A model for relative biological effectiveness of therapeutic proton beams based on a global fit of cell survival data

LET-based approximation of the microdosimetric kinetic model for proton radiotherapy

BACKGROUND

Phenomenological relative biological effectiveness (RBE) models for proton therapy, based on the dose-averaged linear energy transfer (LET), have been developed to address the apparent RBE increase towards the end of the proton range. The results of these phenomenological models substantially differ due to varying empirical assumptions and fitting functions. In contrast, more theory-based approaches are used in carbon ion radiotherapy, such as the microdosimetric kinetic model (MKM). However, implementing microdosimetry-based models in LET-based proton therapy treatment planning systems poses challenges.

PURPOSE

This work presents a LET-based version of the MKM that is practical for clinical use in proton radiotherapy.

METHODS

At first, we derived an approximation of the Mayo Clinic Florida (MCF) MKM for relatively-sparsely ionizing radiation such as protons. The mathematical formalism of the proposed model is equivalent to the original MKM, but it maintains some key features of the MCF MKM, such as the determination of model parameters from measurable cell characteristics. Subsequently, we carried out Monte Carlo calculations with PHITS in different simulated scenarios to establish a heuristic correlation between microdosimetric quantities and the dose averaged LET of protons.

RESULTS

A simple allometric function was found able to describe the relationship between the dose-averaged LET of protons and the dose-mean lineal energy, which includes the contributions of secondary particles. The LET-based MKM was used to model the in vitro clonogenic survival RBE of five human and rodent cell lines (A549, AG01522, CHO, T98G, and U87) exposed to pristine and spread-out Bragg peak (SOBP) proton beams. The results of the LET-based MKM agree well with the biological data in a comparable or better way with respect to the other models included in the study. A sensitivity analysis on the model results was also performed.

CONCLUSIONS

The LET-based MKM integrates the predictive theoretical framework of the MCF MKM with a straightforward mathematical description of the RBE based on the dose-averaged LET, a physical quantity readily available in modern treatment planning systems for proton therapy.

Novel radiation quality metrics accounting for proton energy spectra for RBE proton models

BACKGROUND

For proton therapy, a relative biological effectiveness (RBE) of 1.1 is widely applied clinically. However, due to abundant evidence of variable RBE in vitro, and as suggested in studies of patient outcomes, RBE might increase by the end of the proton tracks, as described by several proposed variable RBE models. Typically, the dose averaged linear energy transfer (LET d $\text{LET}_d$ ) has been used as a radiation quality metric (RQM) for these models. However, the optimal choice of RQM has not been fully explored.

PURPOSE

This study aims to propose novel RQMs that effectively weight protons of different energies, and assess their predictive power for variable RBE in proton therapy. The overall objective is to identify an RQM that better describes the contribution of individual particles to the RBE of proton beams.

METHODS

High-throughput experimental set-ups of in vitro cell survival studies for proton RBE determination are simulated utilizing the SHIELD-HIT12A Monte Carlo particle transport code. For every data point, the proton energy spectra are simulated, allowing the calculation of novel RQMs by applying different power levels to the spectra of LET or effective Q $Q$ (Q eff $Q_\mathrm{eff}$ ) values. A phenomenological linear-quadratic-based RBE model is then applied to the in vitro data, using various RQMs as input variables, and the model performance is evaluated by root-mean-square-error (RMSE) for the logarithm of cell surviving fractions of each data point.

RESULTS

Increasing the power level, that is, putting an even higher weight on higher LET particles when constructing the RQM is generally associated with an increased model performance, with dose averagedLET 3 $\text{LET}^3$ (i.e., dose averaged cubed LET,cLET d $\mathrm{cLET}_d$ ) resulting in a RMSE value 0.31, compared to 0.45 for a model based on (linearly weighted)LET d $\text{LET}_d$ , with similar trends also observed for track averaged andQ eff $Q_\mathrm{eff}$ -based RQMs.

CONCLUSIONS

The results indicate that improved proton variable RBE models can be constructed assuming a non-linear RBE(LET) relationship for individual protons. If similar trends hold also for an in vitro-environment, variable RBE effects are likely better described bycLET d $\mathrm{cLET}_d$ or tracked averaged cubed LET (cLET t $\mathrm{cLET}_t$ ), or correspondingQ eff $Q_\mathrm{eff}$ -based RQM, rather than linearly weightedLET d $\text{LET}_d$ orLET t $\text{LET}_t$ which is conventionally applied today.

Risk of Cerebrovascular Events Among Childhood and Adolescent Patients Receiving Cranial Radiation Therapy: A PENTEC Normal Tissue Outcomes Comprehensive Review

PURPOSE

Radiation-induced cerebrovascular toxicity is a well-documented sequelae that can be both life-altering and potentially fatal. We performed a meta-analysis of the relevant literature to create practical models for predicting the risk of cerebral vasculopathy after cranial irradiation.

METHODS AND MATERIALS

A literature search was performed for studies reporting pediatric radiation therapy (RT) associated cerebral vasculopathy. When available, we used individual patient RT doses delivered to the Circle of Willis (CW) or optic chiasm (as a surrogate), as reported or digitized from original publications, to formulate a dose-response. A logistic fit and a Normal Tissue Complication Probability (NTCP) model was developed to predict future risk of cerebrovascular toxicity and stroke, respectively. This NTCP risk was assessed as a function of prescribed dose.

RESULTS

The search identified 766 abstracts, 5 of which were used for modeling. We identified 101 of 3989 pediatric patients who experienced at least one cerebrovascular toxicity: transient ischemic attack, stroke, moyamoya, or arteriopathy. For a range of shorter follow-ups, as specified in the original publications (approximate attained ages of 17 years), our logistic fit model predicted the incidence of any cerebrovascular toxicity as a function of dose to the CW, or surrogate structure: 0.2% at 30 Gy, 1.3% at 45 Gy, and 4.4% at 54 Gy. At an attained age of 35 years, our NTCP model predicted a stroke incidence of 0.9% to 1.3%, 1.8% to 2.7%, and 2.8% to 4.1%, respectively at prescribed doses of 30 Gy, 45 Gy, and 54 Gy (compared with a baseline risk of 0.2%-0.3%). At an attained age of 45 years, the predicted incidence of stroke was 2.1% to 4.2%, 4.5% to 8.6%, and 6.7% to 13.0%, respectively at prescribed doses of 30 Gy, 45 Gy, and 54 Gy (compared with a baseline risk of 0.5%-1.0%).

CONCLUSIONS

Risk of cerebrovascular toxicity continues to increase with longer follow-up. NTCP stroke predictions are very sensitive to model variables (baseline stroke risk and proportional stroke hazard), both of which found in the literature may be systematically erring on minimization of true risk. We hope this information will assist practitioners in counseling, screening, surveilling, and facilitating risk reduction of RT-related cerebrovascular late effects in this highly sensitive population.

Report on G4-Med, a Geant4 benchmarking system for medical physics applications developed by the Geant4 Medical Simulation Benchmarking Group

BACKGROUND

Geant4 is a Monte Carlo code extensively used in medical physics for a wide range of applications, such as dosimetry, micro- and nanodosimetry, imaging, radiation protection, and nuclear medicine. Geant4 is continuously evolving, so it is crucial to have a system that benchmarks this Monte Carlo code for medical physics against reference data and to perform regression testing.

AIMS

To respond to these needs, we developed G4-Med, a benchmarking and regression testing system of Geant4 for medical physics.

MATERIALS AND METHODS

G4-Med currently includes 18 tests. They range from the benchmarking of fundamental physics quantities to the testing of Monte Carlo simulation setups typical of medical physics applications. Both electromagnetic and hadronic physics processes and models within the prebuilt Geant4 physics lists are tested. The tests included in G4-Med are executed on the CERN computing infrastructure via the use of the geant-val web application, developed at CERN for Geant4 testing. The physical observables can be compared to reference data for benchmarking and to results of previous Geant4 versions for regression testing purposes.

RESULTS

This paper describes the tests included in G4-Med and shows the results derived from the benchmarking of Geant4 10.5 against reference data.

DISCUSSION

Our results indicate that the Geant4 electromagnetic physics constructor G4EmStandardPhysics_option4 gives a good agreement with the reference data for all the tests. The QGSP_BIC_HP physics list provided an overall adequate description of the physics involved in hadron therapy, including proton and carbon ion therapy. New tests should be included in the next stage of the project to extend the benchmarking to other physical quantities and application scenarios of interest for medical physics.

CONCLUSION

The results presented and discussed in this paper will aid users in tailoring physics lists to their particular application.

Exosomes and exosomal microRNA in non-targeted radiation bystander and abscopal effects in the central nervous system

Localized cranial radiotherapy is a dominant treatment for brain cancers. After being subjected to radiation, the central nervous system (CNS) exhibits targeted effects as well as non-targeted radiation bystander effects (RIBE) and abscopal effects (RIAE). Radiation-induced targeted effects in the CNS include autophagy and various changes in tumor cells due to radiation sensitivity, which can be regulated by microRNAs. Non-targeted radiation effects are mainly induced by gap junctional communication between cells, exosomes containing microRNAs can be transduced by intracellular endocytosis to regulate RIBE and RIAE. In this review, we discuss the involvement of microRNAs in radiation-induced targeted effects, as well as exosomes and/or exosomal microRNAs in non-targeted radiation effects in the CNS. As a target pathway, we also discuss the Akt pathway which is regulated by microRNAs, exosomes, and/or exosomal microRNAs in radiation-induced targeted effects and RIBE in CNS tumor cells. As the CNS-derived exosomes can cross the blood-brain-barrier (BBB) into the bloodstream and be isolated from peripheral blood, exosomes and exosomal microRNAs can emerge as promising minimally invasive biomarkers and therapeutic targets for radiation-induced targeted and non-targeted effects in the CNS.

A new approach to modeling the microdosimetry of proton therapy beams

INTRODUCTION

To revisit the formulation of the mean chord length in microdosimetry and replace it by the particle mean free path appropriate for modelings in radiobiology.

METHODS

We perform a collision-by-collision followed by event-by-event Geant4 Monte Carlo simulation and calculate double-averaged stepping length, 〈〈l〉〉, for a range of target sizes from mm down to μm and depth in water. We consider 〈〈l〉〉 to represent the particle mean free path.

RESULTS

We show that 〈〈l〉〉 continuously drops as a function of depth and asymptotically saturates to a minimum value in low energies, where it exhibits a universal scaling behavior, independent of particle nominal beam energy. We correlate 〈〈l〉〉 to linear density of DNA damage, complexities of initial lethal lesions and illustrate a relative difference between predictive RBEs in model calculations using mean chord length vs the proposed mean free path. We demonstrate consistency between rapid increase in RBE within and beyond the Bragg peak and 〈〈l〉〉, a decreasing function of depth.

DISCUSSION AND CONCLUSION

An interplay between localities in imparted energy at nanometer scale and subsequent physio-chemical processes, causalities and pathways in DNA damage requires substitution of geometrical chord length of cell nuclei by mean-free path of proton and charged particles to account for a mean distance among sequential collisions in DNA materials. To this end, the event averaging over cell volume in the current microdosimetry formalism must be superseded by the collision averaging scored within the volume. The former, is fundamentally a global attribute of the cell nuclei surfaces and boundaries and is characterized by their membrane diameters, hence such global indices are not appropriate to quantitatively represent the radiobiological strength of the particles and their RBE variabilities that is associated with the sensitivities to local structure of the collisions and their spatio-temporal collective patterns in DNA materials.

A DNA damage multiscale model for NTCP in proton and hadron therapy

PURPOSE

To develop a first principle and multiscale model for normal tissue complication probability (NTCP) as a function of dose and LET for proton and in general for particle therapy with a goal of incorporating nanoscale radio-chemical to macroscale cell biological pathways, spanning from initial DNA damage to tissue late effects.

METHODS

The method is a combination of analytical and multiscale computational steps including (a) derivation of functional dependencies of NTCP on DNA-driven cell lethality in nanometer and mapping to dose and LET in millimeter, and (b) three-dimensional-surface fitting to Monte Carlo data set generated based on postradiation image change and gathered for a cohort of 14 pediatric patients treated by scanning beam of protons for ependymoma. We categorize voxel-based dose and LET associated with development of necrosis in NTCP.

RESULT

Our model fits well the clinical data, generated for postradiation tissue toxicity and necrosis. The fitting procedure results in extraction of in vivo radio-biological α-β indices and their numerical values.

DISCUSSION AND CONCLUSION

The NTCP model, explored in this work, allows to correlate the tissue toxicities to DNA initial damage, cell lethality and the properties and qualities of radiation, dose, and LET.

Using the Proton Energy Spectrum and Microdosimetry to Model Proton Relative Biological Effectiveness

PURPOSE

We introduce a methodology to calculate the microdosimetric quantity dose-mean lineal energy for input into the microdosimetric kinetic model (MKM) to model the relative biological effectiveness (RBE) of proton irradiation experiments.

METHODS AND MATERIALS

The data from 7 individual proton RBE experiments were included in this study. In each experiment, the RBE at several points along the Bragg curve was measured. Monte Carlo simulations to calculate the lineal energy probability density function of 172 different proton energies were carried out with use of Geant4 DNA. We calculated the fluence-weighted lineal energy probability density function (fw(y)), based on the proton energy spectra calculated through Monte Carlo at each experimental depth, calculated the dose-mean lineal energy yD¯ for input into the MKM, and then computed the RBE. The radius of the domain (rd) was varied to reach the best agreement between the MKM-predicted RBE and experimental RBE. A generic RBE model as a function of dose-averaged linear energy transfer (LETD) with 1 fitting parameter was presented and fit to the experimental RBE data as well to facilitate a comparison to the MKM.

RESULTS

Both the MKM and LETD-based models modeled the RBE from experiments well. Values for rd were similar to those of other cell lines under proton irradiation that were modeled with the MKM. Analysis of the performance of each model revealed that neither model was clearly superior to the other.

CONCLUSIONS

Our 3 key accomplishments include the following: (1) We developed a method that uses the proton energy spectra and lineal energy distributions of those protons to calculate dose-mean lineal energy. (2) We demonstrated that our application of the MKM provides theoretical validation of proton irradiation experiments that show that RBE is significantly greater than 1.1. (3) We showed that there is no clear evidence that the MKM is better than LETD-based RBE models.

Increased risk of pseudoprogression among pediatric low-grade glioma patients treated with proton versus photon radiotherapy

BACKGROUND

Pseudoprogression (PsP) is a recognized phenomenon after radiotherapy (RT) for high-grade glioma but is poorly characterized for low-grade glioma (LGG). We sought to characterize PsP for pediatric LGG patients treated with RT, with particular focus on the role of RT modality using photon-based intensity-modulated RT (IMRT) or proton beam therapy (PBT).

METHODS

Serial MRI scans from 83 pediatric LGG patients managed at 2 institutions between 1998 and 2017 were evaluated. PsP was scored when a progressive lesion subsequently decreased or stabilized for at least a year without therapy.

RESULTS

Thirty-two patients (39%) were treated with IMRT, and 51 (61%) were treated with PBT. Median RT dose for the cohort was 50.4 Gy(RBE) (range, 45-59.4 Gy[RBE]). PsP was identified in 31 patients (37%), including 8/32 IMRT patients (25%) and 23/51 PBT patients (45%). PBT patients were significantly more likely to have post-RT enlargement (hazard ratio [HR] 2.15, 95% CI: 1.06-4.38, P = 0.048). RT dose >50.4 Gy(RBE) similarly predicted higher rates of PsP (HR 2.61, 95% CI: 1.20-5.68, P = 0.016). Multivariable analysis confirmed the independent effects of RT modality (P = 0.03) and RT dose (P = 0.01) on PsP incidence. Local progression occurred in 10 patients: 7 IMRT patients (22%) and 3 PBT patients (6%), with a trend toward improved local control for PBT patients (HR 0.34, 95% CI: 0.10-1.18, P = 0.099).

CONCLUSIONS

These data highlight substantial rates of PsP among pediatric LGG patients, particularly those treated with PBT. PsP should be considered when assessing response to RT in LGG patients within the first year after RT.

Renormalization of radiobiological response functions by energy loss fluctuations and complexities in chromosome aberration induction: deactivation theory for proton therapy from cells to tumor control

We employ a multi-scale mechanistic approach built upon our recent phenomenological/computational methodologies [R. Abolfath et al., Sci. Rep. 7, 8340 (2017)] to investigate radiation induced cell toxicities and deactivation mechanisms as a function of linear energy transfer in hadron therapy. Our theoretical model consists of a system of Markov chains in microscopic and macroscopic spatio-temporal landscapes, i.e., stochastic birth-death processes of cells in millimeter-scale colonies that incorporates a coarse-grained driving force to account for microscopic radiation induced damage. The coupling, hence the driving force in this process, stems from a nano-meter scale radiation induced DNA damage that incorporates the enzymatic end-joining repair and mis-repair mechanisms. We use this model for global fitting of the high-throughput and high accuracy clonogenic cell-survival data acquired under exposure of the therapeutic scanned proton beams, the experimental design that considers γ-H2AX as the biological endpoint and exhibits maximum observed achievable dose and LET, beyond which the majority of the cells undergo collective biological deactivation processes. An estimate to optimal dose and LET calculated from tumor control probability by extension to ~106 cells per mm-size voxels is presented. We attribute the increase in degree of complexity in chromosome aberration to variabilities in the observed biological responses as the beam linear energy transfer (LET) increases, and verify consistency of the predicted cell death probability with the in vitro cell survival assay of approximately 100 non-small cell lung cancer (NSCLC) cells. The present model provides an interesting interpretation to variabilities in α and β indices via perturbative expansion of the cell survival fraction (SF) in terms of specific and lineal energies, z and y, corresponding to continuous transitions in pair-wise to ternary, quaternary and more complex recombination of broken chromosomes from the entrance to the end of the range of proton beam.

Modelling of Cellular Survival Following Radiation-Induced DNA Double-Strand Breaks

A mechanistic model of cellular survival following radiation-induced DNA double-strand breaks (DSBs) was proposed in this study. DSBs were assumed as the initial lesions in the DNA of the cell nucleus induced by ionizing radiation. The non-homologous end-joining (NHEJ) pathway was considered as the domain pathway of DSB repair in mammalian cells. The model was proposed to predict the relationship between radiation-induced DSBs in nucleus and probability of cell survival, which was quantitatively described by two input parameters and six fitting parameters. One input parameter was the average number of primary particles which caused DSB, the other input parameter was the average number of DSBs yielded by each primary particle that caused DSB. The fitting parameters were used to describe the biological characteristics of the irradiated cells. By determining the fitting parameters of the model with experimental data, the model is able to estimate surviving fractions for the same type of cells exposed to particles with different physical parameters. The model further revealed the mechanism of cell death induced by the DSB effect. Relative biological effectiveness (RBE) of charged particles at different survival could be calculated with the model, which would provide reference for clinical treatment.

Proton Relative Biological Effectiveness - Uncertainties and Opportunities

Proton therapy treatments are prescribed using a biological effectiveness relative to photon therapy of 1.1, that is, proton beams are considered to be 10% more biologically effective. Debate is ongoing as to whether this practice needs to be revised. This short review summarizes current knowledge on relative biological effectiveness variations and uncertainties in vitro and in vivo. Clinical relevance is discussed and strategies toward biologically guided treatment planning are presented.