An efficient deconvolution algorithm for estimating oxygen consumption during muscle activities.

The reconstruction of an unknown input function from noisy measurements in a biological system is an ill-posed inverse problem. Any computational algorithm for its solution must use some kind of regularization technique to neutralize the disastrous effects of amplified noise components on the computed solution. In this paper, following a hierarchical Bayesian statistical inversion approach, we seek estimates for the input function and regularization parameter (hyperparameter) that maximize the posterior probability density function. We solve the maximization problem simultaneously for all unknowns, hyperparameter included, by a suitably chosen quasi-Newton method. The optimization approach is compared to the sampling-based Bayesian approach. We demonstrate the efficiency and robustness of the deconvolution algorithm by applying it to reconstructing the time courses of mitochondrial oxygen consumption during muscle state transitions (e.g., from resting state to contraction and recovery), from the simulated noisy output of oxygen concentration dynamics on the muscle surface. The model of oxygen transport and metabolism in skeletal muscle assumes an in vitro cylindrical structure of the muscle in which the oxygen from the surrounding oxygenated solution diffuses into the muscle and is then consumed by the muscle mitochondria. The algorithm can be applied to other deconvolution problems by suitably replacing the forward model of the system.

Parallel activation of mitochondrial oxidative metabolism with increased cardiac energy expenditure is not dependent on fatty acid oxidation in pigs.

Steady state concentrations of ATP and ADP in vivo are similar at low and high cardiac workloads; however, the mechanisms that regulate the activation of substrate metabolism and oxidative phosphorylation that supports this stability are poorly understood. We tested the hypotheses that (1) there is parallel activation of mitochondrial and cytosolic dehydrogenases in the transition from low to high workload, which increases NADH/NAD+ ratio in both compartments, and (2) this response does not require an increase in fatty acid oxidation (FAO). Anaesthetized pigs were subjected to either sham treatment, or an abrupt increase in cardiac workload for 5 min with dobutamine infusion and aortic constriction. Myocardial oxygen consumption and FAO were increased 3- and 2-fold, respectively, but ATP and ADP concentrations did not change. NADH-generating pathways were rapidly activated in both the cytosol and mitochondria, as seen in a 40% depletion in glycogen stores, a 3.6-fold activation of pyruvate dehydrogenase, and a 50% increase in tissue NADH/NAD+. Simulations from a multicompartmental computational model of cardiac energy metabolism predicted that parallel activation of glycolysis and mitochondrial metabolism results in an increase in the NADH/NAD+ ratio in both cytosol and mitochondria. FAO was blocked by 75% in a third group of pigs, and a similar increase in and the NAHD/NAD+ ratio was observed. In conclusion, in the transition to a high cardiac workload there is rapid parallel activation of substrate oxidation that results in an increase in the NADH/NAD+ ratio.

Regulation of myocardial substrate metabolism during increased energy expenditure: insights from computational studies.

In response to exercise, the heart increases its metabolic rate severalfold while maintaining energy species (e.g., ATP, ADP, and Pi) concentrations constant; however, the mechanisms that regulate this response are unclear. Limited experimental studies show that the classic regulatory species NADH and NAD+ are also maintained nearly constant with increased cardiac power generation, but current measurements lump the cytosol and mitochondria and do not provide dynamic information during the early phase of the transition from low to high work states. In the present study, we modified our previously published computational model of cardiac metabolism by incorporating parallel activation of ATP hydrolysis, glycolysis, mitochondrial dehydrogenases, the electron transport chain, and oxidative phosphorylation, and simulated the metabolic responses of the heart to an abrupt increase in energy expenditure. Model simulations showed that myocardial oxygen consumption, pyruvate oxidation, fatty acids oxidation, and ATP generation were all increased with increased energy expenditure, whereas ATP and ADP remained constant. Both cytosolic and mitochondrial NADH/NAD+ increased during the first minutes (by 40% and 20%, respectively) and returned to the resting values by 10-15 min. Furthermore, model simulations showed that an altered substrate selection, induced by either elevated arterial lactate or diabetic conditions, affected cytosolic NADH/NAD+ but had minimal effects on the mitochondrial NADH/NAD+, myocardial oxygen consumption, or ATP production. In conclusion, these results support the concept of parallel activation of metabolic processes generating reducing equivalents during an abrupt increase in cardiac energy expenditure and suggest there is a transient increase in the mitochondrial NADH/NAD+ ratio that is independent of substrate supply.