Computational tools for inversion and uncertainty estimation in respirometry.

In many physiological systems, real-time endogeneous and exogenous signals in living organisms provide critical information and interpretations of physiological functions; however, these signals or variables of interest are not directly accessible and must be estimated from noisy, measured signals. In this paper, we study an inverse problem of recovering gas exchange signals of animals placed in a flow-through respirometry chamber from measured gas concentrations. For large-scale experiments (e.g., long scans with high sampling rate) that have many uncertainties (e.g., noise in the observations or an unknown impulse response function), this is a computationally challenging inverse problem. We first describe various computational tools that can be used for respirometry reconstruction and uncertainty quantification when the impulse response function is known. Then, we address the more challenging problem where the impulse response function is not known or only partially known. We describe nonlinear optimization methods for reconstruction, where both the unknown model parameters and the unknown signal are reconstructed simultaneously. Numerical experiments show the benefits and potential impacts of these methods in respirometry.

Computational methods for image reconstruction.

Reconstructing images from indirect measurements is a central problem in many applications, including the subject of this special issue, quantitative susceptibility mapping (QSM). The process of image reconstruction typically requires solving an inverse problem that is ill-posed and large-scale and thus challenging to solve. Although the research field of inverse problems is thriving and very active with diverse applications, in this part of the special issue we will focus on recent advances in inverse problems that are specific to deconvolution problems, the class of problems to which QSM belongs. We will describe analytic tools that can be used to investigate underlying ill-posedness and apply them to the QSM reconstruction problem and the related extensively studied image deblurring problem. We will discuss state-of-the-art computational tools and methods for image reconstruction, including regularization approaches and regularization parameter selection methods. We finish by outlining some of the current trends and future challenges. Copyright © 2016 John Wiley & Sons, Ltd.

Recovering signals in physiological systems with large datasets.

In many physiological studies, variables of interest are not directly accessible, requiring that they be estimated indirectly from noisy measured signals. Here, we introduce two empirical methods to estimate the true physiological signals from indirectly measured, noisy data. The first method is an extension of Tikhonov regularization to large-scale problems, using a sequential update approach. In the second method, we improve the conditioning of the problem by assuming that the input is uniform over a known time interval, and then use a least-squares method to estimate the input. These methods were validated computationally and experimentally by applying them to flow-through respirometry data. Specifically, we infused CO2 in a flow-through respirometry chamber in a known pattern, and used the methods to recover the known input from the recorded data. The results from these experiments indicate that these methods are capable of sub-second accuracy. We also applied the methods on respiratory data from a grasshopper to investigate the exact timing of abdominal pumping, spiracular opening, and CO2 emission. The methods can be used more generally for input estimation of any linear system.