Radiation Biology III - AMOS Onlineamos3.aapm.org/abstracts/pdf/90-25499-333462-102837.pdf · Radiation Biology III: Biological optimization of radiation therapy ... variability in

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Radiation Biology III:Biological optimization of radiation therapy

David J. Carlson, Ph.D.Assistant ProfessorDept. of Therapeutic [email protected]

56th Annual Meeting of the AAPM

Date and Time: July 24, 2014 from 7:30-9:30 AMLocation: Austin Convention Center, Austin, TX

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Learning Objectives

1. Review commonly used radiobiological models in radiation oncology (and underlying mechanistic basis)

– Can be incorporated into treatment planning as biological objective functions

2. Understand factors that alter radiation response– DNA damage repair, hypoxia & reoxygenation, radiation quality

3. Learn how to apply concepts of biological effective dose (BED) and RBE-weighted dose (RWD)

– Implementation and implications for fractionation and particle therapy

4. Discuss clinical strategies to increase therapeutic ratio– Spatial and temporal optimization of dose delivery (# of n and dose per n)– Concurrent therapeutics, e.g., hypoxic cell radiosensitizers or cytotoxins

5. Appreciate model limitations and sources of uncertainty

Conflict of interest: Nothing to disclose

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Biologically Guided Radiation Therapy (BGRT)– Systematic method to derive prescription doses that integrate patient-

specific information about tumor and normal tissue biology– Problem: derived prescriptions may have large uncertainties

• Uncertainties in physical and biological factors (experimental and clinical) that influence tumor and normal-tissue radiation response

• Incomplete understanding of molecular and cellular mechanisms

Background and Motivation

Dose-Based TP → Physical objective functions• Minimize dose gradients across tumor (uniformity), deliver prescribed

isodose contours to target, minimize max. dose to critical structures, etc.• Uniform dose may not be most desirable

BGRT → Biological objective functions• More direct approach to optimization instead of relying on dose-based

surrogatesMaximize tumor cell killing (LQ) and tumor control probability (TCP)Minimize normal tissue complication probability (NTCP)

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• A DSB is formed when two breaks in the sugar-phosphate backbone occur on opposite sides of DNA helix within ~10 base pairs

• Simple DSB:

• Many experiments for all types of DNAdamage, including DSB, show that damage formation is proportional toabsorbed dose up to hundreds of Gy

The double strand break (DSB)

DSBs are formed through one-track mechanisms

DSB induction in human fibroblasts (MRC-5) irradiated by 90 kVp x-rays (Rothkamm and Lobrich 2003)

(n = 2 lesions)

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One- and two-track radiation damage

Lethal lesions are created by the actions of one or two radiation tracks

1 track damage( D)

2 track damage( D2)

Lethal DSB misrepair, unrepairable damage

Pairwise interaction of two DSBs

Pairwise interaction of two DSBs

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Exchange-type aberrations

Pairwise damage interaction (binary misrepair)

DSB

1 chromosome:

Stable Lethal StableStable Lethal

2 chromosomes:

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Absorbed Dose (Gy)0 2 4 6 8 10 12

Surv

ivin

g Fr

actio

n

10-3

10-2

10-1

100

60 Gy h-1

LQ Fit to Experimental Data ( = 0.128 Gy-1, = 3.46 Gy)

PC-3 prostate carcinoma cells (Deweese et al 1998)

= one-track lethaldamage [Gy-1]

= two-track lethaldamage [Gy-2]

/ [Gy] is clinically useddescriptor of intrinsicradiosensitivity

Linear-quadratic (LQ) cell survival model

(D+D2) = expected number of lethal lesions per cell

2( ) expS D D D

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Repair-misrepair-fixation (RMF) Model

(1 ) [ / ][ ]R R Rf f f

2[ /(2 )][ ]( )Rf

2( ) exp ( ) expS D F D GD

Surviving fraction is related to yield of fatal lesions

fR ≡ fraction of potentially rejoinable DSB ≡ rate of DSB repair (~10-1100 h-1) ≡ rate of binary misrepair (~10-510-4 h-1) ≡ zFfR ≡ # of DSB per track per cell

≡ expected # of DSB (Gy-1 cell-1) ≡ prob. DSB lethally misrepaired/fixed ≡ prob. exchange-type aberration lethal

1. Unrejoinable and lethal damage

2. Lethal misrepairand fixation

3. Intra-track DSB interactions

4. Inter-track DSB interactions

Carlson DJ, Stewart RD, Semenenko VA, Sandison GA. Combined use of Monte Carlo DNA damage simulations and deterministic repair models to examine putative mechanisms of cell killing. Radiat. Res. 2008; 169: 447459.

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Tumor Control Probability (TCP) Model

Mean Dose (Gy)

50 60 70 80 90 100

TCP

0.0

0.2

0.4

0.6

0.8

1.0

Clinical data from MSKCCTCP Model Fit: N = 4.1 x 106 cells .15 Gy-1

3.1 Gy

Tumor Control Probabilities for intermediate- risk prostate cancer patient group (n = 40)(Levegrun et al 2001)

TCP → relates tumor size andradiation dose to the prob. of tumor control (i.e., no tumor cells survive)

2

exp ( )

exp D D

TCP N S D

N e

N = initial # of tumor clonogens

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Inter-patient variability in radiosensitivity

Figure from: Keall PJ, Webb S. Optimum parameters in a model for tumour control probability, including interpatient heterogeneity: evaluation of the log-normal distribution. Phys. Med. Biol. 2007; 52: 291302.

Heterogeneity of human tumour radiation response is well known

Many groups have accounted for variations in interpatient tumour heterogeneity by assuming that radiosensitivity values are normally distributed across the population

If interpatient heterogeneity is ignored, TCP model generally results in an unrealistically steep dose-response curve

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Factors that alter treatment effectiveness

Treatment effectiveness

Treatment duration

mins hours days

DNA repair

Repopulation

Reoxygenation& Redistribution

4 R’s of Radiobiology give rise to “dose rate” effects:

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Divide a tumor into voxels with radiosensitivity i and i. Correct SF for dose heterogeneity, inter- and intra-tumor variability in radiosensitivity and the R’s of radiobiology:

N0 fi is initial #of cells in the ith tissue region

Repopulation rate in ith tissue region

0TCP exp expi i i i i i iN f D G D T

Repair effects ( or )

Oxygen and LET effects ( and )

i

TCP TCPi

Factors that alter treatment effectiveness

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= one-track lethal damage coefficient [Gy-1] = two-track lethal damage coefficient [Gy-2]

G[,t] is the Lea-Catcheside dose protraction factor = ln2/ = rate of DSB rejoining [h-1]

DNA damage repair in the LQ model

2( ) exp ,S D D G t D (D+G[,t]D2) = expected number of lethal lesions per cell

0lim 1

lim 0t

t

G

G

Limiting cases:Instantaneous dose delivery

Infinitely protracted dose

Dose protraction factor often neglected (G =1), only reasonable when irradiation time is short compared to DSB repair half-time

Sachs RK, Hahnfeld P, Brenner DJ. The link between low-LET dose-response relations and the underlying kinetics of damage production/repair/misrepair. Int. J. Radiat. Biol. 72(4): 35174 (1997).

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Dose rate effects and DNA damage repair

Absorbed Dose (Gy)0 5 10 15 20 25 30 35

Surv

ivin

g Fr

actio

n

10-4

10-3

10-2

10-1

100

0.12 Gy h-1

0.5 Gy h-1

45 Gy h-1

CHO cells in vitro

Measured data from Stackhouse M.A. and Bedford J.S. Radiat. Res. 136, 250-254 (1993) and Wells R.L. and Bedford J.S. Radiat. Res. 94(1), 105-134 (1983).

• Cell killing decreases with decreasing dose rate

• If G(,t) included, unique set of parameters can predict the data: = 0.04 Gy-1 , = 0.02 Gy-2, = 6.4 h

• Repair of DNA damage occurs between fractions and during treatment delivery

• Effect increases with increase in delivery time

More important for SBRT, SRS, and brachytherapy

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In vitro estimates:• = 0.090.4 Gy-1

• / = 1.16.3 Gy

In vivo estimates:• = 0.0360.15 Gy-1

• / = 1.53.1 Gy

In vitro and in vivo data support a low /for prostate cancer

Prostate Cancer: review of in vitro and in vivo data

Carlson DJ, Stewart RD, Li XA, Jennings K, Wang JZ, Guerrero M. Comparison of in vitro and in vivo α/β ratios for prostate cancer. Phys. Med. Biol. 49, 4477-4491 (2004).

1) Corrections for intrafraction DNA damage repair have significant impact on /2) Observed variability demonstrates uncertainty associated w/ parameter estimation3) Radiobiology of prostate cancer suggests hypofractionation may ↑ therapeutic ratio

(Gy-1)10-2 10-1 100

(G

y-2)

10-2

10-1

100

Brenner and Hall (1999)Fowler et al (2001)Brenner et al (2002)Wang et al (2003a)Wang et al (2003c)Kal and Van Gellekom (2003)

PC-3

DU-145TSU DU-145

PC-3

LNCaPDU-145

PC-3

PPC-1

TSU-Pr1

LNCaP

(Gy-1)10-2 10-1 100

(G

y-2)

10-2

10-1

100

Brenner and Hall (1999)Fowler et al (2001)Brenner et al (2002)Wang et al (2003a)Wang et al (2003c)Kal and Van Gellekom (2003)

PC-3

DU-145TSU DU-145

PC-3

LNCaPDU-145

PC-3

PPC-1

TSU-Pr1

LNCaP

/=1.5 /=3.0 /=10

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Review of studies deriving prostate /

= 2.7 Gy

At least 24 studies since Brenner & Hall’s 1999 paper:• EB-LDR• EB-HDR• EB alone• in vitro

Modeling: RBE, repair,repopulation, dose heterogeneity, hypoxia

Oliveira SM, Teixeira NJ, Fernandes L. What do we know about the / for prostate cancer? Med. Phys. 2012; 39: 3189-3201.

“Clinical practice of hypofractionation in the treatment of prostate cancer seems not to increase late complication and shows a biochemical outcome superior or equivalent to conventional schedules”

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Biologically Effective Dose (BED)

Recall 2( ) expS D D GD T Take the negative logarithm of S and divide by :

ln ( )BED 1/

S D GD TD

Physical dose

Relative effectiveness“Lost” dose due to repopulation effect

BED is an LQ based estimate of the effective biological dose that accounts for delivered total dose, the dose fractionation, and the radiosensitivity of tissue Commonly used for isoeffect calculations

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Isoeffect Example for Prostate Cancer

Assume / = 3 Gy, for a standard EBRT fractionation of 39 fractions of 2 Gy:

2

2

/ 42 /

3Gy 4 130 Gy2 3 Gy

nBEDd n nn

nn nn

Rearrange simplified BED equation:

Number of fractions0 5 10 15 20 25 30 35 40

Frac

tion

Size

(Gy)

02468

101214161820222426

/ = 3.0 Gy

1

King et al. (2009)

Standard Fractionation

Kupelianet al. (2005)

Yeoh et al. (2006)

2 GyBED 78 Gy 1 130 Gy3 Gy

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Isoeffect Example for Prostate Cancer

Assume / = 3 Gy, for a standard EBRT fractionation of 39 fractions of 2 Gy:

2

2

/ 42 /

3Gy 4 130 Gy2 3 Gy

nBEDd n nn

nn nn

Rearrange simplified BED equation:

2 GyBED 78 Gy 1 130 Gy3 Gy


Frac

tion

Size

(Gy)

02468

101214161820222426

/ = 3.0 Gy/ = 1.5 Gy/ = 10 Gy

1

King et al. (2009)

Standard Fractionation

Kupelianet al. (2005)

Yeoh et al. (2006)

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Radiobiology and the AAPM

Li XA, Alber M, Deasy JO, et al. The use and QA of biologically related models for treatment planning: Short report of the TG-166 of the therapy physics committee of the AAPM. Med. Phys. 2012; 39: 13861409.

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Hypofractionation and Tumor Hypoxia

Point/Counterpoint debate in December 2011 issue of Medical Physics

Carlson DJ, Yenice KM, Orton CG. Point/Counterpoint: Tumor hypoxia is an important mechanism of radioresistance in hypofractionated radiotherapy and must be considered in the treatment planning process. Med. Phys. 38: 6347−6350 (2011).

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Clinical significance of tumor hypoxia

B. Movsas et al., Urology, 2002D.M. Brizel et al., Radiother. Oncol., 1999

Prostate cancerHead and neck cancer

~90% of solid tumors have median values below normal (40-60 mmHg), half have median values <10 mmHg, and a third contain subvolumes with concentrations <2.5 mmHg (Vaupel and Hockel, in Tumour Oxygenation, 1995 and Brown JM, Mol. Med. Today, 2000)

Primarily I-125 LDR brachytherapy to 145 Gy

Hyperfractionation:2 Gy/fx to 66-70 Gy1.25 Gy/fx to 70-75 Gy

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What about tumor hypoxia?

Absorbed Dose (Gy)0 5 10 15 20 25 30 35

Surv

ivin

g Fr

actio

n

10-3

10-2

10-1

100Fit to aerobic dataFit to hypoxic dataSimultaneous fit to aerobicand hypoxic data (OER = 2.96)

H = A/OER = 0.05 Gy-1

(/)H = (/)A*OER = 13.6 Gy

A = 0.15 Gy-1

(/)A = 4.6 Gy

V79 379A Chinese hamster cell survival data from Watts et al. (1986)

OER = 2.96

OER values for cell death are relatively constant over a large dose range

• May actually increase slightly with dose (Wouters and Brown 1997, Nahum et al. 2003)

Statistically, OER ~ OER• Reasonable assumption for large

number of in vitro data sets (Carlson et al. 2006)

Carlson DJ, Stewart RD, Semenenko VA. Effects of oxygen on intrinsic radiation sensitivity - a test of the relationship between aerobic and hypoxic linear-quadratic (LQ) model parameters. Med Phys; 33: 31053115 (2006).

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Effects of Hypoxia and Fractionation on Cell Survival

80.5 Gy for reference H&N treatment

130 Gy for reference prostate treatment


Surv

ivin

g Fr

actio

n

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

0 5 10 15 20 25 30 35 4010-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Fully oxygenated cells Fully oxygenated cells

Head and Neck Cancer(/ = 10 Gy)

Prostate Cancer(/ = 3.0 Gy)

Dose per fraction (Gy) to yield equivalent tumor BED under normoxic conditions3.2 2.7 2.4 2.2 2.03.84.97.518.31.75.3 3.9 3.18.6 2.6 2.2 1.923.8

1 1

2( ) expnn

overall A AS S d d d Carlson DJ, Keall PJ, Loo BW, Chen ZJ, Brown JM. Hypofractionation results in reduced tumor cell kill compared to conventional fractionation for tumors with regions of hypoxia. Int. J. Radiat. Oncol. Biol. Phys. 79: 1188-1195 (2011).

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Surv

ivin

g Fr

actio

n

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

0 5 10 15 20 25 30 35 4010-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100





1 1


Surv

ivin

g Fr

actio

n

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

fhyp = 0.1fhyp = 0.2fhyp = 0.3

0 5 10 15 20 25 30 35 4010-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

fhyp = 0.1fhyp = 0.2fhyp = 0.3





1 1

Effects of Hypoxia and Fractionation on Cell Survival

Carlson DJ, Keall PJ, Loo BW, Chen ZJ, Brown JM. Hypofractionation results in reduced tumor cell kill compared to conventional fractionation for tumors with regions of hypoxia. Int. J. Radiat. Oncol. Biol. Phys. 79: 1188-1195 (2011).

What happens to total cell killing if we include hypoxia?

2 2(1 ) ( ) exp / ( ) / ( )hypnR

overall hyp hyp hyp A AaS f S f f r HRF r d HRF r d dr

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Strategies to overcome tumor hypoxia?

Tumor

Tumor hypoxic volume

Tumor

Tumor hypoxic volume

Biological Target Volume

Hypoxic volume > X% of tumor

orHypoxic volume < X% of tumor

Give patient drug ‘Y’

Do not give patient drug ‘Y’

Alter radiation therapy treatment

plan

Drug clinical trial

Kelada, O.J. and Carlson, D.J. Molecular Imaging of Tumor hypoxia with Positron Emission Tomography. Radiat. Res. 2014; 181: 335-349.

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18F-FMISO PET: Can select patients for drug trials

Hypoxic

Hypoxic

Rischin, D., R. J. Hicks, et al. (2006). "Prognostic significance of [18F]-misonidazole positron emission tomography-detected tumor hypoxia in patients with advanced head and neck cancer" J Clin Oncol 24(13): 2098-2104.

• 45 patients with stage III or IV squamous cell carcinoma of H&N

• Randomly assigned to RT (70 Gy in 35 fx) plus cisplatin + tirapazamine (TPZ) or cisplatin + fluorouracil

• Pretreatment and midtreatment 18F-FMISO PET performed

• In patients with hypoxic tumors, 0 of 8 treated with Cis-TPZ had local failure compared with 6 of 9 treated with Cis-FU

• First clinical evidence to support tirapazamine specifically targets hypoxic tumor cells

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Photon versus proton dosimetry

• Protons allow a reduction of integral dose and lower doses outside target

Photons Protons

Image courtesy of Uwe Oelfke (ICR, London)

S L I D E 28

Proton versus carbon ion dosimetry

• Carbon ions provide a steeper gradient at target edge, but contribute a higher integral dose (distal tail)

Protons Carbon ions


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Physical and Biological Aspects of Particle Theray


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Biological effects of radiation quality

Absorbed Dose (Gy)

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Surv

ivin

g Fr

actio

n

10-3

10-2

10-1

100200/250 kVp X (~2 keV/m)14.9 MeV 2H+ (5.6 keV/m)6.3 MeV 2H+ (11 keV/m)26.8 MeV 4He2+ (25 keV/m)8.3 MeV 4He2+ (61 keV/m)4.0 MeV 4He2+ (110 keV/m)

Barendsen et al. (1960, 1963, 1964, 1966): In vitro cell survival data for human kidney T-1 cells

Increasing LET

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LET (keV/m)1 10 100 1000

(G

y-1)

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

LET (keV/m)1 10 100 1000

(G

y-2)

0.00

0.05

0.10

0.15

0.20

0.25

2/ 2 2Fz

Predicting trends in radiosensitivity

Radiosensitivity parameters for V79 cells irradiated in vitro. Symbols: estimates of α and β reported by Furusawa et al. (2000) for He-3 (blue circles), C-12 (green triangles) and Ne-20 (red squares). Lines: RMF-predicted parameters.

Cell-specific model constants calculated based on low-LET reference parameters for 200 kVp X-rays:

21/

x F

x x

z

2

2 x

x

Frese MC, Yu VK, Stewart RD, Carlson DJ. A mechanism-based approach to predict the relative biological effectiveness of protons and carbon ions in radiation therapy. Int. J. Radiat. Oncol. Biol. Phys. 2012; 83: 442450.

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Clinically-relevant pristine Bragg peaks

Physical and biological properties of proton and carbon ion pristine Bragg peaks:


Dose & LET calculated using analytical approximations (Bortfeld 1997,Wilkens and Oelfke 2003)

DSB yields simulated with MCDS

and calculated assuming chordoma reference parameters

All calculations include Gaussian particle spectrum

S L I D E 33

Depth [cm]

0 2 4 6 8 10 12 14 16 18

Phys

ical

dos

e [G

y] /

RB

E-w

eigh

ted

dose

[Gy

(RB

E)]

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

LET d [

keV

/ m

]

0

2

4

6

8

10

12

14Physical doseRBE-weighted doseLET

RBE for cell killing in Proton SOBP

Conditions:1. Normoxic chordoma cells: x= 0.1 Gy-1, (/)x=2.0 Gy2. Proximal edge of SOBP: 10 cm3. Distal edge of SOBP: 15 cm4. Distance between Bragg peaks: 0.3 cm5. # of Bragg peaks: 17

Results:1. Entrance RBE ~1.02. RBE ranges from 1.03 to

1.34 from proximal to distal edge of the SOBP

3. Mean RBE across SOBP is ~1.11

Dose, energy, and LET calculated using analytical approximation proposed by Bortfeld (1997) and Wilkens and Oelfke (2003)

Potential for biological hot and cold spots within proton SOBP

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RBE for cell killing in Carbon Ion SOBP

Results:1. Entrance RBE ~1.32. RBE ranges from 1.8 to

5.4 from proximal to distal edge of the SOBP

3. Mean RBE across SOBP is ~2.8

Depth [cm]

0 2 4 6 8 10 12 14 16 18

Phys

ical

dos

e [G

y] /

RB

E-w

eigh

ted

dose

[Gy

(RB

E)]

0

1

2

3

4

5

6

LET d [

keV

/ m

]

0

50

100

150

200

250

300Physical doseRBE-weighted doseLET

Dose, energy, and LET calculated using analytical approximation proposed by Bortfeld (1997) and Wilkens and Oelfke (2003)

Conditions:1. Normoxic chordoma cells: x= 0.1 Gy-1, (/)x=2.0 Gy2. Proximal edge of SOBP: 10 cm3. Distal edge of SOBP: 15 cm4. Distance between Bragg peaks: 0.3 cm5. # of Bragg peaks: 17

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Dependence on tissue radiosensitivity

Physical (solid line) and RBE-weighted (RWD) dose for a representative clinical spread-out Bragg peaks in proton and carbon ion radiotherapy. Dashed, dash-dotted, and dotted lines represent RWD for chordoma, prostate, and head and neck cancer, respectively.


S L I D E 36

Physical dose optimization

Spread out Bragg peaks consisting of pristine Bragg peaks whose fluences were optimized to yield a constant RBE-weighted absorbed dose of 3 Gy (RBE) using method of Wilkens and Oelfke (2006)

RBE=1.1

Clinical objective is to deliver a uniform biological effect (RWD)


S L I D E 37

AAPM Task Group #256

• Task Group on “Proton Relative Biological Effectiveness (RBE)” formed in December 2013 by Harald Paganetti

S L I D E 38

Model assumptions and limitations

• Limitations of the LQ model– Does not explicitly capture many important biological factors, e.g., low dose

hyper-radiosensitivity, bystander effects, possibility of other biological targets (e.g., endothelial cell apoptosis in vasculature)

– High dose controversy (approximation for low dose rates and low doses, predictive up to ~10 Gy or higher?)

• Uncertainties in radiosensitivity parameters– Assumed values not meant to be interpreted as only biologically plausible

parameters (inter- and intra-patient variability in radiosensitivity)– Lack of adequate data for many tumor sites and normal tissue

• Best to practice evidence-based medicine– Clinical data is the gold standard must be skeptical of simplified models

and understand limitations– Value of models highest in absence of good data guide treatment decisions

instead of relying on trial and error

S L I D E 39

• BGRT has potential to improve outcomes through optimization based on biological objective functions instead of dose-based surrogates

– Goal to develop systematic methods to derive prescription doses that integrate patient-specific information about tumor and normal tissue radiobiology

• Biologically optimal treatments must balance gains associated with reducing tumor repopulation against potential for a loss of treatment efficacy associated with tumor hypoxia and DNA repair

– Hypoxia imaging can provide prognostic information for cancer patients undergoing radiotherapy

– Potential to overcome radioresistance identified by pre-treatment imaging by optimizing dose fractionations and distributions or drug delivery

• Biologically-motivated mechanistic models can be used for optimization in particle therapy

– Determination of RBE values for cell killing that can be practically used in proton and carbon ion radiotherapy

Conclusions

S L I D E 40

Acknowledgements

• Yale School of Medicine– Olivia Kelada, M.Sc. (University of Heidelberg/DKFZ)– Malte Frese, Ph.D. (University of Heidelberg/DKFZ)– Florian Kamp, M.Sc. (Technical University of Munich)– Roy H. Decker, M.D., Ph.D. (Radiation Oncology)– Richard E. Carson, Ph.D. (Radiology, Director of Yale PET Center)

• Stanford University– J. Martin Brown, Ph.D.– Paul J. Keall, Ph.D.

Work supported by:American Cancer Society Institutional Research Grant (IRG-58-012-52)Pilot Grant from the Yale Comprehensive Cancer Center (YCC)

– Robert D. Stewart, Ph.D. (U. of Washington)– Uwe Oelfke, Ph.D. (Institute of Cancer Research)– Jan Wilkens, Ph.D. (Technical University of Munich)

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Radiation Biology III - AMOS Onlineamos3.aapm.org/abstracts/pdf/90-25499-333462-102837.pdf · Radiation Biology III: Biological optimization of radiation therapy ... variability in