πŸ“’ Ohara 2011

Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation1


Model introduction

  • ORd (O’Hara-Rudy dynamic) model with new EP measurements for the L-type Ca2 +current, K+currents, and Na+/Ca2 +exchange current from undiseased human ventricle.
  • Ca2+/calmodulin dependent protein kinase II (CaMKII) effects on ionic currents and Ca cycling
  • Early afterdepolarizations (EADs) and alternans were reproduc
  • All HH-type gating, no Markov-type ODEs for parameter constraint, efficiency and numerical stability
  • No sigularities and condition statements
  • Transmural Heterogeneity (endo, epi, M cells)

L-type Ca2+ Current (ICaL)

Transient Outward K+ Current (Ito)

Na+/Ca2+ Exchange Current (INaCa)

  • Kang and Hilgemann 2 model
  • Slip allowed (stoichiometry > 3.0)
  • 20% of the exchanger in the subspace

Inward Rectifier K+ Current (IK1)

Voltage dependent, but not pacing rate dependent

Rapid Delayed Rectifier K+ Current (IKr) Participation in AP shortening during steady state pacing at fast rate. (APD90 was a function of IKr conductance) Voltage dependent, but not pacing rate dependent.

Slow Delayed Rectifier K+ Current (IKs)

Ca2 + dependence of IKs was incorporated

Fast Na+ Current and late Na+ current

  • nonfailing human ventricular data from Sakakibara et al
  • Fast and late Na currents have long been understood to represent different gating modes.

Na+/K+ ATPase Current (INaK)

Smith and Crampin model.

Human AP Characteristics and APD
human endocardial AP traces from experiments (small tissue preparations) and model simulations
Undiseased human endocardial AP response to pacing protocols from experiments (small tissue preparations) and model simulations
Pacing protocols with block of various currents
Rate dependence of currents at steady state

Transmural Heterogeneity
Transmural heterogeneity and validation of transmural cell type models

Early Afterdepolarization (EAD)

Na+ and Ca2+ Rate Dependence

Ca2+ Cycling and CaMK


  • APD alternans appeared at CLs <300 ms (rates >200 bpm)

Currents Participating in Steady State APD Rate Dependence and APD Restitution
I–V curves during steady state rate dependent pacing at various CLs (A) and S1S2 restitution at various DIs (panel B)

Ionic Basis for APD Rate Dependence and Restitution
Major causes of steady state APD rate dependence and S1S2 APD restitution

Comparison with Other Human Ventricular AP Models
IKr deactivation is important for APD restitution at very short DIs
Comparison with other human ventricular AP models


This model reproduces

  • CDI versus VDI inactivation of ICaL
  • Reformulated, detailed and accurate kinetics (using weighted time constants) for Ito,INaCa,IK1,IKr,IKs, fast INa, and late INa
  • AP repolarization rate from 30% to 90% repolarization
  • APD at all physiological pacing rates with/without block of major currents
  • APD restitution with/without block of delayed rectifier currents
  • transmural heterogeneity causing upright pseudo ECG T-wave
  • early afterdepolarizations (EADs)
  • effects of CaMK
  • AP and Ca2+ transient alternans


  • Direct measurement of INaK
  • Sarkar and Sobie developed a method for quantitative analysis of parameter constraint and relationships between parameters and target outputs in AP model

  1. O’Hara T, VirΓ‘g L, VarrΓ³ A, Rudy Y. Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation. PLoS Comput. Biol. 2011;7(5):e1002061. doi:10.1371/journal.pcbi.1002061. ↩︎

  2. Kang TM, Hilgemann DW. Multiple transport modes of the cardiac Na+/Ca2+ exchanger. Nature 2004;427(6974):544-548. doi:10.1038/nature02271. Nature ↩︎