A Mathematical Model for Treatment of Papillary Thyroid Cancer Using the Allee Effect

Silva, Jairo Gomes da; Morais, Rafael Martins de; Silva, Izabel Cristina Rodrigues da; Adimy, Mostafa; Mancera, Paulo Fernando de Arruda

doi:10.1142/s0218339020500138

Cited by 6 publications

(3 citation statements)

References 46 publications

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“…By simulating the action of drugs in patients with RAIR-DTC, these models reveal the synergistic effect of targeted therapy with immunotherapy, highlighting the combined approach as the most effective treatment option due to its ability to enhance the immune system's tumor cell elimination rate (16) . These studies show that the combination therapy of lenvatinib and immunotherapeutic pembrolizumab enhances the immune system's ability to eliminate tumor cells, making it a favorable treatment option for RAIR-DTC patients (17,18) . Additionally, the model helps in understanding the synergistic effects of combining therapies, such as the increased radioiodine uptake in certain DTC cell lines after lenvatinib treatment, leading to improved treatment efficacy (12) .…”

Section: Introductionmentioning

confidence: 95%

A Mathematical Model for Differentiated Thyroid Cancer with Combination Therapy

Lavanya,

Jasmine

2024

IJST

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Objectives: Differentiated thyroid cancer (DTC) is usually treated with surgery and radioactive iodine therapy. However, in advanced stages, molecular changes can lead to a progressive loss of sensitivity to iodine, making the cancer resistant to radioactive iodine treatment (known as radioactive iodine-refractory, or RAIR). For cases of RAIR-DTC, alternative treatments such as tyrosine kinase inhibitors and immunotherapy are explored. To better understand the dynamics of these alternative treatments, a new mathematical model has been developed. In this model, Sorafenib represents the tyrosine kinase inhibitor, while Pembrolizumab is the immunotherapy agent under investigation. Methods: Two mathematical models were developed based on systems of ordinary differential equations to study differentiated thyroid cancer treated with (1) Sorafenib alone and (2) a combination of a Sorafenib and Pembrolizumab. The first model included three variables: drug concentration of Sorafenib, number of cancer cells, and number of immune cells with fourteen parameters. The second model additionally incorporated the concentration of the Pembrolizumab. Parameter values were estimated through simulations utilizing the fmincon optimization technique in MATLAB. Local asymptotic stability analysis was performed to investigate the models' behavior around equilibrium points. Moreover, the Lyapunov method was employed to establish global asymptotic stability of the models. Findings: The findings revealed insights into the dynamics of treating RAIR-DTC patients with tyrosine kinase inhibitors and immunotherapy. The stability analysis contributed to the understanding of the system's behavior under different conditions, offering valuable information for clinical application. Numerical simulations were then performed using Simbiology in MATLAB to simulate the treatment dynamics over time. Novelty: This research contributes to the field by presenting a novel mathematical model that integrates tyrosine kinase inhibitors and immunotherapy for the treatment of RAIR-DTC. The comprehensive analysis of equation stability enhances the reliability of the model, while the numerical simulations provide a practical and visual tool for assessing the potential outcomes of the proposed therapeutic strategy. This study offers a valuable framework for further exploration and refinement of treatment approaches for patients with challenging DTC cases. Keywords: Mathematical modeling, Routh Hurwitz Criteria, Jacobian, Differentiated thyroid Cancer, Stability Analysis

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Section: Introductionmentioning

confidence: 95%

A Mathematical Model for Differentiated Thyroid Cancer with Combination Therapy

Lavanya,

Jasmine

2024

IJST

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“…The lack of studies that directly compare 3.7, 5.5, and 7.4 GBq as the initial radioiodine therapy in metastatic DTC. It stands to reason, though, that the intended biological effect will be more pronounced the higher the dose delivered to the metastatic deposit (5) In the tumor microenvironment, inflammatory substances can either encourage or hinder tumor growth. Interleukin is a subset of these that mostly comes from CD3+ and CD4+ T cells and is essential for intercellular communication.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model for Treatment of Differentiated Thyroid Cancer using Radioactive Iodine

Lavanya,

Jasmine

2023

IJST

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Objectives: This study describes a mathematical model with radioactive iodine therapy for differentiated thyroid cancer using a system of non-linear ordinary differential equations. Methods: The four non-linear ordinary differential equations in the proposed model are concentration of thyroglobulin, interleukin concentration, the number of cancer cells, and concentration of radioactive iodine. Findings: This model displays two equilibria, including a drug-free steady state and a drug steady state. This study has created a standard for the radioactive iodine threshold level that the system must reach in order to lower the number of cancer cells. Using parameters obtained from experimental data, numerical simulations are used to support the analytic results. Novelty: The model makes it simple to investigate the effects of radioactive iodine deletion on disease-specific morbidity and recurrence rate. The costs of drug discovery and development can be offset with the use of mathematical modelling and simulations of modifying treatments, which can also promote the creation of new treatments.

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“…In Ref. 23, a mathematical model with Allee effect is proposed to simulate the impact of different dosages of RAI in the treatment of PTC patients. The model used was an ODE system, and the Allee threshold was associated with doses that may sufficiently eliminate tumors.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Lenvatinib and Pembrolizumab on Thyroid Cancer Refractory to Iodine 131i Simulated by Mathematical Modeling

et al. 2022

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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.

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A Mathematical Model for Treatment of Papillary Thyroid Cancer Using the Allee Effect

Cited by 6 publications

References 46 publications

A Mathematical Model for Differentiated Thyroid Cancer with Combination Therapy

A Mathematical Model for Differentiated Thyroid Cancer with Combination Therapy

A Mathematical Model for Treatment of Differentiated Thyroid Cancer using Radioactive Iodine

The Effect of Lenvatinib and Pembrolizumab on Thyroid Cancer Refractory to Iodine 131i Simulated by Mathematical Modeling

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