Heterogeneity In Radiosensitivity Research Articles

Single-Cell Transcriptomics Reveals Early Effects of Ionizing Radiation on Bone Marrow Mononuclear Cells in Mice.

Ionizing radiation exposure can cause damage to diverse tissues and organs, with the hematopoietic system being the most sensitive. However, limited information is available regarding the radiosensitivity of various hematopoietic cell populations in the bone marrow due to the high heterogeneity of the hematopoietic system. In this study, we observed that granulocyte-macrophage progenitors, hematopoietic stem/progenitor cells, and B cells within the bone marrow showed the highest sensitivity, exhibiting a rapid decrease in cell numbers following irradiation. Nonetheless, neutrophils, natural killer (NK) cells, T cells, and dendritic cells demonstrated a certain degree of radioresistance, with neutrophils exhibiting the most pronounced resistance. By employing single-cell transcriptome sequencing, we investigated the early responsive genes in various cell types following irradiation, revealing that distinct gene expression profiles emerged between radiosensitive and radioresistant cells. In B cells, radiation exposure led to a specific upregulation of genes associated with mitochondrial respiratory chain complexes, suggesting a connection between these complexes and cell radiosensitivity. In neutrophils, radiation exposure resulted in fewer gene alterations, indicating their potential for distinct mechanisms in radiation resistance. Collectively, this study provides insights into the molecular mechanism for the heterogeneity of radiosensitivity among the various bone marrow hematopoietic cell populations.

Biological dose optimization incorporating intra-tumoural cellular radiosensitivity heterogeneity in ion-beam therapy treatment planning

Objective. Treatment plans of ion-beam therapy have been made under an assumption that all cancer cells within a tumour equally respond to a given radiation dose. However, an intra-tumoural cellular radiosensitivity heterogeneity clearly exists, and it may lead to an overestimation of therapeutic effects of the radiation. The purpose of this study is to develop a biological model that can incorporate the radiosensitivity heterogeneity into biological optimization for ion-beam therapy treatment planning. Approach. The radiosensitivity heterogeneity was modeled as the variability of a cell-line specific parameter in the microdosimetric kinetic model following the gamma distribution. To validate the developed intra-tumoural-radiosensitivity-heterogeneity-incorporated microdosimetric kinetic (HMK) model, a treatment plan with H-ion beams was made for a chordoma case, assuming a radiosensitivity heterogeneous region within the tumour. To investigate the effects of the radiosensitivity heterogeneity on the biological effectiveness of H-, He-, C-, O-, and Ne-ion beams, the relative biological effectiveness (RBE)-weighted dose distributions were planned for a cuboid target with the stated ion beams without considering the heterogeneity. The planned dose distributions were then recalculated by taking the heterogeneity into account. Main results. The cell survival fraction and corresponding RBE-weighted dose were formulated based on the HMK model. The first derivative of the RBE-weighted dose distribution was also derived, which is needed for fast biological optimization. For the patient plan, the biological optimization increased the dose to the radiosensitivity heterogeneous region to compensate for the heterogeneity-induced reduction in biological effectiveness of the H-ion beams. The reduction in biological effectiveness due to the heterogeneity was pronounced for low linear energy transfer (LET) beams but moderate for high-LET beams. The RBE-weighted dose in the cuboid target decreased by 7.6% for the H-ion beam, while it decreased by just 1.4% for the Ne-ion beam. Significance. Optimal treatment plans that consider intra-tumoural cellular radiosensitivity heterogeneity can be devised using the HMK model.

Radiobiological comparison between Cobalt-60 and Iridium-192 high-dose-rate brachytherapy sources: Part I-cervical cancer.

This study aimed to compare the biological effective doses (BEDs) to clinical target volume (CTV) and organs at risk (OARs) for cervical cancer patients treated with high-dose-rate (HDR) Iridium-192 (192 Ir) or Cobalt-60 (60 Co) brachytherapy (BT) boost and to determine if the radiobiological differences between the two isotopes are clinically relevant. Considering all radiosensitivity parameters and their reported variations, the BEDs to CTV and OARs during HDR 60 Co/192 Ir BT boost were evaluated at the voxel level. The anatomical differences between individuals were also taken into account by retrospectively considering 25 cervical cancer patients. The intrafraction repair, proliferation, hypoxia-induced radiosensitivity heterogeneity, relative biological effectiveness (RBE), and source aging dose-rate variation were also taken into account. The comparisons in CTV were performed based on equivalent uniform BED (EUBED). Considering nominal parameters with no RBE correction, the CTV EUBEDs were almost similar with a median ratio of ∼1.00 (p<0.00001), whereas RBE correction resulted in 3.9%-5.5% (p=0.005, median=4.8%) decrease for 60 Co with respect to 192 Ir. For OARs, the median values of D2cc (in EQD23 ) for 60 Co were lower than that of 192 Ir up to 9.2% and 11.3% (p<0.00001) for nominal parameters and fast repair conditions, respectively. In addition, for a nominal value (reported range) of radiosensitive parameters, the CTV EUBED differences of up to 6% (5%-10%) were assessed for HDR-BT component. The RBE values are the most important cause of discrepancies between the two sources. By comparing BED/EUBEDs to CTV and OARs between 60 Co and 192 Ir sources, this numerical study suggests that a dose escalation to ∼4% is feasible and safe while sparing well the surrounding normal tissues. This 4% dose escalation should be benchmarked with clinical evidences (such as the results of clinical trials) before it can be used in clinical practice.

Personalizing Radiotherapy Prescription Dose Using Genomic Markers of Radiosensitivity and Normal Tissue Toxicity in NSCLC.

Cancer sequencing efforts have revealed that cancer is the most complex and heterogeneous disease that affects humans. However, radiation therapy (RT), one of the most common cancer treatments, is prescribed on the basis of an empirical one-size-fits-all approach. We propose that the field of radiation oncology is operating under an outdated null hypothesis: that all patients are biologically similar and should uniformly respond to the same dose of radiation. We have previously developed the genomic-adjusted radiation dose, a method that accounts for biological heterogeneity and can be used to predict optimal RT dose for an individual patient. In this article, we use genomic-adjusted radiation dose to characterize the biological imprecision of one-size-fits-all RT dosing schemes that result in both over- and under-dosing for most patients treated with RT. To elucidate this inefficiency, and therefore the opportunity for improvement using a personalized dosing scheme, we develop a patient-specific competing hazards style mathematical model combining the canonical equations for tumor control probability and normal tissue complication probability. This model simultaneously optimizes tumor control and toxicity by personalizing RT dose using patient-specific genomics. Using data from two prospectively collected cohorts of patients with NSCLC, we validate the competing hazards model by revealing that it predicts the results of RTOG 0617. We report how the failure of RTOG 0617 can beexplained by the biological imprecision of empirical uniform dose escalation which results in 80% of patients being overexposed to normal tissue toxicity without potential tumor control benefit. Our data reveal a tapestry of radiosensitivity heterogeneity, provide a biological framework that explains the failure of empirical RT dose escalation, and quantify the opportunity to improve clinical outcomes in lung cancer by incorporating genomics into RT.

Classification of Radiosensitivity Index by Gaussian Mixture Modelling to Inform Radiotherapy Dose and Discover Disease Subclassifications

Advances in our understanding of the genetic landscape of cancer has allowed for a more sophisticated understanding of carcinogenesis and progression, as well as a more nuanced approach to treatment. Various cellular environments can favor sensitivity or resistance to irradiation, and recent investigations have suggested that certain genetic markers and transcriptomic nodes are associated with this response. Contrary to the standard null hypothesis in biology that any polygenic trait would exhibit a normal distribution, in a previous investigation of the variance in radiosensitivity across cancers we observed bi- or multi-modal distributions within classically defined cancer types. We hypothesize that these disease sites are aggregations of disparate sub-classes of disease, each with their own normally distributed radiation sensitivity. We utilized the measured distributions of radiation sensitivity, as derived from the well-validated radiation sensitivity index (RSI) from an IRB-approved tissue biorepository of 8,271 cancer patients with a variety of tumors characterized by gene expression. To address the hypothesis that these observed multi-modal distributions were indeed aggregations of normal distributions, and therefore inform clinical sub-classification, we reanalyzed these data. For each site of origin, we minimized the Bayesian information criteria (BIC) and Akaike information criteria (AIC) of multiple mixed-Gaussian models of the calculated RSI. We constructed mixture models for tumor tissue sampled from 20 sites of origin. The corresponding optimization illustrated varying degrees of heterogeneity in radiosensitivity across cancer types. In order to limit the effects of sample size, we restricted our results to sites with greater than 50 samples available for analysis. We subsequently identified varying numbers of distinct subpopulations of disparate radiosensitivity within a specific cancer type, ranging between: 1 [glioma, sarcoma, melanoma], 2 [lung, prostate, esophageal, gastric, H&N], 3 [endometrial, rectal, pancreatic], and 4 [kidney, breast] Gaussian clusters via posterior probability as predicted by the resultant mixture model. Lastly, cumulative distribution functions were constructed and related to a simplified linear-quadratic model to illustrate the potential for dose adjustment in order to maximize treatment efficacy and minimize patient harm. Our results suggest that the dose-response relationship can be better understood as a representation of the cumulative distribution function across the patient population, within which lie discrete sub-populations of disparate sensitivity to radiation. This interpretation indicates further opportunities for biomarker discovery to allow for a more informed approach to dosing decisions and clinical trial stratification in radiation therapy, and provides clues to differences in biology which can be explored in the laboratory.

Tumor Volume Effect on Tumor Control Probability Under Condition of Patient Heterogeneity of Radiosensitivity: Comparison of a Mechanistic Model with Clinical Data of Radiotherapy for Non-Small Cell Lung Cancer

Tumor Volume Effect on Tumor Control Probability Under Condition of Patient Heterogeneity of Radiosensitivity: Comparison of a Mechanistic Model with Clinical Data of Radiotherapy for Non-Small Cell Lung Cancer

Modeling the effect of intratumoral heterogeneity of radiosensitivity on tumor response over the course of fractionated radiation therapy

BackgroundStandard radiobiology theory of radiation response assumes a uniform innate radiosensitivity of tumors. However, experimental data show that there is significant intratumoral heterogeneity of radiosensitivity. Therefore, a model with heterogeneity was developed and tested using existing experimental data to show the potential effects from the presence of an intratumoral distribution of radiosensitivity on radiation therapy response over a protracted radiation therapy treatment course.MethodsThe standard radiation response curve was modified to account for a distribution of radiosensitivity, and for variations in the repopulation rates of the tumor cell subpopulations. Experimental data from the literature were incorporated to determine the boundaries of the model. The proposed model was then used to show the changes in radiosensitivity of the tumor during treatment, and the effects of fraction size, α/β ratio and variation of the repopulation rates of tumor cells.ResultsIn the presence of an intratumoral distribution of radiosensitivity, there is rapid selection of radiation-resistant cells over a course of fractionated radiation therapy. Standard treatment fractionation regimes result in the near-complete replacement of the initial population of sensitive cells with a population of more resistant cells. Further, as treatment progresses, the tumor becomes more resistant to further radiation treatment, making each fractional dose less efficacious. A wider initial distribution induces increased radiation resistance. Hypofractionation is more efficient in a heterogeneous tumor, with increased cell kill for biologically equivalent doses, while inducing less resistance. The model also shows that a higher growth rate in resistant cells can account for the accelerated repopulation that is seen during the clinical treatment of patients.ConclusionsModeling of tumor cell survival with radiosensitivity heterogeneity alters the predicted tumor response, and explains the induction of radiation resistance by radiation treatment, the development of accelerated repopulation, and the potential beneficial effects of hypofractionation. Tumor response to treatment may be better predicted by assaying for the distribution of radiosensitivity, or the extreme of the radiosensitivity, rather than measuring the initial, general radiation sensitivity of the untreated tumor.

PO-0760 Heterogeneity of Radiosensitivity, Recurrence, and PD-L1 in Breast Tumor Single Cell RNA-Seq Data

PO-0760 Heterogeneity of Radiosensitivity, Recurrence, and PD-L1 in Breast Tumor Single Cell RNA-Seq Data

P.2.022 - Gut microbiota as a target for supplementary therapy of chronic stress-related depression in mice

Cancer sequencing efforts have revealed that cancer is the most complex and heterogeneous disease that affects humans. However, radiation therapy (RT), one of the most common cancer treatments, is prescribed on the basis of an empirical one-size-fits-all approach. We propose that the field of radiation oncology is operating under an outdated null hypothesis: that all patients are biologically similar and should uniformly respond to the same dose of radiation.We have previously developed the genomic-adjusted radiation dose, a method that accounts for biological heterogeneity and can be used to predict optimal RT dose for an individual patient. In this article, we use genomic-adjusted radiation dose to characterize the biological imprecision of one-size-fits-all RT dosing schemes that result in both over- and under-dosing for most patients treated with RT. To elucidate this inefficiency, and therefore the opportunity for improvement using a personalized dosing scheme, we develop a patient-specific competing hazards style mathematical model combining the canonical equations for tumor control probability and normal tissue complication probability. This model simultaneously optimizes tumor control and toxicity by personalizing RT dose using patient-specific genomics.Using data from two prospectively collected cohorts of patients with NSCLC, we validate the competing hazards model by revealing that it predicts the results of RTOG 0617. We report how the failure of RTOG 0617 can be explained by the biological imprecision of empirical uniform dose escalation which results in 80% of patients being overexposed to normal tissue toxicity without potential tumor control benefit.Our data reveal a tapestry of radiosensitivity heterogeneity, provide a biological framework that explains the failure of empirical RT dose escalation, and quantify the opportunity to improve clinical outcomes in lung cancer by incorporating genomics into RT.

Unique epigenetic influence of H2AX phosphorylation and H3K56 acetylation on normal stem cell radioresponses.

Normal tissue injury resulting from cancer radiotherapy is often associated with diminished regenerative capacity. We examined the relative radiosensitivity of normal stem cell populations compared with non-stem cells within several radiosensitive tissue niches and culture models. We found that these stem cells are highly radiosensitive, in contrast to their isogenic differentiated progeny. Of interest, they also exhibited a uniquely attenuated DNA damage response (DDR) and muted DNA repair. Whereas stem cells exhibit reduced ATM activation and ionizing radiation-induced foci, they display apoptotic pannuclear H2AX-S139 phosphorylation (γH2AX), indicating unique radioresponses. We also observed persistent phosphorylation of H2AX-Y142 along the DNA breaks in stem cells, which promotes apoptosis while inhibiting DDR signaling. In addition, down-regulation of constitutively elevated histone-3 lysine-56 acetylation (H3K56ac) in stem cells significantly decreased their radiosensitivity, restored DDR function, and increased survival, signifying its role as a key contributor to stem cell radiosensitivity. These results establish that unique epigenetic landscapes affect cellular heterogeneity in radiosensitivity and demonstrate the nonubiquitous nature of radiation responses. We thus elucidate novel epigenetic rheostats that promote ionizing radiation hypersensitivity in various normal stem cell populations, identifying potential molecular targets for pharmacological radioprotection of stem cells and hopefully improving the efficacy of future cancer treatment.

Abstract 4270: Heterogeneous radiosensitivity among phenotypes within intracerebral xenografts initiated from glioblastoma stem like cells

Abstract Intra-tumor heterogeneity is a well established characteristic of human glioblastoma (GB), yet whether this heterogeneity extends to cellular radiosensitivity has not been clearly defined. In contrast to established glioma cell lines, brain tumor xenografts initiated from GB stem like cells are comprised of a mixture of stem cells, progenitors and cells in various states of differentiation, thus providing a clinically relevant model system for defining radiosensitivity as a function of phenotype. Of particular interest is the radiosensitivity of stem like versus non-stem like GB cells. To address this issue, CD133+ stem like cells isolated from a GB neurosphere culture were used to initiate brain tumors in nude mice; we then compared the in vivo radiosensitivity of GB stem like cells (CD133+) versus that of non-stem like GB cells (CD133-). To define radioresponse on an individual cell basis, we used γH2AX foci, which provides an indicator of DNA double strand break (DSB) induction and repair. At the onset of tumor induced morbidity, mice were irradiated (6Gy) and tumors collected at times out to 24h. The maximum number of γH2AX foci induced occurred at 0.5h followed by a rapid reduction to approach control levels by 6h after irradiation. Using dual label immunohistochemistry, γH2AX induction and dispersal were defined specifically in CD133+ and CD133- cells within a given tumor. Whereas each phenotype had a similar time course of foci induction and dispersal, the maximum number of foci induced in CD133+ cells was significantly less than that detected in CD133- tumor cells. Similar results were obtained when radiation induced 53BP1 nuclear foci were analyzed. These data indicate that the initial level of DSBs induced in CD133+ cells is significantly less than that in CD133- cells, which suggests that the stem like phenotype is relatively radioresistant. As an additional approach to evaluating the putative phenotypic difference in radiosensitivity, tumors were irradiated (12Gy) on day 21 post-implantation and % CD133+ cells determined at the time of irradiation and at the onset of morbidity. On the day of irradiation, &amp;gt;60% of the cells within brain tumors initiated from CD133+ cells retained CD133 expression and at morbidity tumors in unirradiated mice contained approximately 10% CD133+ cells. In irradiated mice, however, tumors collected at morbidity contained greater than 20% CD133+ cells. Thus, based on the analysis of individual cell radiosensitivity (nuclear foci) and the relative increase in CD133+ cells, these in vivo results suggest that within this brain tumor xenograft model the stem cell like phenotype comprises a radioresistant subpopulation. Moreover, this study illustrates the potential for combining γH2AX foci and phenotype immunohistochemical analyses as an approach for investigating the intra-tumor heterogeneity in radiosensitivity. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 101st Annual Meeting of the American Association for Cancer Research; 2010 Apr 17-21; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2010;70(8 Suppl):Abstract nr 4270.

Analytic Investigation Into Effect of Population Heterogeneity on Parameter Ratio Estimates

A homogeneous tumor control probability (TCP) model has previously been used to estimate the alpha/beta ratio for prostate cancer from clinical dose-response data. For the ratio to be meaningful, it must be assumed that parameter ratios are not sensitive to the type of tumor control model used. We investigated the validity of this assumption by deriving analytic relationships between the alpha/beta estimates from a homogeneous TCP model, ignoring interpatient heterogeneity, and those of the corresponding heterogeneous (population-averaged) model that incorporated heterogeneity. The homogeneous and heterogeneous TCP models can both be written in terms of the geometric parameters D(50) and gamma(50). We show that the functional forms of these models are similar. This similarity was used to develop an expression relating the homogeneous and heterogeneous estimates for the alpha/beta ratio. The expression was verified numerically by generating pseudo-data from a TCP curve with known parameters and then using the homogeneous and heterogeneous TCP models to estimate the alpha/beta ratio for the pseudo-data. When the dominant form of interpatient heterogeneity is that of radiosensitivity, the homogeneous and heterogeneous alpha/beta estimates differ. This indicates that the presence of this heterogeneity affects the value of the alpha/beta ratio derived from analysis of TCP curves. The alpha/beta ratio estimated from clinical dose-response data is model dependent--a heterogeneous TCP model that accounts for heterogeneity in radiosensitivity will produce a greater alpha/beta estimate than that resulting from a homogeneous TCP model.

SU‐FF‐T‐65: An Analytic Investigation of the Effect of Inter‐Patient Heterogeneity On Alpha/beta Ratio Estimates for Tumors

Purpose: To analytically determine the relationship between the α/β ratio that would be obtained by fitting the individual (non‐averaged) tumor control probability (TCP) model to clinical data and the α/β estimate from a fit of the population‐averaged TCP model to the same clinical dose‐response dataset. Method and Materials: Recently, Carlone et al. (Med. Phys., 2006. 33(6): p. 1634–42) published fundamental forms of the population TCP model for the limits of dominant heterogeneity in radiosensitivity, and in clonogen number. In each case, the model is parameterized by γ50 and D50. The individual Poisson TCP model has also been expressed in terms of these geometric parameters. Since the functional forms of these TCP models are similar, approximately the same γ50 and D50 values would be obtained for each model if they were fit to the same clinical dataset. This fact allows us to determine mapping relationships between parameter ratio estimates obtained from fits using the averaged or non‐averaged TCP model. Mapping relationships are determined for the case of dominant heterogeneity in clonogen number, and in radiosensitivity. Results: When heterogeneity in clonogen number dominates a clinical dataset, the individual and population‐averaged α/β estimates are virtually identical. However, for the case where heterogeneity in radiosensitivity dominates, the individual α/β estimate will not be the same as the corresponding population α/β estimate. Conclusion: Heterogeneity in radiosensitivity is believed to be the dominant form among clinical datasets. Hence, our analytic expressions suggest the individual α/β ratio estimate should be different from the population estimate. Because of this ambiguity, we suggest that modelling has limited value in α/β determination; only the clinical hypofractionation trials will have the ability to validate the hypothesis originally put forth by Brenner and Hall (IJROBP, 1999. 43(5): p. 1095–1101) that prostate cancer responds to fractionation as does a late responding tissue.

Optimum parameters in a model for tumour control probability, including interpatient heterogeneity: evaluation of the log-normal distribution

The heterogeneity of human tumour radiation response is well known. Researchers have used the normal distribution to describe interpatient tumour radiosensitivity. However, many natural phenomena show a log-normal distribution. Log-normal distributions are common when mean values are low, variances are large and values cannot be negative. These conditions apply to radiosensitivity. The aim of this work was to evaluate the log-normal distribution to predict clinical tumour control probability (TCP) data and to compare the results with the homogeneous (δ-function with single α-value) and normal distributions. The clinically derived TCP data for four tumour types—melanoma, breast, squamous cell carcinoma and nodes—were used to fit the TCP models. Three forms of interpatient tumour radiosensitivity were considered: the log-normal, normal and δ-function. The free parameters in the models were the radiosensitivity mean, standard deviation and clonogenic cell density. The evaluation metric was the deviance of the maximum likelihood estimation of the fit of the TCP calculated using the predicted parameters to the clinical data. We conclude that (1) the log-normal and normal distributions of interpatient tumour radiosensitivity heterogeneity more closely describe clinical TCP data than a single radiosensitivity value and (2) the log-normal distribution has some theoretical and practical advantages over the normal distribution. Further work is needed to test these models on higher quality clinical outcome datasets.

SU‐FF‐T‐351: Optimum Parameters An a Model for Tumor Control Probability Including Interpatient Heterogeneity: Evaluation of the Log‐Normal Distribution

Purpose: The heterogeneity of human tumor radiation response to is well known. Researchers have used the normal distribution to describe interpatient tumor radiosensitivity. However, many natural phenomena show a lognormal distribution. Lognormal distributions are common when mean values are low, variances are large and values cannot be negative. These conditions apply to radiosensitivity. The aim of this work was to evaluate the lognormal distribution to predict clinical TCP data and compare the results with the homogeneous (single α value) and normal distributions. Method and Materials: The clinically‐derived TCP data for four tumor types: melanoma, breast, squamous cell carcinoma and nodes were used as the benchmark to fit the TCP models. Three forms of interpatient tumor radiosensitivity were considered: the lognormal, normal and δ‐function (homogeneous). The free parameters in the models were the radiosensitivity mean, standard deviation and clonogenic cell density. The evaluation metric was the minimum square difference between the predicted and clinical data. Results: The normal and lognormal distributions match the clinical data significantly better than the δ‐function distribution. The means and standard deviations of the normal and lognormal distributions are similar. Though the clinical data match was slightly better for the lognormal data, the difference was not statistically significant (p=0.13). The clonogenic cell density value yielding the best clinical data match (101–105) is much less than the expected tumor cell density (107–109). Three explanations are intratumor radiosensitivity heterogeneity, tumor ‘stem’ cells and multiple cells required for tumor growth. Conclusion: The lognormal and normal distribution of interpatient tumor radiosensitivity heterogeneity more closely describe clinical TCP data than a single radiosensitivity value. The lognormal distribution trends towards significance in its ability to match clinical TCP data compared to the normal distribution. The lognormal also has some theoretical and practical advantages over the normal distribution.

Limitations of a TCP model incorporating population heterogeneity

The variation between individuals in their dose-response characteristics complicates attempts to extract estimates of radiobiological parameters (e.g. α, β, etc) from fits to clinical dose-response data. The use of ‘population’ dose-response models that explicitly account for this variability is necessary to avoid obtaining skewed parameter estimates. In this work, we evaluated an example of a ‘population’ tumour control probability (TCP) model in terms of its ability to provide reliable parameter estimates. This was accomplished by performing fits of this population model to ‘pseudo’ data sets, which were generated with Monte Carlo techniques and based on preset values for the various radiobiological parameters. The fitting exercises illustrated considerable correlations between the model parameters. Especially significant was the large correlation observed between the parameter μ = α/σα used to characterize the level of population heterogeneity in radiosensitivity and the α/β parameter typically used to describe the response to fractionation. The results imply that fits to clinical data may not be able to distinguish between tumours exhibiting a high degree of heterogeneity and a strong β-mechanism and those containing little heterogeneity and having a weak β-mechanism. One implication is that basing the design of optimal fractionation regimes on such fitting results may be error-prone. If in vitro assays are to be used to independently determine biologically reasonable ranges for parameter values, an accurate knowledge of the relationship between in vitro and in vivo dose-response characteristics is required.

SU-FF-T-372: Evaluation of the Limits of Accuracy of the High Heterogeneity TCP Model

Purpose: To determine the limits of accuracy of a TCP model that assumes high heterogeneity, such as the Roberts and Hendry (IJROBP 41 689–699 1998) model. Method and Materials: A TCP model that incorporates heterogeneity in radiosensitivity, clonogen number and growth rate is reduced to a two parameter model by grouping variables using a method previously introduced by Carlone et al (Carlone et al Med Phys 30 2832–2848 2003). The model is then approximated in the high heterogeneity limit by approximating the TCP function as a Heaviside step function with a step at 0.577. The high heterogeneity approximation, when plotted in the reduced parameter space has iso-TCP lines that are linear, and cross at a common point. This suggests a further variable reduction such that TCP depends on a single variable, δ: TCP = ½erfc(δ/sqrt(2)). A similar variable substitution can be inserted into the exact TCP model; the result is a function of two variables, however the TCP function depends much more strongly on the variable δ than on the second variable. The limits of accuracy of the approximation are determined by calculating the difference between the two solutions. Results: When only heterogeneity in a is considered, the high heterogeneity TCP approximation is accurate (< 5%) when σαD is larger than 1.6. When σαD is large as compared to 0.577, the TCP function can be accurately evaluated using only parameter ratios (Roberts and Hendry closed formula), however it does depend on the value of sa when σα when σαD ≈ 0.577. When σα is small, maximum errors on the order of 30% to 50% can occur. Conclusion: When the quantity σαD is significantly larger than 1, the heterogeneous TCP function can be accurately modeled using only parameter ratios, and the high heterogeneity approximation.

Effect of heterogeneity in radiosensitivity on LQ based isoeffect formalism for low α/β cancers

Change of fractionation for external beam radiation therapy based on linear-quadratic (LQ) formalism assumes that a single α/β is sufficient to characterize tumour response to dose fractionation. In reality, both inter-patient and intra-tumour heterogeneity might affect the applicability of isoeffectiveness formalism. The impact of heterogeneity on recently proposed hypofractionation schemes for the prostate has been analysed. The α/β ratio was assumed to be Gaussian distributed with a mean value of 1.5 Gy. Gaussian and lognormal distributions for α were modelled. TCP model parameters were adjusted to lead to TCP=0.80 for 70 Gy at 2 Gy per fraction. TCP loss from heterogeneity and doses required to restore TCP=0.80 were calculated. The effect of heterogeneity was moderate. Doses to restore TCP=0.80 in most cases were less than 1 Gy. The largest TCP loss was 4%. The difference between predictions of single α/β and heterogeneity models is too small to be detected in a clinical trial.

Modeling killing and repopulation kinetics of subclinical cancer: direct calculations from clinical data

Purpose Models for cell killing and repopulation can provide insight into the efficacy of therapies. Using clinical data on breast cancer recurrence after lumpectomy with or without radiotherapy (L±RT) and brain metastases after chemotherapy with or without prophylactic cranial irradiation (C±PCI) for small-cell lung cancer, estimates of cell killing and subclinical repopulation were tested against the results from simple radiobiologic models. Methods and materials The rates of local breast cancer recurrence after L±RT and of brain metastases after C±PCI were extracted from published randomized trials. In Method 1, assuming simple exponential growth, the cell number distributions after L±RT and C±PCI were calculated from the clinical data, and the impact of RT on these distributions was determined. In Method 2, “classic” radiobiology dictates that a typical course of breast RT and PCI results in ≈7 and ≈4.5 log of cell kill, respectively. Using an assumption of uniform log-kill, the clinical doubling times (CDTs) can be calculated directly from the clinical data. Results Using Method 1, for breast cancer and assuming a CDT of 110 days and a clinically detectable cell number of 10 9, the calculated cell number distribution would be approximately uniformly distributed from 1 to 10 8 cells, with RT reducing the frequency at all points by ≈75%. From the brain metastasis data, assuming a CDT of 55 days, a cell number distribution of 10 3 to 10 8 cells would be calculated. PCI reduces the frequency of metastases by roughly 40%. For both the breast and the brain data, the effects of RT on the cell number distribution are not consistent with uniform radiosensitivity. Using Method 2, assuming a cell number of 10 after L±RT, the calculated CDTs range from 14 to 124 days. For the brain metastasis case, assuming a starting cell number of 3.16 × 10 3, the CDTs would primarily be in the 10–30-day range. Conclusion The distribution of clinical responses to adjuvant RT suggests a broad range of radiosensitivity, rather than uniform log cell kill. The subpopulation of tumors with minimal cell kill appears to be significant. This heterogeneity may be due to radioresistant subpopulations, failure to irradiate tumor cells, and/or new tumor formation. Similarly, the computed CDTs consistent with the clinical data are shorter than those reported in the literature. Simple radiobiologic models that fail to incorporate heterogeneity of radiosensitivity and/or tumor cell repopulation do not adequately describe clinical outcomes.

Viability of the EUD and TCP concepts as reliable dose indicators

The concept of equivalent uniform dose (EUD) was introduced to provide a method of reporting radiotherapy dose distributions which takes account of the nonlinearity of tissue dose-response, whilst not attempting to make predictions of absolute outcome. The purpose of this investigation was to determine the level of sensitivity of EUD to model parameters for significant variations in dose distribution and consequently the reliability of the factor as a dose-indicator, and to compare EUD with the more familiar index, tumour control probability (TCP). EUD and TCP, derived from the linear-quadratic formalism, were investigated for a test tissue being irradiated non-uniformly. Variations in the parameters of the model (tissue cell characteristics, dose heterogeneity, fractionation parameters) indicated the sensitivity of EUD and TCP to them. For time independent factors - cell density, cell radiosensitivity, radiosensitivity heterogeneity (population averaged) and ratio / - EUD was found to vary insignificantly in comparison with TCP, though this is a function of the actual form of the dose distribution under consideration. For fractionated treatments where the mean dose per fraction is varying (due to dosimetric/positioning errors for example), both EUD and TCP showed little variation with the degree of dose non-uniformity. For other time-dependent factors, fractionation rate and cell repopulation times, TCP again showed significant variation relative to EUD. The relative insensitivity of EUD implies that this index will be useful for dose evaluation when parameters are not known with accuracy, for the intercomparison of dose control studies and as a radiobiologically based optimization objective. However, given confidence in model parameters, the sensitivity of TCP would make it a more reliable tool for indicating potentially successful and unsuccessful irradiation strategies. It is suggested that both parameters be used in conjunction, with EUD and TCP results viewed with an appreciation of the characteristics of each model.