Feed Forward Modeling. Fixing the Force Frequency Relationship

Abstract

The force frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Several attempts were made to construct mathematical descriptions of this phenomenon; from the simple formulation of Koch-Wesser & Blinks in 1963 to the most sophisticated ones of present days. This property of the cardiac muscle is amplified by the β adrenergic stimulation. In a coordinated way the neurohumoral state alters both: frequency (acting on the SA node) and force generation (modifying the ventricular myocytes). This synchronized tuning is needed to meet new metabolic demands. Failure to do so has deleterious consequences. We implemented this physiological coordination in a new version of LabHEART (v5.5) where the cell parameters are updated according to the frequency of stimulation in a sigmoidal fashion (namely: ICaL, IKs, SERCA pump and myofilaments’ Ca-sensitivity). This feed forward modeling helps to reproduce a more realistic cell behavior and complement the information obtained by experiments where frequency has been altered but without adding β-adrenergic agonists. Plots like rate-adaptation or APD vs cycle length can, now, be mapped into the neurohumoral state to provide insights about arrhythmias (or antiarrhythmic drugs). Cardiac modelers have already linked the mechanical and the electrical activity in their formulations and showed how those activities feedback on each other. Feed forward modeling is a step towards reproducing the neurological control and thus, to have a complete description of the heart performance, particularly when changes in frequency are involved. The presumptive sigmoidal dependence of parameters on pacing frequency used here can be refined but is a valid starting point to implement the convergence of cardiac chronotrophy and inotropy.