1. OpenCMISS + CellML David Nickerson & Chris Bradley Auckland Bioengineering Institute University of Auckland New Zealand

2. OpenCMISS Re-engineering of CMISS Main website –http://www.opencmiss.org/http://www.opencmiss.org/ Open source on github –https://github.com/organizations/OpenCMISShttps://github.com/organizations/OpenCMISS

3. OpenCMISS(Iron) library Iron librarycore library openCMISS (cm) FieldML API CellML API openCMISS (cm) FieldML API CellML API openCMISS (cm) CellML API FieldML API FieldML file CellML file Processors History file Language Bindings Fortran C/C++ Python Etc. Language Bindings Fortran C/C++ Python Etc. Language Bindings Fortran C/C++ Python Etc. Language Bindings Fortran C/C++ Python Etc. OpenCMISS (iron) FieldML API CellML API External Program or script

4. OpenCMISS application openCMISS (cm) FieldML API CellML API Com Layer openCMISS (cm) FieldML API CellML API openCMISS (cm) CellML API FieldML API Com Layer FieldML file CellML file OpenCOR Processors CellML API FieldML API Com Layer History file FieldML API CellML API Com Layer Iron Zinc Network

5. Example – Electrical Activation (Bidomain representation) Cell Membrane Intracellular Space  i,  i Extracellular Space  e,  e I ion Cell model =

6. Bidomain equations Where: –V m = transmembrane potential –  i = intracellular potential –  e = extracellular potential –A m = membrane surface/volume ratio –C m = membrane capacitance –  e = intracellular conductivity tensor –  i = intracellular conductivity tensor –I ion = ionic source current from cellular model –I m = transmembrane stimulus current –i i = current injection per volume intro intracellular space –i e = current injection per volume intro extracellular space

7. Cellular processes

8. Problem/Field description Fields: Geometric Fibre Material (  i,  e, A m, C m etc.) Potential (V m,  e, etc.) Source (I ion, etc.) Cellular state variables Cellular intermediate variables Cellular parameter variables

9. Field parameter vector 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 1 3 5 7 15 17 19 21 29 31 33 35 Field variable, u Component, u 1 Component, u 2 Parameter vector, x Global DOFs

10. Electrophysiology - CellML 300% 100% gNa Distribution +50 mV -85 mV Stimulus off +50 mV -85 mV Normal activation +50 mV -85 mV gNa activation

11. Finite Elasticity – Breast Mechanics Courtesy of Prasad Gamage Skin Breast Tissue Undeformed Deformed Under gravity loading

12. Fluid Mechanics – 3D NS Carotid Artery Flow, Re=100 MeshVelocityPressure Courtesy of David Ladd

13. CellML as a DOF black box Field variable Parameter DOF Vector Component 1 Component 2 Component 3 InputsOutputs

14. OpenCMISS CellML Import void computeRates(double VOI, double *PARAMETERS, double *RATES, double *STATES, double *INTERMEDIATE); { const double FIXED[..]; : } StateParametersIntermediate StateParametersIntermediate CellML Variables CellML Environment CellML Model Import Set as known Set as wanted Set as known and wanted

15. CellML Interface ModelsStateParametersIntermediate CellML environ OpenCMISS Field CellML Fields

16. CellML/Field Maps ModelsStateParametersIntermediate CellML environ CellML to field MapField to CellML MapCellML integrate Cellular model Transmembrane Voltage Field

17. CellML/Field Maps ModelsStateParametersIntermediate CellML environ Strain Field Stress Field CellML to field Map Field to CellML Map CellML evaluate Constitutive Law