Abstract
The purpose of this study was to demonstrate a simple and fast method for solving the time-dependent Bloch-McConnell equations describing the behavior of magnetization in magnetic resonance imaging (MRI) in the presence of multiple chemical exchange pools. First, the time-dependent Bloch- McConnell equations were reduced to a homogeneous linear differential equation, and then a simple equation was derived to solve it using a matrix operation and Kronecker tensor product. From these solutions, the longitudinal relaxation rate (R1ρ) and transverse relaxation rate in the rotating frame (R2ρ) and Z-spectra were obtained. As illustrative examples, the numerical solutions for linear and star-type three-pool chemical exchange models and linear, star- type, and kite-type four-pool chemical exchange models were presented. The effects of saturation time (ST) and radiofrequency irradiation power (ω1) on the chemical exchange saturation transfer (CEST) effect in these models were also investigated. Although R1ρ and R2ρ were not affected by the ST, the CEST effect observed in the Z-spectra increased and saturated with increasing ST. When ω1 was varied, the CEST effect increased with increasing ω1 in R1ρ, R2ρ, and Z-spectra. When ω1 was large, however, the spillover effect due to the direct saturation of bulk water protons also increased, suggesting that these parameters must be determined in consideration of both the CEST and spillover effects. Our method will be useful for analyzing the complex CEST contrast mechanism and for investigating the optimal conditions for CEST MRI in the presence of multiple chemical exchange pools.
Highlights
Chemical exchange saturation transfer (CEST) is a novel contrast mechanism for magnetic resonance imaging (MRI) [1] and has been increasingly used to detect dilute proteins via the interaction between labile solute protons and bulk water protons [2] [3] [4]
R1ρ and R2ρ were not affected by the saturation time (ST), the chemical exchange saturation transfer (CEST) effect observed in the Z-spectra increased and saturated with increasing ST
Our method will be useful for analyzing the complex CEST contrast mechanism and for investigating the optimal conditions for CEST MRI in the presence of multiple chemical exchange pools
Summary
Chemical exchange saturation transfer (CEST) is a novel contrast mechanism for magnetic resonance imaging (MRI) [1] and has been increasingly used to detect dilute proteins via the interaction between labile solute protons and bulk water protons [2] [3] [4]. CEST or APT MRI contrast mechanism is complex, depending on the concentration of CEST agents or amide protons, exchange and relaxation properties, and varying with experimental conditions such as magnetic field strength and radiofrequency (RF) power [8]. In analyzing the complex CEST contrast mechanism and for investigating the optimal study conditions, numerical simulations are useful and effective [10] [11]. To perform extensive numerical simulations for CEST or APT MRI, it will be necessary to develop a simple and fast method for obtaining the numerical solutions to the time-dependent Bloch-McConnell equations
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