A radiobiological study of the schemes with a low number of fractions in high-dose-rate brachytherapy as monotherapy for prostate cancer

Purpose Schemes with high doses per fraction and small number of fractions are commonly used in high-dose-rate brachytherapy (HDR-BT) for prostate cancer. Our aim was to analyze the differences between published clinical results and the predictions of radiobiological models for absorbed dose required in a single fraction monotherapy HDR-BT. Material and methods Published HDR-BT clinical results for low- and intermediate-risk patients with prostate cancer were revised. For 13 clinical studies with 16 fractionation schedules between 1 and 9 fractions, a dose-response relation in terms of the biochemical control probability (BC) was established using Monte Carlo-based statistical methods. Results We obtained a value of α/β = 22.8 Gy (15.1-60.2 Gy) (95% CI) much larger than the values in the range 1.5-3.0 Gy that are usually considered to compare the results of different fractionation schemes in prostate cancer radiotherapy using doses per fraction below 6 Gy. The doses in a single fraction producing BC = 90% and 95% were 22.3 Gy (21.5-24.2 Gy) and 24.3 Gy (23.0-27.9 Gy), respectively. Conclusions The α/β obtained in our analysis of 22.8 Gy for a range of dose per fraction between 6 and 20.5 Gy was much greater than the one currently estimated for prostate cancer using low doses per fraction. This high value of α/β explains reasonably well the data available in the region of high doses per fraction considered.Spanish Ministerio de Ciencia y Competitividad FPA2015-67694-PEuropean Union (EU)Junta de Andalucía FQM038

Modelo computacional de esferoides tumorales multicelulares

Propósito: El objetivo de este trabajo es desarrollar y validar un modelo en red basado en agentes que describa el crecimiento de esferoides tumorales multicelulares utilizando herramientas Monte Carlo sencillas, que también simule la evolución de estos esferoides cuando son irradiados, y que nos permita analizar la diferencia entre distintos esquemas de fraccionamiento en radioterapia en diferentes situaciones, además de poder comparar las capacidades predictivas de diferentes modelos matemáticos de crecimiento clásicos. Métodos: El modelo computacional consta de celdas situadas en los vértices de una cuadricula cúbica. Se incluyen diferentes estados celulares (proliferativo, hipóxico y muerte celular), reglas de evolución celular gobernadas por 14 parámetros y la influencia de la distancia al medio de cultivo. Se cultivaron alrededor de 200 esferoides de la línea celular de cáncer de mama humano MCF-7; parte de ellos fueron irradiados a diferentes dosis y otros fueron usados como datos de control. Los datos experimentales se utilizaron para ajustar los parámetros en el proceso de sintonización del modelo y para su validación. Como aplicación, hemos reproducido micro metástasis de cáncer de mama a partir de una imagen de microscopio, y las simulaciones de su evolución nos han permitido comparar su crecimiento con el de agregados tumoral del mismo número de células iniciales. Estas metástasis y agregados han sido sometidos a diferentes esquemas de fraccionamiento. Además, hemos usado los esferoides simulados como pseudo-datos para estudiar tanto la capacidad predictiva como retrospectiva (ajustando a la totalidad de las curvas de crecimiento y también a parte de ellas) de los modelos clásicos de crecimiento exponencial, Gompertz, logístico, potencial y Bertalanffy. Resultados: Los esferoides simulados mostraron características de crecimiento y estructurales, como el tamaño de las diferentes regiones en las que se dividen (proliferativa, hipóxica y núcleo necrótico), que se corresponden con los esferoides experimentales. Además, la relación entre el radio del núcleo necrótico y el radio total del esferoide, así como el número de células, proliferativas e hipóxicas, en función del volumen, coinciden para los esferoides experimentales y simulados. La variabilidad estadística del modelo Monte Carlo no describió todo el rango de volúmenes observados para los esferoides experimentales. Suponiendo que los parámetros del modelo varían dentro de distribuciones gaussianas, se obtuvo una muestra de esferoides que sí reproducía los hallazgos experimentales. Los esferoides irradiados simulados también mostraron un crecimiento adecuado desde el día de la irradiación, imitando razonablemente el crecimiento de los esferoides experimentales. La fracción de supervivencia calculada de los esferoides simulados muestra muy buena concordancia con los datos experimentales. En las simulaciones de patrones reales de micrometástasis, hemos observado diferencias en su evolución tras someterse a diferentes esquemas de fraccionamiento, respecto a agregados únicos de igual número de células. En cuanto a los modelos clásicos, el modelo de Gompertz proporcionó los mejores ajustes para todas las curvas de crecimiento, es decir resultó ser el que tenía las mejores capacidades para describir los datos de crecimiento simulados, arrojando un mejor valor promedio de 2 por grado de libertad, un orden de magnitud menor que los encontrados para los otros modelos. Los modelos de Gompertz y Bertalanffy dieron una capacidad de predicción retrospectiva similar. En lo que se refiere al poder de predicción prospectivo, el modelo de Gompertz mostró, con mucho, el mejor desempeño. Conclusiones: El modelo desarrollado permite describir el crecimiento de esferoides tumorales multicelulares in vitro, incluso si son sometidos a irradiación. Reproduce muy bien la variabilidad experimental y permite aumentar el periodo de seguimiento con respecto a los periodos habituales en los experimentos. La flexibilidad del modelo permite variar tanto los agentes implicados (tipos de células, características del medio, etc.) como las reglas que rigen el crecimiento del esferoide. Se pueden estudiar situaciones más generales, por ejemplo, vascularización tumoral, efectos de la radioterapia sobre tumores sólidos o la validez de los modelos matemáticos de crecimiento tumoral. De todos los modelos analizados, el modelo de Gompertz muestra el mejor poder predictivo. La flexibilidad del modelo también permite reproducir diferentes patrones de micro metástasis y tumores localizados, y someterlos a diferentes fracciones de radioterapia. Se han encontrado diferencias en el comportamiento de metástasis y agregados irradiados.Purpose: The objective of this work is to develop and validate an agent-based network model that describes the growth of multicellular tumor spheroids using simple Monte Carlo tools, that also simulates the evolution of these spheroids when they are irradiated, and that allows us to analyze the difference. between different radiotherapy fractionation schemes in different situations, in addition to being able to compare the predictive capacities of different classical mathematical growth models. Methods: The computational model consists of cells located at the vertices of a cubic grid. Different cell states (proliferative, hypoxic and cell death), cell evolution rules governed by 14 parameters and the influence of the culture medium are included. About 200 spheroids of the human breast cancer cell line MCF-7 were cultured, some of them being irradiated at different doses and others were used as control data. The experimental data were used to adjust the parameters in the model tuning process, and for its validation. As an application, we have reproduced breast cancer micro-metastases from a microscope image, and simulations of their evolution have allowed us to compare their growth with that of tumor aggregates of the same number of initial cells. These metastases and aggregates have been subjected to different fractionation schemes. In addition, we have used the simulated spheroids as pseudo-data to study both the predictive and retrospective capacity (adjusting to the totality of the growth curves and also to part of them) of the classic models of exponential growth, Gompertz, logistic, potential and Bertalanffy. Results: The simulated spheroids showed growth and structural characteristics, such as the size of the different regions in which they divide (proliferative, hypoxic and necrotic nucleus), which correspond to the experimental spheroids. Furthermore, the relationship between the radius of the necrotic nucleus and the total radius of the spheroid, as well as the number of cells, proliferative and hypoxic, as a function of volume, coincide for the experimental and simulated spheroids. The statistical variability of the Monte Carlo model did not describe the entire range of volumes observed for the experimental spheroids. Assuming that the model parameters vary within Gaussian distributions, a sample of spheroids was obtained that did reproduce the experimental findings. The simulated irradiated spheroids also showed adequate growth from the day of irradiation, reasonably mimicking the growth of the experimental spheroids. The calculated survival fraction of the simulated spheroids shows very good agreement with the experimental data. In the simulations of real micrometastasis patterns, we have observed differences in their evolution after undergoing different fractionation schemes, with respect to single aggregates of the same number of cells. Regarding the classical models, the Gompertz model provided the best fits for all growth curves, that is, it turned out to be the one with the best capabilities to describe the simulated growth data, yielding a better average value of 2 per degree of freedom, an order of magnitude less than those found for the other models. The Gompertz and Bertalanffy models gave a similar retrospective predictive ability. In terms of forward-looking predictive power, the Gompertz model showed by far the best performance. Conclusions: The developed model makes it possible to describe the growth of multicellular tumor spheroids in vitro, even if they are subjected to irradiation. It reproduces experimental variability very well and allows the follow-up period to be increased with respect to the usual periods in experiments. The flexibility of the model makes it possible to vary both the agents involved (cell types, characteristics of the environment, etc.) and the rules governing the growth of the spheroid. More general situations can be studied, for example, tumor vascularization, effects of radiotherapy on solid tumors or the validity of mathematical models of tumor growth. Of all the models analyzed, the Gompertz model shows the best predictive power. The flexibility of the model also allows different patterns of micro-metastases and localized tumors to be reproduced and subjected to different radiotherapy fractions. Differences have been found in the behavior of metastases and irradiated aggregates.Tesis Univ. Granada

Evaluation of Classical Mathematical Models of Tumor Growth Using an On-Lattice Agent-Based Monte Carlo Model

Purpose: To analyze the capabilities of different classical mathematical models to describe the growth of multicellular spheroids simulated with an on-lattice agent-based Monte Carlo model that has already been validated. Methods: The exponential, Gompertz, logistic, potential, and Bertalanffy models have been fitted in different situations to volume data generated with a Monte Carlo agent-based model that simulates the spheroid growth. Two samples of pseudo-data, obtained by assuming different variability in the simulation parameters, were considered. The mathematical models were fitted to the whole growth curves and also to parts of them, thus permitting to analyze the predictive power (both prospective and retrospective) of the models. Results: The consideration of the data obtained with a larger variability of the simulation parameters increases the width of the χ2 distributions obtained in the fits. The Gompertz model provided the best fits to the whole growth curves, yielding an average value of the χ2 per degree of freedom of 3.2, an order of magnitude smaller than those found for the other models. Gompertz and Bertalanffy models gave a similar retrospective prediction capability. In what refers to prospective prediction power, the Gompertz model showed by far the best performance. Conclusions: The classical mathematical models that have been analyzed show poor prediction capabilities to reproduce the MTS growth data not used to fit them. Within these poor results, the Gompertz model proves to be the one that better describes the growth data simulated. The simulation of the growth of tumors or multicellular spheroids permits to have follow-up periods longer than in the usual experimental studies and with a much larger number of samples: this has permitted performing the type of analysis presented here

Intraoperative Neurovascular Bundle Preservation with Hyaluronic Acid during Radical Brachytherapy for Localized Prostate Cancer: Technique and MicroMosfet In Vivo Dosimetry

Purpose: To evaluate the reduction in the absorbed dose delivered to the neurovascular bundle (NB) in patients with localized prostate cancer treated with only HDR brachytherapy and NB protection with hyaluronic acid (HA) on the side of the prostate to increase the distance from NB to the radioactive sources. Methods: This is the first published report in the medical literature that studies a new approach to decrease neurovascular bundle toxicity and improve quality of life for patients with prostate cancer treated with radical brachytherapy as monotherapy. Transperineal HA injection on the side of the prostate into the lateral aspect of the prostate fat was used to consistently displace several autonomic fibers and vessels on the lateral wall of the prostate away from radiation sources. Results: When a protection in the form of an HA layer is placed, the reduction effect at the maximum dose is between 46% and 54% (calculated values), which means that the method for protection is highly recommended. The values of the absorbed dose calculated in this project have been compared with the ones given by the treatment planning system. Conclusions: This newly created space decreases absorbed dose in the NB, calculated with the TPS and measured by microMOSFET due to the thickness of HA