Evolutionary optimization in (deformable) registration of medical

The Netherlands Cancer I nstitute
Antoni van Leeuwenhoek Hospital
Evolutionary optimization in
(deformable) registration of medical
images
Ch. Siedschlag, J. Stroom, H. Blaauwgeers1,A. van Baardwijk2,
H. Klomp, M. Wouters, K. Liesker1, R. van Pel, L. Boersma2, K. Gilhuijs
1: Onze Lieve Vrouwe Gasthuis, Amsterdam
2: Maastro Clinic, Maastricht
Overview
• Registration of images: necessary to get
the most out of different modalities
• Small or rigid deformations: affine
transformations suffice
• Bigger/elastic transformations: deformable
registration
• Automation with control loop -> EA
• Sidetrack: EA in treatment optimization?
2
General optimization goal: optimize
similarity
• “Images” are two- or threedimensional
arrays
• For same modalit y: fitness function can be
squared differences of grey values
• For different modalities: corresponding
points are colour-coded differently
• Similarity measure of choice: mutual
information
3
Mutual information
Single image: grey value
histogram conveys
information
Two images: correlated
grey value histogram leads
to measure of similarity
(mutual information, based
on minimalized entropy)
4
• Depending on the organ in question,
deformations can be rigid (e.g. the head) or
non-rigid (lung, breast etc…)
• With rigid deformations: affine
transformations are enough, not interesting
from EA point of view (only 6 parameters in
3D, 9 if scaling is involved)
• Nonrigid deformations are described by
deformable regist ration: high number of
parameters, nonlinear problem -> EA!
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Deformable registration
A deformation field is created by defining the
displacement on a number of control points and
finding an interpolation in between:
n is typically 8-12 (in 2D) and 30 or more (in 3D).
Optimization variables are the displacement
vectors. Extended version: control points +
displacement vectors
Number of parameters: n*D(*2, if extended
version)
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A concrete study on lung cancer
• CT (and PET) scans prior to surgery,
detailed pathology analysis post surgery
• Goal: match the modalities
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The problem
CT scan
CT scan
(masked lung
lobe)
PA photo
match
3D rotate
•Started in 2D
•Has been extended to 3D, but not very
successfully so far…
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Example
First phase: affine transformations
Second phase: non-rigid deformations
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Result of warping
Has the global
optimum been
reached?
Accuracy: 2-3 mm
Is Mutual
Informati on really
behaving the way
we expect it to
behave?
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The complete picture
CT scan with tumor (red:
GTV from CT, yellow: GTV
from PET) and lung lobe
(green)
Warping
Macroscopic and
microscopic pathology
results (dark blue: path.
GTV, light blue:
microscopic CTV)
New margin
recipes based on
warped tumor cell
distributions
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The EA side
• In collaboration with Ofer and Thomas: one
particular algorithm (“DR2”, a (1,10)
evolutionary strategy) behaved particularly
well in laser pulse phase shaping
• Contestor: Particle Swarm Optimization
(PSO)
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PSO algorithm
•
•
•
•
•
Modeled after a swarm of birds
Ingredients: 20 “birds” with coordinate and velocity vectors in
the search space
Position update based on personal and social memory
Parameter w, n1 and n2 are empirically determined, r1 and
r2 are random numbers between 0 and 1
Advantage: extremely simple, can be coded in 5 minutes…
Is it an EA at all?
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Test runs with fixed control points
DR2
PSO
Fitness
8 CPs
12 CPs
# of evaluations
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Test runs with variable control points
DR2
PSO
Fitness
8 CPs
12 CPs
# of evaluations
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Test runs with variable control points and affine
pre-matching (12 CPs)
DR2
Fitness
PSO
# of evaluations
PSO seems to be better , faster &
more robust …
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Explorative: fractionation optimization
•Radiotherapy: treatment plan given by a set of doses D[i] at times
t[i]
•Normal procedure: 2 Gray (just a unit) per day, about 4 to 5 weeks
•Recent advantages in beam shaping: concept should be looked at
again. What’s the optimal treatment plan?
Tumor
healthy
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Model: extended LQ
Surviving cell fraction as function of dose D:
1
é
ù
S = expê- aD - b G(t R ) D 2 + s 2G(t S ) D 2 + H (TTot , Tk )(TTot - Tk ) / Tpd ú
2
ë
û
• Included: repair and resensitization times plus
accelerated proliferation
• For healthy tissue: only first two terms
•Data available for tumor, early reacting normal
tissue and late reacting normal tissue
• Relevant quantity: biologically efficient dose
BED = -1/a*ln(S)
• Goal: keep normal tissue BEDs low , maximize
tumor BED
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H&N tumors (fast proliferating, large a/b), 40 Gy
total delivered in 20 doses:
Simple attempt: restricted to
one delivery every 24 hrs
Dose in normal tissue: 40
percent of tumor dos e
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H&N tumors (fast proliferating, large a/b), 40 Gy
total delivered in 20 doses:
Unrestricted delivery times
Dose in normal tissue: 40
percent of tumor dos e
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H&N tumors (fast proliferating, large a/b), 40 Gy
total delivered in 20 doses:
Unrestricted delivery times
Dose in normal tissue: 20
percent of tumor dos e
Overall: relatively small
effects for H&N tumors !
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Prostate tumor (slowly proliferating, small a/b), 40
Gy in 20 doses
Dose in normal tissue: 20 %
Restricted: one fraction per
day
Daily delivery: skew dose
distribution can already
more than double the tumor
BED (due to the s mall a/b
ratio)
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Prostate tumor (slowly proliferating, small a/b), 40
Gy in 20 doses
Dose in normal tissue: 20 %
Unrestricted delivery times
Huge gains!
Much longer
Might
intervals
be
are
optimal (15-20 days)
something worth
investigating…
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Summary
• Challenging optimization problems in
deformable regist ration
• PSO seems to be at least as good as ES3
• Step to 3D: everything is even more
difficult
• General thought: EA optimization of
treatment possible? Models, retrospective
study analysis?
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