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MSc and PhD opportunities in 2016: Real-time and patient-specific simulation of the heart. Application to rheumatic heart disease and ventricular remodelling Collaborators: Prof Peter Zilla (UCT), Prof Tim Ricken (TU Dortmund), Dr Jagir Hussan (Auckland Bioengineering Institute) Outline: Heart failure accounts for one in eight deaths in USA and almost 10% of individuals over the age of 65 are affected by heart failure [Lloyd-Jones et al., 2010]. In particular acute rheumatic fever (ARF) and rheumatic heart disease (RHD) is a major cause of mortality amongst adolescents in third world and developing countries with 233,000 deaths annually [Seckeler and Hoke, 2011]. The failure mechanisms of RHD are not well studied in comparison to myocardial infarction which prevents e ective treatment of the diseased myocardium. Computational cardiac mechanics is emerging as a rapidly expanding area of research bringing together multidisciplinary research centred on understanding the electrophysiological and mechanical behaviour of the heart at scales ranging from cell to tissue and organ levels. Principles of continuum mechanics are key in creating a realistic multi-scale model of the heart. They allow to describe the directly observable behaviour of the heart by incorporating on micro level its complex heterogeneous and anisotropic structure as well as the coupling mechanisms between mechanical fields on the one hand and chemical and electrical fields on the other. Computational models therefore help to quantify the mechanical environment in health, injury, disease, as well as to identify mechanosensitive responses and their mechanisms. This leads to advance in therapeutic and diagnostic procedures. In contrast to existing computational models, we want to feed our cardiac mechanics models with realistic patient-specific material properties from magnetic resonance imaging (MRI) or 3D echocardiography. This high accuracy with regards to material properties can only be exploited, if the geometric model of the heart features a similar degree of accuracy. The increase in geometry and material detail, however, is matched by an exponential increase in computing time such that it inevitably results in massive supercomputer simulations. The novelty of our approach is to pair unparalleled accuracy with fast computing time such that it is usable on a normal computer and provides instant real-time feedback. This will be achieved by a special model reduction technique, the Proper Orthogonal Decomposition with Interpolation method (PODI) [Niroomandi et al. 2012]. The approach will open a new dimension for heart diagnostics and provide medical researchers as well as practitioner with a computational toolbox enabling them to gain in-depth understanding of the mechanical, electro-physiological and molecular processes and coupled mechanisms which helps in developing new therapy concepts for rheumatic heart disease. References D. Lloyd-Jones, R.J. Adams, T.M. Brown, M. Carnethon, S. Dai, G. De Simone, and T.B. Ferguson et al. 2010. Heart disease and stroke statistics - 2010 update: a report from the american heart association. Circulation, 121:e46-e215. S. Niroomandi, I. Alfaro, E. Cueto, and F. Chinesta, 2012. Accounting for large deformations in real-time simulations of soft tissues based on reduced-order models. Computer Methods and Programs in Biomedicine, 105:1-12. Micro-structural modelling of myocardial tissue Collaborators: Dr. S. Skatulla (University of Cape Town), Prof Tim Ricken (University of Dortmund), Dr Jagir Hussan (University of Auckland, Dr Ntobeko Ntusi (University of Cape Town), Prof Ernesta Meintjes (University of Cape Town), Prof Peter Zilla (University of Cape Town) Outline: Myocardial tissue is a complex heterogeneous material characterized by different muscle fibre hierarchies interwoven by collagen, elastin, coronary capillaries and various proteins. For instance, fiber orientation, dispersion, thickness, length and relative volume fraction have a considerable local character. The myocardium is a laminated structure with a complex hierarchical organization. These approximately four to six cells thick layers or myocardial sheets are loosely interconnected by perimysial collagen fibers which are able to slide over one another with a relatively low slippage resistance. Moreover, the initially crimped and coiled collagen fibers straighten during passive filling. Another consideration is that for small and intermediate levels of strain the myocardial material response and its stiffness is dominated by kinematics of the myocytes or bundles of myocytes. These are linked to the collagen matrix but remain highly deformable in terms of axial and associated transversal deformation as well as torsional and flexural deformation. Only for larger strains, further myocyte deformation is prevented by the cross-linked collagen network which is significantly stiffer than the myocytes. It is therefore the former which takes over dominating the material behaviour of myocardial tissue. In this research, the myocardial material response is obtained from the micro-structural level where it originates. Two different avenues are pursued: (i) generalised continuum methods and (ii) FE-square-based modelling. In case of (i), the fibrous characteristics of the myocardium are modelled by higher-order continua, such as the Cosserat-fibre or the micromorphic-fibre continuum. Both additionally allow for the inclusion of non-local effects due to the heterogeneous material composition at smaller scales. Specifically, the non-local material response is linked to higher-order deformation modes and extra degrees of freedom associated with twisting and bending of an assembly of muscle fibres arising from hierarchical multi-scale features within a representative volume element (RVE). In this sense, a scaling parameter characteristic for the tissue’s underlying micro-structure, becomes a material parameter of the formulation. As the anisotropic material composition of the myocardium throughout the heart is highly non-uniform, the ability to implicitly account for scale-dependent torsion and bending effects in the constitutive law gives this approach an advanced material description over classical formulations. In case of (ii) we want to utilize FE-square modelling which considers finite element discretizations of the material at two scales, the micro and the macro-scale. In this way, the actual micro-structural material composition can be taken into account and by means of solving a boundary value problem an accurate micro-structural stress distribution is obtained which is transferred to the macro-scale via volume averaging. Modelling of seasonal changes in the Antarctic ice-shelf Collaborators: Dr Sebastian Skatulla (University of Cape Town), Dr Keith MacHutchon (Coastal Marine Technology (PTY) Ltd.), A/Prof Marcello Vichi (University of Cape Town) The Antarctic sea-ice has a significant impact on the global climate. The seasonal variations in the occurrence of sea-ice controls the exchange between air and sea and consequently influences atmospheric and oceanic circulation. It is therefore important to understand how sea and air temperatures together with the wave dynamics of the ocean impact on the morphology of the ice. For this purpose, as a first step a continuum mechanical model must be developed which is able to describe the thermodynamics of the ice when subjected to mechanical and temperature loading. In particular, the phase transition of the sea water from frozen to liquid stage and vice versa must be included by suitable multiphase model. As a second step, the model will be calibrated and verified from sea ice cores which are artificially created in laboratory environment and as obtained at expeditions to the Antarctica facilitated by the Department of Oceanography, UCT. A Novel Locking-free Non-linear Finite Element Formulation Collaborators: Prof Carlo Sansour (University of Nottingham, UK) Outline: It is well-known that finite element algorithms require special efforts to avoid unphysical stiffness arising from the numerics. This phenomenon is called locking which is encountered (i) for structures which are thinner in one or two dimensions, such as plates, shells or beams under shear loading, (ii) for three-dimensional structures with nearly incompressible material behaviour, knowns as volumetric locking. There are wellestablished strategies to overcome locking such as enhanced strain or assumed strain formulations and hybrid or mixed methods. The latter treat the stress as additional degrees of freedom besides displacement. All these methods are very involved and completely locking free finite elements for heavily distorted meshes are still not available. Here, a novel approach proposes to couple displacements to rotations which results in very efficient displacement-type finite elements. In contrast to a conventional interpolation ansatz, this framework is based on a non-linear interpolation formula using transformation groups, so-called Lie groups, and the exponential map [Sansour and Skatulla, 2012] which does not require the parameterization of the nodal degrees of freedom. The approach aims at revolutionizing the Finite Element Method by making complex methods to overcome locking obsolete. References V. Sonneville, A. Cardona, O. Bruels, 2013. Geometrically exact beam finite element formulated on the special Euclidean group SE(3) , Computer Methods in Applied Mechanics and Engineering. doi:10.1016/j.cma.2013.10.008