Int. J. Radiation Oncology Biol. Phys., Vol. 79, No. 4, pp. 1188–1195, 2011Copyright � 2011 Elsevier Inc.

Printed in the USA. All rights reserved0360-3016/$ - see front matter

jrobp.2010.10.007

doi:10.1016/j.i

BIOLOGY CONTRIBUTION

HYPOFRACTIONATION RESULTS IN REDUCED TUMOR CELL KILL COMPARED TOCONVENTIONAL FRACTIONATION FOR TUMORS WITH REGIONS OF HYPOXIA

DAVID J. CARLSON, PH.D.,*y PAUL J. KEALL, PH.D.,* BILLY W. LOO, JR., M.D., PH.D.,*ZHE J. CHEN, PH.D.,y AND J. MARTIN BROWN, PH.D.*

*Stanford University School of Medicine, Department of Radiation Oncology, Stanford, CA; andyYale University School of Medicine, Department of Therapeutic Radiology, New Haven, CT

ReprinSchool ofHaven, C8682; E-m

Purpose: Tumor hypoxia has been observed in many human cancers and is associated with treatment failure inradiation therapy. The purpose of this study is to quantify the effect of different radiation fractionation schemeson tumor cell killing, assuming a realistic distribution of tumor oxygenation.Methods andMaterials: A probability density function for the partial pressure of oxygen in a tumor cell populationis quantified as a function of radial distance from the capillary wall. Corresponding hypoxia reduction factors forcell killing are determined. The surviving fraction of a tumor consisting of maximally resistant cells, cells at inter-mediate levels of hypoxia, and normoxic cells is calculated as a function of dose per fraction for an equivalent tu-mor biological effective dose under normoxic conditions.Results: Increasing hypoxia as a function of distance from blood vessels results in a decrease in tumor cell killingfor a typical radiotherapy fractionation scheme by a factor of 105 over a distance of 130 mm. For head-and-neckcancer and prostate cancer, the fraction of tumor clonogens killed over a full treatment course decreases by up toa factor of �103 as the dose per fraction is increased from 2 to 24 Gy and from 2 to 18 Gy, respectively.Conclusions: Hypofractionation of a radiotherapy regimen can result in a significant decrease in tumor cell killingcompared to standard fractionation as a result of tumor hypoxia. There is a potential for large errors when cal-culating alternate fractionations using formalisms that do not account for tumor hypoxia. � 2011 Elsevier Inc.

Hypoxia, Hypofractionation, Linear-quadratic model, Cell survival, Radiosensitizer.

INTRODUCTION

Tumor hypoxia has been observed in many human cancersand has been shown to correlate with treatment failure in ra-diation therapy (1). Approximately 90% of all solid tumorshave median oxygen concentrations less than the typicalvalues of 40 to 60 mmHg found in normal tissues (2). Thedecreased oxygenation of tumor cells is a result of structuraland functional disturbances of the tumor vasculature that in-hibit the normal delivery of oxygen (3). Although hypoxiahas been shown to be associated with increased metastasis(4), treatment failure in radiotherapy for tumors with highlevels of hypoxia can be attributed primarily to the decreasedsensitivity of hypoxic tumor cells to ionizing radiation (5).

The problem of hypoxic radioresistance is reducedthrough fractionation of the total radiation dose by reoxyge-nation (6). Although emerging technologies such as stereo-tactic body radiotherapy (SBRT) provide valuable physicaladvantages over conventional radiation therapy for patientswith solitary tumors (7, 8), hypoxia is expected to be

t requests to: David J. Carlson, Ph.D., Yale UniversityMedicine, Department of Therapeutic Radiology, NewT 06520-8040. Tel: (203)200-2018; Fax: (203)688-ail: david.j.carlson@yale.edu

1188

a significant mechanism of radioresistance in SBRTbecause the total radiation dose is delivered in only a fewfractions and the potential for reoxygenation betweenfractions is reduced.

The purpose of this study is to quantify the effect ofradiation fractionation on tumor cell killing, assuming a realis-tic distribution of tumor oxygenation and full reoxygenationbetween fractions. Sensitivity of the results to variations inthe radiobiologically hypoxic fraction, dose per fraction, andtumor intrinsic radiosensitivity is evaluated. The potentialgain in cell killing through administration of a hypoxic cell ra-diosensitizer is also investigated.

METHODS AND MATERIALS

Development of a cell survival formalism that accounts fora realistic distribution of tumor hypoxia and the temporalpattern of radiation deliveryThe distribution of oxygen in a tumor can be modeled using an

arrangement of straight capillaries surrounded by viable tumor cells

Supported in part by NIH grant P01 CA067166 (JMB) andAmerican Cancer Society IRG-58-012-52 (DJC).Conflict of interest: none.Received March 1, 2010, and in revised form Oct 4, 2010.

Accepted for publication Oct 8, 2010.

Effects of hypoxia in hypofractionated radiotherapy d D. J. CARLSON et al. 1189

(9). Oxygen partial pressure p(r) is expressed as a function of radialdistance r from the capillary wall (10):

pðrÞ ¼ p0R2max

R20

�2ln

Rmax

r� 1þ r2

R2max

�; (1)

where p0 is the initial oxygen partial pressure adjacent to the capil-lary wall and Rmax is the diffusion limit of oxygen in tissue. Theparameter R0 is a constant related to the rates of oxygen consump-tion and diffusion:

R20 ¼ R2

max

�2ln

Rmax

a� 1

�; (2)

where the radius of the capillary a is assumed to be 10 mm.As p(r) decreases in a cell, the quantity of lethal radiation-

induced damage formed through one- and two-track processes isdecreased by a constant and by the square of this constant, respec-tively. Carlson et al. (11) have shown that a single factor can be usedto modify intrinsic radiosensitivity in the linear-quadratic (LQ)model. The fraction of cells at radial distance r from the capillarywall that survive a single fraction of radiation dose dmay bewrittenas:

SðdÞ ¼ exp�� ½aA=HRFðpÞ�d � �

bAGðl; tÞ=HRFðpÞ2�d2�; (3)

where aA and bA are aerobic radiosensitivity parameters. For low-linear energy transfer (LET) radiation, a represents the quantity oflethally misrepaired and unrepaired double-strand breaks (DSBs),and b represents the quantity of lethal exchange-type chromosomeaberrations formed through binary misrepair of two separateDSBs (12). The Lea-Catcheside dose protraction factor G(l,t) isdependent on the duration of a single fraction t and the rate ofDSB repair lhlnð2Þ=t, where t is the DSB repair half-time(13). A hypoxia reduction factor (HRF) is introduced to quantifyreductions in known radiosensitivity parameters aA and bA as theoxygen partial pressure in a tumor cell decreases. The HRF is de-fined as the ratio of the dose at a specific level of hypoxia to thedose under fully aerobic conditions to achieve equal cell killingand is predicted by

HRFðpÞ ¼ mK þ pðrÞK þ pðrÞ ; (4)

where m is the maximum HRF and K is the oxygen partial pressureat which the HRF is half the maximum value.In a tumor cell population, the fraction of cells at radial distance r

per radial distance from the capillary center is

f ðrÞ ¼ 2pr=

ðRhyp

a

2prdr; (5)

where Rhyp is the diffusion distance at which cells become maxi-mally resistant. The surviving fraction of cells characterized by ra-dial oxygen diffusion Sdiff can be expressed as

Sdiff ¼ðRhyp

a

f ðrÞSðrÞdr; (6)

where S(r) is calculated using Eq. 3. The percentage of cells thatsurvive a single fraction of radiation in a population of maximallyresistant tumor cells (i.e., the hypoxic fraction fhyp) and tumor cellsat intermediate and full oxygen levels ½1� fhyp� is

Sfraction ¼ fhypShyp þ�1� fhyp

�Sdiff ; (7)

where Shyp is the surviving fraction of maximally resistant cells pre-dicted by Eq. 3 using the maximum HRF. The total surviving frac-tion of tumor cells for a treatment of n fractions is

Stotal ¼�Sfraction

�n�fhypexp

�ghypðT � TkÞ

�þ �

1� fhyp�exp

�gdiff ðT � TkÞ

��; ð8Þ

where ghlnð2Þ=Td is the rate of cellular proliferation, Td is the celldoubling time, T is total treatment duration, and Tk is the onset orlag-time to cellular proliferation. The formulation above implicitlyassumes that full reoxygenation occurs between fractions becausethe total population of cells returns to the initial oxygen distributionafter each fraction. Several clinical studies (14) have observeda general increase in tumor oxygenation during conventional ther-apy. Such increases work in favor of conventional fractionation andare not relevant to SBRT with a single or a few large doses.

Coadministration of a hypoxic cell radiosensitizerThe radiosensitizing effect of misonidazole has been shown to be

dependent on the administered drug concentration and the oxygenpartial pressure of the cell population (15). A sensitizer enhance-ment ratio (SER) is introduced that is dependent on drug concentra-tion c and p(r), so that the surviving fraction of cells for a singlefraction becomes

SðdÞ ¼ exp�� ½aA,SERðc; pÞ=HRFðpÞ�d

��bAGðl; tÞ,SERðc; pÞ2=HRFðpÞ2

�d2�: (9)

The SER separates the radiosensitizing effects of misonidazole andoxygen and is defined as the quotient of the drug enhancement ratioand the oxygen enhancement ratio (OER) at a known oxygen partialpressure. The SER is predicted by

SERðpÞ ¼ xyþ pðrÞyþ pðrÞ ; (10)

where x is the maximum SER and y is the oxygen partial pressure atwhich the SER is equal to half of the maximum value.

Selection of tumor sites and studies performedClinical data demonstrating a presence of tumor hypoxia in head-

and-neck cancer (HNC) (16) and prostate cancer (17) make thesetumor sites ideal for this study. The surviving fraction of tumor clo-nogens is simulated as a function of distance from the blood vesselbased on radiosensitivity parameters derived from clinical data andHRF values derived from in vitro data. The surviving fraction isestimated for an entire radiotherapy course as a function of totalnumber of fractions. Corresponding doses per fraction are calcu-lated to achieve an equivalent tumor biological effective dose(BED) using the standard LQ model without corrections for tumorhypoxia, intrafraction DSB repair, or clonogen repopulation. Aconventional HNC treatment of 30 fractions of 2.2 Gy yieldsa BED of 80.5 Gy for a radiosensitivity of aA = 0.25 Gy-1 and(a/b)A = 10 Gy (18, 19). A conventional prostate cancertreatment of 39 fractions of 2.0 Gy yields a BED of 130 Gy fora radiosensitivity of aA = 0.15 Gy-1 and (a/b)A = 3.0 Gy (20, 21).Assumed time-dependent parameters for HNC (thyp = 1.0 h, tdiff= 5.0 h, Tk = 21 days, Tdhyp ¼ 6 days, Tddiff ¼ 3 days) and prostatecancer (thyp = 0.5 h, tdiff = 2.5 h, Tk = 60 days, Tdhyp ¼ 84 days,Tddiff ¼ 42 days) were based on the best available data in the liter-ature (20, 22–24). All simulations were performed in FORTRAN95.

erusserPlaitraPnegyxO p )gHmm(

00010.0010.010.101.010.0

Hyp

oxia

Red

ucti

on F

acto

r (H

RF

)

5.0

0.1

5.1

0.2

5.2

0.3

5.3

Fig. 2. Hypoxia reduction factor (HRF) values derived from pub-lished cell survival data. The solid line shows a fit to the values us-ing Eq. 4 with m = 2.8 and K = 1.5.

1190 I. J. Radiation Oncology d Biology d Physics Volume 79, Number 4, 2011

RESULTS

Figure 1 shows oxygen partial pressure as a function of ra-dial distance from the center of a capillary as predicted byEq. 1. The solid line represents the assumed oxygen diffu-sion parameters (p0 = 60 mmHg, Rmax = 150 mm) that aremost consistent with those expected in human tumors (25).This set of parameters results in an average oxygen partialpressure of 6.9 mmHg, assuming that 20% of the tumor cellsare maximally resistant (p < 0.5 mmHg) and 80% of the tu-mor cells are either well-oxygenated (p > 20 mmHg) or atintermediate oxygen levels (p = 0.5–20 mmHg). The valueof p = 6.9 mmHg is consistent with typical median oxygenpartial pressures of 3 to 5 mmHg and 10 to 15 mmHg re-ported for prostate cancers (17) and HNC (16), respectively.

Figure 2 shows the expected decrease in cellular radiosen-sitivity as a function of oxygen partial pressure. HRF valuesderived from data reported by Ling et al. (15), Koch et al.(26), Whillans and Hunt (27), and Carlson et al. (11) are de-noted by white triangles, black circles, white circles, andgray circles, respectively. Reported OER values (15, 26,27) were transformed into HRF values by dividing themaximum OER by the OER for each level of oxygenation.The HRF is at its maximum for anoxic conditions witha value of 2.8 and decreases to unity as the cells approachnormoxic conditions. The dotted line shows the oxygenpartial pressure (p = 0.5 mmHg) below which cells areassumed to be maximally resistant (i.e., radiobiologicallyhypoxic) (9). Eq. 4 with best fit parameters m = 2.8 andK = 1.5 was used to convert the probability density functionof the partial pressure of oxygen into a continuous distribu-tion of HRF values.

Figure 3 shows surviving fraction of tumor clonogens asa function of radial distance from the capillary center forconventional HNC and prostate cancer treatments. Predic-tions are calculated using Eq. 3, neglecting intrafractionDSB repair (G = 1), and the total number of fractions,

morfecnatsidlaidaR (retnecyrallipac )

0120910710510310110907050301

p(r)

(m

mH

g)

0

01

02

03

04

05

06

07

08

09

001

011

021

p0 ,gHmm03= R xam 311= µm

µm

µm

µm

p0 ,gHmm06= R xam 051=

p0 ,gHmm021= R xam 002=

Fig. 1. Oxygen partial pressure as a function of radial distancefrom the center of a capillary. The solid line represents the assumedoxygen diffusion parameters that result in an average oxygen partialpressure of �6.9 mmHg.

i.e., S(d)n. Our simulations predict that tumor cell killing de-creases by a factor of�105 over a radial distance of 130 mm,assuming an oxygen partial pressure of 60 mmHg at the cap-illary wall. The surviving fraction increases from 4.7� 10�9

to 4.1 � 10�4 for HNC and from 1.0 � 10�8 to 1.5 � 10�3

for prostate cancer. This predicted trend is consistent withexperimental data from mouse tumors that show a loss in ra-diosensitivity with distance from blood vessels (28).

Figure 4 shows surviving fraction of HNC and prostate tu-mor clonogens for an entire course of radiotherapy as a func-tion of number of fractions, neglecting intrafraction DSBrepair (G = 1) and clonogen repopulation (g = 0). The equiv-alence of each fractionation schedule is demonstrated by theisoeffect achieved under normoxic conditions (i.e., HRF= 1).Solid symbols show model predictions for hypoxic fractionsof 10%, 20%, and 30%. Tumor hypoxia increases cell sur-vival by a factor of�103 for conventionally fractioned radio-therapy as shown in earlier modeling studies (9). Tumor cellsurvival increases by additional factors of �6 � 102 and �4� 102 as the dose per fraction is increased from 1.7 Gy (n =40) to 24 Gy (n = 1) and from 2.0 Gy (n = 40) to 18 Gy (n = 1)forHNCand prostate cancer, respectively. Figure 5 shows theindividual and combined effects of tumor hypoxia, tumor cellrepopulation, and intrafraction DSB repair on total survivingfraction. Clonogen repopulation is most significant for hy-perfractionated HNC and strongly depends on the assumedlag time. For Tk = 21 days, cell killing decreases by a factorof �6 � 102 as the dose per fraction is decreased from 3.7to 1.7 Gy. For single-fraction treatments, cell killing maybe overpredicted by up to a factor of 24 if intrafractionDSB repair is neglected.

Figure 6 shows the distribution of SER values for the hyp-oxic cell radiosensitizer misonidazole derived from pub-lished in vitro data (15). White triangles and gray circlesrepresent estimates for misonidazole concentrations of 1.2mM and 5.0 mM, respectively. The SER is maximum for an-oxic conditions with values of 1.4 and 2.0 for concentrationsof 1.2 mM and 5.0 mM, respectively, and decreases to unity

(retnecyrallipacmorfecnatsidlaidaR μ )m

0910710510310110907050301

Surv

ivin

g Fr

actio

n

01 01-

01 9-

01 8-

01 7-

01 6-

01 5-

01 4-

01 3-

01 2-

01 1-

01 0

091071051031011090705030101 01-

01 9-

01 8-

01 7-

01 6-

01 5-

01 4-

01 3-

01 2-

01 1-

01 0

sllecdetanegyxoylluF sllecdetanegyxoylluF

recnaCkceNdnadaeH(α /β α /β,yG01= d ,yG2.2= n )03=

recnaCetatsorP( ,yG0.3= d ,yG0.2= n )93=

p 0= 30 mmHg

p 0= 60 mmHg

p 0= 120 mmHg

p 0= 30 mmHg

p 0= 60 mmHg

p 0= 120 mmHg

Fig. 3. Surviving fraction of tumor clonogens as a function of radial distance from the capillary center for conventionalradiotherapy fractionations.

Effects of hypoxia in hypofractionated radiotherapy d D. J. CARLSON et al. 1191

as the cells approach normoxic conditions. Figure 7 showsthe surviving fraction of tumor clonogens for different com-binations of misonidazole and radiation. Values are shownfor the characteristic one to five fractions of SBRT treat-ments. The addition of a hypoxic cell radiosensitizer athigh doses per fraction is shown to be a potential strategyto obtain similar or greater levels of cell killing thanachieved with conventional fractionation. Misonidazolehas a greater sensitizing effect for large doses per fractionbecause of the increased importance of the hypoxic fractionof cells.

DISCUSSION

In this article, we have determined the magnitude of cellkilling lost as a result of tumor hypoxia during hypofractio-nated radiotherapy. To examine this problem, we developeda model that accounts for variations in the distribution of tu-mor hypoxia, tumor intrinsic radiosensitivity, and changes inradiation dose fractionation. Wouters and Brown (9) havepreviously shown that cells at intermediate oxygen levelsare responsible for determining tumor response in conven-tionally fractionated radiotherapy. We have extended theirwork to examine changes in dose fractionation. Our model

rebmuN

045303520251015

Surv

ivin

g Fr

actio

n

01 9-

01 8-

01 7-

01 6-

01 5-

01 4-

01 3-

01 2-

01 1-

01 0

f pyh 1.0 =

f pyh 2.0 =

f pyh 3.0 =

sllec detanegyxo ylluF

recnaC kceN dna daeH( )yG 01 =

aviuqe dleiy ot )yG( noitcarf rep esoD el

7.13.5 1.39.36.8 2.26.2 9.18.32

1

α /β

Fig. 4. Total surviving fraction of tumor clonogens as a functifull reoxygenation between fractions. Dependence of model prcells is shown. BED = biological effective dose.

predicts a loss of up to three logs of cell kill as the doseper fraction is increased from a conventional size (e.g.,2.0�2.2 Gy) to a large single-fraction dose (e.g.,18.3�23.8 Gy). The observed decrease in cell killing withincreasing dose per fraction is attributed to (1) changes inthe effective radiosensitivity (a/b) of tumors with heteroge-neous oxygenation, (2) a reduction in interfraction reoxyge-nation, and (3) an increased importance of maximallyresistant cells (i.e., the hypoxic fraction) in determiningoverall dose response as the total dose is delivered in fewerfractions. This result demonstrates a potential for large er-rors when calculating alternate fractionations using BEDformalisms that do not explicitly account for tumor hypoxia.

Oxygen diffusion vs. a binary hypoxia modelAuthors of previous modeling studies (11, 29) assumed

a binary hypoxia distribution in which cells are eitheranoxic or normoxic. The effect of hypoxia is then modeledusing one or two constant factors that effectively decreaseintrinsic radiosensitivity. Several groups (29) have assumedthat the observed reduction in radiosensitivity due to hyp-oxia is dose range dependent, e.g., aA and bA are scaled bystatistically independent factors HRFa and (HRFb)

2,

snoitcarf fo

04530352025101501 9-

01 8-

01 7-

01 6-

01 5-

01 4-

01 3-

01 2-

01 1-

01 0

f pyh 1.0 =

f pyh 2.0 =

f pyh 3.0 =

sllec detanegyxo ylluF

recnaC etatsorP( )yG 0.3 =

snoitidnoc cixomron rednu DEB romut tn

0.22.24.27.22.38.39.45.73.81

1

α /β

on of dose per fraction, assuming daily fractionation andedictions on the assumed value of the hypoxic fraction of

snoitcarfforebmuN

045303520251015

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ivin

g Fr

actio

n

01 9-

01 8-

01 7-

01 6-

01 5-

01 4-

01 3-

01 2-

01 1-

01 0

snoitcerrocoNriaperANDnoitcarfartnI

aixopyhromuTnoitalupopeR

stceffellafonoitanibmoC

7.11.39.33.5 6.26.8 2.2 9.18.32

1

(recnaCkceNdnadaeH )yG01=

04530352025101501 9-

01 8-

01 7-

01 6-

01 5-

01 4-

01 3-

01 2-

01 1-

01 0

snoitcerrocoNriaperANDnoitcarfartnI

aixopyhromuTnoitalupopeR

stceffellafonoitanibmoC

0.29.4 2.38.35.7 4.27.2 2.23.81

1

(recnaCetatsorP )yG0.3=

viuqedleiyot)yG(noitcarfrepesoD ednuDEBromuttnela snoitidnoccixomronr

α /β α /β

Fig. 5. Total surviving fraction of tumor clonogens as a function of dose per fraction, assuming daily fractionation andfull reoxygenation between fractions. Dependence of model predictions on intrafraction double-strand break repair andclonogen repopulation is shown. BED = biological effective dose.

1192 I. J. Radiation Oncology d Biology d Physics Volume 79, Number 4, 2011

respectively. Carlson et al. (11) proposed that mechanisticconsiderations support that HRFa y HRFb and found thata single factor was able to provide as good a statistical fitto several in vitro data sets as independent factors. This as-sumption is especially convenient when attempting to esti-mate radiosensitivity parameters and HRF factors fromsparse clinical data.

Wouters and Brown (9) first quantified differences in cellsurvival based on a radial oxygen diffusion model and a con-ventional binary model. They concluded that it is essential tocharacterize the oxygenation status of tumors in a realisticway (i.e., a dose–response model for hypoxic tumors mustinclude cells at intermediate oxygen levels). If a binarymodel were used in this study, estimates of cell killing wouldchange by more than two orders of magnitude for conven-tionally fractionated treatments. As illustrated in Fig. 4,a conventional prostate treatment of 39 fractions results ina surviving fraction of 2.8 � 10�5 using a model based onradial oxygen diffusion (fhyp = 0.2). A binary model predicts

erusserP laitraP negyxO p )gHmm(

00010.0010.010.101.010.0

Sens

itiz

er E

nhan

cem

ent R

atio

(SE

R)

8.0

0.1

2.1

4.1

6.1

8.1

0.2

2.2elozadinosim Mm 2.1

elozadinosim Mm 5

5000.0<

Fig. 6. Sensitizer enhancements ratio (SER) values derived frompublished cell survival data (15). Solid lines shows a fit to the valuesusing Eq. 10 with x = 1.4 and y = 0.4 for the 1.2 mM concentrationand x = 2.0 and y = 0.9 for the 5.0 mM concentration.

a surviving fraction of 9.2� 10�8 under the same conditions.Diffusion and binary models result in similar predictions fora single fraction of 18.3 Gy (9.7 � 10�3and 8.5 � 10�3,respectively) because overall response is dominated by thehypoxic fraction of the tumor cell population. A binary hyp-oxia model would therefore overpredict the decrease in tu-mor cell killing expected in hypofractionated radiotherapyas a result of tumor hypoxia.

Strategies to overcome tumor hypoxiaMany strategies have been proposed to overcome and

even exploit tumor hypoxia (3, 30). Hypoxia-activatedprodrugs have been developed to specifically targetradiation-resistant hypoxic cells. Other strategies includehypoxia-selective gene therapy, the use of recombinant obli-gate anaerobic bacteria, and targeting hypoxia-induciblefactor 1 (HIF-1). Ling et al. (31) developed the concept ofhypoxia dose boosting by proposing a biological tumor vol-ume that could be given additional radiation dose intended toovercome hypoxic radioresistance. Many technical difficul-ties exist with this strategy, including recent evidence thatthe distribution of hypoxia can change significantly through-out the treatment for certain patients (32). By contrast, theuse of hypoxic cell radiosensitizers is simpler because theyhave no problems in diffusion to the most hypoxic cellsand effectively sensitize all hypoxic cells, both chronicand acute, to radiation (33). Despite the complexities in-volved with current imaging technology, hypoxia imagingwill be necessary to categorize patients into subpopulationsand determine who will benefit the most and least from strat-egies aimed at overcoming tumor hypoxia.

The model presented in this work will aid in the temporaloptimization of radiation delivery by establishing when theeffects of hypoxia on cell survival are most severe. Our re-sults suggest that tumor hypoxia has the largest negative ef-fect on cell survival below�10 fractions and that treatmentswith n > 10 may be most effective. Alternatively, coadmin-istration of a hypoxic cell radiosensitizer can increase theeffectiveness of hypofractionated radiotherapy to achieve

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01 2-

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01 0

elozadinosimoNelozadinosimMm2.1elozadinosimMm0.5

04530352025101501 9-

01 8-

01 7-

01 6-

01 5-

01 4-

01 3-

01 2-

01 1-

01 0

elozadinosimoNelozadinosimMm2.1elozadinosimMm0.5

sllecdetanegyxoylluF sllecdetanegyxoylluF

aviuqedleiyot)yG(noitcarfrepesoD snoitidnoccixomronrednuDEBromuttnel

0.22.24.27.22.38.39.45.73.817.13.5 1.39.36.8 2.26.2 9.18.32

1 1

HNC( ,yG01= f pyh )2.0=

recnaCetatsorP( ,yG0.3= f pyh )2.0=α /β α /β

Fig. 7. Effect of misonidazole and radiation on surviving fraction of tumor clonogens, assuming a realistic distribution oftumor hypoxia, intrafraction double-strand break repair, and clonogen repopulation. Dotted lines show predictions ne-glecting corrections for hypoxia, repair, and repopulation. BED = biological effective dose; HNC = head and neck cancer.

Effects of hypoxia in hypofractionated radiotherapy d D. J. CARLSON et al. 1193

the same or greater level of cell killing as that obtained byconventional regimens. Hypoxic cell radiosensitizers aremost effective when delivered with a single dose or a fewlarge doses of radiation. An etanidazole concentration of12 g/m2 (tumor concentration of �5 mM) combined witha fraction of 15 to 24 Gy has been shown to be well tolerated(34). The 5.0-mM data in Fig. 7 are included only to be illus-trative because such a large concentration of misonidazolecould be tolerated only once at most. Tepper et al. (35) foundno benefit in overall survival using a misonidazole dosage of3.5 g/m2 in conjunction with an intraoperative radiation ther-apy (IORT) dose of 15 to 20 Gy to the pancreas. These mi-sonidazole dosages provided five- to ten-fold lowersensitizer concentrations than those achieved with an etani-dazole dosage of 12 g/m2 (36). The coadministration ofa hypoxic cell radiosensitizer during SBRT may helpachieve the maximum therapeutic gain for hypoxic tumors.

Model assumptions and limitationsAerobic radiosensitivity parameters for HNC and prostate

cancer are chosen based on a range of reported estimates andrecommendations of American Association of Physicists inMedicine (AAPM) Task Group 137 (18–21). These valuesare not meant to be interpreted as the only biologicallyplausible parameters as it is widely known that there isinter-patient and intra-patient variability in radiosensitivity.For example, reported mean estimates of a for HNC havebeen shown to range from 0.12 to 0.38 Gy�1 (18). Reportedpoint estimates of a/b for prostate cancer range from 0.5 to8.3 Gy and 1.1 to 8.4 Gy for in vivo and in vitro data, respec-tively (20, 37). If we assume a = 0.04 Gy-1 and a/b = 1.5 Gyfor prostate cancer (38), cell survival increases by a factor of4.6 as the dose per fraction is increased from 2.0 Gy (n = 40)to 15.6 Gy (n = 1). This reduction in cell killing is smallerthan observed in Fig. 4 because of the atypically low a valueand not as a result of the lower a/b value. A recent clinicaltrial (39) found an insignificant trend favoring a hyperfractio-

nated arm compared to the standard fractionation for thetreatment of prostate cancer. Although these results may im-ply a higher a/b for prostate cancer or the potential influenceof incomplete repair between fractions, an additional intrigu-ing possibility is that the hyperfractionated arm may beslightly advantageous in the presence of tumor hypoxia.

A common view exists that cells in the hypoxic regions oftumors do not proliferate. Recent data (40) suggest that signif-icant proliferation can exist in hypoxic regions. Assumed tu-mor cell doubling times span the range of reported clinicalestimates (22–24) and are consistent with data suggestingthat cell proliferation may be decreased under hypoxicconditions, on average, by a factor of�2 (40). A common as-sumption made in modeling studies is that intrafraction DSBrepair is negligible in high-dose-rate radiotherapy. However,as the total dose is increased, intrafraction DSB repair be-comes more significant (20). Explicit inclusion of intrafrac-tion DSB repair is shown to further reduce the level of cellkilling predicted at high dose. Assumed DSB repair rates areconsistent with tumor-specific data (20) and evidence thatDSB repair rates may increase under hypoxic conditions (41).

Many investigators question the applicability of the LQmodel at high doses (42, 43). Although more sophisticatedkinetic reaction rate models (44, 45) may provide a betterfit to experimental data at larger doses, the LQ is only anapproximation, and predictions begin to deviate above � 5Gy (13). Guerrero and Li (42) have shown that the LQ canpredict experimental survival data well up to �10 Gy. Bren-ner (46) suggests that the LQ model is appropriate for dosesup to�15 to 18 Gy if used correctly. The LQ is likely appro-priate for use in analyzing hypoxic cell survival data up to aneven higher dose range because hypoxia essentially scalesthe survival curve along the dose axis by a factor of theHRF.

One final aspect of the use of large dose fractions is thepossibility that tumor cell killing might be enhanced by rapidendothelial cell apoptosis in tumor vessels. Garcia-Barroset al. (47) have reported that vascular endothelial cell

1194 I. J. Radiation Oncology d Biology d Physics Volume 79, Number 4, 2011

apoptosis occurs at doses greater than�8 to 10 Gy. Recentlypublished clinical data showing a high rate of short-term lo-cal control for patients with metastatic spinal cord tumorstreated with large single doses have been attributed to thisphenomenon (8). However, although this is an intriguingpossibility, there is a need for more data both preclinicaland clinical before it can be an accepted mechanism forthe effect of high dose fractions (48).

CONCLUSIONS

Tumor hypoxia has a large negative effect on tumor cellkilling even with conventional fractionation assuming fullreoxygenation between fractions. The modeling studiespresented in this work also suggest that hypofractionation

of a radiotherapy regimen will result in a significant de-crease in tumor cell killing compared to standard fraction-ation as a result of tumor hypoxia. Corrections for tumorcell repopulation are shown to increase the effectivenessof hypofractionated treatments compared to conventionaltreatments for rapidly proliferating cancers. Biologicallyoptimal fractionation schedules must balance the treatmentgains associated with reducing tumor repopulation againstthe potential for a loss of treatment efficacy associatedwith tumor hypoxia and intrafraction DSB repair. There ispotential for the introduction of large errors into calcula-tions of alternative dose fractionations when using modelsthat do not account for tumor hypoxia, cellular prolifera-tion, and DSB repair.

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