MULTISCALE SYSTEMS MODELLING OF THE TETRALOGY OF FALLOT 1
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Ron Summers, Tariq Abdulla, Ryan Imms, Jean-Marc Schleich, Guy Carrault, Alfredo Hernandez and Lucile Houyel
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Electronic and Electrical Engineering, SEIC, Loughborough University, Leics, UK, LE11 3TU E-mail:
[email protected] 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 congenital heart defect causing cyanosis, and is defined as four coinciding anomalies: A Pulmonary stenosis B An over-riding aorta, displaced to the right C Ventricular septal defect (always in the membranous septum) D Right ventricle hypertrophy
Several mechanisms are involved in heart development, each of which are controlled by several genes. CHD commonly involves abnormal remodelling of the outflow tract (OFT) which can be caused by a combination of mechanisms, as illustrated below. As the OFT loops behind the atria it septates into the aorta and pulmonary artery and wedges aligned with the atrioventricular septum. Thus there is a range of CHDs caused by abnormal degrees of OFT rotation.
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]
Multiscale Modelling
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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. -4
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Biosimulation
10 m
10 m
10 m
10 m
Protein Interaction
Cell Behaviour
Tissue Transformation
Heart Tube Morphogenesis
Spatial Scale
CA
VEGF
High VEGF
2+
Snail
VE Cadherin
BMP2
Calcineurin p
NFAT
NFAT
Notch
VEGF
Ontology
Data Source Gel Electrophoresis
//computation VAR =
High VEGF
Composite Annotation SNAIL decreased concentration
PRO, GO-MF
endothelial cell
Delta4
Low VEGF
VEGF CA
VE-Cadherin
2+
Calcineurin
Wnt / BetaCat
Low VEGF
p
NFAT
Markup Language SBML Modelling Pathway Models Approach ODEs Petri Nets Boolean Networks
part_of
Snail
VEGF
High VEGF Wnt / BetaCat
BMP4
TGF-beta
TGF-beta
NFAT
BMP
Notch
BMP4
CellML
FieldML
CBML
Stochastic Models
Agent Based Models
Finite Element
Reaction Diffusion PDEs Systems of ODEs Stochastic Petri Nets
Reactive Animation Cellular Automata Cellular Potts
Image Analysis 3D Reconstruction Multiphysics Simulation
PRO, ChEBI
Independent Continuant
FMA, EHDA
CL, FMA, GO-CC
(Proteins, Cells, Structures)
OPB:concentration -1 =53 pg ml
SNAIL decreased concentration endocardial cushion
PATO
Histochemistry
GO-CC CL
Validation
derives_into
Ontologies
GO-MF
Cell Behaviour
PATO, Mammalian Phenotype Dependent Continuant
Segemented MRI
(Functions, Roles, Qualities)
Occurent
GO-BP
(Processes)
OPB:area volume 3 6 =3 x 10 μm
Temporal Scale -6
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10 s
10 s
10 s
10 s
Molecular Events
Cell Signalling
Mitosis
Heart Development
Spatial and temporal scales of the multiscale modelling initiative [2]
OMIM / Snomed / AEPC: Ventricular Septal Defect
decreased volume membranous part of cardiac septum
FMA, EHDA
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 subprocesses 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).
