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Aim: To improve predictive bi-phase model of 131I accumulation in thyroid gland by introducing physically and medically justified prior information.

Material and methods: 2355 sequences, containing 4-9 pairs time-activity, were analysed. They were measured during diagnostics and therapeutic treatment of thyroid gland carcinoma using 131I. For each sequence, a novel bi-phase model was estimated in a Bayesian way. The model is a linear three-parametric regression, relating logarithm of activity to carefully selected functions of time. With this model, even uptake accumulation phase is modelled, unlike with the usual mono-exponential model. The bi-phase model was already shown to improve estimation of diagnostically important residence time, as well as radio-hygienically important prediction of time-activity curve. At the same time, the estimation results were found relatively sensitive to measurement quality, which is often poor in daily practice. For this reason, hard linear prior constraints on estimated parameters were introduced to ensure biophysically meaningful estimates of the time-activity curve and consequently to make the estimate robust. The constraints have induced the need to evaluate the posterior probability density function (pdf) numerically, by transforming it using Markov Chain Monte Carlo method into the predictive pdf of the accumulated activity.

Results: On each measured sequence and all their initial parts having length at least 3, predictive pdf was evaluated and its expectations used as point predictions of the subsequent activity. The relative prediction errors were analysed. Due to the introduced constraints, all predicted sequences were meaningful. Without the constraints, 43% of data sequences with 3 pairs used for identification failed for physical meaninglessness and were useless for prediction. The predictive ability is most critical after 3 diagnostic measurements as it helps in decision on therapeutic amount of 131I administered. This makes us present these results. Mean of relative prediction errors is -0.09, median is -0.17, standard deviation 0.62 minimum -1 and maximum 10. When omitting 2.6% of results with prediction error greater than 1, the skewed heavy tailed distribution becomes more symmetric with the mean -0.13, median -0.17 and standard deviation only 0.38.

Conclusions: Plethora of the obtained results including those presented here shown that the introduced constraints made the estimation of bi-phase model robust. Consequently, it provides reliable characterization of the accumulation kinetics supporting both treatment of thyroid gland carcinoma and radiation protection.

Acknowledgement: This research was supported by AV CR 1ET100750404 and by MSMT CR 1M6798555601.