A predictive mathematical model for the calculation of the final mass of Graves' disease thyroids treated with 131I

Substantial reductions in thyroid volume (up to 70-80%) after radioiodine therapy of Graves' hyperthyroidism are common and have been reported in the literature. A relationship between thyroid volume reduction and outcome of 131I therapy of Graves' disease has been reported by some authors. This important result could be used to decide individually the optimal radioiodine activity A0 (MBq) to administer to the patient, but a predictive model relating the change in gland volume to A0 is required. Recently, a mathematical model of thyroid mass reduction during the clearance phase (30-35 days) after 131I administration to patients with Graves' disease has been published and used as the basis for prescribing the therapeutic thyroid absorbed dose. It is well known that the thyroid volume reduction goes on until 1 year after therapy. In this paper, a mathematical model to predict the final mass of Graves' diseased thyroids submitted to 131I therapy is presented. This model represents a tentative explanation of what occurs macroscopically after the end of the clearance phase of radioiodine in the gland (the so-called second-order effects). It is shown that the final thyroid mass depends on its basal mass, on the radiation dose absorbed by the gland and on a constant value alpha typical of thyroid tissue. Alpha has been evaluated based on a set of measurements made in 15 reference patients affected by Graves' disease and submitted to 131I therapy. A predictive equation for the calculation of the final mass of thyroid is presented. It is based on macroscopic parameters measurable after a diagnostic 131I capsule administration (0.37-1.85 MBq), before giving the therapy. The final mass calculated using this equation is compared to the final mass of thyroid measured 1 year after therapy administration in 22 Graves' diseased patients. The final masses calculated and measured 1 year after therapy are in fairly good agreement (R = 0.81). The possibility, for the physician, to decide a therapeutic activity based on the desired decrease of thyroid mass instead of on a fixed thyroid absorbed dose could be a new opportunity to cure Graves' disease.