The document discusses the radiobiology principles underlying dose fractionation in radiation therapy, focusing on mathematical models like the linear quadratic model that describe cell survival curves and the impact of various fractionation schemes on tumor and normal tissue responses. It covers key concepts such as cell repair mechanisms, the 4Rs of radiobiology (repair, redistribution, repopulation, reoxygenation), and how different dose per fraction affect treatment outcomes. Additionally, it summarizes clinical trial findings on altered fractionation techniques and their implications for optimizing therapy to enhance tumor control while minimizing harm to healthy tissues.

1. The Radiobiology Behind Dose
Fractionation
Dr:- Omer Hashim
Radiation Oncologist
Universal Hospital

2. Objectives
To understand the mathematical bases behind survival
curves
Know the linear quadratic model formulation
Understand how the isoeffect curves for fractionated
radiation vary with tissue and how to use the LQ model to
change dose with dose per fraction
Understand the 4Rs of radiobiology as they relate to
clinical fractionated regimens and the sources of
heterogeneity that impact the concept of equal effect
per fraction
Know the major clinical trials on altered fractionation and
their outcome
Recognize the importance of dose heterogeneity in
modern treatment planning

3. Cells killing theories
• Target Theory:-
Target theory explains the cell damage caused by
radiation based on the principles of probability. It
assumes that there are certain critical molecules or
critical targets within cells that need to be hit or
inactivated by the radiation to kill the cell.

4. Single target–single hit
For viruses and bacteria
Multiple target–single hit
there is more than one target per cell, and a single hit of any of these
targets is required for cell death.Not all targets are hit; some of them are
killed, while others are damaged by low
doses. This type of damage is called sublethal damage (SLD) for
mammlain cells

5. Cell Survival Curves
The number of cells in cell lines within cell cultures can
increase in one of two ways:
• either arithmetically
• or exponentially (geometrically).

6. arithmetically
geometrically

7. When cell culture exposed to radiation P:-
die
reproductive cell death
Divide and form small colonies
form colonies over longer periods
,The remaining cells are not affected by the radiation called surviving
fraction

8. Surviving Fraction:-
The ratio of the number of cells that form
colonies to the number of seed cells under
normal conditions (i.e., no irradiation) in a
cell culture is termed the plating efficiency
(PE). The same ratio obtained under
irradiated conditions and divided by the
PE is called the surviving fraction (SF):

9. Surviving fraction (SF) =
Colony number rad /Seeded cell number rad × PE
e.g 100 cells are seeded … 10 colonies formed
PE = 100/10 =10>>….. IF 450 CGY IS given and 5 colonies
ware formed
then SF =5/[100 × 10/100] = 1/2.
as a cell–dose plot. If the SF is calculated for various doses,
then it can be presented
Combining the points on the plot leads to a cell survival
curve.

10. LD50 value can be obtained from a
sigmoid survival curve (LD50 is the
dose that kills
50% of cells → lethal dose).
0 200 400 600
1
1
0.8
0.6
800
0.4
0.2
0 200 400 600 800
1.0
0.1
0.01
Survival curves are radiobiologically
defined using semilogarithmic
curves, and these
curves provide information on some
parameters such as the number of
cells killed by
the radiation and cell radiosensitivit

11. Exponential Survival Curves :-
These are the survival curves resulting from the single
target–single hit hypothesis of target
theory
0.37
D0
Single target single hit

12. After 100 radiation “hits,” the probability that one of the
hits will be a target→ e−1 (e » 2.718 …).
e−1 is approximately 37%. In other words, 63% of the
targets will be hit after 100 hits, while 37% of the targets will
D0 = dose that decreases the surviving fraction to 37%.
This is the dose required to induce an average damage
per cell.
A D0 dose always kills 63% of the cells in the region in
which it is applied, while 37%
of the cells will survive.
1/D0 = the slope of the survival curve.

13. If n increases → Dq increases → a wide shouldered curve is
observed.
If n decreases → Dq decreases → a narrow shouldered curve is
observed.
If Dq is wide and D0 is narrow, the cell is radioresistant.
The D0 and Dq values for the tumor should be smaller than
those of normal tissue to
achieve clinical success.

16. As the value of D0 decreases → 1/D0 increases → slope
increases → radiosensitive cell.
As the value of D0 increases → 1/D0 decreases → slope
decreases → radioresistant cell

17. Shouldered Survival Curves with Zero Initial Slope :-
These survival curves are based on the multiple
target–single hit hypothesis of target theory

19. D0: the dose that yields a surviving fraction of 37%.
Dq: half-threshold dose → the region of the survival
curve where the shoulder starts
(indicates where the cells start to die exponentially) (=
quasi-threshold dose).
n: extrapolation number (the number of D0 doses
that must be given before all of the
cells have been killed).

21. 1/D1: the slope of the component corresponding to multiple
target–single hit (the slope
of the initial region).
Dq: the dose at which the shoulder starts for the multiple
target–single hit component
(the quasi-threshold dose).
1/D0: the slope of the terminal region of the multiple target–
single hit component.
n: extrapolation number.

22. Components of Shouldered Survival Curves with Nonzero
Initial Slope :-
• Component corresponding to the single target–single hit model (blue in the
figure)
This shows lethal damage.
This shows the cells killed by the direct effect of the radiation.
This shows the effect of high-LET radiation.
• Component corresponding to the multiple target–single hit model (red in the
figure)
This shows the accumulation of SLD.
This shows the cells killed by the indirect effect of the radiation

23. Linear–Quadratic Model (LQ
Model)
In this model, developed by Douglas and Fowler in
1972, it was assumed that cell death due to ionizing
radiation has two components
The first component Directly proportional to dose → D
Linear component
The second component Directly proportional to the
square of the dose → D2 Quadratic component

24. a → shows the intrinsic cell radiosensitivity, and it is the
natural logarithm (loge) of the proportion of cells that
die or will die due to their inability to repair radiation-
induced damage per Gy of ionizing radiation.
b → reflects cell repair mechanisms, and it is the
natural logarithm of the proportion of repairable cells
due to their ability to repair the radiation-induced
damage per Gy of
ionizing radiation.

25. • p1 = aD.a → initial slope of the survival curve (low-
dose region) → linear coefficient.
• If the effect of two radiation hits is p2, then
p2 = bD2
b → quadratic coefficient.
Total effect p1 + p2 = ad + bd2

26. S.F. = e-aD
Single lethal hits
S.F. = e-(aD+bD2)
Single lethal hits plus
accumulated damage
• Cell kill is the result of single lethal
hits plus accumulated damage
from 2 independent sublethal
events
• The generalized formula is E = aD + bD2
• For a fractionated regimen E= nd(a + bd) =
D (a + bd) Where d = dose per fraction and
D = total dose
• a/b is dose at which death due to single
lethal lesions = death due to accumulation
of sublethal lesions i.e. aD = bD2 and D = a/b
in Gy
S.F.
1.0
0.1
0.01
0.001
DOSE Gy
a/b in Gy
aD
bD2
Linear Quadratic Model

27. LQ model used
equivalent
fractionation
schemes.
additional doses
after breaks from
radiotherapy.
information on
acute and late
responses.

28. What total dose (D) to give if the
dose/fx (d) is changed
• New old
Dnew (dnew + a/b) = Dold (dold +a/b)
So, for late responding tissue, what total dose in 1.5Gy
fractions is equivalent to 66Gy in 2Gy fractions?
Dnew (1.5+2) = 66 (2 + 2)
Dnew = 75.4Gy
NB:-Small differences in a/b for late responding tissues can
make a big difference in estimated D!

29. Biologically Effective Dose (BED)
Biologically Effective
Dose Total dose
Relative
Effectiveness
S.F. = e-E = e-(aD+bD2)
E = nd(a + bd)
E/a = nd(1+d/a/b)
35 x 2Gy = B.E.D.of 84Gy10 and 117Gy3
NOTE: 3 x 15Gy = B.E.D.of 113Gy10 and 270Gy3
Normalized total dose2Gy
= BED/RE
= BED/1.2 for a/b of 10Gy
= BED/1.67 for a/bof 3Gy
Equivalent to 162 Gy in 2Gy Fx -unrealistic!
(Fowler et al IJROBP 60: 1241, 2004)

30. BEDN = Nd( 1+ d/αβ)

31. 4Rs OF DOSE FRACTIONATION
These are radiobiological mechanisms that impact the
response to a fractionated course of radiation therapy
• Repair of sublethal damage
o spares late responding normal tissue preferentially
• Redistribution of cells in the cell cycle
o increases acute and tumor damage, no effect on late responding
normal tissue
• Repopulation
o spares acute responding normal tissue, no effect on late effects,
o danger of tumor repopulation
• Reoxygenation
o increases tumor damage, no effect in normal tissues

32. Regeneration assumed to be exponential
• S.F.regeneration = eT = e (ln2/Tp)T
o Where T = overall treatment time; Tp =
effective doubling time
• i.e. S.F. = e-(aD+bD2)+ln2/Tp(T-Tk)
o Where Tk is time of start of regeneration

33. Repair
• Repair” between fractions should be complete - N.B.
we are dealing with tissue recovery rather than DNA
repair
• CHART analysis HNC showed that late morbidity was less than
would be expected assuming complete recovery between
fractions
o Is the T1/2 for recovery for late responding normal tissues
2.5-4.5hrs?

34. Regeneration
• The lag time to regeneration varies with the tissue
• In acute responding tissues,
o Regeneration has a considerable sparing effect
• In human mucosa, regeneration starts 10-12 days into a 2Gy
Fx protocol and increases tissue tolerance by at least 1Gy/dy
o Prolonging treatment time has a sparing effect
o As treatment time is reduced, acute responding tissues become
dose-limiting
• In late responding tissues,
o Prolonging overall treatment time beyond 6wks has little effect,
but
prolonging time to retreatment may increase tissue tolerance

35. Altered Fractionation

36. Total
Dose
Overall
treatment time
(T)
Dose per
fraction (d)
Tumor type
Interval
between
fractions (t)
Late reacting
normal
tissues
Acute reacting
normal tissues

37. Multifraction Effects cell types
• The slope of an isoeffect curve changes with size of dose per
fraction depending on tissue type
• Acute responding tissues have flatter curves than do late
responding tissues
• a/b measures the sensitivity of tumor or tissue to fractionation
i.e. it predicts how total dose for a given effect will change
when you change the size of dose fraction

39. Response to Fractionation Varies With Tissue
16
12
8
4
0
0
.01
.1
1
Dose (Gy)
S.F.
Late Responding
Tissues - a/b= 2Gy
Acute Responding
Tissues a/b= 10Gy
a/b is high (>6Gy) when survival
curve is almost exponential and
low (1-4Gy) when shoulder is wide
20
16
12
8
4
0
0
.01
.1
1
Dose (Gy)
S.F.
Single Dose
Late Effects
a/b= 2Gy
Single Dose
Acute Effects
a/b= 10Gy
Fractionated
Late Effects
Fractionated
Acute Effects
Fractionation spares late responding tissues

40. Isoeffect Curves

41. What are a/b ratios for human cancers?
In fact, for some tumors e.g. prostate, breast, melanoma,
soft tissue sarcoma, and liposarcoma a/b ratios may be
moderately low
Prostate
o Brenner and Hall IJROBP 43:1095, 1999
• comparing implants with EBRT
• a/b ratio is 1.5 Gy [0.8, 2.2]
o Lukka JCO 23: 6132, 2005
• Phase III NCIC 66Gy 33F in 45days vs 52.5Gy 20F in 28 days
• Compatible with a/b ratio of 1.12Gy (-3.3-5.6)
Breast
• UK START Trial
o 50Gy in 25Fx c.w. 39Gy in 13Fx; or 41.6Gy in 13Fx [or 40Gy in 15Fx (3 wks)]
• Breast Cancer a/b = 4.0Gy (1.0-7.8)
• Breast appearance a/b = 3.6Gy; induration a/b = 3.1Gy
• If fractionation sensitivity of a cancer is similar to dose-limiting healthy
tissues, it may be possible to give fewer, larger fractions without
compromising effectiveness or safety

42. TCP
or NTC
Dose
Hyperfractionation
Accelerated
Fractionation
Tumor control
Late responding tissue
complications
Complication-free cure
TCP
or NTC

43. Other Sources of
Heterogeneity
• Biological Dose
o Cell cycle
o Hypoxia/reoxygenation
o Clonogenic “stem cells” (G.F.)
• Number
• Intrinsic radiosensitivity
• Proliferative potential
• Differentiation status
• Physical Dose
o Need to know more about the importance of dose-volume
constraints
Dose
oxic
hypoxic
S.F

44. Fractionation
Types
Conventional
Hyperfractionation
Hypofractionation
Accelerated
fractionation

45. Daily doses (d) of 1.8 to 2 Gy
Dose per week of 9 to 10 Gy
Total dose (D)
of 40 to 70 Gy
Conventional fractionations

46. 2frs/day
Hyperfractionation
Rationale: Spares late responding tissues
Dose per
fraction (d)
less than 1.8
Gy
T is kept the same
number of
fractions (N))

47. Shorter
overall
treatment
time
Dose per
fraction
of 1.8 to 2
Gy
More than
10 Gy per
week
Accelerated fractionation

48. Hypofractionation
Tumor has low a/b ratio and there is
no therapeutic advantage to be gained
with respect to late complications
Reduced total number
of fractions (N)
Dose per fraction (d)
higher than 2.2 Gy

49. Conventional
70 Gy - 35 fx - 7 wks
Very accelerated
with reduction of dose
54 Gy - 36 fx - 12 days
Moderately accelerated
72 Gy - 42 fx - 6 wks
Hyperfractionated
81.6 Gy - 68 fx - 7 wks

50. fractionations
Advantages
Protects normal
tissues from early
side effects
reoxygenation
in tumor cells
Disadvantages
Overall
treatment time
increases
Tumor cell
proliferation
increases

51. hyperfractionation Barcelona (586)
Brazil (112)
RTOG 90-03
EORTC 22791
Toronto (331)

52. TROG
91-01
CHART
(918
GORTE
C 94-02
Accelerated
fractionation

53. EORTC hyperfractionation trial in
oropharynx cancer (N = 356)
Years
LOCAL CONTROL SURVIVAL
Years
Horiot 1992
80.5 Gy - 70 fx - 7 wks control: 70 Gy - 35-40 fx - 7-8 wks
p = 0.02
p = 0.08

54. CHART (N = 918)
• 54 Gy - 36 fx - 12 days control: 66 Gy - 33
fx - 6.5 wks

55. CHART: Morbidity
Mucosal ulceration and
deep necrosis
P = 0.003
Moderate/severe dysphagia
P = 0.04
Laryngeal oedema
P = 0.009

56. RTOG 90-03, Phase III comparison of fractionation
schedules in Stage III and IV SCC of oral cavity,
oropharynx, larynx, hypopharynx (N = 1113)
Conventional
Accelerated with split
70 Gy - 35 fx - 7 wks
67.2 Gy - 42 fx - 6 weeks (including 2-week split)
72 Gy - 42 fx - 6 wks
Hyperfractionated
81.6 Gy - 68 fx - 7 wks
Accelerated with
Concomitant boost
Fu 2000

57. RTOG 90-03, loco-regional
control

58. RTOG 90-03, survival

59. RTOG 90-03, adverse
effects
• Acute
Maxi toxicity Conventional Hyperfract ConcomAcc +
per patient boost split
• Grade 1 15% 4% 4% 7%
Grade 2 57% 39% 36% 41%
Grade 3 35% 54% 58% 49%
Grade1 11% 8% 7% 16%
Grade 2 50% 56% 44% 50%
Grade 3 19% 19% 29%

60. Acute effects in accelerated or
hyperfractionated RT
Author Regimen Grade 3-4 mucositis
Cont Exp
• Horiot (n=356) HF 49% 67%
• Horiot (n=512) Acc fx + split 50% 67%
• Dische (n=918) CHART 43% 73%
• Fu (n=536) Acc fx(CB) 25% 46%
• Fu (n=542) Acc fx + split 25% 41%
• Fu (n=507) HF 25% 42%
• Skladowski (n=99) Acc fx 26% 56%

61. Conclusions for HNSCC
• Hyperfractionation increases TCP and protects late
responding tissues
• Accelerated treatment increase TCP but also increases acute
toxicity
• What should be considered standard for patients treated with
radiation only?
– Hyperfractionated radiotherapy
– Concomitant boost accelerated radiotherapy
• Fractions of 1.8 Gy once daily when given alone, cannot be
considered as an acceptable standard of care
• TCP curves for SSC are frustratingly shallow … selection of
tumors?

62. Hypofractionation
• Delivery of large dose in few fractions well known in
• SBRT and SABT in NSCLC but also in prostate and
breast in which ∞/β ratio is low even lower than
• Late tissues complication so high conformal dose
requirement to save normal tissues

63. Other Major Considerations
• Not all tumors will respond to hyper or accelerated
fractionation like HNSCC, especially if they have a low
a/bratio.
• High single doses or a small number of high dose per
fractions, as are commonly used in SBRT or SRS generally
aim at tissue ablation. Extrapolating based on a linear
quadratic equation to total dose is fraught with danger.
• Addition of chemotherapy or biological therapies to RT
always requires caution and preferably thoughtful pre-
consideration!!!
• Don’t be scared to get away from the homogeneous
field concept, but plan it if you intend to do so.

64. Grade 1 11%
8% 7%
16%
Grade 2 50%
56% 44%
50%
Grade 3 19%
19% 29%
20%
Grade 4 8%
9% 8%
7%
Grade 5 1%
0% 1%
1%