Feed Forward Modeling: an efficient approach for mathematical modeling of the force frequency relationship in the rabbit isolated ventricular myocyte.

Background and Objective. This study addresses the Force-Frequency relationship, a fundamental characteristic of cardiac muscle influenced byβ1-adrenergic stimulation. This relationship reveals that heart rate (HR) changes at the sinoatrial node lead to alterations in ventricular cell contractility, increasing the force and decreasing relaxation time for higher beat rates. Traditional models lacking this relationship offer an incomplete physiological depiction, impacting the interpretation of in silico experiment results. To improve this, we propose a new mathematical model for ventricular myocytes, named 'Feed Forward Modeling' (FFM).Methods. FFM adjusts model parameters like channel conductance and Ca2+pump affinity according to stimulation frequency, in contrast to fixed parameter values. An empirical sigmoid curve guided the adaptation of each parameter, integrated into a rabbit ventricular cell electromechanical model. Model validation was achieved by comparing simulated data with experimental current-voltage (I-V) curves for L-type Calcium and slow Potassium currents.Results. FFM-enhanced simulations align more closely with physiological behaviors, accurately reflecting inotropic and lusitropic responses. For instance, action potential duration at 90% repolarization (APD90) decreased from 206 ms at 1 Hz to 173 ms at 4 Hz using FFM, contrary to the conventional model, where APD90 increased, limiting high-frequency heartbeats. Peak force also showed an increase with FFM, from 8.5 mN mm-2at 1 Hz to 11.9 mN mm-2at 4 Hz, while it barely changed without FFM. Relaxation time at 50% of maximum force (t50) similarly improved, dropping from 114 ms at 1 Hz to 75.9 ms at 4 Hz with FFM, a change not observed without the model.Conclusion. The FFM approach offers computational efficiency, bypassing the need to model all beta-adrenergic pathways, thus facilitating large-scale simulations. The study recommends that frequency change experiments include fractional dosing of isoproterenol to better replicate heart conditionsin vivo.

Silva RRD ，Motta GMS ，de Camargo MLA ，Goroso DG ，Puglisi EJL ... -  《Biomedical Physics & Engineering Express》

β-adrenergic effects on cardiac myofilaments and contraction in an integrated rabbit ventricular myocyte model.

A five-state model of myofilament contraction was integrated into a well-established rabbit ventricular myocyte model of ion channels, Ca(2+) transporters and kinase signaling to analyze the relative contribution of different phosphorylation targets to the overall mechanical response driven by β-adrenergic stimulation (β-AS). β-AS effect on sarcoplasmic reticulum Ca(2+) handling, Ca(2+), K(+) and Cl(-) currents, and Na(+)/K(+)-ATPase properties was included based on experimental data. The inotropic effect on the myofilaments was represented as reduced myofilament Ca(2+) sensitivity (XBCa) and titin stiffness, and increased cross-bridge (XB) cycling rate (XBcy). Assuming independent roles of XBCa and XBcy, the model reproduced experimental β-AS responses on action potentials and Ca(2+) transient amplitude and kinetics. It also replicated the behavior of force-Ca(2+), release-restretch, length-step, stiffness-frequency and force-velocity relationships, and increased force and shortening in isometric and isotonic twitch contractions. The β-AS effect was then switched off from individual targets to analyze their relative impact on contractility. Preventing β-AS effects on L-type Ca(2+) channels or phospholamban limited Ca(2+) transients and contractile responses in parallel, while blocking phospholemman and K(+) channel (IKs) effects enhanced Ca(2+) and inotropy. Removal of β-AS effects from XBCa enhanced contractile force while decreasing peak Ca(2+) (due to greater Ca(2+) buffering), but had less effect on shortening. Conversely, preventing β-AS effects on XBcy preserved Ca(2+) transient effects, but blunted inotropy (both isometric force and especially shortening). Removal of titin effects had little impact on contraction. Finally, exclusion of β-AS from XBCa and XBcy while preserving effects on other targets resulted in preserved peak isometric force response (with slower kinetics) but nearly abolished enhanced shortening. β-AS effects on XBCa and XBcy have greater impact on isometric and isotonic contraction, respectively.

Negroni JA ，Morotti S ，Lascano EC ，Gomes AV ，Grandi E ，Puglisi JL ，Bers DM ... -  《-》

Mathematical model for β(1)-adrenergic regulation of the mouse ventricular myocyte contraction.

Mullins PD ，Bondarenko VE 《-》

Enhanced Depolarization Drive in Failing Rabbit Ventricular Myocytes: Calcium-Dependent and β-Adrenergic Effects on Late Sodium, L-Type Calcium, and Sodium-Calcium Exchange Currents.

Hegyi B ，Morotti S ，Liu C ，Ginsburg KS ，Bossuyt J ，Belardinelli L ，Izu LT ，Chen-Izu Y ，Bányász T ，Grandi E ，Bers DM ... -  《-》

Determinants of beat-to-beat variability of repolarization duration in the canine ventricular myocyte: a computational analysis.

Heijman J ，Zaza A ，Johnson DM ，Rudy Y ，Peeters RL ，Volders PG ，Westra RL ... -  《-》