Cerebral glucose delivery, transport and metabolism: Theory and modeling using four, three, and two tissue compartments.

Flux equations describing brain D-glucose uptake are presented for up to four tissue compartments: blood, endothelial intracellular space in the blood-brain barrier (BBB), extravascular-extracellular space (EES), and intracellular space. Transport rates are described by Michaelis-Menten kinetics, including half-saturation constants ($K_T$) and maximum rates for transport${(T}_{\max })$over the BBB and the cell membrane (CMB). These transport parameters and the maximum rate for hexokinase-catalyzed metabolism ($V_{\max }^{HK}$) were determined by numerical fitting of the models to both steady-state and dynamic D-glucose uptake data in human gray matter from MRS. Two-, three-, and four-compartment results are compared, including effects of incorporating an endothelial compartment with unequal ratios ($R_{A/L}$) of GLUT1 receptors on abluminal and luminal membranes. Four-compartment fitting with$R_{A/L}=2.0$resulted in$T_{\max }^{\mathrm{BBB}}=0.804\pm 0.131\hspace{0.17em}$µmol/g/min,$K_T^{\mathrm{BBB}}=6.20\pm 1.53\hspace{0.17em}$mM,$T_{\max }^{\mathrm{CMB}}=1.04\pm 0.25\hspace{0.17em}$µmol/g/min,$K_T^{\mathrm{CMB}}=3.10\pm 0.70\hspace{0.17em}$mM and$V_{\max }^{HK}=0.260\pm 0.039\hspace{0.17em}$µmol/g/min, comparing well with the simpler models. A model with at least three tissue compartments (blood, EES, cell) is essential for quantification and interpretation of dynamic glucose-enhanced (DGE) MRI data in brain tumors, where signal intensities depend on compartmental pH in addition to concentration, and where the signal contribution from the EES is dominant. It should also be relevant to PET and MR(S) studies of pathologies where the BBB is compromised.