Hanne Tiesler – 1 Identification of Material Parameters for Thermal Ablation Hanne Tiesler University of Bremen, Germany DFG SPP 1253

Hanne Tiesler – 2 Joint work with Inga Altrogge, CeVis, Bremen University, Germany Tim Kröger, CeVis, Bremen University, Germany Heinz-Otto Peitgen, CeVis & MeVis Research, Bremen, Germany Tobias Preusser, CeVis, Bremen University, Germany Christoph Büskens, ZETEM, Bremen University, Germany Matthias Gerdts, University of Birmingham, GB Patrik Kalmbach, ZETEM, Bremen University, Germany Dennis Wassel, ZETEM, Bremen University, Germany MeVis Research, Center for Medical Image Computing, Bremen, Germany Philippe L. Pereira, University Clinic Tübingen, Germany D. Schmidt, University Clinic Tübingen, Germany

Hanne Tiesler – 3 Treatment of lesions in the human liver Transplant „Replace“ the liver Surgical resection Cut the lesion out Chemotherapy Kill tumor by cytotoxic drugs Cryotherapy Kill tumor cells by freezing Thermal Ablation Kill tumor cells by heat Img of lesion

Hanne Tiesler – 4 Treatment-Planning Bipolar or Multipolar

Hanne Tiesler – 5 RF-AblationLesion Local Vessels

Hanne Tiesler – 6 Radio Frequency Ablation High risk of under-ablation No online monitoring No estimation of risk − No dose planning + Minimally invasive Widely used High potential Small equipment

Hanne Tiesler – 7 Support the choice of optimum therapy- parameters Is a lesion destructable by ablation? perfusion Must perfusion be stopped? several probes Must several probes be used? probes be placed How must the probes be placed? How long How long must power be applied? power Which power must be applied? Goals of Numerical Support

Hanne Tiesler – 8 Image based computing pipeline Acquisition Denoising/ Enhancement Segmentation PDE model/ Simulation PDE model/ Simulation Electric potential Heat distribution

Hanne Tiesler – 9 Source/Sink: Simulating RF Ablation Heat-equation: (Bioheat transfer eq.)‏ Electric potential:

Hanne Tiesler – 10 Uncertainty in material properties Material parameters are different for each patient Material parameters in vivo are not known - Water content - Electric conductivity of native tissue - Heat capacity of dry tissue …

Hanne Tiesler – 11 Parameter Identification 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

Hanne Tiesler – 12 Objective functional Inverse problem as an optimal control of semi-linear parabolic equation Minimize With the measured temperature and and regularization coefficients

Hanne Tiesler – 13 Coupled constraints Heat equation: Potential equation:

Hanne Tiesler – 14 Discretization Finite element discretization in space leads to system of ODEs as constraints: Minimize subject to

Hanne Tiesler – 15 Computation 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

Hanne Tiesler – 16 First approaches 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

Hanne Tiesler – 17 Results for constant parameters Error for lambda and sigmaIterations

Error for lambda and sigma Hanne Tiesler – 18 Results for constant parameters Iterations

Hanne Tiesler – 19 Piecewise constant parameters lambda sigma Regularization coefficients = 0.3

Hanne Tiesler – 20 Results for piecewise constant lambda Error for lambda vs number of optimization variables with and without regularization

Hanne Tiesler – 21 Results for piecewise constant lambda Error for lambda vs number of optimization variables with and without regularization

Hanne Tiesler – 22 Results for piecewise constant sigma Error for sigma vs number of optimization variables with and without regularization

Hanne Tiesler – 23 Results for piecewise constant sigma Error for sigma vs number of optimization variables with and without regularization

Hanne Tiesler – 24 Results for piecewise constant lambda with regularization terms

Hanne Tiesler – 25 Results for piecewise constant sigma with regularization terms

Hanne Tiesler – 26 Current work and Outlook 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

Hanne Tiesler – 27 Thank you for your attention