Hanne Tiesler – 1

Identification of Material Parameters for Thermal Ablation

Hanne TieslerCeVis/MeVis/ZeTeM @ University of Bremen,

Germany

DFG SPP 1253

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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

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Treatment of lesions in the human liver

• TransplantTransplant„Replace“ the liver

• Surgical resectionSurgical resectionCut the lesion out

• ChemotherapyChemotherapyKill tumor by cytotoxic drugs

• CryotherapyCryotherapyKill tumor cells by freezing

• Thermal AblationThermal AblationKill tumor cells by heat

Img of lesion

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Treatment-Planning

Bipolar or

Multipolar

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RF-Ablation

LesionLesion

Local VesselsLocal Vessels

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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

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Support the choice of optimum therapy-

parameters

Is a lesion destructable by ablation?

Must perfusionperfusion be stopped?

Must several probes several probes be used?

How must the probes be placedprobes be placed?

How longHow long must power be applied?

Which power power must be applied?

Goals of Numerical Support

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Image based computing pipelineAcquisitionAcquisition Denoising/Denoising/

EnhancementEnhancement

SegmentationSegmentation•PDE model/PDE model/

SimulationSimulation• Electric potential• Heat distribution

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Source/Sink:

Simulating RF Ablation

Heat-equation:(Bioheat transfer eq.)

Electric potential:

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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

…

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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

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Objective functional

• Inverse problem as an optimal control of semi-linear parabolic equation

• Minimize

• With the measured temperature and and regularization coefficients

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Coupled constraints

• Heat equation:

• Potential equation:

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Discretization• Finite element discretization in space leads to system

of ODEs as constraints:

• Minimize

• subject to

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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

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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

Error for lambda and sigma

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Results for constant parameters

Iterations

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Piecewise constant parameterslambda sigma

Regularization coefficients = 0.3

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Results for piecewise constant lambda

Error for lambda

vs number of

optimization

variables with

and without

regularization

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Results for piecewise constant sigma

Error for sigma

vs number of

optimization

variables with

and without

regularization

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Results for piecewise constant lambda with regularization terms

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Results for piecewise constant sigma with regularization terms

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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

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Thank you for your attention