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.

N1 - Funding Information:
Acknowledgment This work is supported in part by the Heartland Affiliate of the American Heart Association (Dallas, TX), the Whitaker Foundation (Roslyn VA), the National Institutes of Health (HL54179, HL04023 Bethesda MD), the Alan A. and Edith L. Wolff Charitable Trust (St. Louis, MO) and the Barnes-Jewish Hospital Foundation. The assistance of the Barnes-Jewish Hospital Catheterization Laboratory staff in data acquisition is gratefully acknowledged.

PY - 2006/12

Y1 - 2006/12

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 -