Modeling the metabolic trajectory of patients with type 1 diabetes using digital twins and markov models

Digital twins represent a promising tool for conducting in-silico clinical trials in type 1 diabetes (T1D), enabling researchers to safely evaluate therapeutic strategies without exposing patients to risk and substantially reducing time and cost. However, current digital twin implementations typically generate daily simulations that are independent of each other, lacking a model of how patient-specific physiological parameters evolve over multiple days. Understanding the temporal trajectory of these parameters is essential for developing multi-day simulators that more accurately reflect metabolic adaptation, stability, or deterioration over time. This thesis aims to model the inter-day metabolic trajectory of patients with type 1 diabetes by analyzing parameter sets extracted from digital twin simulations. A data set comprised approximately 100 patients, each characterized by multiple simulated days. For every patientday instance, a set of physiological and pharmacokinetic parameters was availableincluding basal glucose (Gb), glucose effectiveness (SG), subcutaneous and gastric absorption rates (ka2, kd, kempt), insulin sensitivities in different compartments (SI_B, SI_L, SI_D), and absorption/shape parameters for multiple insulin formulations (kabs_*, beta_*). To investigate whether patient days exhibit distinctive and recurrent metabolic states, these parameters were grouped into nine biologically motivated combinations (combos), each reflecting a specific physiological mechanism or subsystem. For each combination, clustering techniques were applied to identify latent daily metabolic patterns. The resulting cluster sequences, representing the series of metabolic states visited by each digital twin on days, were subsequently modeled using first- order Markov models. The transition matrices derived from these models quantify the probability of moving from one metabolic state to another, thus providing a representation of the patient’s multi-day metabolic dynamics. The results show that several combos yield well-separated clusters, indicating the presence of distinct daily metabolic regimes throughout the simulated population. Markov models derived from these clusters reveal non-uniform, patient-specific transition structures, with certain metabolic states displaying strong persistence while others occur transiently. These findings suggest that the digital twin dynamics encode meaningful temporal patterns that can be captured and formalized probabilistically. Overall, this work demonstrates that the metabolic evolution of digital twin patients can be effectively modeled as a Markov process. The proposed framework lays the groundwork for the construction of multi-day metabolic simulators, which have the potential to accelerate the development and evaluation of therapeutic strategies, improve the realism of in-silico trials, and ultimately support personalized decision- making in the management of type 1 diabetes.