
On the Optimal Initial Conditions for an Inverse Problem of Model Parameter Estimation  a Complementarity Principle
Matonoha, Ctirad ; Papáček, Š.
This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatiotemporal measurements of fluorescent particle concentration, see [6, 1, 3, 4, 5]. More precisely, we continue to look for an optimal bleaching pattern used in FRAP (Fluorescence Recovery After Photobleaching), being the initial condition of the Fickian diffusion equation maximizing a sensitivity measure. As follows, we define an optimization problem and we show the special feature (socalled complementarity principle) of the optimal binaryvalued initial conditions.


On the Optimization of Initial Conditions for a Model Parameter Estimation
Matonoha, Ctirad ; Papáček, Š. ; Kindermann, S.
The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the process of determining model parameters from data. The key concept relies on the analysis of the sensitivity of the measured output with respect to the model parameters. Based on this approach we optimize an experimental design factor, the initial condition for an inverse problem of a model parameter estimation. Our approach, although case independent, is illustrated at the FRAP (Fluorescence Recovery After Photobleaching) experimental technique. The core idea resides in the maximization of a sensitivity measure, which depends on the initial condition. Numerical experiments show that the discretized optimal initial condition attains only two values. The number of jumps between these values is inversely proportional to the value of a diffusion coefficient D (characterizing the biophysical and numerical process). The smaller value of D is, the larger number of jumps occurs.

 

On Two Methods for the Parameter Estimation Problem with SpatioTemporal FRAP Data
Papáček, Š. ; Jablonský, J. ; Matonoha, Ctirad
FRAP (Fluorescence Recovery After Photobleaching) is a measurement technique for determination of the mobility of fluorescent molecules (presumably due to the diffusion process) within the living cells. While the experimental setup and protocol are usually fixed, the method used for the model parameter estimation, i.e. the data processing step, is not well established. In order to enhance the quantitative analysis of experimental (noisy) FRAP data, we firstly formulate the inverse problem of model parameter estimation and then we focus on how the different methods of data pre processing influence the confidence interval of the estimated parameters, namely the diffusion constant $p$. Finally, we present a preliminary study of two methods for the computation of a leastsquares estimate $\hat{p}$ and its confidence interval.

 
 
 
 
 
 