The linear quadratic model: usage, interpretation and challenges

Improved Asymptotic Expansions in High- and Low-Dose Ranges for Generalized Multi-Hit Model of Radiation-Induced Cell Survival

By considering an upper bound on the number of radiation-induced potential lethal damages that can be repaired in a cell, we have proposed the generalized multi-hit (GMH) model with a closed-form solution, which can better fit various radiation-induced cell survival curves. Recent analysis shows that the asymptotic expansions that we gave before can be used to approximate the generalized single-hit single-target (GSHST) model rather than the GMH model. To illustrate the asymptotic trends of radiation-induced cell survival curves, in this study, we improve the asymptotic expansions of the GMH model in low- and high-dose ranges based on the limit formula of the incomplete gamma function in the corresponding dose ranges. When the upper limit of the number of radiation-induced potential lethal damages is one, the improved expansions of the GMH model can be reduced to the previous expansions of the GSHST model, and the improved asymptotic expansions of the GMH model also indicate that the GMH model has the generalized linear-quadratic-linear (LQL) feature. The numerical simulations indicate that the improved asymptotic expansions in high- and low-dose ranges agree well with the non-linear fitting of the GMH model in six kinds of cell lines under the corresponding dose ranges. In addition, we analyze the relative errors of the improved expansions of the GMH model in high- and low-dose ranges to demonstrate the accuracy and effectiveness of the improved expansions. Based on the error analysis, we further give the reasonable ranges of radiation dose applicable to the improved asymptotic expansions of the GMH model.

Microdosimetry modeling with auger emitters in generalized cell geometry

A microdosimetry model was developed for the prediction of cell viability for irregular non-spherical cells that were irradiated by low energy, short range auger electrons. Measured cell survival rates for LNCaP prostate cancer were compared to the computational results for the radioisotopes¹⁷⁷Lu and¹⁶¹Tb (conjugated to PSMA). The cell geometries used for the computations were derived directly from the cell culture images. A general computational approach was developed to handle arbitrary cell geometries, based on distance probability distribution functions (PDFs) derived from basic image processing. The radiation calculations were done per coarse grained PDF bin to reduce computation time, rather than on a pixel/voxel basis. The radiation dose point kernels over the full electron spectrum were derived using Monte Carlo simulations for energies below 50 eV to account for the propagation of auger electrons over length scales at and below a cellular radius. The relative importance of short range auger electrons were evaluated between the two nuclide types. The microdosimetry results were consistent with the cell viability measurements, and it was found that¹⁶¹Tb was more efficient than¹⁷⁷Lu primarily due to the short range auger electrons. We foresee that imaging based microdosimetry can be used to evaluate the relative therapeutic effect between various nuclide candidates.

Phenotypic variation modulates the growth dynamics and response to radiotherapy of solid tumours under normoxia and hypoxia

In cancer, treatment failure and disease recurrence have been associated with small subpopulations of cancer cells with a stem-like phenotype. In this paper, we develop and investigate a phenotype-structured model of solid tumour growth in which cells are structured by a stemness level, which varies continuously between stem-like and terminally differentiated behaviours. Cell evolution is driven by proliferation and death, as well as advection and diffusion with respect to the stemness structure variable. Here, the magnitude and sign of the advective flux are allowed to vary with the oxygen level. We use the model to investigate how the environment, in particular oxygen levels, affects the tumour's population dynamics and composition, and its response to radiotherapy. We use a combination of numerical and analytical techniques to quantify how under physiological oxygen levels the cells evolve to a differentiated phenotype and under low oxygen level (i.e., hypoxia) they de-differentiate. Under normoxia, the proportion of cancer stem cells is typically negligible and the tumour may ultimately become extinct whereas under hypoxia cancer stem cells comprise a dominant proportion of the tumour volume, enhancing radio-resistance and favouring the tumour's long-term survival. We then investigate how such phenotypic heterogeneity impacts the tumour's response to treatment with radiotherapy under normoxia and hypoxia. Of particular interest is establishing how the presence of radio-resistant cancer stem cells can facilitate a tumour's regrowth following radiotherapy. We also use the model to show how radiation-induced changes in tumour oxygen levels can give rise to complex re-growth dynamics. For example, transient periods of hypoxia induced by damage to tumour blood vessels may rescue the cancer cell population from extinction and drive secondary regrowth.

Joint Optimization of Photon-Carbon Ion Treatments for Glioblastoma

PURPOSE

Carbon ions are radiobiologically more effective than photons and are beneficial for treating radioresistant gross tumor volumes (GTV). However, owing to a reduced fractionation effect, they may be disadvantageous for treating infiltrative tumors, in which healthy tissue inside the clinical target volume (CTV) must be protected through fractionation. This work addresses the question: What is the ideal combined photon-carbon ion fluence distribution for treating infiltrative tumors given a specific fraction allocation between photons and carbon ions?

METHODS AND MATERIALS

We present a method to simultaneously optimize sequentially delivered intensity modulated photon (IMRT) and carbon ion (CIRT) treatments based on cumulative biological effect, incorporating both the variable relative biological effect of carbon ions and the fractionation effect within the linear quadratic model. The method is demonstrated for 6 glioblastoma patients in comparison with the current clinical standard of independently optimized CIRT-IMRT plans.

RESULTS

Compared with the reference plan, joint optimization strategies yield inhomogeneous photon and carbon ion dose distributions that cumulatively deliver a homogeneous biological effect distribution. In the optimal distributions, the dose to CTV is mostly delivered by photons and carbon ions are restricted to the GTV with variations depending on tumor size and location. Improvements in conformity of high-dose regions are reflected by a mean EQD2 reduction of 3.29 ± 1.22 Gy in a dose fall-off margin around the CTV. Carbon ions may deliver higher doses to the center of the GTV, and photon contributions are increased at interfaces with CTV and critical structures. This results in a mean EQD2 reduction of 8.3 ± 2.28 Gy, in which the brain stem abuts the target volumes.

CONCLUSIONS

We have developed a biophysical model to optimize combined photon-carbon ion treatments. For 6 glioblastoma patient cases, we show that our approach results in a more targeted application of carbon ions that (1) reduces dose in normal tissues within the target volume, which can only be protected through fractionation; and (2) boosts central target volume regions to reduce integral dose. Joint optimization of IMRT-CIRT treatments enable the exploration of a new spectrum of plans that can better address physical and radiobiological treatment planning challenges.

Effect of Probability Distribution of the Response Variable in Optimal Experimental Design with Applications in Medicine

In optimal experimental design theory it is usually assumed that the response variable follows a normal distribution with constant variance. However, some works assume other probability distributions based on additional information or practitioner’s prior experience. The main goal of this paper is to study the effect, in terms of efficiency, when misspecification in the probability distribution of the response variable occurs. The elemental information matrix, which includes information on the probability distribution of the response variable, provides a generalized Fisher information matrix. This study is performed from a practical perspective, comparing a normal distribution with the Poisson or gamma distribution. First, analytical results are obtained, including results for the linear quadratic model, and these are applied to some real illustrative examples. The nonlinear 4-parameter Hill model is next considered to study the influence of misspecification in a dose-response model. This analysis shows the behavior of the efficiency of the designs obtained in the presence of misspecification, by assuming heteroscedastic normal distributions with respect to the D-optimal designs for the gamma, or Poisson, distribution, as the true one.

Lung Cancer Radiotherapy: Simulation and Analysis Based on a Multicomponent Mathematical Model

Background

Lung cancer has been one of the most deadly illnesses all over the world, and radiotherapy can be an effective approach for treating lung cancer. Now, mathematical model has been extended to many biomedical fields to give a hand for analysis, evaluation, prediction, and optimization.

Methods

In this paper, we propose a multicomponent mathematical model for simulating the lung cancer growth as well as radiotherapy treatment for lung cancer. The model is digitalized and coded for computer simulation, and the model parameters are fitted with many research and clinical data to provide accordant results along with the growth of lung cancer cells in vitro.

Results

Some typical radiotherapy plans such as stereotactic body radiotherapy, conventional fractional radiotherapy, and accelerated hypofractionated radiotherapy are simulated, analyzed, and discussed. The results show that our mathematical model can perform the basic work for analysis and evaluation of the radiotherapy plan.

Conclusion

It will be expected that in the near future, mathematical model will be a valuable tool for optimization in personalized medical treatment.

Towards an Image-Informed Mathematical Model of In Vivo Response to Fractionated Radiation Therapy

Simple Summary

Using medical imaging data and computational models, we develop a modeling framework to provide personalized treatment response forecasts to fractionated radiation therapy for individual tumors. We evaluate this approach in an animal model of brain cancer and forecast changes in tumor cellularity and vasculature.

Abstract

Fractionated radiation therapy is central to the treatment of numerous malignancies, including high-grade gliomas where complete surgical resection is often impractical due to its highly invasive nature. Development of approaches to forecast response to fractionated radiation therapy may provide the ability to optimize or adapt treatment plans for radiotherapy. Towards this end, we have developed a family of 18 biologically-based mathematical models describing the response of both tumor and vasculature to fractionated radiation therapy. Importantly, these models can be personalized for individual tumors via quantitative imaging measurements. To evaluate this family of models, rats (n = 7) with U-87 glioblastomas were imaged with magnetic resonance imaging (MRI) before, during, and after treatment with fractionated radiotherapy (with doses of either 2 Gy/day or 4 Gy/day for up to 10 days). Estimates of tumor and blood volume fractions, provided by diffusion-weighted MRI and dynamic contrast-enhanced MRI, respectively, were used to calibrate tumor-specific model parameters. The Akaike Information Criterion was employed to select the most parsimonious model and determine an ensemble averaged model, and the resulting forecasts were evaluated at the global and local level. At the global level, the selected model’s forecast resulted in less than 16.2% error in tumor volume estimates. At the local (voxel) level, the median Pearson correlation coefficient across all prediction time points ranged from 0.57 to 0.87 for all animals. While the ensemble average forecast resulted in increased error (ranging from 4.0% to 1063%) in tumor volume predictions over the selected model, it increased the voxel wise correlation (by greater than 12.3%) for three of the animals. This study demonstrates the feasibility of calibrating a model of response by serial quantitative MRI data collected during fractionated radiotherapy to predict response at the conclusion of treatment.

Biologically consistent dose accumulation using daily patient imaging

BACKGROUND

This work addresses a basic inconsistency in the way dose is accumulated in radiotherapy when predicting the biological effect based on the linear quadratic model (LQM). To overcome this inconsistency, we introduce and evaluate the concept of the total biological dose, bEQD_d.

METHODS

Daily computed tomography imaging of nine patients treated for prostate carcinoma with intensity-modulated radiotherapy was used to compute the delivered deformed dose on the basis of deformable image registration (DIR). We compared conventional dose accumulation (DA) with the newly introduced bEQD_d, a new method of accumulating biological dose that considers each fraction dose and tissue radiobiology. We investigated the impact of the applied fractionation scheme (conventional/hypofractionated), uncertainties induced by the DIR and by the assigned α/β-value.

RESULTS

bEQD_d was systematically higher than the conventionally accumulated dose with difference hot spots of 3.3-4.9 Gy detected in six out of nine patients in regions of high dose gradient in the bladder and rectum. For hypofractionation, differences are up to 8.4 Gy. The difference amplitude was found to be in a similar range to worst-case uncertainties induced by DIR and was higher than that induced by α/β.

CONCLUSION

Using bEQD_d for dose accumulation overcomes a potential systematic inaccuracy in biological effect prediction based on accumulated dose. Highest impact is found for serial-type late responding organs at risk in dose gradient regions and for hypofractionation. Although hot spot differences are in the order of several Gray, in dose-volume parameters there is little difference compared with using conventional or biological DA. However, when local dose information is used, e.g. dose surface maps, difference hot spots can potentially change outcomes of dose-response modelling and adaptive treatment strategies.

Strategies of Two-Level Green Technology Investments for Coal Supply Chain under Different Dominant Modes

We consider a coal supply chain with a coal enterprise and a manufacturer, where the coal enterprise invests in clean coal technology, and the manufacturer invests in carbon reduction technology. The government offers subsidies for the investments of clean coal technology and carbon reduction technology. We examine optimal clean coal technology inputs in a coal enterprise and carbon reduction quantity in a manufacturer under the modes of coal-enterprise-led and manufacturer-led, respectively, using a Stackelberg game theory model. We obtain some interesting results. First, carbon reduction by the manufacturer is restrained when clean coal technology cost and carbon reduction cost are increased, regardless of the dominant modes, and clean coal technology input decreases when clean coal technology cost increases; however, a high carbon reduction cost has no effect on clean coal technology input when the manufacturer leads. Second, the clean coal technology subsidy for coal enterprises promotes clean coal technology inputs and carbon reductions, and the carbon reduction subsidy encourages carbon reduction without supporting clean coal technology input. Last, carbon reduction performance is better achieved under the manufacturer-led model than the coal-enterprise-led model. However, it should be noticed that the capital resource only relies on government subsidy in this article. In the future, this study could be used for green supply chain investment, and could be helpful for sustainability development.

Using Machine Learning Techniques for Asserting Cellular Damage Induced by High-LET Particle Radiation

This is a study concerning the use of Machine Learning (ML) techniques to ascertain the impacts of particle ionizing radiation (IR) on cell survival and DNA damage. Current empirical models do not always take into account intrinsic complexities and stochastic effects of the interactions of IR and cell populations. Furthermore, these models often lack in biophysical interpretations of the irradiation outcomes. The linear quadratic (LQ) model is a common way to associate the biological response of a cell population with the radiation dose. The parameters of the LQ model are used to extrapolate the relation between the dosage and the survival fraction of a cell population. The goal was to create a ML-based model that predicts the α and β parameters of the well known and established LQ model, along with the key metrics of DNA damage induction. The main target of this effort was, on the one hand, the development of a computational framework that will be able to assess key radiobiophysical quantities, and on the other hand, to provide meaningful interpretations of the outputs. Based on our results, as some metrics of the adaptability and training efficiency, our ML models exhibited 0.18 median error (relative root mean squared error (RRMSE)) in the prediction of the α parameter and errors of less than 0.01 for various DNA damage quantities; the prediction for β exhibited a rather large error of 0.75. Our study is based on experimental data from a publicly available dataset of irradiation studies. All types of complex DNA damage (all clusters), and the number of double-stranded breaks (DSBs), which are widely accepted to be closely related to cell survival and the detrimental biological effects of IR, were calculated using the fast Monte Carlo Damage Simulation software (MCDS). We critically discussed the varying importance of physical parameters such as charge and linear energy transfer (LET); we also discussed the uncertainties of our predictions and future directions, and the dynamics of our approach.

Intracranial germ cells tumour: a single institution experience in Argentina

BACKGROUND

Intracranial germ cell tumor (iGCT) represents a rare and heterogeneous group, with variable incidence and diverse treatment strategies. Although multiagent chemotherapy with reduced radiotherapy strategy has been applied by several cooperative groups in North America and Western Europe, there is a paucity of data to understand if this combined regimen is suitable in low-middle income countries (LMIC).

METHODS

We evaluate the outcome in a cohort of iGCT treated by SIOP-CNS-GCT-96 strategy at hospital J.P Garrahan in Argentina over the last 20 years. Radiation field and dose included focal radiotherapy (FRT) before 2009 or focal radiotherapy plus whole ventricular radiotherapy (WVRT) after 2009 for localized germinoma and FRT or FRT plus WVRT or CSI for non germinomatous germ cell tumors (NGGCT) RESULTS: Sixty iGCT were identified; 39 germinoma and 21 NGGCT. Median follow-up was 6.57 years (range 0.13-20.5). 5-year PFS and OS were 83.5% (95% CI [165.53-223.2]) and 88.7% (95% CI [169.84-223.2]) for the germinoma group, while for the NGGCT group were 75% (95% CI [133.27-219.96]) and 64.2% (95% CI [107.38-201.81]) respectively. The localized germinoma group showed poor results between 2000 and 2009 with 5-year PFS and OS of 69 and 75% respectively, and an excellent outcome between 2010 and 2019 with a 5-years PFS and OS of 92.8 and 100%. A univariable analysis identified this difference in survival as related to the field of radiotherapy, specifically whole ventricular radiotherapy. FRT increased the risk of recurrence in localized germinoma, involving not only ventricular relapses; but spinal cord and disseminated disease as well. There were no relapses of localized NGGCT after FRT and FRT plus WVRT.

CONCLUSION

Herein we demonstrate that intensive chemotherapy followed by FRT plus WVRT for germinoma is a feasible and effective strategy, warranting further study in the developing world.

Modeling low-dose radiation-induced acute myeloid leukemia in male CBA/H mice

The effect of low-dose ionizing radiation exposure on leukemia incidence remains poorly understood. Possible dose-response curves for various forms of leukemia are largely based on cohorts of atomic bomb survivors. Animal studies can contribute to an improved understanding of radiation-induced acute myeloid leukemia (rAML) in humans. In male CBA/H mice, incidence of rAML can be described by a two-hit model involving a radiation-induced deletion with Sfpi1 gene copy loss and a point mutation in the remaining Sfpi1 allele. In the present study (historical) mouse data were used and these processes were translated into a mathematical model to study photon-induced low-dose AML incidence in male CBA/H mice following acute exposure. Numerical model solutions for low-dose rAML incidence and diagnosis times could respectively be approximated with a model linear-quadratic in radiation dose and a normal cumulative distribution function. Interestingly, the low-dose incidence was found to be proportional to the modeled number of cells carrying the Sfpi1 deletion present per mouse following exposure. After making only model-derived high-dose rAML estimates available to extrapolate from, the linear-quadratic model could be used to approximate low-dose rAML incidence calculated with our mouse model. The accuracy in estimating low-dose rAML incidence when extrapolating from a linear model using a low-dose effectiveness factor was found to depend on whether a data transformation was used in the curve fitting procedure.

Proton RBE models: commonalities and differences

Uncertainties in the relative biological effectiveness (RBE) of protons remains a major barrier to the biological optimisation of proton therapy. While a constant value of 1.1 is widely used in treatment planning, extensive preclinical in vitro and in vivo data suggests that proton RBE is variable, depending on proton energy, target tissue, and endpoint. A number of phenomenological models have been developed to try and explain this variation, but agreement between these models is often poor. This has been attributed to both the models' underlying assumptions and the data to which they are fit. In this brief note, we investigate the underlying trends in these models by comparing their predictions as a function of relevant biological and physical parameters, to determine where models are in conceptual agreement or disagreement. By doing this, it can be seen that the primary differences between models arise from how they handle biological parameters (i.e. [Formula: see text] and [Formula: see text] from the linear-quadratic model for photon exposures). By contrast, when specifically explored for linear energy transfer-dependence, all models show extremely good correlation. These observations suggest that there is a pressing need for more systematic exploration of biological variation in RBE across different cells in well-controlled conditions to help distinguish between these different models and identify the true behaviour.

Impact of target dose inhomogeneity on BED and EUD in lung SBRT

PURPOSE

To evaluate the effect of dose heterogeneity in the treatment target on biologically effective dose (BED) for frequently used hypofractionation regimens in stereotactic body radiation therapy (SBRT).

METHODS

In the case of non-uniform target dose, BED in the planning target volume (PTV) is determined by using the linear-quadratic model. An expression for BED is obtained for an arbitrary dose distribution in the PTV in the case of small variance of the target dose. Another analytical expression for BED is obtained by assuming a Gaussian dose distribution in the target.

RESULTS

Analytical expressions for BED as a function of the variance of the target dose have been derived. It is shown that a relatively small dose inhomogeneity (<5%-6%) can cause a significant reduction (i.e. >10%) in the corresponding BED and equivalent uniform dose (EUD) compared to the case of uniform target dose.

CONCLUSIONS

Small variations in the absorbed dose can significantly reduce BED and EUD in the PTV. The effect of dose non-uniformity on BED increases with increasing dose per fraction. The observed reduction in BED compared to that for uniform target dose can be several times greater for SBRT than for standard fractionation with dose per fraction varying between 1.8 and 2 Gy.

In silico dosimetry of low-dose rate brachytherapy using radioactive nanoparticles

PURPOSE

Nanoparticles (NPs) with radioactive atoms incorporated within the structure of the NP or bound to its surface, functionalized with biomolecules are reported as an alternative to low-dose-rate seed-based brachytherapy. In this study, authors report a mathematical dosimetric study on low-dose rate brachytherapy using radioactive NPs.

METHOD

Single-cell dosimetry was performed by calculating cellular S-values for spherical cell model using Au-198, Pd-103 and Sm-153 NPs. The cell survival and tumor volume versus time curves were calculated and compared to the experimental studies on radiotherapeutic efficiency of radioactive NPs published in the literature. Finally, the radiotherapeutic efficiency of Au-198, Pd-103 and Sm-153 NPs was tested for variable: administered radioactivity, tumor volume and tumor cell type.

RESULT

At the cellular level Sm-153 presented the highest S-value, followed by Pd-103 and Au-198. The calculated cell survival and tumor volume curves match very well with the published experimental results. It was found that Au-198 and Sm-153 can effectively treat highly aggressive, large tumor volumes with low radioactivity.

CONCLUSION

The accurate knowledge of uptake rate, washout rate of NPs, radio-sensitivity and tumor repopulation rate is important for the calculation of cell survival curves. Self-absorption of emitted radiation and dose enhancement due to AuNPs must be considered in the calculations. Selection of radionuclide for radioactive NP must consider size of tumor, repopulation rate and radiosensitivity of tumor cells. Au-198 NPs functionalized with Mangiferin are a suitable choice for treating large, radioresistant and rapidly growing tumors.

New Challenges of Treatment for Locally Advanced Head and Neck Cancers in the Covid-19 Pandemic Era

Locally advanced head and neck cancer is a unique challenge for cancer management in the Covid-19 situation. The negative consequences of delaying radio-chemotherapy treatment make it necessary to prioritize these patients, the continuation of radiotherapy being indicated even if SARS-CoV-2 infection is confirmed in the case of patients with moderate and mild symptoms. For an early scenario, the standard chemo-radiotherapy using simultaneous integrated boost (SIB) technique is the preferred option, because it reduces the overall treatment time. For a late scenario with limited resources, hypo-fractionated treatment, with possible omission of chemotherapy for elderly patients and for those who have comorbidities, is recommended. Concurrent chemotherapy is controversial for dose values >2.4 Gy per fraction. The implementation of hypo-fractionated regimens should be based on a careful assessment of dose-volume constraints for organs at risks (OARs), using recommendations from clinical trials or dose conversion based on the linear-quadratic (LQ) model. Induction chemotherapy is not considered the optimal solution in this situation because of the risk of immunosuppression even though in selected groups of patients TPF regimen may bring benefits. Although the MACH-NC meta-analysis of chemotherapy in head and neck cancers did not demonstrate the superiority of induction chemotherapy over concurrent chemoradiotherapy, an induction regimen could be considered for cases with an increased risk of metastasis even in the case of a possible Covid-19 pandemic scenario.

Biological impact of dosimetric perturbations of a fiducial marker and the daily number of fields in proton therapy for prostate cancer

The purpose of this study was to estimate the biological impact of dosimetric perturbations of a fiducial marker and the daily number of fields in proton therapy for prostate cancer. Using a linear-quadratic model, normalized total doses (NTDs) of points where deposited dose was reduced from the prescribed dose by dosimetric perturbation of a fiducial marker were calculated in two hypothetical prostate cancer treatment schedules: a) irradiation of both parallel-opposed lateral fields and b) irradiation of alternate field in each daily treatment. The impact of hypofractionation and sublethal damage repair between irradiation on NTD was also estimated. The NTD of two fields/day schedule becomes lower than that of one field/day schedule. The difference becomes larger as dose reduction from one of two fields becomes more enhanced. The NTD reduction from the total dose in the two fields/day schedule is largest (30% of total dose) where the dose from one beam is completely lost by a fiducial marker. In contrast, the NTD reduction from the total dose in the one field/day schedule is largest (9% of total dose) where the half dose from one beam is decreased by a fiducial marker. In addition, the NTD reduction becomes larger as the fractional dose increases in a hypofractionated regimen, and when the effect of sublethal damage repair was incorporated. These influences become significant in prostate cancer since the radiobiological sensitivity α/β of prostate cancer is lower than other cancer types and normal tissues late complication. Treating with one alternate field in a daily treatment can improve a deteriorating treatment effect by dosimetric distortion of a fiducial marker in prostate cancer treatment. However, the choice of the number of beams in a fraction must also be determined by considering the sparing of normal tissues and patient-specific status.

Generalized stochastic microdosimetric model: The main formulation

The present work introduces a rigorous stochastic model, called the generalized stochastic microdosimetric model (GSM^{2}), to describe biological damage induced by ionizing radiation. Starting from the microdosimetric spectra of energy deposition in tissue, we derive a master equation describing the time evolution of the probability density function of lethal and potentially lethal DNA damage induced by a given radiation to a cell nucleus. The resulting probability distribution is not required to satisfy any a priori conditions. After the initial assumption of instantaneous irradiation, we generalized the master equation to consider damage induced by a continuous dose delivery. In addition, spatial features and damage movement inside the nucleus have been taken into account. In doing so, we provide a general mathematical setting to fully describe the spatiotemporal damage formation and evolution in a cell nucleus. Finally, we provide numerical solutions of the master equation exploiting Monte Carlo simulations to validate the accuracy of GSM^{2}. Development of GSM^{2} can lead to improved modeling of radiation damage to both tumor and normal tissues, and thereby impact treatment regimens for better tumor control and reduced normal tissue toxicities.

Breast cancer radiotherapy: What physicians need to know in the era of the precision medicine

Breast cancer is the most common cancer in women worldwide and encompasses a broad spectrum of diseases in one with significant epidemiological, clinical, and biological heterogeneity, which determines a different natural history and prognostic profile. Although classical tumour staging (TNM) still provides valuable information, the current reality is that the clinicians must consider other biological and molecular factors that directly influence treatment decision-making. The management of breast cancer has changed radically in the last 15 years due to significant advances in our understanding of these tumours. This knowledge has brought with it a major impact regarding surgical and systemic management and has been practice-changing, but it has also created significant uncertainties regarding how best integrate the radiotherapy treatment into the therapeutic scheme. In parallel, radiotherapy itself has also experienced major advances, new radiobiological concepts have emerged, and genomic data and other patient-specific factors must now be integrated into individualised treatment approaches. In this context, "precision medicine" seeks to provide an answer to these open questions and uncertainties. The aim of the present review is to clarify the meaning of this term and to critically evaluate its role and impact on contemporary breast cancer radiotherapy.

Insights into the theranostic value of precision medicine on advanced radiotherapy to breast cancer

Breast cancer is the most common cancer in women worldwide. "Breast cancer" encompasses a broad spectrum of diseases (i.e., subtypes) with significant epidemiological, clinical, and biological heterogeneity. Each of these subtypes has a different natural history and prognostic profile. Although tumour staging (TNM classification) still provides valuable information in the overall management of breast cancer, the current reality is that clinicians must consider other biological and molecular factors that directly influence treatment decision-making, including extent of surgery, indication for chemotherapy, hormonal therapy, and even radiotherapy (and treatment volumes). The management of breast cancer has changed radically in the last 15 years due to significant advances in our understanding of these tumours. While these changes have been extremely positive in terms of surgical and systemic management, they have also created significant uncertainties concerning integration of local and locoregional radiotherapy into the therapeutic scheme. In parallel, radiotherapy itself has also experienced major advances. Beyond the evident technological advances, new radiobiological concepts have emerged, and genomic data and other patient-specific factors must now be integrated into individualized treatment approaches. In this context, "precision medicine" seeks to provide an answer to these open questions and uncertainties. Although precision medicine has been much discussed in the last five years or so, the concept remains somewhat ambiguous, and it often appear to be used as a "catch-all" term. The present review aims to clarify the meaning of this term and, more importantly, to critically evaluate the role and impact of precision medicine on breast cancer radiotherapy. Finally, we will discuss the current and future of precision medicine in radiotherapy.

A kinetic model of continuous radiation damage to populations of cells: comparison to the LQ model and application to molecular radiotherapy

The linear-quadratic (LQ) model to describe the survival of irradiated cells may be the most frequently used biomathematical model in radiotherapy. There has been an intense debate on the mechanistic origin of the LQ model. An interesting approach is that of obtaining LQ-like behavior from kinetic models, systems of differential equations that model the induction and repair of damage. Development of such kinetic models is particularly interesting for application to continuous dose rate therapies, such as molecular radiotherapy or brachytherapy. In this work, we present a simple kinetic model that describes the kinetics of populations of tumor cells, rather than lethal/sub-lethal lesions, which may be especially useful for application to continuous dose rate therapies, as in molecular radiotherapy. The multi-compartment model consists of a set of three differential equations. The model incorporates in an easy way different cross-interacting compartments of cells forming a tumor, and may be of especial interest for studying dynamics of treated tumors. In the fast dose delivery limit, the model can be analytically solved, obtaining a simple closed-form expression. Fitting of several surviving curves with both this solution and the LQ model shows that they produce similar fits, despite being functionally different. We have also investigated the operation of the model in the continuous dose rate scenario, firstly by fitting pre-clinical data of tumor response to ¹³¹I-CLR1404 therapy, and secondly by showing how damage repair and proliferation rates can cause a treatment to achieve control or not. Kinetic models like the one presented in this work may be of special interest when modeling response to molecular radiotherapy.

Development of a new microdosimetric biological weighting function for the RBE10 assessment in case of the V79 cell line exposed to ions from 1H to 238U

An improved biological weighting function (IBWF) is proposed to phenomenologically relate microdosimetric lineal energy probability density distributions with the relative biological effectiveness (RBE) for the in vitro clonogenic cell survival (surviving fraction = 10%) of the most commonly used mammalian cell line, i.e. the Chinese hamster lung fibroblasts (V79). The IBWF, intended as a simple and robust tool for a fast RBE assessment to compare different exposure conditions in particle therapy beams, was determined through an iterative global-fitting process aimed to minimize the average relative deviation between RBE calculations and literature in vitro data in case of exposure to various types of ions from ¹H to ²³⁸U. By using a single particle- and energy- independent function, it was possible to establish an univocal correlation between lineal energy and clonogenic cell survival for particles spanning over an unrestricted linear energy transfer range of almost five orders of magnitude (0.2 keV µm^-1 to 15 000 keV µm^-1 in liquid water). The average deviation between IBWF-derived RBE values and the published in vitro data was ∼14%. The IBWF results were also compared with corresponding calculations (in vitro RBE₁₀ for the V79 cell line) performed using the modified microdosimetric kinetic model (modified MKM). Furthermore, RBE values computed with the reference biological weighting function (BWF) for the in vivo early intestine tolerance in mice were included for comparison and to further explore potential correlations between the BWF results and the in vitro RBE as reported in previous studies. The results suggest that the modified MKM possess limitations in reproducing the experimental in vitro RBE₁₀ for the V79 cell line in case of ions heavier than ²⁰Ne. Furthermore, due to the different modelled endpoint, marked deviations were found between the RBE values assessed using the reference BWF and the IBWF for ions heavier than ²H. Finally, the IBWF was unchangingly applied to calculate RBE values by processing lineal energy density distributions experimentally measured with eight different microdosimeters in 19 ¹H and ¹²C beams at ten different facilities (eight clinical and two research ones). Despite the differences between the detectors, irradiation facilities, beam profiles (pristine or spread out Bragg peak), maximum beam energy, beam delivery (passive or active scanning), energy degradation system (water, PMMA, polyamide or low-density polyethylene), the obtained IBWF-based RBE trends were found to be in good agreement with the corresponding ones in case of computer-simulated microdosimetric spectra (average relative deviation equal to 0.8% and 5.7% for ¹H and ¹²C ions respectively).

Advances in modelling gold nanoparticle radiosensitization using new Geant4-DNA physics models

Gold nanoparticles have demonstrated significant radiosensitization of cancer treatment with x-ray radiotherapy. To understand the mechanisms at the basis of nanoparticle radiosensitization, Monte Carlo simulations are used to investigate the dose enhancement, given a certain nanoparticle concentration and distribution in the biological medium. Earlier studies have ordinarily used condensed history physics models to predict nanoscale dose enhancement with nanoparticles. This study uses Geant4-DNA complemented with novel track structure physics models to accurately describe electron interactions in gold and to calculate the dose surrounding gold nanoparticle structures at nanoscale level. The computed dose in silico due to a clinical kilovoltage beam and the presence of gold nanoparticles was related to in vitro brain cancer cell survival using the local effect model. The comparison of the simulation results with radiobiological experimental measurements shows that Geant4-DNA and local effect model can be used to predict cell survival in silico in the case of x-ray kilovoltage beams.

Targeted Alpha Therapy in mCRPC (Metastatic Castration-Resistant Prostate Cancer) Patients: Predictive Dosimetry and Toxicity Modeling of 225Ac-PSMA (Prostate-Specific Membrane Antigen)

Radioligand therapy is a type of internal radiotherapy combining a short-range radioisotope labeled to a carrier with a high affinity for a specific receptor expressed on tumor cells. Targeted alpha therapy (TAT) combines a high-linear energy transfer (LET) emitter (²²⁵Ac) with a prostate-specific membrane antigen (PSMA) carrier, specifically binding tumor cells in patients with metastatic castration-resistant prostate cancer. Although the antitumor activity of ²²⁵Ac-PSMA is well-documented, this treatment is nowadays only used as salvage therapy because the high incidence of xerostomia limits the therapeutic window. Thus, methods to reduce salivary toxicity and models able to describe xerostomia incidence are needed. We recently studied the efficacy of salivary gland protectors administered in combination with ¹⁷⁷Lu-PSMA therapy. Starting from these data, we performed a predictive dosimetric evaluation of ²²⁵Ac-PSMA to assess the impact of salivary gland protectors in TAT. ²²⁵Ac-PSMA predictive dosimetry was performed in 13 patients treated with ¹⁷⁷Lu-PSMA. Sequential whole-body planar images were acquired 0.5–1, 16–24, 36–48, and 120 h post-injection. ¹⁷⁷Lu time-activity curves were corrected for ²²⁵Ac physical decay and assumed in equilibrium for all daughters. The OLINDA/EXM spherical model was used for dose estimation of the parotid and submandibular glands. The dose for each daughter was calculated and summed for the total dose estimation. The biologically effective dose formalism was extended to high-LET emitters. For the total biologically effective dose formalism extended to high-LET emitters, including the contribution of all daughter isotopes, the brachytherapy formalism for a mixture of radionuclides was implemented. Equivalent doses in 2 Gy/fraction (EQD2) were then calculated and compared with the normal tissue complication probability model derived from external beam radiotherapy for grade ≥2 xerostomia induction. Median predictive doses were 0.86 Bd_RBE5/MBq for parotid glands and 1.05 Bd_RBE5/MBq for submandibular glands, with a 53% reduction compared with previously published data. The results show that the radiobiological model implemented is conservative, as it overestimates the complication rate with respect to the clinical data. Our data shows the possibility of reducing salivary gland uptake in TAT with the coadministration of organ protectors, but these results should be confirmed for TAT with ²²⁵Ac-PSMA by carrying out prospective trials with defined toxicity endpoints and dosimetry procedures.

Tumour control probability of a UK cohort of lung SABR patients

Aims:

The aim of this work is to report on the tumour control probability (TCP) of a UK cohort of lung stereotactic ablative radiotherapy patients (n = 198) for a range of dose and fractionations common in the UK.

Materials and methods:

TCP values for 3 (54 Gy), 5 (55 and 60 Gy) and 8 (50 Gy) fraction (#) schemes were calculated with the linear-quadratic Marsden TCP model using the Biosuite software.

Results:

TCP values of 100% were computed for the 3 # and for 5 # (α/β = 10 Gy) cohorts; reduced to 99% (range 97–100) for the 5 # cohort only when an α/β of 20 Gy was used. The average TCP value for the 50 Gy in 8 # regime was 97% (range 92–99, α/β = 10 Gy) and 64% (range 48–79, α/β = 20 Gy). Statistical significant differences were observed between the α/β of 10 Gy versus 20 Gy groups and between all data grouped by fraction.

Conclusion:

TCPs achievable with current planning techniques in the UK have been presented. The ultra-conservative 50 Gy in 8 # scheme returns a significantly lower TCP than the other regimes.

Local Disease-Free Survival Rate (LSR) Application to Personalize Radiation Therapy Treatments in Breast Cancer Models

Cancer heterogeneity represents the main issue for defining an effective treatment in clinical practice, and the scientific community is progressively moving towards the development of more personalized therapeutic regimens. Radiotherapy (RT) remains a fundamental therapeutic treatment used for many neoplastic diseases, including breast cancer (BC), where high variability at the clinical and molecular level is known. The aim of this work is to apply the generalized linear quadratic (LQ) model to customize the radiant treatment plan for BC, by extracting some characteristic parameters of intrinsic radiosensitivity that are not generic, but may be exclusive for each cell type. We tested the validity of the generalized LQ model and analyzed the local disease-free survival rate (LSR) for breast RT treatment by using four BC cell cultures (both primary and immortalized), irradiated with clinical X-ray beams. BC cells were chosen on the basis of their receptor profiles, in order to simulate a differential response to RT between triple negative breast and luminal adenocarcinomas. The MCF10A breast epithelial cell line was utilized as a healthy control. We show that an RT plan setup based only on α and β values could be limiting and misleading. Indeed, two other parameters, the doubling time and the clonogens number, are important to finely predict the tumor response to treatment. Our findings could be tested at a preclinical level to confirm their application as a variant of the classical LQ model, to create a more personalized approach for RT planning.

Clinical implications of variable relative biological effectiveness in proton therapy for prostate cancer

PURPOSE

To study the potential consequences of differences in the evaluation of variable versus uniform relative biological effectiveness calculations in proton radiotherapy for prostate cancer.

METHODS AND MATERIAL

Experimental data with proton beams suggest that relative biological effectiveness increases with linear energy transfer. This relation also depends on the α / β ratio, characteristic of a tissue and a considered endpoint. Three phenomenological models (Carabe et al., Wedenberg et al. and McNamara et al.) are compared to a mechanistic model based on microdosimetry (microdosimetric kinetic model) and to the current assumption of uniform relative biological effectiveness equal to 1.1 in a prostate case.

RESULTS AND CONCLUSIONS

Phenomenological models clearly predict higher relative biological effectiveness values compared to microdosimetric kinetic model, that seems to approach to the constant value of 1.1 adopted in the clinics, at least for low linear energy transfer values achieved in typical prostate proton plans. All models predict a higher increase of the relative biological effectiveness-weighted dose for the prostate tumor than for the rest of structures involved due to its lower α / β ratio, even when linear energy transfer is, in general, lower in the tumor than on the surroundings tissues. Prostate cancer is, therefore, a good candidate to take advantage of variable relative biological effectiveness, especially if linear energy transfer is enhanced within the tumor. However, the discrepancies among models hinder the clinical implementation of variable relative biological effectiveness.

Modelling Dose Effects from Space Irradiations: Combination of High-LET and Low-LET Radiations with a Modified Microdosimetric Kinetic Model

The Microdosimetric Kinetic Model (MKM) to predict the effects of ionizing radiation on cell colonies is studied and reformulated for the case of high-linear energy transfer (LET) radiations with a low dose. When the number of radiation events happening in a subnuclear domain follows a Poisson distribution, the MKM predicts a linear-quadratic (LQ) survival curve. We show that when few events occur, as for high-LET radiations at doses lower than the mean specific energy imparted to the nucleus, zF,n, a Poisson distribution can no longer be assumed and an initial pure linear relationship between dose and survival fraction should be observed. Predictions of survival curves for combinations of high-LET and low-LET radiations are produced under two assumptions for their comparison: independent and combined action. Survival curves from previously published articles of V79 cell colonies exposed to X-rays, α particles, Ar-ions, Fe-ions, Ne-ions and mixtures of X-rays and each one of the ions are predicted according to the modified MKM. We conclude that mixtures of high-LET and low-LET radiations may enhance the effect of individual actions due to the increase of events in domains provided by the low-LET radiation. This hypothesis is only partially validated by the analyzed experiments.

The impact of dose delivery time on biological effectiveness in proton irradiation with various biological parameters

PURPOSE

The purpose of this study is to evaluate the sublethal damage (SLD) repair effect in prolonged proton irradiation using the biophysical model with various cell-specific parameters of (α/β)_x and T_1/2 (repair half time). At present, most of the model-based studies on protons have focused on acute radiation, neglecting the reduction in biological effectiveness due to SLD repair during the delivery of radiation. Nevertheless, the dose-rate dependency of biological effectiveness may become more important as advanced treatment techniques, such as hypofractionation and respiratory gating, come into clinical practice, as these techniques sometimes require long treatment times. Also, while previous research using the biophysical model revealed a large repair effect with a high physical dose, the dependence of the repair effect on cell-specific parameters has not been evaluated systematically.

METHODS

Biological dose [relative biological effectiveness (RBE) × physical dose] calculation with repair included was carried out using the linear energy transfer (LET)-dependent linear-quadratic (LQ) model combined with the theory of dual radiation action (TDRA). First, we extended the dose protraction factor in the LQ model for the arbitrary number of different LET proton irradiations delivered sequentially with arbitrary time lags, referring to the TDRA. Using the LQ model, the decrease in biological dose due to SLD repair was systematically evaluated for spread-out Bragg peak (SOBP) irradiation in a water phantom with the possible ranges of both (α/β)_x and repair parameters ((α/β)_x  = 1-15 Gy, T_1/2  = 0-90 min). Then, to consider more realistic irradiation conditions, clinical cases of prostate, liver, and lung tumors were examined with the cell-specific parameters for each tumor obtained from the literature. Biological D_99% and biological dose homogeneity coefficient (HC) were calculated for the clinical target volumes (CTVs), assuming dose-rate structures with a total irradiation time of 0-60 min.

RESULTS

The differences in the cell-specific parameters resulted in considerable variation in the repair effect. The biological dose reduction found at the center of the SOBP with 30 min of continuous irradiation varied from 1.13% to 14.4% with a T_1/2 range of 1-90 min when (α/β)_x is fixed as 10 Gy. It varied from 2.3% to 6.8% with an (α/β)_x range of 1-15 Gy for a fixed value of T_1/2  = 30 min. The decrease in biological D_99% per 10 min was 2.6, 1.2, and 3.0% for the prostate, liver, and lung tumor cases, respectively. The value of the biological D_99% reduction was neither in the order of (α/β)_x nor prescribed dose, but both comparably contributed to the repair effect. The variation of HC was within the range of 0.5% for all cases; therefore, the dose distribution was not distorted.

CONCLUSION

The reduction in biological dose caused by the SLD repair largely depends on the cell-specific parameters in addition to the physical dose. The parameters should be considered carefully in the evaluation of the repair effect in prolonged proton irradiation.

A Model for Estimating Dose-Rate Effects on Cell-Killing of Human Melanoma after Boron Neutron Capture Therapy

Boron neutron capture therapy (BNCT) is a type of radiation therapy for eradicating tumor cells through a ¹⁰B(n,α)⁷Li reaction in the presence of ¹⁰B in cancer cells. When delivering a high absorbed dose to cancer cells using BNCT, both the timeline of ¹⁰B concentrations and the relative long dose-delivery time compared to photon therapy must be considered. Changes in radiosensitivity during such a long dose-delivery time can reduce the probability of tumor control; however, such changes have not yet been evaluated. Here, we propose an improved integrated microdosimetric-kinetic model that accounts for changes in microdosimetric quantities and dose rates depending on the ¹⁰B concentration and investigate the cell recovery (dose-rate effects) of melanoma during BNCT irradiation. The integrated microdosimetric–kinetic model used in this study considers both sub-lethal damage repair and changes in microdosimetric quantities during irradiation. The model, coupled with the Monte Carlo track structure simulation code of the Particle and Heavy Ion Transport code System, shows good agreement with in vitro experimental data for acute exposure to ⁶⁰Co γ-rays, thermal neutrons, and BNCT with ¹⁰B concentrations of 10 ppm. This indicates that microdosimetric quantities are important parameters for predicting dose-response curves for cell survival under BNCT irradiations. Furthermore, the model estimation at the endpoint of the mean activation dose exhibits a reduced impact of cell recovery during BNCT irradiations with high linear energy transfer (LET) compared to ⁶⁰Co γ-rays irradiation with low LET. Throughout this study, we discuss the advantages of BNCT for enhancing the killing of cancer cells with a reduced dose-rate dependency. If the neutron spectrum and the timelines for drug and dose delivery are provided, the present model will make it possible to predict radiosensitivity for more realistic dose-delivery schemes in BNCT irradiations.

A theoretical cell-killing model to evaluate oxygen enhancement ratios at DNA damage and cell survival endpoints in radiation therapy

Radio-resistance induced under low oxygen pressure plays an important role in malignant progression in fractionated radiotherapy. For the general approach to predict cell killing under hypoxia, cell-killing models (e.g. the Linear-Quadratic model) have to be fitted to in vitro experimental survival data for both normoxia and hypoxia to obtain the oxygen enhancement ratio (OER). In such a case, model parameters for every oxygen condition needs to be considered by model-fitting approaches. This is inefficient for fractionated irradiation planning. Here, we present an efficient model for fractionated radiotherapy the integrated microdosimetric-kinetic model including cell-cycle distribution and the OER at DNA double-strand break endpoint (OER_DSB). The cell survival curves described by this model can reproduce the in vitro experimental survival data for both acute and chronic low oxygen concentrations. The OER_DSB used for calculating cell survival agrees well with experimental DSB ratio of normoxia to hypoxia. The important parameters of the model are oxygen pressure and cell-cycle distribution, which enables us to predict cell survival probabilities under chronic hypoxia and chronic anoxia. This work provides biological effective dose (BED) under various oxygen conditions including its uncertainty, which can contribute to creating fractionated regimens for multi-fractionated radiotherapy. If the oxygen concentration in a tumor can be quantified by medical imaging, the present model will make it possible to estimate the cell-killing and BED under hypoxia in more realistic intravital situations.

Development of transient radioresistance during fractionated irradiation in vitro

BACKGROUND AND PURPOSE

Effective combination treatments with fractionated radiotherapy rely on a proper understanding of the dynamic responses that occur during treatment. We explored the effect of clinical fractionated radiotherapy on the development and timing of radioresistance in tumor cells.

METHODS AND MATERIALS

Different colon (HT29/HCT116/COLO320/SW480/RKO) and high-grade astrocytoma (D384/U-251MG) cancer cell lines were treated for 6 weeks with daily fractions of 2 Gy, 5 days per week. Clonogenic survival was determined throughout the treatment period. In addition, the radiosensitivity of irradiated and non-irradiated was compared. Finally, the effect of different dose fractions on the development of radioresistance was determined.

RESULTS

All cell lines developed radioresistance within 2-3 weeks during fractionated radiotherapy. This was characterized by the occurrence of a steady state phase of clonogenic survival. In U-251MG cells this was accompanied by increased cell senescence and stemness. After recovering from six weeks of treatment, the radiosensitivity of fractionally irradiated and non-irradiated cells was similar. Including transient radioresistance, described as (α/β)^-(d+1), as a factor in the classic LQ model resulted in a perfect fit with the experimental data observed during fractionated radiotherapy. This was confirmed when different dose fractions were applied.

CONCLUSIONS

Fractionated irradiation of cancer cells in vitro following clinical radiation schedules induces a reversible radioresistance response. This adaptive response can be included in the LQ model as a function of the dose fraction and the alpha/beta-ratio of a given cell line. These findings warrant further investigation of the mechanisms and clinical relevance of adaptive radioresistance.

Proton Irradiation Increases the Necessity for Homologous Recombination Repair Along with the Indispensability of Non-Homologous End Joining

Technical improvements in clinical radiotherapy for maximizing cytotoxicity to the tumor while limiting negative impact on co-irradiated healthy tissues include the increasing use of particle therapy (e.g., proton therapy) worldwide. Yet potential differences in the biology of DNA damage induction and repair between irradiation with X-ray photons and protons remain elusive. We compared the differences in DNA double strand break (DSB) repair and survival of cells compromised in non-homologous end joining (NHEJ), homologous recombination repair (HRR) or both, after irradiation with an equal dose of X-ray photons, entrance plateau (EP) protons, and mid spread-out Bragg peak (SOBP) protons. We used super-resolution microscopy to investigate potential differences in spatial distribution of DNA damage foci upon irradiation. While DNA damage foci were equally distributed throughout the nucleus after X-ray photon irradiation, we observed more clustered DNA damage foci upon proton irradiation. Furthermore, deficiency in essential NHEJ proteins delayed DNA repair kinetics and sensitized cells to both, X-ray photon and proton irradiation, whereas deficiency in HRR proteins sensitized cells only to proton irradiation. We assume that NHEJ is indispensable for processing DNA DSB independent of the irradiation source, whereas the importance of HRR rises with increasing energy of applied irradiation.

Numerical simulation of normal and cancer cells' populations with fractional derivative under radiotherapy

Background This paper presents a numerical simulation of normal and cancer cells' population dynamics during radiotherapy. The model used for the simulation was the improved cancer treatment model with radiotherapy. The model simulated the population changes during a fractionated cancer treatment process. The results gave the final populations of the cells, which provided the final volumes of the tumor and normal cells. Method The improved model was obtained by integrating the previous cancer treatment model with the Caputo fractional derivative. In addition, the cells' population decay due to radiation was accounted for by coupling the linear-quadratic model into the improved model. The simulation of the treatment process was done with numerical variables, numerical parameters, and radiation parameters. The numerical variables include the populations of the cells and the time of treatment. The numerical parameters were the model factors which included the proliferation rates of cells, competition coefficients of cells, and perturbation constant for normal cells. The radiation parameters were clinical data based on the treatment procedure. The numerical parameters were obtained from the previous literature while the numerical variables and radiation parameters, which were clinical data, were obtained from reported data of four cancer patients treated with radiotherapy. The four cancer patients had tumor volumes of 28.4 cm³, 18.8 cm³, 30.6 cm³, and 12.6 cm³ and were treated with different treatment plans and a fractionated dose of 1.8 Gy each. The initial populations of cells were obtained by using the tumor volumes. The computer simulations were done with MATLAB. Results The final volumes of the tumors, from the results of the simulations, were 5.67 cm³, 4.36 cm³, 5.74 cm³, and 6.15 cm³ while the normal cells' volumes were 28.17 cm³, 18.68 cm³, 30.34 cm³, and 12.54 cm³. The powers of the derivatives were 0.16774, 0.16557, 0.16835, and 0.16. A variance-based sensitivity analysis was done to corroborate the model with the clinical data. The result showed that the most sensitive factors were the power of the derivative and the cancer cells' proliferation rate. Conclusion The model provided information concerning the status of treatments and can also predict outcomes of other treatment plans.

Altered fractionation diminishes importance of tumor volume in oropharyngeal cancer: Subgroup analysis of ARTSCAN-trial

BACKGROUND

A large tumor volume negatively impacts the outcome of radiation therapy (RT). Altered fractionation (AF) can improve local control (LC) compared with conventional fractionation (CF). The aim of the present study was to investigate if response to AF differs with tumor volume in oropharyngeal cancer.

METHODS

Three hundred and twenty four patients with oropharyngeal cancer treated in a randomized, phase III trial comparing CF (2 Gy/d, 5 d/wk, 7 weeks, total dose 68 Gy) to AF (1.1 Gy + 2 Gy/d, 5 d/wk, 4.5 weeks, total dose 68 Gy) were analyzed.

RESULTS

Tumor volume had less impact on LC for patients treated with AF. There was an interaction between tumor volume and fractionation schedule (P = .039). This differential response was in favor of CF for small tumors and of AF for large tumors.

CONCLUSION

AF diminishes the importance of tumor volume for local tumor control in oropharyngeal cancer.

A minimal modeling framework of radiation and immune system synergy to assist radiotherapy planning

Recent evidence indicates the ability of radiotherapy to induce local and systemic tumor-specific immune responses as a result of immunogenic cell death. However, fractionation regimes routinely used in clinical practice typically ignore the synergy between radiation and the immune system, and instead attempt to completely eradicate tumors by the direct lethal effect of radiation on cancer cells. This paradigm is expected to change in the near future due to the potential benefits of considering radiation-induced antitumor immunity during treatment planning. Towards this goal, we propose a minimal modeling framework based on key aspects of the tumor-immune system interplay to simulate the effects of radiation on tumors and the immunological consequences of radiotherapy. The impacts of tumor-associated vasculature and intratumoral oxygen-mediated heterogeneity on treatment outcomes are ininvestigated. The model provides estimates of the minimum radiation doses required for tumor eradication given a certain number of treatment fractions. Moreover, estimates of treatment duration for disease control given predetermined fractional radiation doses can be also obtained. Although theoretical in nature, this study motivates the development and establishment of immune-based decision-support tools in radiotherapy planning.

Generalized Multi-Hit Model of Radiation-Induced Cell Survival with a Closed-Form Solution: An Alternative Method for Determining Isoeffect Doses in Practical Radiotherapy

The standard linear-quadratic (LQ) model is currently the preferred model for describing the ionizing radiation-induced cell survival curves and tissue responses. And the LQ model is also widely used to calculate isoeffect doses for comparing different fractionated schemes in clinical radiotherapy. Despite its ubiquity, because the actual dose-response curve may appear linear at high doses in the semilogarithmic plot, the application of the LQ model is greatly challenged in the high-dose region, while the dose employed in stereotactic body radiotherapy (SBRT) is often in this area. Alternatively, the biophysical models of radiation-induced effects with a linear-quadratic-linear (LQL) characteristic can well fit the dose-survival curve of cells in vitro. However, most of these LQL models are phenomenological and have not fully considered the biophysical mechanism of radiation-induced damage and repair, and the fitting quality decreases in some high-dose ranges. In this work, to provide an alternative model to describe the cell survival curves in high-dose ranges and predict the biologically effective dose (BED) for SBRT, we propose a novel generalized multi-hit model with a closed-form solution by considering an upper bound on the number of lethal damages induced by radiation that can be repaired in a cell. This model has a clear biophysical basis and a simple expression, and also has the LQL characteristic under low- and high-dose approximate conditions. The experimental data fitting indicated that compared to the standard LQ model and our previously generalized target model, the current model can better fit the radiation-induced cell survival curves in the high-dose ranges (P < 0.05). The current model parameters and parameter ratios were determined from the fits in different kinds of cell lines irradiated with various dose rates and linear energy transfer (LET), which indicates that the model parameters significantly depend on the dose rate and LET. Based on the current model, we derived two equivalence formulae for the BED calculations in the low- and high-dose ranges, and then calculated the BED for the clinical data of SBRT from 17 selected studies. The correlation analysis showed that there were significant linear correlations between the BED at isocenter and planning target volume (PTV) edge calculated by this model and the LQ model (R > 0.86, P < 0.001). In conclusion, the generalized multi-hit model proposed in this work can be used as an alternative tool to handle in vitro radiation-induced cell survival curves in high-dose ranges, and calculate the in vivo BED for comparing the dose fractionation schemes in clinical radiotherapy.

The FLASH effect depends on oxygen concentration

OBJECTIVE

Recent in vivo results have shown prominent tissue sparing effect of radiotherapy with ultra-high dose rates (FLASH) compared to conventional dose rates (CONV). Oxygen depletion has been proposed as the underlying mechanism, but in vitro data to support this have been lacking. The aim of the current study was to compare FLASH to CONV irradiation under different oxygen concentrations in vitro.

METHODS

Prostate cancer cells were irradiated at different oxygen concentrations (relative partial pressure ranging between 1.6 and 20%) with a 10 MeV electron beam at a dose rate of either 600 Gy/s (FLASH) or 14 Gy/min (CONV), using a modified clinical linear accelerator. We evaluated the surviving fraction of cells using clonogenic assays after irradiation with doses ranging from 0 to 25 Gy.

RESULTS

Under normoxic conditions, no differences between FLASH and CONV irradiation were found. For hypoxic cells (1.6%), the radiation response was similar up to a dose of about 5-10 Gy, above which increased survival was shown for FLASH compared to CONV irradiation. The increased survival was shown to be significant at 18 Gy, and the effect was shown to depend on oxygen concentration.

CONCLUSION

The in vitro FLASH effect depends on oxygen concentration. Further studies to characterize and optimize the use of FLASH in order to widen the therapeutic window are indicated.

ADVANCES IN KNOWLEDGE

This paper shows in vitro evidence for the role of oxygen concentration underlying the difference between FLASH and CONV irradiation.

Modelling variable proton relative biological effectiveness for treatment planning

Dose in proton radiotherapy is generally prescribed by scaling the physical proton dose by a constant value of 1.1. Relative biological effectiveness (RBE) is defined as the ratio of doses required by two radiation modalities to cause the same level of biological effect. The adoption of an RBE of 1.1. assumes that the biological efficacy of protons is similar to photons, allowing decades of clinical dose prescriptions from photon treatments and protocols to be utilized in proton therapy. There is, however, emerging experimental evidence that indicates that proton RBE varies based on technical, tissue and patient factors. The notion that a single scaling factor may be used to equate the effects of photons and protons across all biological endpoints and doses is too simplistic and raises concern for treatment planning decisions. Here, we review the models that have been developed to better predict RBE variations in tissue based on experimental data as well as using a mechanistic approach.

N-Dihydrogalactochitosan Potentiates the Radiosensitivity of Liver Metastatic Tumor Cells Originated from Murine Breast Tumors

Radiation is a widely used therapeutic method for treating breast cancer. N-dihydrogalactochitosan (GC), a biocompatible immunostimulant, is known to enhance the effects of various treatment modalities in different tumor types. However, whether GC can enhance the radiosensitivity of cancer cells remains to be explored. In this study, triple-negative murine 4T1 breast cancer cells transduced with multi-reporter genes were implanted in immunocompetent Balb/C mice to track, dissect, and identify liver-metastatic 4T1 cells. These cells expressed cancer stem cell (CSC) -related characteristics, including the ability to form spheroids, the expression of the CD44 marker, and the increase of protein stability. We then ex vivo investigated the potential effect of GC on the radiosensitivity of the liver-metastatic 4T1 breast cancer cells and compared the results to those of parental 4T1 cells subjected to the same treatment. The cells were irradiated with increased doses of X-rays with or without GC treatment. Colony formation assays were then performed to determine the survival fractions and radiosensitivity of these cells. We found that GC preferably increased the radiosensitivity of liver-metastatic 4T1 breast cancer cells rather than that of the parental cells. Additionally, the single-cell DNA electrophoresis assay (SCDEA) and γ-H2AX foci assay were performed to assess the level of double-stranded DNA breaks (DSBs). Compared to the parental cells, DNA damage was significantly increased in liver-metastatic 4T1 cells after they were treated with GC plus radiation. Further studies on apoptosis showed that this combination treatment increased the sub-G1 population of cells, but not caspase-3 cleavage, in liver-metastatic breast cancer cells. Taken together, the current data suggest that the synergistic effects of GC and irradiation might be used to enhance the efficacy of radiotherapy in treating metastatic tumors.

Toxicity Profiles of Fractionated Radiotherapy, Contemporary Stereotactic Radiosurgery, and Transsphenoidal Surgery in Nonfunctioning Pituitary Macroadenomas

Background: Here, we compared the toxicity profiles of contemporary stereotactic radiosurgery (SRS), modern fractionated radiotherapy (FRT), and transsphenoidal surgery used to treat nonfunctioning pituitary macroadenomas. Methods: We included the data of patients with nonfunctioning pituitary macroadenomas. To compare treatment outcomes, the patients were categorized groups 1 (those receiving modern FRT), 2 (those receiving contemporary SRS), and 3 (those receiving transsphenoidal surgery). The multivariable Cox proportional hazards regression analysis was performed to yielded adjusted hazard ratios (aHRs) and their 95% CIs for local recurrence in groups 2 and 3 compared with group 1. Results: We included the data of 248 patients with nonfunctioning pituitary macroadenomas. The analytical results revealed no significant differences in second primary brain or head and neck cancer, hypopituitarism, or optic nerve injury between the three cohorts. The multivariable Cox proportional hazards regression analysis revealed that compared with group 1, the aHRs (95% CIs) for stroke risk in groups 2 and 3 were 0.37 (0.14–0.99) and 0.51 (0.31–0.84), respectively. Conclusion: Contemporary SRS and transsphenoidal surgery for nonfunctioning pituitary macroadenoma treatment have equivalent toxicity profiles. However, modern FRT for nonfunctioning pituitary macroadenoma treatment might considerably increase stroke risk.

Ultra-hypofractionated versus conventionally fractionated radiotherapy for prostate cancer: 5-year outcomes of the HYPO-RT-PC randomised, non-inferiority, phase 3 trial

BACKGROUND

Hypofractionated radiotherapy for prostate cancer has gained increased attention due to its proposed high radiation-fraction sensitivity. Recent reports from studies comparing moderately hypofractionated and conventionally fractionated radiotherapy support the clinical use of moderate hypofractionation. To date, there are no published randomised studies on ultra-hypofractionated radiotherapy. Here, we report the outcomes of the Scandinavian HYPO-RT-PC phase 3 trial with the aim to show non-inferiority of ultra-hypofractionation compared with conventional fractionation.

METHODS

In this open-label, randomised, phase 3 non-inferiority trial done in 12 centres in Sweden and Denmark, we recruited men up to 75 years of age with intermediate-to-high-risk prostate cancer and a WHO performance status between 0 and 2. Patients were randomly assigned to ultra-hypofractionation (42·7 Gy in seven fractions, 3 days per week for 2·5 weeks) or conventional fractionated radiotherapy (78·0 Gy in 39 fractions, 5 days per week for 8 weeks). No androgen deprivation therapy was allowed. The primary endpoint was time to biochemical or clinical failure, analysed in the per-protocol population. The prespecified non-inferiority margin was 4% at 5 years, corresponding to a critical hazard ratio (HR) limit of 1·338. Physician-recorded toxicity was measured according to the Radiation Therapy Oncology Group (RTOG) morbidity scale and patient-reported outcome measurements with the Prostate Cancer Symptom Scale (PCSS) questionnaire. This trial is registered with the ISRCTN registry, number ISRCTN45905321.

FINDINGS

Between July 1, 2005, and Nov 4, 2015, 1200 patients were randomly assigned to conventional fractionation (n=602) or ultra-hypofractionation (n=598), of whom 1180 (591 conventional fractionation and 589 ultra-hypofractionation) constituted the per-protocol population. 1054 (89%) participants were intermediate risk and 126 (11%) were high risk. Median follow-up time was 5·0 years (IQR 3·1-7·0). The estimated failure-free survival at 5 years was 84% (95% CI 80-87) in both treatment groups, with an adjusted HR of 1·002 (95% CI 0·758-1·325; log-rank p=0·99). There was weak evidence of an increased frequency of acute physician-reported RTOG grade 2 or worse urinary toxicity in the ultra-hypofractionation group at end of radiotherapy (158 [28%] of 569 patients vs 132 [23%] of 578 patients; p=0·057). There were no significant differences in grade 2 or worse urinary or bowel late toxicity between the two treatment groups at any point after radiotherapy, except for an increase in urinary toxicity in the ultra-hypofractionation group compared to the conventional fractionation group at 1-year follow-up (32 [6%] of 528 patients vs 13 [2%] of 529 patients; (p=0·0037). We observed no differences between groups in frequencies at 5 years of RTOG grade 2 or worse urinary toxicity (11 [5%] of 243 patients for the ultra-hypofractionation group vs 12 [5%] of 249 for the conventional fractionation group; p=1·00) and bowel toxicity (three [1%] of 244 patients vs nine [4%] of 249 patients; p=0·14). Patient-reported outcomes revealed significantly higher levels of acute urinary and bowel symptoms in the ultra-hypofractionation group compared with the conventional fractionation group but no significant increases in late symptoms were found, except for increased urinary symptoms at 1-year follow-up, consistent with the physician-evaluated toxicity.

INTERPRETATION

Ultra-hypofractionated radiotherapy is non-inferior to conventionally fractionated radiotherapy for intermediate-to-high risk prostate cancer regarding failure-free survival. Early side-effects are more pronounced with ultra-hypofractionation compared with conventional fractionation whereas late toxicity is similar in both treatment groups. The results support the use of ultra-hypofractionation for radiotherapy of prostate cancer.

FUNDING

The Nordic Cancer Union, the Swedish Cancer Society, and the Swedish Research Council.

Intensity Modulated Radiation Fields Induce Protective Effects and Reduce Importance of Dose-Rate Effects

In advanced radiotherapy, intensity modulated radiation fields and complex dose-delivery are utilized to prescribe higher doses to tumours. Here, we investigated the impact of modulated radiation fields on radio-sensitivity and cell recovery during dose delivery. We generated experimental survival data after single-dose, split-dose and fractionated irradiation in normal human skin fibroblast cells (AGO1522) and human prostate cancer cells (DU145). The dose was delivered to either 50% of the area of a T25 flask containing the cells (half-field) or 100% of the flask (uniform-field). We also modelled the impact of dose-rate effects and intercellular signalling on cell-killing. Applying the model to the survival data, it is found that (i) in-field cell survival under half-field exposure is higher than uniform-field exposure for the same delivered dose; (ii) the importance of sub-lethal damage repair (SLDR) in AGO1522 cells is reduced under half-field exposure; (iii) the yield of initial DNA lesions measured with half-field exposure is smaller than that with uniform-field exposure. These results suggest that increased cell survival under half-field exposure is predominantly attributed not to rescue effects (increased SLDR) but protective effects (reduced induction of initial DNA lesions). In support of these protective effects, the reduced DNA damage leads to modulation of cell-cycle dynamics, i.e., less G₁ arrest 6 h after irradiation. These findings provide a new understanding of the impact of dose-rate effects and protective effects measured after modulated field irradiation.

Novel treatment planning approaches to enhance the therapeutic ratio: targeting the molecular mechanisms of radiation therapy

Radiation acts not only through cell death but has also angiogenic, immunomodulatory and bystander effects. The realization of its systemic implications has led to extensive research on the combination of radiotherapy with systemic treatments, including immunotherapy and antiangiogenic agents. Parameters such as dose, fractionation and sequencing of treatments are key determinants of the outcome. However, recent high-quality research indicates that these are not the only radiation therapy parameters that influence its systemic effect. To effectively integrate systemic agents with radiation therapy, these new aspects of radiation therapy planning will have to be taken into consideration in future clinical trials. Our aim is to review these new treatment planning parameters that can influence the balance between contradicting effects of radiation therapy so as to enhance the therapeutic ratio.

The Special Medical Physics Consult Process for Reirradiation Patients

Purpose

To present a systematic approach to the reirradiation special medical physics consult (ReRT-SMPC) process.

Materials and Methods

An in-house reirradiation committee of physicians and physicists was formed to develop a streamlined and well-documented approach to ReRT-SMPCs. Dosimetric goals and considerations for tissue repair were generated by the committee with input from the literature, clinical trial guidelines, and physician experience. Procedural workflow was also defined.

Results

The total number of ReRT-SMPCs performed in our department in 2018 was 401, corresponding to 369 unique patients and 16% of the total number of patients receiving external beam radiation in our department that year. This constituted a large increase over the 183 ReRT-SMPCs performed in 2017. We have found that a standardized ReRT-SMPC workflow helps to safeguard patients, documents the clinical decision-making process for medical and legal purposes, and facilitates the peer-review process. The data being collected from each consult along with toxicity and outcomes data can be used to help inform future re-treatment guidelines.

Conclusions

As the number of patients returning for additional courses of radiation continues to increase, a uniform method for the ReRT-SMPC workflow and analysis is a powerful tool for ensuring patient safety, understanding and predicting treatment toxicity, and refining reirradiation dosimetric limits.

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.

Pre-Operative Versus Post-Operative Radiosurgery of Brain Metastases-Volumetric and Dosimetric Impact of Treatment Sequence and Margin Concept

BACKGROUND

Pre-operative radiosurgery (SRS) preceding the resection of brain metastases promises to circumvent limitations of post-operative cavity SRS. It minimizes uncertainties regarding delineation and safety margins and could reduce dose exposure of the healthy brain (HB).

METHODS

We performed a systematic treatment plan comparison on 24 patients who received post-operative radiosurgery of the resection cavity at our institution. Comparative treatment plans were calculated for hypofractionated stereotactic radiotherapy (7 × 5 Gray (Gy)) in a hypothetical pre-operative (pre-op) and two post-operative scenarios, either with (extended field, post-op-E) or without the surgical tract (involved field, post-op-I). Detailed volumetric comparison of the resulting target volumes was performed, as well as dosimetric comparison focusing on targets and the HB.

RESULTS

The resection cavity was significantly smaller and different in morphology from the pre-operative lesion, yielding a low Dice Similarity Coefficient (DSC) of 53% (p = 0.019). Post-op-I and post-op-E targets showed high similarity (DSC = 93%), and including the surgical tract moderately enlarged resulting median target size (18.58 ccm vs. 22.89 ccm, p < 0.001). Dosimetric analysis favored the pre-operative treatment setting since it significantly decreased relevant dose exposure of the HB (Median volume receiving 28 Gy: 6.79 vs. 10.79 for pre-op vs. post-op-E, p < 0.001). Dosimetrically, pre-operative SRS is a promising alternative to post-operative cavity irradiation that could furthermore offer practical benefits regarding delineation and treatment planning. Comparative trials are required to evaluate potential clinical advantages of this approach.