Mathematical models applied to thyroid cancer

Assessing chemotherapy dosing strategies in a spatial cell culture model

Predicting patient responses to chemotherapy regimens is a major challenge in cancer treatment. Experimental model systems coupled with quantitative mathematical models to calculate optimal dose and frequency of drugs can enable improved chemotherapy regimens. Here we developed a simple approach to track two-dimensional cell colonies composed of chemo-sensitive and resistant cell populations via fluorescence microscopy and coupled this to computational model predictions. Specifically, we first developed multiple 4T1 breast cancer cell lines resistant to varying concentrations of doxorubicin, and demonstrated how heterogeneous populations expand in a two-dimensional colony. We subjected cell populations to varied dose and frequency of chemotherapy and measured colony growth. We then built a mathematical model to describe the dynamics of both chemosensitive and chemoresistant populations, where we determined which number of doses can produce the smallest tumor size based on parameters in the system. Finally, using an in vitro model we demonstrated multiple doses can decrease overall colony growth as compared to a single dose at the same total dose. In the future, this system can be adapted to optimize dosing strategies in the setting of heterogeneous cell types or patient derived cells with varied chemoresistance.

THE EFFECT OF LENVATINIB AND PEMBROLIZUMAB ON THYROID CANCER REFRACTORY TO IODINE 131I SIMULATED BY MATHEMATICAL MODELING

Immunotherapy and targeted therapy are alternative treatments to differentiated thyroid cancer (DTC), which is usually treated with surgery and radioactive iodine. However, in advanced thyroid carcinomas, molecular alterations can cause a progressive loss of iodine sensitivity, thereby making cancer resistant to radioactive iodine-refractory (RAIR). In the treatment of cancer, tyrosine kinase inhibitors are administered to prevent the growth of cancer cells. One such inhibitor, lenvatinib, forms a targeted therapy for RAIR-DTC, while the immunotherapeutic pembrolizumab, a humanized antibody, prevents the binding of programmed cell death ligand 1 (PD-L1) to the PD-1 receptor. As one of the first studies on treatments for thyroid cancer with mathematical model involving immunotherapy and targeted therapy, we developed an ordinary differential system and tested variables such as concentration of lenvatinib and pembrolizumab, total cancer cells, and number of immune cells (i.e., T cells and natural killer cells). Analyzing local and global stability and the simulated action of drugs in patients with RAIR-DTC, revealed the combined effect of the targeted therapy with pembrolizumab. The scenarios obtained favor the combined therapy as the best treatment option, given its unrivaled ability to boost the immune system’s rate of eliminating tumor cells.

Tracing the footsteps of autophagy in computational biology

Autophagy plays a crucial role in maintaining cellular homeostasis through the degradation of unwanted materials like damaged mitochondria and misfolded proteins. However, the contribution of autophagy toward a healthy cell environment is not only limited to the cleaning process. It also assists in protein synthesis when the system lacks the amino acids’ inflow from the extracellular environment due to diet consumptions. Reduction in the autophagy process is associated with diseases like cancer, diabetes, non-alcoholic steatohepatitis, etc., while uncontrolled autophagy may facilitate cell death. We need a better understanding of the autophagy processes and their regulatory mechanisms at various levels (molecules, cells, tissues). This demands a thorough understanding of the system with the help of mathematical and computational tools. The present review illuminates how systems biology approaches are being used for the study of the autophagy process. A comprehensive insight is provided on the application of computational methods involving mathematical modeling and network analysis in the autophagy process. Various mathematical models based on the system of differential equations for studying autophagy are covered here. We have also highlighted the significance of network analysis and machine learning in capturing the core regulatory machinery governing the autophagy process. We explored the available autophagic databases and related resources along with their attributes that are useful in investigating autophagy through computational methods. We conclude the article addressing the potential future perspective in this area, which might provide a more in-depth insight into the dynamics of autophagy.

The emergence of new trends in clinical laboratory diagnosis

Diagnostic processes typically rely on traditional and laborious methods, that are prone to human error, resulting in frequent misdiagnosis of diseases. Computational approaches are being increasingly used for more precise diagnosis of the clinical pathology, diagnosis of genetic and microbial diseases, and analysis of clinical chemistry data. These approaches are progressively used for improving the reliability of testing, resulting in reduced diagnostic errors. Artificial intelligence (AI)-based computational approaches mostly rely on training sets obtained from patient data stored in clinical databases. However, the use of AI is associated with several ethical issues, including patient privacy and data ownership. The capacity of AI-based mathematical models to interpret complex clinical data frequently leads to data bias and reporting of erroneous results based on patient data. In order to improve the reliability of computational approaches in clinical diagnostics, strategies to reduce data bias and analyzing real-life patient data need to be further refined.

A MATHEMATICAL MODEL FOR TREATMENT OF PAPILLARY THYROID CANCER USING THE ALLEE EFFECT

The incidence of thyroid cancer is rising all over the world, and the papillary subtype (PTC) is the primary factor for this increase. The presence of thyroid tumors is commonly associated with increased levels of cytokines, such as interleukin 6 (IL-6). Considering PTC patients treated with thyroidectomy and radioactive iodine [Formula: see text]I (RAI), we propose an ordinary differential system using four variables: the RAI activity, the number of cancer cells and the serum concentrations of IL-6 and thyroglobulin (Tg). Our objective is to study the efficacy of different therapeutic doses of RAI in the treatment of thyroid cancer. The Allee effect is taken into account when modeling cancer cells growth under the influence of IL-6. From the results obtained, the main factors and conditions correlated with successful treatment, such as the RAI activity used and the tumor response are addressed. The detection of minimal doses of RAI that can cause tumor extinction is performed, though this has also meant longer periods for tumor cell elimination. The critical number of tumor cells due to the Allee effect is analyzed and linked to the immune system or biological factors that can slow the progression of the tumor but are insufficient after thyroid resection surgery.