A Mathematical Model of Thyroid Disease Response to Radiotherapy

Araceli Gago-Arias,Juan Pardo-Montero,Filippo Terragni,Sara Neira

doi:10.3390/math9192365

Abstract

We present a mechanistic biomathematical model of molecular radiotherapy of thyroid disease. The general model consists of a set of differential equations describing the dynamics of different populations of thyroid cells with varying degrees of damage caused by radiotherapy (undamaged cells, sub-lethally damaged cells, doomed cells, and dead cells), as well as the dynamics of thyroglobulin and antithyroglobulin autoantibodies, which are important surrogates of treatment response. The model is presented in two flavours: on the one hand, as a deterministic continuous model, which is useful to fit populational data, and on the other hand, as a stochastic Markov model, which is particularly useful to investigate tumor control probabilities and treatment individualization. The model was used to fit the response dynamics (tumor/thyroid volumes, thyroglobulin and antithyroglobulin autoantibodies) observed in experimental studies of thyroid cancer and Graves’ disease treated with 131I-radiotherapy. A qualitative adequate fitting of the model to the experimental data was achieved. We also used the model to investigate treatment individualization strategies for differentiated thyroid cancer, aiming to improve the tumor control probability. We found that simple individualization strategies based on the absorbed dose in the tumor and tumor radiosensitivity (which are both magnitudes that can potentially be individually determined for every patient) can lead to an important raise of tumor control probabilities.

Highlights

Radioactive iodine, 131I, therapy (RAI) is a type of molecular radiotherapy that has been commonly used for the treatment of differentiated thyroid cancer since the 1940s
We have investigated whether treatment individualization can lead to important gains of Tumor Control Probability (TCP), i.e., rather than injecting the same activity A0 to each patient, the injected activity is adjusted according to patient characteristics/model parameters
Fit to Graves’ Disease Data In Figure 3 we present best-fits to population-averaged response to a single administration of 555 MBq RAI measured in a cohort of 30 patients with Graves’ hyperthyroidism

Summary

Introduction

Radioactive iodine, 131I, therapy (RAI) is a type of molecular radiotherapy ( called targeted radiotherapy) that has been commonly used for the treatment of differentiated thyroid cancer since the 1940s. The systemic nature of this therapy, with a radionuclide that takes several days to disintegrate, makes RAI treatment planning a complex procedure Due to these complexities, RAI treatment administration is usually guided by non-personalized empirical criteria that establish the activity of 131I to be administered, as well as cycle schedules. RAI treatment administration is usually guided by non-personalized empirical criteria that establish the activity of 131I to be administered, as well as cycle schedules This scenario poses a concern of potentially over/under-dosing patients, and there is a need to develop alternative strategies and tools for the development of individualized treatment planning

Methods

Results

Discussion

Conclusion