This document discusses various time-dose models used in radiotherapy, including the Strandqvist, Cohen, NSD, and TDF models. It explains the need for these models to optimize treatment regimes for tumor control while sparing normal tissues. The document also covers gap correction factors used when treatment schedules are interrupted and the various factors that can affect tumor control outcomes due to gaps in treatment. Compensatory methods like accelerated scheduling and increased dosing are presented to account for treatment gaps.

1. Dose regime Models
&
Gap correction factor
Presented by
Jyoti Bisht
(Medical Physicist)
Swami Ram Cancer
Hospital & Research
Center
Haldwani,Nainital

3.  Radio-Biology:
Radio-biology is the branch of Radiation Physics in which the
biological effects of Radiation are observed, measured and evaluated
with respect of irradiation time.
 Basically We need Radiobiology to know
 Normal Tissue Tolerance
 Tumor lethality
 Dose and Toxicity
 Dose optimization
 Consequential Dose

4.  Need for time-dose models-
 The main aim of radiotherapist is to obtain a high probability
of tumor control without exceeding tolerance of normal
tissue.
 Not all diseases are treated with the same time-dose
schedule and not all radiotherapists will treat similar disease
similarly.
 Since, typical treatment plans are quite complicated to
compare.
 With the help of these time-dose models the treatment
regimes now can be easily modified.

5.  BIOEFFECT DOSE MODELS
CLINICAL HUMAN EXPERIMENTAL
TISSUE REACTIONS ANIMAL TISSUE
REACTIONS
CELL SURVIVAL
THEORIES
TIME – DOSE THEORY

6.  Strandquist model.
 In 1944 Strandqvist has published a graphical
representation, describing the result of 280 patients of different type
of skin cancers.
 He plotted an isoeffect line on log-log scale between total dose D and
total treatment time T. The isoeffect line on logarithmic co-ordinates
was drawn, which was as a straight line with a slope of 0.22.
 Mathematically, the total dose D is related to overall treatment
time, T, as;
D=KT0.22
Where K is a constant.

7. Isoeffect curves relating total dose to the
overall treatment time

8.  Cohen model
 Cohen had analyzed three sets of data of skin damage, the end
points were taken as skin erythema and skin tolerance.
 Similar isoeffect lines were plotted for Tumor Lethal Dose (TLD)
of squamous cell carcinoma and basal cell carcinoma in skin
cancer also.
 He further evaluated an exponent of 0.33 for skin erythema / skin
tolerance and 0.22 for skin cancers.
 According to Cohen’s result, the relationship between total dose
and overall treatment time, for normal tissue tolerance and tumors
can be written as :-

9. Dn = K1T0.33
And
Dt = K2T0.22
Where K1 and K2 are proportionality constants. Dn, Dt and
T are normal tissue tolerance dose, tumor lethal dose
and overall treatment time respectively.

10.  Nominal Standard Dose (NSD) formula
 It is given by Ellis(1965).
 The exponent of T in normal tissue is higher than that of tumor,
which indicates that the repair capacity of normal tissue is higher
than that of tumors.
 This difference is termed as “Differential Recovery Rate”.
 The normal tissues are having two types of repair / recovery
capabilities. i.e.,
(i) intracellular recovery and
(ii) extra-cellular recovery.
 He had investigated that the number of fractions (N) were more
important than the overall treatment time (T).

11. This led Ellis to an important realization that the time factor was
actually a composite effect of N and T The exponents for
intracellular and homeostatic recoveries are 0.22 and 0.33-0.22
= 0.11 respectively. Now equation may be transformed to;
D = KT0.22
Now T0.22 can be replaced by N0.22 as intracellular recovery
completes within few hours of irradiation, the equation can be
rewritten as;
D = KN0.22T0.11

12. The conventional treatment schedule is delivered 5 fractions
per week; therefore exponent 0.22 of N replaced by 0.24
and the proportionality constant is replaced by a term NSD.
Hence the final formula, comprising total dose D, at normal
tissue tolerance, number of fractions N and overall
treatment time T, is given by
D = NSD N0.24T0.11
And can be written as
NSD = D N-0.24 T-0.11
Where NSD (the nominal standard dose) is a constant, unit
of NSD is ret(radiation effect therapy).

13.  Drawbacks of NSD concept .
The problems encountered in the application of NSD concept
and its derivatives quoted by Barendsen are as follows :-
 Doubts have been raised concerning the validity of these
models with respect to the type of the tissue involved.
Evidence revealed that for different tissues, the dependence
of tolerance dose fractionation is not the same.
 The doubts have also been raised concerning the validity of
these models with respect to different effects in the same
tissue or organ.

14.  The cumulative Radiation effect (CRE)
 NSD formulas do not say anything about tumor response and the
part of the treatment schedule, which has already been completed.
 The fact that a portion of a treatment schedules, which has already
been completed, might have reached some level of tolerance.
 Kirk et al have extended the NSD concept to the cumulative
radiation effect (CRE) for such type of treatment schedules. This
was based on the concept of sub-tolerance of normal tissue, which
was subjected to irradiation .

15.  In practice, the concept of partial tolerance is very important in
the analysis of a complex treatment protocol, which includes many
number of treatment parts, and is combined together.
 The partial tolerances is additive in nature. i.e.;
PT = (PT)1 + (PT)2 +…………+(PT)n
 The basic NSD formula was written in terms of total dose
D, overall treatment time T and total number of fraction N.
However, in general practice, the dose per fraction d is often the
starting point so that the total dose may be written as D = N.d and
total treatment time T= x.N, where x is the function of number of
fractions per week.

16.  Time, Dose, Fractionation Factor (TDF)
 Given by Orton and Ellis.
 The effectiveness of the treatment should be described in
terms of partial tolerance and its expression is given as;
PT (partial tolerance) = NSD x n/N
 Where, N is the number of fractions of the chosen size
and, frequency, which would result in full connective tissue
tolerance, and n is the number of such fraction actually
given.

17. Now, the equation of NSD may be written as
NSD = N.d.N-0.24 (x.N)-0.11
Or
NSD = d.N0.65 x-0.11
Or
N = [(NSD/d). x-0.11]1.538
Now, substituting the value of N in equation of partial
tolerance, we get
PT = n (NSD)-0.538 d1.538 x-0.169

18. Now equation PT can be written as;
PT = (NSD)-0.538. (TDF). 103
Where,
• TDF is defined as, TDF = n. d1.538 x-0.169. 10-3
• 10-3 is simply a scaling factor that makes TDF values
more convenient to handle.
• x is the function of number of fractions per week.
(5 fractions in7 days.)

19.  Gap correction factor
 In some situations, it became necessary to interrupt a
continuous treatment schedule by interposing a rest period
due to many reasons.
 In such type of treatment schedules, the effectiveness of
the first part of the treatment will have decayed by the time
second part of the treatment is started.
 The two parts of the treatment are well separated,
therefore the TDF values of these two parts of the plan
cannot be added until a decay correction has applied to the
TDF values of first part of the treatment.

20. Orton suggested the use of decay factor.
The decay correction factor is based on the time
component of the basic NSD formula and is given by
Decay / Gap correction Factor (GF) = {T/(T+G)}0.11
Where, the duration of the first part of split course is T
days, and the rest period is G days.

21.  Calculation Process -
 Calculate the normal tissue BED for the prescribed schedule.
This calculation should make use of the dose actually received
by the critical normal tissue.Eq (A).
 Determine the respective pre-gap normal-tissue BED.
 Find the difference between them to determines the late-normal
BED ,still to give’ (the post-gap BED).
 Review the various option (for ex- twice daily fractionation and
hyperfractioonation, increased fraction size) to ascertain which
will be likely to produce the minimum extension to the treatment
time,then calculate required dose per fraction.
 For the selected option , calculate the associated tumour BED
using Eq (B).
 Review the final tumour and normal tissue BEDs which will
preferred compensation option.

22.  Formulas -----
BED= n d [ 1+d/(a/b)] ….Eq(A)
BED= n d[1+d/(a/b)] –K*(T-T delay)
….Eq(B)
where,
n= no. of fractions
d= dose per fraction
a/b= Dose (given in literature)
T= Total treatment time
Tdelay= delay in treatment or prolonged time
K= proportionality constant

23.  Effects of the Gap -
4 R’s of Radiotherapy –
 Repair of sublethal damage of normal cells.
 Reassortment of cells within the cell cycle.
 Repopulation of normal cells.
 Reoxygenation of tumour tissue.
Prolongation of treatment are to spare early reactions and
to allow adequate reoxygenation in tumours.

24.  Data on the basis of a servey in Manchaster, UK
and Toronto, Canada in three years reported for
Gap -
1994 2000 2005
Department-related
Planned
Public holiday/statutory days 46% ----' 39%
Machine service time 31% 37% 35%
Unplanned 7% ----' ----'
Machine breakdown ----' 13% 9%
Patient-related
Radiotherapy reactions 16% 8% 8%
Patient unwillingness ----' 5% 4%
Unspecified ----' 37% 5%
Total 100% 100% 100%

25.  Factors that can affect the tumours control outcome
due to Gap-
 Tumour proliferation (ex: Slow growing tumours & fast
growing tumours)
 Prolongation length .
 Interruption time ((initially breakage or in middle or at last
of the treatment).

26.  Tumour Proliferation -
 Glioblastoma are very fast growing tumours, and there is evidence that
delay in starting therapy affects outcome. 75,76.
 Carcinoma of bladder : Two small reports favor that prolongation may
affect outcome.78,79Two large reports shows no significant affect of
prolongation on outcome.77,80
 Prolongation of slow growing tumours for five days does not
significantly affect patient outcome (Local control and survival)
applicable on Ca anus81-83 and Ca prostate 84-87
 For Ca breast shows adverse effect on local control and survival if
treatment prolonged for more than seven days in a five-week course of
treatment.22,23For shorter courses there is no published data. But
prolongation should not be more than two days.
 In palliative cases the prolongation may reduce the effect of benefit
for ex-Management of cord compression and superior vena cava
obstruction(SVCO).

27.  Prolongation length -
 The minimum length of an interruption which result in
prolongation of treatment time is difficult to determine.
 Data from different course studies show that 14-16 day
interruption definitely effect treatment outcome.
 Prolongation of one week may arise loss of tumour control from 3
to 25%(Median 14%).
 Mathematical modeling of squamous cell carcinoma oh head and
neck, cervix, and lung shows that an unscheduled interruption of
one day(uncompensated) reduces local tumour control by 1 to
1.4%10,15,16.
 For locally advanced cervical cancer the overall treatment time
should not exceed 56 days for squamous carcinoma.
 Ca breast (postoperative) shows that prolongation of more than
seven days for five week treatment increases risk of local
recurrence and death. 22,23

28. Does the timing of interruption matter?
Studies are going on this topic.
 Gap arising in short course of treatment (3-4 days).
 Gap arising earlier than 28 days in a long course of therapy.
 Gap arising after 28 days treatment.
Biological correction for these events will be different .
 Correction for interruption arising later in a long course of
therapy is more difficult because it require the patient to
receive a large no. of fractions over a short time of period and
this may increase the risk of long term late effect.
 According to a study on pig skin it is suggested that an
interruption on a Monday or Friday have a more serious
adverse effect than an interruption mid-week.95,46

29.  Compensatory Methods -
Transfer to a second machine
Accelerated Scheduling
Biological allowance
Increased total dose

30.  Implementation -
Availability of resources
Patient-specific reminders at the time of prescription or
treatment
Communication
Quality assurance
Funding
Research
Supervision
Teaching
Radiobiology Support

31. Reference -
These all references has been taken from the report -
The Timely delivery of radical radiotherapy: standards
and guidelines for the management of unscheduled
treatment interruptions, Third edition, 2008
Published by :Board of faculty of Clinical Oncology
The Royal College of Radiologists