Kalman filter parameter estimation for a nonlinear diffusion model of epithelial cell migration using stochastic collocation and the Karhunen–Loeve expansion

•Four Kalman filter methods are presented for parameter estimation in cell migration.•Stochastic collocation Kalman filter is more efficient that Monte Carlo Kalman filter.•Karhunen Loeve expansion for correlated noise reduces the computational cost.•All algorithms estimate the parameters accurately...

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Bibliographic Details
Published in:Mathematical biosciences Vol. 276; no. C; pp. 133 - 144
Main Authors: Barber, Jared, Tanase, Roxana, Yotov, Ivan
Format: Journal Article
Language:English
Published: United States Elsevier Inc 01.06.2016
Elsevier
Subjects:
Animals
Cell Movement
Computer Simulation
Epithelial cell migration
Epithelial Cells
Humans
Kalman filter
Karhunen–Loeve expansion
Nonlinear Dynamics
Parameter estimation
Stochastic collocation
Stochastic Processes
Karhunen–Loeve expansion
Epithelial cell migration
Parameter estimation
Stochastic collocation
Kalman filter
ISSN:0025-5564, 1879-3134, 1879-3134
Online Access:Get full text
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Summary:•Four Kalman filter methods are presented for parameter estimation in cell migration.•Stochastic collocation Kalman filter is more efficient that Monte Carlo Kalman filter.•Karhunen Loeve expansion for correlated noise reduces the computational cost.•All algorithms estimate the parameters accurately and match well experimental data. Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered —uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen–Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion.
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USDOE
FG02-04ER25618
ISSN:0025-5564
1879-3134
1879-3134
DOI:10.1016/j.mbs.2016.03.018