Optimal Hormone Replacement Therapy in Hypothyroidism - A Model Predictive Control Approach

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. Copyright © 2022 Wolff, Dietrich and Müller

Robust Stability of Gaussian Process Based Moving Horizon Estimation

In this paper, we introduce a Gaussian process based moving horizon estimation (MHE) framework. The scheme is based on offline collected data and offline hyperparameter optimization. In particular, compared to standard MHE schemes, we replace the mathematical model of the system by the posterior mean of the Gaussian process. To account for the uncertainty of the learned model, we exploit the posterior variance of the learned Gaussian process in the weighting matrices of the cost function of the proposed MHE scheme. We prove practical robust exponential stability of the resulting estimator using a recently proposed Lyapunov-based proof technique. Finally, the performance of the Gaussian process based MHE scheme is illustrated via a nonlinear system.Comment: 8 page

Robust Data-Driven Moving Horizon Estimation for Linear Discrete-Time Systems

In this paper, a robust data-driven moving horizon estimation (MHE) scheme for linear time-invariant discrete-time systems is introduced. The scheme solely relies on offline collected data without employing any system identification step. We prove practical robust exponential stability for the setting where both the online measurements and the offline collected data are corrupted by non-vanishing and bounded noise. The behavior of the novel robust data-driven MHE scheme is illustrated by means of simulation examples and compared to a standard model-based MHE scheme, where the model is identified using the same offline data as for the data-driven MHE scheme.Comment: 13 page

Gaussian Process-Based Nonlinear Moving Horizon Estimation

In this paper, we propose a novel Gaussian process-based moving horizon estimation (MHE) framework for unknown nonlinear systems. In the proposed scheme, we take advantage of the properties of Gaussian processes. On the one hand, we approximate the system dynamics by the posterior means of the learned Gaussian processes (GPs). On the other hand, we exploit the posterior variances of the Gaussian processes to design the weighting matrices in the MHE cost function and account for the uncertainty in the learned system dynamics. The data collection and the tuning of the hyperparameters are done offline. We prove robust stability of the GP-based MHE scheme using a Lyapunov-based proof technique. Furthermore, as additional contribution, we analyze under which conditions incremental input/output-to-state stability (a nonlinear detectability notion) is preserved when approximating the system dynamics using, e.g., machine learning techniques. Finally, we illustrate the performance of the GP-based MHE scheme in a simulation case study and show how the chosen weighting matrices can lead to an improved performance compared to standard cost functions.Comment: 16 page

Mathematical modeling and simulation of thyroid homeostasis: Implications for the Allan-Herndon-Dudley syndrome

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 (T4) 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 T4 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 T4 in thyroid cells represents one mechanism responsible for the unusual hormone concentrations of AHDS patients. Moreover, our results suggest that the retention of T4 in thyroid cells could be the main reason for the unusual hormone concentrations of AHDS patients

Mathematical modeling and simulation of thyroid homeostasis: Implications for the Allan-Herndon-Dudley syndrome

IntroductionA 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 (T4) is partially retained in thyroid cells.MethodsThis 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.ResultsIn dynamic simulations, damaged membrane transporters result in a retention of T4 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.DiscussionThe results support the hypothesis that a partial retention of T4 in thyroid cells represents one mechanism responsible for the unusual hormone concentrations of AHDS patients. Moreover, our results suggest that the retention of T4 in thyroid cells could be the main reason for the unusual hormone concentrations of AHDS patients

Studies of the dose-effect relation

Dose-effect relations and, specifically, cell survival curves are surveyed with emphasis on the interplay of the random factors — biological variability, stochastic reaction of the cell, and the statistics of energy deposition —that co-determine their shape. The global parameters mean inactivation dose, , and coefficient of variance, V, represent this interplay better than conventional parameters. Mechanisms such as lesion interaction, misrepair, repair overload, or repair depletion have been invoked to explain sigmoid dose dependencies, but these notions are partly synonymous and are largely undistinguishable on the basis of observed dose dependencies. All dose dependencies reflect, to varying degree, the microdosimetric fluctuations of energy deposition, and these have certain implications, e.g. the linearity of the dose dependence at small doses, that apply regardless of unresolved molecular mechanisms of cellular radiation action

Childhood adversity, mental ill-health and aggressive behavior in an African orphanage: Changes in response to trauma-focused therapy and the implementation of a new instructional system

<p>Abstract</p> <p>Background</p> <p>The number of orphans in Sub-Saharan Africa is constantly rising. While it is known that family or community care is preferable over institutional care of African orphans, little is known about the quality of care in orphanages and possibilities of improvement.</p> <p>Study 1</p> <p>Methods</p> <p>Exposure to traumatic stress, experiences of violence in the home, school and orphanage, as well as mental ill-health and aggression of 38 children (mean age of <it>M </it>= 8.64 years) living in an orphanage in rural Tanzania were assessed at two time points. The severity of post-traumatic stress disorder symptoms (PTSD), depressive symptoms, and internalizing and externalizing problems were used as indicators of mental ill-health.</p> <p>Results</p> <p>Violence experienced in the orphanage correlated more strongly with all indicators of mental ill-health than violence in the former home, school or neighborhood at time point 1. Additionally, violence experienced in the orphanage had a positive relationship with the aggressive behavior of the children at time point 2.</p> <p>Study 2</p> <p>Methods</p> <p>With the help of the pre-post assessment of Study 1, the implementation of a new instructional system and psychotherapeutic treatment (KIDNET) for trauma-related illness were evaluated.</p> <p>Results</p> <p>In response to both, a change in the instructional system and psychotherapeutic treatment of PTSD, a massive decline in experienced violence and in the severity of PTSD-symptoms was found, whereas depressive symptoms and internalizing and externalizing problems exhibited little change.</p> <p>Conclusions</p> <p>These studies show that violence, especially in the orphanage, can severely contribute to mental ill-health in orphans and that mental health can be improved by implementing a new instructional system and psychotherapeutic treatment in an orphanage. Moreover, the results indicate that the experience of violence in an orphanage also plays a crucial role in aggressive behavior of the orphans.</p