Biologically Guided Radiation Therapy (BGRT)faculty.washington.edu/trawets/rds/pdf/st07_mcgill2007...Effects of radiation quality • Use of Monte Carlo DNA damage simulations to predict

School of Health SciencesSchool of Health Scienceshttp://healthsciences.purdue.edu

Rob Stewart, Ph.D.Rob Stewart, Ph.D.Associate ProfessorDirector, Undergraduate Program in Radiological HealthSchool of Health SciencesPurdue [email protected]://rh.healthsciences.purdue.edu/faculty/rds.html

Presented at the

33rdrd annual McGill Workshop on Monte Carlo Techniques in annual McGill Workshop on Monte Carlo Techniques in Radiotherapy Delivery and Verification, May 29Radiotherapy Delivery and Verification, May 29--June 1, 2007, June 1, 2007, McGill University, Montreal, Canada.McGill University, Montreal, Canada.

Biologically GuidedRadiation Therapy (BGRT)

(Biologically Guided Extrapolation of Radiation Therapy Prescription Doses)

HSCI 540 Radiation BiologyHSCI 540 Radiation BiologyPurdue University School of Health SciencesPurdue University School of Health SciencesSlide Slide 22/31/31

AcknowledgmentsAcknowledgments

X. Allen LiX. Allen LiChief of Physics at the

Medical College of Wisconsin

Vladimir SemenenkoVladimir SemenenkoPostdoctoral Fellow at the Medical College of

Wisconsin

David J. CarlsonDavid J. CarlsonMedical Physics Resident

at Stanford

George A. SandisonGeorge A. SandisonAssociate Dean, College of Pharmacy,

Nursing and Health SciencesHead, School of Health Sciences

Professor of Medical Physics

Current Ph.D. StudentsCurrent Ph.D. StudentsJoo Han Park (Medical Physics)Brock South (Medical Physics)Yayun Hsaio (Physics)


OutlineOutline

Physical and Biological Objectives Extrapolation of prescription dose• Short review• Significance of inter- and intra-patient heterogeneity

Effects of radiation quality• Use of Monte Carlo DNA damage simulations to predict LQ

parameters and relative biological effectiveness (RBE)


Biological Objectives Biological Objectives →→ Physical ObjectivesPhysical Objectives

Eradicate the tumor• Tumor control probability (TCP)

Ensure normal tissue structures do not sustain unacceptable levels of damage• Normal tissue complication probability (NTCP)

Increase dose to the tumor (TCP Increase dose to the tumor (TCP ↑↑) ) Reduce dose to normal tissue (NTCP Reduce dose to normal tissue (NTCP ↓↓))

(reduce volume of normal tissue irradiated)

Reasons local tumor control not achievable• Cure impractical because of normal tissue toxicity• Uncertain location of tumor cells, e.g., subclinical disease or metastasis


Biologically Guided Radiotherapy (BGRT)Biologically Guided Radiotherapy (BGRT)

Exploit differential response of tumor and normal tissue structures or differences among patients• Keep TCP same (↔) and reduce NTCP (↓↓)• Keep NTCP same (↔) and increase TCP (↑↑)• Hypofractionation and accelerated hyperfractionation

Save time and labor, increase patient convenience• Reduce number of fractions without altering TCP and NTCP• If a patient misses a treatment day, should we

Add a fraction to the end of the treatment?Adjust size of remaining fractions?If the latter, what fraction size should we use? Regardless, want same TCP and NTCP

New modalities? Individualize treatment plans?• Effects of radiation quality (e.g., proton therapy)?• How can we best use information from functional imaging?

Dose and biologically motivated strategies are Dose and biologically motivated strategies are notnot mutually exclusivemutually exclusive


Poisson TCP modelPoisson TCP model

( )exp ( )TCP VS Dρ= −

cell densitycell density (< 10(< 1099 cmcm--33))

Tumor volumeTumor volume

( )VS Dρ = average number of tumor cells that survivetotal treatment dose D

TCP = probability no tumor cells surviveTCP = probability no tumor cells survive

ln( )( ) TCPS DVρ

= −

Model easily generalized to Model easily generalized to heterogeneous dose distributionsheterogeneous dose distributions

Surviving fraction after total dose Surviving fraction after total dose DD

Surviving fraction closely related to TCPSurviving fraction closely related to TCP


Linear Quadratic (LQ) Survival ModelLinear Quadratic (LQ) Survival Model

( )2( ) expS D D GD Tα β γ= − − +

Repopulation effectsRepopulation effectsOneOne--Track Track

DamageDamage

ln 2 / dTγ =Effective Effective

doubling timedoubling time

Total Total treatment treatment

timetime

InterInter--Track DamageTrack Damage

GG depends on halfdepends on half--time for subtime for sub--lethal lethal damage repair (damage repair (ττ) and the temporal ) and the temporal pattern of radiation deliverypattern of radiation delivery


Problem in a nutshellProblem in a nutshell……

Clinical OutcomesClinical Outcomes(small and noisy datasets)(small and noisy datasets) Biological ParametersBiological Parameters

(highly uncertain)(highly uncertain)

AnalysisAnalysis(with highly (with highly nonnon--linearlinear models)models)

PredictionPrediction(with highly (with highly nonnon--linearlinear models)models)

Clinical OutcomeClinical Outcome(highly uncertain)(highly uncertain)

Surgery + RTSurgery + RTChemo + RTChemo + RT

Seems hopeless, no?Seems hopeless, no?


Isoeffect Calculations (Isoeffect Calculations (““extrapolationextrapolation””))

Treatment 1Treatment 1(37 fractions, 2 Gy)(37 fractions, 2 Gy)

Treatment 2Treatment 2(10 fractions, (10 fractions, ?? Gy)Gy)Same TCP or Same TCP or SS

Variety of techniques used to perform isoeffect calculations• Biologically effective dose (BED) and Equivalent Uniform Dose (EUD)• Most, if not all, methods are related to the LQ survival model

Key Advantage:Key Advantage: isoeffect calculations are relatively insensitive to uncertainties in biological parameters


IsoIso--survival (survival (special case))

( ) ( )2( ) exp expS D D GD T Dα β γ α= − − + ≅ −

Total treatment dose Total treatment dose DD needed to achieve same needed to achieve same SS is independent of the is independent of the temporal pattern of radiation delivery (temporal pattern of radiation delivery (e.g., Brachytherapy vs IMRT))

2D GD Tα β γ>> −2D GDα β>> Slow growing tumorsSlow growing tumors

ln (biologically equivalent dose)SD BEDα

= − ≡


IsoIso--survival (survival (general formula))

( )2( ) expS D D GD Tα β γ= − − +

( )4 ln/ 1 12 ( / )

/ 41 12 ( / )

G S TD

G

G TBEDG

γα βα α β

α β γα β α

⎧ ⎫−⎪ ⎪= − + −⎨ ⎬⎪ ⎪⎩ ⎭⎧ ⎫⎪ ⎪⎛ ⎞= − + + +⎨ ⎬⎜ ⎟

⎝ ⎠⎪ ⎪⎩ ⎭

Take logarithm, apply quadratic formula Take logarithm, apply quadratic formula and rearrange termsand rearrange terms


Protraction Factor (Protraction Factor (external beam therapy))

{ }2

2 ( ) ( )exp ( )t

G dt D t dt D t t tD

λ∞

−∞ −∞

′ ′ ′= − −∫ ∫

Instantaneous absorbed dose Instantaneous absorbed dose rate (rate (e.g., Gy/he.g., Gy/h) at time ) at time tt

Absorbed dose (Gy)Absorbed dose (Gy)Probability per unit time subProbability per unit time sub--lethal lethal damage (= DSB) is rejoineddamage (= DSB) is rejoined

ln 2λτ

=Repair halfRepair half--timetime

GG is is alwaysalways between 0 (between 0 (long irradiation time) and 1 () and 1 (short irradiation times))

Dose Dose dd ((fraction size) delivered during ) delivered during time interval time interval ∆∆tt (fraction delivery time)

21 2( 1) /

ln 2 /

xG e x xx t tλ τ

−= + −≡ ∆ = ∆

1 1n

GGn n

= ≅

Series of Series of nn daily fractions daily fractions

(assumes repair complete between fractions)(assumes repair complete between fractions)


DD →→ SS for Prostate Cancerfor Prostate Cancer

JF Fowler, R Chappell, M Ritter, IJROBP 5050, 1021-1031 (2001)

αα = 0.039 Gy= 0.039 Gy--11

α/βα/β = 1.49 Gy= 1.49 Gyττ = 1.9 h= 1.9 h

TTdd ≅≅ ∞∞

JZ Wang, M Guerrero, XA Li, IJROBP 55, 194-203 (2003)

αα = 0.15 Gy= 0.15 Gy--11

α/βα/β = 3.1 Gy= 3.1 Gyττ = 0.267 h= 0.267 h

TTdd ≅≅ 42 day42 day

37 37 fxfx ×× 2 Gy2 Gy

GGnn ≅≅ 1/371/37

37 37 fxfx ×× 2 Gy2 GyGGnn ≅≅ 1/371/37

SS = 2.677 = 2.677 ×× 1010--88

SS = 1.159 = 1.159 ×× 1010--33


SS →→ DD for Prostate Cancer (37 for Prostate Cancer (37 fxfx ×× 2 Gy)2 Gy)

JF Fowler, R Chappell, M Ritter, IJROBP 5050, 1021-1031 (2001)

JZ Wang, M Guerrero, XA Li, IJROBP 55, 194-203 (2003)

( )

( )3

-1

4 ln/ 1 12 ( / )

4(1/ 37) ln1.159 101.49 Gy 1 1 74.00 Gy2(1/ 37) 0.039 Gy (1.49 Gy)

G S TD

Gγα β

α α β

−

⎧ ⎫−⎪ ⎪= − + −⎨ ⎬⎪ ⎪⎩ ⎭

⎧ ⎫×⎪ ⎪= − + − =⎨ ⎬⎪ ⎪⎩ ⎭

2 Gy per 2 Gy per fxfx

divide by 37divide by 37

( )8

-1

4(1/ 37) ln 2.677 10 50 day ln 2 / 42 day3.1 Gy 1 12(1/ 37) 0.15 Gy (3.1 Gy)

74.00 Gy

D−⎧ ⎫× − ⋅⎪ ⎪= − + −⎨ ⎬

⎪ ⎪⎩ ⎭=


IsoeffectIsoeffect Loop (Loop (DD →→ SS →→ DD))

exp 1/

GDS D Tα γα β

⎧ ⎫⎛ ⎞= − + +⎨ ⎬⎜ ⎟

⎝ ⎠⎩ ⎭

( )4 ln/ 1 12 ( / )

G S TD

Gγα β

α α β

⎧ ⎫−⎪ ⎪= − + −⎨ ⎬⎪ ⎪⎩ ⎭

IsoeffectIsoeffect ““looploop”” is exact, regardless of values used is exact, regardless of values used for for αα, , αα//ββ, , λλ (or (or τ)τ) and and γγ

DD = 74 Gy= 74 Gy

1010--88

(Wang et al.)DD = 74 Gy= 74 Gy

1010--33

(Fowler et al.)


ExtrapolationExtrapolation of prescription doseof prescription dose

( )4 ln/ 1 12 ( / )

RG S TD

Gγα β

α α β

⎧ ⎫−⎪ ⎪= − + −⎨ ⎬⎪ ⎪⎩ ⎭

HypothesisHypothesis:: treatments with same treatments with same SSRR have same clinical outcome have same clinical outcome ((SR is a surrogate for clinical outcome))

1Gn

≅

Total treatment time skipping weekendsTotal treatment time skipping weekends

Compute Compute SSRR for a reference treatment used in clinic (for a reference treatment used in clinic (e.g., 2 Gy × 37 fx))

ExtrapolateExtrapolate to alternate fractionation schedule or treatment modality by to alternate fractionation schedule or treatment modality by selecting appropriate selecting appropriate physical parametersphysical parameters for for GG and and TT

11 2int5

nT n −⎛ ⎞= − + ⎜ ⎟⎝ ⎠


EqvEqv. Prostate Treatments (. Prostate Treatments (““average patient”))

Reference treatmentReference treatment(74 Gy)(74 Gy)

Reference treatmentReference treatment(37 (37 ×× 2 Gy)2 Gy)

Dashed lineDashed line((Wang et al. 2003))

Solid lineSolid line((Fowler et al. 2001))

For 23 to 50 fractions, doses are within 3% of each other For 23 to 50 fractions, doses are within 3% of each other despitedespite almost 5 almost 5 orders of magnitude difference in orders of magnitude difference in SR (10-3 vs 10-8)

IncreasingIncreasingRiskRisk



InterInter--patient heterogeneity?patient heterogeneity?

Distribution of biological Distribution of biological parameters (parameters (αα, , αα//ββ, , ττ, , TTdd) ) among patient populationamong patient population

Distribution of clinical Distribution of clinical outcomes (outcomes (values for SR))

, exp 1( / )

i RR i i R i R

i

G DS D Tα γα β

⎧ ⎫⎛ ⎞⎪ ⎪= − + +⎨ ⎬⎜ ⎟⎪ ⎪⎝ ⎠⎩ ⎭

( ),4 ln( / ) 1 12 ( / )

i R i iii

i i i

G S TD

Gγα β

α α β

⎧ ⎫−⎪ ⎪= − + −⎨ ⎬⎪ ⎪⎩ ⎭

Use same biological parameters to compute Use same biological parameters to compute SSRR and and D, i.e., D, i.e., same outcome in same patient but not necessarily same outcome same outcome in same patient but not necessarily same outcome in different patientsin different patients

Change Change GG and and TT

Clinical response Clinical response of of iithth patientpatient

IsoIso--effective dose effective dose for for iithth patientpatient


Equivalent prostate treatments (Equivalent prostate treatments (population))

Patient population simulated by randomly sampling of Patient population simulated by randomly sampling of 95% CI associated with Fowler 95% CI associated with Fowler et al.et al. 2001 or Wang 2001 or Wang et al.et al. 2003 parameters2003 parameters

RedRed filled squares filled squares ((Wang et al. 2003))

Open circles Open circles ((Fowler et al. 2001))

Reference treatmentReference treatment(74 Gy)(74 Gy)

Reference treatmentReference treatment(37 (37 ×× 2 Gy)2 Gy)




What about intraWhat about intra--tumor heterogeneity?tumor heterogeneity?

Suppose we subSuppose we sub--divide our tumor into divide our tumor into NN regions. regions. Each region has itEach region has it’’s own s own radiosensitivityradiosensitivityparametersparameters……

Conceptually, we can subConceptually, we can sub--divide the tumor into regions that are so small that they contaidivide the tumor into regions that are so small that they contain a n a single cell, i.e., single cell, i.e., every cell in the tumor has itevery cell in the tumor has it’’s own unique biological characteristicss own unique biological characteristics

Hypothesis:Hypothesis: overall treatment effectiveness remains the same overall treatment effectiveness remains the same as long as the surviving fraction in each region is the sameas long as the surviving fraction in each region is the same

( )1 1 1

exp expN N N

i i i i i i ii i i

TCP TCP v S v Sρ ρ= = =

⎛ ⎞= = − = −⎜ ⎟

⎝ ⎠∏ ∏ ∑


What about intraWhat about intra--tumor heterogeneity?tumor heterogeneity?

Compute the dose to each region required to Compute the dose to each region required to produce the same produce the same SS as a reference treatmentas a reference treatment

, exp 1( / )

i RR i i R i R

i

G DS D Tα γα β

⎧ ⎫⎛ ⎞⎪ ⎪= − + +⎨ ⎬⎜ ⎟⎪ ⎪⎝ ⎠⎩ ⎭

( ),4 ln( / ) 1 12 ( / )

i R i iii

i i i

G S TD

Gγα β

α α β

⎧ ⎫−⎪ ⎪= − + −⎨ ⎬⎪ ⎪⎩ ⎭

Dose in region Dose in region ii to achieve same to achieve same SS as reference treatmentas reference treatment

Uniform dose Uniform dose DDRR to entire tumorto entire tumorRadiosensitivity parameters depend on regionRadiosensitivity parameters depend on region

Surviving fractionSurviving fractionin region in region i i

((reference treatment))ChangeChangeGG and and TT


Absorbed Dose (Gy)0 1 2 3 4 5 6 7 8 9 10

Frac

tion

of v

olum

e (%

)

0

10

20

30

40

50

60

70

80

90

100

110

Equivalent DVH (Equivalent DVH (intra-tumor heterogeneity) )

Tumor subTumor sub--divided into divided into 101044 regionsregions

For each region, biological For each region, biological parameters randomly parameters randomly sampled fromsampled from

αα = 0.1= 0.1--0.3 Gy0.3 Gy--11

α/βα/β = 1= 1--10 Gy10 Gyττ = 0.1= 0.1--6 h6 h

TTdd = 30= 30--365 d365 d

D D = 74 Gy= 74 Gy

Reference treatmentReference treatmentnn = 37= 37 dd = 2 Gy= 2 Gy

∆∆tt = 10 min= 10 min

Low RiskLow Risk

IntermediateIntermediateRiskRisk

High RiskHigh Risk

nn = 5= 5

nn = 15= 15

nn = 30= 30

8.03 Gy8.03 Gy3.88 Gy3.88 Gy

2.34 Gy2.34 Gy

(fraction size)(fraction size)


Summary Summary –– dose extrapolationdose extrapolation

Isoeffect calculations are a robust way to guide the selection of equivalent treatments (tumor control)• Equivalent treatments produce the same distribution of patient outcomes

(not same outcome in all patients)• Can assess sensitivity (robustness) by sampling biological parameters

from distributions• Relatively insensitive to inter-patient heterogeneity• Relatively insensitive to intra-tumor heterogeneity

Easy way to manage risks associated with extrapolationextrapolation of prescription doses• n = 37 to n = 30 (low risk)• n = 37 to n = 5 (high risk)


Effects of radiation quality?Effects of radiation quality?

exp 1( / )

L LR L L

L

G DS D Tα γα β

⎧ ⎫⎛ ⎞⎪ ⎪= − + +⎨ ⎬⎜ ⎟⎪ ⎪⎝ ⎠⎩ ⎭

( )4 ln( / ) 1 12 ( / )

H RHH

H H H

G S TD

Gγα β

α α β

⎧ ⎫−⎪ ⎪= − + −⎨ ⎬⎪ ⎪⎩ ⎭

Dose of high LET radiation to achieve same Dose of high LET radiation to achieve same SS as low LET treatmentas low LET treatment

Step 1:Step 1: Compute Compute SSRR for dose of low LET radiation (for dose of low LET radiation (e.g., IMRT with photons))

Step 2:Step 2: Compute equivalent treatment dose for higher LET radiationCompute equivalent treatment dose for higher LET radiation

Need a method to predict Need a method to predict trendstrends in in αα, , αα//ββ and and ττ as a function of as a function of radiation qualityradiation quality

NOTE:NOTE: RBE RBE ≡≡ DDLL//DDHH

Use LQ parameters for Use LQ parameters for low LETlow LET radiationradiation

Use LQ parameters for Use LQ parameters for high LEThigh LET radiation (radiation (assume γ is same for low and high LET))


DSB Induction and LQ parametersDSB Induction and LQ parameters

RepairRepair--misrepairmisrepair--fixationfixation (RMF) models predicts(RMF) models predicts2

Fzα θ κ= Σ + Σ

2 / 2β κ= Σ

2

2// 2

2

F

F

z

z

θ κα βκ

θκ

Σ + Σ=

Σ⎛ ⎞= +⎜ ⎟Σ⎝ ⎠

ΣΣ = DSB Gy= DSB Gy--11 cellcell--11

20.204FLETz

dρ=

DJ Carlson, Mechanisms of Intrinsic Radiation Sensitivity DJ Carlson, Mechanisms of Intrinsic Radiation Sensitivity –– The effects of DNA damage repair, oxygen, and The effects of DNA damage repair, oxygen, and radiation quality. Ph.D. Dissertation, Purdue University School radiation quality. Ph.D. Dissertation, Purdue University School of Health Sciences (2006). of Health Sciences (2006). Available as a PDF Available as a PDF at http://at http://rh.healthsciences.purdue.edu/student/djcarlsonrh.healthsciences.purdue.edu/student/djcarlson//

{ }/ /lim lim exp 1 exp

( / )GD GD

GDS D Dα β α β

α αα β>> >>

⎧ ⎫⎛ ⎞= − + = −⎨ ⎬⎜ ⎟

⎝ ⎠⎩ ⎭

↑↑ as LET as LET ↑↑

As expectedAs expected


Simulation of DSB inductionSimulation of DSB induction

Monte Carlo Damage Simulation (MCDS)• V.A. Semenenko and R.D. Stewart. Fast Monte Carlo simulation of DNA

damage formed by electrons and light ions. Phys. Med. Biol. 51(7), 1693-1706 (2006).

• V.A. Semenenko and R.D. Stewart. A fast Monte Carlo algorithm to simulate the spectrum of DNA damages formed by ionizing radiation. Radiat Res.161(4), 451-457 (2004).

• Software and related information available at http://http://rh.healthsciences.purdue.edu/mcdsrh.healthsciences.purdue.edu/mcds//

Nucleotide-level maps of SSB, DSB and other forms of clustered damage for electrons, protons and αparticles up to ~ 1 GeV

2Fzα θ κ= Σ + Σ

Hypothesis:Hypothesis: θθ and and κκ are independent of radiation qualityare independent of radiation quality


Human kidney THuman kidney T––1 cells irradiated 1 cells irradiated in vitroin vitro

100 101 102 103

α (G

y-1)

0.0

0.5

1.0

1.5

2.00θ =

0κ =

2Fzα θ κ≅ Σ + Σ

DJ Carlson, RD Stewart, VA Semenenko and GA Sandison, Combined use of Monte Carlo DNA damage simulations and deterministic repair models to examine putative mechanisms of cell killing. Submitted Radiation Research (2007)

LET (keV/µm)

3

5

5.93 105.24 10

θ

κ

−

−

= ×

= ×


Kinetic Energy (MeV)10-1 100 101 102 103

α/β

(Gy)

100

101

102

103


α (G

y-1)

10-2

10-1

100

101

LQ parameters for protonsLQ parameters for protons

2Fzα θ κ= Σ + Σ 2/ Fz θα β

κ⎛ ⎞= +⎜ ⎟Σ⎝ ⎠

αα = 0.039 Gy= 0.039 Gy--11

α/βα/β = 1.49 Gy= 1.49 Gy

θ = 7.66×10-4

κ = 6.26×10-4

{ }/lim exp

GDS D

α βα

>>= −

Adjusted Adjusted θθ and and κκ to match to match αα and and αα//ββreported by Fowler reported by Fowler et al.et al. (2001) (2001) –– two two equations and two unknowns (equations and two unknowns (θθ, , κκ))



RB

E

10-1

100

101

102

Predicted RBE for protonsPredicted RBE for protons

37 37 ×× 2 Gy2 Gy

5 5 ×× 8.03 Gy8.03 Gy

15 15 ×× 3.88 Gy3.88 Gy

L

H

DRBED

≡


CS

DA

Ran

ge (m

m)

10-4

10-3

10-2

10-1

100

101

102

103

104

100 cell diameters100 cell diameters


Summary Summary –– effects of radiation qualityeffects of radiation quality

May be feasible to use Monte Carlo DNA damage simulations to predict trends in LQ parameters (and hence RBE)• Additional testing of approach is needed

RBE may be lower than unity for protons with kinetic energies above ~ 10 MeV• Potential for biological cold spots?

Proton RBE may increase rapidly with decreasing kinetic energy below 20 MeV• Tail of the proton track has a real sting!• Effects a few hundred cells per proton


Biologically Guided Radiation TherapyBiologically Guided Radiation Therapy

The future is fast approachingThe future is fast approaching……

PDF of presentation available athttp://http://rh.healthsciences.purdue.edu/faculty/rds.htmlrh.healthsciences.purdue.edu/faculty/rds.html

DCEDCE--CT image of blood CT image of blood perfusion in a MCFperfusion in a MCF--77wtwt tumor tumor

((courtesy M. Cao))

Documents

Biologically Guided Radiation Therapy (BGRT)faculty.washington.edu/trawets/rds/pdf/st07_mcgill2007...Effects of radiation quality • Use of Monte Carlo DNA damage simulations to predict