Material parameters are different for each patient

Material parameters are different for each patient

• Material parameters are different for each patient

• Material parameters in vivo are not known

Temperature distribution can be measured during the ablation

• Temperature distribution can be measured during the ablation

• Temperature depends on the material parameters

• Reconstruct the thermal conductivity and the electrical conductivity of the tissue from measurement data of the temperature distribution

• Fit the temperature to the measured data

Heat equation:

• Heat equation:

• Potential equation:

Finite element discretization in space leads to system of ODEs as constraints:

• Finite element discretization in space leads to system of ODEs as constraints:

• Minimize

• subject to

Solve the optimization problem for and with a SQP-method

• Solve the optimization problem for and with a SQP-method

• Heat equation and potential equation have an effect on the computation of the temperature only

• Box-constraints for and

• Solving with worhp, an SQP solver developed by AG Optimierung und optimale Steuerung at University Bremen

one-dimensional model

• one-dimensional model

• simple heat equation, without perfusion and coefficients and

• additional assumptions for and like constant or piecewise constant

• artificial temperature data, knowledge of the optimal parameters

Error for lambda and sigma

• Error for lambda and sigma

Error for lambda and sigma

• Error for lambda and sigma

Error for lambda vs number of optimization variables with and without regularization

• Error for lambda vs number of optimization variables with and without regularization

Error for lambda vs number of optimization variables with and without regularization

• Error for lambda vs number of optimization variables with and without regularization

Error for sigma vs number of optimization variables with and without regularization

• Error for sigma vs number of optimization variables with and without regularization

Error for sigma vs number of optimization variables with and without regularization

• Error for sigma vs number of optimization variables with and without regularization

Implementation for 3-dimensional model and artificial tumor-data as well as real CT-data

• Implementation for 3-dimensional model and artificial tumor-data as well as real CT-data

• temperature dependence of the material parameters and

• Fitting to real temperature distribution