## 4 Discussion
Interestingly, a lower \(\text{FDG}_{\text{Ventriles}}/\text{FDG}_{\text{Cortex}}\) ratio was also associated with older age, more CSF lactates, and also with lower AD-related pathology (p-tau/A\(\beta\)42). We hypothesize that this parameter may reflect the excess of \"glucose extraction\" from CSF in an attempt to support brain metabolism, an ability that could be progressively lost as the burden of AD pathology increases. These multivariate analyses may partly explain the weaker correlation between \(\text{FDG}_{\text{Cortex}}\) and \(\text{FDG}_{\text{Ventriles}}\) we found in the AD group. Indeed, while only age was associated with these parameters in the CTRLs, in patients with AD, the relationship was influenced by several additional factors, including BBB permeability, the burden of amyloid and tau pathologies, and bioenergetic dysfunctions, which may disrupt the normal metabolic coupling between the cortex and the CSF. Given the cross-sectional design of our study, no causal inferences can be drawn regarding the directionality of the observed associations--i.e., whether BBB dysfunction precedes or follows cerebral metabolic changes. However, our findings raise the hypothesis that alterations in the \(\text{FDG}_{\text{Ventriles}}/\text{FDG}_{\text{Cortex}}\) ratio may reflect early pathophysiological processes in AD. Future longitudinal studies are warranted to explore whether dynamic changes in this ratio over time are predictive of cognitive decline or disease progression. To further explore these associations, we stratified AD patients according to APOE genotype, which highlighted the presence of distinct patterns of association. In the APOE \(\varepsilon\)3 group, no significant link was found between any of the variables and \(\text{FDG}_{\text{Cortex}}\). This lack of association was reflected by the very low adjusted R\({}^{2}\) observed for this model. However, negative associations with both age and CSF lactates were confirmed for \(\text{FDG}_{\text{Ventriles}}\) and for the \(\text{FDG}_{\text{Ventriles}}/\text{FDG}_{\text{Cortex}}\) ratio. In contrast, in the APOE \(\varepsilon\)4 group, lower \(\text{FDG}_{\text{Cortex}}\) was significantly associated with higher plasma glucose levels and BBB permeability. These findings are consistent with the literature, which has demonstrated a strong link between cortical hypometabolism and insulin resistance [35], as well as a higher degree of vascular abnormalities which can impact AD pathology and cognitive decline in APOE \(\varepsilon\)4 carriers [16; 36; 37]. In this subgroup of patients, lower \(\text{FDG}_{\text{Ventriles}}\) was associated with older age, higher BBB permeability, and higher degree of AD-related pathology, while no association was observed with CSF lactates. Finally, regression analysis of the \(\text{FDG}_{\text{Ventriles}}/\text{FDG}_{\text{Cortex}}\) ratio in the APOE \(\varepsilon\)4 group confirmed significant associations with age and AD-related pathology, but again, no relationship was found with CSF lactates. Collectively, these findings suggest that APOE genotype may modulate the association between amyloid pathology, vascular changes, and brain metabolic dysfunction. Specifically, while brain glucose metabolism in APOE \(\varepsilon\)3 patients appears to be primarily associated with bioenergetic failure (e.g., elevated CSF lactates), in APOE \(\varepsilon\)4 carriers, it seems to be influenced by the combined effects of BBB dysfunction and AD-related pathology. Metabolic failure appears to be a common feature among all AD patients, but it is likely more pronounced in APOE \(\varepsilon\)4 carriers [16], in whom additional factors--such as a well-documented higher burden of amyloid and tau pathology [15], as well as greater microvascular damage accompanied by reduced GLUT expression [9]--may further exacerbate metabolic dysfunction.