1. MULTISCALE SYSTEMS MODELLING OF
THE TETRALOGY OF FALLOT
1 1 1 2 2 2 3
Ron Summers, Tariq Abdulla, Ryan Imms, Jean-Marc Schleich, Guy Carrault, Alfredo Hernandez and Lucile Houyel
1
Electronic and Electrical Engineering, SEIC, Loughborough University, Leics, UK, LE11 3TU
E-mail: R.Summers@lboro.ac.uk Web: http://syseng.lboro.ac.uk
2
LTSI, University of Rennes 1, Rennes, F-35000, France
3
Marie-Lannelongue Hospital, Paris, F-92350, France
Introduction
Between week 3 and 6 of embryonic development, the human heart morphs from a linear tube to a four chambered
organ. It is one of the few organs that become functional as it is formed. Remarkably, the conduction system and
blood flow both change radically while maintaining cardiac function at every step of development. Heart defects are
the most common type of congenital disorder, severely affecting 6/1000 live births. A number of genes have been
identified as playing a crucial role in heart morphogenesis. However the mechanisms by which altered gene
transcription affects cell signalling, cell behaviour, and tissue-tissue interactions that lead to altered development
are not well understood. The tetralogy of Fallot is one type of congenital heart disease (CHD), comprising multiple
defects, for which a theory of aetiology exists. However this sits within a spectrum of CHD in which one gene acts
through many mechanisms and can cause one of several diseases. Multiscale modelling, mediated through
information models, provides a means to study heart development as a system.
Tetralogy of Fallot Complexity of CHD
The tetralogy of Fallot is the most common Several mechanisms are involved in heart development, each of which
congenital heart defect causing cyanosis, and is are controlled by several genes. CHD commonly involves abnormal
defined as four coinciding anomalies: remodelling of the outflow tract (OFT) which can be caused by a
A Pulmonary stenosis combination of mechanisms, as illustrated below. As the OFT loops
B An over-riding aorta, displaced to the right behind the atria, it septates into the aorta and pulmonary artery, and
C Ventricular septal defect wedges aligned with the atrioventricular septum. Thus there is a range
(always in the membranous septum) of CHDs caused by abnormal degrees of OFT rotation.
D Right ventricle hypertrophy
Wikipedia
User:Wapcaplet
A
B
C
D
Normal Heart Tetralogy of Fallot
As the four abnormalities co-occur so frequently, it is
likely there is a common cause. One theory is that
hypoplasia of the subpulmonary conus leads to both
pulmonary stenosis and a shorter rotation of the
Outflow Tract (OFT), which leads to anomalies B , C
and D . Several genes control several mechanisms, which lead to one of several CHDs [1]

2. Multiscale Modelling -9 -3
The modelling framework encompasses spatial scales from 10 m (protein interactions) to 10 m (the primitive heart tube) and
-6 6
temporal scales from 10 s (molecular events) to 10 s (weeks of development). This is illustrated schematically below, left. The
approach adopted owes much to other methods including those from: systems engineering (e.g. integration technologies and
information modelling); the world-wide Physiome consortium and the EU-funded Network of Excellence on the Virtual
Physiological Human. Modelling approaches suitable for different levels of scale are illustrated, as well as markup language
specifications. These enable model interchange, potentially between tools that are suitable for modelling at different scales.
-9 -6 -4 -3 Composite
Spatial Scale 10 m 10 m 10 m 10 m Biosimulation Ontology Data Source
Annotation
Protein Cell Tissue Heart Tube Gel Electrophoresis
Interaction Behaviour Transformation Morphogenesis SNAIL
decreased
High VEGF High VEGF //computation concentration PRO, GO-MF
2+ VEGF
CA
BMP2
Snail VE Cadherin
VAR =
Calcineurin
p VEGF
Notch
endothelial cell
NFAT NFAT Delta4
Low VEGF
VEGF VE-Cadherin
2+
CA
TGF-beta
Calcineurin TGF-beta
Wnt /
BetaCat
Low
VEGF
p
NFAT NFAT
VEGF
Snail part_of
High VEGF
Wnt /
BMP
BetaCat
Notch
BMP4 BMP4
Markup
Language SBML CellML CBML FieldML SNAIL Histochemistry
Modelling Pathway Models Stochastic Models Agent Based Models Finite Element decreased PATO
OPB:concentration
Approach ODEs Reaction Diffusion PDEs Reactive Animation Image Analysis
=53 pg ml
-1 concentration
Petri Nets Systems of ODEs Cellular Automata 3D Reconstruction GO-CC
Boolean Networks Stochastic Petri Nets Cellular Potts Multiphysics Simulation endocardial cushion
Independent Continuant CL
PRO, ChEBI CL, FMA, GO-CC FMA, EHDA Validation
(Proteins, Cells, Structures)
derives_into
Ontologies GO-MF Cell Behaviour PATO, Mammalian Phenotype Dependent Continuant Segemented MRI
(Functions, Roles, Qualities)
decreased
GO-BP Occurent OPB:area volume
(Processes) 6 3 volume
=3 x 10 μm
Temporal Scale
membranous part of FMA, EHDA
-6 -3 3 6 cardiac septum
OMIM / Snomed / AEPC:
10 s 10 s 10 s 10 s
Molecular Events Cell Signalling Mitosis Heart Development Ventricular Septal Defect
Spatial and temporal scales of the multiscale modelling initiative [2] Composite annotation of biomedical data from multiscale sources [2]
Reference ontologies applicable to the different levels of scale are illustrated along the bottom of the left-hand figure. These are
further split between occurents, independent continuants and dependent continuants. Occurents are processes that unfold
through time, while continuants are entities that exist in full through a period of time. This provides a clear conceptual division
between the spatial and temporal domains. Annotating models, model components and parameters using well defined
ontologies enables reuse and integration. But multiscale modelling presents a challenge in that no single ontology can include
terms of the required specificity. A post-coordinated annotation strategy, which allows the combination of terms from multiple
ontologies, is a partial solution to this issue, and is illustrated above, right. Modelling of morphogenesis provides the further
challenge of increased importance of the temporal domain, which is currently less well defined ontologically.
Future Work
There are several important mechanisms in heart development, and each of these can be studied as a multiscale system. The
endocardial cushions are swellings in the early heart tube, which fuse to form the valves and membranous septum, and play a role
in OFT remodelling. Endocardial cushions grow by a process of Epithelial to Mesenchymal Transition (EMT). Cellular behaviour
and tissue interaction during EMT can be simulated as Potts models using Compucell3D. Existing models of signal pathways
involved in EMT are modelled as ODEs and are available in Systems Biology Markup Language (SBML). Future plans are to use
the SBML ODE Solver Library (SOSlib) to incorporate reaction networks within Compucell3D and thus determine intracellular
concentrations in a multiscale model. From a chronological perspective, we are using state charts to represent processes and sub-
processes in heart development hierarchically. The UML formalism allows the recursive stacking of state machines, and this
approach neatly matches the problem of modelling in multiple time scales.
References
[1] F. Bajolle, S. Zaffran, and D. Bonnet, "Genetics and embryological mechanisms of congenital heart diseases.," Archives of
cardiovascular diseases, vol. 102, 2009, pp. 59-63.
[2] T. Abdulla, R. Imms, J.M. Schleich, and R. Summers, "Multiscale information modelling for heart morphogenesis," Journal of
Physics: Conference Series (in press).