Biological optimisation of radiation therapy treatment planning – from modelling to
clinical implementation
Iuliana Toma-Dasu
Department of Medical Radiation PhysicsStockholm University and Karolinska Institutet
Radiation therapy optimisation
I. Toma-Dasu, Santiago de Compostela 2010
• The aim of radiation therapy is to eradicate the tumour while sparing the normal tissue as much as possible.
• Radiotherapy should follow the A.H.A.R.A. principle which is to deliver As High radiation dose As possible (Reasonably Achievable) to the clinical target while keeping the dose to other regions and organs as low as possible.
Treatment planning optimisation
I. Toma-Dasu, Santiago de Compostela 2010
Forward calculation
?
!!
!Inverse calculation
! ??
?Classical beam
profiles
Physically optimised beam
profiles
Inverse calculation
Biologically optimised beam profiles
???
(γ,D50)T
(γ,D50)NT
Treatment planning optimisation
I. Toma-Dasu, Santiago de Compostela 2010
What are the variables in treatment optimisation?
• Radiation modality (type and quality)
• Number and direction of beams
• Beam (fluence) modulation
• Fractionation schedule (number of fractions and overall time)
Biological optimisation
I. Toma-Dasu, Santiago de Compostela 2010
• The generally accepted definition of optimisation in radiation therapy is to produce a treatment plan that maximizes the probability of tumour control without causing unacceptable complications in the normal tissue.
• In the current physical optimisation the outcome of the treatment expressed as tumour control and normal tissue complication probabilities does not play an active role but it is indirectly maximised through the optimised dose distribution within the clinical targets and organs at risk.
• In biological optimisation the main aim of radiation therapy expressed as clinical outcome is explicitly defined at the stage of problem formulation.
Biological optimisation
I. Toma-Dasu, Santiago de Compostela 2010
• The current physical optimisation approaches use dose and/or DVH based objective functions.
• This would imply that a higher dose would result in a higher control but the biological response to radiation is not linear.
• Example: underdosing a very small volume of the tumour would not have a significant effect on the objective value of a physical plan but TCP would be greatly diminished, hence the need for biological optimisation.
50 55 60 65 70 75 800
20
40
60
80
100
Therapeuticwindow
Pe
rce
nt o
f va
lue
s
Prescription dose (Gy)
TCP
NTCP
Biological optimisation
I. Toma-Dasu, Santiago de Compostela 2010
Basic requirements for the biological optimisation:
• Radiobiological models for tumour and normal tissue response
• Clearly formulated objectives and constrains
• Optimisation algorithms
Radiobiological models for TCP
I. Toma-Dasu, Santiago de Compostela 2010
Radiobiological models for tumour and normal tissue response are the result of the combination of:
• Radiobiological models for clonogenic cell survival:– Linear Quadratic (LQ) model
– The lethal and potentially lethal damage (LPL) model (Curtis 1986)
– The Repairable - Conditionally Repairable (RCR) damage model (Lind et al 2003)
– etc.
• Dose-response curves fitted with various functions:– Poisson
– Logistic
– Probit
I. Toma-Dasu, Santiago de Compostela 2010
Poisson-LQ Model:
• The LQ model describes the response of individual cells to radiation in the clinical dose range and a Poisson function describes the response of a whole tissue to radiation.
• The probability of eradicating a tumour is given by:
or
2expexp ddnNP
2expexp ddneP
50 55 60 65 70 75 800
20
40
60
80
100
Pe
rcen
t of v
alu
es
Prescription dose (Gy)
dD
dPD
Radiobiological models for TCP
/1
2lnln
50
dD
e
I. Toma-Dasu, Santiago de Compostela 2010
Poisson-LQ Model:
• In case of non-homogeneous irradiation of the tumour:
• Pi is the control probability at the voxel level.
were ρ is the density of clonogenic cell in the voxel i and Vi is its volume.
i
iPTCP
2expexp ddnVP ii
Radiobiological models for TCP
Larynx T1,T2
Kim et al. 1978P
D/ Gy
0.2
0.4
0.6
0.8
0 20 40 60 80
h=0
D50
v
n
63.6
2.8
1.0
16
47.2
2.1
0.2
129
T1 T2
T1 T2
0.2
0.4
0.6
0.8
0 20 40 60 80
P
D/ Gy
Vocal cord T1, T2, T3
Aristizabal et al. 1972
T1
T2
T3
T1
52.0
1.7
0.3
459
T2
65.6
2.2
1.0
159
T3
77.1
2.6
2.9
63
h=0
D50
v
n
h=0.2
D50
v
n
Larynx T1, T2, T3-4
Robertson et al. 1993P
51.7
2.4
0.4
168
58.2
2.1
1.0
82
65.0
1.8
1.7
45
0.2
0.4
0.6
0.8
0 20 40 60 80 D/ Gy
T3-4
T1
T2
T1
T3-4
T2
Supraglottic ca. T1, T2, T3
Shu kovsky 1970P
D/ Gy
0.2
0.4
0.6
0.8
0 20 40 60 80
h=0
D50
v
n
67.0
4.2
3.0
19
T3
60.6
3.8
1.0
33
T2
51.7
3.2
0.2
19
T1
T3T2T1
Larynx T1,T2,T3
Stewart & Jackson 1975P
D/ Gy
0.2
0.4
0.6
0.8
0 20 40 60 80
T3
78.1
3.7
3.3
67
h=0
v
n
D50 69.559.2
2.8
0.3
158
T1
3.5
1.0
82
T2
T1 T2 T3
T1 T2 T3 D50 v D50 v D50 v h
Shukovsky -70 51.7 3.2 0.2 60.6 3.8 1.0 67.0 4.2 3.0 0Stewart et al. -75 59.2 2.8 0.2 69.5 3.5 1.0 78.1 3.7 3.3 0Aristizabal et al.72 52.0 1.7 0.3 65.6 2.2 1.0 77.1 2.6 2.9 0Kim et al. -78 47.2 2.1 0.3 63.6 2.8 1.0 - - - 0Slevin et al. -92 - - - 62.2 2.0 1.0 75.9 2.4 3.3 0Robertson et al. -93 51.7 2.4 0.4 58.2 2.1 1.0 65.0 1.8 1.7 0.2 Mean Values 52.4 2.4 0.2 63.5 2.7 1.0 72.6 2.9 2.8 -Standard deviation 3.9 0.5 0.1 3.9 0.7 - 5.5 0.9 0.6 -Mean Values 59.9 2.9 1.0 (59.9Gy+0.35Gy/dStandard deviation 2.1 0.3 above 41d at 2Gy/f)
RADIOBIOLOGICAL PARAMETERS FOR LARYNX CANCER
I. Toma-Dasu, Santiago de Compostela 2010* By courtesy of Bengt Lind
Radiobiological parameters for TCP calculation
I. Toma-Dasu, Santiago de Compostela 2010
Poisson-LQ Model:
• NTCP can be calculated in a similar manner incorporating also the modelling of organ seriality, expressed by the parameter s.
• The radiobiological response of a serial critical organ is mainly determined by the maximum dose given to the organ while the radiobiological response of parallel critical structures is not as sensitive to hot spots.
Radiobiological models for NTCP
s
i
Vvsi
i
PNTCP/1
/11
I. Toma-Dasu, Santiago de Compostela 2010
n
m
MIXED
0.14 Small bowel 0.20 Heart 0.64 Brain 0.69 Colon 0.86 Skin
m
SERIAL
0 Tumors
0.0003 Liver 0.004 Kidney 0.018 Lung
1.0 Brain Stem 1.5 Small Intestine 3.4 Esophagus 4.0 Spinal Cord 8.4 Brachial Plexus
FunctionalOrganization
INFLUENCE OF FUNCTIONAL ORGANIZATION OF TISSUES ON DOSE RESPONSE RELATION
n
PARALLELm
Relative OrganSeriality:
s = ____
= 1/ n
m n*m
= Functional Sub Unit
n
D50= 57 Gy
= 6.7 s = 1.0
Human Spinal Cord Myelitis Abbatucci et al 1978
Vref = 7 vertebrae
0.2
0.4
0.6
0.8
40 50 60 70 80 90
76543
Number of vertebrae
D/ Gy
PI
D50= 26 ± 1.5 Gy
= 2 ± 0.5 s = 0.018 ± 0.0070.2
0.4
0.6
0.8
0 20 40 60 80 D/ Gy
PI Human lung Radiationpneumonitis Wara et al. 1990 Mah et al. 1987 Emami et al. 1991
1.0 0.67 0.33
Liver Radiation hepatitis Lawrence et al.1992 Emami et al. 1991
0.77 0.50
0.2
0.4
0.6
0.8
20 40 60 80 100
PI
D/ Gy
D50= 39.2 ± 1.5 Gy
= 4.2 ± 0.6 s = 0.0003 ± 0.0002 Vref= 500 cm 3
0.31.02
D50= 49.2 Gy
= 3.0 s = 0.2
Heart Pericarditis Emami et al. 1991
Vref= Whole heart
PI
0.2
0.4
0.6
0.8
0 20 40 60 80 D/ Gy
1.0 0.67 0.33
D50= 60 Gy
= 2.6 s = 0.64
Brain Necrosis Infarction Emami et al. 1991
Vref= whole brain
PI
D/ Gy
0.2
0.4
0.6
0.8
0 20 40 60 80
1.0 0.67 0.33 Vref=Whole lung
PI
0.2
0.4
0.6
0.8
0 20 40 60 80 D/ Gy
0.8Vref = 500 cm3
0.62.0
0.33
1.6
D50= 62 ± 3
Gy = 2.1 ± 0.2 s = 0.14 ± 0.06
Small bowel Stenosis Letschert et al. 1990
1.1
The seriality model – influence of tissue organisation *
* By courtesy of Bengt Lind
I. Toma-Dasu, Santiago de Compostela 2010
Lyman-Kutcher-Burman Model:
• NTCP can be calculated based on some basic assumptions:– Volume dependence: power law relationship for the tolerance doses for different
irradiated volumes
– Dose dependence: described by an integral over a distribution giving a sigmoid-shaped dose response curve
– A single step of a DVH represents the case of uniform irradiation of a subvolume
γ is the slope of the dose-response curve and n gives
the volume dependence
Radiobiological models for NTCP
dtt
NTCPt
2exp
2
1 2
50
50
D
DDt
i
nn
ii D
V
vD /1
I. Toma-Dasu, Santiago de Compostela 2010
• The objective function should be a scalar quantity describing the treatment outcome, eg. quality of life after treatment.
• The objective function is often simplified by using physical (dose) or biological (radiation response of tumour or normal tissue) quantities.
• A quantity that combines the probabilities of tumour control and complication free treatment into one objective function is P+, probability of complication free tumour control.
Composite models
TCP NTCP
NTCPTCPTCPP P+
I. Toma-Dasu, Santiago de Compostela 2010
Probability of complication free tumour control P+ could be calculated in two ways:
• Assuming that TCP and NTCP are uncorrelated
• Assuming that TCP and NTCP are fully correlated
where
Composite models
NTCPTCPP 1
NTCPTCPP
i
iNTCPNTCP 11
j
jTCPTCP
I. Toma-Dasu, Santiago de Compostela 2010
WARNING!
The composite models should be used with great care.
Loss of tumour control and risk of severe complications cannot be compensated by the risk of minor complications.
P+ optimises only one NTCP at the time.
Example: P+ = TCPprostate – NTCPbladder
or P+ = TCPprostate – NTCPrectum
Composite models
I. Toma-Dasu, Santiago de Compostela 2010
Input data:
• Patient anatomy• Target(s) and OARs
• Individual patient radiosensitivity (if available)
• NTCP for each OAR as a function of physical dose distribution including fractionation
• TCP as a function of physical dose distribution including fractionation
Biological optimisation
I. Toma-Dasu, Santiago de Compostela 2010
1. Maximisation of complication free tumour control
2. Maximisation of complication free tumour control followed by a constrained complication probability minimisation
3. Maximisation of complication free tumour control under NTCP constraints
Clinically relevant optimisation problems
)(P maximise
P-)ˆ(P̂)(P subject to
)NTCP( minimise
ipiNTCP subject to
)(P maximise
I. Toma-Dasu, Santiago de Compostela 2010
4. Maximisation of complication free tumour control under dose homogeneity constrains
5. Maximisation of TCP under NTCP constrains
6. Minimisation of NTCP under TCP constrains
Clinically relevant optimisation problems
j
D
j
D DD max// subject to
)(P maximise
level toleranceNTCP)NTCP( subject to
)TCP( maximise
acceptedTCP)TCP( subject to
)NTCP( minimise
Treatment planning optimisation
I. Toma-Dasu, Santiago de Compostela 2010
Forward calculation
?
!!
!Inverse calculation
! ??
?Classical beam
profiles
Physically optimised beam
profiles
Inverse calculation
Biologically optimised beam profiles
?
??
(γ,D50)T
(γ,D50)NT
Biologically individualised
optimised treatment planning
Biological optimisation based on functional imaging
I. Toma-Dasu, Santiago de Compostela 2010
Preclinical models for tracer
validation
Clinical correlation with histopathology
Clinical target validation and
correlation with outcome
Controlled clinical trials
Technical feasibility and
error management
Estimation of the prescription function
& bioeffect modelling
Clinical implementation
Estimation of the prescription function
& bioeffect modelling
• PET-CT is a non-invasive method that can be used for imaging tumours and deriving radiobiological parameters such us tumour metabolism, proliferative activity and tumour hypoxia.
• PET tracers:– Metabolic tracers (e.g., FDG)– Proliferation tracers (e.g., FLT)– Hypoxic tracers (e.g., FMISO, CuATSM,
FETA, FAZA)
• Several clinical studies have indeed shown good correlations between the amount and severity of PET hypoxia and the treatment outcome.
Treatment planning based on functional imaging
I. Toma-Dasu, Santiago de Compostela 2010
?
PET tracer uptake
Dose distribution
?
Treatment planning based on tumour oxygenation
• Several dose modification algorithms have been proposed for planning based on PET images:
– empirical escalation of doses
– dose redistributions
– prescription of doses taking into account the dynamics of the recorded images
– prescription of doses taking into account the uptake properties of the hypoxic markers
I. Toma-Dasu, Santiago de Compostela 2010
PET tracer uptake Dose modifying factors Dose distribution
Treatment planning based on tumour oxygenation
I. Toma-Dasu, Santiago de Compostela 2010
Tracer (FMISO) cellular uptake
0 200 400 600 800 10000
200
400
600
800
1000
Distance (m)
Dis
tanc
e (
m)
0
5
10
15
20
25
30
35
40pO
2 (mmHg)
• Cellular retention of the hypoxic PET tracers depends on oxygen concentration.
• Various PET tracers provide different levels of uptake and discrimination of the hypoxic levels.
• The uptake and the binding of the hypoxic tracer depend on complex factors but among the most important are the tumour vasculature and oxygenation.
0 200 400 600 800 1000
200
400
600
800
1000
Distance (m)
Dis
tanc
e (
m)
1
2
3
4
5
6
7
8
9
10
Uptake (%)
0.1 1 10 1000
5
10
15
20
Nor
mal
ised
upt
ake
(to
60
mm
Hg
)
pO2 (mmHg)
[18F]FMISO
[3H]FMISO
[64Cu]ATSM
[18F]FETA
Hypoxic PET tracers uptake
I. Toma-Dasu, Santiago de Compostela 2010
• The normalised uptake curve for FMISO combined with the relationship between radiation sensitivity and cellular oxygenation could be used for calculating the Dose Escalation Factors.
• Dose Escalation Factor as function of tracer uptake shows the non-linearity of the relationship between the two quantities.
PET hypoxia and Dose Enhancement Factors
0.1 1 10 1000
5
10
15
20
FMISO
Tra
cer
upt
ake
(n
orm
alis
ed
to
60
mm
Hg
)
Oxygen tension (mmHg)
1.0
1.5
2.0
2.5
3.0
OER-1
Re
lative radiosensitivity
2 4 6 8 10 12 14 16 18 201.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
FMISO
Do
se E
scal
atio
n F
act
or
Tracer uptake (normalised to 60 mmHg)
I. Toma-Dasu, Santiago de Compostela 2010
PET tracer uptake Dose modifying factors Dose distribution
2 4 6 8 10 12 14 16 18 201.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
FMISO
Do
se E
sca
latio
n F
act
or
Tracer uptake (normalised to 60 mmHg)
Treatment planning based on tumour oxygenation
I. Toma-Dasu, Santiago de Compostela 2010
2
21
DDP
DD
D
P
(Toma-Dasu et al 2009)
How does this work on patients?
• Acquisition of PET image;• Calibration of the uptake relative to a
reference region;• Converting uptake levels into radiation
sensitivities;• Target segmentation;• Calculation of the prescribed doses for
segments;• Treatment plan optimisation;
• Treatment verification;• Assessment of tumour responsiveness;• Replanning based on subsequent PET
images.
Hypoxic target 98 GyGTV 73 GyCTV 66 Gy
Treatment planning based on tumour oxygenation
Treatment planning based on tumour oxygenation
98
987366
Treatment planning based on tumour oxygenation
98
987366
Patient no. Primary tumour site
Age Gender Clinical T classification
Clinical N classification
1 Larynx 48 M 3 0
2 Larynx 60 M 4a 2c
3 Larynx 61 M 1 2c
4 Oropharynx 57 M 3 2b
5 Oropharynx 60 M 2 2c
6 Oropharynx 48 M 4a 1
7 Oropharynx 55 M 4a 1
Treatment planning based on tumour oxygenation
98
98
7366
70 80 90 100 110 120 1300.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Tu
mo
ur C
ont
rol P
rob
abili
ty
Dose (Gy)
Calculated dose (Gy)
Static oxygenation
Dynamic oxygenation
Segmented method
Patient
no.
Clinical target Clinical target CTV GTV HTV 1
121
77
66
73
98
2
70
70
66
70
72
3
71
68
65
70
73
4
67
69
64
69
71
5
68
66
64
67
70
6
67
65
64
66
70
7
76
75
72
76
78
OARs constrains Spinal cord Mandibula Left parotid gland Right parotid gland Non-specific normal
tissue Maximum dose
38 Gy Maximum DVH
30 Gy to 1% volume Maximum DVH
38 Gy to 5% volume Maximum DVH
38 Gy to 5% volume Maximum DVH 50 Gy to 1.5%
volume
• Treatment planning based on segmentations methods incorporating information about PET hypoxia leads to better results than highly heterogeneous dose distributions especially for rapidly reoxygenatingtumours.
• Customisation of radiation delivery by focusing the radiation dose to the hypoxic areas has the potential to reduce the average tumour dose needed to achieve a certain level of local control.
• The particular features of hypoxia dynamics might require further imaging throughout the treatment and when needed replanning should be employed for further individualisation of the treatment.
Feasibility of planning based on PET hypoxia
• Comparison between various optimisation approaches
• Planning study using different techniques for dose delivery
• Testing the feasibility of the method for various tumour locations
• Clinical study on H&N patients
• Planning accounting for tumour hypoxia and proliferation derived from FLT PET
Future studies
• Johan Uhrdin
• Alexandru Dasu
• Bengt Lind
• Anders Brahme
Acknowledgements
Thank you