Large-vessel BOLD contamination is a serious impediment to localization of neural activity in high-resolution fMRI studies. A new method is presented which estimates and removes the fraction of BOLD signal that arises from oriented vessels, such as cerebral and pial veins in a voxel, by measuring their influence on the phase angle of the complex valued fMRI time series. A maximum likelihood estimator based on a linear leastsquares fit of the BOLD signal phase to the BOLD signal magnitude in a voxel is shown to efficiently suppress the BOLD effect from these larger veins, whose activation is not well colocalized with the neural response. In high-resolution in vivo fMRI data at 4 T, it is estimated that the method is sensitive to the phase changes in the cerebral, larger intracortical, and pial veins. The technique requires no special pulse sequence modifications or acquisition strategies, and is computationally fast and intrinsically robust. At field strengths of 0.5-7 Tesla (1-5), the intensity changes in MRI observed during functional activation using gradient-echo EPI are dominated by the intravascular BOLD changes in the cortical cerebral veins and larger pial veins (macrovascular BOLD). This increases the effective point spread function of the fMRI technique in high-resolution imaging studies (6,7), since these larger veins can extend from several to tens of millimeters from the site of neuronal activity (8). Even at lower resolutions, larger veins can give rise to uncertainty in localization. For example, the presence of a draining vein in the central sulcus (2,8) makes distinguishing pre-from postcentral gyrus activity in the cortex extremely difficult, with obvious implications for other applications, such as presurgical planning in the motor cortex. While many clever techniques, such as spin-echo EPI, spiral, diffusion-weighted EPI, and perfusion-weighted methodologies, have been proposed to suppress the macrovascular BOLD effect, the use of gradient-echo EPI has been virtually ubiquitous in BOLD applications over the past decade because of its speed, multislice capability, ease of acquisition, and robust signal.The objection to the use of the macrovascular BOLD signal in certain brain mapping applications is based on the inhomogeneous distribution of veins in the brain (Ref. 8 and references therein). Cortical cerebral veins can range from 0.5-2.5 mm in radius and are typically found every 5-30 mm along the cortical surface. Because of the folded nature of the cortex, some of these veins can be found in sulci while yet others cross sulci on their way to venous sinuses. The cerebral veins collect deoxygenated blood received from the pial vein network, a dense, branching collection of 25-250-m-radius vessels located every 0.2-3 mm along the cortical surface. The smallest pial veins are formed from the right-angle emergence of an intracortical vein (10 -60 m radius) that penetrates the cortex tangential to the surface. These tangential penetrations occur every 0.25-1.5 mm on the cortical surface, and with ...