Biomedical subjects
Publications and source records attributed to R G Dale.
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The role of low dose rate (LDR) intracavitary radiotherapy in the management of carcinoma of the uterine cervix is well established. However, there are selected groups of patients in whom high dose rate (HDR) intracavitary radiotherapy may have particular advantages. A case report of a patient with carcinoma of the cervix who received both LDR and HDR intracavitary radiotherapy is presented. A comparison of the normal tissue doses produced by the two forms of brachytherapy is made. The choice of dose for the HDR treatment was calculated using standard linear quadratic isoeffect equations. The relative clinical merits of LDR and HDR treatments in gynaecological cancer are discussed.
The rate of loss of tumour control (dP/dt) with extension of treatment time is analysed to assess the relative contributions of radiobiological parameters (radiosensitivity, clonogen doubling time, clonogen numbers and fractionation schedule) on such loss. Linear quadratic modelling and Poisson statistics are used to study individual tumour responses. A heterogeneous tumour population is constructed by the use of random sampling techniques to allow for variations in intrinsic radiosensitivity and clonogen doubling times. Average tumour control probability is calculated for this population for two different fractionation schedules (60 Gy in 30 fractions and 50 Gy in 15 fractions), each given over 15-60 days. The magnitude of dP/dt will depend upon the tumour cure probability (P): the loss of control will be most significant for tumours which have a cure of 37% when the Poisson survival model is used. The analysis suggests that compensation for short unscheduled treatment gaps (e.g. by increasing the total dose or rescheduling with use of weekend treatment sessions) may only be required for difficult tumours (i.e. radioresistant and/or with short clonogen doubling times). Where pre-treatment clonogen numbers are relatively low as in small volume tumours or after surgical debulking, the model predicts that correction for short treatment gaps is probably not required if the average effective clonogen doubling times are longer than 5 days. Different dose-time-fractionation schedules, even though producing similar overall cure rates in clinical practice, may actually be achieving cures in different subpopulations within a population of tumours, since the value of dP/dt in each individual tumour will depend upon the set of radiobiological parameters given above. For a hypothetical randomly selected heterogeneous tumour population the predicted rates of loss of tumour control produced by an extension in treatment time are 0.9 and 1.1% per day, respectively, for the above fractionation schedules. These values are close to those reported in the clinical literature for the first 2 weeks of treatment prolongation (1-2% per day for squamous cell carcinomas). The Poisson method, when combined with random sampling techniques, consequently provides realistic data. Modelling of this clinical problem provides an insight into how tumour sub-populations, each characterized by its own set of radiobiological parameters, can influence the overall rate of loss of tumour control in a heterogeneous population. Random sampling techniques should be considered as necessary precursors for the assessment of the choices of dose-fractionation in future clinical trials particularly when more precise data regarding the radiobiological parameters and their statistical variations become available.
A method is described for incorporating a variable cell loss factor (phi) within the linear-quadratic (LQ) model. By allowing for a progressive reduction in phi as treatment progresses, the revised model behaves in a way which is consistent with the apparent presence of accelerated tumour repopulation during fractionated radiotherapy. Predictions based on a slowing of the cell loss process, rather than a true increase in clonogen proliferation rate, are consistent with the phenomenon of 'unmasking' of potential doubling time described by Fowler (Fowler, J.F. Rapid repopulation in radiotherapy: a debate on mechanism. Radiother Oncol 24: 125, 1992). An optional time delay factor may be included, to allow for the fact that progressive reduction in cell loss may not begin until part of the treatment has been delivered. The model provides a description of the manner in which tumour control doses are likely to increase as overall treatment time is increased.
The linear quadratic equation for fractionated radiotherapy has already been adapted to include a time factor for tumour repopulation: loge cell kill (E) is given as a function of dose per fraction (d), number of fractions (n), overall treatment time (T) and the clonogen doubling time (Tp). By incorporating a normal tissue isoeffect and replacing the relationship between T and n by a function f, the equation for E can be rewritten as a more complex function of d. In this form, E and d are continuous variables so that the dose per fraction (d') required to produce maximum values of E for isoeffective late normal tissue effects can be found by differential calculus. The derived equation takes the form (beta kTp-alpha Tp)d2 + 1.386fd + 0.693fk = 0 and when solved for d provides a direct estimation of the optimum dose per fraction. Where normal tissue sparing is possible and the tumour dose z is related to the normal tissue dose d, the optimum dose per fraction z' can be found by solving the equation (beta kTp-alpha gTp)z2 + 1.386fgz + 0.693fk = 0 The results show that a critical minimum dose per fraction is required to counteract rapid tumour clonogen repopulation in both conventional and accelerated radiotherapy. The calculus method is reasonably accurate for larger fraction numbers, when clonogen doubling times are 3.5 days or longer and for conventional radiotherapy given 5 days per week. The model is even more accurate for accelerated hyperfractionated radiotherapy providing that there is complete repair between successive fractions. Where greater normal tissue sparing is possible, as with focal teletherapy methods and brachytherapy, higher tumour doses per fraction can be used to increase further the tumour cell kill without exceeding normal tissue tolerance. These predicted doses per fraction are consistent with clinical experience when the given constraints in terms of frequency of treatment are considered. The model described can be used for tumours in which repopulation occurs at a constant rate throughout treatment. For tumours in which accelerated repopulation occurs, the optimum dose per fraction can be separately calculated for the initial phase of slow repopulation (for which very small doses per fraction are optimal) and also for the second phase of rapid repopulation (for which either accelerated hyperfractionated treatments or hypofractionated focal methods of treatment would be appropriate). The limitations of the model are fully discussed including the need for accurate radiobiological predictive assays. In the future such assays of pre-treatment doubling times and tumour cell radiosensitivities could be used to determine reasonable ranges for the optimum dose per fraction in experimental tumours and subsequently in clinical trails. This approach could produce major improvements in the therapeutic potential of radiotherapy.
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 K/z, 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.
A tumour shrinkage factor is incorporated into previously derived linear-quadratic (LQ) formulae which allowed radiobiological assessment of the efficacy of permanently implanted radionuclides. The new formulations relate the biologically effective dose (BED) to radionuclide half-life, recovery half-life, tumour radiosensitivity, potential doubling time and linear shrinkage rate. Specific attention has been given to the following radionuclides: gold-198 (half-life, 2.7 days), palladium-103 (half-life, 17 days), ytterbium-169 (half-life, 32 days) and iodine-125 (half-life, 60 days). For each nuclide the log cell kill resulting from typically prescribed doses was calculated for a range of tumour clonogen doubling times at various radiosensitivities and linear shrinkage rates. It is shown that even relatively modest shrinkage rates are capable of enhancing the clinical potential of the longer-lived nuclides. However, even though the effect of tumour shrinkage is minimal in the case of gold-198, for fast growing and/or insensitive tumours there are fewer radiobiological uncertainties associated with the use of this nuclide. The revised equations may also have applications in certain types of biologically targeted radiotherapy.
The adaptation of the linear-quadratic model to allow for the effect of tumour regression and clonogen repopulation between initial teletherapy and subsequent brachytherapy has been extended to include the geometrical conditions encountered in intraluminal and intracavitary brachytherapy. For a radiation line source placed at the centre of a lumen or cavity, regression of any endoluminal tumour towards its mural origin will not result in any change in the minimum brachytherapy-tumour dose with time. In contrast, regression of transmural tumour will cause a potentially advantageous increase in the minimum brachytherapy-tumour dose with time. The latter effect will be opposed by tumour clonogen repopulation. The log(e) cell kill due to brachytherapy has been calculated for tumours of diameters 2, 4 and 6 cm at completion of teletherapy. The centres of the tumours were assumed to be at distances of 0, 1 and 2 cm from the radiation source. Tumour linear regression rates (lambda) ranging from 0.025 to 0.25 per week and tumour clonogen doubling times (Tp) of 2.5, 5 and 15 days were used in the calculations. The results demonstrate the critical importance of the distance of the tumour centre from the line source as well as the influence of tumour diameter, lambda and Tp. In some instances, both maximum and minimum values of log(e) cell kill occur. Calculations of tumour cure probabilities reveal that these variations in log(e) cell kill predicted by the model can produce highly significant differences in tumour control rates. Where the relevant parameters can be assessed directly or estimated from previous experience, the model provides a basis for the design of future intraluminal or intracavitary brachytherapy protocols.
There are, as yet, no standard radiobiological methods for devising compensation for unscheduled interruptions to fractionated radiotherapy. For the foreseeable future it is likely that the concept of biologically effective dose (BED) will play an important role in the intercomparison of treatment regimes, and in the examination of the options available for dealing with unscheduled treatment interruptions. However, comparison of the BEDs associated with different treatment options does not provide an intuitively obvious indication of the magnitude of any associated differences in biological effect--an important consideration in the case of those treatments which are designed to deliver near-tolerance doses. This article reviews the implications which derive from this complication, and discusses the desirable properties of possible "one-number" treatment scoring systems which could utilize the BEDs of both the tumour and the critical normal tissue. One possible form of such a scoring parameter is suggested, and applied to some clinical examples. No special "robustness" is claimed for the proposed scoring system, but the method nevertheless allows the ranking of treatment options such that the least satisfactory may be identified and rejected.
A questionnaire was sent to 50 departments of clinical oncology in the UK in September 1991. The aim was to determine the range of external beam and brachytherapy techniques employed at that time in the radical treatment of carcinoma of the cervix. Replies were received from 35 centres. This paper summarizes the preliminary findings of the study. Low dose rate (LDR) brachytherapy techniques predominated (34/35 = 97%) but 41% of departments (13/32) had future plans for the use of high dose rate (HDR) equipment. For low bulk (Stage I-II) carcinoma of the cervix, there was no detectable association between the total brachytherapy dose prescribed and the brachytherapy dose rate. In bulky (Stage I-II) carcinoma of the cervix treated by initial open teletherapy (without shielding), there was a statistically significant reduction in the prescribed brachytherapy dose with increasing dose rate. There was considerable variation between centres in the measurement or estimation of normal tissue doses during brachytherapy. The range of techniques used and the variation in expected complication rates should be closely monitored via medical audit and a further follow-up questionnaire may reveal important changes.
The linear-quadratic (LQ) model is useful in the radiobiological assessment of a wide variety of radiotherapy treatment techniques, not being confined to analysis of fractionated treatments alone. The model uses parameters that must be separately specified for tumours and dose-limiting normal tissues, and may therefore be used to help identify treatments that are most likely to maximise tumour cell kill while minimising the risk of severe normal-tissue damage. Additionally, the model is capable of making tentative allowance for the tumour repopulation that can occur during extended treatments. Intercomparisons between different types of treatment are made through the concept of the Extrapolated Response Dose (ERD). The ERD is calculated for each critical tissue and takes account of both the radiobiological parameters and the dose/time pattern of radiation delivery. Known tolerance doses for specified organs may be expressed as an ERDtolerance value, and, if a proposed 'new' treatment is to be successful, its associated ERD value must not exceed ERDtolerance. Examples of this procedure are given in this paper. It is particularly important that medical physicists fully appreciate the scope and limitations of LQ equations, as the analysis of radiobiology problems using the model often requires a degree of mathematical understanding that clinicians may not possess.
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Ytterbium 169 (half-life 32 days; mean gamma emission 93 keV, after excluding photons of energy less than 10 keV) is a radionuclide with interesting potential for brachytherapy applications. Although not yet commercially available, its possible application as a clinical radionuclide is currently being considered by Amersham International. This article presents an assessment of some properties of the nuclide that may be clinically relevant. Use is made of some new ideas that allow quantification of the likely dose homogeneity that can be obtained in a brachytherapy distribution, and in this context ytterbium 169 is shown to be superior to some currently available brachytherapy nuclides. The assessment also uses recent extensions to the linear-quadratic model to consider the likely radiobiological implications associated with the use of the nuclide. From this it is suggested that the main potential for ytterbium 169 would be as a source that may be re-used for a number of short-term applications, rather than as a permanently implantable nuclide.
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.
Anderson has proposed an analytical method for deriving volume-dose histograms relating to three-dimensional brachytherapy distributions. Because the mathematical transformation allows the otherwise dominant effects of the inverse-square fall-off about individual sources to be effectively suppressed, the resulting histograms provide the potential for visually and numerically assessing the overall quality of a brachytherapy treatment. In this paper the Anderson equations have been combined with the radial-dose polynomials of Dale, which are applicable to a number of tissue/nuclide combinations, and the predictions of the combined formalism have been used to further investigate the physical aspects of brachytherapy dosimetry. The problems associated with the dosimetry of low-energy gamma-emitters such as 125I are once again highlighted, as are the potential advantages of using a radionuclide with an intermediate gamma-ray energy.
Using commonly assumed alpha/beta ratios for tumours and late-reacting tissues, the linear-quadratic (LQ) model has been used to compare low dose-rate (LDR) gynaecological treatment with high dose-rate (HDR) techniques given in small fraction numbers. Even in the absence of relatively favourable tissue recovery constants (mu values) it is shown that, provided a modest extra amount of geometrical sparing of critical tissues is available (by means of spacing or shielding), HDR treatment in a small number of fractions may be used in place of an LDR regime without loss of therapeutic ratio. This general result, although not universally true, does indicate that HDR treatment delivered in a small number of fractions may be more feasible than is sometimes thought. These findings do not contradict currently accepted radiobiological philosophy, which cautions against the use of small numbers of high-dose fractions. Primarily they serve to emphasize the importance of the recommendations of the ICRU (1985), which stress the need to consider the complete time-dose pattern of radiation delivery to all the critical tissues in an intracavitary treatment.
Tumour proliferation effects can be tentatively quantified in the linear-quadratic (LQ) method by the incorporation of a time-dependent factor, the magnitude of which is related both to the value of alpha in the tumour alpha/beta ratio, and to the tumour doubling time. The method, the principle of which has been suggested by a number of other workers for use in fractionated therapy, is here applied to both fractionated and protracted radiotherapy treatments, and examples of its uses are given. By assuming that repopulation of late-responding tissues is insignificant during normal treatment regimes it is possible to use the method to assess the broader implications for treatment strategies in terms of the behaviour of the Extrapolated Response Dose (ERD). Although the numerical credibility of the analysis used here depends on the reliability of the LQ model, and on the assumption that the rate of repopulation is constant throughout treatment, the predictions are consistent with other lines of reasoning which point to the advantages of accelerated hyperfractionation. In particular, it is demonstrated that accelerated fractionation represents a relatively "forgiving" treatment which enables tumours of a variety of sensitivities and clonogenic growth rates to be treated moderately successfully, even though the critical cellular parameters may not be known in individual cases. The analysis also suggests that tumours which combine low intrinsic sensitivity with a very short doubling time might be better controlled by low dose-rate continuous therapy than by almost any form of accelerated hyperfractionation.
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