Numerical approximation to the general kinetic model for ASL quantification

Purpose To develop a numerical approximation to the general kinetic model for arterial spin labeling (ASL) quantification that will enable greater flexibility in ASL acquisition methods. Theory The Bloch‐McConnell equations are extended to include the effects of single‐compartment inflow and outflow on both the transverse and longitudinal magnetization. These can be solved using an extension of Jaynes’ matrix formalism with piecewise constant approximation of incoming labeled arterial flow and a clearance operator for outgoing venous flow. Methods The proposed numerical approximation is compared with the general kinetic model using simulations of pulsed labeling and pseudo‐continuous labeling and a broad range of transit time and bolus duration for tissue blood flow of 0.6 mL/g/min. Accuracy of the approximation is studied as a function of the timestep using Monte‐Carlo simulations. Three additional scenarios are demonstrated: (1) steady‐pulsed ASL, (2) MR fingerprinting ASL, and (3) balanced SSFP and spoiled gradient‐echo sequences. Results The proposed approximation was found to be arbitrarily accurate for pulsed labeling and pseudo‐continuous labeling. The pulsed labeling/pseudo‐continuous labeling approximation error compared with the general kinetic model was less than 0.002% (