Roger G. Dale

The assessment of RBE effects using the concept of biologically effective dose.

PURPOSE To modify existing linear-quadratic (LQ) equations in order to take account of relative biological effectiveness (RBE) using the concept of biologically effective dose (BED). METHODS AND MATERIALS Clinically useful forms of the LQ model have been modified to incorporate RBE effects in such a way as to allow comparison between high- and low-LET (linear energy transfer) radiations in terms of similar biological dose units. The new parameter in the formulation is RBEM, the intrinsic (or maximum) RBE at zero dose. The principal assumption (following Kellerer and Rossi; ref. 1) is that high-LET radiation modifies the alpha-coefficient of damage while leaving the beta-coefficient unaltered. RESULTS The equations allow a quantitative estimation of how the apparent RBE will change with changes in dose/fraction or dose-rate and of how the magnitude and rate of change is governed by the low-LET alpha/beta ratio of the irradiated tissue. The modifications are applicable to all types of radiotherapy (fractionated, continuous low dose-rate, therapy with decaying sources, etc.). In cases where the normal tissue RBEM is greater than that for the tumor, the revised formulation helps explain why there will be situations where therapeutic index will be adversely affected by use of high-LET radiation. Such clinical advantages as have been observed are more likely to result from favorable geometrical sparing of critical normal tissues and/or the fact that slowly growing tumors may have alpha/beta values more typical of late-responding normal tissues. CONCLUSIONS The incorporation of RBE into existing LQ methodology allows quantitative assessment of clinical applications of high-LET radiations via an examination of the associated BEDs. On the basis of such assessments high-LET radiations are shown to confer few advantages.

Radiobiologically based assessments of the net costs of fractionated focal radiotherapy

PURPOSE To assess the potential changes in the net costs of focal radiotherapy techniques at differing doses per fraction and interfraction intervals. METHODS Linear quadratic radiobiological modeling is used with appropriate variations in the radiosensitivity and tumor cell proliferation parameters. The notional cost of treatment is calculated from the number of fractions, cost per fraction and the cost of treatment failure, which is itself related to (1-TCP) where TCP is the tumor cure probability. Additional Monte Carlo calculations from ranges of radiobiological parameters have been used to simulate the cost of treatment of tumor populations. RESULTS The optimum dose per fraction (and optimum overall cost) for conventional (nonfocal) radiotherapy is generally at low doses of around 2 Gy per fraction. The use of hyperfractionated and accelerated radiotherapy in addition to focal radiotherapy techniques appear to be indicated for more radioresistant tumors and if tumor proliferation is extremely rapid, but the need for treatment acceleration is much reduced where effective focal techniques are used. CONCLUSIONS Radiobiological and economic modeling can be used to guide clinical choices of dose fractionation techniques providing the key radiobiological parameters are known or if the ranges of likely parameters in a tumor population are known. Focal radiotherapy, by the introduction of changes in the physical dose distribution, produces an upward shift in the optimum dose per fraction and a reduced dependency on overall treatment time.

Application of biological effective dose (BED) to estimate the duration of symptomatic relief and repopulation dose equivalent in palliative radiotherapy and chemotherapy

PURPOSE To investigate the potential for mathematic modeling in the assessment of symptom relief in palliative radiotherapy and cytotoxic chemotherapy. METHODS The linear quadratic model of radiation effect with the overall treatment time and the daily dose equivalent of repopulation is modified to include the regrowth time after completion of therapy. RESULTS The predicted times to restore the original tumor volumes after treatment are dependent on the biological effective dose (BED) delivered and the repopulation parameter (K); it is also possible to estimate K values from analysis of palliative treatment response durations. Hypofractionated radiotherapy given at a low total dose may produce long symptom relief in slow-growing tumors because of their low alpha/beta ratios (which confer high fraction sensitivity) and their slow regrowth rates. Cancers that have high alpha/beta ratios (which confer low fraction sensitivity), and that are expected to repopulate rapidly during therapy, are predicted to have short durations of symptom control. The BED concept can be used to estimate the equivalent dose of radiotherapy that will achieve the same duration of symptom relief as palliative chemotherapy. CONCLUSION Relatively simple radiobiologic modeling can be used to guide decision-making regarding the choice of the most appropriate palliative schedules and has important implications in the design of radiotherapy or chemotherapy clinical trials. The methods described provide a rationalization for treatment selection in a wide variety of tumors.

Inclusion of molecular biotherapies with radical radiotherapy: modeling of combined modality treatment schedules

PURPOSE The use of molecular biology based therapies concurrently with radical radiotherapy is likely to offer potential benefits, but there is relatively little use of classical radiobiology in the rationale for such applications. The biological mechanisms that govern the outcomes of radiotherapy need to be completely understood before rational application and optimization of such adjuvant biotherapies with radiotherapy. METHODS AND MATERIALS Existing biomathematical models of radiotherapy can be used to explore the possible impact of biotherapies that modify tumor proliferation rates and/or radiosensitivity parameters during radiotherapy. Equations that show how to incorporate biotherapies with the linear-quadratic model of radiation cell kill are presented. Also considered are changes in tumor physiology, such as improved blood flow with enhanced delivery of biotherapy to the tumor cells and accelerated clonogen repopulation during radiotherapy. Monte Carlo random sampling methods are used to simulate these effects in heterogenous tumor populations with variation in radiosensitivities, clonogen numbers, and doubling times, as well as variations in repopulation onset rates and in vascular perfusion rates with time. RESULTS The time onset and duration of exposure of each type of biotherapy during radical radiotherapy can influence the predicted tumor cure probabilities in subtle ways. In general, the efficacy of biotherapies that radiosensitize will depend upon the number of radiotherapy fractions that are sensitized and the change in blood flow with time during radiotherapy. Biotherapies that control repopulation will depend not only on the duration of exposure but also, where accelerated repopulation occurs, on the time at which biotherapy is initiated during radiotherapy. From the ranges of radiobiological parameters and biotherapy efficacies assumed for exploratory examples, large changes of tumor control probability (TCP) are encountered in individual tumors from the application of cytostatic therapy. There are predictions of smaller increments in TCP in heterogenous tumor populations from the application of cytostatic and radiosensitizing biotherapies in combination. CONCLUSIONS The exercises show how the scheduling of biotherapies may critically influence tumor cure probabilities in subtle ways and give considerable insight into the interacting biological mechanisms that influence these changes. Future therapeutic developments should be guided by these principles.

The effect of tumour shrinkage on biologically effective dose, and possible implications for fractionated high dose rate brachytherapy

Abstract A method for incorporating a tumour shrinkage factor into linear-quadratic (LQ) brachytherapy equations is proposed. When there is a significant degree of ongoing shrinkage throughout a course of brachytherapy, and when the sources are centrally situated within the tumour volume, the biologically effective dose (BED) to the tumour will be higher than that which is calculated with standard equations. Although the analytical method initially assumes that shrinkage is exponential with time, it is shown that the modified equations (for both high and low dose rate brachytherapy) are essentially analogous to existing BED equations, but with the addition of a simple linear time-dependent factor. In this article, which concentrates on the implications for fractionated high dose-rate brachytherapy, it is demonstrated that increasing the time interval between fractions will only improve the BED in some cases, the conditions for which may be identified in terms of the ratio Kz, where K is the daily dose required to combat tumour repopulation and z is the daily linear shrinkage rate. In the absence of predictive assay techniques, or where there is doubt as to whether or not the radiobiological conditions favour an increase in the interval between each dose delivery, relatively close spacing (i.e. acceleration) of brachytherapy fractions appears to be the most prudent option.