Optimization and Identification in Regional Hyperthermia · Optimization and Identification in...
Transcript of Optimization and Identification in Regional Hyperthermia · Optimization and Identification in...
Optimization and Identification in Regional Hyperthermia
Martin Weiser
Zuse Institute Berlin
DFG Research CenterMATHEON
OIPE 2008, Ilmenau, 20080915
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Contents
I Regional Hyperthermia
III Perfusion Identification
IV Antenna Profile Identification
II Treatment Planning
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I Regional Hyperthermia
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Regional Hyperthermia
● tumors are susceptible to heat● support radio or chemotherapy by
heating tumors
● phased array microwave radiation● (focused) ultrasound● magnetic nanoparticle fluids● RFablation
Technology for Regional Hyperthermia
Principle
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Regional Hyperthermia
geometry acquisition
physical & physiolocalmodelling
rot H=iErot E=−iHdiv E =0div H =0
[ L xx −C−C ][ y
]=[ra
r c]
simulation & optimization
clinical implementation
quality assessment & online control
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II Therapy Planning
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Therapy Planning
Bio Heat Transfer Equation
tissue subdomains
[Pennes 1948]
Cost Functional
Constraints
Timeharmonic Maxwell's equation
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Cost Functionals
Ad hoc [Seebaß et al.]
Tumor control protein denaturation (Arrhenius law)
fraction of surviving cancer cells
[Mass et al.]
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Function Space Interior Point Methods
s.t.
s.t.
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Central Path
Convergence
for
Local selfconcordance
● rational barrier function of suitable order● generic solution
linear convergence of short step pathfollowing
[Schiela 2008]
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Function Space Algorithms
Inexact Newton Method
Pathfollowing
Adaptive FE Discretization
Linear Algebra
cont
inuo
usdi
scre
te
homotopystepsize selection
linearizationtolerance selectionerror estimationmesh adaptation
linear equation solution
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Numerical Example: Prostate Tumor
isothermes 43.5°C
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Numerical Example: Applicator Comparison
Sigma60, 8 antennas SigmaEye, 24 antennas
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Numerical Example: Applicator Comparison
Sigma60, 8 antennas SigmaEye, 24 antennas
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III Perfusion Identification
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Perfusion Identification
MR thermometry
MR thermometry slice
coefficients depend on tissue type:● fat● muscle
Tichonov regularization
s.t.
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Tichonov Regularization
Gaussian white noise prior
Gaussian smoothness prior
Positivity
perfusion values spatially uncorrelated
perfusion values related to temperature
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2D Clinical Example
perfusion temperature
reference
identified
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3D Artificial Example
actual perfusion
reference perfusion
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High Noise Setting
actual
identified
measurement
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Low Noise Setting
actual
identified
measurement
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Nonconvexity and Nonuniqueness
Idealized situation
fat:
muscle:
globally nonunique identification in muscle regions where
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IV Antenna Profile Identification
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Identification of Antenna Profiles
Error sources● patient positioning, movement, and geometry● reflections in feed network● power generator behavior● bolus water pollution● electrical conductivity of tissues● ...
FDTD simulation measurement
ARD cross section
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Identification of Antenna Profiles
ARD computation
● FE or FDTD for solving timeharmonic Maxwell's equations● superposition of antenna profiles
ARD measurement in phantoms
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Identification of Antenna Profiles
MR thermometry in phantoms
Pointwise least squares fitting
Degrees of freedomrank defect: 5
highly underdetermined problem
SigmaEye applicator● channels● measurements
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GaußNewton Algorithm
Least change update
Closed loop control
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Closed Control Loop on Phantom
[Weihrauch et al. 2007]
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Closed Control "Loop" on Patient
comptued ARD
computed ARD
measured ARD
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Closed Control "Loop" on Patient
time (min)
temperature difference betweentumor and muscle
central FDTD focused adapted
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Conclusion
Thanks to...
● J. Gellermann, P. Wust, M. Weihrauch (Charité)● A. Schiela, P. Deuflhard (ZIB)● S. Volkwein (U Graz)
● regional hyperthermia poses several optimization & identification problems● the solution of most of which are essential for individually optimal therapy delivery● beneficial effect of identification even for simple models & sparse data● more data needed for perfusion identification