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 we 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. / Master of Science / The goal of an inverse problem is to determine some signal or parameter of interest that is not directly accessible but can be obtained from an observed effect or a processed version that is measurable. Finding the gas exchange signal in animals is an example of an inverse problem. One method to noninvasively measure the gas exchange rate of animals is to put them in a respirometry chamber, flow air through the chamber, and measure the concentration of the respiratory gasses outside the chamber. However, because the gasses mix in the chamber and gradually flow through the gas analyzer, the pattern of the measured gas concentration can be dramatically different than the true pattern of real instantaneous gas exchange of the animal. In this thesis, we present two methods to recover the true signal from the recorded data (i.e., for inverse reconstruction), and we evaluate them computationally and experimentally.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/109178 |
| Date | 11 September 2020 |
| Creators | Pendar, Hodjat |
| Contributors | Mathematics, Chung, Julianne, Socha, John J., Embree, Mark P. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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