Recovering signals in physiological systems with large datasets

Abstract

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.

Computational tools for inversion and uncertainty estimation in respirometry

“…We consider two Tikhonov regularized solutions. Tikhonov- Q incorporates a regularization matrix Q , which is a lower triangular Toeplitz matrix with [1 − 1 0 … 0] ⊤ as the first column [ 5 ], and HyBR-I corresponds to a hybrid iterative projection method with regularization matrix Q = I . For the 1-norm penalty, we investigate a flexible hybrid iterative method called FLSQR-R [ 24 ] and FISTA as described in Algorithm 1.…”

“…We tested different initial guesses for the impulse response function , where the support is 18.4 sec and the delay is 21.3 sec. First, following the work in [ 5 ], we considered density functions of Gamma distributions (e.g., ) for different choices of α and β . Gamma1 corresponds to an initialization with α = 4 and β = 3, and Gamma2 corresponds to an initialization with α = 2 and β = 0.5.…”

“…For small problems, constructing the matrix and the solution in (23) is computationally feasible, and many of the previous works in respirometry reconstruction follow this approach. For example, Tikhonov methods described in [ 5 ] could be used here. However, more sophisticated iterative techniques should be used for large-scale problems.…”

“…Since it is well known that the respirometry problem is ill-posed, which means that small errors or measurement noise in the data may and often do lead to large errors in the reconstruction, regularization must be used. Some previous works that use Tikhonov regularization to solve the linear respirometry reconstruction problem include [3][4][5], among others. Since the forward model used in these regularized deconvolution methods is defined by the choice of the impulse response function, using an inaccurate impulse response function (e.g., one that is estimated experimentally) can result in significant degradation of the reconstruction accuracy.…”

Why do models of insect respiratory patterns fail?

“…The main theoretical effector of variability in whole-animal gas exchange, the spiracle neuromuscular valve system, is thought to be controlled by interacting feedback loops between oxygen-and carbon dioxide-sensing systems (redrawn from Grieshaber and Terblanche, 2015). (B) The oxygen-carbon dioxide phase space model of DGC proposed by Förster and Hetz (2010), which tracks the phases of the DGC cycle as a loop from the top left-hand corner, down towards the bottom left corner, then out towards the right-hand side and then back to the point of origin as the DGC proceeds through the 'constriction' periodic patterns, such as cyclic gas exchange or DGC, are perhaps more easily identified than irregular, more chaotic signals especially in a noisy and/or time-lagged system (Pendar et al, 2016). In noisy systems, it often is unclear whether the noise arises from the actions of the animal or from some kind of experimental or methodological noise.…”