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| Content Provider | Springer Nature Link |
|---|---|
| Author | Bocharov, Gennady Luzyanina, Tatyana Roose, Dirk |
| Copyright Year | 2008 |
| Abstract | In this work we address the problem of the robust identification of unknown parameters of a cell population dynamics model from experimental data on the kinetics of cells labelled with a fluorescence marker defining the division age of the cell. The model is formulated by a first order hyperbolic PDE for the distribution of cells with respect to the structure variable x (or z) being the intensity level (or the log10-transformed intensity level) of the marker. The parameters of the model are the rate functions of cell division, death, label decay and the label dilution factor. We develop a computational approach to the identification of the model parameters with a particular focus on the cell birth rate α(z) as a function of the marker intensity, assuming the other model parameters are scalars to be estimated. To solve the inverse problem numerically, we parameterize α(z) and apply a maximum likelihood approach. The parametrization is based on cubic Hermite splines defined on a coarse mesh with either equally spaced a priori fixed nodes or nodes to be determined in the parameter estimation procedure. Ill-posedness of the inverse problem is indicated by multiple minima. To treat the ill-posed problem, we apply Tikhonov regularization with the regularization parameter determined by the discrepancy principle. We show that the solution of the regularized parameter estimation problem is consistent with the data set with an accuracy within the noise level in the measurements. |
| Ending Page | 603 |
| Page Count | 23 |
| Starting Page | 581 |
| File Format | |
| ISSN | 03036812 |
| e-ISSN | 14321416 |
| Journal | Journal of Mathematical Biology |
| Issue Number | 5 |
| Volume Number | 59 |
| Language | English |
| Publisher | Springer-Verlag |
| Publisher Date | 2008-12-19 |
| Publisher Place | Berlin, Heidelberg |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Label-structured cell population dynamics Computational methods Hyperbolic PDE model Inverse problems Cell biology Mathematical Biology in General Applications of Mathematics Tikhonov regularization Inverse problem |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Agricultural and Biological Sciences Modeling and Simulation |
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