Extensions, validation, and clinical applications of a feedback control system simulator of the hypothalamo-pituitary-thyroid axis

Spatially Dependent Tissue Distribution of Thyroid Hormones by Plasma Thyroid Hormone Binding Proteins

Plasma thyroid hormone (TH) binding proteins (THBPs), including thyroxine-binding globulin (TBG), transthyretin (TTR), and albumin (ALB), carry THs to extrathyroidal sites, where THs are unloaded locally and then taken up via membrane transporters into the tissue proper. The respective roles of THBPs in supplying THs for tissue uptake are not completely understood. To investigate this, we developed a spatial human physiologically based kinetic (PBK) model of THs, which produces several novel findings. (1) Contrary to postulations that TTR and/or ALB are the major local T4 contributors, the three THBPs may unload comparable amounts of T4 in Liver, a rapidly perfused organ; however, their contributions in slowly perfused tissues follow the order of abundances of T4TBG, T4TTR, and T4ALB. The T3 amounts unloaded from or loaded onto THBPs in a tissue acting as a T3 sink or source respectively follow the order of abundance of T3TBG, T3ALB, and T3TTR regardless of perfusion rate. (2) Any THBP alone is sufficient to maintain spatially uniform TH tissue distributions. (3) The TH amounts unloaded by each THBP species are spatially dependent and nonlinear in a tissue, with ALB being the dominant contributor near the arterial end but conceding to TBG near the venous end. (4) Spatial gradients of TH transporters and metabolic enzymes may modulate these contributions, producing spatially invariant or heterogeneous TH tissue concentrations depending on whether the blood-tissue TH exchange operates in near-equilibrium mode. In summary, our modeling provides novel insights into the differential roles of THBPs in local TH tissue distribution.

Automatic Levothyroxine Dosing Algorithm for Patients Suffering from Hashimoto's Thyroiditis

Hypothyroidism is a condition where the patient's thyroid gland cannot produce sufficient thyroid hormones (mainly triiodothyronine and thyroxine). The primary cause of hypothyroidism is autoimmune-mediated destruction of the thyroid gland, referred to as Hashimoto's thyroiditis. A patient's desired thyroid hormone concentration is achieved by oral administration of thyroid hormone, usually levothyroxine. Establishing individual levothyroxine doses to achieve desired thyroid hormone concentrations requires several patient visits. Additionally, clear guidance for the dosing regimen is lacking, and significant inter-individual differences exist. This study aims to design a digital automatic dosing algorithm for patients suffering from Hashimoto's thyroiditis. The dynamic behaviour of the relevant thyroid function is mathematically modelled. Methods of automatic control are exploited for the design of the proposed robust model-based levothyroxine dosing algorithm. Numerical simulations are performed to evaluate the mathematical model and the dosing algorithm. With the help of the developed controller thyroid hormone concentrations of patients, emulated using Thyrosim, have been regulated under the euthyroid state. The proposed concept demonstrates reliable responses amidst varying patient parameters. Our developed model provides a useful basis for the design of automatic levothyroxine dosing algorithms. The proposed robust feedback loop contributes to the first results for computer-assisted thyroid dosing algorithms.

A minimal human physiologically based kinetic model of thyroid hormones and chemical disruption of plasma thyroid hormone binding proteins

The thyroid hormones (THs), thyroxine (T4) and triiodothyronine (T3), are under homeostatic control by the hypothalamic-pituitary-thyroid axis and plasma TH binding proteins (THBPs), including thyroxine-binding globulin (TBG), transthyretin (TTR), and albumin (ALB). THBPs buffer free THs against transient perturbations and distribute THs to tissues. TH binding to THBPs can be perturbed by structurally similar endocrine-disrupting chemicals (EDCs), yet their impact on circulating THs and health risks are unclear. In the present study, we constructed a human physiologically based kinetic (PBK) model of THs and explored the potential effects of THBP-binding EDCs. The model describes the production, distribution, and metabolism of T4 and T3 in the Body Blood, Thyroid, Liver, and Rest-of-Body (RB) compartments, with explicit consideration of the reversible binding between plasma THs and THBPs. Rigorously parameterized based on literature data, the model recapitulates key quantitative TH kinetic characteristics, including free, THBP-bound, and total T4 and T3 concentrations, TH productions, distributions, metabolisms, clearance, and half-lives. Moreover, the model produces several novel findings. (1) The blood-tissue TH exchanges are fast and nearly at equilibrium especially for T4, providing intrinsic robustness against local metabolic perturbations. (2) Tissue influx is limiting for transient tissue uptake of THs when THBPs are present. (3) Continuous exposure to THBP-binding EDCs does not alter the steady-state levels of THs, while intermittent daily exposure to rapidly metabolized TBG-binding EDCs can cause much greater disruptions to plasma and tissue THs. In summary, the PBK model provides novel insights into TH kinetics and the homeostatic roles of THBPs against thyroid disrupting chemicals.

A biologically based computational model for the hypothalamic-pituitary-thyroid (HPT) axis in Xenopus laevis larvae

A biologically based computational model was developed to describe the hypothalamic-pituitary-thyroid (HPT) axis in developing Xenopus laevis larvae. The goal of this effort was to develop a tool that can be used to better understand mechanisms of thyroid hormone-mediated metamorphosis in X. laevis and predict organismal outcomes when those mechanisms are perturbed by chemical toxicants. In this report, we describe efforts to simulate the normal biology of control organisms. The structure of the model borrows from established models of HPT axis function in mammals. Additional features specific to X. laevis account for the effects of organism growth, growth of the thyroid gland, and developmental changes in regulation of thyroid stimulating hormone (TSH) by circulating thyroid hormones (THs). Calibration was achieved by simulating observed changes in stored and circulating levels of THs during a critical developmental window (Nieuwkoop and Faber stages 54-57) that encompasses widely used in vivo chemical testing protocols. The resulting model predicts that multiple homeostatic processes, operating in concert, can act to preserve circulating levels of THs despite profound impairments in TH synthesis. Represented in the model are several biochemical processes for which there are high-throughput in vitro chemical screening assays. By linking the HPT axis model to a toxicokinetic model of chemical uptake and distribution, it may be possible to use this vitro effects information to predict chemical effects in X. laevis larvae resulting from defined chemical exposures.

Clinically practical pharmacometrics computer model to evaluate and personalize pharmacotherapy in pediatric rare diseases: application to Graves' disease

Objectives

Graves' disease (GD) with onset in childhood or adolescence is a rare disease (ORPHA:525731). Current pharmacotherapeutic approaches use antithyroid drugs, such as carbimazole, as monotherapy or in combination with thyroxine hormone substitutes, such as levothyroxine, as block-and-replace therapy to normalize thyroid function and improve patients' quality of life. However, in the context of fluctuating disease activity, especially during puberty, a considerable proportion of pediatric patients with GD is suffering from thyroid hormone concentrations outside the therapeutic reference ranges. Our main goal was to develop a clinically practical pharmacometrics computer model that characterizes and predicts individual disease activity in children with various severity of GD under pharmacotherapy.

Methods

Retrospectively collected clinical data from children and adolescents with GD under up to two years of treatment at four different pediatric hospitals in Switzerland were analyzed. Development of the pharmacometrics computer model is based on the non-linear mixed effects approach accounting for inter-individual variability and incorporating individual patient characteristics. Disease severity groups were defined based on free thyroxine (FT4) measurements at diagnosis.

Results

Data from 44 children with GD (75% female, median age 11 years, 62% receiving monotherapy) were analyzed. FT4 measurements were collected in 13, 15, and 16 pediatric patients with mild, moderate, or severe GD, with a median FT4 at diagnosis of 59.9 pmol/l (IQR 48.4, 76.8), and a total of 494 FT4 measurements during a median follow-up of 1.89 years (IQR 1.69, 1.97). We observed no notable difference between severity groups in terms of patient characteristics, daily carbimazole starting doses, and patient years. The final pharmacometrics computer model was developed based on FT4 measurements and on carbimazole or on carbimazole and levothyroxine doses involving two clinically relevant covariate effects: age at diagnosis and disease severity.

Discussion

We present a tailored pharmacometrics computer model that is able to describe individual FT4 dynamics under both, carbimazole monotherapy and carbimazole/levothyroxine block-and-replace therapy accounting for inter-individual disease progression and treatment response in children and adolescents with GD. Such clinically practical and predictive computer model has the potential to facilitate and enhance personalized pharmacotherapy in pediatric GD, reducing over- and underdosing and avoiding negative short- and long-term consequences. Prospective randomized validation trials are warranted to further validate and fine-tune computer-supported personalized dosing in pediatric GD and other rare pediatric diseases.

The role of supporting and disruptive mechanisms of FT3 homeostasis in regulating the hypothalamic-pituitary-thyroid axis

BACKGROUND

Thyroid hormones are controlled by the hypothalamic-pituitary-thyroid (HPT) axis through a complex network of regulatory loops, involving the hormones TRH, TSH, FT4, and FT3. The relationship between TSH and FT4 is widely used for diagnosing thyroid diseases. However, mechanisms of FT3 homeostasis are not well understood.

OBJECTIVE

We used mathematical modelling to further examine mechanisms that exist in the HPT axis regulation for protecting circulating FT3 levels.

METHODS

A mathematical model consisting of a system of four coupled first-order parameterized non-linear ordinary differential equations (ODEs) was developed, accounting for the interdependencies between the hormones in the HPT axis regulation. While TRH and TSH feed forward to the pituitary and thyroid, respectively, FT4 and FT3 feed backward to both the pituitary and hypothalamus. Stable equilibrium solutions of the ODE system express homeostasis for a particular variable, such as FT3, if this variable stays in a narrow range while certain other parameter(s) and system variable(s) may vary substantially.

RESULTS

The model predicts that (1) TSH-feedforward protects FT3 levels if the FT4 production rate declines and (2) combined negative feedback by FT4 and FT3 on both TSH and TRH production rates keeps FT3 levels insensitive to moderate changes in FT4 production rates and FT4 levels. The optimum FT4 and FT3 feedback and TRH and TSH-feedforward ranges that preserve FT3 homeostasis were found by numerical continuation analysis. Model predictions were in close agreement with clinical studies and individual patient examples of hypothyroidism and hyperthyroidism.

CONCLUSIONS

These findings further extend the concept of HPT axis regulation beyond TSH and FT4 to integrate the more active sister hormone FT3 and mechanisms of FT3 homeostasis. Disruption of homeostatic mechanisms leads to disease. This provides a perspective for novel testable concepts in clinical studies to therapeutically target the disruptive mechanisms.

Levothyroxine: Conventional and novel drug delivery formulations

Despite the fact that levothyroxine is one of the most prescribed medications in the world, its bioavailability has been reported to be impaired by many factors, including interfering drugs or foods and concomitant diseases, and persistent hypothyroidism with a high dose of levothyroxine is thus elicited. Persistent hypothyroidism can also be induced by noninterchangeability between formulations and poor compliance. To address these issues, some strategies have been developed. Novel formulations (liquid solutions and soft-gel capsules) have been designed to eliminate malabsorption. Some other delivery routes (injections, suppositories, sprays, and sublingual and transdermal administrations) are aimed at circumventing different difficulties in dosing, such as thyroid emergencies and dysphagia. Moreover, nanomaterials have been used to develop delivery systems for the sustained release of levothyroxine to improve patient compliance and reduce costs. Some delivery systems encapsulating nanoparticles show promising release profiles. In this review, we first summarize the medical conditions that interfere with the bioavailability of oral levothyroxine and discuss the underlying mechanisms and treatments. The efficacy of liquid solutions and soft-gel capsules are systematically evaluated. We further summarize the novel delivery routes for levothyroxine and their possible applications. Nanomaterials in the levothyroxine field are then discussed and compared based on their load and release profile. We hope the article provides novel insights into the drug delivery of levothyroxine.

Principles of Endocrine Regulation: Reconciling Tensions Between Robustness in Performance and Adaptation to Change

Endocrine regulation in the hypothalamic-pituitary-thyroid (HPT) axis is orchestrated by physiological circuits which integrate multiple internal and external influences. Essentially, it provides either of the two responses to overt biological challenges: to defend the homeostatic range of a target hormone or adapt it to changing environmental conditions. Under certain conditions, such flexibility may exceed the capability of a simple feedback control loop, rather requiring more intricate networks of communication between the system's components. A new minimal mathematical model, in the form of a parametrized nonlinear dynamical system, is here formulated as a proof-of-concept to elucidate the principles of the HPT axis regulation. In particular, it allows uncovering mechanisms for the homeostasis of the key biologically active hormone free triiodothyronine (FT3). One mechanism supports the preservation of FT3 homeostasis, whilst the other is responsible for the adaptation of the homeostatic state to a new level. Together these allow optimum resilience in stressful situations. Preservation of FT3 homeostasis, despite changes in FT4 and TSH levels, is found to be an achievable system goal by joining elements of top-down and bottom-up regulation in a cascade of targeted feedforward and feedback loops. Simultaneously, the model accounts for the combination of properties regarded as essential to endocrine regulation, namely sensitivity, the anticipation of an adverse event, robustness, and adaptation. The model therefore offers fundamental theoretical insights into the effective system control of the HPT axis.

Intrathyroidal feedforward and feedback network regulating thyroid hormone synthesis and secretion

Thyroid hormones (THs), including T4 and T3, are produced and released by the thyroid gland under the stimulation of thyroid-stimulating hormone (TSH). The homeostasis of THs is regulated via the coordination of the hypothalamic-pituitary-thyroid axis, plasma binding proteins, and local metabolism in tissues. TH synthesis and secretion in the thyrocytes-containing thyroid follicles are exquisitely regulated by an elaborate molecular network comprising enzymes, transporters, signal transduction machineries, and transcription factors. In this article, we synthesized the relevant literature, organized and dissected the complex intrathyroidal regulatory network into structures amenable to functional interpretation and systems-level modeling. Multiple intertwined feedforward and feedback motifs were identified and described, centering around the transcriptional and posttranslational regulations involved in TH synthesis and secretion, including those underpinning the Wolff-Chaikoff and Plummer effects and thyroglobulin-mediated feedback regulation. A more thorough characterization of the intrathyroidal network from a systems biology perspective, including its topology, constituent network motifs, and nonlinear quantitative properties, can help us to better understand and predict the thyroidal dynamics in response to physiological signals, therapeutic interventions, and environmental disruptions.

Optimized Replacement T4 and T4+T3 Dosing in Male and Female Hypothyroid Patients With Different BMIs Using a Personalized Mechanistic Model of Thyroid Hormone Regulation Dynamics

OBJECTIVE

A personalized simulation tool, p-THYROSIM, was developed (1) to better optimize replacement LT4 and LT4+LT3 dosing for hypothyroid patients, based on individual hormone levels, BMIs, and gender; and (2) to better understand how gender and BMI impact thyroid dynamical regulation over time in these patients.

METHODS

p-THYROSIM was developed by (1) modifying and refining THYROSIM, an established physiologically based mechanistic model of the system regulating serum T3, T4, and TSH level dynamics; (2) incorporating sex and BMI of individual patients into the model; and (3) quantifying it with 3 experimental datasets and validating it with a fourth containing data from distinct male and female patients across a wide range of BMIs. For validation, we compared our optimized predictions with previously published results on optimized LT4 monotherapies. We also optimized combination T3+T4 dosing and computed unmeasured residual thyroid function (RTF) across a wide range of BMIs from male and female patient data.

RESULTS

Compared with 3 other dosing methods, the accuracy of p-THYROSIM optimized dosages for LT4 monotherapy was better overall (53% vs. 44%, 43%, and 38%) and for extreme BMI patients (63% vs. ~51% low BMI, 48% vs. ~36% and 22% for high BMI). Optimal dosing for combination LT4+LT3 therapy and unmeasured RTFs was predictively computed with p-THYROSIM for male and female patients in low, normal, and high BMI ranges, yielding daily T3 doses of 5 to 7.5 μg of LT3 combined with 62.5-100 μg of LT4 for women or 75-125 μg of LT4 for men. Also, graphs of steady-state serum T3, T4, and TSH concentrations vs. RTF (range 0%-50%) for untreated patients showed that neither BMI nor gender had any effect on RTF predictions for our patient cohort data. Notably, the graphs provide a means for estimating unmeasurable RTFs for individual patients from their hormone measurements before treatment.

CONCLUSIONS

p-THYROSIM can provide accurate monotherapies for male and female hypothyroid patients, personalized with their BMIs. Where combination therapy is warranted, our results predict that not much LT3 is needed in addition to LT4 to restore euthyroid levels, suggesting opportunities for further research exploring combination therapy with lower T3 doses and slow-releasing T3 formulations.

Mathematical Modeling of Free Thyroxine Concentrations During Methimazole Treatment for Graves' Disease: Development and Validation of a Computer-Aided Thyroid Treatment Method

BACKGROUND

Methimazole (MMI) is the first-line treatment for patients with Graves' disease (GD). While there are empirical recommendations for initial MMI doses, there is no clear guidance for subsequent MMI dose titrations. We aimed to (a) develop a mathematical model capturing the dynamics of free thyroxine (FT4) during MMI treatment (b), validate this model by use of numerical simulation in comparison with real-life patient data (c), develop the software application Digital Thyroid (DigiThy) serving either as a practice tool for treating virtual patients or as a decision support system with dosing recommendations for MMI, and (d) validate this software framework by comparing the efficacy of its MMI dosing recommendations with that from clinical endocrinologists.

METHODS

Based on concepts of automatic control and by use of optimization techniques, we developed two first order ordinary differential equations for modeling FT4 dynamics during MMI treatment. Clinical data from patients with GD derived from the outpatient clinic of Endocrinology at the Medical University of Graz, Austria, were used to develop and validate this model. It was subsequently used to create the web-based software application DigiThy as a simulation environment for treating virtual patients and an autonomous computer-aided thyroid treatment (CATT) method providing MMI dosing recommendations.

RESULTS

Based on MMI doses, concentrations of FT4, thyroid-stimulating hormone (TSH), and TSH-receptor antibodies (TRAb), a mathematical model with 8 patient-specific constants was developed. Predicted FT4 concentrations were not significantly different compared to the available consecutively measured FT4 concentrations in 9 patients with GD (52 data pairs, p=0.607). Treatment success of MMI dosing recommendations in 41 virtually generated patients defined by achieved target FT4 concentrations preferably with low required MMI doses was similar between CATT and usual care. Statistically, CATT was significantly superior (p<0.001).

CONCLUSIONS

Our mathematical model produced valid FT4 predictions during MMI treatment in GD and provided the basis for the DigiThy application already serving as a training tool for treating virtual patients. Clinical trial data are required to evaluate whether DigiThy can be approved as a decision support system with automatically generated MMI dosing recommendations.

Modeling of levothyroxine in newborns and infants with congenital hypothyroidism: challenges and opportunities of a rare disease multi-center study

Modeling of retrospectively collected multi-center data of a rare disease in pediatrics is challenging because laboratory data can stem from several decades measured with different assays. Here we present a retrospective pharmacometrics (PMX) based data analysis of the rare disease congenital hypothyroidism (CH) in newborns and infants. Our overall aim is to develop a model that can be applied to optimize dosing in this pediatric patient population since suboptimal treatment of CH during the first 2 years of life is associated with a reduced intelligence quotient between 10 and 14 years. The first goal is to describe a retrospectively collected dataset consisting of 61 newborns and infants with CH up to 2 years of age. Overall, 505 measurements of free thyroxine (FT4) and 510 measurements of thyrotropin or thyroid-stimulating hormone were available from patients receiving substitution treatment with levothyroxine (LT4). The second goal is to introduce a scale/location-scale normalization method to merge available FT4 measurements since 34 different postnatal age- and assay-specific laboratory reference ranges were applied. This method takes into account the change of the distribution of FT4 values over time, i.e. a transformation from right-skewed towards normality during LT4 treatment. The third goal is to develop a practical and useful PMX model for LT4 treatment to characterize FT4 measurements, which is applicable within a clinical setting. In summary, a time-dependent normalization method and a practical PMX model are presented. Since there is no on-going or planned development of new pharmacological approaches for CH, PMX based modeling and simulation can be leveraged to personalize dosing with the goal to enhance longer-term neurological outcome in children with the rare disease CH.

A unified mathematical model of thyroid hormone regulation and implication for personalized treatment of thyroid disorders

Current clinician practice for thyroid hormone regulation of patients is based upon guesswork and experience rather than quantified analysis, which exposes patients under longer risk and discomfort. To quantitatively analyze the thyroid regulation for patients of different thyroid states, we develop a two-dimensional mathematical model that can be applied to analyze the dynamic behaviors of thyroid hormones with or without drug intervention. The unified model can be employed to study the regulation of TSH (thyroid-stimulating hormone) and FT4 (free thyroxine) for euthyroid (normal thyroid) subjects, Hashimoto's thyroiditis, and Graves' disease patients, respectively. The results suggest that the level of TPOAb (thyroid peroxidase antibody) may be a factor determining whether the patient would progress from euthyroid state to subclinical or clinical hypothyroidism, and that increased TRAb (TSH receptor antibody) may lead Graves' disease to deteriorate from the early stage to overt hyperthyroidism. Given the early blood-test data, we demonstrate the feasibility for healthcare professionals to apply our model in choosing an appropriate dosage regimen for patients to achieve the desired TSH and FT4 levels within a specified time frame. This proposed model has the potential to optimize personalized treatment and shorten the therapeutic time for patients suffering from Hashimoto's thyroiditis and Graves' disease.

Mechanistic Computational Model for Extrapolating In vitro Thyroid Peroxidase (TPO) Inhibition Data to Predict Serum Thyroid Hormone Levels in Rats

High throughput (HTP) in vitro assays are developed to screen chemicals for their potential to inhibit thyroid hormones (THs) synthesis. Some of these experiments, such as the thyroid peroxidase (TPO) inhibition assay, are based on thyroid microsomal extracts. However, the regulation of thyroid disruption chemicals (TDCs) is based on THs in vivo serum levels. This necessitates the estimation of TDCs in vivo tissue levels in the thyroid where THs synthesis inhibition by TPO takes place. The in vivo tissue levels of chemicals are controlled by pharmacokinetic determinants such as absorption, distribution, metabolism and excretion (ADME), and can be described quantitatively in physiologically based pharmacokinetic (PBPK) models. An integrative computational model including chemical specific PBPK and TH kinetics models provides a mechanistic quantitative approach to translate thyroidal HTP in vitro assays to in vivo measures of circulating THs serum levels. This computational framework is developed to quantitatively establish the linkage between applied dose, chemical thyroid tissue levels, thyroid TPO inhibition potential, and in vivo TH serum levels. Once this link is established quantitively, the overall model is used to calibrate the TH kinetics parameters using experimental data for THs levels in thyroid tissue and serum for the two drugs Propylthiouracil (PTU) and Methimazole (MMI). The calibrated quantitative framework is then evaluated against literature data for the environmental chemical ethylenethiourea (ETU). The linkage of PBPK and TH kinetics models illustrates a computational framework that can be extrapolated to humans to screen chemicals based on their exposure levels and potential to disrupt serum THs levels in vivo.

Predicting Optimal Combination LT4 + LT3 Therapy for Hypothyroidism Based on Residual Thyroid Function

Objective: To gain insight into the mixed results of reported combination therapy studies conducted with levothyroxine (LT4) and liothyronine (LT3) between 1999 and 2016. Methods: We defined trial success as improved clinical outcome measures and/or patient preference for added LT3. We hypothesized that success depends strongly on residual thyroid function (RTF) as well as the LT3 added to sufficient LT4 dosing to normalize serum T4 and TSH, all rendering T3 levels to at least middle-normal range. The THYROSIM app was used to simulate "what-if" experiments in patients and study designs corresponding to the study trials. The app graphically provided serum total (T4) and free (FT4) thyroxine, total (T3) and free (FT3) triiodothyronine, and TSH responses over time, to different simulated LT4 and combination LT4 + LT3 dosage inputs in patients with primary hypothyroidism. We compared simulation results with available study response data, computed RTF values that matched the data, classified and compared them with trial success measures, and also generated nomograms for optimizing dosages based on RTF estimates. Results: Simulation results generated three categories of patients with different RTFs and T3 and T4 levels at trial endpoints. Four trial groups had >20%, four <10%, and five 10-20% RTF. Four trials were predicted to achieve high, seven medium, and two low T3 levels. From these attributes, we were able to correctly predict 12 of 13 trials deemed successful or not. We generated an algorithm for optimizing dosage combinations suitable for different RTF categories, with the goal of achieving mid-range normal T4, T3 and TSH levels. RTF is estimated from TSH, T4 or T3 measurements prior to any hormone therapy treatment, using three new nonlinear nomograms for computing RTFs from these measurements. Recommended once-daily starting doses are: 100 μg LT4 + 10-12.5 μg LT3; 100 μg LT4 + 7.5-10 μg LT3; and 87.5 μg LT4 + 7.5 μg LT3; for <10%, 10-20%, and >20% RTF, respectively. Conclusion: Unmeasured and variable RTF is a complicating factor in assessing effectiveness of combination LT4 + T3 therapy. We have estimated and partially validated RTFs for most existing trial data, using THYROSIM, and provided an algorithm for estimating RTF from accessible data, and optimizing patient dosing of LT4 + LT3 combinations for future combination therapy trials.

Mathematical Modeling of the Pituitary-Thyroid Feedback Loop: Role of a TSH-T3-Shunt and Sensitivity Analysis

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.

Advances in applied homeostatic modelling of the relationship between thyrotropin and free thyroxine

INTRODUCTION

The relationship between pituitary TSH and thyroid hormones is central to our understanding of thyroid physiology and thyroid function testing. Here, we generated distribution patterns by using validated tools of thyroid modelling.

METHODS

We simulated patterns of individual set points under various conditions, based on a homeostatic model of thyroid feedback control. These were compared with observed data points derived from clinical trials.

RESULTS

A random mix of individual set points was reconstructed by simulative modelling with defined structural parameters. The pattern displayed by the cluster of hypothetical points resembled that observed in a natural control group. Moderate variation of the TSH-FT4 gradient over the functional range introduced further flexibility, implementing a scenario of adaptive set points. Such a scenario may be a realistic possibility for instance in treatment where relationships and equilibria between thyroid parameters are altered by various influences such as LT4 dose and conversion efficiency.

CONCLUSIONS

We validated a physiologically based homeostatic model that permits simulative reconstruction of individual set points. This produced a pattern resembling the observed data under various conditions. Applied modelling, although still experimental at this stage, shows a potential to aid our physiological understanding of the interplay between TSH and thyroid hormones. It should eventually benefit personalised clinical decision making.

An in silico evaluation of treatment regimens for recurrent Clostridium difficile infection

BACKGROUND

Clostridium difficile infection (CDI) is a significant nosocomial infection worldwide, that recurs in as many as 35% of infections. Risk of CDI recurrence varies by ribotype, which also vary in sporulation and germination rates. Whether sporulation/germination mediate risk of recurrence and effectiveness of treatment of recurring CDI remains unclear. We aim to assess the role of sporulation/germination patterns on risk of recurrence, and the relative effectiveness of the recommended tapered/pulsing regimens using an in silico model.

METHODS

We created a compartmental in-host mathematical model of CDI, composed of vegetative cells, toxins, and spores, to explore whether sporulation and germination have an impact on recurrence rates. We also simulated the effectiveness of three tapered/pulsed vancomycin regimens by ribotype.

RESULTS

Simulations underscored the importance of sporulation/germination patterns in determining pathogenicity and transmission. All recommended regimens for recurring CDI tested were effective in reducing risk of an additional recurrence. Most modified regimens were still effective even after reducing the duration or dosage of vancomycin. However, the effectiveness of treatment varied by ribotype.

CONCLUSION

Current CDI vancomycin regimen for treating recurrent cases should be studied further to better balance associated risks and benefits.

Applying a systems approach to thyroid physiology: Looking at the whole with a mitochondrial perspective instead of judging single TSH values or why we should know more about mitochondria to understand metabolism

Classical thinking in endocrine physiology squeezes our diagnostic handling into a simple negative feedback mechanism with a controller and a controlled variable. In the case of the thyroid this is reduced to TSH and fT3 and fT4, respectively. The setting of this tight notion has no free space for any additions. In this paper we want to challenge this model of limited application by proposing a construct based on a systems approach departing from two basic considerations. In first place since the majority of cases of thyroid disease develop and appear during life it has to be considered as an acquired condition. In the second place, our experience with the reversibility of morphological changes makes the autoimmune theory inconsistent.

While medical complexity can expand into the era of OMICS as well as into one where manipulations with the use of knock-outs and -ins are common in science, we have preferred to maintain a simple and practical approach. We will describe the interactions of iron, magnesium, zinc, selenium and coenzyme Q10 with the thyroid axis. The discourse will be then brought into the context of ovarian function, i.e. steroid hormone production. Finally the same elemental players will be presented in relation to the basic mitochondrial machinery that supports the endocrine.

We propose that an intact mitochondrial function can guard the normal endocrine function of both the thyroid as well as of the ovarian axis. The basic elements required for this function appear to be magnesium and iron. In the case of the thyroid, magnesium-ATP acts in iodine uptake and the heme protein peroxidase in thyroid hormone synthesis. A similar biochemical process is found in steroid synthesis with cholesterol uptake being the initial energy-dependent step and later the heme protein ferredoxin 1 which is required for steroid synthesis. Magnesium plays a central role in determining the clinical picture associated with thyroid disease and is also involved in maintaining fertility. With the aid of 3D sonography patients needing selenium and/or coenzyme Q10 can be easily identified. By this we firmly believe that physicians should know more about basic biochemistry and the way it fits into mitochondrial function in order to understand metabolism. Contemplating only TSH is highly reductionistic.

Outline

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Author's profiles and motivation for this analysis

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The philosophical alternatives in science and medicine

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Reductionism vs. systems approach in clinical thyroid disease guidelines

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The entry into complexity: the involvement of the musculoskeletal system

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Integrating East and West: teachings from Chinese Medicine and from evidence based medicine (EBM)

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Can a mathematical model represent complexity in the daily thyroid practice?

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How effective is thyroxine treatment?

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Resolving the situation of residual symptoms in treated patients with thyroid disease

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Importance of iron, zinc and magnesium in relation to thyroid function

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Putting together new concepts related to thyroid function for a systems approach

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Expanding our model into general aspects of medicine

Parameter estimation for multistage clonal expansion models from cancer incidence data: A practical identifiability analysis

Many cancers are understood to be the product of multiple somatic mutations or other rate-limiting events. Multistage clonal expansion (MSCE) models are a class of continuous-time Markov chain models that capture the multi-hit initiation–promotion–malignant-conversion hypothesis of carcinogenesis. These models have been used broadly to investigate the epidemiology of many cancers, assess the impact of carcinogen exposures on cancer risk, and evaluate the potential impact of cancer prevention and control strategies on cancer rates. Structural identifiability (the analysis of the maximum parametric information available for a model given perfectly measured data) of certain MSCE models has been previously investigated. However, structural identifiability is a theoretical property and does not address the limitations of real data. In this study, we use pancreatic cancer as a case study to examine the practical identifiability of the two-, three-, and four-stage clonal expansion models given age-specific cancer incidence data using a numerical profile-likelihood approach. We demonstrate that, in the case of the three- and four-stage models, several parameters that are theoretically structurally identifiable, are, in practice, unidentifiable. This result means that key parameters such as the intermediate cell mutation rates are not individually identifiable from the data and that estimation of those parameters, even if structurally identifiable, will not be stable. We also show that products of these practically unidentifiable parameters are practically identifiable, and, based on this, we propose new reparameterizations of the model hazards that resolve the parameter estimation problems. Our results highlight the importance of identifiability to the interpretation of model parameter estimates.

Parameter estimation from data is an important part of mathematical modeling, and structural identifiability is the study of what parametric information exists, for a given model, in ideal data. Unfortunately, for a variety of reasons, there is often less information available in our real data sets. The study of these problems is called practical identifiability. In this study, we consider a family of models of cancer biology that are commonly used to explain cancer incidence in terms of underlying biological parameters. Using profile likelihoods, a widely applicable numerical tool, we demonstrate that even though the more complex models we consider have theoretically more identifiable parameters, the data contains only three pieces of practically identifiable information for each model: the product of the initiating mutation rates, the net cell proliferation rate, and the scaled malignant conversion rate. This result can be interpreted biologically: we can determine only the product of cell mutation rates not the intermediate rates themselves. Our result limits the interpretability of previous work, but we propose a novel parameterization to resolve the identifiability issue. Ultimately, our analysis demonstrates the importance of verifying the practical identifiability of parameters before assigning too much weight to the interpretation of their estimated values.

THYROSIM App for Education and Research Predicts Potential Health Risks of Over-the-Counter Thyroid Supplements

BACKGROUND

Computer simulation tools for education and research are making increasingly effective use of the Internet and personal devices. To facilitate these activities in endocrinology and metabolism, a mechanistically based simulator of human thyroid hormone and thyrotropin (TSH) regulation dynamics was developed and further validated, and it was implemented as a facile and freely accessible web-based and personal device application: the THYROSIM app. This study elucidates and demonstrates its utility in a research context by exploring key physiological effects of over-the-counter thyroid supplements.

METHODS

THYROSIM has a simple and intuitive user interface for teaching and conducting simulated "what-if" experiments. User-selectable "experimental" test-input dosages (oral, intravenous pulses, intravenous infusions) are represented by animated graphical icons integrated with a cartoon of the hypothalamic-pituitary-thyroid axis. Simulations of familiar triiodothyronine (T3), thyroxine (T4), and TSH temporal dynamic responses to these exogenous stimuli are reported graphically, along with normal ranges on the same single interface page; and multiple sets of simulated experimental results are superimposable to facilitate comparative analyses.

RESULTS AND CONCLUSIONS

This study shows that THYROSIM accurately reproduces a wide range of published clinical study data reporting hormonal kinetic responses to large and small oral hormone challenges. Simulation examples of partial thyroidectomies and malabsorption illustrate typical usage by optionally changing thyroid gland secretion and/or gut absorption rates--expressed as percentages of normal--as well as additions of oral hormone dosing, all directly on the interface, and visualizing the kinetic responses to these challenges. Classroom and patient education usage--with public health implications--is illustrated by predictive simulated responses to nonprescription thyroid health supplements analyzed previously for T3 and T4 content. Notably, it was found that T3 in supplements has potentially more serious pathophysiological effects than does T4--concomitant with low-normal TSH levels. Some preparations contain enough T3 to generate thyrotoxic conditions, with supernormal serum T3-spiking and subnormal serum T4 and TSH levels and, in some cases, with normal or low-normal range TSH levels due to thyroidal axis negative feedback. These results suggest that appropriate regulation of these products is needed.

The Relationship between Population T4/TSH Set Point Data and T4/TSH Physiology

Context. Population studies of the distribution of T4/TSH set points suggest a more complex inverse relationship between T4 and TSH than that suggested by physiological studies. The reasons for the similarities and differences between the curves describing these relationships are unresolved. Methods. We subjected the curve, derived from empiric data, describing the TSH suppression response to T4, and the more mathematically derived curve describing the T4 response to TSH, to the different possible models of population variation. The implied consequences of these in terms of generating a population distribution of T4/TSH equilibrium points (a “population curve”) were generated and compared to the empiric population curve. The physiological responses to primary hypothyroidism and hyperthyroidism were incorporated into the analysis. Conclusions. Though the population curve shows a similarly inverse relationship, it is describing a different relationship than the curve describing the suppression of TSH by T4. The population curve is consistent with the physiological studies of the TSH response to T4 and implies a greater interindividual variation in the positive thyroid T4 response to TSH than in the central inhibitory TSH response to T4. The population curve in the dysthyroid states is consistent with known physiological responses to these states.

Calculated Parameters of Thyroid Homeostasis: Emerging Tools for Differential Diagnosis and Clinical Research

Although technical problems of thyroid testing have largely been resolved by modern assay technology, biological variation remains a challenge. This applies to subclinical thyroid disease, non-thyroidal illness syndrome, and those 10% of hypothyroid patients, who report impaired quality of life, despite normal thyrotropin (TSH) concentrations under levothyroxine (L-T4) replacement. Among multiple explanations for this condition, inadequate treatment dosage and monotherapy with L-T4 in subjects with impaired deiodination have received major attention. Translation to clinical practice is difficult, however, since univariate reference ranges for TSH and thyroid hormones fail to deliver robust decision algorithms for therapeutic interventions in patients with more subtle thyroid dysfunctions. Advances in mathematical and simulative modeling of pituitary-thyroid feedback control have improved our understanding of physiological mechanisms governing the homeostatic behavior. From multiple cybernetic models developed since 1956, four examples have also been translated to applications in medical decision-making and clinical trials. Structure parameters representing fundamental properties of the processing structure include the calculated secretory capacity of the thyroid gland (SPINA-GT), sum activity of peripheral deiodinases (SPINA-GD) and Jostel's TSH index for assessment of thyrotropic pituitary function, supplemented by a recently published algorithm for reconstructing the personal set point of thyroid homeostasis. In addition, a family of integrated models (University of California-Los Angeles platform) provides advanced methods for bioequivalence studies. This perspective article delivers an overview of current clinical research on the basis of mathematical thyroid models. In addition to a summary of large clinical trials, it provides previously unpublished results of validation studies based on simulation and clinical samples.

Identifiability Results for Several Classes of Linear Compartment Models

Identifiability concerns finding which unknown parameters of a model can be estimated, uniquely or otherwise, from given input-output data. If some subset of the parameters of a model cannot be determined given input-output data, then we say the model is unidentifiable. In this work, we study linear compartment models, which are a class of biological models commonly used in pharmacokinetics, physiology, and ecology. In past work, we used commutative algebra and graph theory to identify a class of linear compartment models that we call identifiable cycle models, which are unidentifiable but have the simplest possible identifiable functions (so-called monomial cycles). Here we show how to modify identifiable cycle models by adding inputs, adding outputs, or removing leaks, in such a way that we obtain an identifiable model. We also prove a constructive result on how to combine identifiable models, each corresponding to strongly connected graphs, into a larger identifiable model. We apply these theoretical results to several real-world biological models from physiology, cell biology, and ecology.

Single-dose T3 administration: kinetics and effects on biochemical and physiological parameters

BACKGROUND

As changes in thyroid stimulating hormone (TSH), thyroid hormones, and vital signs after administration of a single dose of liothyronine have typically only been documented for 24 hours, we documented these parameters more than 96 hours.

METHODS

Blood samples were obtained for 4 days after administration of 50-mcg liothyronine to 12 healthy euthyroid participants. Concentrations of total and free triiodothyronine, free and total thyroxine, and TSH were measured. Vital signs were documented.

RESULTS

Triiodothyronine concentrations peaked at 2.5 hours after liothyronine administration. Heart rate (HR) increased by 5 hours after liothyronine administration, subsequently reaching a value higher than baseline (P = 0.009). Suppression of TSH concentrations began at 2 hours. The nadir TSH value at 12 hours was significantly different from baseline (P < 0.001) and remained lower than the baseline value for 2-3 days.

CONCLUSIONS

A single dose of liothyronine has both short-term and long-term effects. There is clearly a different lag time between the serum concentrations of triiodothyronine and its effects on the heart and pituitary, respectively. The increase in serum triiodothyronine concentration occurred within hours and was then followed by an increase in HR. The increased HR was transient and was followed by a reduction in TSH concentration. The suppression of TSH was delayed but was more sustained. Thus, sustained TSH reduction beyond 24 hours was achieved by a single dose of liothyronine that produced only brief increases in serum triiodothyronine levels and transient increases in HR.

Homeostatic Control of the Thyroid-Pituitary Axis: Perspectives for Diagnosis and Treatment

The long-held concept of a proportional negative feedback control between the thyroid and pituitary glands requires reconsideration in the light of more recent studies. Homeostatic equilibria depend on dynamic inter-relationships between thyroid hormones and pituitary thyrotropin (TSH). They display a high degree of individuality, thyroid-state-related hierarchy, and adaptive conditionality. Molecular mechanisms involve multiple feedback loops on several levels of organization, different time scales, and varying conditions of their optimum operation, including a proposed feedforward motif. This supports the concept of a dampened response and multistep regulation, making the interactions between TSH, FT4, and FT3 situational and mathematically more complex. As a homeostatically integrated parameter, TSH becomes neither normatively fixed nor a precise marker of euthyroidism. This is exemplified by the therapeutic situation with l-thyroxine (l-T4) where TSH levels defined for optimum health may not apply equivalently during treatment. In particular, an FT3-FT4 dissociation, discernible FT3-TSH disjoint, and conversion inefficiency have been recognized in l-T4-treated athyreotic patients. In addition to regulating T4 production, TSH appears to play an essential role in maintaining T3 homeostasis by directly controlling deiodinase activity. While still allowing for tissue-specific variation, this questions the currently assumed independence of the local T3 supply. Rather it integrates peripheral and central elements into an overarching control system. On l-T4 treatment, altered equilibria have been shown to give rise to lower circulating FT3 concentrations in the presence of normal serum TSH. While data on T3 in tissues are largely lacking in humans, rodent models suggest that the disequilibria may reflect widespread T3 deficiencies at the tissue level in various organs. As a consequence, the use of TSH, valuable though it is in many situations, should be scaled back to a supporting role that is more representative of its conditional interplay with peripheral thyroid hormones. This reopens the debate on the measurement of free thyroid hormones and encourages the identification of suitable biomarkers. Homeostatic principles conjoin all thyroid parameters into an adaptive context, demanding a more flexible interpretation in the accurate diagnosis and treatment of thyroid dysfunction.

Guidelines for the treatment of hypothyroidism: prepared by the american thyroid association task force on thyroid hormone replacement

BACKGROUND

A number of recent advances in our understanding of thyroid physiology may shed light on why some patients feel unwell while taking levothyroxine monotherapy. The purpose of this task force was to review the goals of levothyroxine therapy, the optimal prescription of conventional levothyroxine therapy, the sources of dissatisfaction with levothyroxine therapy, the evidence on treatment alternatives, and the relevant knowledge gaps. We wished to determine whether there are sufficient new data generated by well-designed studies to provide reason to pursue such therapies and change the current standard of care. This document is intended to inform clinical decision-making on thyroid hormone replacement therapy; it is not a replacement for individualized clinical judgment.

METHODS

Task force members identified 24 questions relevant to the treatment of hypothyroidism. The clinical literature relating to each question was then reviewed. Clinical reviews were supplemented, when relevant, with related mechanistic and bench research literature reviews, performed by our team of translational scientists. Ethics reviews were provided, when relevant, by a bioethicist. The responses to questions were formatted, when possible, in the form of a formal clinical recommendation statement. When responses were not suitable for a formal clinical recommendation, a summary response statement without a formal clinical recommendation was developed. For clinical recommendations, the supporting evidence was appraised, and the strength of each clinical recommendation was assessed, using the American College of Physicians system. The final document was organized so that each topic is introduced with a question, followed by a formal clinical recommendation. Stakeholder input was received at a national meeting, with some subsequent refinement of the clinical questions addressed in the document. Consensus was achieved for all recommendations by the task force.

RESULTS

We reviewed the following therapeutic categories: (i) levothyroxine therapy, (ii) non-levothyroxine-based thyroid hormone therapies, and (iii) use of thyroid hormone analogs. The second category included thyroid extracts, synthetic combination therapy, triiodothyronine therapy, and compounded thyroid hormones.

CONCLUSIONS

We concluded that levothyroxine should remain the standard of care for treating hypothyroidism. We found no consistently strong evidence for the superiority of alternative preparations (e.g., levothyroxine-liothyronine combination therapy, or thyroid extract therapy, or others) over monotherapy with levothyroxine, in improving health outcomes. Some examples of future research needs include the development of superior biomarkers of euthyroidism to supplement thyrotropin measurements, mechanistic research on serum triiodothyronine levels (including effects of age and disease status, relationship with tissue concentrations, as well as potential therapeutic targeting), and long-term outcome clinical trials testing combination therapy or thyroid extracts (including subgroup effects). Additional research is also needed to develop thyroid hormone analogs with a favorable benefit to risk profile.

Determining identifiable parameter combinations using subset profiling

Identifiability is a necessary condition for successful parameter estimation of dynamic system models. A major component of identifiability analysis is determining the identifiable parameter combinations, the functional forms for the dependencies between unidentifiable parameters. Identifiable combinations can help in model reparameterization and also in determining which parameters may be experimentally measured to recover model identifiability. Several numerical approaches to determining identifiability of differential equation models have been developed, however the question of determining identifiable combinations remains incompletely addressed. In this paper, we present a new approach which uses parameter subset selection methods based on the Fisher Information Matrix, together with the profile likelihood, to effectively estimate identifiable combinations. We demonstrate this approach on several example models in pharmacokinetics, cellular biology, and physiology.

Hypothalamus-pituitary-thyroid feedback control: implications of mathematical modeling and consequences for thyrotropin (TSH) and free thyroxine (FT4) reference ranges

The components of thyrotropic feedback control are well established in mainstream physiology and endocrinology, but their relation to the whole system's integrated behavior remains only partly understood. Most modeling research seeks to derive a generalized model for universal application across all individuals. We show how parameterizable models, based on the principles of control theory, tailored to the individual, can fill these gaps. We develop a system network describing the closed-loop behavior of the hypothalamus-pituitary (HP)-thyroid interaction and the set point targeted by the control system at equilibrium. The stability of this system is defined by using loop gain conditions. Defined points of homeostasis of the hypothalamus-pituitary-thyroid (HPT) feedback loop found at the intersections of the HP and thyroid transfer functions at the boundaries of normal reference ranges were evaluated by loop gain calculations. At equilibrium, the feedback control approaches a point defined in both dimensions by a [TSH]-[FT4] coordinate for which the loop gain is greater than unity. This model describes the emergence of homeostasis of the HPT axis from characteristic curves of HP and thyroid, thus supporting the validity of the translation between physiological knowledge and clinical reference ranges.

A novel minimal mathematical model of the hypothalamus-pituitary-thyroid axis validated for individualized clinical applications

The hypothalamus-pituitary-thyroid (HPT) axis represents a complex, non-linear thyroid hormone system in vertebrates governed by numerous variables. The common modeling approach until now aims at a comprehensive inclusion of all known physiological influences. In contrast, we develop a parsimonious mathematical model that integrates the hypothalamus-pituitary (HP) complex as an endocrinologic unit based on a parameterized negative exponential function between free thyroxine (FT4) as stimulus and thyrotropin (thyroid stimulating hormone, TSH) as response. Model validation with clinical data obtained from geographically different hospitals revealed a goodness-of-fit largely ranging between 90% < R² < 99%, each HP characteristic curve being uniquely defined for each individual akin to a fingerprint. Specifically, the HP model represents the afferent feedback limb of the HPT axis while the efferent limb is mathematically depicted by TSH input to the thyroid gland which responds by secreting T4 as its chief output. The complete HPT axis thus forms a closed loop system with negative feedback resulting in an equilibrium state or homeostasis under defined conditions illustrated by the intersection of the HP and thyroid response characteristics. In this treatise, we demonstrate how this mathematical approach facilitates homeostatic set points computation for personalized dosing of thyroid medications of patients to individualized euthyroid states.

Systems pharmacology modeling of drug-induced modulation of thyroid hormones in dogs and translation to human

PURPOSE

To develop a systems pharmacology model based on hormone physiology and pharmacokinetic-pharmacodynamic concepts describing the impact of thyroperoxidase (TPO) inhibition on thyroid hormone homeostasis in the dog and to predict drug-induced changes in thyroid hormones in humans.

METHODS

A population model was developed based on a simultaneous analysis of concentration-time data of T₄, T₃ and TSH in dogs following once daily oral dosing for up to 6-months of a myeloperoxidase inhibitor (MPO-IN1) with TPO inhibiting properties. The model consisted of linked turnover compartments for T₄, T₃ and TSH including a negative feedback from T₄ on TSH concentrations.

RESULTS

The model could well describe the concentration-time profiles of thyroid hormones in dog. Successful model validation was performed by predicting the hormone concentrations during 1-month administration of MPO-IN2 based on its in vitro dog TPO inhibition potency. Using human thyroid hormone turnover rates and TPO inhibitory potency, the human T₄ and TSH concentrations upon MPO-IN1 treatment were predicted well.

CONCLUSIONS

The model provides a scientific framework for the prediction of drug induced effects on plasma thyroid hormones concentrations in humans via TPO inhibition based on results obtained in in vitro and animal studies.

Identifiability and estimation of multiple transmission pathways in cholera and waterborne disease

Cholera and many waterborne diseases exhibit multiple characteristic timescales or pathways of infection, which can be modeled as direct and indirect transmission. A major public health issue for waterborne diseases involves understanding the modes of transmission in order to improve control and prevention strategies. An important epidemiological question is: given data for an outbreak, can we determine the role and relative importance of direct vs. environmental/waterborne routes of transmission? We examine whether parameters for a differential equation model of waterborne disease transmission dynamics can be identified, both in the ideal setting of noise-free data (structural identifiability) and in the more realistic setting in the presence of noise (practical identifiability). We used a differential algebra approach together with several numerical approaches, with a particular emphasis on identifiability of the transmission rates. To examine these issues in a practical public health context, we apply the model to a recent cholera outbreak in Angola (2006). Our results show that the model parameters-including both water and person-to-person transmission routes-are globally structurally identifiable, although they become unidentifiable when the environmental transmission timescale is fast. Even for water dynamics within the identifiable range, when noisy data are considered, only a combination of the water transmission parameters can practically be estimated. This makes the waterborne transmission parameters difficult to estimate, leading to inaccurate estimates of important epidemiological parameters such as the basic reproduction number (R0). However, measurements of pathogen persistence time in environmental water sources or measurements of pathogen concentration in the water can improve model identifiability and allow for more accurate estimation of waterborne transmission pathway parameters as well as R0. Parameter estimates for the Angola outbreak suggest that both transmission pathways are needed to explain the observed cholera dynamics. These results highlight the importance of incorporating environmental data when examining waterborne disease.

TSH and Thyrotropic Agonists: Key Actors in Thyroid Homeostasis

This paper provides the reader with an overview of our current knowledge of hypothalamic-pituitary-thyroid feedback from a cybernetic standpoint. Over the past decades we have gained a plethora of information from biochemical, clinical, and epidemiological investigation, especially on the role of TSH and other thyrotropic agonists as critical components of this complex relationship. Integrating these data into a systems perspective delivers new insights into static and dynamic behaviour of thyroid homeostasis. Explicit usage of this information with mathematical methods promises to deliver a better understanding of thyrotropic feedback control and new options for personalised diagnosis of thyroid dysfunction and targeted therapy, also by permitting a new perspective on the conundrum of the TSH reference range.

Simulation of post-thyroidectomy treatment alternatives for triiodothyronine or thyroxine replacement in pediatric thyroid cancer patients

BACKGROUND

As in adults, thyroidectomy in pediatric patients with differentiated thyroid cancer is often followed by (131)I remnant ablation. A standard protocol is to give normalizing oral thyroxine (T(4)) or triiodothyronine (T(3)) after surgery and then withdraw it for 2 to 6 weeks. Thyroid remnants or metastases are treated most effectively when serum thyrotropin (TSH) is high, but prolonged withdrawals should be avoided to minimize hypothyroid morbidity.

METHODS

A published feedback control system model of adult human thyroid hormone regulation was modified for children using pediatric T(4) kinetic data. The child model was developed from data for patients ranging from 3 to 9 years old. We simulated a range of T(4) and T(3) replacement protocols for children, exploring alternative regimens for minimizing the withdrawal period, while maintaining normal or suppressed TSH during replacement. The results are presented with the intent of providing a quantitative basis to guide further studies of pediatric treatment options. Replacement was simulated for up to 3 weeks post-thyroidectomy, followed by various withdrawal periods. T(4) vs. T(3) replacement, remnant size, dose size, and dose frequency were tested for effects on the time for TSH to reach 25 mU/L (withdrawal period).

RESULTS

For both T(3) and T(4) replacement, higher doses were associated with longer withdrawal periods. T(3) replacement yielded shorter withdrawal periods than T(4) replacement (up to 3.5 days versus 7-10 days). Higher than normal serum T(3) concentrations were required to normalize or suppress TSH during T(3) monotherapy, but not T(4) monotherapy. Larger remnant sizes resulted in longer withdrawal periods if T(4) replacement was used, but had little effect for T(3) replacement.

CONCLUSIONS

T(3) replacement yielded withdrawal periods about half those for T(4) replacement. Higher than normal hormone levels under T(3) monotherapy can be partially alleviated by more frequent, smaller doses (e.g., twice a day). LT(4) may be the preferred option for most children, given the convenience of single daily dosing and familiarity of pediatric endocrinologists with its administration. Remnant effects on withdrawal period highlight the importance of minimizing remnant size.

Predicting chemical impacts on vertebrate endocrine systems

Animals have evolved diverse protective mechanisms for responding to toxic chemicals of both natural and anthropogenic origin. From a governmental regulatory perspective, these protective responses complicate efforts to establish acceptable levels of chemical exposure. To explore this issue, we considered vertebrate endocrine systems as potential targets for environmental contaminants. Using the hypothalamic-pituitary-thyroid (HPT), hypothalamic-pituitary-gonad (HPG), and hypothalamic-pituitary-adrenal (HPA) axes as case examples, we identified features of these systems that allow them to accommodate and recover from chemical insults. In doing so, a distinction was made between effects on adults and those on developing organisms. This distinction was required because endocrine system disruption in early life stages may alter development of organs and organ systems, resulting in permanent changes in phenotypic expression later in life. Risk assessments of chemicals that impact highly regulated systems must consider the dynamics of these systems in relation to complex environmental exposures. A largely unanswered question is whether successful accommodation to a toxic insult exerts a fitness cost on individual animals, resulting in adverse consequences for populations. Mechanistically based mathematical models of endocrine systems provide a means for better understanding accommodation and recovery. In the short term, these models can be used to design experiments and interpret study findings. Over the long term, a set of validated models could be used to extrapolate limited in vitro and in vivo testing data to a broader range of untested chemicals, species, and exposure scenarios. With appropriate modification, Tier 2 assays developed in support of the U.S. Environmental Protection Agency's Endocrine Disruptor Screening Program could be used to assess the potential for accommodation and recovery and inform the development of mechanistically based models.

TSH regulation dynamics in central and extreme primary hypothyroidism

BACKGROUND

Thyrotropin (TSH) changes in extreme primary hypothyroidism include increased secretion, slowed degradation, and diminished or absent TSH circadian rhythms. Diminished rhythms are also observed in central hypothyroid patients and have been speculated to be a cause of central hypothyroidism. We examined whether TSH secretion saturation, previously suggested in extreme primary hypothyroidism, might explain diminished circadian rhythms in both disorders.

METHODS

We augmented and extended the range of our published feedback control system model to reflect nonlinear changes in extreme primary hypothyroidism, including putative TSH secretion saturation, and quantified and validated it using multiple clinical datasets ranging from euthyroid to extreme hypothyroid (postthyroidectomy). We simulated central hypothyroidism by reducing overall TSH secretion and also simulated normal TSH secretion without circadian oscillation, maintaining plasma TSH at constant normal levels. We also utilized the validated model to explore thyroid hormone withdrawal protocols used to prepare remnant ablation in thyroid cancer patients postthyroidectomy.

RESULTS

Both central and extreme primary hypothyroidism simulations yielded low thyroid hormone levels and reduced circadian rhythms, with simulated daytime TSH levels low-to-normal for central hypothyroidism and increased in primary hypothyroidism. Simulated plasma TSH showed a rapid rise immediately following triiodothyronine (T(3)) withdrawal postthyroidectomy, compared with a slower rise after thyroxine withdrawal or postthyroidectomy without replacement.

CONCLUSIONS

Diminished circadian rhythms in central and extreme primary hypothyroidism can both be explained by pituitary TSH secretion reaching maximum capacity. In simulated remnant ablation protocols using the extended model, TSH shows a more rapid rise after T(3) withdrawal than after thyroxine withdrawal postthyroidectomy, supporting the use of replacement with T(3) prior to (131)I treatment.

Competitive inhibition of thyroidal uptake of dietary iodide by perchlorate does not describe perturbations in rat serum total T4 and TSH

BACKGROUND

Perchlorate (ClO4(-)) is an environmental contaminant known to disrupt the thyroid axis of many terrestrial and aquatic species. ClO4(-) competitively inhibits iodide uptake into the thyroid at the sodium/iodide symporter and disrupts hypothalamic-pituitary-thyroid (HPT) axis homeostasis in rodents.

OBJECTIVE

We evaluated the proposed mode of action for ClO4(-)-induced rat HPT axis perturbations using a biologically based dose-response (BBDR) model of the HPT axis coupled with a physiologically based pharmacokinetic model of ClO4(-).

METHODS

We configured a BBDR-HPT/ClO4(-) model to describe competitive inhibition of thyroidal uptake of dietary iodide by ClO4(-) and used it to simulate published adult rat drinking water studies. We compared model-predicted serum thyroid-stimulating hormone (TSH) and total thyroxine (TT4) concentrations with experimental observations reported in these ClO4(-) drinking water studies.

RESULTS

The BBDR-HPT/ClO4(-) model failed to predict the ClO4(-)-induced onset of disturbances in the HPT axis. Using ClO4(-) inhibition of dietary iodide uptake into the thyroid, the model underpredicted both the rapid decrease in serum TT4 concentrations and the rise in serum TSH concentrations.

CONCLUSIONS

Assuming only competitive inhibition of thyroidal uptake of dietary iodide, BBDR-HPT/ClO4(-) model calculations were inconsistent with the rapid decrease in serum TT4 and the corresponding increase in serum TSH. Availability of bound iodide in the thyroid gland governed the rate of hormone secretion from the thyroid. ClO4(-) is translocated into the thyroid gland, where it may act directly or indirectly on thyroid hormone synthesis/secretion in the rat. The rate of decline in serum TT4 in these studies after 1 day of treatment with ClO4(-) appeared consistent with a reduction in thyroid hormone production/secretion. This research demonstrates the utility of a biologically based model to evaluate a proposed mode of action for ClO4(-) in a complex biological process.

TSH-based protocol, tablet instability, and absorption effects on L-T4 bioequivalence

BACKGROUND

FDA Guidance for pharmacokinetic (PK) testing of levothyroxine (L-T(4)) for interbrand bioequivalence has evolved recently. Concerns remain about efficacy and safety of the current protocol, based on PK analysis following supraphysiological L-T(4) dosing in euthyroid volunteers, and recent recalls due to intrabrand manufacturing problems also suggest need for further refinement. We examine these interrelated issues quantitatively, using simulated what-if scenarios testing efficacy of a TSH-based protocol and tablet stability and absorption, to enhance precision of L-T(4) bioequivalence methods.

METHODS

We use an updated simulation model of human thyroid hormone regulation quantified and validated from data that span a wide range of normal and abnormal thyroid system function. Bioequivalence: We explored a TSH-based protocol, using normal replacement dosing in simulated thyroidectomized patients, switching brands after 8 weeks of full replacement dosing. We simulated effects of tablet potency differences and intestinal absorption differences on predicted plasma TSH, T(4), and triiodothyronine (T(3)) dynamics. Stability: We simulated effects of potency decay and lot-by-lot differences in realistic scenarios, using actual tablet potency data spanning 2 years, comparing the recently reduced 95-105% FDA-approved potency range with the original 90-110% range.

RESULTS

A simulated decrease as small as 10-15% in L-T(4) or its absorption generated TSH concentrations outside the bioequivalence target range (0.5-2.5 mU/L TSH), whereas T(3) and T(4) plasma levels were maintained normal. For a 25% reduction, steady-state TSH changed 300% (from 1.5 to 6 mU/L) compared with <25% for both T(4) and T(3) (both within their reference ranges). Stability: TSH, T(4), and T(3) remained within normal ranges for most potency decay scenarios, but tablets of the same dose strength and brand were not bioequivalent between lots and between fresh and near-expired tablets.

CONCLUSIONS

A pharmacodynamic TSH-measurement bioequivalence protocol, using normal L-T(4) replacement dosing in athyreotic volunteers, is likely to be more sensitive and safer than current FDA Guidance based on T(4) PK. The tightened 95-105% allowable potency range for L-T(4) tablets is a significant improvement, but otherwise acceptable potency differences (whether due to potency decay or lot-by-lot inconsistencies) may be problematic for some patients, for example, those undergoing high-dose L-T(4) therapy for cancer.