Regulation of energy liberation during steady sarcomere shortening

Adaptive control of cardiac contraction to changes in loading: from theory of sarcomere dynamics to whole-heart function

The heart accommodates to rapid changes in demands. This review elucidates the adaptive control of cardiac function by loading conditions, and integrates the sarcomeric control of contraction (SCC) with isolated trabeculae and in vivo whole-heart studies. The SCC includes two feedback mechanisms: (1) cooperativity that regulates cross-bridge (XB) recruitment and the force-length relationship, and (2) mechanical feedback, whereby the filament-sliding velocity determines the XB-weakening rate and the force-velocity relationship. An isolated rat trabeculae study tested the suggested mechanisms during sarcomeric lengthening. The observations indicate that lengthening decreases the XB-weakening rate in a velocity-dependent manner, congruent with the suggested hypothesis and in contrast to alternative theories. A whole-heart level study in sheep reveals the existence of a preload-independent linear relationship between the external work (EW) and pressure-time integral during transient vena cava occlusions, for any given afterload, and not just at isovolumic contractions. The slope of this relationship decreases as the afterload increases. These findings highlight the mechanisms underlying the pressure (Frank's phenomenon) and EW (Starling's phenomenon) generation and the roles that the preload and afterload play. The theoretical, isolated fibers and whole-heart studies provide complementary information that strengthens our understanding of cardiac function from the top-down and bottom-up.

Theory of cardiac sarcomere contraction and the adaptive control of cardiac function to changes in demands

This chapter explores the adaptive control of cardiac function by the loading conditions and relates the observed phenomena to our theory of the sarcomeric control of contraction. Our theory includes two feedback mechanisms: cooperativity-regulated cross-bridge recruitment and energy consumption, and mechanical feedback that determines the interplay between the external work and the force-time integral. The latter also suggests that cardiac efficiency is load independent. This paper explores the regulation of cardiac function by loading conditions, and the role of afterload in adult sheep in situ (n=8). Different afterloads were imposed by partial aortic occlusions. Transient inferior vena cava occlusions (IVCOs) were pre-formed at each steady afterload. A novel, highly linear relationship was found between the external work and pressure-time integral during each transient IVCO at constant afterload. Of interest, the slope of this relationship was afterload-dependent also during fast transient changes in the afterload. These observations are congruent with the suggested adaptive sarcomeric control of contraction, and may provide a powerful tool for quantifying cardiac function.

The external work-pressure time integral relationships and the afterload dependence of Frank-Starling mechanism

The mechanisms underlying the Frank-Starling Law of the heart are elusive and the prevalent notion suggests that it is afterload independent. However, isolated fiber studies reveal that the afterload determines cardiac function through cross-bridge dependent mechanisms. The study explores the roles of the afterload, in situ. The LV was exposed by left-thoracotomy in adult sheep (72.6+/-8.2 kg, n=8). Pressure transducers were inserted into the LV and aorta, a flowmeter was placed around the aortic root, and the LV volume was assessed by sonocrystals. Occluders around the aorta and the inferior vena cava enabled control of the afterload and preload. Different afterloads were imposed by partial aortic occlusions. Transient inferior vena cava occlusions (IVCOs) were preformed whenever the afterload was steady. A highly linear relationship was found between the external work (EW) and pressure time integral (PTI) (R(2)=0.98+/-0.01) during each transient IVCO (n=48). The slope of the EW-PTI relationship (WPTiR) was preload independent since, for any given afterload, the EW and PTI lay on a straight line. Interestingly, the slope of the WPTiR was afterload dependant: The slope was 33.3+/-4.1 mJ/mmHg.s at baselines and decreased by 1.0+/-0.50 mJ/mmHg.s with every 1 mmHg.min/L increase in the peripheral resistance. A unique WPTiR was obtained during both the occlusion and release phases of each IVCO, while two distinct EW-preload or PTI-preload relationships were observed. The novel WPTiR ties the Frank (pressure development) and Starling (EW production) phenomena together. The dependence of the WPTiR on the afterload highlights the adaptive control of the Frank-Starling mechanisms to changes in the afterload.

Stability, controllability, and observability of the "four state" model for the sarcomeric control of contraction

A model of the sarcomeric control of contraction at various loading conditions has to maintain three cardinal features: stability, controllability (where the output can be controlled by the input), and observability (where the output reflects the effects of all the state variables). The suggested model of the sarcomere couples calcium kinetics with cross-bridge (XB) cycling and comprises two feedback mechanisms: (i) the cooperativity, whereby the number of force-generating (strong) XBs determines calcium affinity, regulates XB recruitment, and (ii) the mechanical feedback, whereby shortening velocity determines XBs cycling rate, controls the XBs contractile efficiency. The sarcomere is described by a set of four first-order nonlinear differential equations, utilizing the Matlab's Simulink software. Small oscillatory input was imposed when the state variables trajectories reached a steady state. The linearized state-space representations of the model were calculated for various initial sarcomere lengths. The analysis of the state-space representation validates the controllability and observability of the model. The model has four poles: three at the left side of the complex plane and one integrating pole at the origin. Therefore, the system is marginally stable. The Laplace transform confirms that the state representation is minimal and is therefore observable and controllable. The extension of the model to a multi-sarcomere lattice was explored, and the effects of inhomogeneity and nonuniform activation were described.