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

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.