effect significantly influences the longitudinal and shear flexoelectric coefficient of the BaTiO3 nanostructures. For two-dimensional materials, the charge-dipole model extracted their bending flexoelectric coefficients and identified their contributors. It observes that transition metal dichalcogenide monolayers possess the highest flexoelectric coefficients among the studied 2D materials. This work also develops continuum models to characterize flexoelectricity in continuum solid structures, such as flexoelectric composite. A 2D Meshless model and a 3D nonlinear mixed finite element model employ higher-order shape function and extra degrees of freedom to fulfill the C1 continuity requirement of flexoelectricity. Both models show that structure configurations and material properties influence the electromechanical behavior of flexoelectric composites. Besides, the 3D nonlinear mixed finite element model demonstrated the essentialness of the geometrical nonlinearity for an accurate representation of flexoelectricity by continuum models

Doctor of Philosophy

dissertationImage-based biomechanics, particularly numerical modeling using subject-specific data obtained via imaging, has proven useful for elucidating several biomechanical processes, such as prediction of deformation due to external loads, applicable to both normal function and pathophysiology of various organs. As the field evolves towards applications that stretch the limits of imaging hardware and acquisition time, the information traditionally expected as input for numerical routines often becomes incomplete or ambiguous, and requires specific acquisition and processing strategies to ensure physical accuracy and compatibility with predictive mathematical modeling. These strategies, often derivatives or specializations of traditional mechanics, effectively extend the nominal capability of medical imaging hardware providing subject-specific information coupled with the option of using the results for predictive numerical simulations. This research deals with the development of tools for extracting mechanical measurements from a finite set of imaging data and finite element analysis in the context of constructing structural atlases of the heart, understanding the biomechanics of the venous vasculature, and right ventricular failure. The tools include: (1) application of Hyperelastic Warping image registration to displacement-encoded MRI for reconstructing absolute displacement fields, (2) combination of imaging and a material parameter identification approach to measure morphology, deformation, and mechanical properties of vascular tissue, and (3) extrapolation of diffusion tensor MRI acquired at a single time point for the prediction the structural changes across the cardiac cycle with mechanical simulations. Selected tools were then applied to evaluate structural changes in a reversible animal model for right ventricular failure due to pressure overload