Download Real-time and patient-specific simulation of the heart. Application to

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