title: Head-tail interactions in numerical simulations of reentry in a ring of cardiac tissue.
abstract: BACKGROUND
  The relationships between action potential duration (APD) and conduction velocity (CV) to the previous diastolic interval (DI) are known as the APD and CV restitution relationships. There is considerable debate regarding the importance of these relationships in the development and stability of reentry.
  
  
  OBJECTIVE
  The purpose of this study was to increase the understanding of the ionic basis for restitution during reentry.
  
  
  METHODS
  APD and CV were studied numerically during one-dimensional reentry as ring length (L) was shortened. A three-state variable model (u, v, w) was used to analyze the effect of gating variables of the fast (v) and slow (w) currents on the spatial and temporal dynamics of transmembrane potential (u). Three parameter sets were used corresponding to three APD and CV restitution curves.
  
  
  RESULTS
  Sustained spatial oscillations of APD and CV larger than the ring length were observed in two of the parameter sets (cytochalasin-D model [CYTO] and model 3 [M3]) before block occurred at L = 6 cm. The last model (diacetyl monoxime [DAM]) resulted in uniform APD and CV for all L until block occurred at L = 3 cm. Multivalued APD and CV restitution relationships due to "dephasing" of w and v with DI were observed in M3 and CYTO simulations. Overall, these dynamics could be explained by the wavelength-to-ring length ratio and the sensitivity of APD on the value of the gating variables w and v.
  
  
  CONCLUSIONS
  Propagation stability is mostly controlled by APD sensitivity to w, but the APD restitution slope does not always reflect this sensitivity. The interaction of the dynamic history (i.e., memory) of the fast and slow currents and electrotonic effects resulted in multivalued restitution curves.
authors.affiliation: Department of Biomedical Engineering, University of Alabama at Birmingham, Birmingham, Alabama 35294, USA.
authors.forename: Xiaozhong
authors.initials: X
authors.lastname: Chen
authors.forename: Flavio H
authors.initials: FH
authors.lastname: Fenton
authors.forename: Richard A
authors.initials: RA
authors.lastname: Gray
mesh_terms: D000200:Action Potentials; D000818:Animals; D004553:Electric Conductivity; D006327:Heart Block / Q000503:physiopathology; D006329:Heart Conduction System / Q000503:physiopathology*; D006339:Heart Rate; D023421:Models, Animal; D009431:Neural Conduction; D011817:Rabbits; D012107:Research Design; D012680:Sensitivity and Specificity