Integrated Heart - Coupling multiscale and multiphysics models for the simulation of the cardiac function

Mathematical modelling of the human heart and its function can expand our understanding of various cardiac diseases, which remain the most common cause of death in the developed world. Like other physiological systems, the heart can be understood as a complex multiscale system involving interacting phenomena at the molecular, cellular, tissue, and organ levels. This article addresses the numerical modelling of many aspects of heart function, including the interaction of the cardiac electrophysiology system with contractile muscle tissue, the sub-cellular activation-contraction mechanisms, as well as the hemodynamics inside the heart chambers. Resolution of each of these sub-systems requires separate mathematical analysis and specially developed numerical algorithms, which we review in detail. By using specific sub-systems as examples, we also look at systemic stability, and explain for example how physiological concepts such as microscopic force generation in cardiac muscle cells, translate to coupled systems of differential equations, and how their stability properties influence the choice of numerical coupling algorithms. Several numerical examples illustrate three fundamental challenges of developing multiphysics and multiscale numerical models for simulating heart function, namely: (i) the correct upscaling from single-cell models to the entire cardiac muscle, (ii) the proper coupling of electrophysiology and tissue mechanics to simulate electromechanical feedback, and (iii) the stable simulation of ventricular hemodynamics during rapid valve opening and closure

Enhancing multi-scale cardiac simulations by coupling electrophysiology and mechanics: a flexible high performance approach to cardiac electromechanics

This work focuses on the development of computational methods for the simulation of the propagation of the electrical potential in the heart and of the resulting mechanical contraction. The interaction of these two physical phenomena is described by an electromechanical model which consists of the monodomain system, which describes the propagation of the action potential in the cardiac tissue, and the equations of incompressible elasticity, which describe its mechanical response. In fully-coupled electromechanical simulations, two main computational challenges are usually identified in literature: the time integration of the monodomain system and the efficient solution of the equations of incompressible elasticity. These two are the actual bottlenecks in the realization of accurate and efficient fully-coupled electromechanical simulations. The first computational challenge arises from the discretization in time of the equations that describe the electrical activation of cardiac tissue. The monodomain system should be discretized employing both fine spatial grids and small time-steps, to capture the spatial steep gradients typical of the action potential and the behavior of the stiff gating variables, respectively. To obtain an accurate and computationally-cheap numerical solution, we propose a novel method based on coupling high-order backward differentiation formulae with high-order exponential time stepping schemes for the time integration of the monodomain system. We propose a novel quasi-Newton approach for the implicit discretization of the monodomain equation. We also compare this latter approach against a complex step differentiation-based approach. As a result, we show by means of numerical tests the accuracy of the developed strategies and how the use of high-order time integration schemes affects the simulation of post- processed quantities of clinical relevance such as the conduction velocity. The second computational challenge is due to the structure the discretization of the equations of incompressible elasticity. Due to the incompressibility constraint, the arising linear system has a saddle point structure for which standard solution methods such as multigrid or domain de- composition do not provide optimal convergence if not properly adapted. In order to overcome this problematic, we propose a segregated multigrid preconditioned solution method. The segregated approach allows to recast the saddle-point problem into two elliptic problems for which multigrid methods are shown to provide optimal convergence. The electromechanical model is employed to evaluate the effects of geometrical changes due to the contraction of the heart on simulated electrocardiograms. Finally, the effect of different electrical activations on the resulting pressure-volume loops is investigated by coupling the electromechanical model with a lumped model of the circulatory system

Computational Multiscale Solvers for Continuum Approaches

Computational multiscale analyses are currently ubiquitous in science and technology. Different problems of interest-e.g., mechanical, fluid, thermal, or electromagnetic-involving a domain with two or more clearly distinguished spatial or temporal scales, are candidates to be solved by using this technique. Moreover, the predictable capability and potential of multiscale analysis may result in an interesting tool for the development of new concept materials, with desired macroscopic or apparent properties through the design of their microstructure, which is now even more possible with the combination of nanotechnology and additive manufacturing. Indeed, the information in terms of field variables at a finer scale is available by solving its associated localization problem. In this work, a review on the algorithmic treatment of multiscale analyses of several problems with a technological interest is presented. The paper collects both classical and modern techniques of multiscale simulation such as those based on the proper generalized decomposition (PGD) approach. Moreover, an overview of available software for the implementation of such numerical schemes is also carried out. The availability and usefulness of this technique in the design of complex microstructural systems are highlighted along the text. In this review, the fine, and hence the coarse scale, are associated with continuum variables so atomistic approaches and coarse-graining transfer techniques are out of the scope of this paper.Abengoa Researc

Computational multiscale solvers for continuum approaches

Computational multiscale analyses are currently ubiquitous in science and technology. Different problems of interest-e.g., mechanical, fluid, thermal, or electromagnetic-involving a domain with two or more clearly distinguished spatial or temporal scales, are candidates to be solved by using this technique. Moreover, the predictable capability and potential of multiscale analysis may result in an interesting tool for the development of new concept materials, with desired macroscopic or apparent properties through the design of their microstructure, which is now even more possible with the combination of nanotechnology and additive manufacturing. Indeed, the information in terms of field variables at a finer scale is available by solving its associated localization problem. In this work, a review on the algorithmic treatment of multiscale analyses of several problems with a technological interest is presented. The paper collects both classical and modern techniques of multiscale simulation such as those based on the proper generalized decomposition (PGD) approach. Moreover, an overview of available software for the implementation of such numerical schemes is also carried out. The availability and usefulness of this technique in the design of complex microstructural systems are highlighted along the text. In this review, the fine, and hence the coarse scale, are associated with continuum variables so atomistic approaches and coarse-graining transfer techniques are out of the scope of this paper

Accelerated Computational Micromechanics

The development of new materials is an important component of many cutting edge technologies such as space technology, electronics and medical devices. The properties of advanced materials involve phenomena across multiple scales. The material may be heterogeneous on a scale that is small compared to that of applications, or may spontaneously develop fine-scale structure. Numerical simulation of such phenomena can be an effective tool in understanding the complex physics underlying these materials, thereby assisting the development and refinement of such materials, but can also be challenging. This thesis develops a new method to exploit the use of graphical processing units and other accelerators for the computational study of complex phenomena in heterogeneous materials. The governing equations are nonlinear partial differential equations, typically second order in space and first order in time. We propose an operator-splitting scheme to solve these equations by observing that these equations come about by a composition of linear differential constraints like kinematic compatibility and balance laws, and nonlinear but local constitutive equations. We formulate the governing equation as an incremental variational principle. We treat both the deformation and the deformation gradient as independent variables, but enforce kinematic compatibility between them as a constraint using an augmented Lagrangian. The resulting local-global problem is solved using the alternating direction method of multipliers. This enables efficient implementation on massively parallel graphical processing units and other accelerators. We use the study of elastic composites in finite elasticity to verify the method, and to demonstrate its numerical performance. We also compare the performance of the proposed method with that of other emerging approaches. We apply the method to understand the mechanisms responsible for a remarkable in-plane liquid-like property of liquid crystal elastomers (LCEs). LCEs are rubber-like solids where rod-like nematic molecules are incorporated into the main or a side polymer chain. They undergo isotropic to nematic phase transition accompanied by spontaneous deformation which can be exploited for actuation. Further, they display a soft behavior at low temperatures due to the reorientation of the nematic directors. Recent experiments show that LCEs exhibit an in-plane liquid-like behavior under multiaxial loading, where there is shear strain with no shear stress. Our numerical studies of LCEs provides insights into the director distribution and reorientation in polydomain specimens, and how these lead to the observed liquid-like behavior. The results show good agreement with experimental observations. In addition to providing insight, this demonstrates the ability of our computational approach to study multiple coupled fields. The core ideas behind the method developed in this thesis are then applied elsewhere. First, we use it to study multi-stable deployable engineering structures motivated by origami. The approach uses two descriptions of origami kinematics, angle/face based approach and vertex/truss based approach independently, and enforces the relationship between them as a constraint. This is analogous to the treatment of kinematic compatibility above where both the deformation and deformation gradient are used as independent variables. The constraint is treated using a penalty. Stable and rigid-foldable configurations are identified by minimizing the penalty using alternate directions, and pathways between stable states are found using the nudged elastic band method. The approach is demonstrated using various examples. Second, we use a balance law or equilibrium to the problem of determining the stress field from high resolution x-ray diffraction. This experimental approach determines the stress field locally, and errors lead to non-equilibriated fields. It is hypothesized that imposing equilibrium leads to a more accurate stress reconstruction. We use Hodge decomposition to project a non-equilibriated stress field onto the divergence-free (equilibriated) subspace. This projection is numerically implemented using fast Fourier transforms. This method is first verified using synthetic data, and then applied to experimental data obtained from a beta-Ti alloy. It results in large corrections near grain boundaries.</p

Study of spectral sensing using electro-optic films

Fundamental studies on light interacting with liquid crystals (LCs) and polymers have led to innovative application like the omnipresent LCDs, revolutionizing the display industry. This thesis focuses on manipulation of optical propagation through LC/polymer two phase composite material set and in-depth understanding of these systems by studying their morphology and microscopic interactions for multiwavelength sensing applications.Holographically formed Polymer Dispersed Liquid Crystals (HPDLCs) are the composite photorefractive material used in this work. They consist of LC nanodroplets confined in a polymer matrix, arranged in periodic planes. Applying an electric field across them modifies their periodic refractive index to a uniform refractive index state, due to LC realignment. This transforms the reective HPDLCs into an optically transparent state.Fabricating and assembling HPDLCs in different configurations enables wavelength filtering by controlling their optical lineshape output, for wavelength sensing applications. To increase the range of wavelengths spanned, these electro-optic thin films are arranged in serial and parallel design. A novel dynamic time multiplexing technique is used to improve the spectral range of individual HPDLC unit.These types of field controllable HPDLC wavelength filtering devices have remote sensing, imaging spectrometry applications like hyperspectral and multispectral imaging to detect specific spectral signature of an unknown remote object source. Comparing the detected spectra to a database of known spectral fingerprints enables identification of the unknown entity.To further fundamentally comprehend the LC polymer interaction in HPDLC systems structural analysis data using microscopy and spectroscopy techniques is presented. To interpret the nano-scale structure accurately and better understand the confined LC behavior, variable pressure scanning electron microscopy and electron spin resonance spectroscopy is used here for the first time. Berreman 4 4 matrix technique and a phenomenological diffusion model are presented to model and predict their optical output behavior and their multipart wavelength lineshapes. In summary this dissertation focuses on study of multi spectral sensing using HPDLCs, their fundamental studies along with modeling their behavior.Ph.D., Electrical Engineering -- Drexel University, 200

Shape Memory Polymers Charged with Modified Carbon-Based Nanoparticles

In this thesis, shape memory nanocomposites were prepared and characterized. The polymer matrix consisted in an epoxy-based liquid crystalline elastomer (LCE). Multi-walled carbon nanotubes (MWCNT) and graphite nanoplatelets (GNP) were selected as fillers. The influence of different contents of nanofillers on mechanical, thermal and shape memory properties was evaluated. In order to disperse and homogeneously distribute the nanofillers within the polymer matrix an in-depth evaluation on the optimal conditions to synthesize the materials was carried out. These conditions had a substantial influence on the final distribution of the nanofillers within the epoxy-based matrix, which was analyzed from a macroscopic and microscopic point of view. The best results were obtained through a chemical surface modification of the nanoparticles. The chemical modification of MWCNTs consisted in grafting the selected epoxy monomers on the surface. The obtained adducts were characterized in terms of chemical, thermal and morphological features. Concerning GNP, a similar protocol based on surface modification was carried out. In this case, a preliminary oxidation process was performed in order to promote the exfoliation of graphene sheets, in form of graphene oxide (GO), and to favour their dispersion within the polymer matrix. Different degrees of oxidation were attempted. GO nanoparticles were successively modified with epoxy monomers. Also in this case, chemical, morphological, structural and thermal characterization was carried out. Surface modified carbonaceous nanoparticles were then dispersed in varying amounts in the organic matrix. The obtained nanocomposite systems were characterized in their chemical-physical and morphological properties. The adopted compatibilization strategies used for both MWCNTs and GNP were found to be extremely effective to get homogeneous samples and to enable a dramatic enhancement of the actuation extent at low nanofiller content. Moreover, the stress threshold required to trigger the reversible thermomechanical actuation was significantly decreased. The effect of nanoparticles on thermomechanical properties of the materials was correlated to the microstructure and the phase behavior of the host system. Results demonstrated that the incorporation of carbon nanofillers amplified the soft-elastic response of the liquid crystalline phase to external stimuli. Tunable thermomechanical properties of these systems make them suitable for a variety of potential advanced applications ranging to robotics, sensing and actuation, and artificial muscles

Doctor of Philosophy

dissertationPartial differential equations (PDEs) are widely used in science and engineering to model phenomena such as sound, heat, and electrostatics. In many practical science and engineering applications, the solutions of PDEs require the tessellation of computational domains into unstructured meshes and entail computationally expensive and time-consuming processes. Therefore, efficient and fast PDE solving techniques on unstructured meshes are important in these applications. Relative to CPUs, the faster growth curves in the speed and greater power efficiency of the SIMD streaming processors, such as GPUs, have gained them an increasingly important role in the high-performance computing area. Combining suitable parallel algorithms and these streaming processors, we can develop very efficient numerical solvers of PDEs. The contributions of this dissertation are twofold: proposal of two general strategies to design efficient PDE solvers on GPUs and the specific applications of these strategies to solve different types of PDEs. Specifically, this dissertation consists of four parts. First, we describe the general strategies, the domain decomposition strategy and the hybrid gathering strategy. Next, we introduce a parallel algorithm for solving the eikonal equation on fully unstructured meshes efficiently. Third, we present the algorithms and data structures necessary to move the entire FEM pipeline to the GPU. Fourth, we propose a parallel algorithm for solving the levelset equation on fully unstructured 2D or 3D meshes or manifolds. This algorithm combines a narrowband scheme with domain decomposition for efficient levelset equation solving