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Time factors in larynx tumor radiotherapy: Lag times and intertumor heterogeneity in clinical datasets from four centers
Abstract
To use the time-dependent linear-quadratic model, both in the standard form and in a form modified to incorporate intertumor heterogeneity, in a reanalysis of 4 datasets for larynx tumor control, to provide more representative and direct estimates of the lag period, the time factor (lambda/alpha), and the clonogen population inactivation dose ([lnk]/alpha).
The data comprised 2,225 patients treated in Edinburgh (UK), Glasgow (UK), Manchester (UK), or Toronto (Canada), with tumor control assessed after at least 2 years. Heterogeneity in each series was taken into account using the coefficient of variation (CV) of the clonogen radiosensitivity (alpha). Maximum likelihood techniques were used to provide best estimates of the parameters, and also direct estimation of the more stable parameter ratios of interest.
The use of different heterogeneity factors for the different series allowed common dose/time parameters to be fitted across all four series in a way not possible using the standard model, enabling the inherent effect of heterogeneity in flattening dose-response curves and in reducing time factors to be separated from the underlying more-representative values. Radiosensitivity CVs were calculated to be 30% (Edinburgh), 36% (Glasgow), 40% (Manchester), and 71% (Toronto). The lag phase was 32 days (95% CL 20-38 days) which was longer than the value of 23 days (11-36 days) deduced using the standard model without the heterogeneity parameter. The time factor was 1.2 (0.8-2.2) Gy/day, again greater than the value of 0.80 (0.54-1.41) Gy/day derived using the standard model. Similar larger time factors and longer lag periods could be reproduced using the standard model either by using a parameterization based on parameter ratios, or by omitting the discordant Toronto data and refitting just the data from the three UK centers.
It was concluded that the heterogeneity model provides a better representation of the time factor for tumor control when data are analyzed comprising different stages of disease treated at different centers. The model allows different amounts of heterogeneity in different series, which tend to flatten dose-responses curves and reduce time factors, to be taken in to account. Also, direct maximum likelihood estimates can be made of the lag period, the time factor (lambda/alpha), and the fractionation sensitivity (beta/alpha), as well as the clonogen population inactivation dose (lnk)/alpha. Values of these parameter ratios are more robust and stable than the individual parameter values. The results of the present analysis using a total of 2,225 patients from four centers indicate that the average lag period may be somewhat longer and the average time factor somewhat greater (and the 95% confidence limits of the time factor exclude previous estimates), than the values deduced previously using simpler models and more diverse multi-center datasets.
... (D prolif ) j : 0.64 (adjusted for stage and subsite: 0.73) [22] K h : 0.35 [17]; 0.4 [0.74 as in Withers'88) [19]; 0.56 (as in Withers'88) [7]; >0.5 [26]; 0.5-0.6 [31]; 0.6-0.8 [25]; 0.8 [15] Tk c : Lag ≤ 3 weeks [31]; 20 days [25]; 32/34 days (***) [27] LRC a in T1-2N0 glottis cancer: Try to maintain OTT k < 40-47 days [10,[16][17][18]. In any case, avoid OTT k > 60 days [33]. ...
... In any case, avoid gaps ≥3 days for LRC a and OS d [12,28] (*) ↓ 0.6%/day and 4.2%/week LRC a in hypopharynx ± larynx patients. /˛i for hypopharynx, 0.3 Gy/d (D proliff , 0.25 Gy/d) [23] (**) ↓ LC p 0.9%/day for OTT k extension as a whole and 1.6% for gaps ≥ 3 days; /˛i, 1.76 or 2.69, depending on the mathematical model used [28] (***) /˛i 1.2 or 1.63, and Tk c , 32 or 34 days, when 4 or 3 centers, respectively, are analyzed [27] The hazard rate for LCR a failure ↑ 0.067%/day of interruption [18] One NS q study showed a ↓ 12%/week LRC a (as in Fowler'92) [19] NS q lag phase; however, best estimate of Tk c is 21 days [15] Table 2 details the daily and weekly loss of LRC, OS, and the dose/time factor; it also outlines a series of conclusions and recommendations summarized from the literature, as well as other relevant details (discussed below). These data were used to construct Fig. 1 using the horizontal axis as the date of publication of the original article (even when recalculated by others [see Table 2]). ...
... Therefore, we believe the CHART trial cannot be considered Significant or NS and excluded it from the analysis. Data from multicenter prospective randomized clinical trials [15] Data from 2 randomized trials from the British Institute of Radiology fractionation study [23] Prospective non-randomized single-arm study [46] SEER c -Medicare linked database analysis [55] Pooled-data reports [8,9,27,45] a RT, radiotherapy b NS, non-significant. c SEER: Surveillance, Epidemiology, and End Results. ...
Treatment delays in completing radiotherapy (RT) for many neoplasms are a major problem affecting treatment outcome, as increasingly shown in the literature. Overall treatment time (OTT) could be a critical predictor of local tumor control and/or survival. In an attempt to establish a protocol for managing delays during RT, especially for heavily overloaded units, we have extensively reviewed the available literature on head and neck cancer. We confirmed a large deleterious effect of prolonged OTT on both local control and survival of these patients.
... Since then, the existence of a lag period before the onset of accelerated repopulation has been extensively investigated from clinical data [65]. Estimates for the lag time are mostly in the range of 20-32 days [65,66]. Tarnawski et al [67] analysed similar data and found evidence for a lag period of at least 2 weeks to onset of tumour repopulation. ...
... Fowler and Harari [8] observed that a T pot close to 2 days gave the best fit to clinical data from the RTOG 90-03 fractionation trial if a50.35 Gy 21 . Roberts and Hendry [66] fitted a heterogeneity model to a large head and neck cancer dataset. These authors calculated l/a of 1.2 Gy, corresponding to T pot 51.9 days if a50.3 Gy 21 or 1.65 days if a50.35 Gy 21 , with a 32 day lag time. ...
There is often a considerable delay from initial tumour diagnosis to the start of radiotherapy treatment. This paper extends the calculations of a previous paper on the effects of delays before the initiation of radiotherapy treatment to include results from a variety of practical fractionation regimes for three different types of tumour: squamous cell carcinoma (head and neck), breast and prostate. The linear quadratic model of radiation effect, logarithmic tumour growth (coupled with delay times where relevant) and the Poisson model for tumour control probability (TCP) are used to calculate the change in TCP for delays between diagnosis and treatment. Within the limitations of radiobiological modelling, these data can be used to tentatively assess the interactions between delays, dose fractionation and TCP. The results show that delays in the start of radiotherapy treatment do have an adverse effect on tumour control for fast-growing tumours. For example, calculations predict a reduction in local tumour control of up to 1.5% per week's delay for head and neck cancers treated following surgery. In addition, there may be a variety of fractionation regimes that will yield very similar clinical results for each tumour type. It is shown theoretically that, for the tumour types considered here, it is possible to increase the dose per fraction and decrease the number of fractions while maintaining or increasing TCP relative to standard 2 Gy fractionation regimes, although there may be some advantage to using hyperfractionated regimes for head and neck cancers in order to reduce normal tissue effects.
... Thereby, additional dosing was required to counteract the cell proliferation in the prolonged radiation treatment to maintain the same tumor control rate. The kick-off time T k = 28 day according to [19] was used in the calculation. ...
... Thereby, additional dosing was required to counteract the cell proliferation in the prolonged radiation treatment to maintain the same tumor control rate. The kick-off time T k = 28 day according to [19] was used in the calculation. ...
... Refined versions of the model proposed solutions for accounting for heterogeneities in the dose distribution by dividing the tumor volume into subvolumes down to voxel size in which the dose and the radiation sensitivity were assumed to be constant [1][2][3]. The influence of heterogeneity in the intrinsic sensitivity of the cells to radiation within the tumor or from one tumor to another or of the number of clonogenic cells between tumors on the overall outcome was also theoretically explored by several authors [3][4][5][6][7][8][9][10][11][12]. Similar studies have been performed with computer simulations by Harting et al. [13]. ...
This present paper presents an analytical description and numerical simulations of the influence of macroscopic intercell dose variations and intercell sensitivity variations on the probability of controlling the tumour. Computer simulations of tumour control probability accounting for heterogeneity in dose and radiation sensitivity were performed. An analytical expression for tumor control probability accounting for heterogeneity in sensitivity was also proposed and validated against simulations. The results show good agreement between numerical simulations and the calculated TCP using the proposed analytical expression for the case of a heterogeneous dose and sensitivity distributions. When the intratumour variations of dose and sensitivity are taken into account, the total dose required for achieving the same level of control as for the case of homogeneous distribution is only slightly higher, the influence of the variations in the two factors taken into account being additive. The results of this study show that the interplay between cell or tumour variation in the sensitivity to radiation and the inherent heterogeneity in dose distribution is highly complex and therefore should be taken into account when predicting the outcome of a given treatment in terms of tumor control probability.
... Thereby, additional dosing was required to counteract the cell proliferation in the prolonged radiation treatment to maintain the same tumor control rate. The kick-off time T k = 28 day according to [19] was used in the calculation. ...
In vitro survival measurements using two human head-and-neck cancer (HNC) cell lines were performed. The specially designed split-dose surviving fraction was obtained and fitted to the linear-quadratic formalism. The repair halftime (Tr), the potential doubling time (Td), a/β and radiosensitivity a, were estimated. Other radiobiological models: EUD, BED, TCP, etc., were used to examine the potential treatment effectiveness of different IMRT techniques. Our data indicated the repair halftime of ~17 min based on two HNC cell lines. The combined a/β, a and Td are a/β = 8.1 ± 4.1 Gy, a = 0.22 ± 0.08 Gy-1, Td = 4.0 ± 1.8 day, respectively. The prolonged IMRT dose delivery for entire HNC treatment course could possibly result in the loss of biological effectiveness, i.e., the target EUDs decreased by 11% with fraction dose delivery time varying from 5 to 30 min. We determined the sublethal damage repair halftime and other radiobiological parameters for HNC cells, and to evaluate treatment effectiveness of the prolonged dose delivery times associated with different IMRT techniques. The estimated repair halftime for HNC is relatively short and may be comparable to the step-and-shoot IMRT fraction dose delivery time. The effectiveness of IMRT treatment may be improved by reducing the fraction delivery time for HNC treatment.
... This is calculated by adding the dose not given to the estimated dose lost due to prolongation of treatment. They use a value of 0.64 Gy/day for the additional dose needed per day of protraction to keep the same level of tumour control in head and neck carcinoma, although higher values have been reported [62]. ...
... But increasing fraction size, even very slightly, could lead to strong acute reactions, unless extra overall time was allowed, which would decrease tumour control by the equivalent of 1–2 Gy/day [29]. Finally, the maximum tumour EQD was calculated at the ''practical overall time'' for each schedule, using the tumour Tk of 21 days [46], and the resulting log 10 cell kill was estimated. ''Practical'' meant that Saturdays and Sundays were not allowed to be treatment days. ...
In 1989 the British Journal of Radiology published a review proposing the term biologically effective dose (BED), based on linear quadratic cell survival in radiobiology. It aimed to indicate quantitatively the biological effect of any radiotherapy treatment, taking account of changes in dose-per-fraction or dose rate, total dose and (the new factor) overall time. How has it done so far? Acceptable clinical results have been generally reported using BED, and it is in increasing use, although sometimes mistaken for "biologically equivalent dose", from which it differs by large factors, as explained here. The continuously bending nature of the linear quadratic curve has been questioned but BED has worked well for comparing treatments in many modalities, including some with large fractions. Two important improvements occurred in the BED formula. First, in 1999, high linear energy transfer (LET) radiation was included; second, in 2003, when time parameters for acute mucosal tolerance were proposed, optimum overall times could then be "triangulated" to optimise tumour BED and cell kill. This occurs only when both early and late BEDs meet their full constraints simultaneously. New methods of dose delivery (intensity modulated radiation therapy, stereotactic body radiation therapy, protons, tomotherapy, rapid arc and cyberknife) use a few large fractions and obviously oppose well-known fractionation schedules. Careful biological modelling is required to balance the differing trends of fraction size and local dose gradient, as explained in the discussion "How Fractionation Really Works". BED is now used for dose escalation studies, radiochemotherapy, brachytherapy, high-LET particle beams, radionuclide-targeted therapy, and for quantifying any treatments using ionising radiation.
... This is calculated by adding the dose not given to the estimated dose lost due to prolongation of treatment. They use a value of 0.64 Gy/day for the additional dose needed per day of protraction to keep the same level of tumour control in head and neck carcinoma, although higher values have been reported [62]. ...
To evaluate the compliance of the prescribed OTT in a normal clinical practice and to establish the incidence, duration and causes of unplanned interruptions of radiation therapy. To quantify the impact of an institutional policy to maintain the OTT counteracting some short interruptions by treating patients on Saturday morning.
The treatment charts of all new patients treated with curative intent in a period of one year were reviewed retrospectively. All treatments started on Monday or Tuesday and split-course was not used. The difference between the actual realized and the planned OTT was calculated as a measure of compliance. Recalculations of OTT were made to quantify the impact of compensating short gaps by treating patients on Saturday. The cause of interruption was also recorded and classified.
The charts of 478 consecutive patients treated with curative intent were reviewed. The overall incidence of unplanned interruptions was 76.6%. Public holidays and machine maintenance caused most of interruptions, and machine breakdown caused 13%. 17.9% of the interruptions were greater than 5 days and 5.6% greater than 10 days. Only 23.4% of patients finished their radiotherapy in the planned OTT (12.6% if no compensation on Saturday). 48.9% of head and neck cancer patients finished their treatment in the planned OTT (19.5% if no compensation on Saturday). The time in excess ranged up to 44 days, and the average time in excess was 3.3 days for the entire group (4.2 days if no compensation on Saturday). For head and neck cancer patients, the time in excess was 1.9 days (3.9 days if no compensation on Saturday).
This study has documented that the incidence and duration of unplanned interruptions of standard treatment schedules is a major problem in normal clinical practice. Most interruptions are short and due mainly to public holidays and machine maintenance and for these reasons they can be planned. In spite of the extra costs, counteracting some short interruptions by treating patients on Saturday is a good way to maintain the OTT without loss of local control.
... In recent years considerable progress has been made in understanding such influences, it now being possible to analyse conventional and other forms of radiotherapy in an increasingly reliable and quantitative manner, with the result that the ways in which treatment might be improved are becoming easier to identify (e.g. Jones et al., 1995;Roberts and Hendry, 1999;Jones andDale, 2000, 2007;Bentzen et al., 2003;Fowler, 2007). ...
Radiation therapy remains a very effective tool in the clinical management and cure of cancer and new techniques of radiation delivery continue to be developed. Of particular note is the growing world-wide interest in particle beam therapy (PBT) using protons or light ions. Such beams (particularly light ions) are associated with an increased relative biological effectiveness (RBE) which, when viewed alongside the more favourable physical distributions of radiation dose available with all forms of particle beams, makes them especially attractive for treating tumours which are associated with disappointing outcomes following conventional X-ray therapy. Although the large body of clinical experience already gained with conventional X-ray therapy will be of paramount importance in guiding the development of treatment programmes using particle beams, understanding and quantification of the RBE effects which are unique to the latter will also be essential. This is because the magnitude of RBE effect is not fixed for any one radiation/tissue combination but is subject to a number of other radiobiological influences. Such relationships may be quantified within the linear-quadratic radiobiological model, within which the associated concept of biologically effective dose (BED) provides a way of inter-comparing the overall biological impact of existing and projected treatments. This paper summarises the main features of RBE and BED, discusses the main quantitative implications for PBT and highlights why clear understanding of RBE effects will be essential to make best use of PBT. It also summarises other clinical applications where knowledge of and allowance for RBE effects is important and suggests that more needs to be done to allow safer practical applications.
... Although there are many biological indicators which are upregulated within hours or minutes of irradiation by a radiotherapy-fraction sized dose of irradiation, the gross clinical information, extracted by careful analysis of H&N tumor results, is that Tk is as long as 21 to 35 days (27,28). We are unlikely to have any better information until a series of clinical results are available with overall times spanning from 2 to 5 weeks. ...
Optimum fractionation in radiotherapy occurs when tumor control is improved without enhancement of complications. The main influence on choice of overall time, total dose and fraction size is biological: the proliferation status of tumors. For rapidly proliferating tumors, shorter schedules than 6 to 8 weeks are necessary. Optimum overall time is similar to Tk, the time after beginning cytotoxic treatment when rapid proliferation in tumors starts: 21 to 35 days in head and neck tumors. These, and non-small cell lung tumors, have a clonogenic cell doubling time during radiotherapy of about 3 days. New developments in designing optimum schedules for such tumors are presented: carefully regulated hypofractionation (CRH). For slowly proliferating tumors, especially prostate adenocarcinoma, intracellular repair is large, so larger doses per fraction will be necessary. New evidence is presented showing that their alpha/beta ratio may indeed be lower than 3 Gy. For an entirely different reason from that above, hypofractionation should be tested.
... Since then more sophisticated analyses of multi-centre data have shown that K values are likely to be higher than originally believed. Roberts and Hendry [15] have conducted a metaanalysis of larynx treatment results from Edinburgh, Glasgow, Manchester and Toronto, leading to an upwardly revised K estimate of 1.2 (95% CL 0.8-2.2) Gy day 1 . The results of the RTOG9003 head and neck trial [16] also lend support to the likelihood of higher K values with early analyses of those data suggesting K values of 0.94-0.99 ...
Unscheduled interruption of a radiotherapy treatment can lead to significant loss in local tumour control, particularly in tumours that repopulate rapidly. General guidelines for dealing with such treatment gaps have been issued by the Royal College of Radiologists and more specific advice on the use of compensation methods has been published previously [Hendry et al., Clin Oncol 1996;8:297-307; Slevin et al., Radiother Oncol 1992;24:215-220]. This article further elaborates on the practical application of these methods. It sets out the main considerations arising in the especially critical case of head and neck treatments and simple calculations are used to illustrate the approaches which may be adapted for particular situations. Radiobiological parameter values are suggested for use in the calculations, but these may require modification in the light of further research in this important area.
... Estimates for the lag time are mostly in the range of 20-32 days Hendry 1998, 1999). In this paper a lag time of 27 days is assumed for SCC head and neck, which is an average of the lag time estimated by Roberts and Hendry (1999) for 2225 patients from four centres, both with and without taking heterogeneity into account. Published data for cervix cancer do not include analysis of delay to onset of accelerated repopulation, but a deleterious effect of prolongation of overall treatment time on the outcome has been reported (Petereit et al 1995). ...
There is often a considerable delay from initial tumour diagnosis to the start of radiotherapy treatment, which may be due to factors such as waiting lists and referral delays. This paper uses widely published models and clinical parameters to calculate the effect of delays in treatment on local tumour control for four different types of tumour-squamous cell carcinoma (head and neck), breast, cervix and prostate. The Poisson model for tumour control probability (TCP), an exponential function for tumour growth and the linear quadratic model of cell kill are used to calculate the change in TCP for delays between diagnosis and treatment of up to 100 days. Typical values of the clinical parameters have been taken from the literature; these include alpha and beta, sigma(alpha), tumour size at diagnosis, pre-treatment doubling time, delay in onset of accelerated repopulation and doubling time during treatment. It is acknowledged that there are limitations in the reliability of these data for predicting absolute values of tumour control, but models are still useful for predicting how changes in treatment parameters are likely to affect the outcome. It is shown that for fast-growing tumours a delay of 1-2 months can have a significant adverse effect on the outcome, whereas for slow-growing tumours such as Ca prostate a delay of a few months does not significantly reduce the probability of tumour control. These calculations show the importance of ensuring that delays from diagnosis through to treatment are minimized, especially for patients with rapidly proliferating tumours.
... In our multidisciplinary tumor board, we explain the advantages and disadvantages of the various treatment modalities to the patients , who ultimately decide for themselves. Numerous reports regarding the treatment of early glottic cancer have evaluated a number of prognostic factors, i.e., tumor volume and stage [20, 28, 37], tumor kinetics including p53 status [3, 13, 48] , histological differentiation, intrinsic ra- diosensitivity [28], smoking habits and hypoxia [9] , pretreatment hemoglobin level [14, 59, 69], dose per fraction [70] , total dose [62], overall treatment time [4, 10, 18, 27, 52, 53, 58], field size [64], beam energy [16, 19], radiation technique [61], and anterior commissure involvement [41, 51]. These factors were not always reported to have a prognostic influence by all authors [17, 30, 46, 66, 67]. ...
To assess the patterns of failure in the treatment of early-stage squamous cell carcinoma of the glottic larynx.
Between 1983-2000, 122 consecutive patients treated for early laryngeal cancer (UICC T1N0 and T2N0) by radical radiation therapy (RT) were retrospectively studied. Male-to-female ratio was 106 : 16, and median age 62 years (35-92 years). There were 68 patients with T1a, 18 with T1b, and 36 with T2 tumors. Diagnosis was made by biopsy in 104 patients, and by laser vaporization or stripping in 18. Treatment planning consisted of three-dimensional (3-D) conformal RT in 49 (40%) patients including nine patients irradiated using arytenoid protection. A median dose of 70 Gy (60-74 Gy) was given (2 Gy/fraction) over a median period of 46 days (21-79 days). Median follow-up period was 85 months.
The 5-year overall, cancer-specific, and disease-free survival amounted to 80%, 94%, and 70%, respectively. 5-year local control was 83%. Median time to local recurrence in 19 patients was 13 months (5-58 months). Salvage treatment consisted of surgery in 17 patients (one patient refused salvage and one was inoperable; total laryngectomy in eleven, and partial laryngectomy or cordectomy in six patients). Six patients died because of laryngeal cancer. Univariate analyses revealed that prognostic factors negatively influencing local control were anterior commissure extension, arytenoid protection, and total RT dose < 66 Gy. Among the factors analyzed, multivariate analysis (Cox model) demonstrated that anterior commissure extension, arytenoid protection, and male gender were the worst independent prognostic factors in terms of local control.
For early-stage laryngeal cancer, outcome after RT is excellent. In case of anterior commissure extension, surgery or higher RT doses are warranted. Because of a high relapse risk, arytenoid protection should not be attempted.
... Also, it is generally Table 4. * Statistically significant. recognized that treatment prolonged beyond about 28 days in head-and-neck cancers can reduce the effect of the dose delivered owing to increased cell proliferation (38,39). Treatment breaks occurring later in the treatment course have not often been studied in head-and-neck cancer (17,36,40). ...
This population-based study describes the treatment of early glottic cancer in Ontario, Canada and assesses whether treatment variations were associated with treatment effectiveness.
We studied 491 T1N0 and 213 T2N0 patients. Data abstracted from charts included age, sex, stage, treatment details, disease control, and survival.
The total dose ranged from 50 to 70 Gy, and the daily dose ranged from 1.9 to 2.8 Gy. In 90%, treatment duration was between 25 and 50 days. Field sizes, field reductions, beam arrangement, and beam energy varied. Late treatment breaks occurred in 13.6% of T1N0 and 27.1% of T2N0 cases. Local control was comparable to other reports for T1N0 (82% at 5 years), but was only 63.2% in T2N0. Variables associated with local failure in T1N0 were age less than 49 years (relative risk [RR], 3.21; 95% confidence interval [CI], 1.49-6.90) and >3 treatment interruption days (RR, 2.43; 95% CI, 1.00-5.91). In T2N0, these were field reduction (RR, 2.33; 95% CI, 1.23-4.42) and late treatment breaks (RR, 2.19; 95% CI, 1.09-4.41).
Some aspects of treatment for early glottic cancer were associated with worse local control. Problems with protracted treatment are of particular concern, underscoring the need for randomized studies to intensify radiotherapy.
... 407 therefore clearly exists for some tumor types (also cf. Ref. [23]). Finally, 1(T ÁT k ) denotes the Heaviside function, which is equal to zero if 0 5/T B/T k and equal to 1 if T k 5/T. ...
It is shown that in order to derive a general model for tumor control probability (TCP) the two assumptions that on the microscopic level (1) clonogens are non-interacting and (2) clonogen killings are uncorrelated events are not necessary. In fact, these two assumptions can be replaced with two weaker ones that only ask that (a) therapy fractions are independent and non-overlapping and (b) the probability of an event only depends on the number of incidents happening during a time interval and the length of this time interval but not on time itself. This change in assumptions implies that TCP models based on clinical data are flexible enough to include interaction of clonogens on the microscopic level and therefore also a possible bystander effect in cell killing. Based on this new set of assumptions the equation for TCP is derived, first for the homogenous case and then for the general case of a heterogeneous ensemble of tumors irradiated in-homogeneously.
... However, such schedules may allow tumor cell repopulation, which is detrimental to tumor cure. It is now well established that for head and neck cancers, repopulation of tumor clonogens starts after three to four weeks of treatment (25,26). On the other hand, accelerated (shorter) treatments, which will be completed before tumor cell repopulation becomes important, can increase acute reactions and thus may increase consequential late reactions as well. ...
This paper describes the biological mechanisms of normal tissue reactions after radiation therapy, with reference to conventional treatments, new treatments, and treatments in developing countries. It also describes biological reasons for the latency period before tissue complications arise, the relationship of dose to incidence, the effect of increasing the size of the irradiated volume, early and late tissue reactions, effects of changes in dose fractionation and dose rate, and combined chemotherapy and radiotherapy responses. Examples are given of increases in knowledge of clinical radiobiology from trials of new protocols. Potential modification to treatments include the use of biological response modifiers. The introduction of "response prediction" modifications to treatments might also be available in the near future. Finally, the paper points out that in some radiotherapy centers, the biologically-effective doses prescribed for combined brachytherapy and teletherapy treatment of cervix cancer are lower than those prescribed in other centers. This issue needs to be addressed further. The wealth of preclinical and clinical data has led to a much greater understanding of the biological basis to radiotherapy. This understanding has underpinned a variety of new approaches in radiotherapy, including both physical and biological strategies. There is also the important issue of treatment of a large number of cancers in developing countries, for which efficacious resource-sparing protocols are being continuously developed. A unified scoring system should be widely accepted as the new standard in reporting the adverse effects of radiation therapy. Likewise, late toxicity should be reported on an actuarial basis as a mandatory endpoint.
... where K is the biologic dose required to offset each day's worth of tumor repopulation. For intermediate-and favorable-risk prostate adenocarcinoma, K is typically of the order of 0.1 Gyday Ϫ1 or less (13), whereas for fast-growing head and neck tumors it may be of the order of 0.9 Gyday Ϫ1 or higher (14,15). T eff in Eq. 3 is the effective treatment time. ...
To use tumor growth kinetics and other biologic parameters in an extended version of the linear-quadratic (LQ) formulation to determine radiobiologically optimized half-lives of radionuclides which might be used in permanent brachytherapy implants.
A version of the LQ model suitable for the analysis of permanent brachytherapy implants has been modified to investigate the radionuclide half-lives that will maximize the biologically effective dose (BED) delivered to tumors with repopulation rates (K values) in the range 0.01-1.1 Gyday(-1). The method assumes that part of the physical dose delivered to the tumor may be radiobiologically wasted because of the repopulation phenomenon, whereas adjacent normal tissues will exhibit little or no wastage. To perform the analysis, it is necessary to stipulate alpha/beta ratios and sublethal damage recovery rates together with the normal tissue tolerance BED. The analysis also takes into account a range of likely relative biological effectiveness (RBE) values.
Rapidly growing tumors require the shortest radionuclide half-lives, but even slow-growing tumors such as prostate adenocarcinomas can be satisfactorily treated with radionuclides possessing half-lives substantially less than that associated with I(125). The likelihood that prostate tumors possess an alpha/beta value which is comparable with, or lower than, that associated with late-responding normal tissues would also mitigate against the use of long-lived radionuclides. Although a number of parameter assumptions are involved, the results suggest that, for a wide range of tumor types, shorter-lived radionuclides are more versatile for achieving reasonable clinical results. The theoretically derived optimum half-lives typically range from around 0-5 days for fast-repopulating tumors (K 1.1 Gyday(-1)) to approximately 14-50 days for slow-growing tumors (K approximately 0.1 Gyday(-1) or less). For prostate implantation, 103Pd is overall a better choice than 125I.
With so many variables and parameter uncertainties, it is not appropriate to attempt to define optimum radionuclide half-lives too closely. However, this study suggests that half-lives in the approximate range 4-17 days are likely to be significantly better for a wide range of tumor types for which the radiobiologic characteristics may not be precisely known in advance.
We developed a tumor control probability (TCP) model that incorporates variable time intervals between fractions and a kick-off time (Tk) for radiation-induced accelerated tumor proliferation. The resulting Lee-Rosen model, TCPLR, was used to compute TCPs for treatment courses with and without weekend treatment for tumors with different proliferation rates - slow (prostate), moderate (breast), and rapid (head and neck). TCPs were computed using ideal uniform dose distributions and actual patient plans. The doses for the uniform plans were the mean doses for the prostate and breast cases and the minimum tumor dose for the head and neck case. The TCPLR model predictions agreed with expectations that TCP increases with increasing Tk in all cases. For standard fractionation, as Tk increased from 0 to 4 weeks, TCP increased for the patient distributions by 74.7% for the head and neck cancer, by 6.2% for the breast cancer, and by 2.4% for the prostate cancers. For the uniform dose distributions, the increases were 79.2%, 5.7%, and 2.3%, respectively. TCP increased as the number of weekend breaks decreased. The effect of weekend breaks decreased as the tumor proliferation rate decreased. For the head and neck tumor, notable decreases in TCP of 6.0% (uniform dose distribution) and 6.8% (actual plan dose distribution) were observed with Friday starts compared to Monday starts for the standard 5 fx/wk schedule (Tk = 4 wk). The 7 fx/wk schedule produced increases in TCP of 17.0% and 20.5% for the uniform and patient dose distributions, respectively, compared to the standard schedule. For the breast cancer, starting the 5 fx/wk schedule on Friday decreased the TCP by 0.2% (Tk = 4 wk) compared to a Monday start. The 7 fx/wk schedule produced increases of 0.3% and 0.4% in TCP compared to the standard schedule for the uniform and patient dose distributions, respectively (Tk = 4 wk). For the prostate cancer, the change in TCP for 5 fx/wk schedules starting on different days was 0.1%. The 7 fx/wk schedule increased TCP by 0.8% compared to the standard schedule (Tk = 4 wk). TCP values for the uniform dose distributions for the standard schedule (Tk = 4 wk) agreed with the TCP values for the actual dose distributions within 4.5% for the head and neck tumor and within 0.2% for the breast and prostate tumors. This good agreement suggests that the doses chosen for the uniform dose distributions were good approximations to the clinical doses. The results for head and neck tumors support, in part, the current practice of hyperfractionated / accelerated radiotherapy. They also suggest that shortening the overall treatment time for conventional fractions by eliminating weekend breaks might be beneficial. The predicted effect on TCP of the various schedules studied was insignificant for prostate and breast tumors, suggesting that a weekend treatment might not be necessary for patients starting radiotherapy on a Friday. There is significant uncertainty in the values of the model parameters chosen for these calculations, and no consideration was given to the potential effects of these various schedules on normal tissues.
This 9-section chapter begins with an elementary explanation of the Linear Quadratic model of Radiation Response, to make sure readers haven’t missed out on understanding this robust and reliable way of comparing different schedules in Radiation Oncology. A detailed account of its many applications has recently been published as “21 Years of BED (Biologically Effective Dose)” (Fowler Br J Radiol 83:554–568, 2010). The essential feature of this modeling is that a given dose has very different biological effects on neighbouring but different tissues because of their biological alpha/beta ratios and their “kick-off” or “onset” times of repopulation during continuing irradiation. In Sections 4 and 5 comparisons of actual clinical trials are presented that have shaped the current and emerging schedules of treatments of Head & Neck tumors, going on to SBRT (Stereotactic Body Radiation Therapy), IMRT (intensity Modulated Radiation Therapy) and IGRT (Image Guided Radiation Therapy). Some insights into how the biological strategies of fractionated radiotherapy actually deliver therapeutic advantages are introduced. Section 6 explains how Optimum Overall Times can now be predicted, using basially least two constraints, one for Late Complications and the other for Acute Tolerance Doses. This is a fairly new
break-through (2008). Section 7 goes into detail on why Overall Times might be too short or too long, with examples from modern schedules still being clinically trialed. Section 8 goes further into non-standard schedules, with updated emphasis on the Recovery Times of various tissues and tumors, intervals between fractions and extended fraction times. The chapter ends with an explanatory table of best and next-to-best schedules for Head and Neck radiation oncology. The continuing need to obtain data on individual tumor T-\( {\raise0.5ex\hbox{$\scriptstyle {1}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {2}$}} \) and repopulation is emphasized.
Doses in radiotherapy are limited not by their effect on tumours (except for a few very radiosensitive types of tumour) but by their effects on normal tissues. It would therefore be helpful to be able to predict NTCP reliably. The steps from DVH or DSH to a biologically-corrected "effective uniform dose" or "mean normalised dose (to 2 Gy)" can be made fairly robustly, and used for optimization. It is clear that the dose in every voxel should be normalised (by multiplying by [1+d.$$$$/$$$]/[1+d ref.$$$$/$$$]; for NTCP no time factor is usually needed). However, the further steps to NTCP (or TCP) depend on further variables which are not so well known for any tissue and which make NTCP a very sensitive number. After a brief discussion of current models, a review of the uncertain nature of response-dose and response-volume slopes is made. A particular discontinuity is expected for parallel organs when the volume irradiated becomes smaller than the reserve capacity of the organ. No single parameter is expected to describe this volume response, except as a poor surrogate for enormous variability. Comparisons between models show some agreements, but also differences in predicted NTCPs, especially for small volumes (< 1/3rd of organ irradiated) and at high doses. Comparisons of observed and predicted NTCPs include spinal cord, rectal complications after prostate radiotherapy, and pneumonitis after radiotherapy for lung cancer. Agreement between models is best for CNS, where the simplest probability algorithm "effect is proportional to volume irradiated" seems to apply. However, prediction of a percentage incidence (NTCP) depends so steeply on the values of parameters chosen for any model that we must await further clinical data before being able to agree on the best values.
: Background and Purpose. Optimal treatment dura-tion of altered fractionation schedules in head and neck cancer isstill undefined. A retrospective study on local tumor control, sur-vival, and complications of accelerated hyperfractionated irradia-tion in head and neck cancer was undertaken to investigatewhether there was an advantage in further shortening overalltime from 6.5 weeks.Methods. Four hundred nineteen consecutive male patientstreated with radiation alone for cure 1987–1998 were analyzed.Patients with stage I, or treated also with brachytherapy implantsor chemotherapy, were excluded. Treatment with accelerated hy-perfractionation was performed twice daily, at a median of 1.6Gy/fraction, to a total median dose of 68 Gy in 39 days. Thepatient population was divided into two groups: those with #39days overall treatment time (group A, n= 227; median, 33 days)and those with >39 days (group B, n= 192; median, 46 days).Group A received a significant median tumor dose reduction of7% compared with group B.Results. The 7-year actuarial local control (LC) rates were59% and 48% for groups A and B, respectively (p= .02). Theactuarial LC rates for T1–2 patients were 79% and 74% at 7years for groups A and B, respectively (p = NS). Similarly,for T3–4 patients, they were 47% and 35% (p = .02), respec-tively. The 7-year actuarial disease-free survival (DFS) rates forgroups A and B were 39% and 26% (p= .01), respectively. Forstage II patients, DFS was 62% and 60% at 7 years (p= NS)for groups A and B, respectively. And similarly, for stage III–IVpatients, DFS was 33% and 20% (p = .04), respectively, at 7years. LC and DFS rates at 7 years for T4 and stage IV patients,respectively, were significantly improved in group A. Cox regres-sion analyses for LC showed that both T stage and overall timewere significant prognostic factors. Similarly, UICC clinical stageand overall time were significant prognostic factors for DFS.There was no difference in acute morbidity between the twogroups: 3% of patients in both groups required tube or parenteralfeeding. The 7-year actuarial probability of RTOG/EORTCgrades 3–5 late effects was 15% and 13%, respectively, for eachgroup (p= NS).Conclusions. This study, with the limitations of a retrospec-tive study, has shown a significant improvement in local tumorcontrol and disease-free survival, in patients treated with shorteroverall treatment times (median, 33 days) with an acceleratedhyperfractionated irradiation schedule compared with those
Cancers of the oral cavity, pharynx, and larynx occur with a yearly incidence of around 500,000 new cases. They are frequent in developed countries, about equally in North America and the European Community where they have a particularly high incidence in France. Most of these cancers are squamous-cell carcinomas (SCCs) occurring in rather debilitated patients after a long history of tobacco consumption and alcohol abuse. The vast majority of patients are males aged around 50 years, but there is a tendency to an increasing incidence in females and young adults. In addition, the sociocultural profile of patients suffering from head and neck SCC is often poor. In general, SCCs of the head and neck often proliferate rapidly, are locally aggressive, and carry a high tendency to metastasize to cervical lymph nodes. In presentations with very large lymph nodes, or when lymph nodes are very numerous, the possibility of distant metastasis increases significantly. This natural history explains why that these SCCs are most often diagnosed at an advanced stage, requiring combined therapies. The outcome for this patient population is poor for several reasons: the risk of failure for the index tumor; the risk of developing subsequent SCCs along the upper aerodigestive tract, esophagus, and lung; and the frequency of intercurrent diseases. The risks from comorbity and second cancers arise almost exclusively from the common etiologic association with alcohol and tobacco abuse. SCCs of the oral cavity, pharynx, and larynx are a major public health problem. Apart from large campaigns against tobacco use and alcohol abuse and information that may encourage earlier diagnosis, efforts should be made to assess prognostic factors capable of predicting both outcome and the response to various treatments. In turn, this should help select appropriate therapeutic protocols.
Now that the follow-up time has exceeded 5 years, an estimate of the α/β ratio can be presented. The additional late outcomes in patients treated with three-dimensional conformal external beam radiotherapy for localized prostate cancer using a hypofractionated vs. a standard fractionation regimen are reported from this prospective nonrandomized contemporary comparison.
A total of 114 nonrandomized patients chose hypofractionation delivered in 20 fractions of 3 Gy or 3.15 Gy (mean 3.06 Gy) for localized prostate cancer within a median overall time of 32 days (range, 29-49) using four fractions weekly. A total of 160 comparable patients were contemporarily treated within a median of 55 days (range 49-66). The median follow-up was 66 months (range, 24-95) for the hypofractionated arm and 63 months (range, 36-92) for the standard arm. The percentage of patients in the low-, medium-, and high-risk groups was 36%, 46%, and 18% in the hypofractionated arm and 44%, 50%, and 6% in standard arm (2 Gy), respectively.
The 5-year actuarial biochemical absence of disease (prostate-specific antigen nadir + 2 ng/mL) and disease-free survival rate was the same at 89% in both arms, making the α/β calculation unambiguous. The point ratio of α/β was 1.86 (95% confidence interval, 0.7-5.1 Gy). The 95% confidence interval was determined entirely by the binomial confidence limits in the numbers of patients. Rectal reactions of grade 3 and 4 occurred in 1 of 114 (hypofractionated) and 2 of 160 (standard) patients.
The presented three-dimensional conformal regimen was acceptable, and the α/β value was 1.8, in agreement with other very recent low meta-analyses (reviewed in the "Discussion" section).
We present a software for choosing the best radiotherapy treatment schedule for head and neck cancers as a beginning radiotherapy plan or a temporarily interrupted plan. Its application occurs according to two modalities: the first adopts the best estimates for model parameters; the second takes into account the parameters' uncertainty too. In both cases, the choice becomes the schedule with the highest uncomplicated tumor control probability (UTCP). In the UTCP valuation, the normal tissue complication probability (NTCP) of each organ is related to the gravity of its possible late injury. For NTCP calculation, it has been adopted the empirical LKB (Lyman-Kutcher-Burman) model corrected for dose/fraction via linear-quadratic model and the incomplete repair effect. The tumor control probability (TCP) model is Poisson based and contains corrections for dose/fraction and regrowth effect; optionally, it can be accounted for the incomplete repair effect as well. At the end of processing, a detailed file with all informations about UTCP, TCP and single organ NTCP is furnished for every examined schedule. Moreover, a useful 3-D graphic representation of the schedule's UTCP is available, allowing the physician to easily understand the schedules with the highest radiotherapeutic efficacy. The open source characteristic allows the program to adapt to the individual clinical case as well as to be a valid support in radiobiological research.
Radiobiologic modeling is increasingly used to estimate the effects of altered treatment plans, especially for dose escalation. The present article shows how much the linear-quadratic (LQ) (calculated biologically equivalent dose [BED] varies when individual parameters of the LQ formula are varied by +/-20% and by 1%.
Equivalent total doses (EQD2 = normalized total doses (NTD) in 2-Gy fractions for tumor control, acute mucosal reactions, and late complications were calculated using the linear- quadratic formula with overall time: BED = nd (1 + d/ [alpha/beta]) - log(e)2 (T - Tk) / alphaTp, where BED is BED = total dose x relative effectiveness (RE = nd (1 + d/ [alpha/beta]). Each of the five biologic parameters in turn was altered by +/-10%, and the altered EQD2s tabulated; the difference was finally divided by 20. EQD2 or NTD is obtained by dividing BED by the RE for 2-Gy fractions, using the appropriate alpha/beta ratio.
Variations in tumor and acute mucosal EQD ranged from 0.1% to 0.45% per 1% change in each parameter for conventional schedules, the largest variation being caused by overall time. Variations in "late" EQD were 0.4% to 0.6% per 1% change in the only biologic parameter, the alpha/beta ratio. For stereotactic body radiotherapy schedules, variations were larger, up to 0.6 to 0.9 for tumor and 1.6% to 1.9% for late, per 1% change in parameter.
Robustness occurs similar to that of equivalent uniform dose (EUD), for the same reasons. Total dose, dose per fraction, and dose-rate cause their major effects, as well known.
To evaluate the efficacy and toxicity of staged stereotactic radiotherapy with a 2-week interfraction interval for unresectable brain metastases more than 10 cm(3) in volume.
Subjects included 43 patients (24 men and 19 women), ranging in age from 41 to 84 years, who had large brain metastases (> 10 cc in volume). Primary tumors were in the colon in 14 patients, lung in 12, breast in 11, and other in 6. The peripheral dose was 10 Gy in three fractions. The interval between fractions was 2 weeks. The mean tumor volume before treatment was 17.6 +/- 6.3 cm(3) (mean +/- SD). Mean follow-up interval was 7.8 months. The local tumor control rate, as well as overall, neurological, and qualitative survivals, were calculated using the Kaplan-Meier method.
At the time of the second and third fractions, mean tumor volumes were 14.3 +/- 6.5 (18.8% reduction) and 10.6 +/- 6.1 cm(3) (39.8% reduction), respectively, showing significant reductions. The median overall survival period was 8.8 months. Neurological and qualitative survivals at 12 months were 81.8% and 76.2%, respectively. Local tumor control rates were 89.8% and 75.9% at 6 and 12 months, respectively. Tumor recurrence-free and symptomatic edema-free rates at 12 months were 80.7% and 84.4%, respectively.
The 2-week interval allowed significant reduction of the treatment volume. Our results suggest staged stereotactic radiotherapy using our protocol to be a possible alternative for treating large brain metastases.
To describe the radiobiological rationale for dose-per-fraction escalation in non-small-cell lung cancer (NSCLC) and to devise a novel Phase I scheme to implement this strategy using advanced radiotherapy delivery technologies.
The data from previous dose escalation trials in NSCLC are reanalyzed to establish a dose-response relationship in this disease. We also use data relating prolongation in treatment time to survival to compute the potential doubling time for lung tumors. On the basis of these results, and using a Bayesian model to determine the probability of pneumonitis as a function of mean normalized lung dose, a dose-per-fraction escalation strategy is developed.
Standard approaches to dose escalation using 2 Gy per fraction, five fractions per week, require doses in excess of 85 Gy to achieve 50% long-term control rate. This is partly because NSCLCs repopulate rapidly, with a 1.6% per day loss in survival from prolongation in overall treatment time beyond 6 weeks, and a cell doubling time of only 2.5 to 3.3 days. A dose-per-fraction escalation strategy, with a constant number of fractions, 25, and overall time, 5 weeks, is projected to produce tumor control rates predicted to be 10%-15% better than 2 Gy per fraction dose escalation, with equivalent late effects. This Phase I clinical study is divided into three parts. Step 1 examines the feasibility of the maximum breath-holding technique and junctioning of tomotherapy slices. Step 2 treats 10 patients with 30 fractions of 2 Gy over 6 weeks and then reduces duration to 5 weeks using fewer but larger fractions in 10 patients. Step 3 will consist of a dose-per-fraction escalation study on roughly 50 patients, maintaining 25 fractions in 5 weeks. Bayesian methodology (a modification of the Continual Reassessment Method) will be used in Step 3 to allow consistent and efficient escalation within five volume bins.
A dose-per-fraction escalation approach in NSCLC should yield superior outcomes, compared to standard dose escalation approaches using a fixed dose per fraction, for a given level of pneumonitis and late toxicity. Highly conformal radiotherapy techniques, such as intensity modulated radiotherapy (IMRT) and helical tomotherapy with its adaptive capabilities, will be necessary to achieve significant dose-per-fraction escalation without unacceptable lung and esophageal morbidity.
To evaluate the adequacy of a Poisson tumor control probability (tcp) model and the impact of hypoxia on tumor cure.
A human colon adenocarcinoma cell line, WiDr, was grown as multicellular spheroids of different diameters. Measurements were made of cell survival and spheroid cure following 300-kV X-ray external beam irradiation in air and nitrogen. Cell survival data were fitted using a two-compartment and an oxygen diffusion model. Spheroid cure data were fitted using the tcp model.
Hypoxia was seen only for spheroids greater than 500 microm in diameter. For small spheroids tcp estimates of radiosensitivity and clonogenic number showed excellent agreement with experimentally derived values. For large spheroids, although tcp estimates of radiosensitivity were comparable with measurements, estimates of the clonogenic number were considerably lower than the experimental count. Reoxygenation of large spheroids before irradiation resulted in the tcp estimates of the number of clonogenic cells agreeing with measured values.
When hypoxia was absent, the tcp model accurately predicted cure from measured radiosensitivity and clonogen number. When hypoxia was present, the number of cells capable of regrowth in situ was considerably lower than the number of clonogenic cells that initially survived irradiation. As this counteracted the decreased radiosensitivity, hypoxia was less important for cure than predicted from cell survival assays. This finding suggests that chronic hypoxia may not limit directly the success of radiation therapy.
Optimal treatment duration of altered fractionation schedules in head and neck cancer is still undefined. A retrospective study on local tumor control, survival, and complications of accelerated hyperfractionated irradiation in head and neck cancer was undertaken to investigate whether there was an advantage in further shortening overall time from 6.5 weeks.
Four hundred nineteen consecutive male patients treated with radiation alone for cure 1987-1998 were analyzed. Patients with stage I, or treated also with brachytherapy implants or chemotherapy, were excluded. Treatment with accelerated hyperfractionation was performed twice daily, at a median of 1.6 Gy/fraction, to a total median dose of 68 Gy in 39 days. The patient population was divided into two groups: those with < or =39 days overall treatment time (group A, n = 227; median, 33 days) and those with >39 days (group B, n = 192; median, 46 days). Group A received a significant median tumor dose reduction of 7% compared with group B.
The 7-year actuarial local control (LC) rates were 59% and 48% for groups A and B, respectively (p =.02). The actuarial LC rates for T1-2 patients were 79% and 74% at 7 years for groups A and B, respectively (p = NS). Similarly, for T3-4 patients, they were 47% and 35% (p =.02), respectively. The 7-year actuarial disease-free survival (DFS) rates for groups A and B were 39% and 26% (p =.01), respectively. For stage II patients, DFS was 62% and 60% at 7 years (p = NS) for groups A and B, respectively. And similarly, for stage III-IV patients, DFS was 33% and 20% (p =.04), respectively, at 7 years. LC and DFS rates at 7 years for T4 and stage IV patients, respectively, were significantly improved in group A. Cox regression analyses for LC showed that both T stage and overall time were significant prognostic factors. Similarly, UICC clinical stage and overall time were significant prognostic factors for DFS. There was no difference in acute morbidity between the two groups: 3% of patients in both groups required tube or parenteral feeding. The 7-year actuarial probability of RTOG/EORTC grades 3-5 late effects was 15% and 13%, respectively, for each group (p = NS).
This study, with the limitations of a retrospective study, has shown a significant improvement in local tumor control and disease-free survival, in patients treated with shorter overall treatment times (median, 33 days) with an accelerated hyperfractionated irradiation schedule compared with those treated with a median duration of 46 days. No significant enhancement of acute reactions and late morbidity were observed with the shorter schedule.
Losses in tumor control are estimated for cold spots of various "sizes" and degrees of "cold dose." This question is important in the context of intensity modulated radiotherapy where differential dose-volume histograms (DVHs) for targets that abut a critical structure often exhibit a cold dose tail. This can be detrimental to tumor control probability (TCP) for fractions of cold volumes even as small as 1%, if the cold dose is lower than the prescribed dose by substantially more than 10%. The Niemierko-Goitein linear-quadratic algorithm with gamma50 slope 1-3 was used to study the effect of cold spots of various degrees (dose deficit below the prescription dose) and size (fractional volume of the cold dose). A two-bin model DVH has been constructed in which the cold dose bin is allowed to vary from a dose deficit of 1%-50% below prescription dose and to have volumes varying from 1% to 90%. In order to study and quantify the effect of a small volume of cold dose on TCP and effective uniform dose (EUD), a four-bin DVH model has been constructed in which the lowest dose bin, which has a fractional volume of 1%, is allowed to vary from 10% to 45% dose deficit below prescription dose. The highest dose bin represents a simultaneous boost. For fixed size of the cold spot the calculated values of TCP decreased rapidly with increasing degrees of cold dose for any size of the cold spot, even as small as 1% fractional volume. For the four-subvolume model, in which the highest dose bin has a fractional volume of 80% and is set at a boost dose of 10% above prescription dose, it is found that the loss in TCP and EUD is moderate as long as the cold 1% subvolume has a deficit less than approximately 20%. However, as the dose deficit in the 1% subvolume bin increases further it drives TCP and EUD rapidly down and can lead to a serious loss in TCP and EUD. Since a dose deficit to a 1% volume of the target that is larger than 20% of the prescription dose may lead to serious loss of TCP, even if 80% of the target receives a 10% boost, particular attention has to be paid to small-volume cold regions in the target. The effect of cold regions on TCP can be minimized if the EUD associated with the target DVH is constrained to be equal to or larger than the prescription dose.
CHART (Continuous Hyperfractionated Accelerated Radiotherapy) has been shown to improve the tumour control probability and survival relative to conventional radiotherapy in patients with inoperable non-small cell lung cancer (NSCLC). CHARTWEL (CHART Weekend-less) is a further development of this schedule escalating the physical dose to 60 Gy while maintaining the low dose per fraction of 1.5 Gy. In this schedule, three fractions, with a minimum interval of 6 h between fractions, are delivered 5 days per week. This extends overall treatment time from the 12 days of CHART to 18 days. Radiobiological modelling is used to estimate the expected tumour control and normal tissue morbidity after CHARTWEL relative to CHART. The estimations are based on the outcome of the CHART trial and published values for dose-fractionation and dose-response parameters for human tissues and tumours. Two new estimates of quantitative radiobiological parameters for early normal-tissue morbidity after chest irradiation are reported here. For radiation pneumonitis, the dose recovered per day is estimated at 0.44 Gy/day with 95% confidence limits 0.07 Gy/day and 0.80 Gy/day. For oesophagitis, the normalized dose-response gradient, gamma50, is estimated at 2.1 with 95% confidence limits 1.4 and 3.6. With regard to normal tissue effects, the increase in total dose when going from CHART to CHARTWEL is moderated by the slightly longer overall treatment time in case of early morbidity while the introduction of the weekend gaps may moderate the effect for late-responding normal tissues with a long repair halftime. Tumour control at 3 years is expected to increase by some 7-14 percentage points (from 19% to 26-33%) whereas the incidence of moderate and severe early oesophagitis and pneumonitis is expected to increase by about 2 percentage points. The incidence of late morbidity, lung fibrosis and oesophageal strictures, is expected to increase by 3-4 percentage points. The analyses conclude that CHARTWEL is likely to improve the therapeutic ratio relative to CHART.
Linear quadratic (LQ) modelling allows easy comparison of different fractionation schedules in radiotherapy. However, estimating the radiation effect of a single fractionated treatment introduces many questions with respect to the parameters to be used in the modelling process. Several studies have used tumour control probability (TCP) curves in order to derive the values for the LQ parameters that may be used further for the analysis and ranking of treatment plans. Unfortunately, little attention has been paid to the biological relevance of these derived parameters, either for the initial number of cells or their intrinsic radiosensitivity, or both. This paper investigates the relationship between single values for the TCP parameters and the resulting dose-response curve. The results of this modelling study show how clinical observations for the position and steepness of the TCP curve can be explained only by the choice of extreme values for the parameters, if they are single values. These extreme values are in contradiction with experimental observations. This contradiction suggests that single values for the parameters are not likely to explain reasonably the clinical observations and that some distributions of input parameters should be taken into consideration.
In previous modelling of tumour control probability (TCP) for inhomogeneously irradiated tumours we used an expression that did not include a proliferation correction term, which should be lambda(T - Tk). We did not use that term in the specific examples in our previous work to model slowly growing tumours in order to avoid unnecessary mathematical complexity. We have now considered how to do so in more detail, and there are some variations, such as schedules that depart from a number of equal fractions over the entire course of treatment, if one wishes to compensate for proliferation in the remaining fractions by increasing the dose per fraction after the kick-off time has passed in order to achieve the same TCP when proliferation is neglected.
We find the dose distribution that maximizes the tumour control probability (TCP) for a fixed mean tumour dose per fraction. We consider a heterogeneous tumour volume having a radiation response characterized by the linear quadratic model with heterogeneous radiosensitivity and repopulation rate that may vary in time. Using variational calculus methods a general solution is obtained. We demonstrate the spatial dependence of the optimal dose distribution by explicitly evaluating the solution for different functional forms of the tumour properties. For homogeneous radiosensitivity and growth rate, we find that the dose distribution that maximizes TCP is homogeneous when the clonogen cell density is homogeneous, while for a heterogeneous initial tumour density we find that the first dose fraction is inhomogeneous, which homogenizes the clonogen cell density, and subsequent dose fractions are homogeneous. When the tumour properties have explicit spatial dependence, we show that the spatial variation of the optimized dose distribution is insensitive to the functional form. However, the dose distribution and tumour clonogen density are sensitive to the value of the repopulation rate. The optimized dose distribution yields a higher TCP than a typical clinical dose distribution or a homogeneous dose distribution.
The "four Rs" of radiobiology play an important role in the design of radiation therapy treatment protocol. The purpose of this work is to explore their influence on external beam radiotherapy for fast and slowly proliferating tumors and develop an optimization framework for tumor-biology specific dose-time-fractionation scheme. The linear quadratic model is used to describe radiation response of tumor, in which the time dependence of sublethal damage repair and the redistribution and reoxygenation effects are included. The optimum radiotherapeutic strategy is defined as the treatment scheme that maximizes tumor biologically effective dose (BED) while keeping normal tissue BED constant. The influence of different model parameters on total dose, overall treatment time, fraction size, and intervals is also studied. The results showed that, for fast proliferating tumors, the optimum overall time is similar to the assumed kickoff time T(k) and almost independent of interval patterns. Significant increase in tumor control can be achieved using accelerated schemes for the tumors with doubling time smaller than 3 days, but little is gained for those with doubling time greater than 5 days. The incomplete repair of normal tissues between two consecutive fractions in standard fractionation has almost no influence on the fractional doses, even for the hyperfractionation with an interval time of 8 h. However, when the resensitization effect is included, the fractional doses at the beginning and end of each irradiated week become obviously higher than others in the optimum scheme and the hyperfractionation scheme has little advantage over the standard or hypofractionation one. For slowly proliferating tumors, provided that the alpha/beta ratio of the tumor is comparable to that of the normal tissues, a hypofractionation is more favorable. The overall treatment time should be larger than a minimum, which is predominantly determined by the resensitization time. The proposed technique provides a useful tool to systematically optimize radiotherapy for fast and slow proliferating tumors and sheds important insight into the complex problem of dose-time fractionation.
To test by modelling whether a non-standard fractionated schedule giving optimum log cell kill could be expected, between short (accelerated) and longer multiple fraction/day schedules.
Linear quadratic modelling was carried out for many schedules, with biologically effective doses converted to normalised total doses (NTDs; in 2 Gy fractions). Late complication and acute mucosal NTDs were calculated as constraint doses for each schedule, and the highest tumour NTDs and log cell kill values within both constraints were calculated. This modelling is robust and agrees with conclusions in a very recent meta-analysis (Bourhis J, Overgaard J, Audry H, et al. Hyperfractionated or accelerated radiotherapy in head and neck cancer: a meta-analysis. www.thelancet.com. Published online August 17, 2006).
The six schedules that gave the highest tumour log cell kill deliver a narrow range of 11.1-11.2 log10 cell kill in the present parameters. Other regularly used schedules give closer to 10 log10. Using one fraction/day fails to achieve the highest therapeutic ratios. Suggestions are made for escalating certain UK schedules. Fractionated radiotherapy results in a nearly constant tumour cell kill if the acute mucosal NTD is held constant. However, a small (3%) gain in tumour cell kill occurs from 3 weeks to 73 fractions of 1.15 Gy in 7 weeks. That is how fractionation works, within both acute and late constraints. Short accelerated schedules enable fewer late complications, but do not do as well for the minority of head and neck tumours that repopulate slowly.
Schedules of 4-6 weeks overall time could be chosen to give at least 11 log10 cell kill, which are safe. Most tumours would require two fractions/day, until routine monitoring of repopulation rates becomes feasible to select individual tumours. There is no 'optimum schedule', but each chosen schedule can be balanced against its own risk of excessive acute or late complications, as shown in these examples.
A previous paper in this journal (part I) concluded that there was no pronounced optimum overall time, at least up to 70 fractions of 1.15 Gy at two fractions/day in 50 days. The maximum tolerable tumour doses increased only 2% from the best short schedules of 21 or 23 days to those of 50 days. Only this range was modelled in part I because it covered the fewest and the most fractions, and the longest overall times that will probably be used in practice. Most UK schedules, typically using five fractions a week, yield tumour effective doses about 10% less than the best schedules in other developed countries. The present paper covers a much wider range of fraction numbers from one to 115, and from 1 to 80 days. Some numerical errors in the Tables in part I are also corrected in the present appendix. These made no difference to the main conclusions just described.
To correct several elementary radiobiologic errors in the otherwise admirable article by Kasibhatla, Kirkpatrick, and Brizel (2007) on estimating the equivalent radiation effect of the concomitant chemotherapy in head-and-neck chemoradiotherapy.
(1) Their equation was wrong because it omitted the lag or onset time of repopulation in tumors, Tk. Instead of zero days this should be 18-35 days. (2) Instead of a doubling time of 5 days, at most 3 days should be used for head-and-neck tumors. (3) Their slope "S" (the gamma-50 slope) for head-and-neck tumors should be 1.7, not 1.1. The same percentages of increased locoregional control as quoted by Kasibhatla et al. are used.
The average time-corrected biologically effective dose for the 16 schedules listed should be 72.4 instead of 63.1 Gy(10). The average gains in locoregional tumor control are the equivalent of 8.8 Gy(10), not 10.6 Gy(10) (p = 0.05).
The equivalent number of 2-Gy fractions of concomitant chemotherapy as used in the 16 listed schedules is 3.6 (95% confidence interval, 2.7-4.1), not 5 as claimed by Kasibhatla et al. The difference is statistically significant (p < 0.001).
While radiotherapy is proceeding, tumour cells may proliferate. The use of small individual doses reduces late morbidity. Continuous hyperfractionated accelerated radiation therapy (CHART), which reduces overall treatment from 6-7 weeks to 12 days and gives 36 small fractions, has now been tested in multicentre randomised controlled clinical trials. The trial in non-small-cell lung cancer included 563 patients and showed improvement in survival; 30% of the CHART patients were alive at 2 years compared with 20% in the control group (P = 0.006). In the 918 head and neck cases, there was only a small, non-significant improvement in the disease-free interval. In this interim analysis there was a trend for those with more advanced disease (T3 and T4) to show advantage; this will be subject to further analysis when the data are more mature. The early mucosal reactions appeared sooner and were more troublesome with CHART, however they quickly settled; so far no difference in long-term morbidity has emerged. These results support the hypothesis that tumour cell repopulation can occur during a conventional course of radiotherapy and be a cause of treatment failure.
There is much evidence for the detrimental effect on tumour control of missed treatment days during radiotherapy, amounting for example to approximately a 1.6% absolute decrease in local control probability per day of treatment prolongation in the case of head and neck squamous cell cancer. Various methods to compensate for missed treatment days are compared quantitatively in this article, using the linear-quadratic formalism. The overall time and fraction size can be maintained by either treating on weekend days (the preferred way (Method 1a), although with unsocial hours and at extra cost) or using two fractions per day to "catch up' (Method 1b). The latter might incur a small loss of tolerance regarding late reactions, when intervals of 6-8 h are used rather than 24 h, and there may be logistical/scheduling difficulties with larger numbers of patients in some centres when using this method. A second type of strategy retains overall treatment time, and also one fraction per day, but the size of the dose per fraction is increased. For example, this may be done for the same number of "post-gap' days as gap days (Method 2). However, with this method, calculated isoeffect doses regarding late reactions indicate a probable decrease in tumour control rate (Method 2a). Otherwise, isoeffective doses regarding tumour control result in an increase in late reactions (Method 2b). In addition, this method is unsuitable for short regimens already using high doses per fraction. To reduce this problem, overall treatment time can also be retained by using fewer fractions, all of greater size in the case of planned gaps (statutory holidays), or larger remaining fractions after unplanned gaps (Method 2c). The problem also with this method is that equivalence for tumour control gives an increase in late reactions. The least satisfactory strategy (Method 3) is to accept the protraction caused by the missed treatment days, and give either the same prescribed number of (slightly larger) fractions or the planned treatment followed by one (or more) extra fraction to compensate for the gap. This would retain the expected local control rate, but there would be an increase in late reactions. An example of this, using average parameter values, is that a 3-day gap (necessitating four extra days to complete treatment with one fraction of 2.4 Gy) might maintain a 70% local control rate for glottic carcinoma, but severe reactions might rise from 1% to 4% and minor/moderate reactions from 37% to 50%. In this example, the inclusion of an extra weekend would increase the required extra dose and hence may further increase the morbidity rates. A final point is that the effect of treatment interruptions for an individual patient is expected to be greater than that for a group of patients because of interpatient heterogeneity tending to flatten dose-response curves. Calculations show that the above value of 1.6% loss of local control per day for a group of patients may reflect values for individual patients that range around a median value of as much as 5% per day, so stressing further the importance of gaps in treatment. It is concluded that, wherever possible, treatment days should not be missed. If they are missed, it is important to compensate for them, preferably by one of the first of the above methods (1a or 1b), in order to keep as close as possible to the original/standard prescription in terms of total dose, dose per fraction and overall time.
A study was made of the intrinsic radiosensitivity of 140 biopsy and surgical specimens of malignant head and neck tumours of different histologies. Using a soft-agar clonogenic assay, the material was assessed for the ability to grow in culture (colony-forming efficiency; CFE) and inherent tumour radiosensitivity (surviving fraction at 2 Gy, SF2). The success rate for obtaining growth was 74% (104/140) with a mean CFE of 0.093% (median 0.031) and a range of 0.002-1.3%. SF2 was obtained for 88 of 140 specimens, representing a success rate of 63% with a mean SF2 of 0.48 (median 0.43) and a range of 0.10-1.00. There were no significant differences in radiosensitivity between different sites of the head and neck region. There were no significant relationships between SF2 and disease stage, nodal status, tumour grade, patient age, primary tumour growth pattern and CFE. The results were compared with those for other tumour types previously analysed with the same assay. The distribution of the SF2 values for the head and neck tumours was similar to that for 145 cervix carcinomas and there was no significant difference in mean radiosensitivity between the two tumour types. Also, there was no significant difference in radiosensitivity between head and neck tumours and either breast or colorectal cancers. However, a group of eight lymphomas was significantly more radiosensitive. These results confirm the feasibility of carrying out radiosensitivity measurements using a soft-agar clonogenic assay on head and neck tumours. In addition, the work has shown that radiosensitivity is independent of many clinical parameters and that the mean value is similar to that reported for cervix carcinomas.
Images
Figure 1
When analysis of results of radiotherapy for nearly 500 patients with oropharyngeal cancer showed evidence for rapid tumor regrowth during extensions of treatment from about 5 weeks to about 8 weeks, we searched the literature on radiotherapy for head and neck cancer to determine whether it revealed similar evidence of accelerated tumor regrowth. Estimates of doses to achieve local control in 50% of cases (TCD50) were made from published local control rates, and the dependence of these doses on overall treatment duration was evaluated. In parallel, published scattergrams were analyzed to estimate the rate of tumor regrowth over the period of 4-10 weeks from initiation of therapy. Both analyses suggested that, on average, clonogen repopulation in squamous cell carcinomas of the head and neck accelerates only after a lag period of the order of 4 +/- 1 weeks after initiation of radiotherapy and that a dose increment of about 0.6 Gy per day is required to compensate for this repopulation. Such a dose increment is consistent with a 4-day clonogen doubling rate, compared with a median of about 60 days in published reports of unperturbed tumor growth rates. The values presented here are average values for a large number of patients: it is necessary, not only to verify the results of these retrospective analyses in prospective studies, but also to develop methods to predict the time of onset and rate of accelerated tumor clonogen repopulation in the individual patient.
The visual information on a scatterplot can be greatly enhanced, with little additional cost, by computing and plotting smoothed points. Robust locally weighted regression is a method for smoothing a scatterplot, (x i , y i ), i = 1, …, n, in which the fitted value at z k is the value of a polynomial fit to the data using weighted least squares, where the weight for (x i , y i ) is large if x i is close to x k and small if it is not. A robust fitting procedure is used that guards against deviant points distorting the smoothed points. Visual, computational, and statistical issues of robust locally weighted regression are discussed. Several examples, including data on lead intoxication, are used to illustrate the methodology.
Inter-tumour heterogeneity in radiobiological parameters has been proposed as an explanation for the quite shallow dose-response curves for local tumour control after radiotherapy observed in clinical data. Variability in the intrinsic radiosensitivity is potentially a very strong source of variation in local control. A method is presented for forcing such variability into a direct analysis (maximum-likelihood estimation) of tumour control data. The method is used to reanalyse a series of local tumour control data in 181 patients with squamous cell carcinoma of the oropharynx taking the distribution of in vitro radiosensitivities from an independent series of patients into account. It is concluded that direct application of the in vitro radiosensitivities leads to an unrealistically high estimate for the number of target cells per cm3. A more realistic fit is obtained after including a dose-modifying factor to correct for the apparent difference between in vitro and clinical radiosensitivities. The value of this factor is estimated at 2.4 with approximate 95% confidence interval (CI) (1.3, 5.9). It is suggested that hypoxia plays a role in reducing the radiosensitivity of tumours in clinical radiotherapy. Using this method provides more biologically reasonable estimates of other radiobiological parameters. The target-cell doubling time during treatment is estimated at 3.2 days with 95% CI (1.7, 8.7) days. Estimates of the target cell density in typical patients vary between 1.8 x 10(-6) and 6.6 x 10(-4) when the delay before accelerated tumour growth is assumed to vary between 0 and 28 days. Using the method presented here, the shallow clinical dose-control curve is interpreted as a superposition of quite steep dose-response relationships in individual patients. The steepness of the dose-control curve for a typical patient is characterized by a normalized dose-response gradient (the percentage change in tumour control for a 1% change in total dose) of 7.3 after stratification for intrinsic radiosensitivity as compared with 1.6 if such stratification is not performed.
Local control of cancer by radiotherapy may be prejudiced by accelerated tumour clonogen repopulation particularly during protracted treatment schedules. A series of 496 cases of T2 and T3 larynx cancer treated here by radiotherapy has been studied to examine the impact on local control of treatment durations ranging from 9 to 41 days. Data were analysed using a linear-quadratic formulation describing the fractionation sensitivity, with the incorporation of a parameter relating to treatment time. Using combined T2 and T3 data, the increase in dose required to maintain a constant local control (the time factor) was between 0.5 and 0.6 Gy per day. These values are similar to those reported for 4 weeks or more in the literature. Also, the calculated dose to control 50% of tumours, given over the standard Christie duration of 21 days, was on the line projected back from literature data over 28-66 days. The present data are consistent with the presence of such a time factor following a lag phase of not more than 3 weeks after starting radiotherapy. Hence, further consideration should be given to using shorter overall treatment times in radiotherapy for head and neck cancer.
A significant effect of overall treatment time on local control was found in a retrospective review of 1012 radically irradiated squamous cell carcinomas of the larynx. The actuarial local relapse free rate (LRFR) at 5 years for the whole group was 59%. The effect of treatment time on local control was modelled to the linear-quadratic equation. Using logistic regression analysis treatment time and dose were significant (p = 0.008 and p = 0.04, respectively). When the analysis was adjusted for the influence of stage and laryngeal subsite treatment time remained a significant prognostic factor (p = 0.02). The derived value of gamma/alpha was 0.7 Gy/day and when adjusted for stage and sub-site 0.8 Gy/day. This equates to a dose increment to maintain iso-effective local control of 0.64 Gy/day and 0.73 Gy/day respectively for daily fractions of 2.5 Gy and an assumed alpha/beta for tumour of 25 Gy. To provide an estimate of the clinical impact of treatment interruptions not compensated for by dose escalation a Cox regression was performed. Significant variables were T stage, N stage, sex, total dose and total length of treatment interruption. Using the proportional hazard model it was calculated that each day of treatment interruption resulted in an increase in the hazard of local relapse by 4.8% (p = 0.006). Based on our data it was calculated that this would result in a decrease in local control of 1.4% for each day of uncompensated treatment interruption.
The second British Institute of Radiology trial of dose fractionation in radiotherapy compared two groups of prospectively randomized patients with squamous carcinoma of the laryngo-pharynx; one group was treated in a short (less than or equal to 4 weeks) and the other in a long (greater than 4 weeks) overall time. Treatment in any one centre could be given, with no planned gap in the course of treatment, either as a conventional, daily (5 fractions per week regime) or as 3 fractions per week. A total of 611 patients were allocated to treatment, of whom nine have had to be excluded from the analysis for a lack of information. Patients were admitted to the trial from January 1976 to December 1985 and were followed up for a maximum of 10 years and a minimum of 3 years. A reduction in total dose was made for use in the short compared with the long treatment regime. This reduction in total dose varied between 18% and 22% depending on whether 5 fractions or 3 fractions per week regimes were used. Overall, no statistically significant differences have been found between the two arms of the trial. The patients treated with 5 fractions per week in a short overall treatment time showed fewer late normal tissue effects. An analysis based on stratification by age, stage and anatomical site gave a relative risk (short/long overall treatment time) for deaths of 1.23 with a 95% confidence interval from 0.96 to 1.59. Analyses stratified for stage and site gave relative risks with 95% confidence intervals of 1 x 10 (0.84-1.44) for local recurrences/tumour persistence, and 1.01 (0.70-1.45) for laryngectomies.
The 10 year follow-up of a clinical trial involving the comparison of 3F/wk versus 5F/wk in radiotherapy of squamous cell carcinoma of the larynx and hypopharynx has now been completed. The trial involved an intake of 734 patients between 1966 and 1975. The classification of all patients has been revised to conform with the latest TNM publication. A reduction in total dose was made for 3F/wk compared with 5F/wk. This varied between 13% and 11% in centres treating over 3 weeks and 6 weeks, respectively. No statistically significant differences have been found between the two arms (3F/wk versus 5F/wk) of the trial in any of the main group analyses. A number of sub-group analyses relating to survival, tumour-free and laryngectomy-free rates and to the comparison of acute or late normal-tissue radiation damage have also been performed. No differences have been found that could be considered to be statistically significant in relation to the particular sub-group. Previous interim reports suggested minor differences in sub-group analyses between the 3F/wk and 5F/wk regimes in this trial; these have diminished now that the full follow-up data are available. This trial has provided evidence on which clinicians may base their choice between either a 3F/wk fractionation regime or a conventional 5F/wk treatment protocol in the treatment of carcinoma of the laryngo-pharynx.
The accuracy and interpretation of the "LQ + time" model (E = D(alpha + beta d) - gamma T) are discussed. Evidence is presented, based on data in the literature, that this model does not accurately describe the changes in isoeffect dose occurring with protraction of the overall treatment time during fractionated irradiation of the lung. This lack of fit of the model explains, in part, the surprisingly large values of gamma/alpha that have been derived from experimental lung data. The large apparent time factors for lung suggested by the model are also partly explained by the fact that gamma T/alpha, despite having units of dose, actually measures the influence of treatment time on the effect scale, not the dose scale, and is shown to consistently overestimate the change in total dose. The unusually high values of alpha/beta that have been derived for lung using the model (approximately 5 Gy) are shown to be influenced by the method by which the model was fitted to data. Reanalyses of the data using a more statistically valid regression procedure produce estimates of alpha/beta more typical of those usually cited for lung (approximately 3 Gy). Most importantly, published isoeffect data from lung indicate that the true deviation from the linear-quadratic (LQ) model is nonlinear in time, instead of linear, and also depends on other factors such as the effect level and the size of dose per fraction. Thus, we do not advocate the use of the "LQ + time" expression as a general isoeffect model.
The intrinsic radiosensitivity of human tumor cell cultures correlates with the clinical radiosensitivity of several different tumor histologies, as evidenced by analyses of low dose parameters of radiation survival curves generated from a large number of cell lines. Such radiosensitivity has therefore served as a basis of attempts to develop predictive assays of tumor radiocurability. In this study, the tumors from 72 patients with head and neck squamous carcinoma have been grown in an adhesive tumor-cell assay system and radiosensitivity (S2: survival at 2.0 Gy) values have been measured. The characteristics of these cultures, such as growth rate, clonogenicity and growth enhancement by epidermal growth factor, do not correlate with S2. The average S2 value of the 72 cultures is 0.33, which is lower than for cultures derived from melanomas and lung adenocarcinomas. Twenty-six patients followed up for at least 15 months have been evaluated for local tumor control. The average S2 value of the seven patients with recurrences in this group is slightly higher (0.43) than that from the other patients (0.30). There is considerable overlap of S2 values in the two groups, and more patients must be evaluated before the groups can be compared statistically.
In a retrospective study, local control of the primary tumor in 498 squamous cell carcinomas of the oral cavity and oropharynx was analyzed with respect to initial tumor volume, total dose after normalization for variations in fraction size, and to overall treatment time. Primary tumors were grouped into 4 sites, tongue (175), oral cavity including floor of mouth, faucial pillar, soft and hard palate and gingiva (210), tonsil (72) and buccal mucosa (41). Total doses of 60Co irradiation ranged from 30 Gy to 72 Gy, overall treatment times from 15 to 80 days and dose per fraction from 1.8 to 6 Gy. The large number of patients and diversity of dose fractionation patterns permitted assessment of the independent contributions to treatment outcome of stage, fraction size and overall treatment duration. The following conclusions were drawn: (1) Overall treatment time influenced strongly the probability of local tumor control. Over the interval of about 30-55 days used in treating most of this series of patients, an increase of 60 cGy per day, on average, was required for a constant control rate. (2) The increase in dose was attributed to accelerated tumor clonogen growth rate. Such accelerated growth could be a major determinant of failure in protracted regimens. (3) The accelerated rate of regrowth was similar for all tumor sites and stages. (4) The dose for tumor control was relatively independent of variations in fraction size within a range of about 1.6 Gy to 3 Gy: the alpha/beta value in the linear quadratic isoeffect equation was at least 15 Gy. (5) Local control at the primary site required an average of about 3 Gy more for each increase in T stage. This increase most likely reflected an increased number of tumor clonogens, not a decreased tumor cell radiosensitivity. (6) The probability of control at the primary site was less likely if lymph nodes were positive, but this association was only shown to be statistically significant for primaries classified here as oral cavity and oropharynx, not tonsil, tongue or buccal mucosa. (7) After allowing for differences in treatment parameters, especially for heterogeneity in overall treatment times, tumor control probability increased steeply with increase in total dose. (8) A general principle of radiotherapy, at least for squamous carcinomas of head and neck, should be to deliver the desired fractionated dose regimen without unnecessary interruptions and in the shortest time compatible with no reduction in dose below that tolerated by the late-responding normal tissues.
When analysis of results of radiotherapy for nearly 500 patients with oropharyngeal cancer showed evidence for rapid tumor regrowth during extensions of treatment from about 5 weeks to about 8 weeks, we searched the literature on radiotherapy for head and neck cancer to determine whether it revealed similar evidence of accelerated tumor regrowth. Estimates of doses to achieve local control in 50% of cases (TCD50) were made from published local control rates, and the dependence of these doses on overall treatment duration was evaluated. In parallel, published scattergrams were analyzed to estimate the rate of tumor regrowth over the period of 4-10 weeks from initiation of therapy. Both analyses suggested that, on average, clonogen repopulation in squamous cell carcinomas of the head and neck accelerates only after a lag period of the order of 4 +/- 1 weeks after initiation of radiotherapy and that a dose increment of about 0.6 Gy per day is required to compensate for this repopulation. Such a dose increment is consistent with a 4-day clonogen doubling rate, compared with a median of about 60 days in published reports of unperturbed tumor growth rates. The values presented here are average values for a large number of patients: it is necessary, not only to verify the results of these retrospective analyses in prospective studies, but also to develop methods to predict the time of onset and rate of accelerated tumor clonogen repopulation in the individual patient.
A direct analysis is proposed for quantal (all-or-nothing) responses to fractionated radiation and endpoint-dilution assays of cell survival. As opposed to two-step methods such as the reciprocal-dose technique, in which ED50 values are first estimated for different fractionation schemes and then fit (as reciprocals) against dose per fraction, all raw data are included in a single maximum-likelihood treatment. The method accommodates variations such as short-interval fractionation regimens designed to determine tissue repair kinetics, tissue response to continuous exposures, and data obtained using endpoint-dilution assays of cell survival after fractionated doses. Monte-Carlo techniques were used to compare the direct and reciprocal-dose methods for analysis of small-scale and large-scale studies of response to fractionated doses. Both methods tended toward biased estimates in the analysis of the small-scale (3 fraction numbers) studies. The alpha/beta ratios showed less scatter when estimated by the direct method. Most important, the 95 per cent confidence intervals determined by the direct method were more appropriate than those determined by reciprocal-dose analysis, for which 18 per cent (small-scale study) or 8 per cent (large-scale study) of the confidence intervals did not include the 'true' value of alpha/beta.
The radiation sensitivity of cells isolated directly from human tumor surgical specimens was studied using the Courtenay soft agar colony assay. Aerobic cell survival curves covering 2-3 decades were achieved for eight melanomas, seven ovarian, six cervix, five breast, four bladder, and four squamous cell carcinomas of the head and neck and two seminomas. Cell survival following exposure to 2.0 Gy was measured also for several other tumors of these histological types. Experiments repeated with cells stored in liquid nitrogen showed that the survival assay gave highly reproducible results. The D0 (0.61-1.65 Gy) as well as the surviving fraction at 2.0 Gy (0.12-0.66) differed considerably among individual tumors of the same histological type. Neither of these parameters was therefore significantly different for the seven tumor categories. However, about one-third of the melanomas showed a higher surviving fraction at 2.0 Gy than the highest value measured for the other tumors. Two of three seminomas showed surviving fractions at 2.0 Gy in the absolute lower range, i.e., below 0.20. Altogether the data were consistent with the suggestion recently put forward that the clinical radiocurability of tumors may be correlated to the cell surviving fraction in vitro at 2.0 Gy. However, it was not possible on the basis of individual tumors to investigate whether the surviving fraction at 2.0 Gy was correlated to the clinical radiocurability, since adequate clinical data were not available for the parent tumors. It is suggested that melanomas may be especially suitable for prospective studies aimed at establishing whether such a correlation really does exist. If a significant correlation can be verified, then a very important conclusion may be drawn from our data: the radiocurability of human tumors may differ almost just as much among individual tumors of the same histological type as among individual tumors of different histology.
A comparison has been made of the influence of treatment time on tumour control rates for 496 (T2 and T3) larynx cancer cases in Manchester, UK and 1001 (T1-T4) cases in Toronto, Canada. Both series of patients were treated in fairly short overall times, commonly 3 weeks in Manchester and 4-5 weeks in Toronto. All the tumour control data were analysed using the same method to obtain values of fitted dose, fractionation and time parameters. The analysis showed the following. (a) Differences between the total combined (T2 + T3) data sets from the two centres, fitted using direct analysis and the LQ model incorporating a parameter for overall treatment time, were not significant (p = 0.17) and close similarity in control rates was observed using treatment regimens common to both series. (b) The Manchester series over 9-41 days and the Toronto series over 14-84 days are both consistent in showing for (T2 + T3) tumours the presence of a mean time factor of 0.6-0.8 Gy/day required to abrogate the decrease in tumour control concomitant with an increase in overall treatment time from the minimum the maximum employed in each series. (c) When a parameter was included in the model to test for the possible presence of a lag period before the time factor became operative, the lag was not significant for the Toronto data, in contrast to a significant lag for the Manchester data alone (T2 + T3 data).(ABSTRACT TRUNCATED AT 250 WORDS)
This study analyses node-negative laryngeal tumour control data from two clinical trials conducted by the British Institute of Radiology in order to determine the time factors and the presence or absence of a lag period before the time factor takes effect. A direct maximum likelihood approach is used to fit a double-logarithmic model including a repopulation term which commences after an initial lag period, Tk. The analysis yields a time factor of 0.8 Gy per day (95% confidence interval 0.5-1.1 Gy per day) as the extra dose required to counteract the reduction in tumour control probability (TCP) with extension of the treatment time. The latter reduction amounted to between 5 and 12% TCP per week, depending on the stage and time period. With this dataset, where few patients were treated for short times, no statistically significant lag phase can be demonstrated. However, the best estimate of Tk is 21 days (95% confidence interval 0-27 days), which is consistent with estimates from other studies on other datasets. If a lag phase exists, this study would indicate that the duration is less than 27 days. Other studies have used retrospective data and are subject to a number of potential biases. The present study, using data from multicentre prospective randomized clinical trials, is free from some of these sources of bias. The fact that very similar estimates of the radiobiological parameters are obtained lends credence to these other studies and suggests that the potential biases may be small in practice.
The worldwide collection of control data for head and neck tumours presented by Withers et al. (Withers, H.R., Taylor, J.M.G. and Maciejewski, B. Acta Oncol. 27: 131-146, 1988) was reanalysed using a model which includes an explicit lag phase before the onset of tumour clonogen repopulation. A direct maximum-likelihood approach was used and the methodology extended to include the computation of profile-likelihood confidence limits. A statistically significant (p = 0.02) lag of 29 days was obtained with 95% confidence limits covering the range 17-31 days. However, the confidence interval was disconnected, and excluded the period 21-23 days. The analysis gave a time factor of 0.66 Gy/day. The mean values confirm the conclusions drawn by the original authors using a two-stage (indirect) method, and the values are similar to those calculated here for another data set comprising 496 patients (lag period = 26 (19-33) days). However, the data set itself is retrospective, and potentially subject to a number of biases. Therefore any clinical conclusions can only be tentative. A new feature of the methodology is the computation of profile-likelihood confidence limits and this will be useful in future direct analyses of clinical data of this type. The more usually computed normal approximation to the confidence limits have been shown to be inadequate in this analysis, and either profile-likelihood limits or likelihood ratio tests must be employed to determine the significance of the model parameters.
To determine whether in vitro radiosensitivity parameters are predictive of treatment outcome.
Biopsies were obtained from patients with head and neck cancers (57) and cervical carcinomas (20) and in vitro radiosensitivity parameters were obtained using the CAM plate assay.
In most cases (75%) patients were treated with radiation alone. The median follow up was 461 days. When the whole group of head and neck cancers and cervical carcinomas was considered, patients with a SF2 value below 0.36 had a higher 2-year local control rate (93% versus 68%) and a higher 2-year survival rate (71% vs. 62%) than those with SF2 values above that threshold, but differences were not significant. These trends persisted when head and neck cancers were considered alone with a higher local control rate (86% vs. 67%) and a higher survival rate (75% vs. 52.5%) obtained for patients with a SF2 value below 0.36. When the alpha value was evaluated for the whole group of patients a significantly higher local control rate (80.5% vs. 40.5%) and overall survival rate (71% versus 37.5%) at 2 years were obtained for patients with alpha values above 0.07 Gy-1. When only the group of head and neck cancers was considered, local control rate was significantly higher (79% vs. 33%) but overall survival rate (65.5% vs. 33%) was not significantly higher for alpha values above 0.07 Gy-1.
These results are encouraging but need to be confirmed with a larger number of patients with a longer follow-up.
Laryngeal tumours, especially T1N0M0 and T2N0M0 lesions, are readily controlled by radiotherapy. Studies have shown that control varies with the dose of radiotherapy delivered to the tumour. Other factors, including the dose per fraction and the time over which the treatment schedule is delivered are also important. The varying biological effectiveness of a number of different dose fraction time schedules used in the management of laryngeal tumours of different stages are considered, the end points being tumour control and associated morbidity. Special attention has been given to the length of time over which the schedule is delivered. Of the schedules examined the results would suggest that a dose of 60 Gy given in 25 fractions over a period of 35 days is the best of the six schedules studied for T1, T2, T3 and T4 lesions with minimal associated morbidity. It is possible, however, that the poor results shown on the Kaplan-Meier curves for patients treated with the schedule of 60 Gy in 30 fractions over a period of 42 days could be due to geographical misses of the tumours as 56% were treated without a beam directed shell. The poor result obtained when patients were treated with the schedule of 60 Gy given in 30 fractions over 49+ days may be due to tumour repopulation occurring during the rest period though the possibility of geographical misses may contribute to the poor tumour control results. Mathematical modelling using linear quadratic analysis suggests that the shorter the period of time over which the treatment is given the better chance of achieving tumour control irrespective of the stage of the disease. These models were developed for patients treated with a beam directed shell thus excluding those patients who are most likely to be at risk from a geographic miss of the tumour. Linear quadratic analysis of the treatment data suggests that the ratio alpha/beta for tumour cells is estimated in the region of 13 Gy. For T1 lesions the tumour doubling time is in the order of 6 days, with longer doubling times for the more advanced stages. The analysis provides some support for investigative use of accelerated treatment schedules. This analysis also shows the importance of using beam directed shells when treating small fields especially in the head and neck region.
Interindividual heterogeneity of the radiobiological characteristics of malignant and normal tissues hampers the derivation of radiobiological parameters from clinical data. Focusing on the ratio Dprolif, i.e., the dose to compensate 1 day of treatment interruption, this article investigates the hypothesis that ratios of parameters might be less sensitive to interpatient heterogeneity and may constitute a more reliable description of the radiobiological properties of tissues than the parameters themselves.
Analytic calculations were performed in an idealized example in which the only source of heterogeneity was the number of clonogenic cells. Computer simulations were used to assess the effects of heterogeneity in radiosensitivity and in proliferative capacity. Treatment outcome was simulated in pseudopatients with increasing dose-time correlation.
Interindividual heterogeneity in clonogenic cell number, radiosensitivity, or proliferative ability results in a marked underestimation of the response parameters describing these processes. In contrast, the estimates of the ratio Dprolif were more stable. The coefficients of variation increased with increasing heterogeneity. However, this only became unacceptable when heterogeneity in radiosensitivity was marked, or when total dose and treatment time were closely correlated.
Parameter ratios may provide more robust radiobiological information than single parameters estimated from clinical data except when interindividual heterogeneity is very large or when the treatment modalities are too highly correlated. As usual, caution is advised in the presence of patient selection, a correlation between treatment prescription and expected outcome, or limited ranges of dose-time treatment patterns.
A correlation has been demonstrated between unplanned prolongation of radiotherapy and increased local relapse. This review was performed to assess the importance of overall time on the outcome of curative radiotherapy of larynx cancer.
Retrospective analysis was performed of 383 patients with laryngeal cancer managed by elective radiotherapy between 1976-1988 in the Department of Clinical Oncology, University of Edinburgh, Western General Hospital, Edinburgh All cancers were confirmed histologically to be squamous cell carcinomas. All subjects received radiotherapy in 20 daily fractions (except Saturdays and Sundays), employing individual beam direction techniques and computer dose distribution calculations. Main outcome measures were complete resolution of the cancer in the irradiated volume; local relapse; survival and cause-specific survival rates.
Radiotherapy was completed without any unplanned interruption (28 +/- 2 days) in 230/383 (60%) of patients. A statistically significant two-fold increase in local relapse rates was observed when treatment was given in 31 days or more. There also was a statistically significant four-fold increase in laryngeal cancer deaths when the treatment time exceeded 30 days.
In patients with laryngeal cancer, accelerated repopulation of cancer cells probably occurs after the start of radiotherapy. When the overall treatment time is 4 weeks or less, gaps at weekends are not detrimental. However, long holiday periods or gaps in treatment longer than 4 days increase the risk of laryngeal cancer relapse and cancer-related mortality. Significant gaps in treatment should be avoided. If treatment has to be prolonged, additional radiation dose should be prescribed to compensate for increased tumour cell proliferation.
A critical appraisal is given of the possible benefit from a reliable pre-treatment knowledge of individual normal-tissue sensitivity to radiotherapy. The considerations are in part, but not exclusively, based on the recent experience with in vitro colony-forming assays of the surviving fraction at 2 Gy, the SF2. Three strategies are reviewed: (1) to screen for rare cases with extreme radiosensitivity, so-called over-reactors, and treat these with reduced total dose, (2) to identify the sensitive tail of the distribution of 'normal' radiosensitivities, refer these patients to other treatment, and to escalate the dose to the remaining patients, or (3) to individualize dose prescriptions based on individual radiosensitivity, i.e. treating to isoeffect rather than to a specific dose-fractionation schedule. It is shown that these strategies will have a small, if any, impact on routine radiotherapy. Screening for over-reactors is hampered by the low prevalence of these among otherwise un-selected patients that leads to a low positive predictive value of in vitro radiosensitivity assays. It is argued, that this problem may persist even if the noise on current assays could be reduced to (the unrealistic value of) zero, simply because of the large biological variation in SF2. Removing the sensitive tail of the patient population, will only have a minor effect on the dose that could be delivered to the remaining patients, because of the sigmoid shape of empirical dose-response relationships. Finally, individualizing dose prescriptions based exclusively on information from a normal-tissue radiosensitivity assay, leads to a nearly symmetrical distribution of dose-changes that would produce a very small gain, or even a loss, of tumor control probability if implemented in the clinic. From a theoretical point of view, other strategies could be devised and some of these are considered in this review. Right now the most promising clinical use of in vitro radiosensitivity assays may be as a guide for the prescription of treatment schedules that are costly or involves a high risk of complications. Examples of this are certain strategies attempting to widen the therapeutic window, the use of very high doses or re-irradiation of a previously irradiated region, or the selection of patients for experimental strategies like the use of biological response modifiers to reduce normal-tissue toxicity. Finally, published data are summarized on the possible correlation between the radiosensitivities of tumor and normal tissues or between the sensitivities of various normal tissues.
A 5 week-hyperfractionated and accelerated radiotherapy regimen without reduction of the total dose was developed to fight tumour repopulation during treatment and tumour hypoxia. The purpose of the study was to try to improve loco-regional control in high risk head and neck carcinoma treated with curative radiotherapy.
From 1985 to 1995, a randomised controlled trial of the EORTC Cooperative Group of Radiotherapy (EORTC 22851) compared the experimental regimen (72 Gy/45 fractions/5 weeks) to standard fractionation and overall treatment time (70 Gy/35 fractions/7 weeks) in T2, T3 and T4 head and neck cancers (hypopharynx excluded). The end-point criteria were local and loco-regional control, overall and disease-free survival, and acute and late toxicities. Five hundred twelve patients were accrued.
Patients in the AF (accelerated fractionation) arm did significantly better with regard to loco-regional control (P = 0.02) resulting at 5 years in a 13% gain (95% CI 3-23% gain) in loco-regional control over the CF (conventional fractionation) arm. This improvement is of larger magnitude in patients with poorer prognosis (N2-3 any T, T4 any N) than in patients with more favourable stage. Multivariate analysis confirmed AF as an independent prognostic factor of good prognosis for loco-regional control (P = 0.03). Specific survival shows a trend (P = 0.06) in favour of the AF arm. ACUTE AND LATE TOXICITIES: Acute and late toxicity were increased in the AF arm. Late severe functional irradiation damage occurred in 14% of patients of the AF arm versus 4% in the CF arm. Two cases of radiation-induced myelitis occurred after doses of 42 and 48 Gy to the spinal cord.
This trial shows that accelerated radiotherapy improves loco-regional control in head and neck squamous cell carcinomas. A less toxic scheme should, however, be investigated and documented before using accelerated radiotherapy as a standard regimen of curative radiotherapy for head and neck cancers.
A number of previous studies have used direct maximum-likelihood methods to derive the values of radiobiological parameters of the linear-quadratic model for head and neck tumors from large clinical datasets. Time factors for accelerated repopulation were included, along with a lag period before the start of this repopulation. This study was performed to attempt to utilise these results from clinical datasets to compare treatment regimes in common clinical use in the UK, along with other schedules used historically in a number of clinical series in North America and elsewhere, and to determine if an optimal treatment regime could be derived based on these clinical data.
The biologically-based linear-quadratic model, applied to local tumor control and late morbidity, has been used to derive theoretical optimum (maximising tumor control whilst not exceeding tolerance for late reactions) radiotherapy schedules based on daily fractions. The specific case of T2 laryngeal carcinoma was considered as this is treated primarily by radiotherapy in many centers. Parameter values for local control were taken from previous analyses of several large single-center and national datasets. A time factor and a lag period were included in the modelling. Values for the alpha/beta ratio for late morbidity were used in the range 1-4 Gy, which is compatible with the limited range of values reported in the literature for particular complications following radiotherapy for head and neck cancer. Early reactions and their consequential late morbidity were not modelled in this study, but assumed to be within tolerance.
For treatments using daily fractions there was a broad optimum treatment time of between 3-6 weeks. The theoretical optimum depended to some extent on the value of the alpha/beta ratio for late morbidity, but in many cases was at or just beyond the end of the purported lag period of 3-4 weeks, although small values of alpha/beta between 1-2 Gy favour longer treatment times. Similar results were obtained using a range of parameter values derived from four independent clinical datasets.
The mathematical modelling of this broad range of once-daily treatments for most of which differences in local control and late morbidity are essentially undetectable (< 5%) has shown how this clinically-recognised phenomenon is interpreted in terms of the combination of dose-response slopes, fractionation sensitivities and time factors for both tumor control and normal tissue morbidity. Although the conclusions are inevitably tempered by a number of caveats concerning confounding factors in different centers; for example, the use of different treatment volumes, the present analysis provides a framework with which to explore the potential value of modifications to conventional treatment schedules, such as the use of multiple fractions per day.
Data on patients with cancer of the larynx are analyzed using statistical models to estimate the effect of gaps in the treatment time on the local control of the tumor.
Patients from four centers, Edinburgh, Glasgow, Manchester, and Toronto, with carcinoma of the larynx and treated by radiotherapy were followed up and the disease-free period recorded. In all centers the end point was control of the primary tumor after irradiation alone. The local control rates at > or = 2 years, Pc, were analyzed by log linear models, and Cox proportional hazard models were used to model the disease-free period.
T stage, nodal involvement, and site of the tumor were important determinants of the disease-free interval, as was the radiation schedule used. Elongation of the treatment time by 1 day, or a gap of 1 day, was associated with a decrease in Pc of 0.68% per day for Pc = 0.80, with a 95% confidence interval of (0.28, 1.08)%. An increase of 5 days was associated with a 3.5% reduction in Pc from 0.80 to 0.77. At Pc = 0.60 an increase of 5 days was associated with an 7.9% decrease in Pc. The time factor in the Linear Quadratic model, gamma/alpha, was estimated as 0.89 Gy/day, 95% confidence interval (0.35, 1.43) Gy/day.
Any gaps (public holidays are the majority) in the treatment schedule have the same deleterious effect on the disease free period as an increase in the prescribed treatment time. For a schedule, where dose and fraction number are specified, any gap in treatment is potentially damaging.
To investigate the role of intertumor heterogeneity in clinical tumor control datasets and the relationship to in vitro measurements of tumor biopsy samples. Specifically, to develop a modified linear-quadratic (LQ) model incorporating such heterogeneity that it is practical to fit to clinical tumor-control datasets.
We developed a modified version of the linear-quadratic (LQ) model for tumor control, incorporating a (lagged) time factor to allow for tumor cell repopulation. We explicitly took into account the interpatient heterogeneity in clonogen number, radiosensitivity, and repopulation rate. Using this model, we could generate realistic TCP curves using parameter estimates consistent with those reported from in vitro studies, subject to the inclusion of a radiosensitivity (or dose)-modifying factor. We then demonstrated that the model was dominated by the heterogeneity in alpha (tumor radiosensitivity) and derived an approximate simplified model incorporating this heterogeneity. This simplified model is expressible in a compact closed form, which it is practical to fit to clinical datasets. Using two previously analysed datasets, we fit the model using direct maximum-likelihood techniques and obtained parameter estimates that were, again, consistent with the experimental data on the radiosensitivity of primary human tumor cells. This heterogeneity model includes the same number of adjustable parameters as the standard LQ model.
The modified model provides parameter estimates that can easily be reconciled with the in vitro measurements. The simplified (approximate) form of the heterogeneity model is a compact, closed-form probit function that can readily be fitted to clinical series by conventional maximum-likelihood methodology. This heterogeneity model provides a slightly better fit to the datasets than the conventional LQ model, with the same numbers of fitted parameters. The parameter estimates of the clinically important time factors and lag periods are very similar to those obtained from the conventional LQ model, but with slightly narrower confidence intervals, reflecting the better fit to the clinical data.
We have demonstrated, as have others, the importance of intertumor heterogeneity in the response of patient populations to radiotherapy. With the possible inclusion of a radiosensitivity-modifying factor (in vitro/in vivo) of around 1.7, the in vivo data can be made consistent with the in vitro SF2 and Tpot data. Fitting two previously analyzed multicenter datasets indicated that previous analyses based on conventional LQ models gave results for clinically important time factors and lags periods that were not significantly biased by the failure to include intertumor heterogeneity, with slightly narrower confidence intervals, reflecting the better fit to the clinical data. The simple closed-form model we have developed allows direct estimation of the heterogeneity in radiosensitivity within clinical series, and should prove useful in the analysis of other clinical series.
To model the increases in local tumour control that may be achieved, without increasing normal tissue complications, by prescribing a patient's dose based on cellular radiosensitivity measured using an assay possessing inherent variability.
Patient populations with varying radiosensitivity were simulated, based on measured distributions among cancer patients of the surviving fraction of their fibroblasts given a dose of 2 Gy in vitro (SF2). The dose-response curve for complications in the population was assessed using a formula relating SF2 to normal tissue complication probability (NTCP), by summing the data for the individuals. This curve was similar to clinically-derived dose-response curves. The effect of individualizing the patients' doses was explored, based on individual radiosensitivities measured by SF2, so that every patient had the same low (5%) value of NTCP.
It was found that a significant gain (up to around 30%) in tumour control probability (TCP) was predicted for the population when the doses were individualized using a predictive assay result strongly correlated with NTCP. A greater gain in TCP was predicted when each of the individuals were assumed to have a higher sensitivity and the distribution of radiosensitivity in the population was widened to compensate. The gain in TCP was less (around 20%) when considering less-sensitive patients and a narrower distribution of radiosensitivities. The effect of assay variability and other factors that could affect the predictive power of the assay was simulated. Assay variability and an imperfect correlation between in vitro cell survival and tissue complications, rapidly increased the NTCP for the population when treated with individualized doses. However the individualized doses could be reduced so that NTCP declined to an acceptable level, but in this case the TCP for the population also declined. For example, when the assay variability was half the true variability in SF2, the gain in TCP was reduced to around 6%. Also, the predicted gains in population TCP were higher if tumour and normal tissue radiosensitivity were assumed to be correlated. In this case, and in the absence of assay variability, increases in population TCP of about 50% and 30% were predicted, depending on the assumed relative sensitivities of the individual patients compared with that of the population average. For practical application, the division of the patient population simply into three groups of high, average and low radiosensitivity was also examined. The three groups were treated with different doses and the NTCP for the population was kept below 5%. Although the gain in population TCP was less than that predicted with the full individualization, considerable gains of up to 20% were still predicted. This method of dividing the population was more resilient to assay variability and other factors that may affect complications in patients. The modelling suggests that small improvements in TCP (5-10%) may still be achievable even if the correlation between SF2 and late complications is lower at around - 0.4 to - 0.6, as reported in some clinical series.
Modelling based on measured distributions of fibroblast radiosensitivity shows that improvements in tumour control rates may be achievable through the individualization of radiotherapy dose prescriptions of cancer patients, when assay variability is less than about 50% of the true variability in radiosensitivity, and with greater benefits if tumour and normal tissue radiosensitivity are correlated. Tripartite stratification of the population proved to be less sensitive to assay uncertainty, and can provide most of the benefits of the full individualization.
The linear-quadratic approach to fractionation and calculation of iso-effect relationships
- Joiner
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Joiner MC, van der Kogel AJ. The linear-quadratic approach to fractionation and calculation of iso-effect relationships. In: Steel GG, editor. Basic clinical radiobiology. London: Arnold; 1997. p. 106 –122.
Similar de-creases in local tumor control are calculated for treatment protraction and for interruptions in the radiotherapy of carci-noma of the larynx in four centres
- Robertson Ag Hendry
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Robertson C, Robertson AG, Hendry JH, et al. Similar de-creases in local tumor control are calculated for treatment protraction and for interruptions in the radiotherapy of carci-noma of the larynx in four centres. Int J Radiat Oncol Phys 1998;40:319 –329.
The influence of radiotherapy treatment time on the control of laryngeal cancer
- Roberts
The delay before onset of accelerated tumour cell repopulation during radiotherapy
- Roberts
Final report on the second British Institute of Radiology fractionation study
- Wiernik
The linear-quadratic approach to fractionation and calculation of iso-effect relationships
- Joiner
Influence of radiotherapy treatment time on control of laryngeal cancer
- Hendry