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.