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...

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Bibliographic Details
Published in:Magnetic resonance in medicine Vol. 84; no. 5; pp. 2846 - 2857
Main Authors: Lee, Nam G., Javed, Ahsan, Jao, Terrence R., Nayak, Krishna S.
Format: Journal Article
Language:English
Published: United States Wiley Subscription Services, Inc 01.11.2020
John Wiley and Sons Inc
Subjects:
Approximation
arterial spin labeling
Arteries
Blood flow
Cerebrovascular Circulation
Computer simulation
Design of experiments
Fingerprinting
fingerprinting ASL
Flexibility
Kinetics
Labeling
Magnetic Resonance Angiography
Magnetization
Mathematical analysis
Mathematical models
Note—Computer Processing and Modeling
Numerical methods
Operators (mathematics)
perfusion
quantification
Simulation
Spin labeling
Spin Labels
steady‐pulsed ASL
Transit time
fingerprinting ASL
steady-pulsed ASL
perfusion
quantification
blood flow
arterial spin labeling
ISSN:0740-3194, 1522-2594, 1522-2594
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Summary: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% (<0.002%) and less than 0.05% (<0.05%) for timesteps of 3 ms and 35 ms, respectively. The proposed approximation matched well with customized signal expressions of steady‐pulsed ASL and MR fingerprinting ASL. The simulations of simultaneous modeling of flow, T2, and magnetization transfer showed an increase in steady‐state balanced SSFP and spoiled gradient signals. Conclusion We demonstrate a numerical approximation of the “Bloch–McConnell flow” equations that enables arbitrarily accurate modeling of pulsed ASL and pseudo‐continuous labeling signals comparable to the general kinetic model. This enables increased flexibility in the experiment design for quantitative ASL.
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A preliminary version of this work was presented at ISMRM 2019 (Abstract #2191).
ISSN:0740-3194
1522-2594
1522-2594
DOI:10.1002/mrm.28304