Computational tools for inversion and uncertainty estimation in respirometry

Abstract

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.

Impulse Response Functions for Nonlinear, Nonstationary, and Heterogeneous Systems, Estimated by Deconvolution and Demixing of Noisy Time Series

“…Three examples from environmental science, for example, are (a) understanding how streamflow time series reflect landscape-scale responses to precipitation inputs, (b) quantifying source-receiver relationships for airborne or waterborne contaminants and pathogens, and (c) estimating how ecosystems' rates of photosynthesis, respiration, and transpiration fluctuate in response to external forcings, such as solar radiation, precipitation, and nutrient concentrations. Many other examples can be found in fields ranging from chemistry [1], engineering [2], and economics [3,4] to systems biology [5], neuroscience [6,7], physiology [8] and epidemiology [9][10][11].…”