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Modeling of Oxygen and Carbon Dioxide Transport and - imag wiki


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									 Adaptive Multiscale Modeling: Concepts,
        Difficulties and Successes
James Bassingthwaighte, Howard Chizeck, Les Atlas, Hong Qian, Brian
                   Carlson, and Stephen Hawley
        Bioeng. and Elect. Eng., U. Washington, Seattle, WA

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
Why integrate modules into composite systems?
      Emergent behavior of enzymes and receptors
The reporting and archiving of models
     Collaborative efforts leading to publications

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

    Error Inhibition and Correction in Modeling

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

    Error Inhibition and Correction in Modeling

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

    Error Inhibition and Correction in Modeling

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

     Handling Units: Balances and Interconversions

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

Module reduction to gain speed (compromising robustness)

    Transport and Metabolism:
     NIBIB Simulation Resource at the University of Washington

capillaries                Model for

                   For the Cardiome, multiscale modeling is required
                         to cover the range of levels of function
                 Organ                                 Structure of heart defines
                                                       spread of excitation
            Tissue                                     (Mcculloch, UCSD)

           The Human Physiome                                                            Contracting heart driven by
                                                                                         spread of excitation (Hunter
                                                                                         & Smith in Auckland, with
                                                                                         D.Beard’s coronaries)
                               Ion channel activation
                                      requires metabolism:
Muscle contraction follows
  ion channel activation:

                                                                    Beard, Jafri, Kemp et al
Pathways of Oxygen and Carbon Dioxide
Transport and Exchange – A Big Picture

                              Exchange Systems

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

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

The Process of Transport and Exchange
of Oxygen

                                        + Mb   MbO

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

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

 The Supply Side

Capillaries are parallel (5 mm
diam., 800 mm long) and radial
intercapillary distances for
diffusion are
< 20 microns.

                                 (Yipintsoi, Harvey & Bassingthwaighte, 1974)   16
General blood-tissue exchange model

Dual Oxygen/Water Model
for analyzing PET images by Residue detection

      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.

  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
       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

        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

            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.
            Documentation: Each model should be
                     accompanied by:

  12. A full 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
  16. Reference to higher level models incorporating this model into a
larger more integrated system, illustrating the position of this model
in the hierarchy.

         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.
           Computer modeling as a clinical tool

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

        Constraints in modeling, scientific and psychological

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

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


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