Renate

Muller-Runkel,

PhD

#{149} Srinivasan

Vijayakumar,

Equivalent Total Doses Fractionation Schemes, on the Linear Quadratic A majority of patients receiving radical radiation therapy are treated with 1.8-2.0-Gy fractions, a dose that has evolved from clinical expenience. However, other fractionation schemes can be advantageous. When fractionation is altered, the total dose prescribed should lead to equivalent or higher tumor control with the same or less tissue toxicity. To facilitate the use of different fractionation schemes, the authors compiled tables for equivalent biologic doses for late toxicity in normal tissues and tumoricidal doses for epithelial tumors, for various fraction sizes. The linear quadratic model according to Fowler was used. It is shown how these tables should be modified for prolif eration of tumors during the course of radiation therapy. The tables make the use of different fractionation schemes easy. They also allow adjustment of total dose if fractionation needs to be changed during the course of treatment. Index

terms:

sure

Dosimetry

to patients

time-dose

and

studies

#{149} Radiations,

personnel a

Radiobiology.

a

Therapeutic

expo-

radiology,

physics

Radiology

i

1991;

From

Hospital

the

Oncology

and

Health

Aye,

Hammond,

Center

for

Hospital, the

1990

December 8, 1991;

179:573-577

Center,

4, 1990;

revision reprint

From

DMRT

for Different Based Model’

a majority of patients receiving radical (curative) radiation therapy are treated with i .82.0-Gy fractions 5 days a week. This fractionation has evolved from empirical clinical experience. However, this “straitjacket” approach of treating all tumors arising from all sites in the same way may not be optimal in achieving the highest tumor control with the least toxicity. Tumor kinetics differ not only among tumors of different histopathobogic type but also among different tumors of the same histopathologic type. In fact, there can be differences within a given tumor as well as at different time points during a course (ie, weeks) of radiation therapy. Recent clinical evidence has shown that tumor control can be improved with accelerated/hyperfractionated radiation therapy (1-3). However, the optimal doses to achieve the maximum tumor control with acceptable late toxicity are not known. One needs some guidelines in designing clinical trials when fractionation schemes are altered. In addition, during a course of radiation therapy, clinicians are often faced with unplanned interruptions in the treatment (eg, due to intercurrent disease) or a need to change the fractionation and total dose (eg, for a tumor that grows during radiation therapy). Such need to compare different fractionation schemes has led to the development of time dose fractionation formulas and nominal standard dose factors (4,5). However, the consensus is that nominal standard dose tables are useful only for skin and subcutaneous tolerance and are not applicable to tumors or other normal tissues. More recently, the linear quadratic model has been found useful in explaining some of the clinical observaURRENTLY,

tions in the tions” clinic The provide compare schemes doses model; guide plify cobs.

and is being used increasingly application of “bench observain radiation biology in the (6-8). purpose of this article is to tables and schematics to different fractionation for generally used total with use of the linear quadratic such tables can serve as a for the busy clinician and simthe planning of research proto-

MATERIALS Linear Survival The

Quadratic

linear

cell survival ponential

s/so

AND

=

where

METHODS

Model

quadratic after function:

of Cell

model

describes

irradiation

exp [-(aD

+ f3D2)

S/So

fraction

is the

with

+ ‘y(T

an

Tk)],

-

by

aD. Damage

suitable is given indicates

conditions, by $D2. the dose

is reflected

repairable under the other hand, The cs/fl ratio

(1)

of surviving

cells after exposure to a single dose f3, and ‘y are tissue-specific parameters scribing the radiosensitivity. Irreparable damage

ex-

D; a, dethat

is

on at

which the linear and quadratic components of cell kill are equal. Ratios for lateresponding tissues are lower than for acutely responding tissues and tumors, reflecting the earlier bend in their dose response The rects ment

curve. second

term

mor proliferation the start of radiation mous neck,

cell this

at about

The versely bling

-V =

in

the

for tumor proliferation time T. It appears sets

carcinomas enhanced 3-4

weeks

exponent that

cor-

during enhanced

treattu-

in at a time Tk after treatment. For squaof the head proliferation

and occurs

(9).

tissue-specific

parameter

proportional to the time T,, of clonogenic ln2/T,,.

‘y is

potential tumor

in-

doucells:

Received

requested January

the Reese

(S.V.).

assembly.

received

January 21. Address ( RSNA, 1991

and

Michael

of Chicago scientific

Hohman

(R.M.R.)

Therapy.

University

revision

5454

IN 46320

Radiation RSNA

St Margaret

Centers,

C

MBBS,

January 18; accepted

requests

to R.M.R.

Abbreviations:

BED

biologically

effective

dose,

RE

relative

effectiveness.

573

Figures

1, 2. (1) Maximization of therapeutic gain with respect to treatment duration. (Adapted from reference 10.) TCD tumor control dose, FX fraction. (2) Multiplication factor (RE0/RE) for equivalent total doses for various fractionation schemes (see Eq [5]).

i.e

100 Maxbnwn

Toisratad

Acuta

wd

Gansik

Doa

1.4

ConaacisrdI

/

Lata

Lata

Tian

TD

50

..A3 0.8

Fx 72 Gy at 1.8 Gy/d

-

0.8

Linear Time

Quadratic Factor

For

late-responding

eration

is slow

large

and

time

factor,

can

Model

be

tissues,

or absent;

consequently

neglected

cell

is almost when

Accalratad

prolif-

i:

,,,,.....

0

1

that is, T,, is is small. The

‘‘

therefore,

0.4

without

late

one

2

Fx 0.2

3

4

5

6

7

of Treatment

DLfation

8

9

10

1

2

(wks)

3

4

5

Dose/fraction

6

7

8

(Gy)

2.

and

effects

are

considered.

For

fractionated

n fractions

radiation

at dosage

tal dose tion-without

nd

therapy

d per

D, the time

with

fraction

to a to-

cell survival factor-takes

functhe

form

s/so

exp[-nd(a

=

Following

+ /3d)].

Fowler’s

E

exponent

approach

D(cr

=

(2)

+ fid)

(8),

can

be

the

written

as

follows:

BED E/cr

has

the

D[1 +

E/cr

=

dimension

d/(a//3)].

(3)

of a dose

and

can

be interpreted as the biologically effective dose (BED). It is the product of the tal dose D and the relative effectiveness (RE): RE = 1 + d/(cs/f3). Two treatment schedules

that

ferent dose fractionations in their effect on a tissue,

terized

by

D1[1 +

if their

It is easily

seen

fraction

that

require

equivalent

BEDs

D,[1 +

=

are

equal:

(4)

d2/(a/f3)].

smaller

a higher

tissue

dif-

are equivalent which is charac-

a/a,

d1/(a//3)]

use

to-

dosages total

dose

per for

tion.

effects.

These

clinical

data

need

to be

gathered

from

experience.

can

be calculated

tion

(5)

tions:

Linear Time In

Quadratic Factor the

therapy,

with

of patients external

clonogenic

receiving beam radiacell

proliferation

during the course of treatment cern. Further prolonging the schedule will require a higher to compensate Shorter hand,

for

treatment are more

trol but tions. Peters

also

optimal

is a contreatment total dose

proliferation.

schedules, effective for

cause

more

et al (10)

ing approach peutic gain ment time:

tumor

on the other tumor con-

severe

suggested

time

acute the

for optimizing with respect As illustrated

treatment

6-

reac-

follow-

the therato overall treatin Figure 1, the is that

for

which

“both acute and late reactions are dose limiting, in other words, when the maximum dose that can be tolerated by late reacting tissues is given in the shortest time that permits its tolerance by acutely reacting

tissues.”

ment

time,

monicidal earlyand

To

doses and late-reacting

as a function

574

a

select

knowledge

Radiology

of overall

such

optimal

is required tolerance tissues treatment

treatof tu-

doses for involved dura-

Equivalent Different without

Total Doses Fractionation Time Factor

We refer to a Gy fractions as D0 denotes the standard scheme. tab dose D for a scheme is given

for Schemes

that

the and

scheme that uses 2.0the standard scheme; total dose used in the The equivalent tonew fractionation by the equation

DD0(a/f3+2)/(ct/f3+d) =

D0(RE0/RE),

(a)

if only

known tissues

where d is the dosage per fraction in the new scheme. The factor by which D0 is multiplied is the ratio of the RE of the standard and the new fractionation scheme. This ratio is listed in Table 1 for various fractionation schemes and a range of a/j9 ratios. Tumor proliferation during weeks of radiation treatment has been neglected so far. Total equivalent doses for different fractionation schemes

treatment the time

the

con-

same

as

(c) if time is shorter than Tk of enhanced tumor cell

standard

and

for

are

treatment

scheme,

(d)

cbonogenic

if the tumor

doubling cells

is

barge and tumor proliferation during the course of treatment need not be a concern. Figure 2 shows the ratio of RE as a function of dosage per fraction. This figure

(5)

the

to Equacondi-

effects

overall

is approximately for

proliferation, time

according following late

(b) if the

sidened,

RESULTS

time

majority of radical

7 weeks tion

Model

the

under

tios)

illustrates

the

observation (characterized tolerate

higher

clinically

well-

that late-reacting by low a/f3 total

doses

nathan

do tumors or early-reacting tissues (with larger a/f3 ratios) when such a dose is given in small fractions. If a treatment schedule is changed from a standard scheme to a hyperfractionated regimen with bower dosages per fraction, a higher total dose can be administered without changing late effects. Such a higher dose achieves a better tumor control but

May

1991

a/li

late

effects are Tables 2 and show examples

80

echama

70

2

4

doses calculated according to Equation 5 (with use of the RE ratios from Table 1) for various common fractionation schemes.

.e0 .d.aiia

to stay the same. 3 and Figures 3 and of equivalent total

2

‘50 40 30

Therapeutic 3

2

4

a

8

Dose/fraction

7

1

8

2

3

4

5

Dose/fraction

(Gy)

6

7

8

(Gy)

4.

3. Figures schemes

3, 4. and

Table Total

Equivalent (4) constant

total tumor

dose for control

(3) constant and different

late

effects fractionation

and

different schemes.

fractionation

2 (Gy) for Constant

Doses

Late Effects a/fiRatio

Scheme A (25 fractions X 2 Gy = 50 Gy)

per

Dose

Scheme C (35 fractions X 2 Gy 70 Gy)

Scheme B (30 fractions X 2 Gy 60 Gy)

1.5

2

3

4

0.9 1.0 1_i 1.2 1.5 1.8 2.0 2.25 2.5 3.0 4.0 5.0 6.0 7.0 8.0

72.9 70.0 67.3 64.8 58.5 53.0 50.0 46.7 43.8 38.9 31.8 26.9 23.3 20.6 18.4

69.0 66.7 64.5 62.5 57.1 52.6 50.0 47.1 44.4 40.0 33.3 28.6 25.0 22.2 20.0

64.1 62.5 61.0 59.5 55.6 52.1 50.0 47.6 45.5 41.7 35.7 31.3 27.8 25.0

61.2 60.0 58.8 57.7

22.7

54.5 51.7 50.0 48.0 46.2 42.9 37.5 33.3 30.0 27.3 25.0

1.5

87.5 84.0 80.8 77.8 70.0 63.6 60.0 56.0 52.5 46.7 38.2 32.3 28.0 24.7 22.1

2

3

4

1.5

2

3

4

82.8 80.0 77.4 75.0 68.6 63.2 60.0 56.5 53.3 48.0 40.0 34.3 30.0 26.7 24.0

76.9 75.0 73.2 71.4 66.7 62.5 60.0 57.1

73.5 72.0 70.6 69.2 65.5 62.1 60.0 57.6 55.4 51.4 45.0 40.0 36.0 32.7 30.0

102.1 98.0 94.2 90.7 81.7 74.2 70.0 65.3 61.3 54.4 44.5 37.7 32.7 28.8 25.8

96.6 93.3 90.3 87.5 80.0 73.7 70.0 65.9 62.2 56.0 46.7 40.0 35.0 31.i 28.0

89.7 87.5 85.4 83.3 77.8 72.9 70.0 66.7 63.6 58.3 50.0 43.8 38.9 35.0 31.8

85.7 84.0 82.4 80.8 76.4 72.4 70.0 67.2 64.6 60.0 52.5

54.5 50.0 42.9 37.5 33.3 30.0 27.3

The therapeutic gain of one schedule relative to another is defined as the ratio of BEDs (BED/BED0) for tumon divided by the ratio of BEDs for late-reacting tissues. Table 4 lists the therapeutic gains for various dose fractionations and typical a/flratios for tumors and late-reacting tissues. Figure 5 is a graphic illustration of this table. It shows that the therapeutic gain is highest when low dose fractions are used for tumors with high a/f3 ratios growing close to latereacting tissues with a low a/j3ratio. On the other tions are least tion.

Fraction (Gy)

Equivalent Factor

by

The the

42.0 38.2 35.0

(Gy)

for Same

Tumor

Control

(for

Scheme A (25 fractions X 2 Gy 50 Gy)

Dose per Fraction (Gy) 0.9 1.0 1.1 1.2 1.5 1.8 2.0 2.25 2.5 3.0 4.0 5.0 6.0 7.0 8.0

also causes more liminary clinical observation On the other

Volume

=

Again, equivalent

179

a

Slowly

Proliferating

-

Ratio

10

15

6

10

15

6

10

15

58.0 57.1 56.3 55.6 53.3 51.3 50.0 48.5 47.1 44.4 40.0 36.4 33.3 30.8 28.6

55.0 54.5 54.1 53.6 52.2 50.8 50.0 49.0 48.0

53.5 53.1 52.8 52.5 51.5 50.6 50.0 49.3 48.6 47.2

69.6 68.6 67.6 66.7 64.0 61.5 60.0 58.2 56.5 53.3

66.1 65.5

44.7

48.0

42.5 40.5 38.6 37.0

43.6 40.0 36.9

64.3 62.6 61.0 60.0 58.8 57.6 55.4 51.4 48.0 45.0 42.4

40.0

81.1 80.0 78.9 77.8 74.7 71.8 70.0 67.9 65.9 62.2 56.0 50.9 46.7 43.1 40.0

77.1 76.4 75.7 75.0 73.0 71.2 70.0 68.6 67.2 64.6 60.0 56.0 52.5 49.4 46.7

74.8 74.4 73.9 73.5 72.1 70.8 70.0 69.0 68.0 66.1 62.6 59.5

34.3

64.2 63.8 63.4 63.0 61.8 60.7 60.0 59.1 58.3 56.7 53.7 51.0 48.6 46.4 44.3

46.2 42.9 40.0 37.5 35.3 33.3

acute reactions. Preexperience confirms (ii). hand,

Number

late-reacting

2

64.9

tissues schedules tion (Fig schemes

are

less with 2). The therefore

D/T

54.1 51.7

total dose in such must be reduced

is given

+ d/(a/fi)] -

schedules BEDs are -

Tk). are the

(/a)(T0

-

same: Tk)

+ d/(a/f3)] (‘y/a)(T

-

Tk).

tios from Table 1 and an additional dose i.D that compensates for cell proliferation during the excess treatment time T. Substituting these expressions for D’ and T, it can be shown that

56.7

tolerant to treatment high dosages per

factor

Time

D0 and T0 are total dose and overall treatment time, respectively, for the standard schedule at 2.0-Gy fractions, while D’, d, and T refer to the new fractionation scheme: D’ D + iD and T = T0 + T. D’ is the sum of D calculated according to Equation (5) with RE ra-

Scheme C (35 fractions X 2 Gy 70 Gy)

6

with

(‘y/a)(T

+ 2/(ct/f3)]

Tumors)

Scheme B (30 fractions X 2 Gy 60 Gy)

D[i

treatment if their

D’[i

dose fracin this situa-

Doses time

-

3

a/9

this

BED with equation

=

Doses

hand, large favorable

Total

BED

46.7

D0[i

Table Total

Gain

fracif

=

/(a

+ f3d)

(‘y/cr)/RE.

(8)

The additionally required dose .D is positive if the new fractionation scheme is longer than the standard one and negative if it is shorter. To calculate the additional dose per additional treatment day, three parameters need to be known: a, and Td. Figure 6 shows ID/T as a

Radiology

a

575

function of dosage per fraction for a range of a, f., and Td values typical for many tumors. It can be seen from this figure as well as Equation (8) that tumors with shorter clonogenic doubling times require larger compensating doses for each additional treatment day. Larger dose corrections are also needed for more radiation-resistant tumors, that is, tumors with small a values. The dependence on dose fractionation for larger cx/f3 ratios (tumors with an a/9 ratio greater than 10) is small. For a hypothetical tumor with a T of 5 days, an a/fl ratio of 10, and an a value of 0.35 (average values for tumors [8]), the additional dose required for each additional day of treatment ranges between 0.3 and 0.35 GyId for fraction sizes between 4 and 1 Gy per fraction. This agrees well with the empirical 30 rad/d (0.3 Gyld) linear dose increment for extending overall treatment times (12). For squamous cell carcinoma of the head and neck with an a/f3 ratio of six, an a value of 0.273, and a Td of 4 days (13), the additional dose required per additional treatment day is 0.42 Gy for fractions of 3 Gy, and 0.54 Gy for fractions of 1 Gy. This is somewhat lower but still close to the value of 0.6 Gy/d at 2-Gy fractions obtained by Withers et al (9) from an analysis of published clinical data. This dose correction should be applied only for treatment times longer than Tk, the time of enhanced tumor proliferation. For head and neck tumors, a Tk of 28 days has been reported (9), but different times may apply for other tumors.

DISCUSSION The linear quadratic model without time factor offers a simple method of calculating equivalent total doses when fractionations other than the standard 2.0-Gy per fraction are to be used. Since BEDs are additive, changing a fractionation during the course of treatment poses no difficulty: The sum of BEDs for each fractionation segment should equal BED0 of the standard scheme. A single table or graph suffices to calculate equivalent total doses for a variety of fractionation schemes and any given dose level. One need only specify the a//3 value of the latereacting tissue or tumor, for which the effect of the new fractionation scheme shall be the same as the old one. The therapeutic gain for a given tumor-late-reacting tissue combina576

a

Radiology

0

0.7

I

0.0 p0.5

Td.3d 0.4 0.3 --------------------------.

Td

‘-.-----.,--------------------.

Td-8d

0.2

0.7

0.1

1

2

4

Doseilraction

0

7

2

3

4

Gj/fractlon 6.

5.

Figures tion ment

1

(Gy)

5, 6. (5) Therapeutic scheme. (6) Additional schedules. : a/fl

gain of different dose needed per 6, a 0.273; I: a/

tion depends on the employed fnaction size alone and is independent of whether total doses were chosen to obtain the same tumor control or to keep late effects constant. Low dose fractions (less than 2 Gy) lead to a therapeutic gain greaten than one, because doses for the same tumor control cause less severe late reactions; doses for constant bate reactions, on the other hand, achieve better tumor control. At high dose fractions (those greater than 2 Gy), the therapeutic gain is always less than one: Doses for constant tumor control cause more severe late reactions, whereas doses that keep late reactions the same compromise tumor control. In accelerated and hypenfractionated radiation therapy, two or more smaller dose fractions per day are administered. The time interval between fractions is not considered in this form of the linear quadratic model. To account for short intervals

fractionations over standard 2.0-Gy-per-fracadditional treatment day for prolonged treat10, a 0.35; 0: a/3 = 15, a 0.45.

between fractions, (14) suggest adding plete

repair)

van an

de Geijn et al “IR” (incom-

analogous to (8) proposes of a modified RE to account for complete repair. This additional time

factor

factor.

plication, intervals

the use incom-

Fowler

however, between

kept

as long

least

4.5

hours

can dose

as possible (15)

to

be avoided fractions but

allow

if are

are

at

for

ade-

quate repair of normal tissue. When the time factor is inconporated into the linear quadratic model, much more detailed knowledge of the tumor is required. Instead of one radiobiobogic parameter (a/f.), four parameters-a, /3, T1, and Tk-need to be known, and these parameters may not remain constant during the course of the treatment. Our approach to incorporating the time factor into the calculation of equivalent doses does not distinguish between treatment breaks and evenly protracted treatment schedules. A constant cbonogenic doubling time

May

1991

between proliferation treatment

Tk (when enhanced sets in) and the is assumed.

tionalby ing this

tumor end of

knowledge

The linear quadratic model with time factor assumes a linear time dependence of the additionally required dose to compensate for tumor

proliferation.

This

seems

hours-to of normal

individual

patients,

especially

pa-

case

with

the interare not

bly

hours,

6-8

but

allow tissue.

tumor

not for

less

than

adequate

4.5

be-

and

the

cisions regarding 3. The additional

overall treatment times of up to 8 weeks. Equation (8) should not be applied to much longer treatment schedules. 4. A break in treatment may alter the radiation-induced tumor probiferation and thereby change the effective tumor doubling time used in Equation (8). Our tables should be considered part of an evolving process in the application of radiobiobogic parameters

these

ta-

CONCLUSION On model,

graphs

the basis we have

that

of the linear developed

can

serve

quadratic tables and

as a guide

for

comparing different fractionation schemes. When the time factor in the linear quadratic model can be neglected, a single table suffices for cabculating equivalent total doses for a variety of commonly used fractionation schemes and any total dose 1evel. Our tables also allow adjustment of total dose if fractionation needs to be changed during the course of treatment. When clonogenic tumor cell proliferation during a course of treatment is a concern, a higher total dose will be required for extended treatment schedules. We have presented a simple equation for calculating the addi-

for

tumor

a prolonged a linear time

proliferation

treatment dependence

of future

8.

10.

Physicists

11.

disfor

in clinical radiation therapy and probably will require modifications in the course of time dictated by the results trials.

7.

individual patients. dose required to

into bles.

during plays

research

and

12. 13.

14.

15.

clinical

U

References 1.

2.

3.

Svoboda VHJ. Radiotherapy by several sessions a day. Br J Radiol 1975; 48:131133. Saunders MI, Dische S. Radiotherapy employing three fractions in each day over a continuous period of 12 days. Br J Radiol 1986; 59:523-525. Wang CC, Blitzer PH, Sink H. Twice a day

head

radiation

and

therapy

neck.

Cancer

for

cancer

1985;

Dose, time hypothesis.

and fractionation: Clin Radiol 1969;

a

20:1-7.

vol-

compensate

in developing

Orton CG, Ellis F. A simplification in the use of the NSD concept in practical radiotherapy. Br J Radiol 1973; 46:529-537. Fowler JF. La ronde: radiation sciences and medical radiology. Radiother Oncol 1983; 1:1-22. Tubiana M. Repopulation in human tumors: a biological background for fractionation in radiotherapy. Acta Oncol 1988; 27:83-88. Fowler JF. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol 1989; 62:679-694. Withers HR. Taylor JMG, Maciejewski M, et al. The hazard of accelerated tumor clonogen repopulation during radiotherapy. Acta Radiol 1988; 27:131-146. Peters U, Ang KK, Thames HD. Tumor cell regeneration and accelerated fractionated strategies. American Association of

9.

volume

cause a “volume factor”-that is, the volume of tumor and volume of normal tissue irradiated-was not taken

account

5.

repair

ume of normal irradiated tissue are not taken into account in developing these tables. Therefore, caution and clinical experience should guide dein

Ellis F. clinical

6.

model,

These intervals should as long as possible-prefera-

2. The

to

4.

conclusions

considered. be kept

is of

We want and clinical decisions

Applyrequires

radiobiobogic

1 . In hyperfnactionation, between dose fractions

of the needed compensating dose per day versus prolonged treatment time

questions. that caution should guide

day.

from any theoretical caveats are in order:

vals

these

of four

As is the drawn certain

to be a valid

sigmoid shape. More detailed research correlated with clinical findings is needed to

dose per however,

rameters.

approximation for conventionally used treatment schedules up to 8 weeks (9). However, Denekamp (16) showed that for mouse skin, the plot

answer emphasize experience

needed equation,

16.

in

Medicine

symposium

pro-

ceedings no. 7. American Institute of Physics, New York, 1988; 27-38. Cox JD, Pajak TF, Marcial VA, et al. Interfraction interval is major determinant of late effects, but not acute effects or tumor control, with hyperfractionated irradiation of carcinomas of upper respiratory and digestive tracts (abstr). mt J Radiat Oncol Biol Phys 1990; 19(suppl 1):196. Liversage WE. A critical look at the ret. Br J Radiol 1971; 44:91-100. Yaes RJ, Wierzbicki J, Berner B, Maruyama Y. Modified linear quadratic model isoeffect relations for proliferating cells. AAPM symposium proceedings no. 7. American Institute of Physics, New York, 1988; 263-271. van de Geijn J, Goffman T, Chen J. Hyperfractionation in radiotherapy using an extended linear quadratic model (abstr). Int J Radiat Oncol Biol Phys 1990; 19(suppl 1):243. Marcial VA, Pajak TF, Chang C, Tupdrong L, Stetz J. Hyperfractionated photon radiation therapy in the treatment of advanced squamous cell carcinoma of the oral cavity, larynx and sinuses, using radiation therapy as the only planned modality. mt J Radiat Oncol Biol Phys 1987; 13:41-47. Denekamp J. The change in the rate of repopulation during multifraction irradiation of mouse skin. Br J Radiol 1973; 46: 381-387.

of the

55:2100-

2104.

Volume

179

a

Number

2

Radiology

a

577