TY - JOUR

T1 - Derivation and left ventricular pressure phase plane based validation of a time dependent isometric crossbridge attachment model

AU - Zhang, Wei

AU - Chung, Charles S.

AU - Kovács, Sándor J.

PY - 2006/12/1

Y1 - 2006/12/1

N2 - 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.

AB - 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.

KW - Crossbridge

KW - Mathematical model

KW - Pressure phase-plane

UR - http://www.scopus.com/inward/record.url?scp=33845524991&partnerID=8YFLogxK

U2 - 10.1007/s10558-006-9020-6

DO - 10.1007/s10558-006-9020-6

M3 - Article

C2 - 17111228

AN - SCOPUS:33845524991

VL - 6

SP - 132

EP - 144

JO - Cardiovascular Engineering

JF - Cardiovascular Engineering

SN - 1567-8822

IS - 4

ER -