All physiological systems are associated with the interactions of multiple physical processes, not least because tissues grow and adapt to their continually changing environments. These ‘multi-physics’ systems are also multi-scale: processes at the cell and tissue scales are linked intimately with molecular events at the gene and protein levels. One example can be seen in the study of cerebral aneurysms, as illustrated in . Alterations of flow in the cerebral blood vessels induce a pressure and shear response that, via numerous cellular signaling pathways, produces a change in the composition of the tissue (primarily collagen, elastin and smooth muscle). The resulting change in the mechanical properties of the tissue is reflected in the wall mechanics and hence aneurysm shape. This shape then influences the flow solutions.
Figure 2 The major components involved in linking signaling pathways at the cell level to continuum mechanics at the tissue level. Large deformation soft tissue mechanics is used to solve for the shape of the aneurysm. 3D CFD within this arterial volume then gives (more ...)
To understand and quantify these complex multi-scale and multi-physics processes, the physiome modeling community are currently developing three model encoding standards: SBML1
(for 0D+time biochemical pathways), CellML2
(for 0D+time biophysical models) and FieldML3
(for n-dimensional spatial fields). The standards define how models are structured, how the mathematical equations are encoded and how units are defined. They typically use XML as the means of serialization. Two major model repositories have been developed–Biomodels4
(primarily SBML pathways models) and the CellML5
repository. The SBML and CellML groups are now working together to produce common metadata standards, based on ontologies, for annotating the models with biological and biophysical information. These metadata standards are needed both for checking the biological and biophysical correctness of models but also to ease the process of combining models into composite models (e.g. combining electrophysiological models with calcium transport models, myofilament mechanics models and signal transduction models) and for using the cell models in tissue level simulations. Another metadata standard under development by the SBML and CellML communities is SED-ML for encoding the numerical algorithms and associated parameters for running a model simulation.
Establishing these standards and model repositories has been an important step in achieving a robust foundation for the modeling community – particularly when the curated models are available at the time of publication, as is increasingly the case. The next goal for this work is to develop data standards and improved databases for model parameter sets, including the ability to record the provenance of parameters. Parameter sets can be stored in CellML files (for example) but there are currently no mechanisms for annotating the experimental origin of these parameters and their dependence on species, temperature, pH, etc, is often obscure. Having the models and data available in standardized formats with clearly stated dependencies will improve the utility of models and facilitate the creation of workflows that can generate model results from parameter sets and input data in order to compare model predictions with experimental data in an automated fashion. The goal here is to greatly improve the reusability of models and clarify their limitations.
The general strategy adopted by the community developing the modeling standards is as follows:
- Develop markup languages (MLs) for encoding models, including metadata, and data.
- Develop application programming interfaces (APIs) based on the MLs.
- Develop libraries of open source tools that can read and write the ML encoded files.
- Develop data and model repositories based on MLs.
- Implement work flows that enable model results to be demonstrably reproduced.
A software framework is also being developed by the Physiome Project, based on the markup languages and model repositories, to solve the equations for these multi-scale, multi-physics processes. The framework is open source and based on internationally collaborative efforts. For example, some components of this framework are:
- OpenCell (www.cellml.org/tools/opencell) is the open source code for running CellML models.
- Cmgui (www.cmiss.org/cmgui) is the open source code for rendering FieldML files.
- OpenCMISS (www.cmiss.org/openCMISS) is being developed as the open source computational code for solving the equations representing the physical laws – e.g. (for the example in ) Navier-Stokes equations for the flow, large deformation elasticity equations for the arterial wall mechanics, reaction-diffusion equations for transmural signaling. It is designed to handle the nonlinear, anisotropic and inhomogenous material properties characteristic of soft biological tissues. OpenCMISS has interfaces to both CellML and FieldML. The 3D geometry and other spatial input fields used in OpenCMISS are read from FieldML files. The mechanical constitutive laws and signaling pathway models are encoded in CellML. OpenCMISS uses MPI for distributed memory parallel programming.
For example, in relation to the problem mentioned above of modeling cerebral aneurysms, the modeling language CellML allows individual signaling pathways to be modeled and checked in OpenCell then combined into signaling networks that link shear stress signals on endothelial cells to the production of collagen, elastin and smooth muscle in the arterial wall. The mass and orientation of these arterial wall constituents is then coupled via mixture theory to the constitutive laws of large deformation elasticity theory. The signal transduction pathways that control smooth muscle cells and fibroblasts are modeled in CellML as systems of ordinary differential equations and nonlinear algebraic equations describing the signaling networks. The shear stress acting on the endothelial cells provides the input to this signaling network and the output is linked via mixture theory to the constitutive laws used in openCMISS for solving the tissue mechanics.
Bioinformatics is another enabling methodology for systems biology and physiome projects. The term bioinformatics was first introduced to mean the application of information technology to the field of molecular biology. However, the term has evolved and its limits have been expanding to now include not only computer analysis of genomic and proteomic information, but also analysis of complex signaling and metabolic pathways, protein-protein, protein-DNA interactions, and analysis of various anatomical images and biological signals (e.g., EKG). Thus, more generally bioinformatics can be viewed as a methodology to generate hypotheses and derive scientific knowledge from computer analysis of complex biological experimental data. Medical informatics is both a branch of bioinformatics dealing with human patients data, and a process of managing medical information for more general non-scientific purposes. Bioinformatics is a major enabling methodology for systems biology and physiome projects. Bioinformatics will continue to evolve as new areas of application emerge; e.g., future applications of bioinformatics are likely to include analysis of computational models stored in model repositories.