OpenCMISS + CellML

David Nickerson & Chris BradleyAuckland Bioengineering InstituteUniversity of AucklandNew Zealand

OpenCMISS

• Re-engineering of CMISS• Main website

– http://www.opencmiss.org/

• Open source on github– https://github.com/organizations/OpenCMISS

OpenCMISS(Iron) libraryIron librarycore library

openCMISS

(cm)Field

ML

API

CellM

L A

PIopenCMIS

S(cm)Fi

eld

ML

API

CellM

L A

PIopenCMIS

S(cm)

CellM

L A

PI

Field

ML

API

FieldML file

CellML file

Proc

esso

rs

History file

Language

BindingsFortran

C/C++

Python

Etc.

Language

BindingsFortran

C/C++

Python

Etc.

Language

BindingsFortran

C/C++

Python

Etc.

Language

BindingsFortran

C/C++

Python

Etc.

OpenCMISS(iron)

Field

ML

API

CellM

L A

PI

External Program or script

External Program or script

External Program or script

External Program or script

OpenCMISS application

openCMISS

(cm)Field

ML

API

CellM

L A

PI

Com

La

yer

Com

La

yer

openCMISS

(cm)Field

ML

API

CellM

L A

PI

openCMISS

(cm)

CellM

L A

PI

Field

ML

API

Com

La

yer

FieldML file

CellML fileOpenCOR

Proc

esso

rs

CellM

L A

PI

Field

ML

API

Com

La

yer

History fileFi

eld

ML

API

CellM

L A

PI

Com

La

yer

Iron

Zinc Network

Example – Electrical Activation (Bidomain representation)

Cell Membrane

Intracellular Spacei, i

Extracellular Spacee, e

Iion

Cell model =

Bidomain equations

Where:– Vm = transmembrane potential– i = intracellular potential– e = extracellular potential– Am = membrane surface/volume ratio– Cm = membrane capacitance– e = intracellular conductivity tensor– i = intracellular conductivity tensor– Iion = ionic source current from cellular model– Im = transmembrane stimulus current– ii = current injection per volume intro intracellular space– ie = current injection per volume intro extracellular space

eimieie

imionmeimim

mm

eim

iiV

iIIAVt

VCA

V

σσσ

σσ

Cellular processes

ATP

IKr2

K+

K+

K+ K

+ K+ K

+

IKATP

IK1IKto

IKr1

IKs

INa-stretch

IAn-stretch

INS-stretch

IK-stretch

ICa-stretch

H2PO-4

2Na+

H+Lac

Na+

H+

HCO-3

Cl-

CBEOH-

Cl-

CHE

HCO-3Na

+

NBCNHELAT NPE

MgADP Mg2+

MgATP

MgPi

Magnesium Buffering

K+ Ca2+

MgADP+Pi+H+ MgATPOxPhos

ImKATP

3H+H+

2Lac

3MgATP

3MgADP+3Pi

Glycogenolysis Contraction

AK

CK

ADP

AMP

MgADP

MgATP

Cr

PCr ADP+H+

VCO2transport

CO2H+

H2PO4-

Intrinsic Buffers

Ca2+TropC

Calmodulin

Calcium Buffering

3Na+

NCE Ca2+

IpNa

Na+

IbNa

INa

DS

Na+

Na+

NSRJSR

MgATP Ca2+

Ca2+Vtr

Ca2+

Ca2+

Vleak

Vrel

VupCa2+

Na+K+

Vdecay

IbCa

3Na+

2K+

MgATP+

Problem/Field description

ATP

IKr2

K+

K+

K+

K+K+

K+

IKATP

IK1

IKto

IKr1

IKs

I

N

a-

st

re

tc

h

I

A

n-

st

re

tc

h

I

N

S-

st

re

tc

h

I

K

-

st

re

tc

h

I

C

a-

st

re

tc

h

H2PO-4

2Na+

H+Lac

Na+

H+

HCO-3

Cl-

CBE

OH-

Cl-

CHE

HCO-3

Na+

NBCNHELAT

NPE

MgADP Mg2+

MgATP

MgPi

K+Ca2+

MgADP+Pi+H+ MgATP

OxPhos

ImKATP

3H+H+

2Lac

3MgATP

3MgADP+3Pi

AK

CK

ADP

AMP

MgADP

MgATP

Cr

PCr ADP+H+

VCO2transport

CO2H+

H2PO4-

Intrinsic Buffers

Ca2+

TropC

Calmodulin

3Na+

NCE

Ca2+

IpNa

Na+

IbNa

INa

DS

Na+

Na+

NSR

JSR

MgATP Ca2+

Ca2+

Vtr

Ca2+

Ca2+

Vleak

Vrel

Vup

Ca2+

Na+

K+

Vdecay

IbCa

3Na+

2K+

MgATP+

Fields:• Geometric• Fibre• Material (i, e, Am, Cm etc.)

• Potential (Vm, e, etc.)

• Source (Iion, etc.)

• Cellular state variables• Cellular intermediate

variables• Cellular parameter variables

Field parameter vector

12 3

4 56 7

89 10 11 12

13 1415

16 17 18 19

20 2122

2324 25 26

272829 30

3132

33 34

35

13

57

1517

19

21

29

3133

35

Fieldvariable,

u

Component,u1

Component,u2

Parameter vector,

x

GlobalDOFs

Electrophysiology - CellML300%

100%

gNa Distribution

+50 mV

-85 mV

Stimulus off

+50 mV

-85 mV

Normal activation

+50 mV

-85 mV

gNa activation

Finite Elasticity – Breast Mechanics

Courtesy of Prasad Gamage

Skin

Breast Tissue

Undeformed

DeformedUnder gravityloading

Fluid Mechanics – 3D NSCarotid Artery Flow, Re=100

Mesh Velocity Pressure

Courtesy of David Ladd

CellML as a DOF black box

Fieldvariable

ParameterDOF Vector

Component1

Component2

Component3

Inputs Outputs

OpenCMISS CellML Import

void computeRates( double VOI, double *PARAMETERS, double *RATES, double *STATES, double

*INTERMEDIATE);{

const double FIXED[..];

::

}

State Parameters Intermediate

ATP

IKr2

K+

K+

K+

K+

K+

K+

I

K

A

T

P

IK1

IKto

IKr1

IKs

INa-stretch

IAn-stretch

INS-stretch

IK-stretch

ICa-stretch

H2

PO-

4

2Na+

H+Lac

Na+

H+

HCO-3

Cl-

CBE

OH-

Cl-

CHE

HCO-3

Na+

NBCNHE

LAT

NPE

MgADP Mg2+

MgATP

MgPi

K+

Ca2+

MgADP+Pi+H+ MgATP

OxPhos

ImKATP

3H+

H+

2Lac

3MgATP

3MgADP+3Pi

AK

CK

ADP

AMP

MgADP

MgATP

Cr

PCr ADP+H+

VCO2transport

CO2H+

H2PO4-

Intrinsic Buffers

Ca2+

TropC

Calmodulin

3Na+

NCE

Ca2+

IpNa

Na+

IbNa

INa

DS

Na+

Na+

NSR

JSR

MgATP Ca2+

Ca2+

Vtr

Ca2+

Ca2+

Vleak

Vrel

Vup

Ca2+

Na+

K+

Vdecay

IbCa

3Na+

2K+

MgATP+

StateParametersIntermediate

CellML Variables

CellML Environment

CellML Model

Import

Set as known

Set as wanted

Set as known and wanted

CellML Interface

ATP

IKr2

K+

K+

K+

K+K+ K+

IKATP

IK1

IKto

IKr1

IKs

INa-stretch

IAn-stretch

INS-stretch

IK-stretch

ICa-stretch

H2PO-4

2Na+

H+Lac

Na+

H+

HCO-3

Cl-

CBE

OH-

Cl-

CHE

HCO-3

Na+

NBCNHELAT

NPE

MgADP Mg2+

MgATP

MgPi

K+Ca2+

MgADP+Pi+H+ MgATP

OxPhos

ImKATP

3H+H+

2Lac

3MgATP

3MgADP+3Pi

AK

CK

ADP

AMP

MgADP

MgATP

Cr

PCr ADP+H+

VCO2transport

CO2H+

H2PO4-

Intrinsic Buffers

Ca2+

TropC

Calmodulin

3Na+

NCE

Ca2+

IpNa

Na+

IbNa

INa

DS

Na+

Na+

NSR

JSR

MgATP Ca2+

Ca2+Vtr

Ca2+

Ca2+

Vleak

Vrel

VupCa2+

Na+

K+

Vdecay

IbCa

3Na+

2K+

MgATP+ ModelsState ParametersIntermediate

CellM

Len

vir

on

OpenCMISSField

CellMLFields

CellML/Field Maps

ModelsState ParametersIntermediate

CellM

Len

vir

on

CellML to field MapField to CellML MapCellML integrate

Cellular model

TransmembraneVoltage Field

CellML/Field Maps

ModelsState ParametersIntermediate

CellM

Len

vir

on

StrainField

StressField

CellML to field MapField to CellML MapCellML evaluate

Constitutive

Law