Quantitative description of proton exchange processes between water and endogenous and exogenous agents for WEX, CEST, and APT experiments

The proton exchange processes between water and solutes containing exchangeable protons have recently become of interest for monitoring pH effects, detecting cellular mobile proteins and peptides, and enhancing the detection sensitivity of various low-concentration endogenous and exogenous species. In this work, the analytic expressions for water exchange (WEX) filter spectroscopy, chemical exchange-dependent saturation transfer (CEST), and amide proton transfer (APT) experiments are derived by the use of Bloch equations with exchange terms. The effects of the initial states for the system, the difference between a steady state and a saturation state, and the relative contributions of the forward and backward exchange processes are discussed. The theory, in combination with numerical calculations, provides a useful tool for designing experimental schemes and assessing magnetization transfer (MT) processes between water protons and solvent-exchangeable protons. As an example, the case of endogenous amide proton exchange in the rat brain at 4.7 T is analyzed in detail.