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This paper proves a $Γ$-convergence result for the discrete energy (to the continuous one) of the matching problem for signals defined on surfaces. In particular, we highlight some geometric properties that must be guaranteed in the discretization process to ensure the convergence of minimizers. The proof is given in the framework of functional shapes introduced in \cite{ABN}. In particular, we consider a varifold-type attachment term, and a $BV$ penalty term is used instead of the original $L^2$ norm.

BackgroundLevodopa (LD) is the most effective drug in the treatment of Parkinson’s disease (PD). Unfortunately, prolonged use of LD leads to complications, mainly motor/non-motor fluctuations (MNMF) and dyskinesias (DYS). Women seem more prone to develop such LD-related complications. Nonetheless, there is a paucity of prospective studies examining gender-related predictors of MNMF and DYS. Among several factors, which concur with a very complex scenario, changes in LD pharmacokinetics influence the drug’s effectiveness. The present study aimed to assess gender-related differences in LD pharmacokinetics in patients with PD at their first-ever intake of LD.Materials and MethodsThis is a multicentric study enrolling patients with PD, who were LD-naïve and received a single dose of LD/benserazide (100/25 mg) formulation. All participants gave their written informed consent, and the study was approved by the local Ethics Committees. To measure plasma LD concentrations and pharmacokinetic parameters (AUC, Cmax, Tmax, t1/2), fasting blood samples were collected before drug intake and then at 8-time points until 260 min. LD concentrations were measured by ultra-high-performance liquid chromatography coupled with mass spectrometry (UHPLC-MS). Multiple linear regression analyses were performed to identify the predictors of the parameters.ResultsThirty-five patients (16 women and 19 men) were consecutively enrolled. Area under curve (AUC) and maximum plasma concentration (Cmax) were significantly higher in women than men (p = 0.0006 and p = 0.0014, respectively). No statistically significant difference was found regarding Tmax and t1/2. Multiple linear regression analyses revealed that female sex (β = 1.559116, 95% CI 0.8314479 2.286785; p < 0.0001) and body mass index (BMI) (β = −0.0970631, 95% CI −0.1733004 −0.0208258; p = 0.014) significantly predicted AUC. Only female sex significantly predicted Cmax (β = 1,582.499, 95% CI 731.581 2,433.417; p = 0.001). Moreover, only BMI significantly predicted t1/2 (β = 0.0756267, 95% CI 0.0143407 0.1369126; p = 0.017). Stratifying by gender, BMI was confirmed to significantly predict t1/2 in women (β = 0.1300486, 95% CI 0.0172322 0.242865; p = 0.027), but not in men.ConclusionThis study provides novel insights on gender differences in LD pharmacokinetics, possibly contributing to the later development of motor complications and dyskinesia in PD.