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Open access 2026

Associations between thyroid axis changes and glycemic improvement after weight loss in type 2 diabetes: a mediation analysis.

OBJECTIVE To explore whether the favorable association between weight loss and glycemic improvement in patients with obesity and type 2 diabetes mellitus (T2DM) is partially mediated by weight loss-induced changes in the hypothalamic-pituitary-thyroid (HPT) axis, including alterations in thyroid-stimulating hormone (ΔTSH), free triiodothyronine (ΔFT3), and free thyroxine (ΔFT4). METHODS A total of 364 patients with obesity and T2DM who underwent bariatric surgery, glucagon-like peptide-1 receptor agonist (GLP-1RA) therapy, or standardized lifestyle intervention were enrolled in this retrospective real-world cohort study. Anthropometric, glycemic, and thyroid function indicators were measured at baseline and after a median follow-up of approximately 12 months. RESULTS Weight loss interventions led to significant reductions in body weight, glycated hemoglobin (HbA1c), fasting plasma glucose (FPG), and homeostatic model assessment for insulin resistance (HOMA-IR), as well as a significant increase in homeostatic model assessment for β-cell function (HOMA-β) (all P < 0.001). Serum TSH and FT3 levels decreased markedly after intervention (both P < 0.001), whereas FT4 levels remained stable (P = 0.542). Changes in TSH and FT3 were significantly correlated with changes in HbA1c (ΔTSH: r = 0.319, P < 0.001; ΔFT3: r = 0.135, P = 0.010). The HPT axis exerted a significant total indirect mediating effect of 10.7% on the association between weight loss and HbA1c improvement (P = 0.032), with ΔTSH contributing 5.5% and ΔFT3 contributing 5.2% of the total effect. Subgroup analysis showed that the indirect mediating effect was more prominent in patients with higher baseline TSH levels. CONCLUSION Changes in thyroid axis markers, specifically reductions in TSH and FT3, significantly and indirectly mediate the improvement in glycemic control following weight loss interventions in T2DM patients. Although this mediating effect is modest in overall magnitude, it is augmented in individuals with elevated baseline TSH levels. These findings suggest a novel auxiliary mechanism underlying the metabolic benefits of weight loss mediated by HPT axis remodeling.

Peng Li, Jingjing Zhang, Meiqi Li · 0 citations
Open access Jul 2026

​Optimality conditions of fuzzy fractional optimization and its application in the problems of energy efficiency optimization

Fuzzy-valued fractional optimization is an important topic in uncertain mathematical programming. It is related to efficiency-oriented decision-making problems in management, economics, and engineering. For example, in communication systems, energy-efficiency optimization in non-orthogonal multiple access systems naturally involves fractional objectives and uncertain parameters. However, optimality conditions for fuzzy-valued fractional optimization problems under granular differentiability have not been sufficiently studied. Therefore, this paper investigates Karush--Kuhn--Tucker (KKT) optimality conditions for fuzzy-valued fractional optimization problems under granular differentiability. First, horizontal membership functions are used to characterize fuzzy numbers and incorporate fuzzy parameters into the fractional optimization framework, providing a parameterized basis for granular analysis. Second, under granular differentiability and convexity assumptions, the relationship between the fuzzy-valued fractional optimization problem (FVFOP) and its associated fuzzy-valued optimization problem (FVOP) is established through a Dinkelbach-type transformation. Based on this relationship, KKT optimality conditions are derived for the original FVFOP. Finally, numerical examples are provided to illustrate the feasibility of the proposed theoretical results. The framework is further applied to energy-efficiency optimization in non-orthogonal multiple access systems and fuel-efficiency optimization in multi-generator systems, showing its potential relevance to efficiency-oriented decision-making under fuzzy uncertainty.

Jianke Zhang, Meiqi Li, Huani Li · 0 citations

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