Dynamics of Breast Cancer under Different Rates of Chemoradiotherapy

Radiation necrosis after radiation therapy treatment of brain metastases: A computational approach

Metastasis is the process through which cancer cells break away from a primary tumor, travel through the blood or lymph system, and form new tumors in distant tissues. One of the preferred sites for metastatic dissemination is the brain, affecting more than 20% of all cancer patients. This figure is increasing steadily due to improvements in treatments of primary tumors. Stereotactic radiosurgery (SRS) is one of the main treatment options for patients with a small or moderate number of brain metastases (BMs). A frequent adverse event of SRS is radiation necrosis (RN), an inflammatory condition caused by late normal tissue cell death. A major diagnostic problem is that RNs are difficult to distinguish from BM recurrences, due to their similarities on standard magnetic resonance images (MRIs). However, this distinction is key to choosing the best therapeutic approach since RNs resolve often without further interventions, while relapsing BMs may require open brain surgery. Recent research has shown that RNs have a faster growth dynamics than recurrent BMs, providing a way to differentiate the two entities, but no mechanistic explanation has been provided for those observations. In this study, computational frameworks were developed based on mathematical models of increasing complexity, providing mechanistic explanations for the differential growth dynamics of BMs relapse versus RN events and explaining the observed clinical phenomenology. Simulated tumor relapses were found to have growth exponents substantially smaller than the group in which there was inflammation due to damage induced by SRS to normal brain tissue adjacent to the BMs, thus leading to RN. ROC curves with the synthetic data had an optimal threshold that maximized the sensitivity and specificity values for a growth exponent β* = 1.05, very close to that observed in patient datasets.

[18F]-FDHT PET for the Imaging of Androgen Receptor in Prostate and Breast Cancer: A Systematic Review

The aim of this systematic review is to provide a comprehensive overview of the role of fluoro-5α-dihydrotestosterone ([18F]-FDHT) for the in vivo imaging of androgen receptors (AR) through positron emission tomography (PET) in metastatic breast (mBC) and metastatic castration-resistant prostate cancer (mCRPC). Relevant studies published from 2013 up to May 2023 were selected by searching Scopus, PubMed and Web of Science. The selected imaging studies were analyzed using a modified version of the critical Appraisal Skills Programme (CASP). Eleven studies encompassing 321 patients were selected. Seven of the eleven selected papers included 266 subjects (82.2%) affected by mCRPC, while four encompassed 55 (17.2%) patients affected by mBC. [18F]-FDHT PET showed a satisfying test/retest reproducibility, and when compared to a histochemical analysis, it provided encouraging results for in vivo AR quantification both in mCRPC and mBC. [18F]-FDHT PET had a prognostic relevance in mCRPC patients submitted to AR-targeted therapy, while a clear association between [18F]-FDHT uptake and the bicalutamide response was not observed in women affected by AR-positive mBC. Further studies are needed to better define the role of [18F]-FDHT PET, alone or in combination with other tracers (i.e., [18F]-FDG/[18F]-FES), for patients' selection and monitoring during AR-targeted therapy, especially in the case of mBC.

Mathematical model for the estrogen paradox in breast cancer treatment

Estrogen is known to stimulate the growth of breast cancer, but is also effective in treating the disease. This is referred to as the"estrogen paradox". Furthermore, short-term treatment with estrogen can successfully eliminate breast cancer, whereas long-term treatment can cause cancer recurrence. Studies highlighted clinical correlations between estrogen and the protein p53 which plays a pivotal role in breast cancer suppression. We sought to investigate how the interplay between estrogen and p53 impacts the dynamics of breast cancer, and further explore if this could be a plausible explanation for the estrogen paradox and the paradoxical tumor recurrence that results from prolonged treatment with estrogen. For this, we propose a novel ODE based mathematical model that accounts for dormant and active cancer cells, along with the estrogen hormone and the p53 protein. We analyze the model's global stability behavior using the Poincaré-Bendixson theorem and results from differential inequalities. We also perform a bifurcation analysis and carry out numerical simulations that elucidate the roles of estrogen and p53 in the estrogen paradox and its long term estrogen paradoxical effect. The mathematical and numerical analyses suggest that the apparent paradoxical role of estrogen could be the result of an interplay between estrogen and p53, and provide explicit conditions under which the paradoxical effect of long-term treatment may be prevented.

Mathematical modeling and machine learning for public health decision-making: the case of breast cancer in Benin

Breast cancer is the most common type of cancer in women. Its mortality rate is high due to late detection and cardiotoxic effects of chemotherapy. In this work, we used the Support Vector Machine (SVM) method to classify tumors and proposed a new mathematical model of the patient dynamics of the breast cancer population. Numerical simulations were performed to study the behavior of the solutions around the equilibrium point. The findings revealed that the equilibrium point is stable regardless of the initial conditions. Moreover, this study will help public health decision-making as the results can be used to minimize the number of cardiotoxic patients and increase the number of recovered patients after chemotherapy.

Crosstalk between HER2 and PD-1/PD-L1 in Breast Cancer: From Clinical Applications to Mathematical Models

Breast cancer is one of the major causes of mortality in women worldwide. The most aggressive breast cancer subtypes are human epidermal growth factor receptor-positive (HER2+) and triple-negative breast cancers. Therapies targeting HER2 receptors have significantly improved HER2+ breast cancer patient outcomes. However, several recent studies have pointed out the deficiency of existing treatment protocols in combatting disease relapse and improving response rates to treatment. Overriding the inherent actions of the immune system to detect and annihilate cancer via the immune checkpoint pathways is one of the important hallmarks of cancer. Thus, restoration of these pathways by various means of immunomodulation has shown beneficial effects in the management of various types of cancers, including breast. We herein review the recent progress in the management of HER2+ breast cancer via HER2-targeted therapies, and its association with the programmed death receptor-1 (PD-1)/programmed death ligand-1 (PD-L1) axis. In order to link research in the areas of medicine and mathematics and point out specific opportunities for providing efficient theoretical analysis related to HER2+ breast cancer management, we also review mathematical models pertaining to the dynamics of HER2+ breast cancer and immune checkpoint inhibitors.