title: Derivation and left ventricular pressure phase plane based validation of a time dependent isometric crossbridge attachment model.
abstract: Huxley's crossbridge attachment model predicts tension (contractile force) development in isometric (fixed length) cells using constant attachment and detachment rates. Alternative models incorporating time-varying calcium concentrations are complex (coupled linear differential equations) and use time-dependent inputs (calcium, elastance, etc.) to model multiple states. We hypothesize that by incorporating the known significant rise and fall in intracellular calcium, via either an asymmetric damped function or a symmetric Gaussian function, into a time-varying, rather than constant, attachment rate function, the Huxley model prediction for tension (i.e., chamber pressure) in isovolumic (isometric) non-ejecting beats will improve. To test the hypothesis that the time-dependent model-predicted (TDM) pressure fits the in vivo isometric (isovolumic) LV pressure phase-plane (PPP) contour better than the constant attachment rate predicted pressure, we used the TDM to fit non-ejecting, premature ventricular contraction (PVC) PPP contours in 6 subjects. Conventional model fit was poor (relative error 74.0%+/-12.5%), while the asymmetric damped TDM rate function provided slight improvement relative to the conventional time-independent model (relative error 55.4%+/-9.8%). The symmetric Gaussian rate function TDM provided the best PPP fit to all non-ejecting beats tested (relative error 19.8%+/-4.8%). We conclude that approximating the lumped attachment rate via a time-varying, rather than constant, rate function generates a physiologically viable model of crossbridge behavior. The PPP provides the optimal arena for alternate mathematical formulation assessment of LVP contour prediction by time-dependent attachment rate functions and facilitates modeling of cardiac contraction and relaxation.
authors.affiliation: Cardiovascular Biophysics Laboratory, Cardiovascular Division, Washington University School of Medicine, 660 South Euclid Ave, Box 8086, St. Louis, MO 63110, USA.
authors.forename: Wei
authors.initials: W
authors.lastname: Zhang
authors.forename: Charles S
authors.initials: CS
authors.lastname: Chung
authors.forename: Sándor J
authors.initials: SJ
authors.lastname: Kovács
mesh_terms: D000328:Adult; D000368:Aged; D000465:Algorithms; D001794:Blood Pressure / Q000502:physiology*; D003198:Computer Simulation; D005260:Female; D006801:Humans; D007537:Isometric Contraction / Q000502:physiology*; D008297:Male; D008875:Middle Aged; D008955:Models, Cardiovascular; D009200:Myocardial Contraction / Q000502:physiology*; D012518:Sarcomeres / Q000502:physiology*; D016276:Ventricular Function