Modeling therapeutic response to radioiodine in metastatic thyroid cancer: a proof-of-concept study for individualized medicine

Mathematical modeling of brain metastases growth and response to therapies: A review

Brain metastases (BMs) are the most common intracranial tumor type and a significant health concern, affecting approximately 10% to 30% of all oncological patients. Although significant progress is being made, many aspects of the metastatic process to the brain and the growth of the resulting lesions are still not well understood. There is a need for an improved understanding of the growth dynamics and the response to treatment of these tumors. Mathematical models have been proven valuable for drawing inferences and making predictions in different fields of cancer research, but few mathematical works have considered BMs. This comprehensive review aims to establish a unified platform and contribute to fostering emerging efforts dedicated to enhancing our mathematical understanding of this intricate and challenging disease. We focus on the progress made in the initial stages of mathematical modeling research regarding BMs and the significant insights gained from such studies. We also explore the vital role of mathematical modeling in predicting treatment outcomes and enhancing the quality of clinical decision-making for patients facing BMs.

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.

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.

Iodine-131 and Iodine-131-Meta-iodobenzylguanidine Dosimetry in Cancer Therapy

Radioactive iodine was first used for the treatment of benign thyroid disease and thyroid cancer 80 years ago. I-131 mIBG was later developed for the treatment of adult and pediatric neuroendocrine tumors. Physicists were closely involved from the outset to measure retention, to quantify uptake and to calculate radiation dosimetry. As the treatment became widespread, contrasting treatment regimes were followed, either given with empirically derived fixed levels of activity or guided according to the radiation doses delivered. As for external beam radiotherapy, individualized treatments for both thyroid cancer and neuroendocrine tumors were developed based on the aim of maximizing the radiation doses delivered to target volumes while restricting the radiation doses delivered to organs-at-risk, particularly the bone marrow. The challenge of marrow dosimetry has been met by using surrogate measures, often the blood dose for thyroid treatments and the whole-body dose in the case of treatment of neuroblastoma with I-131 mIBG. A number of studies have sought to establish threshold absorbed doses to ensure therapeutic efficacy. Although different values have been postulated, it has nevertheless been conclusively demonstrated that a fixed activity approach leads to a wide range of absorbed doses delivered to target volumes and to normal organs. Personalized treatment planning is now technically feasible with ongoing multicenter clinical trials and investigations into image quantification, biokinetic modelling and radiobiology.

Adjustment of the iodine ICRP population pharmacokinetic model for the use in thyroid cancer patients after thyroidectomy

Biokinetic models developed for healthy humans are not appropriate to describe biokinetics in thyroid cancer patients following thyroidectomy. The aim of this study was to adjust the population model for iodine proposed by the International Commission on Radiological Protection (ICRP) for the use in these patients. Rate constants of the ICRP publication 128 model for iodine were adjusted using the population modelling software package Monolix to describe activity retention in whole-body, thyroid, blood and protein-bound iodine observed in 23 patients. The new set of rate constants was compared to the four uptake scenarios proposed in ICRP publication 128. Flow from the inorganic iodide in blood compartment into the first thyroid compartment decreases to 0.15 d^-1compared to a value of 7.27 d^-1for the ICRP publication 128 model with a medium uptake. The transfer from first to second thyroid compartments and the outflow from the second thyroid compartment increases. An increased turnover rate of extrathyroidal organic iodine is observed. The rate constant from inorganic iodide in blood to kidney was also adjusted. Overall a good agreement was found between the adjusted model and the activity retention in thyroid cancer patients. The adjustment of population pharmacokinetic models to describe the biokinetic properties of specific patient populations for therapeutic radiopharmaceuticals is essential to capture the changes in biokinetics. The proposed set of rate constants for the established ICRP publication 128 model can be used to more accurately assess radiation protection requirements for the treatment of thyroid cancer patients using radioiodine.

A kinetic model of continuous radiation damage to populations of cells: comparison to the LQ model and application to molecular radiotherapy

The linear-quadratic (LQ) model to describe the survival of irradiated cells may be the most frequently used biomathematical model in radiotherapy. There has been an intense debate on the mechanistic origin of the LQ model. An interesting approach is that of obtaining LQ-like behavior from kinetic models, systems of differential equations that model the induction and repair of damage. Development of such kinetic models is particularly interesting for application to continuous dose rate therapies, such as molecular radiotherapy or brachytherapy. In this work, we present a simple kinetic model that describes the kinetics of populations of tumor cells, rather than lethal/sub-lethal lesions, which may be especially useful for application to continuous dose rate therapies, as in molecular radiotherapy. The multi-compartment model consists of a set of three differential equations. The model incorporates in an easy way different cross-interacting compartments of cells forming a tumor, and may be of especial interest for studying dynamics of treated tumors. In the fast dose delivery limit, the model can be analytically solved, obtaining a simple closed-form expression. Fitting of several surviving curves with both this solution and the LQ model shows that they produce similar fits, despite being functionally different. We have also investigated the operation of the model in the continuous dose rate scenario, firstly by fitting pre-clinical data of tumor response to ¹³¹I-CLR1404 therapy, and secondly by showing how damage repair and proliferation rates can cause a treatment to achieve control or not. Kinetic models like the one presented in this work may be of special interest when modeling response to molecular radiotherapy.

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.

Appraisal of radioiodine refractory thyroid cancer: advances and challenges

The incidence of thyroid cancer ranks top among all endocrine cancers, which has increased worldwide. Some patients suffer from recurrent/residual diseases after primary treatment. The recurrent/residual disease often turns out to be radioiodine refractory and shows poor response to radioiodine therapy. A lot of studies have explored the precise appraisal of radioiodine refractory disease in recent years. The mechanism of iodine uptake and the definition of radioiodine refractory disease have been summarized and discussed. The advances in tumor characteristics, histologies, and mutant conditions have been explored for a more accurate method in the early-stage appraisal. We then offer a review of opinions in the evaluation of refractory disease during follow-up, including Tg doubling time, ¹⁸F PET/CT, ¹³¹I WBS, and others. The sensitivity and specificity have been compared between different diagnostic methods. Some novel methods may be introduced for more precise appraisal, such as a scoring system and RNA expression profiling. This review aims to provide physicians a broad insight into the appraisal of radioiodine refractory disease and to pave way for future study.

Personalized treatment options for thyroid cancer: current perspectives

Thyroid cancer is one of the most common endocrine malignancies, with increasing incidence all over the world. In spite of good prognosis for differentiated thyroid carcinoma, for an unknown reason, about 5–10% of the patients, the cancer will show aggressive behavior, develop metastasis, and be refractory to treatment strategies like radioactive iodine. Regarding the genetic information, each thyroid cancer patient can be considered as an individual unique one, with unique genetic information. Contrary to standard chemotherapy drugs, target therapy components aim at one or more definite molecular pathway on cancer cells, so their selection is underlying patient’s genetic information. Nowadays, several mutations and rearrangements including BRAF, VEGF receptors, RET, and RET/PTC, KDR, KIT, PDGFRA, CD274, and JAK2 are taken into account for the therapeutic components like larotrectinib (TRK inhibitor), vemurafenib, sunitinib, sorafenib, selumetinib, and axitinib. With the new concept of personalized treatment of thyroid cancer diagnoses, planning treatment, finding out how well treatment will work, and estimating a prognosis has changed for the better over the last decade.

Mathematical models applied to thyroid cancer

Thyroid cancer is the most prevalent endocrine neoplasia in the world. The use of mathematical models on the development of tumors has yielded numerous results in this field and modeling with differential equations is present in many papers on cancer. In order to know the use of mathematical models with differential equations or similar in the study of thyroid cancer, studies since 2006 to date was reviewed. Systems with ordinary or partial differential equations were the means most frequently adopted by the authors. The models deal with tumor growth, effective half-life of radioiodine applied after thyroidectomy, the treatment with iodine-131, thyroid volume before thyroidectomy, and others. The variables usually employed in the models includes tumor volume, thyroid volume, amount of iodine, thyroglobulin and thyroxine hormone, radioiodine activity, and physical characteristics such as pressure, density, and displacement of the thyroid molecules. In conclusion, the mathematical models used so far with differential equations approach several aspects of thyroid cancer, including participation in methods of execution or follow-up of treatments. With the development of new models, an increase in the current understanding of the detection, evolution, and treatment of diseases is a step that should be considered.

Update on radionuclide therapy in oncology

Unstable isotopes and their capacity to emit ionizing radiation have been employed in clinical practice not only for diagnostic, but also for therapeutic purposes, with significant contribution in several fields of medicine and primarily in the management of oncologic patients. Their efficacy is associated with their ability to provide the targeted delivery of ionizing radiation for a determined duration. These compounds can be used for curative or palliative treatment, as well as for a diagnostic-therapeutic (theranostic) approach. This review summarises the most recent trends in radionuclide treatment for several malignancies, including prostate cancer, neuroendocrine tumours, and hematological and thyroid malignancies, in which radionuclide-based therapies have been employed with high effectiveness.