1. www.eu-eela.org E-science grid facility for Europe and Latin America FISIOCOMP - Laboratory of Computational Physiology Computer Science Department Universidade Federal de Juiz de Fora (UFJF) Juiz de Fora - MG - Brazil Gustavo Miranda Teixeira Ricardo Silva Campos Heart Simulator

2. www.eu-eela.org E-science grid facility for Europe and Latin America Group Professors Prof. Rodrigo Weber dos Santos, Dr. Math. * Prof. Marcelo Lobosco, Dr. Comp. Sci. * Prof. Ciro Barros Barbosa, Dr. Comp. Sci. Prof. Rubens Oliveira, Dr. Eng. Prof. Luis Paulo Barra, Dr. Eng. Prof. Elson Toledo, Dr. Eng. Master Students Carolina Xavier Ronan M. Amorim Franciane Peters * Grid team Undergraduate Students Caroline Costa Gustavo Miranda * Ricardo Campos * Guilherme Montebrune Former Master Students Rafael Sachetto Oliveira Fernando Otaviano Campos Bernardo Rocha Daves Martins Ely Fonseca

3. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Overview Computational physiology The heart Heart models Computational Framework Inverse Problems Gridification Goals 3

4. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Computational Physiology Physiology: The study of the (bio) functions Computational Physiology: The use and development of mathematical and computational models to describe biological functions 4

5. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Computational Physiology The bad news: –It is a wide gap connecting multiple scales, genes, proteins, cells, tissues, organs...; –multiple physics: quantum, molecular dynamics, chemistry, electro-mechanics…; 5

6. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Computational Physiology The models representation are based and depend on multiple and diverse data MODEL 6

7. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 The Heart 7

8. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 The Heart The blood pump Cells contract changing the organ geometry and the blood is expelled 8

9. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 The Heart Cellular contraction: –An electric potential difference develops across the cell membrane and triggers a chain of electrochemical reactions that results in cellular contraction (intracellular Calcium spike, ATP, etc) 9

10. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 The interior of the cells are connected by special proteins that allow the electric potential to propagate. A fast electric wave propagates and triggers heart contraction. The Heart 10

11. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Models of Cardiac Electro-Mechanics Cardiac disease is the #1 cause of death in the globe (30%) Today, computational models of the heart provide a better understanding of the complex phenomenon and support the development of new drugs, therapies, biomedical equipments and clinical diagnostic methods 11

12. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Bottom-up design –Sub-cellular and cellular mathematical models Models of Cardiac Electro-Mechanics 12

13. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Models of Cardiac Electro-Mechanics Bottom-up design –Tissue mathematical models: electric activity 13

14. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Models of Cardiac Electro-Mechanics Bottom-up design –Tissue mathematical models: mechanical coupling 14

15. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Models of Cardiac Electro-Mechanics Bottom-up design –Organ modeling 15

16. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Introduction to cardiac modelling Two basic components: 1) A cell model that describes the electric behavior of a single cell; 2) A tissue model which describes how the cardiac electric wave propagates from one cell to another 16

17. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Cell model Bi-lipid layer: Ionic channels: Special arrangement of proteins cut thru the membrane and allow the flow of specific ions, such as Sodium, Potassium and Calcium. Intracellular space Extracellular space Ionic channel 17

18. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 ee ii CmCm I ion IcIc Cardiac cell models Hodgkin-Huxley based models Membrane works as a capacitor, isolating charges The ionic channel currents and the transmembrane potential satisfy a set of ordinary differential equations 18

19. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Cell models Canine ventricular model: Beeler-Reuter (9 eqs) Rabbit atrial model: Lindblad (27 eqs) Rat ventricular model: Pandit et al (26 eqs) Human atrial model: Nygren et al (30 eqs) Simplified ventricular model based on FHN (2 eqs) Guinea pig ventricular model: Luo-Rudy II (14 eqs) Human atrial model: Courtemanche et al (20 eqs) 19

20. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Cardiac Bidomain Model Tissue Model for cardiac electrophysiology Intracellurar and extracellular spaces (domains) modeled from an electrostatic point of view The coupling of the two domains is via non- linear cell modeling. Total cell membrane current spreads to both intracellurar and extracellular spaces 20

21. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Cardiac Bidomain Model 21

22. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Complex Models 22 Involves the coupling of several components (submodels) and data (geometry, biophysical parameters) Each component is a complex mathematical formulation, typically with tens of variables and hundreds of parameters New detailed models (components) are created and validated every week

23. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Modeling Challenges: Multi-scale and Multiphysics Computational Challenges: Simulations are computationally expensive (one heart beat = a couple of days in a parallel machine) Integration Challenge: Patient Specific Heart Model Complex Models 23

24. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Results 24

25. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 We have a 2D simulator We needed a computational framework that would facilitate, stimulate and broadcast the use and benefits of cardiac modeling. The framework combines: The parallel simulator for bidomain-based models Cluster Computing An automatic code generator for models described by CellML User-Friendly Graphical Interfaces Web Server Results 25

26. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 CellML XML based language (machine-readable) Describes mathematical models (MathML) Repository contains over 300 biophysical models A model is described via the connection of units, variables and components, in a hierarchical fashion 26

27. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 CellML The goal: Accelerating the development of new models Computational Frameworks and tools On the way: Ontology and web semantic Grid Computing 27

28. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 A couple of tools exist for edition, validation and simulation of models described in CellML Today two CellMl-based frameworks provide both cell and tissue level simulations: COR, a MS-Windows based environment, from the University of Oxford (cor.physiol.ox.ac.uk) AGOS, A web-based framework from FISIOCOMP- UFJF CellML-based tools 28

29. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Goal: Reach the biologists Computational Framework that hides many of the technical issues of cardiac modeling Agos Framework 29

30. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 It provides support to cardiac electrophysiology modeling A editor to CellML language A translator of CellML code into C++ code A user-friendly Web form to setup parameters and visualize results Web Server Cluster Computing The Computational Framework 30

31. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 API Generator to ODE Solutions Cellular models are described in CellML/MathML It translates CellML code into a object oriented C++ code Through the API generated, it is possible to simulate the model and setup parameters Agos Translator 31

32. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Tissue Model 32

33. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Inverse Problem 1.Forward Models of Cardiac Physiology 2.Inverse Problem 33

34. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Inverse Problem The forward problem –The user has to know all parameters, such as geometry of the organ and values of conductivity –It returns the potential diference along the time and space Inverse problem –The user knows the potential diference –He or she may want calculate the geometry and all another parameters 34

35. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Inverse Problems Estimate the values of electrical activity on the cardiac tissue Given a number of observed transmural electrograms estimate possible changes on the conductivity ( ,  ) of a known and specific region of the heart. 35

36. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Pathological Tissue Region with altered conductivity (,)(,) Motivation: focal variations of tissue conductivity values (both intra and extra) are observed in many different cardiac diseases: Acute ischemia, Infarct, Chagas Disease, Myocarditis Inverse Problems 36

37. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Inverse Problem More computational costly than the foward problem It solves the forward problem lots of time sequentionally InvCell and InvTissue 37

38. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 INVCell We are adjusting a model which GA takes one day long to run. Asynchronous x Synchronous. –Heterogeneity x Homogeneity. It uses the AGOS API lots of times –ODEs are solved sequentionally 38

39. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 InvCell Genetic algorithm –Based on Darwin’s evolutionary theory –Aims to optmization (maximize/minimize) –It works simulating the process of natural reproduction, mutation, and selecting the fittest individual

40. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 INVCell GA implementation: –The individuals are the parameters –We know the solution – calculated by the simulator –Each iteration gets more closer to the final solution –Parallel GA – master-slaves. –Floating point representation; –Elitist selection; –The initial population is randomly generated ; –A new generation depends of their parents; 40

41. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 INVTissue It solves an inverse problem associated to the simulation of cardiac tissue models. It also has an implementation of a Genetic Algorithm parallelized with MPI. It runs the simulator to each individual Quite slow! 41

42. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 INVTissue Investigate the solution of an inverse problem associated to cardiac electrophysiology The goal is to estimate values for the electrical conductivity of cardiac tissue, taking as known some information concerning the electrical activity of the heart Asynchronous non generational GA Parallelized using master-slave 42

43. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Goals Porting InvCell –It should be the easiest; Porting InvTissue –More complicated – lots of dependencies; Porting of a basic version of the Heart Simulator –Hardest problem; 43

44. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Goals The heart simulator uses : –C code –Petsc library –MPI Numerical methods to solve lots of equations Each iteration have lots of dependencies on the previous one 44

45. www.eu-eela.eu Itacuruça (Brazil), E2GRIS1, 2.11.2008 – 15.11.2008 Questions … 45