Classification of tolerable/intolerable mucosal toxicity of head-and-neck radiotherapy schedules with a biomathematical model of cell dynamics

Purpose: The purpose of this study is to present a biomathematical model based on the dynamics of cell populations to predict the tolerability/intolerability of mucosal toxicity in head-and-neck radiotherapy. Methods and Materials: Our model is based on the dynamics of proliferative and functional cell populations in irradiated mucosa, and incorporates the three As: Accelerated proliferation, loss of Asymmetric proliferation, and Abortive divisions. The model consists of a set of delay differential equations, and tolerability is based on the depletion of functional cells during treatment. We calculate the sensitivity (sen) and specificity (spe) of the model in a dataset of 108 radiotherapy schedules, and compare the results with those obtained with three phenomenological classification models, two based on a biologically effective dose (BED) function describing the tolerability boundary (Fowler and Fenwick) and one based on an equivalent dose in 2 Gy fractions (EQD2) boundary (Strigari). We also perform a machine learning-like cross-validation of all the models, splitting the database in two, one for training and one for validation. Results: When fitting our model to the whole dataset, we obtain predictive values (sen + spe) up to 1.824. The predictive value of our model is very similar to that of the phenomenological models of Fowler (1.785), Fenwick (1.806), and Strigari (1.774). When performing a k = 2 cross-validation, the specificity and sensitivity in the validation dataset decrease for all models, from ˜1.82 to ˜1.55–1.63. For Fowler, the worsening is higher, down to 1.49. Conclusions: Our model has proved useful to predict the tolerability/intolerability of a dataset of 108 schedules. As the model is more mechanistic than other available models, it could prove helpful when designing unconventional dose fractionations, schedules not covered by datasets to which phenomenological models of toxicity have been fitted

Chemoradiotherapy of locally-advanced non-small cell lung cancer: Analysis of radiation dose–response, chemotherapy and survival-limiting toxicity effects indicates a low α/β ratio

Purpose: To analyse changes in 2-year overall survival (OS2yr) with radiotherapy (RT) dose, dose-per-fraction, treatment duration and chemotherapy use, in data compiled from prospective trials of RT and chemo-RT (CRT) for locally-advanced non-small cell lung cancer (LA-NSCLC). Material and methods: OS2yr data was analysed for 6957 patients treated on 68 trial arms (21 RT-only, 27 sequential CRT, 20 concurrent CRT) delivering doses-per-fraction ≤4.0 Gy. An initial model considering dose, dose-per-fraction and RT duration was fitted using maximum-likelihood techniques. Model extensions describing chemotherapy effects and survival-limiting toxicity at high doses were assessed using likelihood-ratio testing, the Akaike Information Criterion (AIC) and cross-validation. Results: A model including chemotherapy effects and survival-limiting toxicity described the data significantly better than simpler models (p < 10−14), and had better AIC and cross-validation scores. The fitted α/β ratio for LA-NSCLC was 4.0 Gy (95%CI: 2.8–6.0 Gy), repopulation negated 0.38 (95%CI: 0.31–0.47) Gy EQD2/day beyond day 12 of RT, and concurrent CRT increased the effective tumour EQD2 by 23% (95%CI: 16–31%). For schedules delivered in 2 Gy fractions over 40 days, maximum modelled OS2yr for RT was 52% and 38% for stages IIIA and IIIB NSCLC respectively, rising to 59% and 42% for CRT. These survival rates required 80 and 87 Gy (RT or sequential CRT) and 67 and 73 Gy (concurrent CRT). Modelled OS2yr rates fell at higher doses. Conclusions: Fitted dose–response curves indicate that gains of ~10% in OS2yr can be made by escalating RT and sequential CRT beyond 64 Gy, with smaller gains for concurrent CRT. Schedule acceleration achieved via hypofractionation potentially offers an additional 5–10% improvement in OS2yr. Further 10–20% OS2yr gains might be made, according to the model fit, if critical normal structures in which survival-limiting toxicities arise can be identified and selectively spared

A mathematical model of dynamics of cell populations in squamous epithelium after irradiation

Purpose: To develop multi-compartment mechanistic models of dynamics of stem and functional cell populations in epithelium after irradiation. Methods and materials: We present two models, with three (3C) and four (4C) compartments respectively. We use delay differential equations, and include accelerated proliferation, loss of division asymmetry, progressive death of abortive stem cells, and turnover of functional cells. The models are used to fit experimental data on the variations of the number of cells in mice mucosa after irradiation with 13 Gy and 20 Gy. Akaike information criteria (AIC) was used to evaluate the performance of each model. Results: Both 3C and 4C models provide good fits to experimental data for 13 Gy. Fits for 20 Gy are slightly poorer and may be affected by larger uncertainties and fluctuations of experimental data. Best fits are obtained by imposing constraints on the fitting parameters, so to have values that are within experimental ranges. There is some degeneration in the fits, as different sets of parameters provide similarly good fits. Conclusions: The models provide good fits to experimental data. Mechanistic approaches like this can facilitate the development of mucositis response models to nonstandard schedules/treatment combinations not covered by datasets to which phenomenological models have been fitted. Studying the dynamics of cell populations in multifraction treatments, and finding links with induced toxicity, is the next step of this work

4D-PET reconstruction using a spline-residue model with spatial and temporal roughness penalties

4D reconstruction of dynamic positron emission tomography (dPET) data can improve the signal-to-noise ratio in reconstructed image sequences by fitting smooth temporal functions to the voxel time-activity-curves (TACs) during the reconstruction, though the optimal choice of function remains an open question. We propose a spline-residue model, which describes TACs as weighted sums of convolutions of the arterial input function with cubic B-spline basis functions. Convolution with the input function constrains the spline-residue model at early time-points, potentially enhancing noise suppression in early time-frames, while still allowing a wide range of TAC descriptions over the entire imaged time-course, thus limiting bias. &#13; Spline-residue based 4D-reconstruction is compared to that of a conventional (non-4D) maximum a posteriori (MAP) algorithm, and to 4D-reconstructions based on adaptive-knot cubic B-splines, the spectral model and an irreversible two-tissue compartment ('2C3K') model. 4D reconstructions were carried out using a nested-MAP algorithm including spatial and temporal roughness penalties. The algorithms were tested using Monte-Carlo simulated scanner data, generated for a digital thoracic phantom with uptake kinetics based on a dynamic [18F]-Fluromisonidazole scan of a non-small cell lung cancer patient. For every algorithm, parametric maps were calculated by fitting each voxel TAC within a sub-region of the reconstructed images with the 2C3K model. &#13; Compared to conventional MAP reconstruction, spline-residue-based 4D reconstruction achieved &gt;50% improvements for 5 of the 8 combinations of the 4 kinetics parameters for which parametric maps were created with the bias and noise measures used to analyse them, and produced better results for 5/8 combinations than any of the other reconstruction algorithms studied, while spectral model-based 4D reconstruction produced the best results for 2/8. 2C3K model-based 4D reconstruction generated the most biased parametric maps. Inclusion of a temporal roughness penalty function improved the performance of 4D reconstruction based on the cubic B-spline, spectral and spline-residue models.&#13

The PTW microSilicon diode: Performance in small 6 and 15 MV photon fields and utility of density compensation

PURPOSE: We have experimentally and computationally characterized the PTW microSilicon 60023-type diode's performance in 6 and 15 MV photon fields ≥5 × 5 mm2 projected to isocenter. We tested the detector on- and off-axis at 5 and 15 cm depths in water, and investigated whether its response could be improved by including within it a thin airgap. METHODS: Experimentally, detector readings were taken in fields generated by a Varian TrueBeam linac and compared with doses-to-water measured using Gafchromic film and ionization chambers. An unmodified 60023-type diode was tested along with detectors modified to include 0.6, 0.8, and 1.0 mm thick airgaps. Computationally, doses absorbed by water and detectors’ sensitive volumes were calculated using the EGSnrc/BEAMnrc Monte Carlo radiation transport code. Detector response was characterized using K^{fdin, 4cm}_{Qclin, 4cm}, a factor that corrects for differences in the ratio of dose-to-water to detector reading between small fields and the reference condition, in this study 5 cm deep on-axis in a 4 × 4 cm2 field. RESULTS: The greatest errors in measurements of small field doses made using uncorrected readings from the unmodified 60023-type detector were over-responses of 2.6% ± 0.5% and 5.3% ± 2.0% determined computationally and experimentally, relative to the reading-per-dose in the reference field. Corresponding largest errors for the earlier 60017-type detector were 11.9% ± 0.6% and 11.7% ± 1.4% over-responses. Adding even the thinnest, 0.6 mm, airgap to the 60023-type detector over-corrected it, leading to under-responses of up to 4.8% ± 0.6% and 5.0% ± 1.8% determined computationally and experimentally. Further, Monte Carlo calculations indicate that a detector with a 0.3 mm airgap would read correctly to within 1.3% on-axis. The ratio of doses at 15 and 5 cm depths in water in a 6 MV 4 × 4 cm2 field was measured more accurately using the unmodified 60023-type detector than using the 60017-type detector, and was within 0.3% of the ratio measured using an ion chamber. The 60023-type diode's sensitivity also varied negligibly as dose-rate was reduced from 13 to 4 Gy min–1 by decreasing the linac pulse repetition frequency, whereas the sensitivity of the 60017-type detector fell by 1.5%. CONCLUSIONS: The 60023-type detector performed well in small fields across a wide range of beam energies, field sizes, depths, and off-axis positions. Its response can potentially be further improved by adding a thin, 0.3 mm, airgap

A Biomathematical Model of Tumor Response to Radioimmunotherapy with PDL1 and CTLA4

There is evidence of synergy between radiotherapy and immunotherapy. Radiotherapy can increase liberation of tumor antigens, causing activation of antitumor T-cells. This effect can be boosted with immunotherapy. Radioimmunotherapy has potential to increase tumor control rates. Biomathematical models of response to radioimmunotherapy may help on understanding of the mechanisms affecting response, and assist clinicians on the design of optimal treatment strategies. In this work we present a biomathematical model of tumor response to radioimmunotherapy. The model uses the linear-quadratic response of tumor cells to radiation (or variation of it), and builds on previous developments to include the radiation-induced immune effect. We have focused this study on the combined effect of radiotherapy and PDL1/CTLA4 therapies. The model can fit preclinical data of volume dynamics and control obtained with different dose fractionations and PDL1/CTLA4. A biomathematical study of optimal combination strategies suggests that a good understanding of the involved biological delays, the biokinetics of the immunotherapy drug, and the interplay between them, may be of paramount importance to design optimal radioimmunotherapy schedules. Biomathematical models like the one we present can help to interpret experimental data on the synergy between radiotherapy and immunotherapy, and to assist in the design of more effective treatments

Density compensated diodes for small field dosimetry: Comprehensive testing and implications for design

Purpose. In small megavoltage photon fields, the accuracies of an unmodified PTW 60017-type diode dosimeter and six diodes modified by adding airgaps of thickness 0.6-1.6 mm and diameter 3.6 mm have been comprehensively characterized experimentally and computationally. The optimally thick airgap for density compensation was determined, and detectors were micro-CT imaged to investigate differences between experimentally measured radiation responses and those predicted computationally. Methods. Detectors were tested on- and off-axis, at 5 and 15 cm depths in 6 and 15 MV fields ≥ 0.5 0.5 cm2. Computational studies were carried out using the EGSnrc/BEAMnrc Monte Carlo radiation transport code. Experimentally, radiation was delivered using a Varian TrueBeam linac and doses absorbed by water were measured using Gafchromic EBT3 film and ionization chambers, and compared with diode readings. Detector response was characterized via the formalism, choosing a 4 4 cm2 reference field. Results. For the unmodified 60017 diode, the maximum error in small field doses obtained from diode readings uncorrected by factors was determined as 11.9% computationally at +0.25 mm off-axis and 5 cm depth in a 15 MV 0.5 0.5 cm2 field, and 11.7% experimentally at -0.30 mm off-axis and 5 cm depth in the same field. A detector modified to include a 1.6 mm thick airgap performed best, with maximum computationally and experimentally determined errors of 2.2% and 4.1%. The 1.6 mm airgap deepened the modified dosimeter's effective point of measurement by 0.5 mm. For some detectors significant differences existed between responses in small fields determined computationally and experimentally, micro-CT imaging indicating that these differences were due to within-tolerance variations in the thickness of an epoxy resin layer. Conclusions. The dosimetric performance of a 60017 diode detector was comprehensively improved throughout 6 and 15 MV small photon fields via density compensation. For this approach to work well with good detector-to-detector reproducibility, tolerances on dense component dimensions should be reduced to limit associated variations of response in small fields, or these components should be modified to have more water-like densities

Cardiac-sparing radiotherapy for locally advanced non-small cell lung cancer

Background We have carried out a study to determine the scope for reducing heart doses in photon beam radiotherapy of locally advanced non-small cell lung cancer (LA-NSCLC). Materials and methods Baseline VMAT plans were created for 20 LA-NSCLC patients following the IDEAL-CRT isotoxic protocol, and were re-optimized after adding an objective limiting heart mean dose (MDHeart). Reductions in MDHeart achievable without breaching limits on target coverage or normal tissue irradiation were determined. The process was repeated for objectives limiting the heart volume receiving ≥ 50 Gy (VHeart-50-Gy) and left atrial wall volume receiving ≥ 63 Gy (VLAwall-63-Gy). Results Following re-optimization, mean MDHeart, VHeart-50-Gy and VLAwall-63-Gy values fell by 4.8 Gy and 2.2% and 2.4% absolute respectively. On the basis of associations observed between survival and cardiac irradiation in an independent dataset, the purposefully-achieved reduction in MDHeart is expected to lead to the largest improvement in overall survival. It also led to useful knock-on reductions in many measures of cardiac irradiation including VHeart-50-Gy and VLAwall-63-Gy, providing some insurance against survival being more strongly related to these measures than to MDHeart. The predicted hazard ratio (HR) for death corresponding to the purposefully-achieved mean reduction in MDHeart was 0.806, according to which a randomized trial would require 1140 patients to test improved survival with 0.05 significance and 80% power. In patients whose baseline MDHeart values exceeded the median value in a published series, the average MDHeart reduction was particularly large, 8.8 Gy. The corresponding predicted HR is potentially testable in trials recruiting 359 patients enriched for greater MDHeart values. Conclusions Cardiac irradiation in RT of LA-NSCLC can be reduced substantially. Of the measures studied, reduction of MDHeart led to the greatest predicted increase in survival, and to useful knock-on reductions in other cardiac irradiation measures reported to be associated with survival. Potential improvements in survival can be trialled more efficiently in a population enriched for patients with greater baseline MDHeart levels, for whom larger reductions in heart doses can be achieved

4D-PET reconstruction of dynamic non-small cell lung cancer [18-F]-FMISO-PET data using adaptive-knot cubic B-splines

4D-PET reconstruction has the potential to significantly increase the signal-to-noise ratio in dynamic PET by fitting smooth temporal functions during the reconstruction. However, the optimal choice of temporal function remains an open question. A 4D-PET reconstruction algorithm using adaptive-knot cubic B-splines is proposed. Using realistic Monte-Carlo simulated data from a digital patient phantom representing an [18-F]-FMISO-PET scan of a non-small cell lung cancer patient, this method was compared to a spectral model based 4D-PET reconstruction and the conventional MLEM and MAP algorithms. Within the entire patient region the proposed algorithm produced the best bias-noise trade-off, while within the tumor region the spline- and spectral model-based reconstructions gave comparable results