Time-invariant oxygen cost of mechanical energy in dog left ventricle: consistency and inconsistency of time-varying elastance model with myocardial energetics

On the theoretical limits of detecting cyclic changes in cardiac high-energy phosphates and creatine kinase reaction kinetics using in vivo ³¹P MRS

Adenosine triphosphate (ATP) is absolutely required to fuel normal cyclic contractions of the heart. The creatine kinase (CK) reaction is a major energy reserve reaction that rapidly converts creatine phosphate (PCr) to ATP during the cardiac cycle and at times of stress and ischemia, but is significantly impaired in conditions such as hypertrophy and heart failure. Because the magnitudes of possible in vivo cyclic changes in cardiac high-energy phosphates (HEPs) during the cardiac cycle are not well known from previous work, this study uses mathematical modeling to assess whether, and to what extent, cyclic variations in HEPs and in the rate of ATP synthesis through CK (CK flux) could exist in the human heart, and whether they could be measured with current in vivo (31)P MRS methods. Multi-site exchange models incorporating enzymatic rate equations were used to study the cyclic dynamics of the CK reaction, and Bloch equations were used to simulate (31)P MRS saturation transfer measurements of the CK reaction. The simulations show that short-term buffering of ATP by CK requires temporal variations over the cardiac cycle in the CK reaction velocities modeled by enzymatic rate equations. The maximum variation in HEPs in the normal human heart beating at 60 min(-1) was approximately 0.4 mM and proportional to the velocity of ATP hydrolysis. Such HEP variations are at or below the current limits of detection by in vivo (31)P MRS methods. Bloch equation simulations show that (31)P MRS saturation transfer estimates the time-averaged, pseudo-first-order forward rate constant, k(f,ap)', of the CK reaction, and that periodic short-term fluctuations in kf ' and CK flux are not likely to be detectable in human studies employing current in vivo (31)P MRS methods.

An integrated coronary circulation teaching model

OBJECTIVES

We present in this paper a model of the coronary circulation. This model is integrated with a model of the systemic circulation, and contains models for oxygen supply and demand.

METHODS

Three compartments are created: one for the right ventricle, one for the epicardial segment of the left ventricle and one for the endo-cardial segment of the left ventricle. The model was implemented in the Java programming language and contains a visual representation of the left and right ventricles which beat in real time. Color shading is used to represent the partial pressure of oxygen in the segments. A multitude of model parameters can be changed to simulate different scenarios.

RESULTS

The output of the model was characterized under different conditions and the results verified by clinicians.

CONCLUSIONS

Educational models of human physiology can be very useful for a more in depth understanding of complete physiologic systems. The models must however have enough complexity, interaction with other systems, and realism to show the concepts being taught.

Left Ventricular Mechanoenergetics in Small Animals

Studies on left ventricular mechanical work and energetics in rat and mouse hearts are reviewed. First, left ventricular linear end-systolic pressure-volume relation (ESPVR) and curved end-diastolic pressure-volume relation (EDPVR) in canine hearts and left ventricular curved ESPVR and curved EDPVR in rat hearts are reviewed. Second, as an index for total mechanical energy per beat in rat hearts as in canine hearts, a systolic pressure-volume area (PVA) is proposed. By the use of our original system for measuring continuous oxygen consumption for rat left ventricular mechanical work, the linear left ventricular myocardial oxygen consumption per beat (VO2)-PVA relation is obtained as in canine hearts. The slope of VO2-PVA relation (oxygen cost of PVA) indicates a ratio of chemomechanical energy transduction. VO2 intercept (PVA-independent VO2) indicates the summation of oxygen consumption for Ca2+ handling in excitation-contraction coupling and for basal metabolism. An equivalent maximal elastance (eEmax) is proposed as a new left ventricular contractility index based on PVA at the midrange left ventricular volume. The slope of the linear relation between PVA-independent VO2 and eEmax (oxygen cost of eEmax) indicates changes in oxygen consumption for Ca2+ handling in excitation-contraction coupling per unit changes in left ventricular contractility. The key framework of VO2-PVA-eEmax can give us a better understanding for the biology and mechanisms of physiological and various failing rat heart models in terms of mechanical work and energetics.

Regulation of energy consumption in cardiac muscle: analysis of isometric contractions

The well-known linear relationship between oxygen consumption and force-length area or the force-time integral is analyzed here for isometric contractions. The analysis, which is based on a biochemical model that couples calcium kinetics with cross-bridge cycling, indicates that the change in the number of force-generating cross bridges with the change in the sarcomere length depends on the force generated by the cross bridges. This positive-feedback phenomenon is consistent with our reported cooperativity mechanism, whereby the affinity of the troponin for calcium and, hence, cross-bridge recruitment depends on the number of force-generating cross bridges. Moreover, it is demonstrated that a model that does not include a feedback mechanism cannot describe the dependence of energy consumption on the loading conditions. The cooperativity mechanism, which has been shown to determine the force-length relationship and the related Frank-Starling law, is shown here to provide the basis for the regulation of energy consumption in the cardiac muscle.

Increased work in cardiac trabeculae causes decreased mitochondrial NADH fluorescence followed by slow recovery

The oxidative phosphorylation rate in isolated mitochondria is stimulated by increased [ADP], resulting in decreased [NADH]. In intact hearts, however, increased mechanical work has generally not been shown to cause an increase in [ADP]. Therefore, increased [NADH] has been suggested as an alternative for stimulating the phosphorylation rate. Such a rise in [NADH] could result from stimulation of various substrate dehydrogenases by increased intracellular [Ca2+] (e.g., during increased pacing frequency). We have monitored mitochondrial [NADH] in isolated rat ventricular trabeculae, using a novel fluorescence spectroscopy method where a native fluorescence signal was used to correct for motion artifacts. Work was controlled by increased pacing frequency and assessed using time-averaged force. At low-pacing rates (approximately 0.1 Hz), [NADH] immediately decreased during contraction and then slowly recovered (approximately 5 s) before the next contraction. At higher rates, [NADH] initially decreased by an amount related to pacing rate (i.e., work). However, during prolonged stimulation, [NADH] slowly (approximately 60 s) recovered to a new steady-state level below the initial level. We conclude that 1) during increased work, oxidative phosphorylation is not initially stimulated by increased mitochondrial [NADH]; and 2) increased pacing frequency slowly causes stimulation of NADH production.

Ejecting activation differs in energetics from ordinary positive inotropism in the canine left ventricle

Ventricular ejection is known to have dual effects on the end-systolic pressure: the ejecting deactivation by a relatively large ejection against a low afterload versus the ejecting activation by a relatively small ejection against a high afterload. We studied how the increase in contractility index (Emax) by the ejecting activation would affect myocardial oxygen consumption (VO2). To this end, left ventricular steady-state ejecting contractions were produced with various stroke volumes from a fixed end-diastolic volume in an excised cross-circulated canine heart. The effect of the ejection-activated Emax on VO2 was assessed by the relation between VO2 and pressure-volume area (PVA). PVA is the total mechanical energy generated by ventricular contraction. In contrast to the elevation of the linear VO2-PVA relation in a parallel manner with an enhanced Emax by ordinary positive inotropic agents such as catecholamines and calcium, the ejection-activated Emax did not elevate the VO2-PVA relation. This result indicates that the ejecting activation enhances Emax in an energetically different manner from ordinary positive inotropism in the canine left ventricle.

The step response of left ventricular pressure to ejection flow: a system oriented approach

Left ventricular pressure is dependent on both ventricular volume and ventricular ejection flow. These dependencies are usually expressed by ventricular elastance, and resistance, respectively. Resistance is a one-valued effect only, when ejection flow either is constant or increases. Decreasing ejection flow elicits a third effect: a decrease of elastance. The effects of elastance, resistance and elastance depression were modeled in a three-compartment model consisting of a dead-volume compartment, an elastance compartment, and a second series-elastance compartment connected to the elastance compartment by a resistance. This model was identified with the pressure response determined experimentally by imposing pumped constant-flow ejection epochs on isolated rabbit hearts. The experimental flow epochs consisted of two phases of constant flow separated by an increasing or decreasing flow step. It was found that elastance is not changed after the flow step if this is positive or zero. Negative flow steps induced a deactivation of elastance that is linearly dependent on the difference between isovolumic pressure that would be developed at the volume existing at the time of measurement and actual pressure. The parameters found from the identification procedure are ventricular active volume, nondepressed elastance, series-elastance, resistance, and the elastance deactivation factor. The first four parameter values were found in agreement with other results reported in literature. The elastance depression factor is a new parameter that could be of physiological or clinical significance since it may be related to the inability of the force generators in the heart muscle to be restored to their full number, after being inactivated or decoupled by filament sliding associated with ejection. On the basis of the results, an alinear state-model of the ventricle, for arbitrary, including physiological flow patterns is proposed.

The energy cost of relaxation in control and hypertrophic rabbit papillary muscles

The energy cost of the onset and relaxation phases of cardiac isometric contractions has been investigated by ergometer controlled-length releases occurring at different times during the contraction cycle, to test the hypothesis that the energy cost of relaxation is normally small. Energy flux has been measured myothermically in 20 or 30 contractions of rabbit papillary muscles. The ergometer releases took place after different delays, starting during the latency period and incrementing in 50 ms steps, until eventually, releases were occurring late into the relaxation phase. The release step was kept constant and of a magnitude sufficient to prevent significant redevelopment of active stress at any release interval. The rate of release was several times greater than the maximum shortening velocity of the papillary muscle preparations. The heat production in each train of contractions was measured, but in order to estimate the total energy output, the elastic energy in the muscle-lever system which was removed by the ergometer release had to be added to the heat. This was estimated by integration of the stress-strain relationship found for each muscle. In normal animals the contraction peak, at 27 degrees C and a 1.0 Hz stimulus rate, was located between the 215 and 265 ms release times, at which point the total energy flux was estimated to be 80%-90% of that measured in a normal isometric contraction. Additional experiments were performed in a group of volume-overloaded hearts and the data were compared with results from sham-operated controls.(ABSTRACT TRUNCATED AT 250 WORDS)

Force-time integral does not improve predictability of cardiac O2 consumption from pressure-volume area (PVA) in dog left ventricle

We have proposed the systolic pressure-volume area (PVA) as a measure of the total mechanical energy generated by ventricular contraction, and we found a closely linear correlation between PVA and cardiac oxygen consumption (VO2). Although the force-time integral (FTI) has long been considered to be the most reliable correlate of cardiac oxygen consumption (VO2), we have already shown that VO2 remained constant although FTI was changed while PVA was kept constant in the excised, cross-circulated dog left ventricle. This means that PVA is superior to FTI as a predictor of VO2. In the present study, we studied whether a linear addition of FTI to PVA could improve the prediction of VO2 from PVA in isovolumic and ejecting contractions with different afterload pressures in the same type of dog left ventricle preparation. Although left ventricular VO2 was always closely correlated with either PVA (r = 0.967, mean after z-transformation) or FTI (mean r = 0.925), multiple regression analysis indicated that PVA alone accounted for as much as 94% (mean) of the variance of VO2 and that FTI linearly added to PVA accounted for an additional few percent of the variance (statistically significant in less than half the cases). We conclude that the addition of FTI to PVA does not improve the predictability of VO2 from PVA in ordinary contractions.