Material parameters are different for each patient



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tarix11.09.2018
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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






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