Closed-loop robust control of long-term diabetes progression via physical activity management

TL;DR

This paper addresses long-term control of type 2 diabetes progression by managing physical activity. It develops a control-oriented five-state model with IL-6–mediated exercise effects and introduces an equivalent input $u_{eq}$ to capture the average exercise impact, enabling a Model Predictive Control (MPC) strategy. The MPC is shown to be robust to initial conditions and parameter perturbations and yields exercise prescriptions that slow, halt, or reverse disease progression with lower total exercise effort than a constant-feedforward approach. The work offers a path toward quantitative, clinically actionable exercise recommendations for diabetes prevention and decision support, with validation on higher-dimensional models foreseen.

Abstract

Large clinical evidence acknowledges the crucial role played by physical activity in delaying the progression of type-2 diabetes. However, the literature lacks control approaches that leverage exercise for type-2 diabetes control and more in general lacks a quantitative assessment of medical guidelines on the recommended amount of physical activity to be performed, mainly due to the absence of mathematical models that suitably estimate its benefits on diabetes progression. In this work, in order to provide a control-theoretical formulation of the exercise, we design a feedback law in terms of recommended physical activity, following a model predictive control approach, based on a widespread compact diabetes progression model, suitably modified to properly account for the long-term effect of the exercise. Moreover we illustrate how the proposed approach proves to show reliable robustness properties with respect to initial conditions and parameter perturbations, which may be used to reflect inter-patient variability. Results are encouraging in view of the validation of the control law on comprehensive high-dimensional models of diabetes progression, with the aim of translating the prediction of the controller into reasonable recommendations and to quantitatively support medical decision-making.

Figures (5)

• Figure 1: Basal glucose concentration as a function of time in the open-loop case (dashed blue line), in the feedforward control case (dashed red and yellow lines) and in the MPC controlled case (solid purple line) using the nominal parameters in Table \ref{["tab:Topp's_parameters_values_units_extended"]}.
• Figure 2: Equivalent control input $u_{eq}$ predicted by the MPC controller as a function of time, with the nominal parameters in Table \ref{["tab:Topp's_parameters_values_units_extended"]}.
• Figure 3: Recommended duration of single exercise sessions as a function of time computed by means of the inverse map \ref{['eq_inverse_map']}, with the nominal parameters in Table \ref{["tab:Topp's_parameters_values_units_extended"]}: feedforward control case with $u_{eq}=1.1$ (dashed red line) vs MPC controlled case (blue stem lines and dashed purple line).
• Figure 4: Basal glucose concentration as a function of time in the controlled case considering initial condition and parameter perturbations ($100$ simulations).
• Figure 5: Beta-cell mass as a function of time in the controlled case considering initial condition and parameter perturbations ($100$ simulations).