The liver is a highly vascular organ with a dual blood supply, and it performs a remarkable number of vital functions. Here, we show, through measurement of blood oxygen level‐dependent (BOLD) signal, that liver arterial and hepatic portal blood supplies can be modulated through hyperoxia exposure and by consumption of a standardized meal, respectively. As such, we suggest that hyperoxia modulates the hepatic arterial BOLD signal, whereas a controlled meal changes predominantly the hepatic portal BOLD signal. The hemodynamics of the dual liver blood supplies in response to the aforementioned challenges are complex and variable across subjects, making a general linear model‐based analysis difficult. Therefore, we present the application of two local (at each voxel) hemodynamic response‐independent techniques—principal component analysis and partial least squares—to observe the hypothesized reduction in BOLD contrast during cycles of hyperoxic breathing, when comparing preprandial versus postprandial states in a normally functioning liver. We illustrate the ability of our techniques to differentiate between healthy and diseased livers with an analysis of 17 subjects—11 with normal livers and 6 with liver disease (hepatitis or cirrhosis). Our local analysis can correctly classify all of the subjects. Copyright © 2012 John Wiley & Sons, Ltd.