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

Effects of a differentiating therapy on cancer-stem-cell-driven tumors

The growth of many solid tumors has been found to be driven by chemo- and radiotherapy-resistant cancer stem cells (CSCs). A suitable therapeutic avenue in these cases may involve the use of a differentiating agent (DA) to force the differentiation of the CSCs and of conventional therapies to eliminate the remaining differentiated cancer cells (DCCs). To describe the effects of a DA that reprograms CSCs into DCCs, we adapt a differential equation model developed to investigate tumorspheres, which are assumed to consist of jointly evolving CSC and DCC populations. We analyze the mathematical properties of the model, finding the equilibria and their stability. We also present numerical solutions and phase diagrams to describe the system evolution and the therapy effects, denoting the DA strength by a parameter adif. To obtain realistic predictions, we choose the other model parameters to be those determined previously from fits to various experimental datasets. These datasets characterize the progression of the tumor under various culture conditions. Typically, for small values of adif the tumor evolves towards a final state that contains a CSC fraction, but a strong therapy leads to the suppression of this phenotype. Nonetheless, different external conditions lead to very diverse behaviors. For microchamber-grown tumorspheres, there is a threshold in therapy strength below which both subpopulations survive, while high values of adif lead to the complete elimination of the CSC phenotype. For tumorspheres grown on hard and soft agar and in the presence of growth factors, the model predicts a threshold not only in the therapy strength, but also in its starting time, an early beginning being potentially crucial. In summary, our model shows how the effects of a DA depend critically not only on the dosage and timing of the drug application, but also on the tumor nature and its environment.

Assessing the therapeutic response of tumors to hypoxia-targeted prodrugs with an in silico approach

Tumor hypoxia is commonly recognized as a condition stimulating the progress of the aggressive phenotype of tumor cells. Hypoxic tumor cells inhibit the delivery of cytotoxic drugs, causing hypoxic areas to receive insufficient amounts of anticancer agents, which results in adverse treatment responses. Being such an obstruction to conventional therapies for cancer, hypoxia might be considered a target to facilitate the efficacy of treatments in the resistive environment of tumor sites. In this regard, benefiting from prodrugs that selectively target hypoxic regions remains an effective approach. Additionally, combining hypoxia-activated prodrugs (HAPs) with conventional chemotherapeutic drugs has been used as a promising strategy to eradicate hypoxic cells. However, determining the appropriate sequencing and scheduling of the combination therapy is also of great importance in obtaining favorable results in anticancer therapy. Here, benefiting from a modeling approach, we study the efficacy of HAPs in combination with chemotherapeutic drugs on tumor growth and the treatment response. Different treatment schedules have been investigated to see the importance of determining the optimal schedule in combination therapy. The effectiveness of HAPs in varying hypoxic conditions has also been explored in the study. The model provides qualitative conclusions about the treatment response, as the maximal benefit is obtained from combination therapy with greater cell death for highly hypoxic tumors. It has also been observed that the antitumor effects of HAPs show a hypoxia-dependent profile.

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.

Approaches to combat hypoxia in cancer therapy and the potential for in silico models in their evaluation

AIM

The negative impact of tumour hypoxia on cancer treatment outcome has been long-known, yet there has been little success combating it. This paper investigates the potential role of in silico modelling to help test emerging hypoxia-targeting treatments in cancer therapy.

METHODS

A Medline search was undertaken on the current landscape of in silico models that simulate cancer therapy and evaluate their ability to test hypoxia-targeting treatments. Techniques and treatments to combat tumour hypoxia and their current challenges are also presented.

RESULTS

Hypoxia-targeting treatments include tumour reoxygenation, hypoxic cell radiosensitization with nitroimidazoles, hypoxia-activated prodrugs and molecular targeting. Their main challenges are toxicity and not achieving adequate delivery to hypoxic regions of the tumour. There is promising research toward combining two or more of these techniques. Different types of in silico therapy models have been developed ranging from temporal to spatial and from stochastic to deterministic models. Numerous models have compared the effectiveness of different radiotherapy fractionation schedules for controlling hypoxic tumours. Similarly, models could help identify and optimize new treatments for overcoming hypoxia that utilize novel hypoxia-targeting technology.

CONCLUSION

Current therapy models should attempt to incorporate more sophisticated modelling of tumour angiogenesis/vasculature and vessel perfusion in order to become more useful for testing hypoxia-targeting treatments, which typically rely upon the tumour vasculature for delivery of additional oxygen, (pro)drugs and nanoparticles.

Studying the regression profiles of cervical tumours during radiotherapy treatment using a patient-specific multiscale model

Apart from offering insight into the biomechanisms involved in cancer, many recent mathematical modeling efforts aspire to the ultimate goal of clinical translation, wherein models are designed to be used in the future as clinical decision support systems in the patient-individualized context. Most significant challenges are the integration of multiscale biodata and the patient-specific model parameterization. A central aim of this study was the design of a clinically-relevant parameterization methodology for a patient-specific computational model of cervical cancer response to radiotherapy treatment with concomitant cisplatin, built around a tumour features-based search of the parameter space. Additionally, a methodological framework for the predictive use of the model was designed, including a scoring method to quantitatively reflect the similarity and bilateral predictive ability of any two tumours in terms of their regression profile. The methodology was applied to the datasets of eight patients. Tumour scenarios in accordance with the available longitudinal data have been determined. Predictive investigations identified three patient cases, anyone of which can be used to predict the volumetric evolution throughout therapy of the tumours of the other two with very good results. Our observations show that the presented approach is promising in quantifiably differentiating tumours with distinct regression profiles.

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.