A mathematical model for velocity-selective arterial spin labeling

Purpose To present a theoretical framework that rigorously defines and analyzes key concepts and quantities for velocity selective arterial spin labeling (VSASL). Theory and Methods An expression for the VSASL arterial delivery function is derived based on (1) labeling and saturation profiles as a function of velocity and (2) physiologically plausible approximations of changes in acceleration and velocity across the vascular system. The dependence of labeling efficiency on the amplitude and effective bolus width of the arterial delivery function is defined. Factors that affect the effective bolus width are examined, and timing requirements to minimize quantitation errors are derived. Results The model predicts that a flow-dependent negative bias in the effective bolus width can occur when velocity selective inversion (VSI) is used for the labeling module and velocity selective saturation (VSS) is used for the vascular crushing module. The bias can be minimized by choosing a nominal labeling cutoff velocity that is lower than the nominal cutoff velocity of the vascular crushing module. Conclusion The elements of the model are specified in a general fashion such that future advances can be readily integrated. The model can facilitate further efforts to understand and characterize the performance of VSASL and provide critical theoretical insights that can be used to design future experiments and develop novel VSASL approaches.