Adaptive Multiscale Modeling: Concepts, Difficulties and Successes

1. Adaptive Multiscale Modeling: Concepts, Difficulties and Successes On-line prediction: A goal for multiscale modeling Error reduction in model construction: Modularity, Unit Balancing (JSim), Reduction Standards, physical constraints, verification, validation Parameter shifts with model reduction: physical -> empirical? Example: Circulation and O2/CO2 exchange modeling Physiome/cardiome Why integrate modules into composite systems? Emergent behavior of enzymes and receptors The reporting and archiving of models James Bassingthwaighte, Howard Chizeck, Les Atlas, Hong Qian, Brian Carlson, and Stephen Hawley Bioeng. and Elect. Eng., U. Washington, Seattle, WA

2. Collaborative efforts leading to publications • 1D circulatory system as boundary conditions for finite element 4D models: • Kirckhoffs et al. (UCSD, McCulloch) Ann Biomed Eng. 37: 1-18, (Jan) 2007 • Errors in parameters introduced in model reduction: • Anderson and JBB (PNNL/UW) J. Nutrit. Accepted 2007 • 1D and 2D linked models for respiratory airway exchange (PNNL/UW) • Anderson and Hlastala. J Appl.Physiol. Revision prior to accept. • Hemoglobin transport, precession, and alveolar-arterial O2 differences • Carlson et al (UW/MCW/CWRU) NYAcad Sci (in press) 2007 • Buffering of ATP balance by AMP deamination cycle • Feng, Beard et al.( MCW, UW) Am J Physiol (submitted) • Standards for modeling physiological systems • N.Smith , D Beard, JBB(Oxfrod, MCW, UW) Proc Roy Soc Lond 2007 (in press)

3. Error Inhibition and Correction in Modeling • Adherence to standards: • Balances of mass, charge, energy • Well-defined assumptions • Platform Independence: • JSim is Java-based (Linux, Unix, Windows, MacOSX) • A general interface with graphics with replacable GUI • Unit balance checking on equations: • Allows multiple systems of units, SI, MKS, cgs, English • Automatic unit conversion from one system or scale to another • Solution speed, allowing focused attention during usage: • Run-time Java at 300 times Matlab/Simulink speed • Shared memory multiprocessing (but not yet distributed memory) • Accepts SBML and CellML model constructs

4. Error Inhibition and Correction in Modeling • Multiple choices of ODE solvers in JSim: • Allows rapid comparisons of solution with various solvers, t • Several Runge-Kuttas, Dopris5, Euler • Radau and CVode for stiff systems • Multiple choices of 1D PDE solvers in JSim: • Allows comparisons with different solvers, grid and step sizes • LSFEA, TOMS690 , TOMS731, MacCormack • Multiple choices of Optimizers in JSim: • Allows switching from one optimizer to another • NL2SOL, Glad-Goldstein, SENSOP, Gridsearch, StepT, simulated annealing

5. Error Inhibition and Correction in Modeling • Multiple models run in 1 JSim program : • Ease in comparing reduced model forms with detailed forms • Setting to optimize reduced model to parent model • Allows translations from empirical parameter values in reduced models to the physically meaningful values • Multiple choices of GUIs specific for each model: • Model display can serve as parameter control panel • Slider control of selected parameters coming • Sensitivity analysis and model behavioral displays: • Mapping of results from a succession of parameter values • Single or multiple parameter looping • Sensitivity analysis speeded by shared memory multiprocessing

6. Handling Units: Balances and Interconversions • A unit check on every equation: • Like ribosomal sequence checking on transcription, doesn’t check the math, but checks consistency • A great aid to model reproducibility • An essential check in linking modules into larger systems: • Unit conversions to basic SI unit system eliminates conflicts • Removes need for manual conversion of units • Basic units are: kg, m, sec, ampere, kelvin, mole, candela • Scaling prefixes understood and converted: e.g. milli, micro, nano, pico, kilo, etc. • Dimensionless is an allowed declaration • Multiple choices of GUIs specific for each model: • Model display can serve as parameter control panel • Slider control of selected parameters coming

7. Module reduction to gain speed (compromising robustness)

8. Transport and Metabolism: NIBIB Simulation Resource at the University of Washington Myocardial capillaries Model for capillary-tissue exchange

9. Health Organism Structure of heart defines spread of excitation (Mcculloch, UCSD) Organ Tissue Cell Molecule The Human Physiome Gene Ion channel activation requires metabolism: Muscle contraction follows ion channel activation: Beard, Jafri, Kemp et al For the Cardiome, multiscale modeling is required to cover the range of levels of function Contracting heart driven by spread of excitation (Hunter & Smith in Auckland, with D.Beard’s coronaries)

10. Exchange Systems Pathways of Oxygen and Carbon Dioxide Transport and Exchange – A Big Picture

11. EMD: Empirical Mode Decomposition, a methodfor identification of changes in signal characteristics “Data”: Model solutions for CV system at onset of blood loss.

12. EMD: Empirical Mode Decomposition, a methodfor identification of changes in signal characteristics “Signal decomposition”: Event indication at 120 and 250 sec.

13. + Mb MbO The Process of Transport and Exchange of Oxygen

14. Capillary-tissue exchange across a thin membrane:bolus injection at t=0

15. Capillary-tissue exchange across a thin membrane:bolus injection at t=0

16. Capillaries are parallel (5 mm diam., 800 mm long) and radial intercapillary distances for diffusion are < 20 microns. The Supply Side (Yipintsoi, Harvey & Bassingthwaighte, 1974)

17. General blood-tissue exchange model

18. Dual Oxygen/Water Modelfor analyzing PET images by Residue detection

23. Modeling Standards:The Keys to Successful Sharing • Really good models are attractive currency • The best ones are the style setters • The great ones top the citation lists • Reproducibility is fundamental • Full exposure is paramount! • Unit checking is the single most powerful error reduction technique.

24. Characteristics of biophysically-based models, validated and available to the user community • Units balanced, fundamental balances addressed • Completely documented, verified and validated • Assumptions all listed • Constraints to correctness defined • Accompanied by test data sets showing validity • A fully described model is a working hypothesis that can be challenged. It is then suitable for archiving in a Physiome Database and for publication!

25. Requirements for archiving a model : Biophysically based models should have these basic balances: 1. Unitary Balance – exact balancing of units in all equations. 2. Mass Balance – total conservation of mass of individual components. (Conservation of volume should follow from this if all partial molar volumes are known.) 3. Charge Balance – accounting for charge transfer across membranes and for membrane potentials and Donnan equilibria. 4. Osmotic Balance – accounts for water and solute fluxes in transient and steady states 5. Thermodynamic balance – obeys Haldane constraints for reactions, and has energy balance

26. Verification:The mathematical expressions defining the model are complete and the computation gives correct solutions. • 6. Equations mathematically correct, complete, with unitary • balance, initial and boundary conditions, and with explicit • definitions, units, and unambiguous descriptions of each • parameter and variable. • 7. Running code supplied in commonly used form. Code exhibits: • numerical solutions matching appropriate reduced cases • having analytical solutions, etc. • runs correctly with no, or at least little, dependence on step size • runs from varied initial conditions to appropriate steady states • runs on more than 1 platform

27. Demonstrated to be valid re describing anatomic data and physiological dynamics: 8. Initial conditions: consistent with a physiological steady state (constant or oscillatory) 9. Data to be fitted by the model should be provided for public download, with sets of parameters defined through good fits of model to data. Provide also of data sets which cannot be fitted, and therefore serve as challenges to the model. 10. Results of fitting data sets from different studies, showing applicability of the model to high quality experimental data from different sources and of different sorts. 11. Parameter evaluation: parameters not determined via fitting the selected data should be justified through citations, calculations, etc. The parameters determined via model analysis should be described by estimated means and confidence ranges.

28. Documentation: Each model should be accompanied by: 12. Afull description and a peer reviewed publication, or equivalent, with the verification and validation. 13. A phylogenetic heritage of the model and its historical and contemporary setting. 14. Documentation with references for parameter values, appropriate to the species, age, sex, etc. 15. Descriptions of modules or submodels and their sources, if applicable. 16. Reference to higher level models incorporating this model into a larger more integrated system, illustrating the position of this model in the hierarchy.

29. Obeisance to Good Modeling Practices: Fundamental assumptions Limitation and shortcomings List of alternative models to be considered Describe level of detail used in the model and where it fits into the hierarchy envisaged. Provision for Critique, Commentary and Discussion: This would presumably be supported on the website providing the model and would include: Commentary by authors, by reviewers, and responses by authors. Commentary as in letters to the editor. Critiques published subsequently by other authors or the same authors. Listings of references to competing or alternative models.

30. Computer modeling as a clinical tool • Modeling Analysis of Data: • Optimization, requiring iteration • Heterogeneous systems, such as the normal heart, require regional parameterization for local blood flows, oxygen consumption, etc. • Clinical data analysis could use supercomputing, e.g. for combined CT-PET reconstruction and analysis -> functional images

31. Constraints in modeling, scientific and psychological • Impatience: To think fast, see the results fast. • Minimal models - incomplete, misleading. • Forget Occam’s razor: get it right, use redundant information. Avoid “minimal models” other than for description or for diagnostic classification. • Structure, composition, prior data are critical to developing valid, robust models. • Conservation (mass, volumes, energy, etc.) • Physics counts! • Thermodynamics too, but that’s just physics.

32. Conclusions • Realistic clinically useful models are often complicated, even complex. • Spatially distributed models are commonly required, but these are not more complicated than compartmental models, just more realistic. • Models are in day-to-day use in medical practice using imaging. • First principle models provide insight into the biology and can be built upon. • Model archiving with complete documentation is essential to making them publicly available by download.