Stochastic multicellular modeling of x-ray irradiation, DNA damage induction, DNA free-end misrejoining and cell death.

The repair or misrepair of DNA double-strand breaks (DSBs) largely determines whether a cell will survive radiation insult or die. A new computational model of multicellular, track structure-based and pO2-dependent radiation-induced cell death was developed and used to investigate the contribution to cell killing by the mechanism of DNA free-end misrejoining for low-LET radiation. A simulated tumor of 1224 squamous cells was irradiated with 6 MV x-rays using the Monte Carlo toolkit Geant4 with low-energy Geant4-DNA physics and chemistry modules up to a uniform dose of 1 Gy. DNA damage including DSBs were simulated from ionizations, excitations and hydroxyl radical interactions along track segments through cell nuclei, with a higher cellular pO2 enhancing the conversion of DNA radicals to strand breaks. DNA free-ends produced by complex DSBs (cDSBs) were able to misrejoin and produce exchange-type chromosome aberrations, some of which were asymmetric and lethal. A sensitivity analysis was performed and conditions of full oxia and anoxia were simulated. The linear component of cell killing from misrejoining was consistently small compared to values in the literature for the linear component of cell killing for head and neck squamous cell carcinoma (HNSCC). This indicated that misrejoinings involving DSBs from the same x-ray (including all associated secondary electrons) were rare and that other mechanisms (e.g. unrejoined ends) may be important. Ignoring the contribution by the indirect effect toward DNA damage caused the DSB yield to drop to a third of its original value and the cDSB yield to drop to a tenth of its original value. Track structure-based cell killing was simulated in all 135306 viable cells of a 1 mm3 hypoxic HNSCC tumor for a uniform dose of 1 Gy.

Monte Carlo Simulation of the Oxygen Effect in DNA Damage Induction by Ionizing Radiation.

DNA damage induced by ionizing radiation exposure is enhanced in the presence of oxygen (the "oxygen effect"). Despite its practical importance in radiotherapy, the oxygen effect has largely been excluded from models that predict DNA damage from radiation tracks. A Monte Carlo-based algorithm was developed in MATLAB software to predict DNA damage from physical and chemical tracks through a cell nucleus simulated in Geant4-DNA, taking into account the effects of cellular oxygenation (pO2) on DNA radical chemistry processes. An initial spatial distribution of DNA base and sugar radicals was determined by spatially clustering direct events (that deposited at least 10.79 eV) and hydroxyl radical (•OH) interactions. The oxygen effect was modeled by increasing the efficiency with which sugar radicals from direct-type effects were converted to strand breaks from 0.6 to 1, the efficiency with which sugar radicals from the indirect effect were converted to strand breaks from 0.28 to 1 and the efficiency of base-to-sugar radical transfer from •OH-mediated base radicals from 0 to 0.03 with increasing pO2 from 0 to 760 mmHg. The DNA damage induction algorithm was applied to tracks from electrons, protons and alphas with LET values from 0.2 to 150 keV/µm under different pO2 conditions. The oxygen enhancement ratio for double-strand break induction was 3.0 for low-LET radiation up to approximately 15 keV/µm, after which it gradually decreased to a value of 1.3 at 150 keV/µm. These values were consistent with a range of experimental data published in the literature. The DNA damage yields were verified using experimental data in the literature and results from other theoretical models. The spatial clustering approach developed in this work has low memory requirements and may be suitable for particle tracking simulations with a large number of cells.

Simulation of head and neck cancer oxygenation and doubling time in a 4D cellular model with angiogenesis.

Tumor oxygenation has been correlated with treatment outcome for radiotherapy. In this work, the dependence of tumor oxygenation on tumor vascularity and blood oxygenation was determined quantitatively in a 4D stochastic computational model of head and neck squamous cell carcinoma (HNSCC) tumor growth and angiogenesis. Additionally, the impacts of the tumor oxygenation and the cancer stem cell (CSC) symmetric division probability on the tumor volume doubling time and the proportion of CSCs in the tumor were also quantified. Clinically relevant vascularities and blood oxygenations for HNSCC yielded tumor oxygenations in agreement with clinical data for HNSCC. The doubling time varied by a factor of 3 from well oxygenated tumors to the most severely hypoxic tumors of HNSCC. To obtain the doubling times and CSC proportions clinically observed in HNSCC, the model predicts a CSC symmetric division probability of approximately 2% before treatment. To obtain the doubling times clinically observed during treatment when accelerated repopulation is occurring, the model predicts a CSC symmetric division probability of approximately 50%, which also results in CSC proportions of 30-35% during this time.

A review of the development of tumor vasculature and its effects on the tumor microenvironment.

BACKGROUND: The imbalance of angiogenic regulators in tumors drives tumor angiogenesis and causes the vasculature to develop much differently in tumors than in normal tissue. There are several cancer therapy techniques currently being used and developed that target the tumor vasculature for the treatment of solid tumors. This article reviews the aspects of the tumor vasculature that are relevant to most cancer therapies but particularly to vascular targeting techniques. MATERIALS AND METHODS: We conducted a review of identified experiments in which tumors were transplanted into animals to study the development of the tumor vasculature with tumor growth. Quantitative vasculature morphology data for spontaneous human head and neck cancers are reviewed. Parameters assessed include the highest microvascular density (h-MVD) and the relative vascular volume (RVV). The effects of the vasculature on the tumor microenvironment are discussed, including the distributions of hypoxia and proliferation. RESULTS: Data for the h-MVD and RVV in head and neck cancers are highly varied, partly due to methodological differences. However, it is clear that the cancers are typically more vascularized than the corresponding normal tissue. The commonly observed chronic hypoxia and acute hypoxia in these tumors are due to high intratumor heterogeneity in MVD and lower than normal blood oxygenation levels through the abnormally developed tumor vasculature. Hypoxic regions are associated with decreased cell proliferation. CONCLUSION: The morphology of the vasculature strongly influences the tumor microenvironment, with important implications for tumor response to medical intervention such as radiotherapy. Quantitative vasculature morphology data herein may be used to inform computational models that simulate the spatial tumor vasculature. Such models may play an important role in exploring and optimizing vascular targeting cancer therapies.

Development of an in silico stochastic 4D model of tumor growth with angiogenesis.

PURPOSE: A stochastic computer model of tumour growth with spatial and temporal components that includes tumour angiogenesis was developed. In the current work it was used to simulate head and neck tumour growth. The model also provides the foundation for a 4D cellular radiotherapy simulation tool. METHODS: The model, developed in Matlab, contains cell positions randomised in 3D space without overlap. Blood vessels are represented by strings of blood vessel units which branch outwards to achieve the desired tumour relative vascular volume. Hypoxic cells have an increased cell cycle time and become quiescent at oxygen tensions less than 1 mmHg. Necrotic cells are resorbed. A hierarchy of stem cells, transit cells and differentiated cells is considered along with differentiated cell loss. Model parameters include the relative vascular volume (2-10%), blood oxygenation (20-100 mmHg), distance from vessels to the onset of necrosis (80-300 µm) and probability for stem cells to undergo symmetric division (2%). Simulations were performed to observe the effects of hypoxia on tumour growth rate for head and neck cancers. Simulations were run on a supercomputer with eligible parts running in parallel on 12 cores. RESULTS: Using biologically plausible model parameters for head and neck cancers, the tumour volume doubling time varied from 45 ± 5 days (n = 3) for well oxygenated tumours to 87 ± 5 days (n = 3) for severely hypoxic tumours. CONCLUSIONS: The main achievements of the current model were randomised cell positions and the connected vasculature structure between the cells. These developments will also be beneficial when irradiating the simulated tumours using Monte Carlo track structure methods.

Stochastic Predictions of Cell Kill During Stereotactic Ablative Radiation Therapy: Do Hypoxia and Reoxygenation Really Matter?

PURPOSE: To simulate stereotactic ablative radiation therapy on hypoxic and well-oxygenated in silico tumors, incorporating probabilistic parameter distributions and linear-quadratic versus linear-quadratic-cubic methodology and the evaluation of optimal fractionation schemes using biological effective dose (BEDα/ß=10 or 3) comparisons. METHODS AND MATERIALS: A temporal tumor growth and radiation therapy algorithm simulated high-dose external beam radiation therapy using stochastic methods. Realistic biological proliferative cellular hierarchy and pO2 histograms were incorporated into the 10(8)-cell tumor model, with randomized radiation therapy applied during continual cell proliferation and volume-based gradual tumor reoxygenation. Dose fractions ranged from 6-35 Gy, with predictive outcomes presented in terms of the total doses (converted to BED) required to eliminate all cells that could potentially regenerate the tumor. RESULTS: Well-oxygenated tumor control BED10 outcomes were not significantly different for high-dose versus conventional radiation therapy (BED10: 79-84 Gy; Equivalent Dose in 2 Gy fractions with α/ß of 10: 66-70 Gy); however, total treatment times decreased from 7 down to 1-3 weeks. For hypoxic tumors, an additional 28 Gy (51 Gy BED10) was required, with BED10 increasing with dose per fraction due to wasted dose in the final fraction. Fractions of 9 Gy compromised well for total treatment time and BED, with BED10:BED3 of 84:176 Gy for oxic and 132:278 Gy for non-reoxygenating hypoxic tumors. Initial doses of 12 Gy followed by 6 Gy further increased the therapeutic ratio. When delivering ≥9 Gy per fraction, applying reoxygenation and/or linear-quadratic-cubic cell survival both affected tumor control doses by a significant 1-2 fractions. CONCLUSIONS: The complex temporal dynamics of tumor oxygenation combined with probabilistic cell kinetics in the modeling of radiation therapy requires sophisticated stochastic modeling to predict tumor cell kill. For stereotactic ablative radiation therapy, high doses in the first week followed by doses that are more moderate may be beneficial because a high percentage of hypoxic cells could be eradicated early while keeping the required BED10 relatively low and BED3 toxicity to tolerable levels.

Hypoxia in head and neck cancer in theory and practice: a PET-based imaging approach.

Hypoxia plays an important role in tumour recurrence among head and neck cancer patients. The identification and quantification of hypoxic regions are therefore an essential aspect of disease management. Several predictive assays for tumour oxygenation status have been developed in the past with varying degrees of success. To date, functional imaging techniques employing positron emission tomography (PET) have been shown to be an important tool for both pretreatment assessment and tumour response evaluation during therapy. Hypoxia-specific PET markers have been implemented in several clinics to quantify hypoxic tumour subvolumes for dose painting and personalized treatment planning and delivery. Several new radiotracers are under investigation. PET-derived functional parameters and tracer pharmacokinetics serve as valuable input data for computational models aiming at simulating or interpreting PET acquired data, for the purposes of input into treatment planning or radio/chemotherapy response prediction programs. The present paper aims to cover the current status of hypoxia imaging in head and neck cancer together with the justification for the need and the role of computer models based on PET parameters in understanding patient-specific tumour behaviour.

In silico modelling of treatment-induced tumour cell kill: developments and advances.

Mathematical and stochastic computer (in silico) models of tumour growth and treatment response of the past and current eras are presented, outlining the aims of the models, model methodology, the key parameters used to describe the tumour system, and treatment modality applied, as well as reported outcomes from simulations. Fractionated radiotherapy, chemotherapy, and combined therapies are reviewed, providing a comprehensive overview of the modelling literature for current modellers and radiobiologists to ignite the interest of other computational scientists and health professionals of the ever evolving and clinically relevant field of tumour modelling.