Editorial: Mechanistic, machine learning and hybrid models of the “other” endocrine regulatory systems in health & disease

This work addresses endocrine regulation rather teleologically, using a new mechanistic model of thyroid hormone feedback regulation to demonstrate the thesis of the Hoermann group. Endocrine regulation in the hypothalamic-pituitary-thyroid (HPT) axis is orchestrated by physiological circuits which integrate multiple internal and external influences, with the goal of providing responses to overt biological challenges, either to defend the homeostatic range of a target hormone, or adapt it to changing environmental conditions. As a proof-of-concept, the authors develop their nonlinear ordinary differential equation (ODE) model in a manner that elucidates the principles of and insights into HPT axis regulation, as a cascade of targeted and nonlinear feedforward and feedback pathways. For thyroid hormone (TH) regulation, it includes mechanisms for both homeostasis of the biologically active hormone free triiodothyronine (FT3), and adaptation of the homeostatic state of FT3 to new levels, when needed, thereby providing optimum resilience in stressful situations.Approach doi.org/10.3389/fendo.202 The Wolff group addresses the problem of optimal thyroid hormone replacement therapy for average human hypothyroid patients, using engineering optimal control theory applied to their published nonlinear ODE model. They apply a model predictive controller (MPC) approach to determine optimal dosages that normalize hormone levels, using either single hormone LT4 or LT4/LT3 combined therapy. Their simulation experiments resulted in combined dosages slightly better for most. But in patients with several rare and specific genetic variants -a particular novelty of this work, fine tuning their model simulations suggests one or the other modality depending on the variant. The Cruz-Loya -Chu group refined and adapted their published ODE model of TH (T3 and T4) regulation in average humans, THYROSIM, turning it into a personalized model and simulation tool, p-THYROSIM -with personalization based on gender, BMI and individual hormone levels. The goal was to better optimize replacement single hormone LT4 and combined LT4+LT3 dosing for hypothyroid patients, and also to better understand how gender and BMI impact thyroid dynamical regulation over time. They quantified their new model with 3 large experimental datasets and validated it with a fourth containing data from distinct male and female patients across a wide range of BMIs. They also computed unmeasured residual thyroid function (RTF) across a wide range of BMIs -a novelty of this work -from this male and female patient data and showed that neither BMI nor gender had any effect on RTF predictions for their patient cohort data -supporting tight TH regulation independent of gender and body size.They showed that p-THYROSIM can provide accurate monotherapies for male and female hypothyroid patients, personalized with their BMIs. Where combination therapy is warranted, their results predict that very little (5-7.5 μg) LT3 is needed in addition to LT4 to restore euthyroid levels in all patient cohorts. As another novelty, graphs provided allow estimation of unmeasurable RTFs for individual patients from their hormone measurements before treatment.Light-induced synchronization of the SCN coupled oscillators and implications for entraining the HPA axis doi.org/10.3389/fendo.202The suprachiasmatic nucleus (SCN) synchronizes the physiological rhythms to the external light-dark cycle and tunes the dynamics of circadian rhythms to photoperiod fluctuations. Its output regulates adrenal glucocorticoid levels, elevated in short photoperiods and associated with peak disease incidence. The Li and Androulakis group propose a new mechanistic mathematical model that includes a multi-cellular SCN compartment and the HPA (HP-adrenal) axis and investigate the properties of the circadian timing system under photoperiod changes using their model. It predicts that this network is more energy-efficient than the distance-dependent network. Coupling the SCN network by intra-subpopulation and inter-subpopulation forces, they identified the negative correlation between robustness and plasticity of the oscillatory network. The HPA rhythms were predicted to be strongly entrained to the SCN rhythms with a proinflammatory high-amplitude glucocorticoid profile under SP. They postulate that these synchronization and circadian dynamics alterations might govern the seasonal variation of disease incidence and its symptom severity.Network properties of electrically coupled bursting pituitary cells doi.org/10.3389/fendo.2022.936160Individual pituitary cells are nonneuronal excitable cells exhibiting a variety of neuronlike "bursting" behavior. In this modeling and computational study, Fazli and Bertram investigate the coupled network properties of endocrine pituitary cells. This issue is crucial, as the functioning of the pituitary gland at the multicellular level remains unclear. Within the framework of slow-fast multiple time scale) dynamical systems applied to electrophysiology, they examined how local coupling properties between pituitary cells support large-scale network activity and synchronization of bursting oscillations among the population. The authors made the surprising, counter-intuitive finding that structural hubs (cells with extensive couplings to other cells) are typically not functional hubs (cells synchronized with many other cells), which is an important step toward understanding pituitary cell networks.Impulsive Time Series Modeling with Application to Luteinizing Hormone Data doi.org/10.3389/fendo.2022 Pituitary and hypothalamic hormones, especially gonadotropin releasing hormone (GnRH) and luteinizing hormone (LH), two major players in reproductive function, exhibit remarkable pulsatile secretion patterns. In this modeling and data-analysis study, reconstruction of pulse times from undersampled hormonal time series data is addressed using control theory and "impulsive" ODEs. Runvik and Medvedev use an innovative approach, jointly estimating impulsive time series inputs and continuous system parameters for analyzing LH secretion rhythms in males. They also illustrate, with cortisol data, how their method can be applied to other endocrine systems.A mechanism for ovulation number control doi.org/10.3389/fendo.2022.816967In mammals the number of ovulations is species-specific and tightly controlled. Ovulation is the endpoint of an extremely complex process, ovarian follicle development and selection from the most mature follicles. Despite this complexity, phenomenological models can capture salient features of follicle selection and its quantitative output, ovulation number. In this modeling and computational study, Shilo, Mayo and Alon revisit the seminal Lacker's model, introducing a physiologically-based, androgen-like, biphasic effect that can signal relative follicle sizes. Through a thorough qualitative analysis, they explain how their model manages to reproduce both the linear growth of dominant follicles in physiological situations, and the decline of growth-arrested follicles in the pathologic situation of polycystic ovary syndrome.An overview of deep learning applications in precocious puberty and thyroid dysfunction doi.org/10.3389/fendo.202 This paper, which includes a useful tutorial introduction to ML methods, reviews deep learning (DL) methods and their applications in clinical endocrinology, with a special focus on the assessment of thyroid status (hypo-, eu-or hyperthyroid) and diagnosis of precocious puberty. The authors provide comprehensive cues for critical analysis of DL approaches in an endocrine context, including dataset building and preprocessing, management of imbalanced data or missing values, selection and implementation of neural network architecture, and use of metrics to assess accuracy and computing results. While already developed DL approaches are efficient in predicting the thyroid status from standard lab tests and assessing the biological bone age as a witness of precocious puberty, further improvements are expected from embedding multisource information in DL-based endocrine diagnoses.The mechanistic and ML modeling techniques used or developed in these works by seasoned and new researchers are highly sophisticated; and their application to endocrine systems has resulted in deep insights or clinically useful results in several of them. We solicited but did not get any submissions on true hybrid MEC-ML modeling in endocrinology, although we know some groups are working on this melding of methodologies. MEC models inherently include enormous informational "data" about system connectivity (mechanism), the kind of data that greatly constrain the space of possible solution outputs for given exogenous inputs, initial conditions or internal system perturbations. For this very reason, they typically can be successfully quantified with relatively small input-output response data sets -because informational data about mechanism is inherently equivalent to a great deal of input-output data. In contrast, ML models require very large, sometimes enormously large, input-output data sets to succeed in satisfying their prediction goals.The two distinct methodologies are being increasingly used together, in complementary ways, to model and solve biomedical problems, e.g. (Alber, Buganza Tepole et al. 2019, Lagergren JH 2020, Arzani, Wang et al. 2022, Seedat, Imrie et al. 2022), but with no clear hybridization unfolding yet. We believe they can be combined more deeply within existing modeling theory -perhaps new mathematical systems and statistical theoryand thus become well-integrated and more useful.We envision a solid hybridized theory will develop in the near future for effectively merging mechanistic and machine learning modeling methods. It's a "no-brainer" to imagine how the whole will be much bigger than the sum of its parts, given how much information is embedded in MEC models about the systems that generate the data for biosystem ML modeling -information that, with few exceptions, now goes unused in ML modeling. https://team.inria.fr/musca/members/frederique-clement/ November 18, 2022 at Los Angeles, Paris and Toronto

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