The capacity of the liver to convert the metabolic input received from the incoming portal and arterial blood into the metabolic output of the outgoing venous blood has three major determinants: The intra-hepatic blood flow, the transport of metabolites between blood vessels (sinusoids) and hepatocytes and the metabolic capacity of hepatocytes. These determinants are not constant across the organ: Even in the normal organ, but much more pronounced in the fibrotic and cirrhotic liver, regional variability of the capillary blood pressure, tissue architecture and the expression level of metabolic enzymes (zonation) have been reported. Understanding how this variability may affect the regional metabolic capacity of the liver is important for the interpretation of functional liver tests and planning of pharmacological and surgical interventions. Here we present a mathematical model of the sinusoidal tissue unit (STU) that is composed of a single sinusoid surrounded by the space of Disse and a monolayer of hepatocytes. The total metabolic output of the liver (arterio-venous glucose difference) is obtained by integration across the metabolic output of a representative number of STUs. Application of the model to the hepatic glucose metabolism provided the following insights: (i) At portal glucose concentrations between 6-8 mM, an intra-sinusoidal glucose cycle may occur which is constituted by glucose producing periportal hepatocytes and glucose consuming pericentral hepatocytes, (ii) Regional variability of hepatic blood flow is higher than the corresponding regional variability of the metabolic output, (iii) a spatially resolved metabolic functiogram of the liver is constructed. Variations of tissue parameters are equally important as variations of enzyme activities for the control of the arterio-venous glucose difference.