Analysis of a large number of clinical studies for breast cancer radiotherapy: estimation of radiobiological parameters for treatment planning

AAPM Task Group Report 267: A joint AAPM GEC-ESTRO report on biophysical models and tools for the planning and evaluation of brachytherapy

Brachytherapy utilizes a multitude of radioactive sources and treatment techniques that often exhibit widely different spatial and temporal dose delivery patterns. Biophysical models, capable of modeling the key interacting effects of dose delivery patterns with the underlying cellular processes of the irradiated tissues, can be a potentially useful tool for elucidating the radiobiological effects of complex brachytherapy dose delivery patterns and for comparing their relative clinical effectiveness. While the biophysical models have been used largely in research settings by experts, it has also been used increasingly by clinical medical physicists over the last two decades. A good understanding of the potentials and limitations of the biophysical models and their intended use is critically important in the widespread use of these models. To facilitate meaningful and consistent use of biophysical models in brachytherapy, Task Group 267 (TG-267) was formed jointly with the American Association of Physics in Medicine (AAPM) and The Groupe Européen de Curiethérapie and the European Society for Radiotherapy & Oncology (GEC-ESTRO) to review the existing biophysical models, model parameters, and their use in selected brachytherapy modalities and to develop practice guidelines for clinical medical physicists regarding the selection, use, and interpretation of biophysical models. The report provides an overview of the clinical background and the rationale for the development of biophysical models in radiation oncology and, particularly, in brachytherapy; a summary of the results of literature review of the existing biophysical models that have been used in brachytherapy; a focused discussion of the applications of relevant biophysical models for five selected brachytherapy modalities; and the task group recommendations on the use, reporting, and implementation of biophysical models for brachytherapy treatment planning and evaluation. The report concludes with discussions on the challenges and opportunities in using biophysical models for brachytherapy and with an outlook for future developments.

A Dosimetric Parameter Reference Look-Up Table for GRID Collimator-Based Spatially Fractionated Radiation Therapy

Simple Summary

Dose prescription for the inhomogeneous dosing in spatially fractionated radiation therapy (SFRT) is challenging, and further hampered by the inability of several planning systems to incorporate complex SFRT dose patterns. We developed dosing reference tables for an inventory of tumour scenarios and tested their accuracy with water phantom measurements of GRID therapy, delivered by a standard commercial GRID collimator. We find that dose heterogeneity parameters and EUD modeling are consistent across tumour sizes, configurations, and treatment depths. These results suggest that the developed reference tables can be used as a practical clinical resource for clinical decision-making on GRID therapy and to facilitate heterogeneity dose estimates in clinical patients when this commercially available GRID device is used.

Abstract

Computations of heterogeneity dose parameters in GRID therapy remain challenging in many treatment planning systems (TPS). To address this difficulty, we developed reference dose tables for a standard GRID collimator and validate their accuracy. The .decimal Inc. GRID collimator was implemented within the Eclipse TPS. The accuracy of the dose calculation was confirmed in the commissioning process. Representative sets of simulated ellipsoidal tumours ranging from 6–20 cm in diameter at a 3-cm depth; 16-cm ellipsoidal tumours at 3, 6, and 10 cm in depth were studied. All were treated with 6MV photons to a 20 Gy prescription dose at the tumour center. From these, the GRID therapy dosimetric parameters (previously recommended by the Radiosurgery Society white paper) were derived. Differences in D5 through D95 and EUD between different tumour sizes at the same depth were within 5% of the prescription dose. PVDR from profile measurements at the tumour center differed from D10/D90, but D10/D90 variations for the same tumour depths were within 11%. Three approximation equations were developed for calculating EUDs of different prescription doses for three radiosensitivity levels for 3-cm deep tumours. Dosimetric parameters were consistent and predictable across tumour sizes and depths. Our study results support the use of the developed tables as a reference tool for GRID therapy.

Development of generalized time-dependent TCP model and the investigation of the effect of repopulation and weekend breaks in fractionated external beam therapy

We developed a tumor control probability (TCP) model that incorporates variable time intervals between fractions and a kick-off time (T_k) for radiation-induced accelerated tumor proliferation. The resulting Lee-Rosen model, TCP_LR, was used to compute TCPs for treatment courses with and without weekend treatment for tumors with different proliferation rates - slow (prostate), moderate (breast), and rapid (head and neck). TCPs were computed using ideal uniform dose distributions and actual patient plans. The doses for the uniform plans were the mean doses for the prostate and breast cases and the minimum tumor dose for the head and neck case. The TCP_LR model predictions agreed with expectations that TCP increases with increasing T_k in all cases. For standard fractionation, as T_k increased from 0 to 4 weeks, TCP increased for the patient distributions by 74.7% for the head and neck cancer, by 6.2% for the breast cancer, and by 2.4% for the prostate cancers. For the uniform dose distributions, the increases were 79.2%, 5.7%, and 2.3%, respectively. TCP increased as the number of weekend breaks decreased. The effect of weekend breaks decreased as the tumor proliferation rate decreased. For the head and neck tumor, notable decreases in TCP of 6.0% (uniform dose distribution) and 6.8% (actual plan dose distribution) were observed with Friday starts compared to Monday starts for the standard 5 fx/wk schedule (T_k = 4 wk). The 7 fx/wk schedule produced increases in TCP of 17.0% and 20.5% for the uniform and patient dose distributions, respectively, compared to the standard schedule. For the breast cancer, starting the 5 fx/wk schedule on Friday decreased the TCP by 0.2% (T_k = 4 wk) compared to a Monday start. The 7 fx/wk schedule produced increases of 0.3% and 0.4% in TCP compared to the standard schedule for the uniform and patient dose distributions, respectively (T_k = 4 wk). For the prostate cancer, the change in TCP for 5 fx/wk schedules starting on different days was 0.1%. The 7 fx/wk schedule increased TCP by 0.8% compared to the standard schedule (T_k = 4 wk). TCP values for the uniform dose distributions for the standard schedule (T_k = 4 wk) agreed with the TCP values for the actual dose distributions within 4.5% for the head and neck tumor and within 0.2% for the breast and prostate tumors. This good agreement suggests that the doses chosen for the uniform dose distributions were good approximations to the clinical doses. The results for head and neck tumors support, in part, the current practice of hyperfractionated/accelerated radiotherapy. They also suggest that shortening the overall treatment time for conventional fractions by eliminating weekend breaks might be beneficial. The predicted effect on TCP of the various schedules studied was insignificant for prostate and breast tumors, suggesting that a weekend treatment might not be necessary for patients starting radiotherapy on a Friday. There is significant uncertainty in the values of the model parameters chosen for these calculations, and no consideration was given to the potential effects of these various schedules on normal tissues.

A simple dosimetric approach to spatially fractionated GRID radiation therapy using the multileaf collimator for treatment of breast cancers in the prone position

The purpose of this study was to explore the treatment planning methods of spatially fractionated radiation therapy (SFRT), commonly referred to as GRID therapy, in the treatment of breast cancer patients using multileaf collimator (MLC) in the prone position. A total of 12 patients with either left or right breast cancer were retrospectively chosen. The computed tomography (CT) images taken for the whole breast external beam radiation therapy (WB‐EBRT) were used for GRID therapy planning. Each GRID plan was made by using two portals and each portal had two fields with 1‐cm aperture size. The dose prescription point was placed at the center of the target volume, and a dose of 20 Gy with 6‐MV beams was prescribed. Dose‐volume histogram (DVH) curves were generated to evaluate dosimetric properties. A modified linear‐quadratic (MLQ) radiobiological response model was used to assess the equivalent uniform doses (EUD) and therapeutic ratios (TRs) of all GRID plans. The DVH curves indicated that these MLC‐based GRID therapy plans can deliver heterogeneous dose distribution in the target volume as seen with the conventional cerrobend GRID block. The plans generated by the MLC technique also demonstrated the advantage for accommodating different target shapes, sparing normal structures, and reporting dose metrics to the targets and the organs at risks. All GRID plans showed to have similar dosimetric parameters, implying the plans can be made in a consistent quality regardless of the shape of the target and the size of volume. The mean dose of lung and heart were respectively below 0.6 and 0.7 Gy. When the size of aperture is increased from 1 to 2 cm, the EUD and TR became smaller, but the peak/valley dose ratio (PVDR) became greater. The dosimetric approach of this study was proven to be simple, practical and easy to be implemented in clinic.

Immunologic Consequences of Sequencing Cancer Radiotherapy and Surgery

PURPOSE

Early-stage cancers are routinely treated with surgery followed by radiotherapy (SR). Radiotherapy before surgery (RS) has been widely ignored for some cancers. We evaluate overall survival (OS) and disease-free survival (DFS) with SR and RS for different cancer types and simulate the plausibility of RS- and SR-induced antitumor immunity contributing to outcomes.

MATERIALS AND METHODS

We analyzed a SEER data set of early-stage cancers treated with SR or RS. OS and DFS were calculated for cancers with sufficient numbers for statistical power (cancers of lung and bronchus, esophagus, rectum, cervix uteri, corpus uteri, and breast). We simulated the immunologic consequences of SR, RS, and radiotherapy alone in a mathematical model of tumor-immune interactions.

RESULTS

RS improved OS for cancers with low 20-year survival rates (lung: hazard ratio [HR], 0.88; P = .046) and improved DFS for cancers with higher survival (breast: HR = 0.64; P < .001). For rectal cancer, with intermediate 20-year survival, RS improved both OS (HR = 0.89; P = .006) and DFS (HR = 0.86; P = .04). Model simulations suggested that RS could increase OS by eliminating cancer for a broader range of model parameters and radiotherapy-induced antitumor immunity compared with SR for selected parameter combinations. This could create an immune memory that may explain increased DFS after RS for certain cancers.

CONCLUSION

Study results suggest plausibility that radiation to the bulk of the tumor could induce a more robust immune response and better harness the synergy of radiotherapy and antitumor immunity than postsurgical radiation to the tumor bed. This exploratory study provides motivation for prospective evaluation of immune activation of RS versus SR in controlled clinical studies.

Radiobiological Implications of Nanoparticles Following Radiation Treatment

Materials with a high atomic number (Z) are shown to cause an increase in the level of cell kill by ionizing radiation when introduced into tumor cells. This study uses in vitro experiments to investigate the differences in radiosensitization between two cell lines (MCF-7 and U87) and three commercially available nanoparticles (gold, gadolinium, and iron oxide) irradiated by 6 MV X-rays. To assess cell survival, clonogenic assays are carried out for all variables considered, with a concentration of 0.5 mg mL-1 for each nanoparticle material used. This study demonstrates differences in cell survival between nanoparticles and cell line. U87 shows the greatest enhancement with gadolinium nanoparticles (2.02 ± 0.36), whereas MCF-7 cells have higher enhancement with gold nanoparticles (1.74 ± 0.08). Mass spectrometry, however, shows highest elemental uptake with iron oxide and U87 cells with 4.95 ± 0.82 pg of iron oxide per cell. A complex relationship between cellular elemental uptake is demonstrated, highlighting an inverse correlation with the enhancement, but a positive relation with DNA damage when comparing the same nanoparticle between the two cell lines.

Hyperthermia with radiotherapy reduces tumour alpha/beta: Insights from trials of thermoradiotherapy vs radiotherapy alone

PURPOSE

Hyperthermia inhibits the repair of irradiation-induced DNA damage and thereby could alter the α/β values of tumours. This study estimates the clinical α/β_HTRT values from clinical trials of thermoradiotherapy (HTRT) vs radiotherapy (RT) in recurrent breast (RcBC), head and neck (III/IV) (LAHNC) and cervix cancers (IIB-IVA) (LACC).

METHODS

Three recently published meta-analyses for HTRT vs RT in RcBC, LAHNC and LACC were evaluated for complete response (CR). Studies with specified RT dose (D), dose/fraction (d) and corresponding CRs were selected. Tumour biological effective dose (BED) for each study with RT (BED_RT) was computed assuming an α/β_RT of 10 Gy. As outcomes were favourable with HTRT, thermoradiobiological BED (BED_HTRT) was calculated as a product of BED_RT and %CR_HTRT/%CR_RT. The α/β_HTRT was estimated as Dd/(BED_HTRT - D).

RESULTS

12 trials with 864 patients were shortlisted - RcBC (3 studies, n = 259), LAHNC (5 studies, n = 338) and LACC (4 studies, n = 267). Overall risk difference of 0.28 favoured HTRT (p < 0.001). Mean BED_RT and BED_HTRT were 64.7 Gy (SD: ±15.5) and 109.5 Gy (SD: ±32.1) respectively and global α/β_HTRT was 2.25 Gy (SD: ±0.79). Mean α/β_HTRT for RcBC, LAHNC and LACC were 2.05 Gy, 1.74 Gy and 3.03 Gy respectively. On meta-regression, α/β_HTRT was the sole predictor for the corresponding risk differences of the studies (coefficient = -0.096; p = 0.03).

CONCLUSION

Thermoradiobiological effects on the repair of RT induced DNA damage results in reduction in α/β values of tumours. This should be considered to effectively optimize HTRT dose-fractionation schedules in the clinic.

The alfa and beta of tumours: a review of parameters of the linear-quadratic model, derived from clinical radiotherapy studies

BACKGROUND

Prediction of radiobiological response is a major challenge in radiotherapy. Of several radiobiological models, the linear-quadratic (LQ) model has been best validated by experimental and clinical data. Clinically, the LQ model is mainly used to estimate equivalent radiotherapy schedules (e.g. calculate the equivalent dose in 2 Gy fractions, EQD₂), but increasingly also to predict tumour control probability (TCP) and normal tissue complication probability (NTCP) using logistic models. The selection of accurate LQ parameters α, β and α/β is pivotal for a reliable estimate of radiation response. The aim of this review is to provide an overview of published values for the LQ parameters of human tumours as a guideline for radiation oncologists and radiation researchers to select appropriate radiobiological parameter values for LQ modelling in clinical radiotherapy.

METHODS AND MATERIALS

We performed a systematic literature search and found sixty-four clinical studies reporting α, β and α/β for tumours. Tumour site, histology, stage, number of patients, type of LQ model, radiation type, TCP model, clinical endpoint and radiobiological parameter estimates were extracted. Next, we stratified by tumour site and by tumour histology. Study heterogeneity was expressed by the I² statistic, i.e. the percentage of variance in reported values not explained by chance.

RESULTS

A large heterogeneity in LQ parameters was found within and between studies (I² > 75%). For the same tumour site, differences in histology partially explain differences in the LQ parameters: epithelial tumours have higher α/β values than adenocarcinomas. For tumour sites with different histologies, such as in oesophageal cancer, the α/β estimates correlate well with histology. However, many other factors contribute to the study heterogeneity of LQ parameters, e.g. tumour stage, type of LQ model, TCP model and clinical endpoint (i.e. survival, tumour control and biochemical control).

CONCLUSIONS

The value of LQ parameters for tumours as published in clinical radiotherapy studies depends on many clinical and methodological factors. Therefore, for clinical use of the LQ model, LQ parameters for tumour should be selected carefully, based on tumour site, histology and the applied LQ model. To account for uncertainties in LQ parameter estimates, exploring a range of values is recommended.

The alfa and beta of tumours: a review of parameters of the linear-quadratic model, derived from clinical radiotherapy studies

Background

Prediction of radiobiological response is a major challenge in radiotherapy. Of several radiobiological models, the linear-quadratic (LQ) model has been best validated by experimental and clinical data. Clinically, the LQ model is mainly used to estimate equivalent radiotherapy schedules (e.g. calculate the equivalent dose in 2 Gy fractions, EQD₂), but increasingly also to predict tumour control probability (TCP) and normal tissue complication probability (NTCP) using logistic models. The selection of accurate LQ parameters α, β and α/β is pivotal for a reliable estimate of radiation response. The aim of this review is to provide an overview of published values for the LQ parameters of human tumours as a guideline for radiation oncologists and radiation researchers to select appropriate radiobiological parameter values for LQ modelling in clinical radiotherapy.

Methods and materials

We performed a systematic literature search and found sixty-four clinical studies reporting α, β and α/β for tumours. Tumour site, histology, stage, number of patients, type of LQ model, radiation type, TCP model, clinical endpoint and radiobiological parameter estimates were extracted. Next, we stratified by tumour site and by tumour histology. Study heterogeneity was expressed by the I² statistic, i.e. the percentage of variance in reported values not explained by chance.

Results

A large heterogeneity in LQ parameters was found within and between studies (I² > 75%). For the same tumour site, differences in histology partially explain differences in the LQ parameters: epithelial tumours have higher α/β values than adenocarcinomas. For tumour sites with different histologies, such as in oesophageal cancer, the α/β estimates correlate well with histology. However, many other factors contribute to the study heterogeneity of LQ parameters, e.g. tumour stage, type of LQ model, TCP model and clinical endpoint (i.e. survival, tumour control and biochemical control).

Conclusions

The value of LQ parameters for tumours as published in clinical radiotherapy studies depends on many clinical and methodological factors. Therefore, for clinical use of the LQ model, LQ parameters for tumour should be selected carefully, based on tumour site, histology and the applied LQ model. To account for uncertainties in LQ parameter estimates, exploring a range of values is recommended.

Electronic supplementary material

The online version of this article (10.1186/s13014-018-1040-z) contains supplementary material, which is available to authorized users.

Therapeutic analysis of Intrabeam-based intraoperative radiation therapy in the treatment of unicentric breast cancer lesions utilizing a spherical target volume model

It is postulated that the outcomes in treating breast cancer with intraoperative radiotherapy (IORT) would be affected by the residual cancer cell distribution within the tumor bed. The three-dimensional (3D) radiation doses of Intrabeam^TM (IB) IORT with a 4-cm spherical applicator at the energy of 50 and 40 kV were calculated. The modified linear quadratic model (MLQ) was used to estimate the radiobiological responses of the cancer cells and interspersed normal tissues with various radiosensitivities. By comparing the average survival fraction of normal tissues in IB-IORT and uniform dose treatment for the same level of cancer cell killing, the therapeutic ratios (TRs) were derived. The equivalent uniform dose (EUD) was found to increase with the prescription dose and decrease with the cancer cell infiltrating distance. For 50 kV beam at the 20 Gy prescription dose, the EUDs are 18.03, 16.49 and 13.56, 11. 29, and 9.28 Gy respectively, for 1.5, 3.0, 6.0, 9, and 15.0 mm of the cancer cell infiltrating distance into surrounding tissue. The dose rate of 50 kV is at least 1.87× higher than that of 40 kV beam. The EUDs of 50 kV beam are up to 15% higher than that of the 40 kV beam. The TR increases with the prescription dose, but decreases with the distance of cancer cell infiltration distance. Average TRs of 50 kV beam are up to 30% larger than that of 40 kV beam. In conclusion, IB-IORT can provide a possible therapeutic advantage on sparing more normal tissue compared with the External Beam IORT (EB-IORT) for shallowly populated unicentric breast lesion. Our data suggest that IB-IORT dose size should be adjusted based on the individual patient's cancer cell infiltrating distance for delivering an effective dose, one dose-fits-all regimen may have undertreated some patients with large cancer infiltrating distance.

Dosimetric and radiobiological comparison of TG-43 and Monte Carlo calculations in 192Ir breast brachytherapy applications

PURPOSE

To investigate the clinical significance of introducing model based dose calculation algorithms (MBDCAs) as an alternative to TG-43 in ¹⁹²Ir interstitial breast brachytherapy.

MATERIALS AND METHODS

A 57 patient cohort was used in a retrospective comparison between TG-43 based dosimetry data exported from a treatment planning system and Monte Carlo (MC) dosimetry performed using MCNP v. 6.1 with plan and anatomy information in DICOM-RT format. Comparison was performed for the target, ipsilateral lung, heart, skin, breast and ribs, using dose distributions, dose-volume histograms (DVH) and plan quality indices clinically used for plan evaluation, as well as radiobiological parameters.

RESULTS

TG-43 overestimation of target DVH parameters is statistically significant but small (less than 2% for the target coverage indices and 4% for homogeneity indices, on average). Significant dose differences (>5%) were observed close to the skin and at relatively large distances from the implant leading to a TG-43 dose overestimation for the organs at risk. These differences correspond to low dose regions (<50% of the prescribed dose), being less than 2% of the prescribed dose. Detected dosimetric differences did not induce clinically significant differences in calculated tumor control probabilities (mean absolute difference <0.2%) and normal tissue complication probabilities.

CONCLUSION

While TG-43 shows a statistically significant overestimation of most indices used for plan evaluation, differences are small and therefore not clinically significant. Improved MBDCA dosimetry could be important for re-irradiation, technique inter-comparison and/or the assessment of secondary cancer induction risk, where accurate dosimetry in the whole patient anatomy is of the essence.

A note on modeling of tumor regression for estimation of radiobiological parameters

PURPOSE

Accurate calculation of radiobiological parameters is crucial to predicting radiation treatment response. Modeling differences may have a significant impact on derived parameters. In this study, the authors have integrated two existing models with kinetic differential equations to formulate a new tumor regression model for estimation of radiobiological parameters for individual patients.

METHODS

A system of differential equations that characterizes the birth-and-death process of tumor cells in radiation treatment was analytically solved. The solution of this system was used to construct an iterative model (Z-model). The model consists of three parameters: tumor doubling time Td, half-life of dead cells Tr, and cell survival fraction SFD under dose D. The Jacobian determinant of this model was proposed as a constraint to optimize the three parameters for six head and neck cancer patients. The derived parameters were compared with those generated from the two existing models: Chvetsov's model (C-model) and Lim's model (L-model). The C-model and L-model were optimized with the parameter Td fixed.

RESULTS

With the Jacobian-constrained Z-model, the mean of the optimized cell survival fractions is 0.43 ± 0.08, and the half-life of dead cells averaged over the six patients is 17.5 ± 3.2 days. The parameters Tr and SFD optimized with the Z-model differ by 1.2% and 20.3% from those optimized with the Td-fixed C-model, and by 32.1% and 112.3% from those optimized with the Td-fixed L-model, respectively.

CONCLUSIONS

The Z-model was analytically constructed from the differential equations of cell populations that describe changes in the number of different tumor cells during the course of radiation treatment. The Jacobian constraints were proposed to optimize the three radiobiological parameters. The generated model and its optimization method may help develop high-quality treatment regimens for individual patients.

A simulation framework for modeling tumor control probability in breast conserving therapy

BACKGROUND AND PURPOSE

Microscopic disease (MSD) left after tumorectomy is a major cause of local recurrence in breast conserving therapy (BCT). However, the effect of microscopic disease and RT dose on tumor control probability (TCP) was seldom studied quantitatively. A simulation framework was therefore constructed to explore the relationship between tumor load, radiation dose and TCP.

MATERIALS AND METHODS

First, we modeled total disease load and microscopic spread with a pathology dataset. Then we estimated the remaining disease load after tumorectomy through surgery simulation. The Webb-Nahum TCP model was extended by clonogenic cell fraction to model the risk of local recurrence. The model parameters were estimated by fitting the simulated results to the observations in two clinical trials.

RESULTS

Higher histopathology grade has a strong correlation with larger MSD cell quantity. On average 12.5% of the MSD cells remained in the patient's breast after surgery but varied considerably among patients (0-100%); illustrating the role of radiotherapy. A small clonogenic cell fraction was optimal in our model (one in every 2.7*10(6)cells). The mean radiosensitivity was estimated at 0.067Gy(-1) with standard deviation of 0.022Gy(-1).

CONCLUSION

A relationship between radiation dose and TCP was established in a newly designed simulation framework with detailed disease load, surgery and radiotherapy models.

Towards predicting the response of a solid tumour to chemotherapy and radiotherapy treatments: clinical insights from a computational model

In this paper we use a hybrid multiscale mathematical model that incorporates both individual cell behaviour through the cell-cycle and the effects of the changing microenvironment through oxygen dynamics to study the multiple effects of radiation therapy. The oxygenation status of the cells is considered as one of the important prognostic markers for determining radiation therapy, as hypoxic cells are less radiosensitive. Another factor that critically affects radiation sensitivity is cell-cycle regulation. The effects of radiation therapy are included in the model using a modified linear quadratic model for the radiation damage, incorporating the effects of hypoxia and cell-cycle in determining the cell-cycle phase-specific radiosensitivity. Furthermore, after irradiation, an individual cell's cell-cycle dynamics are intrinsically modified through the activation of pathways responsible for repair mechanisms, often resulting in a delay/arrest in the cell-cycle. The model is then used to study various combinations of multiple doses of cell-cycle dependent chemotherapies and radiation therapy, as radiation may work better by the partial synchronisation of cells in the most radiosensitive phase of the cell-cycle. Moreover, using this multi-scale model, we investigate the optimum sequencing and scheduling of these multi-modality treatments, and the impact of internal and external heterogeneity on the spatio-temporal patterning of the distribution of tumour cells and their response to different treatment schedules.

Anti-cancer treatments such as radiotherapy and chemotherapy have evolved through clinical trial-and-error over decades, and although they cure some cases and are partially effective in many, the majority of such cancers ultimately recur. Doctors turn to new, expensive drugs as they emerge, but perhaps fail to study and learn how to use the therapies they already have most effectively. This is partly because clinical trials are expensive to conduct, both in terms of time and money. The cancer cell is complicated, but many mechanisms that control its response to treatment are now understood. We show here how a mathematical model accurately reproduces the results of previous biological experiments of cancer treatment, opening up the possibility of using it to predict which combinations of drugs and radiotherapy would be best for patients.

Impact of negative margin width on local recurrence in breast conserving therapy

BACKGROUND AND PURPOSE

This study aims to explain the unexpected weak association between the width of the negative surgical margin and the risk of local recurrence in breast conserving therapy.

MATERIALS AND METHODS

We utilized a classical tumor-control probability (TCP) model to estimate the risk of local recurrence, considering the heterogeneity of microscopic disease spread observed around the invasive index tumor in a pathology dataset (N=60). The estimated result was compared with the true risk observed in the EORTC boost-versus-no-boost trial (N=1616).

RESULTS

The disease volume beyond any given distance from the edge of the index tumor varied considerably among patients. Adopting this disease volume variation in the TCP model accurately reproduced the local recurrence rate as function of surgical margin width in the boost-versus-no-boost trial (Pearson's correlation coefficients are 0.652 and 0.862, and significant at the 0.05 and 0.01 level for absence and presence of a radiation boost, respectively).

CONCLUSIONS

The impact of a negative margin width on local recurrence is limited due to the large variation of microscopic disease that can reach large quantities beyond any given distance from the edge of the index tumor across the patient population of breast-conserving therapy.

Consequences of dose heterogeneity on the biological efficiency of ¹⁰³Pd permanent breast seed implants

Brachytherapy is associated with highly heterogeneous spatial dose distributions. This heterogeneity is usually ignored when estimating the biological effective dose (BED). In addition, the heterogeneities of the medium including the tissue heterogeneity (TH) and the interseed attenuation (ISA) are also contributing to the heterogeneity of the dose distribution, but they are both ignored in Task Group 43 (TG43)-based protocols. This study investigates the effect of dose heterogeneity, TH and ISA on metrics that are commonly used to quantify biological efficiency in brachytherapy. The special case of 29 breast cancer patients treated with permanent (103)Pd seed implant is considered here. BED is compared to equivalent uniform BED (EUBED) capable of considering the spatial heterogeneity of the dose distribution. The effects of TH and ISA on biological efficiency of treatments are taken into account by comparing TG43 with Monte Carlo (MC) dose calculations for each patient. The effect of clonogenic repopulation is also considered. The analysis is performed for different sets of (α/β, α) ratios of (2, 0.3), (4, 0.27) and (10, 0.3) [Gy, Gy(-1)] covering the whole range of reported α/β values in the literature. BED is sometimes larger and sometimes smaller than EUBED(TG43) indicating that the effect of the dose heterogeneity is not similar among patients. The effect of the dose heterogeneity can be characterized by using the D(99) dose metric. For each set of the radiobiological parameters considered, a D(99) threshold is found over which dose heterogeneity will cause an overestimation of the biological efficiencies while the inverse happens for smaller D(99) values. EUBED(MC) is always larger than EUBED(TG43) indicating that by neglecting TH and ISA in TG43-based dosimetry algorithms, the biological efficiencies may be underestimated by about 10 Gy. Overall, by going from BED to the more accurate EUBED(MC) there is a gain of about 9.6 to 13 Gy on the biological efficiency. The efficiency gain is about 10.8 to 14 Gy when the repopulation is considered. Dose heterogeneity does not have a constant impact on the biological efficiencies and may under- or overestimate the efficacy in different patients. However, the combined effect of neglecting dose heterogeneity, TH and ISA results in underestimation of the biological efficiencies in permanent breast seed implants.

Radiobiological characterization of post-lumpectomy focal brachytherapy with lipid nanoparticle-carried radionuclides

Post-operative radiotherapy has commonly been used for early stage breast cancer to treat residual disease. The primary objective of this work was to characterize, through dosimetric and radiobiological modeling, a novel focal brachytherapy technique which uses direct intracavitary infusion of β-emitting radionuclides (186Re/188Re) carried by lipid nanoparticles (liposomes). Absorbed dose calculations were performed for a spherical lumpectomy cavity with a uniformly injected activity distribution using a dose point kernel convolution technique. Radiobiological indices were used to relate predicted therapy outcome and normal tissue complication of this technique with equivalent external beam radiotherapy treatment regimens. Modeled stromal damage was used as a measure of the inhibition of the stimulatory effect on tumor growth driven by the wound healing response. A sample treatment plan delivering 50 Gy at a therapeutic range of 2.0 mm for 186Re-liposomes and 5.0 mm for 188Re-liposomes takes advantage of the dose delivery characteristics of the β-emissions, providing significant EUD (58.2 Gy and 72.5 Gy for 186Re and 188Re, respectively) with a minimal NTCP (0.046%) of the healthy ipsilateral breast. Modeling of kidney BED and ipsilateral breast NTCP showed that large injected activity concentrations of both radionuclides could be safely administered without significant complications.

A radiobiological investigation on dose and dose rate for permanent implant brachytherapy of breast using 125I or 103Pd sources

PURPOSE

The present report addresses the question of what could be the appropriate dose and dose rate for 125I and 103PD permanent seed implants for breast cancer as monotherapy for early stage breast cancer. This is addressed by employing a radiobiological methodology, which is based on the linear quadratic model, to identify a biologically effective dose (BED) to the prescription point of the brachytherapy implant, which would produce equivalent cell killing (or same cell survival) when compared to a specified external radiotherapy scheme.

METHODS

In the present analysis, the tumor and normal tissue BED ratios of brachytherapy and external radiotherapy are examined for different combinations of tumor proliferation constant (K), alpha/beta ratios, initial dose rate (R0), and reference external radiotherapy scheme (50 or 60 Gy in 2 Gy per fraction). The results of the radiobiological analysis are compared against other reports and clinical protocols in order to examine possible opportunities of improvement.

RESULTS

The analysis indicates that physical doses of approximately 100-110 Gy delivered with an initial dose rate of around 0.05 Gyh(-1) and 78-80 Gy delivered at 0.135 Gyh(-1) for 125I and 103Pd permanent implants, respectively, are equivalent to 50 Gy external beam radiotherapy (EBRT) in 2 Gy per fraction. Similarly, for physical doses of approximately 115-127 Gy delivered with an initia dose rate of around 0.059 Gyh(-1) and 92 Gy delivered at 0.157 Gyh(-1) for 125I and 103Pd, respectively, are equivalent to 60 Gy EBRT in 2 Gy per fraction. It is shown that the initial dose rate required to produce isoeffective tumor response with 50 or 60 Gy EBRT in 2 Gy per fraction increases as the repopulation factor K increases, even though repopulation is also considered in EBRT. Also, the initial dose rate increases as the value of the alpha/beta ratio decreases. The impact of the different alpha/beta ratios on the ratio of the tumor BEDs is significantly large for both the 125I and 103Pd implants with the deviation between the alpha/beta = 10.0 Gy ratios and those using the 4.0 and 3.5 Gy values ranging between 18% and 22% in most of the cases.

CONCLUSIONS

For the cases of 125I and 103Pd, the equivalent physical doses to 50 Gy EBRT in 2 Gy per fraction are associated with an overdosage of the involved normal tissue in the range of 4%-16% and an underdosage by 10%-15% for a BED for normal tissue, using an alpha/beta value of 3.0 Gy (BEDNT,3 Gy) of 100 Gy. These values are lower by 10%-20% than the published value of 124 Gy for 125I and by about 13% when compared to the published isoeffective dose of 90 Gy for 103Pd. Similarly, the equivalent physical doses to 60 Gy EBRT in 2 Gy per fraction are associated with an overdosage of the involved normal tissue by 10%-20% and an underdosage by 4%-10% for BEDNT,3 Gy of 110 Gy.

Respiratory organ motion and dosimetric impact on breast and nodal irradiation

PURPOSE

To examine the respiratory motion for target and normal structures during whole breast and nodal irradiation and the resulting dosimetric impact.

METHODS AND MATERIALS

Four-dimensional CT data sets of 18 patients with early-stage breast cancer were analyzed retrospectively. A three-dimensional conformal dosimetric plan designed to irradiate the breast was generated on the basis of CT images at 20% respiratory phase (reference phase). The reference plans were copied to other respiratory phases at 0% (end of inspiration) and 50% (end of expiration) to simulate the effects of breathing motion on whole breast irradiation. Dose-volume histograms, equivalent uniform dose, and normal tissue complication probability were evaluated and compared.

RESULTS

Organ motion of up to 8.8mm was observed during free breathing. A large lung centroid movement was typically associated with a large shift of other organs. The variation of planning target volume coverage during a free breathing cycle is generally within 1%-5% (17 of 18 patients) compared with the reference plan. However, up to 28% of V(45) variation for the internal mammary nodes was observed. Interphase mean dose variations of 2.2%, 1.2%, and 1.4% were observed for planning target volume, ipsilateral lung, and heart, respectively. Dose variations for the axillary nodes and brachial plexus were minimal.

CONCLUSIONS

The doses delivered to the target and normal structures are different from the planned dose based on the reference phase. During normal breathing, the dosimetric impact of respiratory motion is clinically insignificant with the exception of internal mammary nodes. However, noticeable degradation in dosimetric plan quality may be expected for the patients with large respiratory motion.

Investigation of source position uncertainties & balloon deformation in MammoSite brachytherapy on treatment effectiveness

The MammoSite breast high dose rate brachytherapy is used in treatment of early-stage breast cancer. The tumour bed volume is irradiated with high dose per fraction in a relatively small number of fractions. Uncertainties in the source positioning and MammoSite balloon deformation will alter the prescribed dose within the treated volume. They may also expose the normal tissues in balloon proximity to excessive dose. The purpose of this work is to explore the impact of these two uncertainties on the MammoSite dose distribution in the breast using dose volume histograms and Monte Carlo simulations. The Lyman-Kutcher and relative seriality models were employed to estimate the normal tissues complications associated with the MammoSite dose distributions. The tumour control probability was calculated using the Poisson model. This study gives low probabilities for developing heart and lung complications. The probability of complications of the skin and normal breast tissues depends on the location of the source inside the balloon and the volume receiving high dose. Incorrect source position and balloon deformation had significant effect on the prescribed dose within the treated volume. A 4 mm balloon deformation resulted in reduction of the tumour control probability by 24%. Monte Carlo calculations using EGSnrc showed that a deviation of the source by 1 mm caused approximately 7% dose reduction in the treated target volume at 1 cm from the balloon surface. In conclusion, accurate positioning of the (192)Ir source at the balloon centre and minimal balloon deformation are critical for proper dose delivery with the MammoSite brachytherapy applicator. On the basis of this study, we suggest that the MammoSite treatment protocols should allow for a balloon deformation of < or = 2 mm and a maximum source deviation of < or = 1 mm.

Accelerated partial breast irradiation as part of breast conserving therapy of early breast carcinoma: a systematic review

New strategies for adjuvant radiotherapy of early breast cancer are being investigated in several phase III randomised trials at the present time. Accelerated partial breast irradiation (APBI) is a way to offer an early breast cancer patient, who has had breast conservative surgery, an adjuvant radiotherapy of short duration aimed at the tumour bed with a certain margin. The rationale of this strategy is that most local recurrences appear close to the tumorectomy cavity and a wish to spare the patient late radiation morbidity. This review discusses the background for APBI, the different techniques, and we highlight possible pitfalls using these techniques. A systematic overview of all phase I and II studies is provided. Patient selection for this therapy is pivotal and based on evidence from previous studies on patient/tumour characteristics and pattern of local recurrences we propose inclusion criteria for patients in APBI protocols.

BGRT: biologically guided radiation therapy-the future is fast approaching!

Rapid advances in functional and biological imaging, predictive assays, and our understanding of the molecular and cellular responses underpinning treatment outcomes herald the coming of the long-sought goal of implementing patient-specific biologically guided radiation therapy (BGRT) in the clinic. Biological imaging and predictive assays have the potential to provide patient-specific, three-dimensional information to characterize the radiation response characteristics of tumor and normal structures. Within the next decade, it will be possible to combine such information with advanced delivery technologies to design and deliver biologically conformed, individualized therapies in the clinic. The full implementation of BGRT in the clinic will require new technologies and additional research. However, even the partial implementation of BGRT treatment planning may have the potential to substantially impact clinical outcomes.

Comparison of three accelerated partial breast irradiation techniques: Treatment effectiveness based upon biological models

BACKGROUND AND PURPOSE

Accelerated partial breast irradiation (APBI) is being studied in a phase III randomized trial as an alternative to whole breast irradiation (WBI) for early stage breast cancer patients. There are three methods for APBI: multi-catheter brachytherapy (MCT), MammoSite brachytherapy (MST), or 3D conformal (3DCRT). There is a paucity of data comparing among methods. Using a linear-quadratic (LQ) model, we evaluated the anticipated efficacy among the APBI methods for equivalent uniform dose (EUD), Tumor Control Probability (TCP), and Normal Tissue Complication Probability (NTCP).

MATERIALS AND METHODS

Treatment plans from five patients treated by each APBI modality were retrospectively selected. Dose-volume-histograms (DVH) for planning target volume (PTV), breast, and lung were generated. The LQ parameters alpha=0.3Gy(-1) and alpha/beta=10Gy were used for calculations. The values of EUD, TCP, and NTCP were calculated based on DVHs.

RESULTS

The average EUD (normalized to 3.4Gy BID) for the MCT, MST, and 3DCRT APBI was 35, 37.2, and 37.6Gy. When normalized to 2Gy fractionation these become, 42.2, 46.4, and 46.9Gy. Average TCP for MCT, MST, and 3DCRT PBI was 94.8%, 99.1%, and 99.2%. The NTCP values for breast and lung were low for all three methods.

CONCLUSIONS

The EUD for PTV and TCP were most similar in MST and 3DCRT APBI and were lower in MCT APBI. This questions the equivalence of the three APBI modalities that are currently being evaluated in the NSABP-B39/RTOG 0413 protocol.

Adjuvant stereotactic permanent seed breast implant: A boost series in view of partial breast irradiation

PURPOSE

The aim of this study was to use permanent seed implants in the breast and describe our experience with 15 cases, using iodine seed implants as a tumor bed boost.

METHODS AND MATERIALS

Breasts were fixed with a thermoplastic sheet, a template bridge applied, the thorax scanned and the images rotated to be perpendicular to the implant axis. Skin, heart, and lung were delineated. A preplan was made, prescribing 50 Gy to the clinical target volume (CTV), consisting in this boost series of nearly a quadrant. Iodine (125) seeds were stereotactically implanted through the template, and results were checked with a postplan computed tomographic (CT) scan.

RESULTS

The breast was immobilized reproducibly. Simulation, scanning, and implant were performed without difficulties. Preplan CTV D90% (the dose delivered to 90% of the CTV) was 66 Gy, and postoperative fluoroscopic or CT scan checks were satisfactory. Pre- and postplan dose-volume histogram showed good organ sparing: mean postplan skin, heart, and lung V30 Gy (the organ volume receiving a dose of 30 Gy) of 2 +/- 2.2 mL, 0.24 +/- 0.34 mL, and 3.5 +/- 5 mL, respectively. No short-term toxicity above Grade 1 was noted, except for transient Grade 3 neuropathy in 1 patient.

CONCLUSIONS

Seeds remained in the right place, as assessed by fluoroscopy, absence of significant pre- to postplan dose-volume histogram change for critical organs, and total irradiated breast volume. The method could be proposed as a boost when high dosimetric selectivity is required (young patients after cardiotoxic chemotherapy for left-sided cancer). This boost series was a preliminary step before testing partial breast irradiation by permanent seed implant in a prospective trial.

On relating the generalized equivalent uniform dose formalism to the linear-quadratic model

Two main approaches are commonly used in the literature for computing the equivalent uniform dose (EUD) in radiotherapy. The first approach is based on the cell-survival curve as defined in the linear-quadratic model. The second approach assumes that EUD can be computed as the generalized mean of the dose distribution with an appropriate fitting parameter. We have analyzed the connection between these two formalisms by deriving explicit formulas for the EUD which are applicable to normal distributions. From these formulas we have established an explicit connection between the two formalisms. We found that the EUD parameter has strong dependence on the parameters that characterize the distribution, namely the mean dose and the standard deviation around the mean. By computing the corresponding parameters for clinical dose distributions, which in general do not follow the normal distribution, we have shown that our results are also applicable to actual dose distributions. Our analysis suggests that caution should be used in using generalized EUD approach for reporting and analyzing dose distributions.

Three-Dimensional Conformal External Beam Radiotherapy (3D-CRT) for Accelerated Partial Breast Irradiation (APBI)

OBJECTIVE

This study is an evaluation of the biologic equivalence of the dose prescriptions for brachytherapy and 3-dimensional conformal external beam radiotherapy (3D-CRT) accelerated partial breast irradiation (APBI), using actual patient dose matrix data, and is based on the concept of equivalent uniform biologically effective dose (EUBED). This formalism allows a nonuniform dose distribution to be reduced to an equivalent uniform dose, while also accounting for fraction size.

MATERIALS AND METHODS

Five computed tomography scans were selected from a group of patients treated with multicatheter interstitial APBI. Dose matrices for the brachytherapy plans were computed and analyzed with in-house software. For each patient, the EUBED for the brachytherapy dose matrix was generated based on calculations performed at the voxel-level. These EUBED values were then used to calculate the biologically equivalent fraction size for 3D-CRT (eud).

RESULTS

The mean equivalent fraction size (eudmean) and maximum equivalent fraction size (eudmax) were calculated for each patient using 100 different values of the alpha/beta ratio. The eudmean ranged from 3.67 to 3.69 Gy, while the eudmax ranged from 3.79 to 3.82 Gy. For all values of the alpha/beta ratio, the maximum fraction size calculated to deliver a biologically equivalent dose with 3D-CRT was 3.82 Gy, with an equivalent total prescription dose of 38.2 Gy.

CONCLUSION

Utilizing a wide range of established radiobiological parameters, this study suggests that the maximum fraction size needed to deliver a biologically equivalent dose using 3D-CRT is 3.82 Gy, supporting the continued use of 3.85Gy BID in the current national cooperative trial.

Fundamental form of a population TCP model in the limit of large heterogeneity

A population tumor control probability (TCP) model for fractionated external beam radiotherapy, based on Poisson statistics and in the limit of large parameter heterogeneity, is studied. A reduction of a general eight-parameter TCP equation, which incorporates heterogeneity in parameters characterizing linear-quadratic radiosensitivity, repopulation, and clonogen number, to an equation with four parameters is obtained. The four parameters represent the mean and standard deviation for both clonogen number and a generalized radiosensitivity that includes linear-quadratic and repopulation descriptors. Further, owing to parameter inter-relationship, it is possible to express these four parameters as three ratios of parameters in the large heterogeneity limit. These ratios can be directly linked to two defining features of the TCP dose response: D50 and gamma50. In the general case, the TCP model can be written in terms of D50, gamma50 and a third parameter indicating the ratio of the levels of heterogeneity in clonogen number and generalized radiosensitivity; however, the third parameter is unnecessary when either of these two sources of heterogeneity is dominant. It is shown that heterogeneity in clonogen number will have little impact on the TCP formula for clinical scenarios, and thus it will generally be the case that the fundamental form of the Poisson-based population TCP model can be specified completely in terms of D50 and gamma50: TCP= 1/2 erfc[square root of pi(gamma50)(D50/D-1)]. This implies that limited radiobiological information can be determined by the analysis of dose response data: information about parameter ratios can be ascertained, but knowledge of absolute values for the fundamental radiobiological parameters will require independent auxiliary measurements.

Mathematical modelling of radiotherapy strategies for early breast cancer

Targeted intraoperative radiotherapy (Targit) is a new concept of partial breast irradiation where single fraction radiotherapy is delivered directly to the tumour bed. Apart from logistic advantages, this strategy minimizes the risk of missing the tumour bed and avoids delay between surgery and radiotherapy. It is presently being compared with the standard fractionated external beam radiotherapy (EBRT) in randomized trials. In this paper we present a mathematical model for the growth and invasion of a solid tumour into a domain of tissue (in this case breast tissue), and then a model for surgery and radiation treatment of this tumour. We use the established linear-quadratic (LQ) model to compute the survival probabilities for both tumour cells and irradiated breast tissue and then simulate the effects of conventional EBRT and Targit. True local recurrence of the tumour could arise either from stray tumour cells, or the tumour bed that harbours morphologically normal cells having a predisposition to genetic changes, such as a loss of heterozygosity (LOH) in genes that are crucial for tumourigenesis, e.g. tumour suppressor genes (TSGs). Our mathematical model predicts that the single high dose of radiotherapy delivered by Targit would result in eliminating all these sources of recurrence, whereas the fractionated EBRT would eliminate stray tumour cells, but allow (by virtue of its very schedule) the cells with LOH in TSGs or cell-cycle checkpoint genes to pass on low-dose radiation-induced DNA damage and consequently mutations that may favour the development of a new tumour. The mathematical model presented here is an initial attempt to model a biologically complex phenomenon that has until now received little attention in the literature and provides a 'proof of principle' that it is possible to produce clinically testable hypotheses on the effects of different approaches of radiotherapy for breast cancer.

Simultaneous integrated boost for breast cancer using imrt: a radiobiological and treatment planning study

PURPOSE

The purpose of this work is to explore the possibility of using intensity-modulated radiation therapy (IMRT) to deliver the boost dose to the tumor bed simultaneously with the whole-breast IMRT to reduce the radiation treatment time by 1-2 weeks.

METHODS AND MATERIALS

The biologically effective dose (BED) for different treatments was calculated using the linear-quadratic (LQ) model with parameters previously derived for breast cancer from clinical data (alpha/beta = 10Gy, alpha = 0.3Gy(-1)). A potential doubling time of 15 days (from in vitro measurements) for breast cancer and a generic alpha/beta ratio of 3 Gy for normal tissues were used. A series of regimens that use IMRT as initial treatment and an IMRT simultaneous integrated boost (SIB) were derived using biologic equivalence to conventional schedules. Possible treatment plans with IMRT SIB to the tumor bed were generated for 2 selected breast patients, 1 with a shallow tumor and 1 with a deep-seated tumor. Plans with a simultaneous integrated electron boost were also generated for comparison. Dosimetric merits of these plans were evaluated based on dose volume histograms.

RESULTS

A commonly used conventional treatment of 45 Gy (1.8 Gy x 25) to the whole breast and then a boost of 20 Gy (2 Gy x 10) is biologically equivalent to an alternative plan of 1.8 Gy x 25 to the whole breast with a 2.4 Gy x 25 SIB to the tumor bed. The new regime reduces treatment time from 7 to 5 weeks. For the patient with a deep-seated tumor, the IMRT plans reduce the volume of the breast that receives high doses (compared with the conventional photon boost plan) and provides good coverage of the target volumes.

CONCLUSION

It is biologically and dosimetrically feasible to reduce the overall treatment time for breast radiotherapy by using an IMRT simultaneous integrated boost. For selected patient groups, IMRT plans with a new regimen can be equal to or better than conventional plans.