Accuracy of the cylinder approximation for susceptometric measurement of intravascular oxygen saturation

Susceptometry-based MR oximetry has previously been shown suitable for quantifying hemoglobin oxygen saturation in large vessels for studying vascular reactivity and quantification of global cerebral metabolic rate of oxygen utilization. A key assumption underlying this method is that large vessels can be modeled as long paramagnetic cylinders. However, bifurcations, tapering, noncircular cross-section, and curvature of these vessels produce substantial deviations from cylindrical geometry, which may lead to errors in hemoglobin oxygen saturation quantification. Here, the accuracy of the "long cylinder" approximation is evaluated via numerical computation of the induced magnetic field from 3D segmented renditions of three veins of interest (superior sagittal sinus, femoral and jugular vein). At a typical venous oxygen saturation of 65%, the absolute error in hemoglobin oxygen saturation estimated via a closed-form cylinder approximation was 2.6% hemoglobin oxygen saturation averaged over three locations in the three veins studied and did not exceed 5% for vessel tilt angles <30° at any one location. In conclusion, the simulation results provide a significant level of confidence for the validity of the cylinder approximation underlying MR susceptometry-based oximetry of large vessels.