Abramson, David

Amirriazi, Saleh

Chang, Stephany

Michailova, Anuska

Peachey, Tom

University of Queensland eSpace

 Optimizing Cardiac Excitation-Metabolic Model By Using 
Parallel Grid Computing     
   
CONCLUSIONS 
ABSTRACT 
RESULTS 
Saleh Amirriazi*, Stephany Chang*, Tom Peachey#, David Abramson#, and Anushka Michailova* 
*Department of Bioengineering, University of California San Diego, La Jolla, CA, USA, 
#Monash University, Clayton, Victoria, Australia  
Supported by NSF (PRIME), NIH funded NBCR, 
California Institute for Telecommunication 
and Information Technology 
INTRODUCTION 
MODEL 
The enzymatically isolated cardiac cells from epicardial and 
endocardial regions differ primarily with respect to their 
repolarization characteristics and Ca2+ activity1,2,5. The epicardial 
myocytes display (a) shorter action potential duration due to 
differences in variant ionic currents (INa, Ito, IKr, IKs), and (b) 
shorter time to peak and duration of the global Ca2+ transient due 
to variations in SERCA expression. The epicardial myocytes 
respond also differently to pathophysiological states. It has been 
suggested that changes in ATP-sensitive K+ channel (KATP) 
sensitivity to ATP among the cell sub-types might be partially 
responsible for the greater action potential shortening in the 
epicardial region during ischemia4. However, little is known (a) 
how local Ca2+ transients in the juctional, subsarcolemmal and 
cytosolic spaces are regulated among the cell sub-types, and (b) 
how the distribution of KATP channels may affect the cell 
excitability and contractility under pathological conditions. To 
investigate further these mechanisms we extended the Shannon-
Bers ionic model in rabbits3 to incorporate (a) the regional 
variations in ion channel densities and SERCA pump expression, 
and (b) equations for Mg2+-nucleotide regulation of KATP channel, 
L-type Ca2+ channel, sarcolemmal and sarcoplasmic Ca2+-
ATPases, and Na+/K+ pump4. We used a distributed parameter 
optimization tool (Nimrod)6 to stabilize the epi- and endocardial 
Ca2+ transients in  the juctional, subsarcolemmal and cytosolic 
compartments under normal conditions for time interval of 3 min 
at 0.5Hz. 
The model currently includes (see Figure 1)  
• The Shannon-Bers model, describing ion channel currents and 
Ca2+ transport in rabbit ventricular myocytes 
• The regional variations in ion channel densities (Gi) and SERCA 
pump expression  
• KATP channel regulation by free ATP and MgADP 
• MgATP and MgADP regulation of L-type Ca2+ channel, SR Ca2+ 
ATPase, Na+/K+ pump and sarcolemmal Ca2+ pump  
• The realistic ATP, ADP, Pi, creatine (Cr), creatine phosphate (PCr) 
concentrations and extra- and intracellular diastolic ionic levels 
(Na+, K+, Mg2+, H+) in normal rabbit cells 
Assumptions 
• Among the cell sub-types total metabolite (ATP, ADP, AMP), Pi, Cr, 
PCr, Mg2+, and pH levels are equal and spatially uniform 
Figure 2: Left panel: Screenshot of Nimrod Portal Experimental Design Planning Page. Right panel: Length plot for Nimrod/E Experiment: A-K_MgATP_NaK; 
 B-K_MgADP_NaK; C-K_MgATP_ICa; D-K_MgATP_IpCa1; E-K_MgADP_IpCa; F-K_MgATP_IpCa2; G-K_MgATP_SERCA; H-K_MgADP_SERCA1; J- K_MgADP_SERCA2 
Figure 3: Action potentials and Ca2+ transients in the juctional, subsarcolemmal, and cytosolic 
compartments among the cell sub-types for time interval of 3 min at  0.5 Hz. Epicardium – green 
lines. Endocardium – blue lines. Normal conditions – [ATP]tot 4.9 mM, [ADP]tot 0.113 mM, [AMP]tot 
0.003 mM, [Cr]i 7.1mM, [PCr]tot 18.1 mM, Pi 2.78 mM, pHi 7.1, [Mg2+]i 1 mM, [Mg2+]tot 5.56 mM.  
Figure 1: Ionic-metabolic model in rabbit ventricular myocytes 
• Nimrod/E experiment suggests: (1) the model 
outputs will be highly sensitive to SERCA 
parameter changes, less sensitive to ICa and 
INaK parameter changes while IpCa parameter 
changes are expected to have insignificant 
impact; (2) MgATP and MgADP-dependent 
parameter changes alone will have opposite 
effects on the simulated curves; (3) the 
simultaneous changes in SERCA (G, J) or INaK 
(A,B) parameter values will have the most 
pronounced effect on the model outputs. 
 
• In rabbit epicardial myocytes model predicts 
(a) faster Ca2+ transient decay and shorter time 
to peak in the bulk cytosol, (b) faster Ca2+ 
transient decay in the juctional and 
subsarcolemmal spaces, (c) shorter action 
potential duration. 
 
• Model provides good basis for further studies 
of how the distribution of KATP channels may 
regulate the excitation-contraction coupling 
under pathological conditions when IKATP 
current is activated.     
Table: Ion channel conductance and scaling term for SERCA pump 
among the cell sub-types 
We have extended the Shannon-Bers model in order to 
investigate excitation-contraction coupling in rabbit epicardial 
and endocardial ventricular myocytes3. We couple cytosolic 
metabolism to the cell electrical activity and include rate 
expressions for Mg2+-nucleotide regulation of ATP-sensitive K+ 
channel, L-type Ca2+ channel, sarcolemmal and sarcoplasmic 
Ca2+-ATPases, and Na+/K+ pump4. The work was performed 
with a distributed parameter optimization tool (Nimrod) to 
search for stable model solutions6. The Nimrod experiment 
involved validation of the updated model by varying (a) input 
current parameters to stabilize the normal epi- and endocardial 
Ca2+ transients for time interval of 3 min at 0.5Hz, (b) input 
metabolic constants to fit the predicted normal ionic currents 
to be as close as possible to the experimentally suggested. The 
results suggest that the distribution of ATP-sensitive K+ 
channels might be important mechanism regulating the 
excitation-contraction coupling during ischemia. 
 
REFEREENCES 
[1] Antzelevitch et al., (1991) Circ Res 69: 1427-49. 
[2] Cordeiro et al., (2004) Am J Physiol 286: H1471-79.  
[3] Shannon et al., (2004) Biophys J 87: 3351-71. 
[4] Michailova et al., (2007) AJP Cell Physiol 293: C542-57. 
[5] Flaim et al., (2006) AJP Heart Circ Physiol 291: H2617-29.   
[6] Nimrod Portal 
http://www.csse.monash.edu.au/~davida/nimrod/portal.htm 
Epi Endo 
GNa (ms/µF)  6.0 7.0 
Gto(ms/µF) 0.06 0.025 
GKr (ms/µF) 0.04 0.03 
GKs(ms/µF) 0.75 0.3 
SERCA 2 1 
MgATP/MgADP kinetic equations  
*
2.6
_
1( ) ( )
1
[ ]
Ca Ca
MgATP ICa
i
I t I t
k
MgATP
=
 
+  
 
1
_*
_ 1 _ 2
[ ] [ ]( ) 1 1 ( )
[ ]
MgATP SERCA i i
up up
i MgADP SERCA MgADP SERCA
K MgADP MgADPJ t J t
MgATP K K
−
    
= + + +            
1
_*
_
[ ]( ) 1 1 ( )
[ ]
MgATP NaK i
NaK NaK
i MgADP NaK
K MgADPI t I t
MgATP K
−
  
= + +      
1 1
_ 1 _ 2*
( )
_
[ ]( ) 1 1 1 ( )
[ ] [ ]
MgATP IpCa MgATP IpCai
pCa p Ca
i MgADP IpCa i
K KMgADPI t I t
MgATP K MgATP
− −    
 = + + + +          
L-type Ca2+ current 
SERCA pump 
Na+/K+ pump 
Sarcolemmal Ca2+ pump 
 
 
A 1.0E-5 
B 1.46 
C 1.0 
D 2.50 
E 4.95 
F 3.20 
G 1.0E-4 
H 1.90 
J 100 


Optimizing cardiac excitation-metabolic model by using parallel grid computing

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Optimizing cardiac excitation-metabolic model by using parallel grid computing

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