In this work, we demonstrate the effects of chemical exchanges on T1 relaxation times as well as magnetization ratios under various experimental conditions in three-site chemical exchange network (i.e., $$$PCr\leftrightarrow\gamma ATP \leftrightarrow Pi$$$). And we present a novel strategy to simultaneously quantify creatine kinase (CK) and ATP synthase (ATPase) reaction kinetics as well as metabolite pool size ratio with correcting T₁ saturation and chemical exchange effect in ³¹P magnetization saturation transfer (MST) experiment. Finally, we validate our method on rat brain data in vivo.

The evolution of spin magnetization under chemical exchanging network can be characterized by modified Bloch-McConnell equation with matrix form as follow: $$$\frac{\text{d}M}{\text{d}t}=A\cdot [M(t)-M_{0}] $$$ where M is a vector, in which three components are equal to the longitudinal magnetizations of PCr, γATP and Pi, respectively and M0 is magnetization vector at thermal equilibrium. And A is a dynamic matrix involving the intrinsic T₁ (T₁^int ) of the metabolites and reaction rates. The solution of above equation is $$$ M(t)=(I-e^{A\cdot TR})\cdot M_{0}+e^{A\cdot TR}\cdot M(0) $$$ where I is a $$$3 \times 3 $$$ unity matrix. M(0) is the initial magnetizations at t=0. T₁^int is intrinsic spin-lattice relaxation time without considering chemical exchange effect, which can be measured by using conventional progressive MST experiment. T₁^mix is defined as apparent T₁ of a spin when chemical exchange is involved. It could be obtained by single-exponential fitting of simulated magnetization from above equation. And T₁^app is defined as apparent T₁ of a spin when the resonance of γATP is saturated. Using spectra obtained without (M_c) and with saturation (M_s) on γATP resonance in short TR sequence, Xiong et al.¹ derived an approximately linear relationship between magnetization ratios (M_c/M_s) and forward reaction constant (k_f) values under various acquisition conditions as following equation: $$$ \frac{M_{c,PCr(Pi)}}{M_{s,PCr(Pi)}}\cong \beta +T_{1,PCr(Pi)}^{nom}\cdot k_{f,CK(ATPase)} $$$ where T₁^nom is nominal T₁ and can be defined as the slope of the line obtained by linear regression of the simulated M_c/ M_s versus k_f plot. Using calculated T₁^nom and experimental measure of M_c^mea and M_s^mea, k_f value can be obtained using above equation. Then, the k_f value is used for calculation of control magnetization (M_c^cal) in modified Bloch-McConnell equation. Finally, fully relaxed new magnetization can be calculated using following equation: $$$ M_{0,PCr(\gamma ATP,Pi)}^{new}=\frac{M_{0,PCr(\gamma ATP,Pi)}^{ini}\times M_{c,PCr(\gamma ATP,Pi)}^{mea}}{M_{c,PCr(\gamma ATP,Pi)}^{cal}}$$$. The procedures are repeated until calculated M_c^cal is close enough to the measured M_c^mea (i.e., percent difference below than 3 %). The pulse sequence used for the in vivo 31P MST experiments² is shown in Fig.1. 31P spectra were acquired using the following acquisition parameters: spectral width 5000 Hz, 1024 data points. For MST, In order to achieve complete saturation of γATP resonance, BISTRO scheme³ was used. Both approximately full relaxation (TR=9 sec; FA=90°; tsat= 8.6 sec; NT=128) and partially relaxed saturation transfer experiments (TR= 3 sec; FA=45°; tsat= 2.6 sec; NT=128) were performed to validate our methods.

As can be seen in Fig. 2, it is clear that T₁ of PCr and Pi is in order of T₁^int >T₁^mix >T₁^app, except for γ-ATP. Fig. 3 shows simulation results of magnetization ratios with and without considering chemical exchange effects. For practicality, the simulated magnetizations are shown in terms of resonance ratios (i.e., PCr/γATP, γATP/Pi, and PCr/Pi) as function of TR. It is clear that the magnetization ratios are clearly sensitive to acquisition parameters (TR, FA) as well as chemical exchange system. For example, if we use TR=3 sec with FA=45° in 31P-MRS experiment without considering chemical exchange effects, we may underestimate the PCr/γATP by 13 % and overestimate γATP/Pi ratios by 10%. The larger FA results in higher error in quantification of metabolic levels. To validate our method, we compared CK and ATPase activity measurement as well as magnetization ratios between full (TR=9) and partial relaxation condition (TR=3). Table 1 shows CK and ATPase activity measurement, indicating there was no significant difference between two measures (p > 0.05). Table 2 shows magnetization ratios measured from both full (TR=9) and partial relaxation condition (TR=3). By correcting chemical exchange and T₁ saturation effect, we could observe no significant difference in all magnetization ratios between two measures (p > 0.05). Our proposed method demonstrated that accurate metabolite quantification as well as calculation of forward CK/ATPase reaction constants could be possible with clinically reasonable scan time by correcting T₁ relaxation time under chemical exchange system.