Effective Doubling Time Research Articles

Epidemiological measures for assessing the dynamics of the SARS-CoV-2-outbreak: Simulation study about bias by incomplete case-detection.

During the SARS-CoV-2 outbreak, several epidemiological measures, such as cumulative case-counts (CCC), incidence rates, effective reproduction numbers (Reff) and doubling times, have been used to inform the general public and to justify interventions such as lockdown. It has been very likely that not all infectious people have been identified during the course of the epidemic, which lead to incomplete case-detection. We compare CCC, incidence rates, Reff and doubling times in the presence of incomplete case-detection. For this, an infection-age-structured SIR model is used to simulate a SARS-CoV-2 outbreak followed by a lockdown in a hypothetical population. Different scenarios about temporal variations in case-detection are applied to the four measures during outbreak and lockdown. The biases resulting from incomplete case-detection on the four measures are compared in terms of relative errors. CCC is most prone to bias by incomplete case-detection in all of our settings. Reff is the least biased measure. The possibly biased CCC may lead to erroneous conclusions in cross-country comparisons. With a view to future reporting about this or other epidemics, we recommend including and placing an emphasis on Reff in those epidemiological measures used for informing the general public and policy makers.

Impact of intervention on the spread of COVID-19 in India: A model based study

The outbreak of coronavirus disease 2019 (COVID-19), caused by the virus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has already created emergency situations in almost every country of the world. The disease spreads all over the world within a very short period of time after its first identification in Wuhan, China in December, 2019. In India, the outbreak, starts on 2nd March, 2020 and after that the cases are increasing exponentially. Very high population density, the unavailability of specific medicines or vaccines, insufficient evidences regarding the transmission mechanism of the disease also make it more difficult to fight against the disease properly in India. Mathematical models have been used to predict the disease dynamics and also to assess the efficiency of the intervention strategies in reducing the disease burden. In this work, we propose a mathematical model to describe the disease transmission mechanism between the individuals. Our proposed model is fitted to the daily new reported cases in India during the period 2nd March, 2020 to 12th November, 2020. We estimate the basic reproduction number, effective reproduction number and epidemic doubling time from the incidence data for the above-mentioned period. We further assess the effect of implementing preventive measures in reducing the new cases. Our model projects the daily new COVID-19 cases in India during 13th November, 2020 to 25th February, 2021 for a range of intervention strength. We also investigate that higher intervention effort is required to control the disease outbreak within a shorter period of time in India. Moreover, our analysis reveals that the strength of the intervention should be increased over the time to eradicate the disease effectively.

TH-AB-BRB-07: A Feasibility Study for Personalized Fractionation Schedule for Lung Cancer

Purpose: Investigate the feasibility of using spatio-temporal optimization, i.e., fractionation schedule optimization combined with IMRT to select the patient-specific fractionation schedule that best maximizes the tumor biologically equivalent dose (BED). Methods and materials: The optimal fractionation schedule for a patient depends on the tumor and organ at-risk (OAR) sensitivity to fraction size (i.e., α/β), the effective tumor doubling time, and the size and location of tumor target relative to one or more OAR. We used a novel spatio-temporal optimization method to identify the number of fractions N that maximizes the tumor BED using 3D BED distribution for sixteen lung phantom cases. The selection of the optimal fractionation schedule used equivalent 30-fraction OAR constraints for the heart (Dmean < 45 Gy), lungs (Dmean < 20 Gy), cord (Dmax < 45 Gy), esophagus (Dmax < 63 Gy), and unspecified tissues (D05 < 63 Gy). To asses plan quality, we considered the min, mean, max and D95 tumor BED and the equivalent uniform dose (EUD) for optimized plans to the corresponding BED values for a conventional IMRT plan (60 Gy in 30 fractions). A sensitivity analysis was performed to assess the effects on optimal fractionation schedule of the effective tumor doubling time (Td = 3–100 days) and lag-time for accelerated repopulation (Tk = 0 to 10 days) Results: For a tumor α/β = 10Gy, tumor max, min, mean, and D95 BED were about 20% larger than the BED for the conventional prescription. The EUD for the optimized fractionation schedule was up to 17% larger than conventional prescription. For fast proliferating tumor (Td < 10 days), there was no significant increase in tumor dose but the treatment course could be shortened, offering convenience for patients and efficient allocation of resources.

Utilitarian prioritization of radiation oncology patients based on maximization of population tumour control

An objective method for establishing patient prioritization in the context of a radiotherapy waiting list is investigated. This is based on a utilitarian objective, being the greatest probability of local tumour control in the population of patients. A numerical simulation is developed and a clinical patient case-mix is used to determine the influence of the characteristics of the patient population on resulting optimal patient scheduling. With the utilitarian objective, large gains in tumour control probability (TCP) can be achieved for individuals or cohorts by prioritizing patients for that fraction of the patient population with relatively small sacrifices in TCP for a smaller fraction of the population. For a waiting list in steady state with five patients per day commencing treatment and leaving the list (and so with five patients per day entering the list), and a mean wait time of 35 days and a maximum of 90 days, optimized wait times ranged from a mean of one day for patients with tumour types with short effective doubling times to a mean of 66.9 days for prostate cancer patients. It is found that, when seeking the optimal daily order of patients on the waiting list in a constrained simulation, the relative rather than absolute value of TCP is the determinant of the resulting optimal waiting times. An increase in the mean waiting time mostly influences (increases) the optimal waiting times of patients with fast-growing tumours. The proportional representation of groups (separated by tumour type) in the patient population has an influence on the resulting distribution of optimal waiting times for patients in those groups, though has only a minor influence on the optimal mean waiting time for each group.

Occult breast tumor reservoir: biological properties and clinical significance.

Small, occult, undiagnosed breast cancers are found at autopsy in up to 15.6 % of women dying from unrelated causes with an average of 7 % from eight separate studies. The mammographic detection threshold of breast tumors ranges from 0.88 to 1.66 cm in diameter based on the patient's age. Tumor growth rates, expressed as "effective doubling times," vary from 10 to >700 days. We previously reported two models, based on iterative analysis of these parameters, to describe the biologic behavior of undiagnosed, occult breast tumors. Our models facilitate interpretation of the Women's Health Initiative (WHI) and antiestrogen breast cancer prevention studies. A nude mouse xenograft model was used to validate our assumption that breast tumors grow in a log-linear fashion. We then used our previously reported occult tumor growth (OTG) and computer-simulated tumor growth models to analyze various clinical trial data. Parameters used in the OTG model included a 200-day effective doubling time, 7 % prevalence of occult tumors, and 1.16 cm detection threshold. These models had been validated by comparing predicted with observed incidence of breast cancer in eight different populations of women. Our model suggests that menopausal hormone therapy with estrogens plus a progestogen (E + P) in the WHI trial primarily promoted the growth of pre-existing, occult lesions and minimally initiated de novo tumors. We provide a potential explanation for the lack of an increase in breast cancer incidence in the subgroup of women in the WHI who had not received E + P prior to randomization. This result may have reflected a leftward skew in the distribution of occult tumor doublings and insufficient time for stimulated tumors to reach the detection threshold. Our model predicted that estrogen alone reduced the incidence of breast cancer as a result of apoptosis. Understanding of the biology of occult tumors suggests that breast cancer "prevention" with antiestrogens or aromatase inhibitors represents early treatment rather than a reduction in de novo tumor formation. Our models suggest that occult, undiagnosed tumors are prevalent, grow slowly, and are the biologic targets of a hormone therapy in menopausal women and of antiestrogen therapy for prevention.

Estimate of the accelerated proliferation by protein tyrosine phosphatase (PTEN) over expression in postoperative radiotherapy of head and neck squamous cell carcinoma

To estimate the impact of PTEN expression in terms of effective doubling time (T(d)) and dose per fraction which compensates the accelerated proliferation during the radiotherapy (D(prolif)) when the overall treatment time (OTT) is reduced in accelerated radiotherapy of head and neck squamous cell carcinoma (HNSCC). Data were carried out from a recent paper comparing the local control rate (LCR) for patients with HNSCC that underwent a conventional (p-CF) or accelerated radiotherapy (p-CAIR) and a pretreatment assessment of PTEN expression. The impact of PTEN over expression was assessed using the Clinical Efficacy Factor (C) and assuming a plausible range of intrinsic radiosensitivity (α). Statistical analysis was made by evaluating the LCR from Kaplan-Meier curves and log-rank test with significance of 0.05. C indexes were 1.46 and 0.23 for the high- versus low-PTEN group, corresponding to a considerable reduction of doubling time of more than six times (6.6 versus 42.2 days). The median estimate of D(prolif) was 0.51 versus 0.08 Gy/day if referred to a median value in the adopted range of α. The PTEN expression has a significant implication on the clinical management of these patient groups. Our data support the hypothesis that the high-PTEN group would benefit from a hypo-fractionation with a reduction of the OTT to compensate for the increase in the proliferation rate, while the low-PTEN group could benefits from a hyper-fractionation which would result in a reduced toxicity for all the organs at risk.

Correlation between egfr expression and accelerated proliferation during radiotherapy of head and neck squamous cell carcinoma

PurposeTo investigate the correlation between the expression of Epidermal Growth Factor receptor (EGFr) and the reduction of the effective doubling time (TD) during radiotherapy treatment and also to determine the dose per fraction to be taken into account when the overall treatment time (OTT) is reduced in accelerated radiotherapy of head and neck squamous cell carcinoma (HNSCC).MethodsA survey of the published papers comparing 3-years of local regional control rate (LCR) for a total of 2162 patients treated with conventional and accelerated radiotherapy and with a pretreatment assessment of EGFr expression, was made. Different values of TD were obtained by a model incorporating the overall time corrected biologically effective dose (BED) and a 3-year clinical LCR for high and low EGFr groups of patients (HEGFr and LEGFr), respectively. By obtaining the TD from the above analysis and the sub-sites’ potential doubling time (Tpot) from flow cytometry and immunohistochemical methods, we were able to estimate the average TD for each sub-site included in the analysis. Moreover, the dose that would be required to offset the modified proliferation occurring in one day (Dprolif), was estimated.ResultsThe averages of TD were 77 (27-90)95% days in LEGFr and 8.8 (7.3-11.0)95% days in HEGFr, if an onset of accelerated proliferation TK at day 21 was assumed. The correspondent HEGFr sub-sites’ TD were 5.9 (6.6), 5.9 (6.6), 4.6 (6.1), 14.3 (12.9) days, with respect to literature immunohistochemical (flow cytometry) data of Tpot for Oral-Cavity, Oro-pharynx, Hypo-pharynx, and Larynx respectively. The Dprolif for the HEGFr groups were 0.33 (0.29), 0.33 (0.29), 0.42 (0.31), 0.14 (0.15) Gy/day if α = 0.3 Gy-1 and α/β = 10 Gy were assumed.ConclusionsA higher expression of the EGFr leads to enhanced proliferation. This study allowed to quantify the extent of the effect which EGFr expression has in terms of reduced TD and Dprolif for each head and neck sub-site.

Modeling of the growth kinetics of occult breast tumors: role in interpretation of studies of prevention and menopausal hormone therapy.

Autopsy studies report a reservoir of small, occult, undiagnosed breast cancers in up to 15.6% of women dying from unrelated causes. The effective doubling times (EDT) of these occult neoplasms range from 70 to 350 days and mammographic detection threshold diameters from 0.88 to 1.66 cm. Modeling of the biologic behavior of these occult tumors facilitates interpretation of tamoxifen breast cancer prevention and menopausal hormone therapy studies. We used iterative and mathematical techniques to develop a model of occult tumor growth (OTG) whose parameters included prevalence, EDT, and detection threshold. The model was validated by comparing predicted with observed incidence of breast cancer in several populations. Iterative analysis identified a 200-day EDT, 7% prevalence and 1.16 cm detection threshold as optimal parameters for an OTG model as judged by comparison with Surveillance Epidemiology and End Results (SEER) population incidence rates in the United States. We validated the model by comparing predicted incidence rates with those observed in five separate population databases, in three long-term contralateral breast cancer detection studies, and with data from a computer-simulated tumor growth (CSTG) model. Our model strongly suggests that breast cancer prevention with anti-estrogens or aromatase inhibitors represents early treatment not prevention. In addition, menopausal hormone therapy does not primarily induce de novo tumors but promotes the growth of occult lesions. Our OGTG model suggests that occult, undiagnosed tumors are prevalent, grow slowly, and are the biologic targets of anti-estrogen therapy for prevention and hormone therapy for menopausal women.

Highlights of This Issue

Dogs serve as attractive systems for identifying the genes associated with certain cancers, especially cancers that are difficult to study in humans but that occur frequently in certain dog breeds. For example, histiocytic sarcoma is rare in humans but occurs in 15% to 25% of Bernese Mountain Dogs. To examine the genetics of histiocytic sarcoma, Shearin and colleagues analyzed genomic DNA from Bernese Mountain Dogs, and report a cancer-associated locus spanning the MTAP and CDKN2A genes. The locus is within a region homologous to human chromosome 9p21, which has been implicated in several human cancers. This study demonstrates the power of examining distinctive malignancies in predisposed dog breeds.Although increased breast cancer risk has been observed in night shift workers, the reasons for this are unclear. Peplonska and colleagues investigated the hypothesis that rotating night shift work is associated with disruptions in melatonin synthesis and increased mammographic density. They measured the urinary 6-sulfatoxymelatonin (MT6) levels and mammographic density in 640 night shift workers and found no significant associations between rotating night shift work exposure and mammographic density or between MT6 levels and mammographic density. The results of this study suggest that the development of breast cancer in rotating night shift workers is not mediated by increased mammographic density.Autopsy studies reveal a reservoir of small, occult, undiagnosed breast cancers in women who have died from unrelated causes. To better understand the behavior of these occult tumors, Santen and colleagues used iterative and mathematical techniques to develop a model of occult tumor growth (OTG). The OTG model identified a 200-day effective doubling time, a 7% prevalence rate, and a 1.16-cm detection threshold. The model was validated through comparison of predicted incidence rates with those observed in population databases. The results of this study suggest that occult breast tumors are prevalent, grow slowly, and are the biologic targets of antiestrogen therapy.Lung cancer is the leading cause of cancer mortality. Chest X-rays continue to be used as lung cancer screening tests even though low-dose computed tomography (LDCT) has been found to be more sensitive in early lung cancer detection. Doria-Rose and colleagues estimated the prevalence of chest X-ray and LDCT use in the United States based on data from the 2010 National Health Interview Survey. They report that although LDCT screening rates are low, approximately 8.7 million adults in the United States would be eligible for LDCT screening. Patient education may help ensure that lung cancer screening is used appropriately in those most likely to benefit.

When tumor repopulation starts? The onset time of prostate cancer during radiation therapy

Purpose. To analyze published clinical data and provide a preliminary estimate of tumor repopulation rate and its onset time during radiation therapy for prostate cancer. Methods. Data on prostate cancer treated with external beam radiotherapy (EBRT) by Perez et al. (2004), Amdur et al. (1990) and Lai et al. (1991) were analyzed in this study. The stage-combined pelvic control rate from Perez et al. was calculated to be 0.95±0.01, 0.87±0.02, and 0.72±0.04 for patients treated ≤7 weeks, 7.1–9 weeks, and >9 weeks respectively. Based on the Linear-Quadratic model, extended to account for tumor repopulation, the least χ2 method was used to fit the clinical data and derive the onset time (Tk) and effective doubling time (Td) for prostate cancer. Similar analysis was performed for the other two datasets. Results. Best fit was achieved with onset time Tk=34±7 days and doubling time Td=12±2 days. These parameters were independent of the choice of the α/β values currently published in the literature. Analyses of the other two datasets showed Tk=42±7 days with Td=9 ± 3 days, and Tk=34±6 days with Td=34±5 days, respectively. Tk was found to be dependent on tumor stage. Conclusions. Consistent values for onset time Tk were obtained from different datasets, while the range of doubling time Td was large. Tumor repopulation starts no later than 58 days (at 90% confidence level) in the course of EBRT for prostate cancer.

Impact of tumor repopulation on radiotherapy planning

Biologic/functional imaging (e.g., fluorodeoxyglucose/3'-deoxy-3'-fluorothymidine-positron emission tomography) is promising to provide information on tumor cell repopulation. Such information is important in the design of biologically conformal radiotherapy for cancer. The questions remaining unclear are whether it is necessary to escalate the dose to the regions with rapid cell repopulation in the tumor target and, if so, by how much. The purpose of this work was to address these questions using radiobiologic modeling. The generalized linear-quadratic model, extended to account for the effect of clonogenic cell repopulation, was used to calculate the cell-killing efficiency of radiotherapy. The standard Poisson tumor control probability (TCP) model was used to bridge cell killing to treatment outcome. Prostate cancer was chosen as the example for this study. In situ measurements of prostate cancer patients have shown that the potential doubling time of tumor cells has a large variation, ranging from 15 to 170 days. On the basis of the linear-quadratic and TCP parameters (alpha = 0.14 Gy(-1), alpha/beta = 3.1 Gy, and the number of clonogens K = 10(6)-10(7) cells) determined in earlier studies, we evaluated the influence of tumor cell repopulation during protracted treatment courses on treatment outcome. The dose escalations, which can be used to combat aggressive cell repopulation in regions with different doubling times (15-170 days) and sizes (5, 10, 15, and 40 cm(3) of a 40-cm(3) tumor), were calculated for commonly practiced radiotherapy modalities. The influence of linear-quadratic parameters on this calculation was also considered. The impact of tumor cell repopulation on TCP and the corresponding dose escalation required to account for this impact were investigated for both external beam radiotherapy and permanent implantation. The results indicated that for regions with aggressive tumor cell growth, dose escalation is necessary to compensate for the repopulation effect. For example, for tumors with an effective doubling time changing from 42 days to 15 days, the prescription dose of external beam radiotherapy needs to be increased from 75.6 to 81 Gy to maintain a target TCP of 80% for intermediate-risk prostate cancer. For (125)I implants, dose escalation from 152 to 160 Gy is required for the same target TCP. These data were calculated on the basis of an alpha/beta ratio of 3.1 Gy. Greater dose escalations are required if the alpha/beta ratio is 1.5 Gy (e.g., 88 Gy for external beam radiotherapy or 180 Gy for (125)I implantation for the same treatment outcome). Our study results showed that it is important to cover the entire tumor volume, including all aggressive spots, with the desired prescription dose, especially for low-dose-rate brachytherapy. Dose escalation is necessary to offset the accelerated tumor cell repopulation during prolonged treatment courses. This study provides a preliminary estimate of the dose escalation for prostate cancer based on the in situ measurements of potential doubling time and radiobiologic models. The proposed dose prescriptions are technically feasible for clinical trials.

Extinction of the weakest

Purpose: To examine whether changes in the effective doubling time of tumor cells during irradiation of head-and-neck cancer are linked to accumulating dose.Methods and Materials: Optimal fitting of the results of four apparently iso-effective regimens in three recently reported randomized controlled trials (continuous hyperfractionated accelerated radiation therapy [CHART], Radiation Therapy Oncology Group [RTOG] 90-03, and Trans-Tasman Radiation Oncology Group [TROG] 91.01) was attempted using two different types of model of the change in effective doubling time that may occur during treatment. The first involved the traditional approach where doubling time changes at specific times after the start of treatment regardless of fractionation used (“fixed response time” models). The second is where changes in doubling time are linked to accumulating biologic dose (“cellular depletion” models).Results: Changes in effective doubling time occur during radiotherapy for head-and-neck cancer. Data from the three trials can be fitted successfully by functions that imply a continuous reduction in effective doubling time. Models linking the reductions in effective doubling time to the cellular depletion that occurs in the tumor during radiotherapy fit the data satisfactorily. Effective doubling time ultimately reduces to 2 days, or slightly less, during high-dose radiotherapy regimens designed to cure squamous head-and-neck cancer.Conclusions: If the assumption of iso-effectivity is justified then this study indicates that the “repopulation phenomenon” may be best described by a function that depicts a reduction in effective tumor cell doubling time that decreases continuously during treatment down to a certain minimum value. Furthermore, this reduction may be linked to cellular depletion.

Is there a future for cell kinetic measurements using IdUrd or BdUrd?

Purpose: The analysis of causes of radiation failure both in retrospective series of patients with head and neck cancer and in several randomized clinical trials suggests a loss of local control as the overall treatment time increases for the same total dose. This is attributed to tumor cell proliferation during fractionated radiotherapy. As longer treatment times lead to loss of local control, it has been suggested that shorter treatment times could lead to an increase in local control. For this reason accelerated treatment regimens have been and are being designed. However, these treatments may cause severe acute reactions. Due to this, lower total doses are sometimes given. Slowly proliferating tumors, therefore, may do worse when treated with accelerated schedules compared with conventional schedules. In addition, it is not desirable to subject all patients to the more intense acute reactions of accelerated schedules. It would thus be useful to predict which tumors will rapidly proliferate during treatment and are likely to benefit from accelerated radiotherapy. The potential doubling time (Tpot) is defined as the time within which the cell population of a tumor would double if there were no cell loss. The hypothesis is that the median Tpot measured before treatment might correlate with the effective doubling time (Tp) during treatment. Conclusion: Tpot can be calculated knowing the labeling index (LI; proportion of cells incorporating the DNA precursor IdUrd or BdUrd) and Ts (the DNA synthesis time) measured by flow cytometry. A recent multicenter analysis has shown that the only pretreatment kinetic parameter for which some evidence is found for an association with local control is LI, not Tpot. Pitfalls associated with cell kinetic measurements such as assay variability, intratumor and intertumor variability, interlaboratory variability and the problem of an admixture of normal and malignant cells make Tpot not accurate and reproducible enough for a robust predictive assay. It therefore appears that pretreatment Tpot measurements using flow cytometry, provide only a relatively weak predictor of outcome after radiotherapy in head and neck cancer. Immunohistochemistry allows a simple measure of LI and may give additional independent information from labeling patterns, suggesting that this method is the (short term) future for clinical cell kinetic measurements using BdUrd or IdUrd.

Repopulation capacity during fractionated irradiation of squamous cell carcinomas and glioblastomas in vitro

Determination of clonogenic cell proliferation of three highly malignant squamous cell carcinomas (SCC) and two glioblastoma cell lines during a 20-day course of fractionated irradiation under in vitro conditions. Tumor cells in exponential growth phase were plated in 24-well plastic flasks and irradiated 24 h after plating with 250 kV x-rays at room temperature. Six fractions with single doses between 0.6 and 9 Gy were administered in 1.67, 5, 10, 15, and 20 days. Colony growth was monitored for at least 60 days after completion of irradiation. Wells with confluent colonies were considered as "recurrences" and wells without colonies as "controlled." The dose required to control 50% of irradiated wells (WCD50) was estimated by a logistic regression for the different overall treatment times. The effective doubling time of clonogenic cells (T[eff]) was determined by a direct fit using the maximum likelihood method. The increase of WCD50 within 18.3 days was highly significant for all tumor cell lines accounting for 7.9 and 12.0 Gy in the two glioblastoma cell lines and for 12.7, 14.0, and 21.7 Gy in the three SCC cell lines. The corresponding T(eff)s were 4.4 and 2.0 days for glioblastoma cell lines and 2.4, 4.2, and 1.8 days for SCC cell lines. Population doubling times (PDT) of untreated tumor cells ranged from 1.0 to 1.9 days, showing no correlation with T(eff)s. T(eff) was significantly longer than PDT in three of five tumor cell lines. No significant differences were observed comparing glioblastomas and SCC. Increase of WCD50 with time did not correlate with T(eff) but with T(eff) InSF2 (surviving fraction at 2 Gy). The intrinsic ability of SCC and glioblastoma cells to repopulate during fractionated irradiation could be demonstrated. Repopulation induced dose loss per day depends on T(eff) and intrinsic radiation sensitivity. Proliferation during treatment was decelerated compared to pretreatment PDT in the majority of cell lines. Pretreatment cell kinetics did not predict for tumor cell proliferation during treatment.

Distinctions Between CD8+ and CD4+ T-Cell Regenerative Pathways Result in Prolonged T-Cell Subset Imbalance After Intensive Chemotherapy

Rapid recovery of CD4+ T cells after intensive chemotherapy is limited by an age-dependent decline in thymopoiesis. Here we sought to determine whether similar limitations exist for CD8+ T-cell regeneration. After intensive chemotherapy, CD8+ T cells had a faster effective doubling time than CD4+ T cells (median, 12.6 v 28.2 days, P < .05). Accordingly, at 3 months posttherapy, mean CD8+ T-cell number had returned to baseline, whereas mean CD4+ T-cell number was only 35% of pretherapy values (P < .05). These differences were primarily due to very rapid expansion of CD8+CD57+ and CD8+CD28- subsets. At 3 months posttherapy, there was no relationship between age and CD8+ T-cell number (R = -.02), whereas CD4+ T-cell number was inversely related to age (R = -.66) and there were no discernible differences in CD8+ recovery among patients with or without thymic enlargement, whereas CD4+ recovery was enhanced in patients with thymic enlargement after chemotherapy (P < .01). Therefore thymic-independent pathways of T-cell regeneration appear to rapidly regenerate substantial numbers of CD8+, but not CD4+ T cells, resulting in prolonged T-cell subset imbalance after T-cell depletion. These inherent distinctions between CD4+ v CD8+ T-cell regeneration may have significant implications for immunotherapeutic strategies undertaken to eradicate minimal residual neoplastic disease after cytoreductive chemotherapy.

Distinctions Between CD8+ and CD4+ T-Cell Regenerative Pathways Result in Prolonged T-Cell Subset Imbalance After Intensive Chemotherapy

AbstractRapid recovery of CD4+ T cells after intensive chemotherapy is limited by an age-dependent decline in thymopoiesis. Here we sought to determine whether similar limitations exist for CD8+ T-cell regeneration. After intensive chemotherapy, CD8+ T cells had a faster effective doubling time than CD4+ T cells (median, 12.6 v 28.2 days, P < .05). Accordingly, at 3 months posttherapy, mean CD8+ T-cell number had returned to baseline, whereas mean CD4+ T-cell number was only 35% of pretherapy values (P < .05). These differences were primarily due to very rapid expansion of CD8+CD57+ and CD8+CD28− subsets. At 3 months posttherapy, there was no relationship between age and CD8+ T-cell number (R = −.02), whereas CD4+ T-cell number was inversely related to age (R = −.66) and there were no discernible differences in CD8+ recovery among patients with or without thymic enlargement, whereas CD4+ recovery was enhanced in patients with thymic enlargement after chemotherapy (P < .01). Therefore thymic-independent pathways of T-cell regeneration appear to rapidly regenerate substantial numbers of CD8+, but not CD4+ T cells, resulting in prolonged T-cell subset imbalance after T-cell depletion. These inherent distinctions between CD4+v CD8+ T-cell regeneration may have significant implications for immunotherapeutic strategies undertaken to eradicate minimal residual neoplastic disease after cytoreductive chemotherapy.

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.

Infectivity and Host Responses in Creutzfeldt–Jakob Disease

The relationship between viral titer and host responses was evaluated in Creutzfeldt–Jakob Disease (CJD). Rapid clearing of 97% of the virus from hamster brain occurred within 5 days, and residual virus was dispersed equally to both hemispheres. Exponential replication began only after a long eclipse phase of ∼30 days, and by 100 days showed an >3 log increase in titer. However, from 100 to 135 days, titers were restricted to plateau levels of ∼108/g. In comparison, previous studies show no appreciable eclipse phase and ≥100-fold higher brain titers in hamster scrapie. Our calculations also revealed an effective doubling time (ti) of 7.6 days in CJD and a markedly differenttiof ∼3 days in scrapie. Thus different initiation and replication programs are encoded by each of these strains. The most pertinent host molecular responses included early astrocytic activity by 54 days, unaccompanied by morphological or behavioral changes. Changes in host PrP were minimal until 87 days when titers were already 2 × 107/g. In the next 20 days 60% of brain PrP became resistant to limited proteolysis but total PrP did not increase. These fulminant PrP changes preceded viral arrest and subsequent spongiform degeneration. Because these and other data are not consistent with PrP itself being the infectious agent, we discuss a model in which progressive PrP and glial activation are part of a final host strategy to contain a virus that is innocuous at low titers. This strategy is flawed because PrP is an independent provocateur of self-destruction in the brain. However, in the periphery this strategy may eliminate rare infected cells.

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.

The effect of the overall treatment time of fractionated irradiation on the tumor control probability of a human soft tissue sarcoma xenograft in nude mice

Purpose : To study the impact of the overall treatment time of fractionated irradiation on the tumor control probability (TCP) of a human soft tissue sarcoma xenograft growing in nude mice, as well as to compare the pretreatment potential doubling time (T pot) of this tumor to the effective doubling time (T eff) derived from three different schedules of irradiation using the same total number of fractions with different overall treatment times. Methods and Materials : The TCP was assessed using the TCD 50 value (the 50% tumor control dose) as an end pont. A total of 240 male nude mice, 7–8 weeks old were used in three experimental groups that received the same total number of fractions (30 fractions) with different overall treatment times. In group 1, the animals received three equal fractions/day for 10 consecutive days, in group 2 they received two equal fractions/day for 15 consecutive days, and in group 3 one fraction/day for 30 consecutive days. All irradiations were given under normal blood flow conditions to air breathing animals. The mean tumor diameter at the start of irradiation was 7–8 mm. The mean interfraction intervals were from 8–24 h. The T pot was measured using Iododeoxyuridine (IudR) labeling and flow cytometry adn was compared to T eff. Results : The TCD 50 values of the three different treatment schedules were 58.8 Gy, 63.2 Gy, and 75.6 Gy for groups 1, 2, and 3, respectively. This difference in TCD 50 values was significant ( p < 0.05) between groups 1 and 2 (30 fractions/10 days and 30 fractions/15 days) vs. group 3 (30 fractions/30 days). The loss in TCP due to the prolongation of teh overall treatment time for 10 days to 30 days was found to be 1.35–1.4 Gy/day. The pretreatment T pot (2.4 days) was longer than the calculated T eff in groups 2 and 3 (1.35 days). Conclusion : Our data show a significant loss in TCP with prolongation of the overall treatment time. This is most probably due to an accelerated repopulation of tumor clongens. The pretreatment T pot of this tumor model does not reflect the actual dougling of the clonogens in a protracted regimen.