Multiscale cardiac modeling focuses three main areas: 1) tissue-level models of electrophysiology, 2) models of myofilaments, the basic functional unit of contraction, and 3) organ-level models of electromechanics. Each area requires its own mathematical formulations and computational approached for tractable solutions in timescales appropriate for basic science and clinical applications. In the Cardioid Heart Modeling Project, we develop codes that run on the Blue Gene series of computers that have rank some of the fasted computers in the world. We also work with a diverse set of collaborators to understand basic physiology from the molecule level to the whole organism.Research Direction for Cardiac Modeling
- Tissue-level models of cardiac electrophysiology
- Models of cardiac myofilaments
- Organ level models of cardiac electromechanics
- Download myofilament model codes
Tissue-level models of cardiac electrophysiology
The heart is composed of discrete cells that are discrete and individual in the sense that each is an excitable system. Models of the cardiac cells have been in developed since the 1960s and are considered to be one the most developed areas of computational biological models. Detailed models of cardiac cells are still under active develop and continue to increase in sophistication and require solution of nonlinear, and often stiff, sets of ordinary differential equations. Because each cell in the muscle in heart needs to be simulated parallel with these sets of ODEs, there is huge computational cost that exceeds practical solution times on even the largest supercompters.
To address the need for ever greater computational needs, we have been developing new algorithms to execute tissue-level cardiac models with unprecedented levels of parallelism. We have developed codes that run on the Blue Gene series of computers that have ranked some of the fasted computers in the world (Top500.org), and also importantly, the most energy efficient ( green500.org). To efficiently utilize massively these parallel machines, new decomposition strategies were developed to decompose the heart tissue into small pieces of equal work units that evenly distribute the work up to 32K computational cores. Because cardiac cells must communicate with their neighbors, the interconnect network between nodes becomes highly critical for the ability to scale codes to very large numbers of nodes. In the Cardioid Heart Modeling Project, we will work in collaboration with Lawrence Livermore National Laboratory (LLNL) to develop codes that run on Sequoia, a Blue Gene/Q series of computers that will have 1.6 petabytes of memory, 96 racks, 98,304 compute nodes, and 1.6 million cores. Though orders of magnitude more powerful than such predecessor systems as ASC Purple and BlueGene/L, Sequoia will be 160 times more power efficient than Purple and 17 times more than BlueGene/L.
More about the Cardioid Cardiac Modeling Project can be found here:
- Smarter Planet Blog: Sequoia supercomputer simulates the human heart in dramatic detail
- IBM Research Blog: Coding the human heart
- Cardioid Project: Video on You Tube
- ISGTW: World’s second most powerful supercomputer goes straight for the heart
- Popular Mechanics: World’s top supercomputer simulates the human heart
Models of cardiac myofilaments
Genomics and Systems Biology group is developing other modeling approaches to better understand how gross muscle properties emerge from the interactions at the molecular level. Our approach incorporates results from recent advances in experimental techniques that allow the fundamental interactions of the system to be probed. These techniques include EM reconstructions that reveal proteins conformations, nucleotide substitutions that modify the behavior of myosin motors, and genetic mutations that alter the regulatory proteins. The availability of increased computing power will make possible new classes of biological models that include detailed representations of proteins and protein complexes with spatial interactions. Along these lines, we are developing a model of the interaction of actin and myosin within one pair of thick and thin filaments in the cardiac sarcomere. The model includes explicit representations of actin, myosin, and regulatory proteins. The preliminary version of the work is detailed in Hussan et al., 2006 (A spatially detailed myofilament model as a basis for large-scale biological simulations ). Although this is not an atomic-scale model, as would be the case for molecular dynamics simulations, the model seeks to represent spatial interactions between protein complexes that are thought to produce characteristic cardiac muscle responses at larger scales. While the model simulates the microscopic scale, when model results are extrapolated to larger structures, the model recapitulates complex, non-linear behavior. For example, the model recapitulates the steep sensitivity of developed force as function of activator Ca, as seen in real muscle. By bridging spatial scales, the model provides a plausible and quantitative explanation for several unexplained phenomena observed at the tissue level in cardiac muscle. Model execution entails Monte Carlo based simulations of Markov representations of calcium regulation and actin-myosin interactions. While most of the results presented so far are preliminary, we propose that this model will be suitable to serve as a basis for larger-scale simulations of multiple fibers assembled into larger sarcomere structures. For example, the shows a possible mapping of 32-sarcomere myofibril model onto one rack of a Blue Gene L computer.
The detailed model that includes explicit representations of actin, myosin, and regulatory proteins was also used to guide the construction of an approximate model of the cardiac myofilament (MF) of the using highly efficient ordinary differential equations (ODEs). We develop a point model to simulate wide variety of experimental muscle characterizations including Force-Ca relations and twitches under isometric, isosarcometric, isotonic and auxotonic conditions. Complex MF behaviors are difficult to model because spatial interactions cannot be directly implemented as ODEs. We therefore allow phenomenological approximations with careful consideration to the relationships with the underlying biophysical mechanisms. We describe new formulations that avoid mean-field approximations found in most existing MF models. To increase the scope and applicability of the model, we include length- and temperature-dependent effects that play important roles in MF response. We have also included a representation of passive restoring forces to simulate isolated cell shortening protocols. Possessing both computational efficiency and the ability to simulate a wide variety of muscle responses, the MF representation is well-suited for coupling to existing cardiac cell models of electrophysiology and Ca-handling mechanisms. To illustrate this suitability, the MF model is coupled to the Chicago rabbit cardiomyocyte model. The combined model generates realistic appearing action potentials, intracellular Ca transients, and cell shortening signals. The combined model also demonstrates that the feedback effects of force on Ca binding to troponin can modify the cystolic Ca transient. This work is published in the following paper:
Rice, J.J., Wang, F., Bers, D.M.. and De Tombe, P.P. Approximate model of cooperative activation and crossbridge cycling in cardiac muscle using ordinary differential equations, Biophysical Journal (2008) (Pubmed).Also, the model codes from the paper can downloaded below.
Organ level models of cardiac electromechanics The primary function of the heart is a pump to move the blood through the lungs and body. Cardiac electromechanical models represent both the electrical activation (as in the electrophysiological models described above) and mechanical deformation that ejects blood from the heart. On a heart beat, each and every heart muscle cell is electrically excited that produces a secondary influx of calcium ions into the cell that in turn will activate the myofilaments to contract. The force developed by each cell is computed using the approximate ODE(ordinary differential equations)-based model of the myofilaments as described above. The sum of the force of the contracting cells generates the force to contract the heart and eject the blood. However, the final calculation require more that just summing the cell forces because there are additional contributions from the passive tissue properties, the complex arrangement of muscle fibers and the pressure of the blood to be ejected. The example below shows a fairly simplified heart model with low spatial resolution. Future work will involve developing higher spatial resolution models that can contain more of detail that is thought to be important increase the predictive accuracy of cardiac models. However, the greater detail will come at the cost of much greater computational demands. To address these demands, we will be developing new algorithms to execute tissue-level cardiac models with unprecedented levels of parallelism available with the Blue Gene series of computers.
As a service to the cardiac modeling community, we are freely distributing source code for the models from:
Rice, J.J., Wang, F., Bers, D.M.. and De Tombe, P.P. Approximate model of cooperative activation and crossbridge cycling in cardiac muscle using ordinary differential equations, Biophysical Journal (2008) (Pubmed).
Note: There is a typo in the equations in the paper. These values are transposed. The correct values are:
kn_p = 0.50 /ms
kp_n = 0.050 /ms
Source code for the ODE-based myofilament model is available for download in the following formats:
- XPP code(implementation from published paper for Figs. 3-8)
- C++ code for combined Chicago and myofilament model (implentation for published paper for Figs. 9-10)
- Matlab implementation of the rat model(not used in the orginally published paper)
XPP (code used for published paper for Figs. 3-8)
XPP is a freely distributed package to implement and execute dynamical models. While this simulation package may not be at well known as others, the code is stable, reliable, portable, well-documented, and free. XPP is a freely available package to implement and execute dynamical systems. XPP has many advantages for investigating ODE-based models such as easy searching of parameter space and multiple integration methods. The provided code implements the model and gives instructions to recreate the figures in the paper. The standard file to code and execute a model is in XPP is an .ODE file. To run this model, the user will need to install XPP on their computer from the website. Using the parameter sets provided in the ODE file, the user can recreate Figs. 3-8. More detailed instructions to recreate the figures are included in the .ODE file. Three sample output files are provided so that the user can be sure the code is executing correctly. The sample output files are plain text files and are located in the directory named: “SampleOutput”. The following link will download a zipped directory with the XPP and C++ code - CodeDistribution_XPP_CPP.zip.
C++ code for combined Chicago and myofilament model (implentation for published paper for Figs. 9-10)
This package of code implements the Chicago model of the rabbit ventricular myocyte. This directory contains a C++ source code called ChicagoMyofilement.cpp. This is the main routine to implement the combined Chicago model and myofilament model at shown in Figs. 9-10. The integration routine is CVODE that free distributed by Lawrence Livermore National Laboratories. The code was compiled and executing using the Eclipse Integrated Development Environment (IDE). This package can be downloaded for free and installed from Eclipse.Org. One can also use other compilers and a sample make file is provided as a guide. The main routine as defined in ChicagoMyofilement.cpp contains detailed instructions to recreate the Figs. 9-10. Three sample output files are provided so that the user can be sure the code is executing correctly. The subdirectory CVODE The sample output files are plain text files and are located in the directory named: “SampleOutput”. The following link will download a zipped directory with the XPP and C++ code - CodeDistribution_XPP_CPP.zip.
Matlab implentation of the rat myofilament model (not used in original publication)
This rountine implements a rat version of the myofilament model. The code is generously provided by Jason Yang of University of Virginia. The file is plain text, but has a .M extension for Matlab. The code implements a subroutine that is suitable to interface with a model of electrophysiology and Ca handling. The following link will a text file with the Matlab code - MyofilamentRat.M