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Introduction: A mathematical model of the pituitary-thyroid feedback loop is extended to deepen the understanding of the Allan-Herndon-Dudley syndrome (AHDS). The AHDS is characterized by unusual thyroid hormone concentrations and a mutation in the SLC16A2 gene encoding for the monocarboxylate transporter 8 (MCT8). This mutation leads to a loss of thyroid hormone transport activity. One hypothesis to explain the unusual hormone concentrations of AHDS patients is that due to the loss of thyroid hormone transport activity, thyroxine (T 4) is partially retained in thyroid cells. Methods: This hypothesis is investigated by extending a mathematical model of the pituitary-thyroid feedback loop to include a model of the net effects of membrane transporters such that the thyroid hormone transport activity can be considered. A nonlinear modeling approach based on the Michaelis-Menten kinetics and its linear approximation are employed to consider the membrane transporters. The unknown parameters are estimated through a constrained parameter optimization. Results: In dynamic simulations, damaged membrane transporters result in a retention of T 4 in thyroid cells and ultimately in the unusual hormone concentrations of AHDS patients. The Michaelis-Menten modeling approach and its linear approximation lead to similar results. Discussion: The results support the hypothesis that a partial retention of T 4 in thyroid cells represents one mechanism responsible for the unusual hormone concentrations of AHDS patients. Moreover, our results suggest that the retention of T 4 in thyroid cells could be the main reason for the unusual hormone concentrations of AHDS patients.

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In this paper, we address the problem of optimal thyroid hormone replacement strategy development for hypothyroid patients. This is challenging for the following reasons. First, it is difficult to determine the correct dosage leading to normalized serum thyroid hormone concentrations of a patient. Second, it remains unclear whether a levothyroxine L-T4) monotherapy or a liothyronine/levothyroxine (L-T3/L-T4) combined therapy is more suitable to treat hypothyroidism. Third, the optimal intake frequency of L-T3/L-T4 is unclear. We address these issues by extending a mathematical model of the pituitary-thyroid feedback loop to be able to consider an oral intake of L-T3/L-T4. A model predictive controller (MPC) is employed to determine optimal dosages with respect to the thyroid hormone concentrations for each type of therapy. The results indicate that the L-T3/L-T4 combined therapy is slightly better (in terms of the achieved hormone concentrations) to treat hypothyroidism than the L-T4 monotherapy. In case of a specific genetic variant, namely genotype CC in polymorphism rs2235544 of gene DIO1, the simulation results suggest that the L-T4 monotherapy is better to treat hypothyroidism. In turn, when genotype AA is considered, the L-T3/L-T4 combined therapy is better to treat hypothyroidism. Furthermore, when genotype CC of polymorphism rs225014 (also referred to as c.274A>G or p.Thr92Ala) in the DIO2 gene is considered, the outcome of the L-T3/L-T4 combined therapy is better in terms of the steady-state hormone concentrations (for a triiodothyronine setpoint at the upper limit of the reference range of healthy individuals). Finally, the results suggest that two daily intakes of L-T3 could be the best trade-off between stable hormone concentrations and inconveniences for the patient.

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Continuous control using internal models appears to be quite straightforward explaining human motor control. However, it demands both, a high computational effort and a high model preciseness as the whole trajectory needs to be converted. Intermittent control shows great promise for avoiding these drawbacks of continuous control, at least to a certain extent. In this contribution, we study intermittency at the motoneuron level. We ask: how many different, but constant muscle stimulation sets are necessary to generate a stable movement for a specific motor task? Intermittent control, in our perspective, can be assumed only if the number of transitions is relatively small. As application case, a single-joint arm movement is considered. The muscle contraction dynamics is described by a Hill-type muscle model, for the muscle activation dynamics both Hatze's and Zajac's approach are considered. To actuate the lower arm, up to four muscle groups are implemented. A systems-theoretic approach is used to find the smallest number of transitions between constant stimulation sets. A method for a stability analysis of human motion is presented. A Lyapunov function candidate is specified. Thanks to sum-of-squares methods, the presented procedure is generally applicable and computationally feasible. The region-of-attraction of a transition point, and the number of transitions necessary to perform stable arm movements are estimated. The results support the intermittent control theory on this level of motor control, because only very few transitions are necessary.

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Despite significant progress in assay technology, diagnosis of functional thyroid disorders may still be a challenge, as illustrated by the vague upper limit of the reference range for serum thyrotropin (TSH). Diagnostical problems also apply to subjects affected by syndrome T, i.e., those 10% of hypothyroid patients who continue to suffer from poor quality of life despite normal TSH concentrations under substitution therapy with levothyroxine (L-T4). In this paper, we extend a mathematical model of the pituitary-thyroid feedback loop in order to improve the understanding of thyroid hormone homeostasis. In particular, we incorporate a TSH-T3-shunt inside the thyroid, whose existence has recently been demonstrated in several clinical studies. The resulting extended model shows good accordance with various clinical observations, such as a circadian rhythm in free peripheral triiodothyronine (FT3). Furthermore, we perform a sensitivity analysis of the derived model, revealing the dependence of TSH and hormone concentrations on different system parameters. The results have implications for clinical interpretation of thyroid tests, e.g., in the differential diagnosis of subclinical hypothyroidism.