Clinical Investigations
A simple method of obtaining equivalent doses for use in HDR brachytherapy

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Abstract

Purpose: To develop a simple program that can be easily used by clinicians to calculate the tumor and late tissue equivalent doses (as if given in 2 Gy/day fractions) for different high-dose-rate (HDR) brachytherapy regimens. The program should take into account the normal tissue sparing effect of brachytherapy.

Methods and Materials: Using Microsoft Excel, a program was developed incorporating the linear-quadratic (LQ) formula to calculate the biologically equivalent dose (BED). To express the BED in terms more familiar to all clinicians, it was reconverted to equivalent doses as if given as fractionated irradiation at 2 Gy/fraction. Since doses given to normal tissues in HDR brachytherapy treatments are different from those given to tumor, a normal tissue dose modifying factor (DMF) was applied in this spreadsheet (depending on the anticipated dose to normal tissue) to obtain more realistic equivalent normal tissue effects.

Results: The spreadsheet program created requires the clinician to enter only the external beam total dose and dose/fraction, HDR dose, and the number of HDR fractions. It automatically calculates the equivalent doses for tumor and normal tissue effects, respectively. Generally, the DMF applied is < 1 since the doses to normal tissues are less than the doses to the tumor. However, in certain circumstances, a DMF of > 1 may need to be applied if the dose to critical normal tissues is higher than the dose to tumor. Additionally, the α/β ratios for tumor and normal tissues can be changed from their default values of 10 Gy and 3 Gy, respectively. This program has been used to determine HDR doses needed for treatment of cancers of the cervix, prostate, and other organs. It can also been used to predict the late normal tissue effects, alerting the clinician to the possibility of undue morbidity of a new HDR regimen.

Conclusion: A simple Excel spreadsheet program has been developed to assist clinicians to easily calculate equivalent doses to be used in HDR brachytherapy regimens. The novelty of this program is that the equivalent doses are expressed as if given at 2 Gy per fraction rather than as BED values and a more realistic equivalent normal tissue effect is obtained by applying a DMF. Its ease of use should promote the use of LQ radiobiological modeling to determine doses to be used for HDR brachytherapy. The program is to be used judiciously as a guide only and should be correlated with clinical outcome.

Introduction

Most radiation oncologists are familiar with low-dose-rate (LDR) brachytherapy. Recently, there has been a trend towards increased use of high-dose-rate (HDR) brachytherapy due to its advantages, namely that it eliminates radiation exposure to caregivers, requires only short treatment times, and that its dose distribution can be optimized by varying the dwell times. HDR is generally given as fractionated treatments to decrease normal tissue toxicity. The dose effect relationship in radiation therapy is not linear, but may be assumed to follow a linear-quadratic (LQ) function (1). Hence, doses from different treatment modalities cannot be added linearly to determine the combined effect. Many radiation oncologists are not very familiar with the fractionation schemes to be used in HDR brachytherapy. Further, there is a marked difference between the biological effects in the tumor and those in late reacting normal tissue (1). Besides, patients are often treated with external beam radiotherapy combined with HDR brachytherapy, which poses the added challenge of determining the combined effect of the two treatments.

One way to calculate the biologically equivalent doses (BEDs) of different dose fractionation schemes is to use the LQ equation (eq. 1 in Appendix 1). In this equation, the α/β ratio is usually taken to be 10 Gy for tumor/early effects and 3 Gy for late effects (2). The concept of LQ modeling is familiar to most radiation oncologists. However, this calculation is cumbersome, and the resultant BED values are not familiar to the clinicians. Further, it does not take into consideration that, in brachytherapy, doses to normal tissues are generally lower than doses to tumor tissues. For these reasons, radiobiological modeling is not widely used on a routine basis. However, simplifying the calculations for the LQ radiobiological model, applying a dose modifying factor (DMF) to take into consideration that the doses to normal tissues are different from the doses to the tumor, and expressing the results in terms of equivalent doses given at 2 Gy per day rather than as the BED would make it more likely that the LQ model would be used clinically.

With these considerations in mind, we developed a program that could be run on commonly available personal computers. This program quickly performs the calculations and express the results in clinically familiar equivalent doses given at 2 Gy per day, applying a DMF. The details of all calculations and formulations used in this article are explained in Appendix 1. The reader can program these calculations into an Excel spreadsheet; alternatively, a computer disk with this program can be made available to those requesting it.

Section snippets

Methods and materials

Excel program was selected because it is a commonly available spreadsheet for personal computers and is accessible to most clinicians. Inputs to this spreadsheet fall into two categories:

  • 1.

    Parameters affecting tissue characteristics and equivalence calculations: α/β ratio for early and late effects, dose per fraction for equivalence calculation, and normal tissue dose modifying factor for HDR brachytherapy (DMF). The default values of these parameters are set as follows: α/β ratio (late) = 3 Gy,

Results

Following are some examples of the use of this program.

Example 1. The Radiation Therapy Oncology Group (RTOG) wished to develop a protocol that would allow the use of HDR brachytherapy to treat cancer of the cervix. Various doses of pelvic EBRT were to be allowed. We needed to determine the HDR dose per fraction required to deliver an equivalent tumor dose of about 85 Gy while keeping the equivalent dose for late effects below 75 Gy. The clinicians entered the various allowable pelvic EBRT

Discussion

Various empirical formulas, such as the nominal standard dose (NSD), cumulative radiation effect (CRE), and time-dose-fractionation (TDF), have been used to determine the equivalent doses of various dose fractionation schemes in the past (5). The LQ formula currently used is considered a better model because it is based on the radiation effect in deoxyribonucleic acid (DNA) and can account for differences between tumor and normal tissue response 1, 2, 6, 7, 8, 9, 10, 11. The LQ equation can be

Summary

A simple Excel spreadsheet program has been developed to assist clinicians to easily calculate equivalent doses to be used in HDR brachytherapy regimens. The novelty of this program is that the equivalent doses are expressed as if given at 2 Gy per fraction rather than as BED values, and a more realistic equivalent normal tissue effect is obtained by applying a DMF. Its ease of use should promote the use of LQ radiobiological modeling to determine HDR brachytherapy doses. The program is to be

Acknowledgements

The authors wish to express their gratitude to David Carpenter for editorial assistance. This study was supported in part by Grant 5P30CS16058 from the National Cancer Institute, Bethesda, MD.

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