We investigated to what extent maximal ventricular elastance ( Emax) is dynamically controlled by the arterial baroreflex and force-frequency relation in conscious dogs and to what extent these mechanisms are attenuated after the induction of heart failure (HF). We mathematically analyzed spontaneous beat-to-beat hemodynamic variability. First, we estimated Emax for each beat during a baseline period using the ventricular unstressed volume determined with the traditional multiple beat method during vena cava occlusion. We then jointly identified the transfer functions (system gain value and time delay per frequency) relating beat-to-beat fluctuations in arterial blood pressure (ABP) to Emax (ABP→ Emax) and beat-to-beat fluctuations in heart rate (HR) to Emax (HR→ Emax) to characterize the dynamic properties of the arterial baroreflex and force-frequency relation, respectively. During the control condition, the ABP→ Emax transfer function revealed that ABP perturbations caused opposite direction Emax changes with a gain value of −0.023 ± 0.012 ml−1, whereas the HR→ Emax transfer function indicated that HR alterations caused same direction Emax changes with a gain value of 0.013 ± 0.005 mmHg·ml−1·(beats/min)−1. Both transfer functions behaved as low-pass filters. However, the ABP→ Emax transfer function was more sluggish than the HR→ Emax transfer function with overall time constants (indicator of full system response time to a sudden input change) of 11.2 ± 2.8 and 1.7 ± 0.5 s ( P < 0.05), respectively. During the HF condition, the ABP→ Emax and HR→ Emax transfer functions were markedly depressed with gain values reduced to −0.0002 ± 0.007 ml−1 and −0.001 ± 0.004 mmHg·ml−1·(beats/min)−1 ( P < 0.1). Emax is rapidly and significantly controlled at rest, but this modulation is virtually abolished in HF.
Vibration Equation of Fractional Order Describing Viscoelasticity and Viscous Inertia
