An analysis of dose rate correction factors using the multiple component model applied to LDR brachytherapy of carcinoma of uterine cervix patients.

T. S. Kehwar, M. K. Gupta*, Ruby Gupta**, V. K. Dangwal, K.S.Thind, Hardip Singh

Department of Radiotherapy, Post Graduate Institute of Medical Education and Research, Chandigarh, India. *Department of Radiotherapy, Indra Gandhi Medical College, Shimla, India. **Department of Gynaecology, Tara Hospital, Shimla, India. Department of Radiotherapy, Govt. Medical College, Amritsar,  India. Department of Physics, Guru Nanak Dev University, Amritsar, India.

Corresponding Address :

Correspondence Address:-T. S. Kehwar, DRP, PhD, DSc, Department of Radiation Oncology, Sanchez Cancer Center, Mercy Health Center, 1700 E. Saunders St. Laredo, Texas 78041 USA. E-mail:



The aim of this study is to present an analysis and an assessment of the dose rate correction factors applied in to groups of the patients of carcinoma of uterine cervix. A MC model analysis has been done using the multiple component (MC) model for each of the patient. The dose rate corrections of 20% and 14.5% were applied to the Manchester dose of 70Gy, to get equivalent tumour control, in group -I and II respectively. An increased tumour control was recorded in the patients who were treated with a correction factor of 14. 5% with slightly more acute and late complications. During the intracavitory treatment of group-I patients an average dose rate at point A was about 1. 78 Gy and for group - II patients, it was about 1.64 Gy. The clinically observed and theoretically predicted changes in early / late effects and tumour control were not statistically significant (p>0.05). The MC model predicts a range of dose rate correction factors for group - I and II for different values of recovery constant to get equivalent biological effects to that of the Manchester schedule. The applied correction factors, in this trial, are in the range of correction factors derived for m=1.2 and 1.4 h -1 for equivalent acute reactions and tumour control. The model has predicated the changes in normal tissue reactions and tumour control, in group -I and II, with a fair accuracy.

Key words: MC model, Dose rate correction factors, Low-dose-rate, Early effects, Late effects.


Brachytherapy is the mode of treatment in which maximum radiation dose can be delivered to the tumour to get better tumour control without excessive damage to the surrounding normal tissues. The surrounding normal tissue damage and tumour control depends on the dose distribution within the irradiated volume and dose rate. The ICRU-38 report for Gynaecological Brachytherapy3 has divided a broad spectrum of dose rates into three categories viz (1) low dose rate, from 0.4 Gy/hr to 2.0 Gy/hr, (2) medium dose rate, from 2 Gy/hr to12.0 Gy/hr and (3) high dose rate greater than 12.0 Gy/hr or 0.2 Gy/min. The different tissues respond in different manner with changing dose rates2. Hence the above described distinction in dose rates has a great demerit that it vaguely understates the existence of only three groups of relatively uniform biological responsiveness, which is absolutely wrong. There is a single spectrum of biological responsiveness with the dose rate variation, which is the paramount of clinical importance.

In this paper radiobiological analysis of the patients of carcinoma of uterine cervix has been done using the multiple component (MC) model5-7. These patients were treated in the department of Radiotherapy, Cancer Hospital and Research Institute, Gwalior (MP), India, by a two patient selectron LDR/MDR intracavitory after loading system. The activity per pellet, of Cs-137 sources, was 40 mCi and dose rate at point A was 180 Gy/hr in June 19861. The patients treated till December 1989, a dose rate correction of 20% was applied to get a biological equivalence of Manchester system of dose rate 0.5 Gy/hr was applied, and the results of these two groups are compared. A clinical analysis of the study was presented elsewhere




One hundred fifty five patients of carcinoma of uterine cervix were included in this study who were treated and followed up from June 1986 to December 1992. All patients were of histologically proven squamous cell carcinoma. These patients were divided into two groups. Group I, of 75 patients treated from June 1986 to May 1987 and followed up till December 1989. In this group, 22 patients were of early stages (1b and 2a) and 53 were of late stages (2b and 3). The group -II comprises 80 patients, who were treated from January 1990 to December 1990 and followed up till December 1992. Among these, 30 patients were of early stages (1b and 2a) and 50 were of late stages (2b and 3). The stage wise distribution of the patients, in booth the groups, was as follows. There were 6 and 8 patients of stage 1b, 16 and 12 of 2a, 13 and 16 of 2b, and 40 and 44 of 3 in group -I and II, respectively.


All the patients were treated by Co-60 teletherapy unit and a Cs-137 Selectron LDR/MDR remote controlled unit. In June 1986, the dose rate at point "A", of Selectron LDR/MDR unit, was 1.80 Gy/hr and became 1.76 Gy/hr in May 1987. The patient treated through June 1986 to May 1987 falls in group -I. In the patients of early stages, a dose of 40 Gy in 20 fractions within 4 weeks was planned to be given by external beam radiation therapy (EBRT) with a midline pelvic shielding which allow less than 5% transmission of the primary beam. The total contribution of EBRT dose to point "A" was 25% due to transmission of the primary beam through central shielding and phantom scattering thus giving rise to a dose of 10 Gy. An equivalent dose to 70 Gy with a 20% correction i.e. a dose of 56 Gy was planned to give via two insertions of intracavitory radiation therapy (ICRT) of equal dose of 28 Gy with one week interval. The gap between teletherapy and first ICRT application was kept equal to two weeks. A total dose to point A was 66Gy (Table -1). In advanced cases a dose of 45Gy in 25 fractions within 5 weeks was delivered by EBRT without a midline pelvic shielding. After two weeks of external irradiation a single ICRT application of dose 28Gy, to point A, was given. A total dose to point A from ExRT and ICRT was 73Gy (Table -1).

The patients of group-II, were treated through January 1990 to December 1990 and followed up till December 1992. The selectron LDR/MDR dose rate was 1.62-1.66Gy/hr to point A during this period. The patients of early stages, in this group, were treated with same protocol, as in the early stage patients of first group except the intracavitory dose. The equivalent dose to 70Gy with 14.5% dose-rate correction, i.e. 60 Gy was delivered in two equal fractions of intracavitory applications. Thus in the patients of early stages, total dose to point A was 70 Gy from external irradiation and two intracavitory applications while in advanced cases a EBRT dose of 45Gy/25fr/5wk  was from application, this total dose to point A was 75 Gy (Table -1).

Table - 1: Treatment protocol for EBRT, applied in both groups and  its corresponding  BRD values at point A.


Total dose / No. of fractions



at point 'A'

  BRD(Gy) Values at point A

Early effects

Late effects


Early cases



Advance cases


with midline shielding


45Gy/25# without midline shielding



























The biologically responsive dose (BRD), for each patient, was calculated in a standard way for early reacting tissues, tumour response and late reacting tissues. BRD values for each patients, for ExRT was calculated using the equation of multiple component (MC) model for fractionated irradiation6,7.

BRDebrt= D exp(bd)                                               (1)

Where 'b' is a tissue specific constant, D the total dose delivered in 'n' number of fractions with 'd' dose delivered in 'n' number of fractions with 'd' dose per fraction. The BRD values for ICRT was calculated using the equation of the MC model for continuous irradiation (Table-2)5 and is given as.

BRDicrt = D exp(bDG)                                           (2)

Where D is the dose given in each intracavitory application and G is a factor that accounts for the simultaneous accumulation and repair of sublethal damage during intracavitory irradiation. In the equations of BRD the subscripts 'ebrt' and 'icrt' are added for ICRT and EBRT applications, respectively. The factor G is given by

G=(2/mT) [1-(1-e-mT)/(mT)]                                   (3)

In equation (3), T is the duration of the intracavitory irradiation in hours and m=0.693/T1/2. Here   T1/2 is the half time repair of sublenthal damage.

Table - 2: Treatment protocol for ICRT and corresponding BRD values at point 'A'.



Total dose (Gy) at point 'A'/No. of fraction

Dose rate at point 'A' (Gy/hr)

                                                                                  BRD(Gy) values at point A

Early effects


   Late effects







Group I. Early cases
















Group I Advanced cases
















Group II  Early cases
















Group II Advanced cases



















Table-3: Total BRD Values at point A from EBRT and ICRT protocols.



    Early effects


    Late effects
















Early cases

78.27-78.55Gy (Ave 78.41Gy)

105.43-106.36Gy (Ave 105.89Gy)

76.11-76.34Gy (Ave 76.23Gy)

97.54-98.25Gy (Ave 97.89Gy)

150.99-153.53Gy (Ave 152.26Gy)

220.97-226.27Gy (Ave 223.62Gy)

Advanced cases

85.90-86.04Gy (Ave 85.97Gy)

99.48-99.94Gy (Ave 99.71Gy)

83.66-83.77Gy (Ave 83.72Gy)

94.37-94.72Gy (Ave 94.55Gy)

134.47-135.77Gy (Ave 135.11Gy)

169.46-172.11Gy (Ave 170.78Gy)








Early cases

82.09-82.41Gy (Ave 82.25Gy)

109.07-110.13Gy (Ave 109.60Gy)

79.98-80.24Gy (Ave 80.11Gy)


(Ave 101.75Gy)

152.02-154.79Gy (Ave 153.41Gy)

219.07-224.71Gy (Ave 221.89Gy)

Advanced cases

87.81-87.97Gy (Ave 87.89Gy)

101.30-101.83Gy (Ave 101.56Gy)

85.59-85.72Gy (Ave 85.66Gy)

96.27-96.68Gy (Ave 96.47Gy)

134.99-136.37Gy (Ave 135.68Gy)

168.51-171.33Gy (Ave 169.92Gy)




Table 4: clinically observed and theoretically predicted changes in early and late effects of group 1 and group 2 patients.


            Early effects

Predicted change

               Late effects

Predicted change






Clinically observed change





Clinically observed changes

μ =0.7h-1

μ =0.46h-1

Early cases

14.29% (2/14)

18.75% (3/16)




7.14% (1/14)

6.25% (1/16)




Advance cases

17.14% (6/35)

18.18% (8/44)




11.43% (4/35)

20.45% (9/44)




Total cases

16.33% (8/49)

18.33% (11/60)




10.20% (5/49)

16.67% (10/60)










In the calculations of BRD, the values of b=0.08, 0.2 and 0.067 Gy-1, for early reacting, late reacting tissues and tumours have been assumed5 respectively. The values of repair constant, i.e. m=1.4 and 0.46h-1 (T1/2=0.5 and 1.5h) for early reacting tissues/tumours, and m=0.7 and 0.46h-1 (T1/2=1.0 and1.5h) for late reacting tissues were used5. The effective BRD was computed by adding BRDebrt and BRDicrt for individual patient.


Only 40 and 60 patients were on regular follow up for 2 to 3 years respectively in group first and second. All the patients had mild diarrhea during external irradiation. Only 16.3% and 18.3% patients had developed mild bladder and bowel complications within one to two month after completion of treatment in group -I and II patients respectively, which were managed on outdoor basis. There were 10.20% and 16.67% patients, of group-I and -II respectively, who developed late complications after six month of the completion of treatment (Table-4). Treatment protocols and clinically observed and radiobiologically predicted results are shown in Tables 1-4.

Table-I enlists a common treatment protocol for external beam radiation therapy (EBRT) employed in both the patient groups, with the corresponding BDR values for early / late reacting tissues and tumour response. In the patients of early stages, the effective dose per fraction, at point A was 0.5 Gy due to midline shielding and in advanced cases it was 1.8Gy. The BRD, at point A, from EBRT, for early reacting tissues and tumours are approximately equal, while it is higher for late reacting tissues than that for early reacting tissues and tumours.

The treatment protocols for ICRT employed in the group -I and -II with a dose rate correction factors of 20% and 14.5%, respectively, to get equivalent biological effect to that of the Manchester schedule and corresponding BRD values are given in Table -2. The effective BRD is the sum of the BRDs delivered by EBRT and ICRT, for both the groups at point A and enlisted in Table- 3. In the first group, 14.29% and 17.14% patients of early and advanced stages, respectively, and in the second group, 18.75% and 18.18% patients of early and advanced stages, respectively, have developed acute reactions in the form of mild to moderate degree of diarrhea, acute cystitis, proctitis and abdominal cramps (Table -4). The overall early effects observed in two groups were 16.33% and 18.33% respectively (Table 4). Only 10.20% and 16.67% of the patients in group-I  and -II, respectively, have developed late effects. The two year local control in group-I and -II were about 85.7% and 93.75% of the patients of early stages, and 74.28% and 81.82% of the patients of advanced stage (Table -5).

Table-5: Clinically observed and theoretically predicted changes in local tumour control for 2 years.


Group -I

Group II

% observed change

%predicted change




Early cases

85.70% (12/14)






Advanced cases

74.28% (26/35)






Total cases

77.55% (38/49)








A comparison of the early effects in both the groups reveals that there was an increase of about 4.46%, from 14.29% to 18.75%, in early effects in the patients of early stages, while these were increased by 1.04%, from 17.14% to 18.18%, in the patients of advanced stages. In total patients there was an average increases in early effects of about 2.00%. The MC model predicts an increase, in these effects, of about 3.5% and 2.68% in the patients for m=1.4 and 0.46h-1 respectively, in total patients when dose rate correction factor was changed from 20% to 14.5%. In the patients of group-II, 6.47% more patient had developed late complications than that of the group-I. While MC model predicts an increase of 0.60%, for m=0.7h-1, and a decrease of 0.66%m for m=0.46%h-1, in late effects in group -II patients which were not significantly different than what have been observed clinically (Table -4). The difference in clinically observed and theoretically predicted early and late effects, in both the groups of the patients, were not statistically significant (p>0.5).

The local tumour control was increased marginally in second group of the patient, where total ICRT dose was adjusted by a dose rate correction factor of 14.5%, instead of 20% applied in group -I, thus about 3-6% higher dose was delivered to point 'A'. The increased two year tumour control in second group is not statistically significant than the predicted increase by MC model (p>0.5).

To find out the biological equivalent dose, for higher dose rates, to that of the Manchester schedule, the MC model has been applied. For these treatment schedules, employed in group -I and -II, the MC model advocates correction factors as shown in Table -6. For dose rates of 1.78 Gy/hr (1.76-1.80 Gy/hr) and 1.64 Gy/hr (1.62-1.66Gy/hr) to get equivalent early effects/tumour control. The predicted dose rate correction factors, for above-said dose rates for equivalent late effects, are quite higher than what was being used generally in these dose rates.

The dose rate correction factors, applied in group -I and -II, fall in the range of theoretically derived correction factors, for m=1.2 and 1.4h-1, to get equivalent early effects and tumour control. These are very low than that derived for late effects.

Comparison of the applied dose rate correction factors, in group -I and -II, and theoretically predicted correction factors, reveals that the correction factors applied in these patient are adequate but lower than what generally being applied in clinical practice. Since total number of patients, in this trial, was very less who were on regular followed up for 3 years, hence a good statistical analysis could not be done which is the limitation of this study.


Table 6: Correction factors for group -I and -II patients predicted by MC model for different μs.

Values of μ/ hour

Equivalent early effects

Equivalent Tumour control


Group -I


































It can be seen that the clinically observed early effects and tumour control are equivalent to that predicted by MC model, of the value of m has been chosen close to 1.4h-1. The clinically observed late effects, in this trial, were significantly higher in group -II than group -I, which indicates that the change in late effects was much different than the predicted ones. On the other hand the predicted late effects, in this trial, are very higher than that of the Manchester schedule. Anatomical structure of the pelvis indicates that late reacting organs in the vicinity of the uterine cervix are namely rectum and bladder. The dose rate in the tissue decreases exponentially. Hence at rectum and bladder the dose rate would be quite lower than that at the point A. therefore, the late effects are lower at rectum and bladder. In our earlier study4 which was carried out in CHRI, Gawalior, India, during the same period of this study, we have done rectal and bladder dosimetry of the patients undergoing intracavitory therapy, where the dose at ICRU reference points of these organs was less than 60% of that was delivered to point 'A'. Only few percent of the patients were found to received dose between 60-70% at ICRU reference points of these organs than that was delivered to point A. the average dose to whole of the organ was very less in compare to the total dose to point A. with the use of the results of this dosimetric study in the computation of late effects of these organs indicate that the average BRD, for two groups of the patients, were very less than the BRD delivered in conventional fractionation schedule of 50Gy/2Gy/5wk which was considered to be an upper tolerance limits of rectum and bladder. Hence the late effects, in both the groups, were comparable what actually we got in this study. It is advisable that at the time of prediction of late effects of late reacting tissues, the dose rate at the organ should be used, not the dose rate at point A, otherwise it would lead to an inaccuracy. The dose rate correction factor should be applied with respect to either early effects or tumour control.

It can be concluded from this study that the MC model is an appropriate radiobiological model, which can effectively used to predicate the effects of clinical trials with a fairly accurate outcome. During the calculation of the effects of a particular tissue or organ, care should be taken in the selection of the parameters of the MC model.


We would like to express our thanks to Dr.S.C.Sharma, Head of Radiotherapy Department and  Drs. F.D.Patel, D.P.Singh, Sushmita Ghoshal and Sushil Beriwal for their valuable comments and suggestion given during this work. We are also very much grateful to Mr. Arun Singh Kehwar S/O Dr. T. S. Kehwar, who has used his skills and taken lot of pain in the typing and preparation of the text.


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