Comparison of the predictions of the LQ and CRE models for normal tissue damage due to biologically targeted radiotherapy with exponentially decaying dose rates

Biological equivalance of low dose rate to multifractionated high dose rate irradiations: investigations in mouse lip mucosa

BACKGROUND AND PURPOSE

The aim of this study was to evaluate the biological equivalence of continuous low dose rate (LDR) irradiations to multifractionated high dose rate (HDR) regimes. The applicability of the LQ model was analysed for fraction sizes and dose rates relevant for the clinic.

MATERIAL AND METHODS

Investigations were performed in mouse lip mucosa. HDR fractions were given in an overall treatment time ranging from 10 h to 3.5 days. The dose rate effect was analysed in the range of 84 to 0.76 Gy/h. For an assessment of biological equivalence in comparison to LDR, HDR irradiations have been performed in the same overall treatment time as the corresponding LDR regimes.

RESULTS

Recovery leads to sparing of radiation damage as the dose rate is reduced from 84 to 0.76 Gy/h (20.0 versus 45.7 Gy ED50). No significant additional sparing from 0.9 to 0.76 Gy/h could be demonstrated (44.9 versus 45.7 Gy ED50). Even 30 HDR fractions in 24 h were not sufficient to match the effect of LDR over the same time period (38.2 versus 41.1 Gy ED50). The present data give evidence for a bi-exponential repair process in mouse lip mucosa (T1/2 fast 27 min, T1/2 slow 150 min). Repair is dominated by the faster component (> 80%).

CONCLUSIONS

LDR is the most efficient way to deliver radiation if recovery is to be maximised and the overall time kept as short as possible. When used with realistic parameters the LQ model is capable of providing quantitative guidelines in areas of clinical interest.

Optimal scheduling of biologically targeted radiotherapy and total body irradiation with bone marrow rescue for the treatment of systemic malignant disease

A mathematical model analysis is used to address the question of optimal scheduling of combined treatments consisting of biologically targeted radiotherapy (BTR), total body irradiation (TBI), and bone marrow rescue. Radiation effects on normal tissue are described using an extension of the LQ model. Tumor effects are described using a simple model that allows for radiation-induced sterilization and exponential proliferation of tumor cells, a proportion of which completely escapes the effects of targeted radiotherapy. The effect on a tumor cell population of a set of treatment schedules, composed partly of targeted radiotherapy and partly of fractionated external beam irradiation, are calculated. Treatment schedules are chosen to be biologically equivalent, for a "late responding" organ, to a fractionated TBI schedule of 7 fractions of 2 Gy. The tumor effects of the treatment schedules depend on the specificity of targeting, represented by the ratio of initial dose-rate for the tumor cells to that in the dose-limiting organ, and the heterogeneity of targeting, represented by the proportion of tumor cells that escape irradiation by targeted radiotherapy. The main mechanism determining optimal combinations is an overkill of effectively targeted tumor cells. Treatment regiments consisting of targeted radiotherapy alone fail, due to the unimpeded growth of those tumor cells that escape targeted irradiation. Optimal schedules almost invariably consist of elements of both BTR and TBI. Although it is recognized that the model is simplistic in a number of respects, these findings provide support for the clinical use of integrated BTR, TBI, and bone marrow rescue for the treatment of systemic malignant disease.

The 1989 James Kirk memorial lecture. The potential for radiobiological modelling in radiotherapy treatment design

The application of the linear-quadratic (LQ) model to various types of fractionated radiotherapy is now well established, and has demonstrated ways in which treatment might be improved. Whilst attitudes to fractionated therapy are undergoing radical review, other aspects of radiotherapy are also moving through a period of significant change. In recent years there has been a growing interest in other, more complex techniques, e.g. the use of permanent implants of iodine-125 seeds, the use of more versatile brachytherapy units which may treat a variety of sites at a range of dose-rates, and the use of biologically targetted radionuclides. The quantitative radiobiological assessment of such treatments poses a number of new problems, a complete understanding of which may take some while to provide. In spite of current limitations the LQ model has, in its more general form, the potential to be applied to a wider variety of clinical circumstances than is sometimes appreciated. Additionally, although the model does not provide a rigorous description of all the underlying radiobiological phenomena which govern the outcome of radiation treatment, it does have the capacity (unlike previous models) to draw clearer distinctions between the various contributing processes, and to focus attention on those parameters which are most likely to govern radiotherapy.