Download Heart Simulator - EELA Documents

E-science grid facility for Europe and Latin America
Heart Simulator
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
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
Undergraduate Students
Caroline Costa
Gustavo Miranda *
Ricardo Campos *
Guilherme Montebrune
Former Master Students
Rafael Sachetto Oliveira
Fernando Otaviano Campos
Bernardo Rocha
Daves Martins
* Grid team
www.eu-eela.org
Ely Fonseca
Overview
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Computational physiology
The heart
Heart models
Computational Framework
Inverse Problems
Gridification Goals
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Computational Physiology
• Physiology: The study of the (bio) functions
• Computational Physiology: The use and development
of mathematical and computational models to describe
biological functions
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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…;
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Computational Physiology
• The models representation are based and depend on
multiple and diverse data
MODEL
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The Heart
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The Heart
• The blood pump
• Cells contract changing
the organ geometry and
the blood is expelled
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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)
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The Heart
• 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.
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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
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Models of Cardiac Electro-Mechanics
• Bottom-up design
– Sub-cellular and cellular mathematical models
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Models of Cardiac Electro-Mechanics
• Bottom-up design
– Tissue mathematical models: electric activity
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Models of Cardiac Electro-Mechanics
• Bottom-up design
– Tissue mathematical models: mechanical coupling
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Models of Cardiac Electro-Mechanics
• Bottom-up design
– Organ modeling
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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
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Cell model
• Bi-lipid layer:
Cm 
q

Cm  q
Cm
d dq

 Ic
dt dt
• Ionic channels: Special
arrangement of proteins
cut thru the membrane
and allow the flow of
specific ions, such as
Sodium, Potassium and
Calcium.
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Intracellular space
Extracellular space
Ionic channel
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Cardiac cell models
e
Cm
Ic
Iion
i
• 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
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Cell models
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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)
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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 nonlinear cell modeling. Total cell membrane
current spreads to both intracellurar and
extracellular spaces
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Cardiac Bidomain Model
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Complex Models
• 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
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Complex Models
• 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
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Results
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Results
• We have a 2D simulator
• We needed a computational framework that would facilitate,
stimulate and broadcast the use and benefits of cardiac
modeling.
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• 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
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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
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CellML
• The goal:
• Accelerating the development of new models
• Computational Frameworks and tools
• On the way:
• Ontology and web semantic
• Grid Computing
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CellML-based tools
• 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 FISIOCOMPUFJF
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Agos Framework
• Goal: Reach the biologists
• Computational Framework that hides many of the
technical issues of cardiac modeling
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The Computational Framework
• 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
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Agos Translator
• 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
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Tissue Model
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Inverse Problem
1.
Forward Models of
Cardiac Physiology
2.
Inverse Problem
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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
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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.
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Inverse Problems
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
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Inverse Problem
• More computational costly than the foward
problem
• It solves the forward problem lots of time
sequentionally
• InvCell and InvTissue
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INVCell
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We are adjusting a model which GA takes
one day long to run.
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Asynchronous x Synchronous.
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Heterogeneity x Homogeneity.
It uses the AGOS API lots of times
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ODEs are solved sequentionally
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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
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INVCell
• GA implementation:
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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;
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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!
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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
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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;
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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
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Questions …
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