Radiobiological Modelling in Radiation Therapy (of Prostate Cancer)

4th Annual LLU Algorithm Workshop

Klinik für Strahlentherapie und Radioonkologie

Elisabetta Gargioni, Alexandra Albanis, Tom Sokolinski, Ilse König, Preena Mehta, Julia Einhausen, Annette Raabe, Rudolf Schwarz

Hamburg: big international port on the Elbe river

Radiotherapy @UKE

Approx. 2,000 patients/yearApprox 1,700 outpatients/year

1 Brachytherapy unit3 Varian TrueBeam linacs1 Siemens 4D-CT 1 Elekta Simulator 1 IntraBeam Intraoperative RT unit1 TomoTherapy

22 doctors (13 specialists)12 physicists/engineers30 radiology assistants/medical technicians

… no protons...

Conventional treatment plan evaluation

• 3D dose distribution• Dose-Volume histograms

Radiotherapy: balance between cure and toxicity

Nr. 4

0 10 20 30 40 50 60 70 80 90

100

0 10 20 30 40 50 60 70Rel.

str

uctu

re v

olum

e in

%

Dose in Gy

target vol.Rectum

Bladder

Basis of radiotherapy: Cell survival and LQ model

mammal cells

SF = exp(−αD−βD2)

Source: M. Joiner and A. van der Kogel (Eds.), “Basic Clinical Radiobiology”, Edward Arnold (2009)

a/b for tumor and normal tissue

for most tumors:

a/b = 10 Gy

BUT:

- Prostate ≈ 1.5 Gy

- Breast ≈ 4.6 Gy

- Oesophagus ≈ 4.9 Gy

- Melanoma ≈ 0.6 Gy

- Liposarcoma ≈ 0.4 Gy

e.g. skin, mucosa

e.g. lung (fibrosis), eyes, spinal canal (myelopathy)

Quelle: P. Mayles, A. Nahum, J.-C. Rosenwald (Eds.), Handbook of Radiotherapy Physics, Taylor & Francis (2007)

Fractionation and a/b

10 2 4 6 8 10

Dose (Gy)

0 2 4 6 8 10Dose (Gy)

Sur

vivi

ng fr

actio

n

0.1

0.01

0.001

1 × 10 Gy2 × 5 Gy5 × 2 Gy10 × 1Gy

1 × 10 Gy2 × 5 Gy5 × 2 Gy10 × 1Gy

0.0001

1

Sur

vivi

ng fr

actio

n

0.1

0.01

0.0001

0.001

0.00001

0.000001(a) (b)

FIGURE 55.1Effect of fractionation (a) on tumour (b) on late-responding normal tissue.

Sur

vivi

ng fr

actio

n

Sur

vivi

ng fr

actio

n

Dose (Gy) Dose (Gy)

0.25 Gy/h

0.5 Gy/h

2 Gy/h

240 Gy/h

0.25 Gy/h

0.5 Gy/h

2 Gy/h

240 Gy/h(a) (b)

0 2 4 6 8 10 0 2 4 6 8 10

0.1

0.01

0.001

0.0001

0.00001

0.1

0.01

0.001

0.0001

0.00001

FIGURE 55.2Effect of changing dose rate (a) on tumour (b) on normal tissue.

CHAPTER 55: RADIOBIOLOGY OF BRACHYTHERAPY 1183

q 2007 by Taylor & Francis Group, LLC

Big a/bSmall a/b

Source: Handbook of Radiotherapy Physics

• dose escalation to the tumor - based on MRI or PET imaging à better identification of high-proliferation or hypoxic regions

• hypofractionation

• stereotactic body radiation therapy

“Emerging” irradiation concepts in prostate cancer

Common issues: • image guidance for margin reduction & motion management • toxicity reduction / isotoxicity

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

Tumordosis (Gy)

Tum

orko

ntro

lle (%

)

This project

Using radiobiological models(e.g. for describing TCP, NTCP) during the treatment planning process

20

40

60

80

100

Normal tissue

complication

probability(%)

Com

plic

atio

nfr

eeco

ntro

lrat

e (%

)

Tum

or c

ontr

olpr

obab

ility

(%)

Tumor dose (Gy)

Curves typically obtained from experimental (clinical) data àmathematical or mechanistic models to describe them

Radiobiological models in radiotherapy

Several levels:

• Use of dose-response curves for determining the probability of tumor control or toxicity rate for a given treatment plan and fractionation scheme

• Use of dose-response curves for optimizing fractionation scheme and prescription dose on an individual basis

• Use of radiobiological models for optimizing the (biological) dose distribution on an individual basis

Typically based on the linear-quadratic model of cell survival & Poisson statistics

Or, more sophisticated, considering population-based data à variation of a

“Calculating” the TCP

TCP = exp −N0 exp(−αD−βdD)[ ]

TCP = 1σα 2π

exp −ρV exp −αD(1+ d / (α / β)[ ]{ }0

∞

∫ exp − (α −α )2

2σα2

$

%&

'

()dα

“Marsden-LQ Model”: see J Uzan & A E Nahum, Br. J. Radiol (2012) 85: 1279-1286

Lyman-Kutcher-Burman (LKB) model:

Relative Seriality (RS) model:

“Calculating” the NTCP

NTCP = 12π

exp(−u2 / 2)du−∞

(µ−µ50 )/mµ50

∫ µ = Deff = viD1/n

i∑"

#$

%

&'

n

P(Di ) = 2−e

eγs 1−DiD50

"

#$$

%

&''

NTCP = 1− 1−P(Di )s"# $%vi

i=1

N

∏'

()

*

+,

1/s

predisposing factor, respectively). Patients who underwentprevious abdominal surgery should thus be subjected tomore severe dose constraints. Taking a second clinical pa-rameter (cardiovascular history) into account, was also sig-nificant (p = 0.015), while including a third (smoking) wasnot anymore (p = 0.16). Figure 2 depicts the consecutiveLKB model fits together with the observations (and their un-certainties). Table 2 shows the parameters obtained with thedifferent fits together with the parameter uncertainties, LLHvalues, LR test significances, and AUC. Figure 3 depicts theROC curves for the consecutive LKB fits.

The same analysis was performed using the RS model.Best fit parameters without clinical information (Table 3)were D50 = 78.9 Gy, gs = 2.24 and s = 0.47 (LLH =-105.04). The same procedure of adding significant clinicalvariables was carried out also resulting in an optimal five-parameter model (two clinical variables) (Table 3, Fig. 4).

Finally, the logistic model incorporated EUD as dosimetricregressor (using Vx did not show any improvement). Togetherwith two significant clinical factors the optimal five-parametermodel was obtained. Detailed results of the consecutive logis-tic fits can be found in Table 4. Figure 4 depicts the optimal fitfor each of the three models. The AUC values of the optimalmodels were nearly the same (0.765–0.767).

The LKB and RS model fits showed similar relations be-tween the NTCP and the EUD or D

¼for the four clinical sub-

groups, despite the different order of patients (and thusdifferent bins). The values of D50 were very similar in thedifferent optimal model fits (ranging from 81.6 Gy to 82.9Gy), whereas the impact of the two clinical factors wasnearly identical (dmfs of 0.91 and/or 0.92 in all models). Vol-ume parameter n was the same in LKB and logistic fits (n =0.18), whereas s = 0.48 was obtained in the RS model. Thelogistic model fit resulted in a (not significantly) higherg50 of 3.46 (2.86 and 2.54 in LKB and RS model,respectively).

High stool frequencyThe time versus complication rate curve in Figure 1

shows that only two events were reported to have occurredafter the 3-year cutoff (both in the fourth year). Thirty-threepatients presented with high stool frequency (6.4%), ofwhich 16 patients in the high-dose group (7.0%) and 17 pa-tients in the low-dose group (6.0%). The difference betweenthe two dose levels in this dataset was not significant as wasalso found by Al-Mamgani et al. (14). However, for eachstructure at least some DVH volume points were signifi-cantly related to outcome, which was most pronouncedfor anorectal wall (V45, p = 0.007). The only significantclinical variable was the patient’s baseline stool frequency.The acute toxicity score was as well significant, but thiswas judged not relevant as it is not known at the momentof treatment planning. The best cutoff value for baselinefrequency was ‘‘3 times a day’’ (p = 0.002). For the LKBmodel, the best fit (Table 2) resulted in a mean dose model(n = 1): D50 = 97.4 Gy and m = 0.34 (LLH = -119.84). Thethree-parameter model did not perform significantly better

Fig. 4. Optimal model fits for Lyman-Kutcher-Burman (LKB),identical to Fig. 2c (n = 0.18) (a), RS (s = 0.48) (b), and logistic re-gression models (n = 0.18) (c), for the rectal bleeding endpoint(anorectal wall dose–volume histogram).

1238 I. J. Radiation Oncology d Biology d Physics Volume 82, Number 3, 2012

Source: Defraene et al. (2012)

Evaluating alternative fractionation schemes in prostate cancer RT

Nr. 13

65,2

72,2

79,6

05

10152025303540455055606570758085

TCP

[%]

41 x 1,8 Gy

20 x 2,968 Gy

6 x 6,328 Gy

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

NTC

P [%

] 41x1,8Gy

20x2,97Gy

6x6,33Gy

• Original plan: 41 x 1.8 Gy

• Alternative plans: 20 x 3.0 Gy

6 x 6.3 Gy

iso-effective with respect to late rectal bleeding

higher TCP if a/b = 1.5 Gy

a/b for prostate cancer: literature

Are these models robust for predicting complications andtumor control rate?

Nr. 15

Model parameters available from literature have quite large uncertainties

• We analyzed the effect of such uncertainties on model predictions • Variation of the model parameter values within ± 20% of the reported values

Results for prostate cancer, Marsden-LQ model

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0 10 20 30 40 50 60 70 80 90

100

40 60 80 100 120 140 160

TCP in %

Tumour dose in Gy

TCP BioSuite_/` = 1.8 Gy_/` = 1.2 Gy

_ = 0.185 Gy-1_ = 0.130 Gy-1m_ = 0.071 Gy

-1

m_ = 0.050 Gy-1

l = 106 cm-3l = 108 cm-3

TCP = 1σα 2π

exp −ρV exp −αD(1+ d / (α / β)[ ]{ }0

∞

∫ exp − (α −α )2

2σα2

$

%&

'

()dα

Starting values (BioSuite)*:a/b = 1.5 Gy, a = 0.155 Gy-1,

r = 107 cm-3

* J Uzan & A E Nahum, Br. J. Radiol (2012) 85: 1279-1286

Results for late rectal complications, LKB model

Nr. 17

* J.M. Michalski et al. (2010), Int. J. Radiation Oncology Biol. Phys. 76: S123-S129.

NTCP = 12π

exp(−u2 / 2)du−∞

(µ−µ50 )/mµ50

∫ µ = Deff = viD1/n

i∑"

#$

%

&'

n

0 10 20 30 40 50 60 70 80 90

100

60 80 100 120 140 160

NTCP in %

Deff in Gy

NTCP, LKBn = 0.108n = 0.075m = 0.156m = 0.108

µ50 = 92.16 Gyµ50 = 64.08 Gy_/` = 3.6 Gy_/` = 2.5 Gy

Starting values*:n = 0.09,

m = 0.13, µ50 = 76.9 Gy,a/b = 3 Gy

Endpoint: rectal bleeding grade ≥ 2

Results for late rectal complications, RS model

Nr. 18

* T Rancati et al. (2004). Radiother. Oncology 73: 21-32.

J. Einhausen et al., Strahlentherapie und Onkologie Vol. 190 (2014)

P(Di ) = 2−e

eγs 1−DiD50

"

#$$

%

&''

NTCP = 1− 1−P(Di )s"# $%vi

i=1

N

∏'

()

*

+,

1/s

0

10

20

30

40

50

60

70

80

60 80 100 120 140 160

NTCP

in

%

Deq in Gy

NTCP, RSa = 1.183a = 1.704s = 0.6

s = 0.42D50 = 69.7 Gy

D50 = 100.3 Gy_/` = 3.6 Gy_/` = 2.5 Gy

Starting values*:g = 1.42, s = 0.5,

D50 = 83.6 Gy,, a/b = 3 Gy

Endpoint: rectal bleeding grade ≥ 2

Are these models robust for plan optimization?

Nr. 19

Models seem to be robust with respect to the most crucial parameters, still important to know whether the uncertainties could affect their clinical use

• We analysed the effect of such uncertainties on NTCP-based plan optimization

• Use of LKB model for NTCP

• Variation of the model parameter values within - ± 20% of the reported values, except µ50

- ± 6% for µ50

• Dosimetric constraint: 72 Gy to PTV, in 40 fractions

• Endpoints for NTCP: late rectal bleeding grade ≥ 2, late bladder toxicity grade ≥ 3

Are these models robust?

Nr. 20

PTVRectumBladderFemoral head leftFemoral head right

filled symbols: conventionally optimized VMAT/ TomoTherapy plans

Open symbols: biologically optimized IMRT plans

E. Gargioni et al., Radiotherapy and Oncology 115:S459 (2015)

Larger deviations among plans for variations of µ50, stronger for low-dose distribution in rectum

What about personalized dose escalation?

Nr. 21E. Gargioni et al., Radiotherapy and Oncology 115:S459 (2015)

MRI-contoured tumor (GTV)Biological optimization à maximizing TCP for GTV & minimizing NTCP as before

Dose constraint for PTV: 72 Gy in 40 fractions

Variation of a/b for prostate cancer:

1.5 Gy3 Gy4.5 Gy

What about personalized dose escalation?

Nr. 22P. Mehta et al., Radiotherapy and Oncology 119:S808-S809 (2016)

GTVPTVRectumBladder

Solid: a/b = 1.5 Gy Dashed: a/b = 3 GyDotted: a/b = 4.5 Gy

Dose (Gy)82.079.275.672.068.4

61.2

36.0

What about personalized dose escalation?

Nr. 23P. Mehta et al., Radiotherapy and Oncology 119:S808-S809 (2016)

Dose (Gy)82.079.275.672.068.4

61.2

36.0

GTVPTVRectumBladder

Solid: a/b = 1.5 Gy Dashed: a/b = 3 GyDotted: a/b = 4.5 Gy

Radiotherapy of Prostate Cancer

Photons vs Protons: How to compare?

Nr. 25

NTCP-based selection…

Nr. 26