## 3 Results
### Regression Analyses  
We performed multivariate regression analysis to evaluate which factors among BBB integrity (Qalb), the burden of AD pathology (CSF p-tau/A\(\beta\)42), and mitochondrial dysfunction (CSF lactates) were associated with variation in \(\mathrm{FDG_{Cortex}}\), \(\mathrm{FDG_{Ventricles}}\), and \(\mathrm{FDG_{Ventricles}}\)/\(\mathrm{FDG_{Cortex}}\). We added in the model possible confounding factors, namely age, sex, and plasma glucose levels (Table 2). In the CTRL group, both lower \(\mathrm{FDG_{Cortex}}\) (\(\beta=-0.455\); \(p=0.044\)) and lower \(\mathrm{FDG_{Ventricles}}\) (\(\beta=-0.608\); \(p=0.004\)) were associated with older age. In the AD group, \(\mathrm{FDG_{Cortex}}\) was negatively associated with glucose plasma levels (\(\beta=-0.147\); \(p=0.036\)) and Qalb (\(\beta=-0.158\); \(p=0.033\)). Lower \(\mathrm{FDG_{Ventricles}}\) was associated with older age (\(\beta=-0.255\); \(p<0.001\)) and more CSF lactates (\(\beta=-0.207\); \(p=0.002\)). A lower \(\mathrm{FDG_{Ventricles}}\)/\(\mathrm{FDG_{Cortex}}\) ratio was again associated with older age (\(\beta=-0.264\); \(p<0.001\)) and more CSF lactates (\(\beta=-0.214\); \(p=0.002\)) but also with lower CSF p-tau/A\(\beta\)42 (\(\beta=0.136\); \(p=0.034\)). Finally, we stratified AD patients according to APOE genotype and performed separate multivariate regression analyses considering, all factors which were significantly associated with \(\mathrm{FDG_{Cortex}}\), \(\mathrm{FDG_{Ventricles}}\), and \(\mathrm{FDG_{Ventricles}}\)/\(\mathrm{FDG_{Cortex}}\) in the all AD group analysis (Table 3). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**CTRL**} & \multicolumn{2}{c}{**All AD**} \\ \hline  & \(\beta\) & \(p\) & \(\beta\) & \(p\) \\ \hline \(\mathrm{FDG_{Cortex}}\) & & & & \\ Age & \(-0.455\) & \(\mathbf{0.044}\) & \(-0.013\) & \(0.854\) \\ Sex & n.a. & \(0.532\) & n.a. & \(0.480\) \\ Plasma glucose (mg/dL) & \(-0.080\) & \(0.689\) & \(-0.147\) & \(\mathbf{0.036}\) \\ Qalb & \(0.098\) & \(0.588\) & \(-0.158\) & \(\mathbf{0.033}\) \\ CSF p-tau/A\(\beta\)42 & \(0.037\) & \(0.869\) & \(-0.071\) & \(0.295\) \\ CSF lactates & \(0.082\) & \(0.698\) & \(0.011\) & \(0.876\) \\ Adjusted R\({}^{2}\) & \(0.019\) & & \(0.036\) & \\ \hline \(\mathrm{FDG_{Ventricles}}\) & & & & \\ Age & \(-0.608\) & \(\mathbf{0.004}\) & \(-0.255\) & \(\mathbf{<0.001}\) \\ Sex & n.a. & \(0.188\) & n.a. & \(0.053\) \\ Plasma glucose (mg/dL) & \(0.013\) & \(0.940\) & \(-0.002\) & \(0.978\) \\ Qalb & \(0.226\) & \(0.173\) & \(-0.067\) & \(0.333\) \\ CSF p-tau/A\(\beta\)42 & \(0.254\) & \(0.207\) & \(0.075\) & \(0.238\) \\ CSF lactates & \(0.026\) & \(0.893\) & \(-0.207\) & \(\mathbf{0.002}\) \\ Adjusted R\({}^{2}\) & \(0.212\) & & \(0.148\) & \\ \hline \(\mathrm{FDG_{Ventricles}}\)/\(\mathrm{FDG_{Cortex}}\) & & & & \\ Age & \(-0.200\) & \(0.397\) & \(-0.264\) & \(\mathbf{<0.001}\) \\ Sex & n.a. & \(0.481\) & n.a. & \(0.100\) \\ Plasma glucose (mg/dL) & \(0.081\) & \(0.707\) & \(0.082\) & \(0.213\) \\ Qalb & \(0.152\) & \(0.439\) & \(0.010\) & \(0.885\) \\ CSF p-tau/A\(\beta\)42 & \(0.213\) & \(0.375\) & \(0.136\) & \(\mathbf{0.034}\) \\ CSF lactates & \(-0.047\) & \(0.838\) & \(-0.214\) & \(\mathbf{0.002}\) \\ Adjusted R\({}^{2}\) & \(-0.139\) & & \(0.144\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Multivariate regression analyses in CTRLs and AD patients. Considering the APOE \(\epsilon 3\) group, we did not retrieve any significant association with \(\mathrm{FDG_{Cortex}}\), but we confirmed negative associations between \(\mathrm{FDG_{Ventircles}}\) and both age (\(\beta=-0.247;p=0.008\)) and CSF lactates (\(\beta=-0.201;p=0.035\)). Similarly, we confirmed the negative associations of both age (\(\beta=-0.238;p=0.010\)) and CSF lactates (\(\beta=-0.260\); \(p=0.006\)) with \(\mathrm{FDG_{Ventircles}}/\mathrm{FDG_{Cortex}}\). In the APOE \(\epsilon 4\) group, we retrieved negative associations between both plasma glucose (\(\beta=-0.268;p=0.010\)) and Qalb (\(\beta=-0.240;p=0.019\)) and \(\mathrm{FDG_{Cortex}}\).