biological optimisation of radiation therapy treatment - nodo cesga

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


Forward calculation

?

!!

!Inverse calculation

! ??

?Classical beam

profiles

Physically optimised beam

profiles

Inverse calculation

Biologically optimised beam profiles

???

(γ,D50)T

(γ,D50)NT



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


• 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.



• 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



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


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


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


/1

2lnln

50

dD

e


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


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


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


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


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


• 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+


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


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


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



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


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



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


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


?

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


PET tracer uptake Dose modifying factors Dose distribution



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


• 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)


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)



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



98

987366


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


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

biological optimisation of radiation therapy treatment - nodo cesga

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