A mathematical model appraising the effect of metabolic control on joint mobility in young diabetic patients: a preliminary study

Abstract

Objective. The impairment of glycemic control can induce limited joint mobility even in young type 1 diabetic (T1DM) patients. The aims of this study were to verify the presence of ankle joint mobility (AJM) deficits in young T1DM subjects and define a mathematical model of diabetes mellitus long-term effects on AJM. Methods. AJM was evaluated using an inclinometer in 37 patients and 53 healthy, sex- BMI- and age-matched controls. To set up the mathematical model, we assumed that reduced metabolic control affects AJM according to a lognormal function: requiring some time for development of a reduction of joint mobility, which then persists for a long period, before fading out over time (if glycemic control has been recovered). A non-linear optimization determined the model parameters to achieve the best fit for a series of patients. Results. Both plantar and dorsiflexion AJM was significantly lower in diabetic subjects than in controls (plantarflexion: 28.5°±7.5 vs 35.2°±6.5; dorsiflexion: 93.9°±16.0 vs 104.7±12.8; p<0.01). The defined model approximates the experimental data with good accuracy; after optimization, the lognormal curve obtained is in line with empirical estimates: lack of glycemic control needs to persist for at least a few months before producing a significant effect, that lasts up until one year. The fitting procedure indicated the optimal solution is p = (37; 30; 3:5; 6:7; 137); thus, the optimal _im(t) corresponds to the curve reported. Conclusion. AJM was significantly reduced in young T1DM patients. The mathematical model represents the experimental data accurately.