Clonogen Doubling Time Research Articles

Abstract B52: The role of extracellular superoxide dismutase activity in pancreatic cancer biology and therapy

Abstract Introduction: Pancreatic ductal adenocarcinoma (PDA) cells are known to produce excessive amounts of reactive oxygen species (ROS), particularly superoxide (O2•-), which may contribute to the aggressive nature of this disease. Extracellular superoxide dismutase (EcSOD) is an antioxidant enzyme that catalyzes the dismutation of O2•- to hydrogen peroxide (H2O2) in the extracellular environment. By limiting O2•- concentration and producing H2O2, EcSOD is thought to regulate the redox state of the tumor microenvironment that could contribute to pancreatic cancer progression. The current work tests the hypothesis that EcSOD modulates PDA growth and invasion by modifying the balance between H2O2 and ONOO- formation. Methods: EcSOD and 3-nitrotyrosine (3-NT), a marker of protein nitration by ONOO-, were evaluated in specimens from patients with PDA. EcSOD expression was correlated with clinicopathologic and treatment-related variables and survival in a tissue microarray (TMA) of 114 patients with Stage I-IV PDA. EcSOD was constitutively overexpressed in two primary PDA cell lines and clonogenic survival and doubling time were measured. A Matrigel invasion assay was used to determine the impact of EcSOD on PDA tumor cell invasive capacity. We also utilized and GC4419, a selective SOD mimic currently in clinical development. GC4419 dismutates O2•- but does not react with H2O2 under physiologic conditions. PDA cells stably expressing EcSOD and luciferase were used to create hind leg xenografts in athymic nude mice to assess the impact of EcSOD on tumor growth and then via peritoneal injection to determine the impact on peritoneal metastasis formation using bioluminescence imaging (BLI). Results: EcSOD expression was reduced in PDA compared to normal pancreas in 11/16 specimens evaluated (69%). A decrease in expression was also seen in areas of premalignant ductal epithelium (PanIN-3) relative to adjacent pancreas. In normal pancreas tissue, there was no evidence of immunoreactive 3-NT; however, 11/16 PDA specimens (69%) had robust levels of immunoreactive 3-NT. In the TMA, EcSOD expression was absent in 41/114 of the PDA biopsies (36%). The median survival of patients with intact EcSOD expression was 11.0 months vs. 6.5 months for patients with loss of EcSOD expression. Compared to patients with intact EcSOD, patients with loss of EcSOD more often had advanced stage disease and were less likely to be treated with surgery. In an adjusted proportional hazard model of more than 10 clinical variables, the HR for death with loss of EcSOD was 1.63 (95% CI=1.02-2.58, p=0.04). EcSOD overexpression significantly reduced clonogenic survival, doubling time, and tumor cell invasion relative to controls. GC4419 also significantly reduced PDA invasiveness in the Matrigel assay. PDA cells stably expressing EcSOD showed decreased growth and doubling time in hind limb xenografts and significantly less peritoneal metastasis using BLI. Conclusions: Loss of EcSOD expression and oxidative stress as indicated by the presence of 3-NT is a common finding in PDA. Loss of EcSOD expression correlates with negative prognostic factors and shorter survival in patients with PDA. Overexpression of EcSOD resulted in reduced PDA growth, invasion, and peritoneal metastasis. The selective SOD mimic GC4419 also reduced invasion of PDA tumor cells. Together these findings support the hypothesis that modulating O2•- in the PDA microenvironment alters parameters of progression, oxidative damage, and may represent a target for limiting the spread of PDA. (Supported by The American Surgical Association Foundation Fellowship (JJM) and the American Cancer Society (JJM). Citation Format: James J. Mezhir, Brianne R. O'Leary, Andrew M. Bellizzi, Sean Altekruse, Charles F. Lynch, Brenda Y. Hernandez, Wendy Cozen, Michael D. Henry, Jeffrey Keene, Robert A. Beardsley, Douglas R. Spitz, Frederick E. Domann. The role of extracellular superoxide dismutase activity in pancreatic cancer biology and therapy. [abstract]. In: Proceedings of the AACR Special Conference on Pancreatic Cancer: Innovations in Research and Treatment; May 18-21, 2014; New Orleans, LA. Philadelphia (PA): AACR; Cancer Res 2015;75(13 Suppl):Abstract nr B52.

Combining the LKB NTCP model with radiosensitivity parameters to characterize toxicity of radionuclides based on a multiclonogen kidney model: a theoretical assessment

The Lyman-Kutcher-Burman (LKB) normal tissue complication probability (NTCP) model is often used to estimate the damage level to normal tissue. However, it does not manifestly involve the influence of radiosensitivity parameters. This work replaces the generalized mean equivalent uniform dose (gEUD) with the equivalent uniform dose (EUD) in the LKB model to investigate the effect of a variety of radiobiological parameters on the NTCP to characterize the toxicity of five types of radionuclides. The dose for 50% complication probability (D (50)) is replaced by the corresponding EUD for 50% complication probability (EUD(50)). The properties of a variety of radiobiological characteristics, such as biologically effective dose (BED), NTCP, and EUD, for five types of radioisotope ((131)I, (186)Re, (188)Re, (90)Y, and (67)Cu) are investigated by various radiosensitivity parameters such as intrinsic radiosensitivity α, alpha-beta ratio α/β, cell repair half-time, cell mean clonogen doubling time, etc. The high-energy beta emitters ((90)Y and (188)Re) have high initial dose rate and mean absorbed dose per injected activity in kidney, and their kidney toxicity should be of greater concern if they are excreted through kidneys. The radiobiological effect of (188)Re changes most sharply with the radiobiological parameters due to its high-energy electrons and very short physical half-life. The dose for a probability of 50% injury within 5y (D (50/5)) 28Gy for whole-kidney irradiation should be adjusted according to different radionuclides and different radiosensitivity of individuals. The D (50/5) of individuals with low α/β or low α, or low biological clearance half-time, will be less than 28Gy. The 50% complication probability dose for (67)Cu and (188)Re could be 25Gy and 22Gy. The same mean absorbed dose generally corresponds to different degrees of damage for tissues of different radiosensitivity and different radionuclides. The influence of various radiobiological parameters should be taken into consideration in the NTCP model.

Determination of the optimum dose per fraction in fractionated radiotherapy when there is delayed onset of tumour repopulation during treatment.

The choice of fractionation in radiotherapy involves a compromise between a number of competing radiobiological factors. The severity of late normal tissue effects may be highly dependent on fraction size, thus requiring the dose per fraction to be relatively small. This in turn leads to more fractions being used in order to maintain the tumour effect, resulting in a longer overall treatment time. In contrast, tumours possessing short clonogen doubling times ideally require shorter treatment times for improved tumour cell kill in order to reduce the impact of tumour cell repopulation. A mathematical model has been previously developed to investigate ways of optimizing the theoretical treatment outcome by estimating the optimum dose per fraction required for a given set of radiobiological parameters [1, 2]. The earlier model assumed that tumour repopulation proceeds at a constant rate right from the initiation of treatment, i.e. that there is no delay time before the repopulation process begins. However, especially for head and neck tumours, there is evidence for the existence of a lag time before the onset of compensatory re-growth [3, 4]. This report describes a modification to the earlier model and which provides a non-analytical, re-iterative, method for deriving the optimum dose per fraction which produces the maximum biologically effective dose (BED) to the tumour in the presence of a delayed start to repopulation.

Repopulation of moderately well-differentiated and keratinizing GL human squamous cell carcinomas growing in nude mice

Purpose It has been suggested that, reminiscent of the regulated proliferative response of normal squamous epithelium, squamous cell carcinomas that have preserved characteristics of differentiation have a greater repopulation capacity during fractionated irradiation than undifferentiated tumors. The aim of the present study was to investigate repopulation in moderately well-differentiated and keratinizing GL human squamous cell carcinomas in nude mice. Methods and materials GL human squamous cell carcinomas were transplanted s.c. into the right hind leg of NMRI nu/nu mice. Irradiation was performed with 5.4 Gy fractions under clamp hypoxia or with 2 Gy fractions under ambient conditions. Six, 12, or 18 fractions were given daily, every second day, or every third day. Graded top-up doses were applied under clamp hypoxia to determine the tumor control dose 50% ( TCD 50). A total of 20 TCD 50 assays were performed and analyzed using maximum-likelihood techniques. Results With an increasing number of daily 5.4 Gy fractions under clamp hypoxia, the top-up TCD 50 values decreased significantly from 50.9 Gy (95% CI: 47, 54) after single doses to 0 Gy after 18 fractions. For the same number of fractions, the top-up TCD 50 increased with increasing overall treatment time. The results are consistent with a constant repopulation rate with a clonogenic doubling time ( T clon ) of 12.7 days (8.6, 16.8). Under ambient blood flow, the top-up TCD 50s for daily 2 Gy fractions decreased significantly, but were less pronounced than for 5.4 Gy fractions under clamp hypoxia. For a given number of fractions under ambient conditions, the top-up TCD 50s did not increase significantly with overall treatment time, except for irradiation with 12 fractions in 36 days compared to 12 and 24 days. The T clon value from these data was 24.0 days (11.6, 36.4). Conclusion Our data demonstrate a slow but significant rate of repopulation of clonogenic tumor cells during fractionated irradiation of GL human squamous cell carcinomas under clamp hypoxia without indication of a change of the repopulation rate during treatment. Less pronounced repopulation was observed for irradiation under ambient conditions, which might be explained by preferential survival of hypoxic and therefore nonproliferating cells. Taken together with our previous studies on poorly differentiated FaDu tumors (Petersen et al., IJROBP 2001;51:483–493), the results support important heterogeneity of kinetics and mechanisms of repopulation, in particular of the influence of the oxygenation status of surviving clonogenic cells on the repopulation rate during fractionated irradiation, in different experimental squamous cell carcinoma.

Repopulation of FaDu human squamous cell carcinoma during fractionated radiotherapy correlateswith reoxygenation

Purpose: FaDu human squamous cell carcinoma (FaDu-hSCC) showed a clear-cut time factor during fractionated radiotherapy (RT) under ambient blood flow. It remained unclear whether this is caused solely by proliferation or if radioresistance resulting from increasing hypoxia contributed to this phenomenon. To address this question, repopulation of clonogenic FaDu cells during fractionated RT under clamp hypoxia was determined by local tumor control assays, and compared to the results after irradiation with the same regimen under ambient blood flow.Methods and Materials: FaDu-hSCC was transplanted into the right hind leg of NMRI nu/nu mice. In the first set of experiments, irradiation was performed under clamp hypoxia. After increasing numbers of 3 Gy fractions (time intervals 24 h or 48 h), graded top-up doses were given to determine the TCD50 (dose required to control 50% of the tumors). In the second set of experiments, all 3 Gy fractions were applied under ambient conditions, but as in the previous experiments the graded top-up doses were given under clamp hypoxia. A total of 26 TCD50 assays were performed and analyzed using maximum likelihood techniques.Results: With increasing numbers of daily fractions, the top-up TCD50 under clamp hypoxia decreased from 39.4 Gy [95% CI 36, 42] after single dose to 19.8 Gy [15, 24] after 18 fractions in 18 days and to 37.8 Gy [31, 44] after 18 fractions in 36 days. The results were consistent with biphasic repopulation, with a switch to rapid repopulation after about 22 days [13, 30]. The clonogen doubling time (Tclon) decreased from 9.8 days [0, 21] in the beginning of RT to 3.4 days after 22 days. Under ambient blood flow the top-up TCD50 decreased from 37.6 Gy [34, 40] after single dose irradiation to 0 Gy [0, 1] after 18 fractions in 18 days and 22.4 Gy [18, 27] after 18 fractions in 36 days. Similar to results from irradiations under clamp hypoxia, the ambient data were consistent with a biphasic course of clonogen inactivation. Comparison of both data sets revealed significant reoxygenation after 12 fractions.Conclusions: Our data are most consistent with a biphasic course of clonogen repopulation during fractionated RT of FaDu-hSCC under clamp hypoxia with a switch in Tclon after about 22 days of treatment (“dog-leg”). A similar biphasic course of cell repopulation was observed under ambient conditions. The temporal coincidence between repopulation and reoxygenation suggests that the latter might be the stimulus for proliferation in FaDu tumors.

Biological Factors Influencing Optimum Fractionation in Radiation Therapy

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 f g ratio may indeed be lower than 3 Gy. For an entirely different reason from that above, hypofractionation should be tested.

Radiobiological considerations in the design of fractionation strategies for intensity-modulated radiation therapy of head and neck cancers

Purpose: The dose distributions of intensity-modulated radiotherapy (IMRT) treatment plans can be shown to be significantly superior in terms of higher conformality if designed to simultaneously deliver high dose to the primary disease and lower dose to the subclinical disease or electively treated regions. We use the term “simultaneous integrated boost” (SIB) to define such a treatment. The purpose of this paper is to develop suitable fractionation strategies based on radiobiological principles for clinical trials and routine use of IMRT of head and neck (HN) cancers. The fractionation strategies are intended to allow escalation of tumor dose while adequately sparing normal tissues outside the target volume and considering the tolerances of normal tissues embedded within the primary target volume. Methods and Materials: IMRT fractionation regimens are specified in terms of “normalized total dose” (NTD), i.e., the biologically equivalent dose given in 2 Gy/fx. A linear-quadratic isoeffect formula is applied to convert NTDs into “nominal” prescription doses. Nominal prescription doses for a high dose to the primary disease, an intermediate dose to regional microscopic disease, and lower dose to electively treated nodes are used for optimizing IMRT plans. The resulting nominal dose distributions are converted back into NTD distributions for the evaluation of treatment plans. Similar calculations for critical normal tissues are also performed. Methods developed were applied for the intercomparison of several HN treatment regimens, including conventional regimens used currently and in the past, as well as SIB strategies. This was accomplished by comparing the biologically equivalent NTD values for the gross tumor and regional disease, and bone, muscle, and mucosa embedded in the gross tumor volume. Results: (1) A schematic HN example was used to demonstrate that dose distributions for SIB IMRT are more conformal compared to dose distributions when IMRT is divided into a large-field phase and a boost phase. Both were shown to be significantly superior compared to dose distributions obtained using conventional beams for the large-field phase followed by IMRT for the boost phase. (2) The relationship between NTD and nominal dose for HN tumors was found to be quite sensitive to the choice of tumor clonogen doubling time but relatively insensitive to other parameters. (3) For late effect normal tissues embedded in the tumor volume and assumed to receive the same dose as the tumor, the biologically equivalent NTD for the SIB IMRT may be significantly higher. (4) Normal tissues outside the target volume receive lower dose due to the higher conformality of the IMRT plans. The biologically equivalent NTDs are even lower due to the lower dose per fraction in the SIB strategy. Conclusions: IMRT dose distributions are most conformal when designed to be delivered as SIB. Using isoeffect radiobiological relationships and published HN data, fractionation strategies can be designed in which the nominal dose levels to the primary, regional disease and electively treated volumes are appropriately adjusted, each receiving different dose/fx. Normal tissues outside the treated volumes are at reduced risk in such strategies since they receive lower total dose as well as lower dose/fx. However, the late effect toxicities of tissues embedded within the primary target volume and assumed to receive the same dose as the primary may pose a problem. The efficacy and safety of the proposed fractionation strategies will need to be evaluated with careful clinical trials.

Mathematical Models of Tumour and Normal Tissue Response

The historical application of mathematics in the natural sciences and in radiotherapy is compared. The various forms of mathematical models and their limitations are discussed. The Linear Quadratic (LQ) model can be modified to include (i) radiobiological parameter changes that occur during fractionated radiotherapy, (ii) situations such as focal forms of radiotherapy, (iii) normal tissue responses, and (iv) to allow for the process of optimization. The inclusion of a variable cell loss factor in the LQ model repopulation term produces a more flexible clonogenic doubling time, which can simulate the phenomenon of 'accelerated repopulation'. Differential calculus can be applied to the LQ model after elimination of the fraction number integers. The optimum dose per fraction (maximum cell kill relative to a given normal tissue fractionation sensitivity) is then estimated from the clonogen doubling times and the radiosensitivity parameters (or alpha/beta ratios). Economic treatment optimization is described. Tumour volume studies during or following teletherapy are used to optimize brachytherapy. The radiation responses of both individual tumours and tumour populations (by random sampling 'Monte-Carlo' techniques from statistical ranges of radiobiological and physical parameters) can be estimated. Computerized preclinical trials can be used to guide choice of dose fractionation scheduling in clinical trials. The potential impact of gene and other biological therapies on the results of radical radiotherapy are testable. New and experimentally testable hypotheses are generated from limited clinical data by exploratory modelling exercises.

The reduction of tumour control with increasing overall time: mathematical considerations.

The rate of loss of tumour control (dP/dt) with extension of treatment time is analysed to assess the relative contributions of radiobiological parameters (radiosensitivity, clonogen doubling time, clonogen numbers and fractionation schedule) on such loss. Linear quadratic modelling and Poisson statistics are used to study individual tumour responses. A heterogeneous tumour population is constructed by the use of random sampling techniques to allow for variations in intrinsic radiosensitivity and clonogen doubling times. Average tumour control probability is calculated for this population for two different fractionation schedules (60 Gy in 30 fractions and 50 Gy in 15 fractions), each given over 15-60 days. The magnitude of dP/dt will depend upon the tumour cure probability (P): the loss of control will be most significant for tumours which have a cure of 37% when the Poisson survival model is used. The analysis suggests that compensation for short unscheduled treatment gaps (e.g. by increasing the total dose or rescheduling with use of weekend treatment sessions) may only be required for difficult tumours (i.e. radioresistant and/or with short clonogen doubling times). Where pre-treatment clonogen numbers are relatively low as in small volume tumours or after surgical debulking, the model predicts that correction for short treatment gaps is probably not required if the average effective clonogen doubling times are longer than 5 days. Different dose-time-fractionation schedules, even though producing similar overall cure rates in clinical practice, may actually be achieving cures in different subpopulations within a population of tumours, since the value of dP/dt in each individual tumour will depend upon the set of radiobiological parameters given above. For a hypothetical randomly selected heterogeneous tumour population the predicted rates of loss of tumour control produced by an extension in treatment time are 0.9 and 1.1% per day, respectively, for the above fractionation schedules. These values are close to those reported in the clinical literature for the first 2 weeks of treatment prolongation (1-2% per day for squamous cell carcinomas). The Poisson method, when combined with random sampling techniques, consequently provides realistic data. Modelling of this clinical problem provides an insight into how tumour sub-populations, each characterized by its own set of radiobiological parameters, can influence the overall rate of loss of tumour control in a heterogeneous population. Random sampling techniques should be considered as necessary precursors for the assessment of the choices of dose-fractionation in future clinical trials particularly when more precise data regarding the radiobiological parameters and their statistical variations become available.

Repopulation in the SCCVII squamous cell carcinoma assessed by an in vivo-in vitro excision assay

An in vivo-in vitro excision assay was used to study repopulation after a single dose of clamped irradiation (40 Gy) in the SCCVII tumour implanted in the foot of C3H/Km mice. The growth pattern of clonogenic cells was analysed by two different mathematical models: the logistic model and the Gompertz model. The logistic model described the data better than the Gompertz model. Accelerated repopulation was found when the regrowth rate after irradiation was compared to the growth rate at the time of treatment, and when it was compared to the growth rate in untreated tumours with a number of cells equivalent to the number that was found after irradiation. The clonogenic doubling time (cDT) was estimated at 15.1 h (95% c.i.: 14.2; 16.0) after irradiation, and 27.8 h (95% c.i.: 16.7; 43.5) in untreated controls of matching size. However, the estimate relies on the mathematical model chosen and on extrapolation below actually measured data. A small cDT points to shortening of the cell cycle time and recruitment of non-cycling clonogenic tumour cells to be the main mechanism behind the accelerated repopulation.

Improved models of tumour cure.

The standard mechanistic model for the probability of tumour cure (the "Poisson model') is based on the assumption that the number of surviving clonogens at the end of treatment follows a Poisson distribution from tumour to tumour. This assumption is not correct, however, if proliferation of tumour clonogens occurs during treatment, as would be expected in general during a fractionated course of radiotherapy. In the present study, the possible magnitude of the error in the Poisson model was investigated for tumours treated with either conventional fractionation or split-course therapy. An example is presented in which the Poisson model has an absolute error of nearly 100%, predicting a cure rate of 0% when in fact the cure rate was close to 100%. The largest errors in the Poisson model found in this study were for very small tumours (approximately 100 clonogens), but for larger tumours (> or = 10(6) clonogens), the Poisson model may still be highly inaccurate, predicting a cure rate that differs from the actual cure rate by as much as 40%. Three new tumour-cure models are proposed (the GS, PS, and GS+ models), and their accuracy is also investigated. Two of these (the GS and PS models) are better than the Poisson model for the clinically relevant cases tested here. The third model, the GS+ model, consistently produced the most accurate estimate of the tumour cure rate, but has more limited use than the GS and PS models because it is more highly parametrized. It is demonstrated here that no tumour-cure model based on the effective clonogen doubling time will be perfectly accurate in all cases, since the cure rate depends on the details of the cell kinetics contributing to the effective doubling time.

Derivation of the optimum dose per fraction from the linear quadratic model.

The linear quadratic equation for fractionated radiotherapy has already been adapted to include a time factor for tumour repopulation: loge cell kill (E) is given as a function of dose per fraction (d), number of fractions (n), overall treatment time (T) and the clonogen doubling time (Tp). By incorporating a normal tissue isoeffect and replacing the relationship between T and n by a function f, the equation for E can be rewritten as a more complex function of d. In this form, E and d are continuous variables so that the dose per fraction (d') required to produce maximum values of E for isoeffective late normal tissue effects can be found by differential calculus. The derived equation takes the form (beta kTp-alpha Tp)d2 + 1.386fd + 0.693fk = 0 and when solved for d provides a direct estimation of the optimum dose per fraction. Where normal tissue sparing is possible and the tumour dose z is related to the normal tissue dose d, the optimum dose per fraction z' can be found by solving the equation (beta kTp-alpha gTp)z2 + 1.386fgz + 0.693fk = 0 The results show that a critical minimum dose per fraction is required to counteract rapid tumour clonogen repopulation in both conventional and accelerated radiotherapy. The calculus method is reasonably accurate for larger fraction numbers, when clonogen doubling times are 3.5 days or longer and for conventional radiotherapy given 5 days per week. The model is even more accurate for accelerated hyperfractionated radiotherapy providing that there is complete repair between successive fractions. Where greater normal tissue sparing is possible, as with focal teletherapy methods and brachytherapy, higher tumour doses per fraction can be used to increase further the tumour cell kill without exceeding normal tissue tolerance. These predicted doses per fraction are consistent with clinical experience when the given constraints in terms of frequency of treatment are considered. The model described can be used for tumours in which repopulation occurs at a constant rate throughout treatment. For tumours in which accelerated repopulation occurs, the optimum dose per fraction can be separately calculated for the initial phase of slow repopulation (for which very small doses per fraction are optimal) and also for the second phase of rapid repopulation (for which either accelerated hyperfractionated treatments or hypofractionated focal methods of treatment would be appropriate). The limitations of the model are fully discussed including the need for accurate radiobiological predictive assays. In the future such assays of pre-treatment doubling times and tumour cell radiosensitivities could be used to determine reasonable ranges for the optimum dose per fraction in experimental tumours and subsequently in clinical trails. This approach could produce major improvements in the therapeutic potential of radiotherapy.

A mathematical model of intraluminal and intracavitary brachytherapy.

The adaptation of the linear-quadratic model to allow for the effect of tumour regression and clonogen repopulation between initial teletherapy and subsequent brachytherapy has been extended to include the geometrical conditions encountered in intraluminal and intracavitary brachytherapy. For a radiation line source placed at the centre of a lumen or cavity, regression of any endoluminal tumour towards its mural origin will not result in any change in the minimum brachytherapy-tumour dose with time. In contrast, regression of transmural tumour will cause a potentially advantageous increase in the minimum brachytherapy-tumour dose with time. The latter effect will be opposed by tumour clonogen repopulation. The log(e) cell kill due to brachytherapy has been calculated for tumours of diameters 2, 4 and 6 cm at completion of teletherapy. The centres of the tumours were assumed to be at distances of 0, 1 and 2 cm from the radiation source. Tumour linear regression rates (lambda) ranging from 0.025 to 0.25 per week and tumour clonogen doubling times (Tp) of 2.5, 5 and 15 days were used in the calculations. The results demonstrate the critical importance of the distance of the tumour centre from the line source as well as the influence of tumour diameter, lambda and Tp. In some instances, both maximum and minimum values of log(e) cell kill occur. Calculations of tumour cure probabilities reveal that these variations in log(e) cell kill predicted by the model can produce highly significant differences in tumour control rates. Where the relevant parameters can be assessed directly or estimated from previous experience, the model provides a basis for the design of future intraluminal or intracavitary brachytherapy protocols.

Effect of tumour shrinkage on the biological effectiveness of permanent brachytherapy implants

A tumour shrinkage factor is incorporated into previously derived linear-quadratic (LQ) formulae which allowed radiobiological assessment of the efficacy of permanently implanted radionuclides. The new formulations relate the biologically effective dose (BED) to radionuclide half-life, recovery half-life, tumour radiosensitivity, potential doubling time and linear shrinkage rate. Specific attention has been given to the following radionuclides: gold-198 (half-life, 2.7 days), palladium-103 (half-life, 17 days), ytterbium-169 (half-life, 32 days) and iodine-125 (half-life, 60 days). For each nuclide the log cell kill resulting from typically prescribed doses was calculated for a range of tumour clonogen doubling times at various radiosensitivities and linear shrinkage rates. It is shown that even relatively modest shrinkage rates are capable of enhancing the clinical potential of the longer-lived nuclides. However, even though the effect of tumour shrinkage is minimal in the case of gold-198, for fast growing and/or insensitive tumours there are fewer radiobiological uncertainties associated with the use of this nuclide. The revised equations may also have applications in certain types of biologically targeted radiotherapy.

Effect of overall time when radiotherapy includes teletherapy and brachytherapy: a mathematical model.

By expanding the linear quadratic equations to allow for the interval of time between teletherapy and brachytherapy in a model which assumes continual exponential tumour regression following teletherapy, the loge cell kill resulting from brachytherapy is found to depend on radiosensitivity, tumour regression rate (lambda) and tumour clonogen doubling time (Tp). When lambda is relatively small the precise timing of brachytherapy following teletherapy is shown to influence the tumour cure probabilities. The model predicts a reduction in tumour control if brachytherapy is delayed when lambda values are small and Tp values are short, but when Tp values are long, deferral of brachytherapy may be advantageous. By differential calculus the occurrence of a minimum value of log cell kill can be found. Application of these concepts may improve the results of clinical radiotherapy.

Changes in TCD 50 as a measure of clonogen doubling time in irradiated and unirradiated tumors

Dose-cure experiments have been carried out on a moderately well differentiated murine mammary carcinoma, designated MCA-4, at different stages of growth after tumor-cell inoculation or after 8 mm established tumors had been exposed to 60 Gy. TCD 50 assays were performed at 1, 3, 7, 14, or 21 days after tumor cell inoculation, or when tumors reached a size of 6 or 8 mm. Likewise, TCD 50 assays were performed at 0.25, 1, 3, 5, 8, 12, 16, or 21 days after 8 mm tumors had been exposed to a 60 Gy priming dose, or when the recurrent tumors reached 6 or 8 mm. All irradiations were performed under hypoxic conditions. The TCD 50 (95% confidence limits) was 64.0 (61.7–68.3) Gy for the 6-mm and 71.9 (70.1–73.9) Gy for the 8 mm tumors, and these values were unaffected by preirradiation. Direct analysis was used for the simultaneous estimation of D 0, clonogen number, and clonogen doubling time from the pooled data. There was no significant difference between D 0 estimates for the preirradiated and control tumors, and the pooled estimate was 10.6 (9.6–11.8) Gy for tumors assayed at specified time points where the size was unknown. This is clearly higher than in tumors of known size [estimate for 6- and 8-mm tumors: D 0= 5.4 (4.5–6.6) Gy] owing to size and other heterogeneity. The clonogen doubling times (T clon) were 3.4 (3.0–4.0) days in the preirradiated tumors and 5.8 (4.9–7.1) days in the unirradiated tumors. It is not unreasonable to assume that the systematic error due to heterogeneity was approximately the same for D 0 and T clon (since variable clonogen number is likely the predominant source of heterogeneity), and thus the ratio of Do for tumors of unknown sizes (10.6 Gy) and D 0 for tumors of known sizes (5.4 Gy) can be used to “correct” the T clon estimates, with the result that T clon (preirradiated) = 1.7 days and T clon (unirradiated) = 3.0 days. We conclude that the clonogen doubling time was shorter in tumors exposed to a single high-dose irradiation than in unirradiated controls, which implies the existence of faster cell repopulation in irradiated tumors.

Dose fractionation and tumour repopulation in radiotherapy for bladder cancer

Local control of the 77 transitional cell carcinoma of the bladder was analysed with respect to total dose after normalization for variations in fraction size and to overall treatment time. For the TCD 50 of 63.3 Gy protraction of overall treatment time from 40 to 55 days average gave the decrease in local control rate from 50 % to about 5 %j The decrease in local tumour control with extension of overall treatment time likely reflects accelerated tumour repopulation during the treatment. To determine the time onset of the accelerated tumour clonogen repopulation, data taken from the literature were analysed. Results show that on average tumour clonogen repopulation in transitional cell cancer of the bladder accelerates after a lag period of about 5–6 weeks after the start of treatment and that a dose increment of 0.36 Gy per day is required to compensate for this repopulation. Such a dose increment is consistent with about 5–8 day clonogen doubling time. It suggests that overall treatment time is an important factor in the dose fractionation and protraction of time may have a significant impact on treatment outcome. Thus, radiotherapy for bladder cancer should be completed as soon as possible and total dose for high probability of local tumour control should consequently be delivered in more than 5 fractions per week.

Tumour cell repopulation during fractionated radiotherapy: Correlation between flow cytometric and radiobiological data in three murine tumours

This study tested whether the potential doubling time of tumour cells measured before or during treatment could predict the repopulation rate of surviving clonogens during fractionated radiotherapy. Tumours used for the study were a fibrosarcoma (SSK 2), an adenocarcinoma (AT 7) and a squamous cell carcinoma (AT 478), all grown subcutaneously in the C3H mouse. Potential doubling times (Tpot) were measured using the thymidine nanalogue iododeoxyuridine (IUdR) and flow cytometry. Results were compared with previous radiobiological studies on these tumours in which repopulation rates during radiotherapy were estimated using the tumour growth delay and tumour cure assays. Fractionated treatments consisted of daily doses of 4 or 8 Gy to clamped (hypoxic) tumours, 6 days per week for 1–3 weeks. Tpot values increased markedly during therapy for two of the tumours (SSK 2 and AT 478), by a factor of more than 10 for AT 478 in the third treatment week. Tpot remained approximately constant for the third tumour (AT 7). In no case was there evidence from the labelling studies of a shortening of Tpot which would suggest accelerated repopulation. From the radiobiological data, effective clonogen doubling times during radiotherapy were calculated from the doses required to produce a given effect in short and long treatment schedules. In the second week of treatment, effective clonogen doubling times in two tumours were approximately equal to the pretreatment Tpot, and shorter than the pretreatment Tpot in the third tumour. At some time during treatment, the surviving clonogens in these tumours therefore proliferated at the same rate or faster than before treatment. The difference between the labelling and radiobiological measurements was ascribed to the fact that, shortly after the start of a fractionated treatment, the IUdR labelling technique measures primarily doomed cells. These results show that kinetic measurements using DNA labelling techniques made during fractionated radiotherapy in most cases do not reflect the proliferation status of the surviving cells which are responsible for treatment outcome. Pretreatment Tpot measurements give a much better indication of the proliferation rate of surviving cells but in some cases may underestimate repopulation during radiotherapy.

Repopulation in Murine Skin after X-Ray Treatments with Multiple Fractions per Day

The kinetics of repopulation of clonogens in skin after fractionated X-ray exposures was studied in a series of experiments using a top-up design. The feet of mice were exposed to small X-ray doses (1.5 or 2 Gy), given two or three times a day on consecutive days with a minimum interfraction interval of 8 h. A single top-up dose of d(4)-Be neutrons was then given at various intervals after the last X-ray fraction, typically on Days 1,4,8, 15, and 19. The acute skin reaction produced was scored an analyzed by both a standard 23-day averaging and a 7-day averaging procedure. Either method gave similar results and led to the same conclusions. The amount of top-up dose needed to produce a fixed skin reaction was used as a measure of the net effect of the X-ray treatments. This net effect is a result of the initial reduction in skin clonogens due to X rays, and their repopulation before the top-up dose was given. Repopulation was not detected during any of these courses of fractionated treatment, up to an overall time of at least 12 and possibly 16 days. On completion of X-ray schedules lasting 6-16 days, repopulation started 4 days later. In contrast, this delay lengthened to approximately 8 days for shorter overall treatment times of 3-4 days. Once repopulation started, it proceeded rapidly over 11 days so that by 15 days after the cessation of X rays, the skin was restored almost to its normal state with respect to radiosensitivity. The residual damage from Day 15 to Day 19 postirradiation was 3-13% of a full-effect level. The rate of repopulation can be expressed as a clonogen doubling time (Tclon), assuming that an average skin reaction of 1.5 is equivalent to a clonogen surviving fraction of 1.7 x 10(-5). Tclon varied inversely with the amount of initial damage inflicted by the X rays, with the shortest values (1-1.3 days) seen following X-ray doses that gave an initial damage level of 60-80% of full effect. These data are consistent with a hypothesis that damage is "sensed" only 10-12 days after the first X-ray fraction, which provides the stimulus for repopulation of the target cells in the basal layer, the keratinoblasts.(ABSTRACT TRUNCATED AT 250 WORDS)

The selection of patients for accelerated radiotherapy on the basis of tumor growth kinetics and intrinsic radio sensitivity

Mathematical modeling was used to reach qualitative conclusions concerning the relative rate of local tumor control that might be achieved by using accelerated fractionation to treat only the patients with the most rapidly growing tumors, compared with the control rates that could be expected from either conventional or accelerated radiotherapy alone. The results suggest that concomitant boost therapy is equally or more effective than conventional dose fractionation for all tumors, regardless of their growth kinetics. For tumors with very short clonogen doubling times, CHART (continuous hyperfractionated accelerated radiotherapy) may be even more effective than concomitant boost treatment, but CHART is less effective than conventional or concomitant boost therapy for tumors with longer clonogen doubling times. Thus, there is a rationale for using a predictive assay of tumor clonogen doubling times to identify the patients who should be treated with CHART. However, improvements in local tumor control resulting from concomitant boost treatment or the selective use of CHART are not likely to be apparent in the population as a whole, because the overall control rates are largely determined by refractory tumors having little chance of control with any of the treatments and by highly responsive tumors that are likely to be controlled regardless of the treatment choice. Differences in control rates with different treatment strategies are most apparent in the stochastic fraction of the population, which excludes those patients for whom there is either very little chance (e.g. < 1%) or a very high chance (e.g. > 99%) of achieving local control with both treatments. The stochastic fraction can be approximated by excluding those patients with the most radioresistant and the most radiosensitive tumors, since intrinsic tumor radio sensitivity appears to be the single most important factor determining treatment outcome.