A review of optimization and quantification techniques for chemical exchange saturation transfer (CEST) MRI toward sensitive in vivo imaging

Abstract

Chemical exchange saturation transfer (CEST) MRI is a versatile imaging method that probes the chemical exchange between bulk water and exchangeable protons. CEST imaging indirectly detects dilute labile protons via bulk water signal changes following selective saturation of exchangeable protons, which offers substantial sensitivity enhancement and has sparked numerous biomedical applications. Over the past decade, CEST imaging techniques have rapidly evolved due to contributions from multiple domains, including the development of CEST mathematical models, innovative contrast agent designs, sensitive data acquisition schemes, efficient field inhomogeneity correction algorithms, and quantitative CEST (qCEST) analysis. The CEST system that underlies the apparent CEST-weighted effect, however, is complex. The experimentally measurable CEST effect depends not only on parameters such as CEST agent concentration, pH and temperature, but also on relaxation rate, magnetic field strength and more importantly, experimental parameters including repetition time, RF irradiation amplitude and scheme, and image readout. Thorough understanding of the underlying CEST system using qCEST analysis may augment the diagnostic capability of conventional imaging. In this review, we provide a concise explanation of CEST acquisition methods and processing algorithms, including their advantages and limitations, for optimization and quantification of CEST MRI experiments.

1. Introduction

The use of nuclear magnetic resonance (NMR) to detect chemical exchanges originated from the pioneering work of Forsen and Hoffman, who first proposed the double-resonance NMR method for measuring intermediate chemical exchanges (1,2). Their work eventually ushered in the field of chemical exchange saturation transfer (CEST) MRI, a sensitive method for measuring the chemical exchanges and chemical kinetics of dilute macromolecules (3-9). CEST MRI has shown the ability to detect a variety of compounds (e.g., glucose, glycogen, lactate), proteins and enzymes for molecular imaging (10-24). Development of exogenous CEST agents, including diamagnetic CEST (DIACEST) and paramagnetic CEST (PARACEST) agents, greatly enhanced the sensitivity and specificity of CEST imaging (25-34). In addition, CEST MRI provides a novel imaging approach to track tumor cells, bacterial/viral infections, pH and temperature changes (35-41). Moreover, endogenous CEST effects attributable to labile proton groups from endogenous proteins, peptides and metabolites have been applied to study disorders such as acute stroke, renal injury, tumors and multiple sclerosis (MS) (42-47).

The CEST effect is sensitive to labile proton concentration and exchange rate and, hence, parameters that affect the exchange rate, such as pH and temperature. However, the CEST effect also depends on relaxation rate, magnetic field strength and more importantly, experimental parameters including repetition time, RF irradiation amplitude and scheme, and image readout, which confound CEST measurements (48). Mathematical tools have been established to quantify CEST experiments. With the development of novel CEST agents, it has become increasingly important to optimize CEST experiments for enhanced detectability. Importantly, recent work has demonstrated that the CEST agent concentration and exchange rate can be determined concurrently (49,50). Such advanced post-processing algorithms transform routine CEST-weighted information towards quantitative CEST (qCEST) analysis, which is promising in providing additional insights into underlying biomedical systems (51). Indeed, CEST imaging has seen rapid development due to innovative concepts and improvement in mathematical models, novel contrast agent designs, sensitive data acquisition schemes, post-processing algorithms, and qCEST analysis. Therefore, a comprehensive survey of these new developments is warranted to enhance general understanding of CEST imaging. Herein, we provide a summarized review of the CEST contrast mechanism and methods for optimization and quantification of CEST MRI.

2. Quantitative Description Of CEST MRI

Mathematical models, both numerical and analytical solutions, have been established to describe the CEST contrast mechanism (52-54). A solid mathematical description of the CEST phenomenon is pragmatically useful for optimization and quantification of the CEST effect.

a. Bloch-McConnell solution

The CEST contrast mechanism can be described using Bloch-McConnell equations, which are two sets of Bloch equations coupled by means of chemical exchange. For a typical 2-pool chemical exchange model, assuming the irradiation RF field is applied along the x-axis, we have

$$\begin{array}{cc}\hfill \frac{{\mathrm{dM}}_{\mathrm{x}}^{\mathrm{w}}}{\mathrm{dt}}=& -{\mathrm{R}}_{2\mathrm{w}}{\mathrm{M}}_{\mathrm{x}}^{\mathrm{w}}-\Delta {\omega }_{\mathrm{w}}{\mathrm{M}}_{\mathrm{y}}^{\mathrm{w}}+{\mathrm{k}}_{\mathrm{sw}}{\mathrm{M}}_{\mathrm{x}}^{\mathrm{s}}-{\mathrm{k}}_{\mathrm{ws}}{\mathrm{M}}_{\mathrm{x}}^{\mathrm{w}}\hfill \\ \hfill \frac{{\mathrm{dM}}_{\mathrm{y}}^{\mathrm{w}}}{\mathrm{dt}}=& \Delta {\omega }_{\mathrm{w}}{\mathrm{M}}_{\mathrm{x}}^{\mathrm{w}}-{\mathrm{R}}_{2\mathrm{w}}{\mathrm{M}}_{\mathrm{y}}^{\mathrm{w}}+{\mathrm{k}}_{\mathrm{sw}}{\mathrm{M}}_{\mathrm{y}}^{\mathrm{s}}-{\mathrm{k}}_{\mathrm{ws}}{\mathrm{M}}_{\mathrm{y}}^{\mathrm{w}}+{\omega }_1{\mathrm{M}}_{\mathrm{z}}^{\mathrm{w}}\hfill \\ \hfill \frac{{\mathrm{dM}}_{\mathrm{z}}^{\mathrm{w}}}{\mathrm{dt}}=& -{\omega }_1{\mathrm{M}}_{\mathrm{y}}^{\mathrm{w}}-{\mathrm{R}}_{1\mathrm{w}}{\mathrm{M}}_{\mathrm{z}}^{\mathrm{w}}+{\mathrm{k}}_{\mathrm{sw}}{\mathrm{M}}_{\mathrm{z}}^{\mathrm{s}}-{\mathrm{k}}_{\mathrm{ws}}{\mathrm{M}}_{\mathrm{z}}^{\mathrm{w}}+{\mathrm{R}}_{1\mathrm{w}}{\mathrm{M}}_0^{\mathrm{w}}\hfill \\ \hfill \frac{{\mathrm{dM}}_{\mathrm{x}}^{\mathrm{s}}}{\mathrm{dt}}=& -{\mathrm{R}}_{2\mathrm{s}}{\mathrm{M}}_{\mathrm{x}}^{\mathrm{s}}-\Delta {\omega }_{\mathrm{s}}{\mathrm{M}}_{\mathrm{y}}^{\mathrm{s}}+{\mathrm{k}}_{\mathrm{ws}}{\mathrm{M}}_{\mathrm{x}}^{\mathrm{w}}-{\mathrm{k}}_{\mathrm{sw}}{\mathrm{M}}_{\mathrm{x}}^{\mathrm{s}}\hfill \\ \hfill \frac{{\mathrm{dM}}_{\mathrm{y}}^{\mathrm{s}}}{\mathrm{dt}}=& \Delta {\omega }_{\mathrm{s}}{\mathrm{M}}_{\mathrm{x}}^{\mathrm{s}}-{\mathrm{R}}_{2\mathrm{s}}{\mathrm{M}}_{\mathrm{y}}^{\mathrm{s}}+{\mathrm{k}}_{\mathrm{ws}}{\mathrm{M}}_{\mathrm{y}}^{\mathrm{w}}-{\mathrm{k}}_{\mathrm{sw}}{\mathrm{M}}_{\mathrm{y}}^{\mathrm{s}}+{\omega }_1{\mathrm{M}}_{\mathrm{z}}^{\mathrm{s}}\hfill \\ \hfill \frac{{\mathrm{dM}}_{\mathrm{z}}^{\mathrm{s}}}{\mathrm{dt}}=& -{\omega }_1{\mathrm{M}}_{\mathrm{y}}^{\mathrm{s}}-{\mathrm{R}}_{1\mathrm{s}}{\mathrm{M}}_{\mathrm{z}}^{\mathrm{s}}+{\mathrm{k}}_{\mathrm{ws}}{\mathrm{M}}_{\mathrm{z}}^{\mathrm{w}}-{\mathrm{k}}_{\mathrm{sw}}{\mathrm{M}}_{\mathrm{z}}^{\mathrm{s}}+{\mathrm{R}}_{1\mathrm{s}}{\mathrm{M}}_0^{\mathrm{s}}\hfill \end{array}$$ [1]

where ${\mathrm{M}}_0^{\mathrm{w},\mathrm{s}}$ are the equilibrium magnetizations for bulk water (w) and solute pool (s); ${\mathrm{M}}_{\mathrm{x},\mathrm{y},\mathrm{z}}^{\mathrm{w},\mathrm{s}}$ are bulk water and solute magnetizations along x, y and z directions; R_1w,s and R_2w,s are their longitudinal and transverse relaxation rates, respectively; and k_sw and k_ws are chemical exchange rates of protons from pool s to pool w and vice versa. In addition, ω₁ is the RF irradiation amplitude, and Δω_w,s is the frequency difference between irradiation RF offset and bulk water, and labile proton chemical shifts, respectively. Bloch-McConnell equations enable not only simulation of CEST experiments but also numerical fitting of CEST measurements (54,55). Furthermore, extended Bloch-McConnell equations that describe multi-pool CEST phenomena can properly take into account concomitant RF irradiation effects, including nuclear overhauser effects (NOE) and magnetization transfer (MT) (56).

b. Modified Bloch-McConnell equations for quantifying the CEST effect

Although the CEST effect is commonly described using the simplistic 2-pool exchange model, CEST systems in reality often involve multiple exchangeable sites (57-59). The extended Bloch-McConnell equations that describe multi-pool CEST systems are mathematically tedious, as the coupling matrix scales with the number of exchangeable sites. To overcome this difficulty, a scalable solution based on the classic 2-pool model has been developed to describe multi-pool CEST phenomena (60). For dilute labile protons that undergo slow or intermediate chemical exchanges, the CEST effect, expressed as CEST ratio (CESTR), can be calculated using the CEST asymmetry analysis as

$$\mathrm{CESTR}({\omega }_1,\Delta {\omega }_{\mathrm{s}})=\frac{{\mathrm{I}}_{\mathrm{ref}}({\omega }_1,\Delta {\omega }_{\mathrm{s}})-{\mathrm{I}}_{\mathrm{label}}({\omega }_1,\Delta {\omega }_{\mathrm{s}})}{{\mathrm{I}}_0}$$ [2]

where I_ref and I_label are the signal intensity with RF irradiation applied at the reference and labile proton frequency, respectively. For well-separated CEST groups, the first order approximation of the CEST effect can be obtained by linear superposition of CESTR for each labile proton group as $\mathrm{CESTR}({\omega }_1,\Delta \omega )={\sum }_{\mathrm{i}}{\mathrm{CESTR}}_{\mathrm{i}}({\omega }_1,\Delta {\omega }_{\mathrm{si}})$, where Δω_si is the chemical shift offset of the ith labile group.

Incorporation of cross terms that represent the coupling of CEST effects from multiple labile protons yield

$$\begin{array}{cc}\hfill \mathrm{CESTR}({\omega }_1,\Delta \omega )& \approx \sum _{\mathrm{i}}{\mathrm{CESTR}}_{\mathrm{i}}({\omega }_1,\Delta {\omega }_{\mathrm{si}})\hfill \\ \hfill & -\sum _{\mathrm{i}>\mathrm{j}}\left[\begin{array}{c}{\mathrm{CESTR}}_{\mathrm{i}}{({\omega }_1,\Delta {\omega }_{\mathrm{s}})}^{\ast }{\mathrm{CESTR}}_{\mathrm{j}}{({\omega }_1,\Delta {\omega }_{\mathrm{sj}})}^{\ast }\hfill \\ (2-{\mathrm{CESTR}}_{\mathrm{i}}({\omega }_1,\Delta {\omega }_{\mathrm{si}})-{\mathrm{CESTR}}_{\mathrm{j}}({\omega }_1,\Delta {\omega }_{\mathrm{sj}}))\hfill \end{array}\right].\hfill \end{array}$$ [3]

It has been shown that the simplified approach is in good agreement with conventional simulation algorithms and yet expends markedly shorter simulation times. In addition, this simplified approach offers a scalable solution that can be easily expanded using the same simulation routine when CEST systems involve an arbitrary and large number of exchangeable sites.

c. Simplified solution for quantifying the CEST effect

Although numerical methods are useful to quantify CEST phenomena, analytical solutions for CEST imaging can provide further insight into complex CEST effects. Zhou et al. assumed that RF irradiation instantaneously saturates labile protons without direct saturation of bulk water signals, so the Bloch-McConnell equations could be simplified as (53)

$$\begin{array}{cc}\hfill \frac{{\mathrm{dM}}_{\mathrm{y}}^{\mathrm{s}}}{\mathrm{dt}}=& {\omega }_1{\mathrm{m}}_{\mathrm{z}}^{\mathrm{s}}-{\mathrm{r}}_{2\mathrm{s}}{\mathrm{M}}_{\mathrm{y}}^{\mathrm{s}}+{\mathrm{k}}_{\mathrm{ws}}{\mathrm{M}}_{\mathrm{y}}^{\mathrm{w}}+{\omega }_1{\mathrm{M}}_0^{\mathrm{s}}\hfill \\ \hfill \frac{{\mathrm{dm}}_{\mathrm{z}}^{\mathrm{s}}}{\mathrm{dt}}=& {\omega }_1{\mathrm{M}}_{\mathrm{y}}^{\mathrm{s}}-{\mathrm{r}}_{1\mathrm{s}}{\mathrm{m}}_{\mathrm{z}}^{\mathrm{s}}+{\mathrm{k}}_{\mathrm{ws}}{\mathrm{m}}_{\mathrm{z}}^{\mathrm{w}}\hfill \\ \hfill \frac{{\mathrm{dM}}_{\mathrm{y}}^{\mathrm{w}}}{\mathrm{dt}}=& -{\mathrm{r}}_{2\mathrm{w}}{\mathrm{M}}_{\mathrm{y}}^{\mathrm{w}}+{\mathrm{k}}_{\mathrm{SW}}{\mathrm{M}}_{\mathrm{y}}^{\mathrm{s}}\hfill \\ \hfill \frac{{\mathrm{dm}}_{\mathrm{z}}^{\mathrm{w}}}{\mathrm{dt}}=& -{\mathrm{r}}_{1\mathrm{w}}{\mathrm{m}}_{\mathrm{z}}^{\mathrm{w}}+{\mathrm{k}}_{\mathrm{sw}}{\mathrm{m}}_{\mathrm{z}}^{\mathrm{s}}\hfill \end{array}$$ [4]

with r_1s,w = R_1s,w+k_sw,ws, r_2s,w = R_ksw,ws, ${\mathrm{m}}_{\mathrm{z}}^{\mathrm{s}}={\mathrm{M}}_{\mathrm{z}}^{\mathrm{s}}-{\mathrm{M}}_0^{\mathrm{s}}$, and ${\mathrm{m}}_{\mathrm{z}}^{\mathrm{w}}-{\mathrm{M}}_{\mathrm{z}}^{\mathrm{w}}-{\mathrm{M}}_0^{\mathrm{w}}$. The CEST effect can be solved as

$$\mathrm{CESTR}=\frac{{\mathrm{M}}_0^{\mathrm{w}}-{\mathrm{M}}_{\mathrm{z}}^{\mathrm{w}}\left(\mathrm{TS}\right)}{{\mathrm{M}}_0^{\mathrm{w}}}=\frac{{\mathrm{f}}_{\mathrm{s}}{\mathrm{k}}_{\mathrm{sw}}}{{\mathrm{R}}_{1\mathrm{w}}+{\mathrm{f}}_{\mathrm{s}}{\mathrm{k}}_{\mathrm{sw}}}\alpha [1-{\mathrm{e}}^{-({\mathrm{R}}_{1\mathrm{w}}+{\mathrm{k}}_{\mathrm{ws}})\mathrm{TS}}]$$ [5]

where TS is the RF saturation time, f_s is labile proton ratio with respect to bulk water, and $\frac{{\mathrm{f}}_{\mathrm{s}}\cdot {\mathrm{k}}_{\mathrm{sw}}}{{\mathrm{R}}_{1\mathrm{w}}+{\mathrm{f}}_{\mathrm{s}}\cdot {\mathrm{k}}_{\mathrm{sw}}}$ is the simplistic CEST solution assuming complete saturation of labile protons without RF spillover effects. Importantly, $\alpha =\frac{{\omega }_1^2}{{\omega }_1^2+\mathrm{pq}}$ is the saturation efficiency of labile protons (labeling coefficient), where $\mathrm{p}={\mathrm{R}}_{2\mathrm{s}}+{\mathrm{k}}_{\mathrm{sw}}-\frac{{\mathrm{k}}_{\mathrm{sw}}{\mathrm{k}}_{\mathrm{ws}}}{{\mathrm{R}}_{2\mathrm{w}}+{\mathrm{k}}_{\mathrm{ws}}}$ and $\mathrm{q}={\mathrm{R}}_{1\mathrm{s}}+{\mathrm{k}}_{\mathrm{sw}}-\frac{{\mathrm{k}}_{\mathrm{sw}}{\mathrm{k}}_{\mathrm{ws}}}{{\mathrm{R}}_{1\mathrm{w}}+{\mathrm{k}}_{\mathrm{ws}}}$. This equation can adequately describe the CEST effect when assuming negligible direct RF saturation (weak RF irradiation).

d. RF spillover effect-corrected empirical solution for quantifying the CEST effect

The RF spillover effect refers to the concomitant saturation of water protons due to RF irradiation that aims to specifically saturate labile protons. Although Eq. 5 is valid when assuming a weak B₁ field, the concomitant RF spillover effect may not be negligible, particularly in DIACEST MRI experiments where the labile proton chemical shift is in close proximity to that of bulk water resonance (53,61,62). Both labile proton saturation and RF spillover effects are strongly B₁-dependent — the labeling coefficient increases with RF power and so does the concomitant RF spillover effect (63). Therefore, the maximal apparent CEST effect can be achieved at an intermediate RF power level. Sun et al.(63) modified the simplistic solution with a correction of the RF spillover effect as follows:

$$\mathrm{CESTR}=\frac{{\mathrm{f}}_{\mathrm{s}}\cdot {\mathrm{k}}_{\mathrm{sw}}}{{\mathrm{R}}_{1\mathrm{w}}+{\mathrm{f}}_{\mathrm{s}}\cdot {\mathrm{k}}_{\mathrm{sw}}}\cdot \alpha \cdot (1-\sigma )$$ [6]

where σ is the RF spillover factor, given by

$$\sigma =1-\frac{{\mathrm{r}}_{1\mathrm{w}}}{{\mathrm{f}}_{\mathrm{s}}\cdot {\mathrm{k}}_{\mathrm{sw}}}\left(\frac{{\mathrm{R}}_{1\mathrm{w}}{\mathrm{r}}_{\mathrm{zs}}{\cos }^2\theta +{\mathrm{R}}_{1\mathrm{s}}{\mathrm{k}}_{\mathrm{ws}}\cos \theta {\cos }^2(\theta ∕2)}{{\mathrm{r}}_{\mathrm{zw}}{\mathrm{r}}_{\mathrm{zs}}-{\mathrm{k}}_{\mathrm{ws}}{\mathrm{k}}_{\mathrm{sw}}{\cos }^2(\theta ∕2)}-\frac{{\mathrm{R}}_{1\mathrm{w}}{\mathrm{r}}_{2\mathrm{s}}{\cos }^2\theta }{{\mathrm{r}}_{zw}{\mathrm{r}}_{1\mathrm{s}}-{\mathrm{k}}_{\mathrm{ws}}{\mathrm{k}}_{\mathrm{sw}}{\mathrm{sikn}}^2\theta }\right)$$ [7]

in which $\theta ={\tan }^{-1}\left(\frac{{\omega }_1}{\Delta \omega }\right)$, r_ZS =r_1s cos² θ +r_2s sin² θ r_ZW = r_1W cos² (θ/2) +r_2W sin² (θ/2). It shows that with weak RF power, the spillover factor is negligible (i.e., σ=0), and the modified solution is consistent with that of Zhou et al.

e. Lorentzian fitting for quantifying CEST effects

The Z-spectrum is a plot of the water signal when RF irradiation is swept around the bulk water resonance. For a simplified 3-pool model that includes the CEST effect, direct water saturation (DWS) and macromolecular MT effects, it is reasonable to assume that the concomitant effects are symmetric around the water resonance. A Lorentzian model has been introduced to analyze the combined saturation based on the weak saturation pulse (WSP) approximation (64-66). Lorentzian line shapes for proton transfer ratio (PTR) and DWS are stated as

$$\mathrm{L}(\mathrm{A},\Gamma ,\Delta \omega )=\frac{\mathrm{A}\cdot {\Gamma }^2∕4}{{\Gamma }^2∕4+\Delta {\omega }^2}$$ [8]

with A and Γ being the peak and full width at half maximum (FWHM) of the effect. In addition, the parameters within direct water saturation (L₀(A0,Γ₀)) and CEST effects (L₁(A₁,Γ₁)) are

$$\begin{array}{cc}\hfill & {\mathrm{A}}_0=\frac{{\omega }_1^2}{{\omega }_1^2+\mathrm{PQ}},{\Gamma }_0=2\sqrt{{\omega }_1^2\frac{\mathrm{P}}{\mathrm{Q}}+{\mathrm{p}}^2},{\mathrm{A}}_1=\frac{{\mathrm{k}}_{\mathrm{ws}}}{{\mathrm{R}}_{1\mathrm{w}}+{\mathrm{k}}_{\mathrm{ws}}}\frac{{\omega }_1^2}{{\omega }_1^2+\mathrm{pq}},{\Gamma }_1=2\sqrt{{\omega }_1^2\frac{\mathrm{p}}{\mathrm{q}}+{\mathrm{p}}^2},\text{where}\hfill \\ \hfill \mathrm{P}=& {\mathrm{R}}_{2\mathrm{w}}+{\mathrm{k}}_{\mathrm{ws}}-\frac{{\mathrm{k}}_{\mathrm{ws}}\mathrm{k}\mathrm{sw}}{{\mathrm{R}}_{2\mathrm{s}}+{\mathrm{k}}_{\mathrm{sw}}},\mathrm{Q}={\mathrm{R}}_{1\mathrm{w}}+{\mathrm{k}}_{\mathrm{ws}}-\frac{{\mathrm{k}}_{\mathrm{ws}}{\mathrm{k}}_{\mathrm{sw}}}{{\mathrm{R}}_{1\mathrm{s}}+{\mathrm{k}}_{\mathrm{sw}}}.\hfill \end{array}$$

The underlying MT effect can be integrated into the multi-pool approximation function (60), and the combined transfer rate (CTR) is

$$\mathrm{CTR}=\frac{{\mathrm{L}}_1\left(\Delta \omega \right)+{\mathrm{L}}_2\left(\Delta \omega \right)-2\cdot {\mathrm{L}}_1\left(\Delta \omega \right)\cdot {\mathrm{L}}_2\left(\Delta \omega \right)}{1-{\mathrm{L}}_1\left(\Delta \omega \right)\cdot {\mathrm{L}}_2\left(\Delta \omega \right)}$$ [9]

where L₁ = PTR and L₂ is a Lorentzian function representing MTR′_asym. Similarly, Sheth et al. proposed a model function of multiple Lorentzian lines to fit the CEST spectrum as (67)

$$1-\frac{{\mathrm{M}}_{\mathrm{S}}}{{\mathrm{M}}_0}=\frac{{\mathrm{A}}_1{\mathrm{w}}_1}{\pi [{(\mathrm{sf}-\Delta {\mathrm{w}}_1)}^2+{\mathrm{w}}_1^2]}+\frac{{\mathrm{A}}_2{\mathrm{w}}_2}{\pi [{(\mathrm{sf}-\Delta {\mathrm{w}}_2)}^2+{\mathrm{w}}_2^2]}+\frac{{\mathrm{A}}_3{\mathrm{w}}_3}{\pi [{(\mathrm{sf}-\Delta {\mathrm{w}}_3)}^2+{\mathrm{w}}_3^2]}+\frac{{\mathrm{A}}_4}{\pi {\mathrm{w}}_4}\sqrt{\frac{2}{\pi }}{\int }_0^{\frac{\pi }{2}}\frac{{\mathrm{e}}^{-2{\left[\frac{2(\mathrm{sf}-\Delta {\omega }_4)}{{\mathrm{w}}_4\mid 3{\cos }^2\theta -1\mid }\right]}^2}}{\mid 3{\cos }^2\theta -1\mid }\sin \theta \mathrm{d}\theta$$ [10]

where A, w and Δω are the area, FWHM and center of Lorentzian spectra, respectively. The formula successfully modeled in vivo measurement of tumor extracellular pH in conjunction with administration of PARACEST agents (67). Indeed, Desmond et al. constructed endogenous CEST parameter maps of tumor xenografts by decomposing CEST spectra into four Lorentzian line shapes that represent the direct effect, amide, amine, and aliphatic peaks (66).

f. Spin locking theory for quantifying the CEST effect

Quantification of the chemical exchange process using off-resonance spin locking (SL) MRI is shown to be comparable to conventional Z-spectral imaging for slow to intermediate chemical exchanges (68-71). For the classic 2-pool exchange model, the steady-state solution $\left({\mathrm{M}}_{\mathrm{ss}}^{\mathrm{w}}\right)$ is given as

$$\begin{array}{cc}\hfill {\mathrm{M}}_{\mathrm{ss}}^{\mathrm{w}}& \approx {\mathrm{M}}_0^{\mathrm{w}}\cdot \frac{{\mathrm{R}}_{1\mathrm{w}}{\cos }^2\theta }{{\mathrm{R}}_{1\mathrm{p}}}\hfill \\ \hfill & ={\mathrm{M}}_0^{\mathrm{w}}\cdot \frac{{\mathrm{R}}_{1\mathrm{w}}{\cos }^2\theta }{{\mathrm{R}}_{1\mathrm{w}}{\cos }^2\theta +({\mathrm{R}}_{2\mathrm{w}}+{\mathrm{k}}_{\mathrm{sw}}){\sin }^2\theta }\hfill \end{array}$$ [11]

where R_1ρ is the longitudinal relaxation rate in the rotating frame. Notably, the CEST effect can be quantified using the inverse difference of the CEST ratio (CESTR_ind) as follows:

$$\begin{array}{cc}\hfill {\mathrm{CESTR}}_{\mathrm{ind}}=& \frac{{\mathrm{M}}_0^{\mathrm{w}}}{{\mathrm{M}}_{\mathrm{ss}}^{\mathrm{w}}\left(\Delta {\omega }_{\mathrm{s}}\right)}-\frac{{\mathrm{M}}_0^{\mathrm{w}}}{{\mathrm{M}}_{\mathrm{ss}}^{\mathrm{w}}(-\Delta {\omega }_{\mathrm{s}})}\hfill \\ \hfill =& \frac{{\mathrm{f}}_{\mathrm{s}}\cdot {\mathrm{k}}_{\mathrm{sw}}}{{\mathrm{R}}_{1\mathrm{w}}{\cos }^2\theta }\cdot \alpha \hfill \end{array}$$ [12]

The inverse difference solution of the CEST effect corrects the concomitant RF spillover effect, providing improved quantification of CEST measurement, which is particularly important for DIACEST MRI (72). Note that optimized sensitivity occurs by selecting a moderate RF power, albeit the CESTR_ind calculation is immune to RF spillover effects.

3. Dependence Of CEST MRI Measurement

The experimentally measurable CEST effect depends not only on CEST agent concentration and exchange rate, but also on relaxation rate and a number of experimental variables such as field strength, RF irradiation power level and acquisition schemes, including repetition time and flip angle (51). These confounding factors, therefore, need to be carefully examined for qCEST analysis.

a. Relaxation rate

The strong T₁ relaxation rate (T_1w) dependence of the CEST effect is explained by the fact that saturation transfer-induced signal reduction is counterbalanced with signal recovery from longitudinal relaxation of the bulk water signal (3). Likewise, the T₂ relaxation rate (T_2w) comes into play through the concomitant RF spillover effect (63). Notably, the exchangeable proton pool with a short T_2w (i.e., broad spectral width) is exposed to direct RF saturation with the bulk water pool. The empirical solution determining the relationship between the CEST effect and relaxation rates is given in Eq. 7.

b. Magnetic field strength

CEST experiments demonstrate a strong correlation between the CEST effect and field strength through the variability of T_1w and T_2w, which eventually impacts the spillover effect and the optimal B₁ irradiation level. Figure 1 shows a simulated T_1w (Fig. 1a) and T_2w (Fig. 1b) for brain gray matter (GM) as a function of field strength (73,74). Simulated CESTR (Eq. 6) of endogenous amide proton transfer ratio (APTR) using an empirical solution demonstrates increasing APTR concomitantly with field strength level that is likely attributable to prolonged T₁ and increased optimal B₁ levels (Fig. 1c). Moreover, APTR initially increases linearly with field strength and gradually plateaus at a very high field regime because the chemical exchange rate of amide protons is relatively slow (Fig. 1d) (42,75). On the other hand, the CEST effect on groups of higher exchange rates, such as amine and hydroxyl groups, significantly increases with field strength.

Fig. 1.

Plot of T₁ (a) and T₂ (b) as a function of field strength in grey matter (GM). Simulated CEST effect (CESTR) as a function of B₁ irradiation power (c), and the maximal CEST effect for a given field strength (d).

c. B₁ irradiation level

A lower labeling coefficient from weak RF power (i.e., inefficient labile proton saturation) leads to an attenuated CEST effect. Contrarily, very strong RF power induces a non-negligible RF spillover effect, which is more pronounced in DIACEST MRI where labile proton resonance is in close proximity to that of bulk water. The B₁ dependence of the CEST effect can be described reasonably well with the empirical solution (Eq. 6), which eventually leads to an answer for the optimal RF level that maximizes the CEST effect. Jones et al. (65) investigated the effect of saturation strength and duration on the pulsed steady-state APT effect for a three-compartment model of semisolid macromolecular protons, solute amide protons and bulk water protons. The simulation shows that MTC and DS strongly reduce with B₁ decrease, and a moderate RF irradiation level maximizes APTR by reasonably balancing the labeling coefficient and spillover factor (Fig.2).

Fig. 2.

(a) APTR effect, and (b) MTC and DS as a function of RF saturation strength and duration for a three-compartment model of semisolid macromolecular protons, solute amide protons, and bulk water protons.

d. CEST agent properties

For dilute CEST agents with slow and intermediate chemical exchange rates, the CEST effect approximately linearly correlates with labile proton concentration and exchange rates. However, the CEST effect deviates from the linear relationship when the reverse exchange rate is comparable to the relaxation rate (i.e., k_ws=f_s·k_sw~R_1w). The equation describes CEST agent kinetics and is analogous to the Michaelis-Menten equation of enzyme kinetics, which can be used to correlate the CEST effect with the concentration of the agent in solution (76). It has been shown that k_ws can be estimated and adequately corrected with T₁ normalization (77). Additionally, the relationship between the exchange rate and the CEST effect is complicated by confounding experimental factors, particularly the labeling coefficient and spillover factor that are largely independent of the labile proton fraction ratio (78).

4. Optimization Of CEST MRI Experiments

Optimization of CEST MRI is important particularly in endogenous CEST MRI whose effects are typically small. In this section, we introduce signal-to-noise ratio per unit time (SNR_put) for optimizing CEST experiments, as well as experimental parameters that include B₁ level, RF irradiation scheme, repetition time and flip angle.

a. Signal-to-noise ratio efficiency for optimization of CEST MRI

The signal-to-noise ratio (SNR) of the CEST asymmetry effect has been derived as (51)

$${\mathrm{SNR}}_{\mathrm{CESTR}}=\frac{\mathrm{CESTR}}{\sqrt{2+{\mathrm{CESTR}}^2}}\cdot {\mathrm{SNR}}_{{\mathrm{I}}_0}$$ [13]

where SNR_I0 is SNR of the control image. This shows that the SNR of CEST imaging varies not only with the magnitude of the CEST effect (i.e., CESTR) but also with SNR_I0. Experimental parameters, repetition time, echo time and flip angle are determining factors of SNR_I0, which dictate CEST sensitivity. Notably, SNR SNR efficiency (i.e., ${\mathrm{SNR}}_{\mathrm{put}}=\frac{{\mathrm{SNR}}_{\mathrm{CESTR}}}{\sqrt{\mathrm{TR}\cdot \mathrm{NSA}}}$) is inversely related with repetition time and number of signal average (NSA). A typical steady-state CEST sequence is comprised of a long RF irradiation module, followed by fast image readout, such as echo planar imaging (EPI), which confers relatively good SNR and spatiotemporal resolution (42,65,71,79,80). Figure 3 shows experimental validation of CEST MRI SNR comparison from an in vitro pH phantom. Although the CESTR contrast between two pH compartments (ΔCESTR) steadily increases with TR (Fig. 3a), CNR_put (i.e., ${\mathrm{CNR}}_{\mathrm{put}}=\frac{{\mathrm{CESTR}\mid }_{\mathrm{pH}\left(\mathrm{a}\right)}-{\mathrm{CESTR}\mid }_{\mathrm{pH}\left(\mathrm{b}\right)}}{\sqrt{{\sigma }_{\mathrm{pH}\left(\mathrm{a}\right)}^2+{\sigma }_{\mathrm{pH}\left(\mathrm{b}\right)}^2)∕2}}\cdot \frac{1}{\sqrt{\mathrm{TR}\cdot \mathrm{NSA}}}$) peaks at an intermediate TR — approximately twice the T₁ (Fig. 3b). Under the optimal TR, we found that both ΔCESTR (Fig. 3a) and CNR_put (Fig. 3b) increase with the RF duty cycle. Hence, within the permissible range of scan time and specific absorption rate (SAR) limits, the longest-achievable TS is generally preferred to obtain maximized CEST MRI contrast. Moreover, ΔCESTR decreases with the RF flip angle (Fig. 3a), while CNR_put increases with the RF flip angle, which peaks at approximately 75° (Fig. 3b). This result indicates that both the amplitude and SNR efficiency have to be considered when optimizing CEST MRI experiments.

Fig. 3.

Experimental validation of optimal experimental condition in an in vitro pH CEST phantom. The pH-weighted CEST contrast (ΔCESTR) increases with TR (a), while its contrast-to-noise ratio efficiency (CNR_put) peaks at an intermediate TR (b). Both ΔCESTR (a) and CNR_put (b) increase with RF duty cycle. In addition, ΔCESTR decreases with RF flip angle (a), while CNR_put initially increased with RF flip angle and peaked at about 75° (b).

b. Continuous wave (CW) RF irradiation for optimization of CEST MRI

The optimal RF power that maximizes the CEST effect is deduced when the saturation efficiency and spillover factor are balanced (63) as follows:

$${\omega }_1=\sqrt{\mathrm{pq}}\left\{\sqrt{1+\frac{4({\mathrm{f}}_{\mathrm{S}}+{\mathrm{f}}_{\mathrm{W}})\stackrel{‒}{\beta }{\eta }_{2\mathrm{S}}}{[{\mathrm{f}}_{\mathrm{S}}{\eta }_{2\mathrm{S}}(1+2\stackrel{‒}{\beta }+{\eta }_{\mathrm{S}}+4{\eta }_{\mathrm{W}})+{\mathrm{f}}_{\mathrm{W}}(4+4{\beta }^2+{\eta }_{2\mathrm{S}}(5+{\eta }_{2\mathrm{S}}+e{\eta }_{\mathrm{W}})-4\beta (2+{\eta }_{\mathrm{W}})-4\beta (2+{\eta }_{2\mathrm{S}}+{\eta }_{2\mathrm{S}}{\eta }_{\mathrm{W}}))]}\frac{\Delta {\omega }^2}{\mathrm{pq}}-1}\right\}$$ [14]

with $\beta =\frac{{\mathrm{k}}_{\mathrm{WS}}{\mathrm{k}}_{\mathrm{SW}}}{{\mathrm{r}}_{1\mathrm{W}}{\mathrm{r}}_{1\mathrm{S}}}$, $\stackrel{‒}{\beta }=1-\beta$, ${\eta }_{\mathrm{W}}=\frac{{\mathrm{r}}_{\mathrm{W}}}{{\mathrm{r}}_{\mathrm{W}}}$, ${\eta }_{\mathrm{S}}=\frac{{\mathrm{r}}_{\mathrm{S}}}{{\mathrm{r}}_{1\mathrm{S}}}$, ${\eta }_{2\mathrm{S}}=\frac{{\mathrm{r}}_{2\mathrm{S}}}{{\mathrm{r}}_{1\mathrm{S}}}$, r_W = r_2W – r_1W, r_S = r_2S – r_1S, ${\mathrm{f}}_{\mathrm{W}}=\frac{{\mathrm{R}}_{1\mathrm{W}}}{{\mathrm{r}}_{1\mathrm{W}}}$ and ${\mathrm{f}}_{\mathrm{S}}=\frac{{\mathrm{R}}_{1\mathrm{S}}}{{\mathrm{k}}_{\mathrm{SW}}}$. This indicates that the optimal B₁ level depends not only on the labile proton ratio, exchange rate and chemical shift, but also on relaxation rates. Figure 4 shows a numerical simulation of the optimal B₁ irradiation level as a function of field strength and chemical shift when typical T₁ and T₂ values of the GM are assumed (73,74). Note that the “exchange rate normalized” optimal B₁ level (i.e., γB₁/k_sw) approaches unity at high field and large chemical shift due to a reduced RF spillover effect. At typical clinical field strengths, the optimal RF power level of the DIACEST agents, whose chemical shifts are often less than 5 ppm from the bulk water, is substantially reduced from the exchange rate.

Fig. 4.

Numerically determined optimal B₁ level as a function of field strength and chemical shift. The exchange rate normalized optimal B₁ level approaches unit at high field and chemical shift due to mitigated RF spillover effects.

c. Pulsed RF irradiation for optimization of CEST MRI

CEST imaging has been accomplished using long block pulses, a series of short pulses (“pulse train”) that has a saturation efficiency similar to that of the long hard pulse, or alternatively steady-state approaches using alternating brief saturation and image acquisition (65). Although the pulse train CEST has been used in some early CEST experiments (42), long continuous-wave (CW) RF irradiation is commonly used in preclinical scanners to establish the steady-state CEST effect prior to image acquisition where the limitations of the RF duty cycle are less of a concern. However, CW irradiation is often not feasible on clinical scanners, which necessitates the use of a pulsed RF or pulse train irradiation scheme (81-84). The pulsed RF irradiation carries at least three parameters to optimize, namely, irradiation pulse duration, flip angle, and inter-pulse delay, in contrast to only one parameter (i.e., B₁) requiring optimization in the case of CW irradiation. Sun et al. investigated the effects of the RF irradiation pulse train and labile proton properties on the pulsed-CEST MRI measurement (82,85), which showed that the optimal pulse irradiation can be reasonably inferred from the well-prescribed CW design. The optimal irradiation flip angle of pulsed irradiation is approximately 180° and is not dependent on acquisition parameters and sample properties. In pulsed-CEST imaging for slow chemical exchange, a flip angle of approximately 180° for each irradiation pulse is suitable because, in this case, an inversion pulse retains labile and bulk water protons in opposite phases. However, the inter-pulse delay of pulsed-CEST MRI degrades saturation efficiency and, hence, measureable CEST effect when imaging intermediate and fast chemical exchanges. In addition, Zu et al. found that the optimal average power and flip angle of pulsed irradiation are independent of each other. Both simulated and experimental results showed the pulsed-CEST contrast peaks at the flip angle of 180°(Fig. 5), and the optimal average power of pulsed irradiation is similar to the optimal RF field amplitude for CW-CEST MRI (86). Schmitt et al. proposed using long-period saturation pulse trains with balanced duty-cycles, which have the advantages of fewer hardware specifications, easy implementation, and low SAR without compromising CEST contrast (87).

Fig. 5.

(a) Simulated and (b) experimental pulsed-CEST contrast as a function of average power and flip angle of pulsed irradiation at 9.4T with a duty cycle of 50%. Stars represent the experimental results.

PARACEST MRI agents have large chemical shifts, which enable detection of labile protons undergoing a chemical exchange that is faster than DIACEST MRI. However, it requires relatively strong RF irradiation in order to saturate fast labile protons, resulting in an intense SAR. Vinogradov et al. proposed a WALTZ-16 pulse train with amplitude and phase modulation positioned on the bulk water resonance for detection of PARACEST agents that leads to less saturation RF power demand (88). Development of sophisticated on-resonance irradiation pulse schemes with composite pulses can further mitigate the susceptibility to field inhomogeneity for on-resonance CEST imaging schemes. Recently, a time-interleaved parallel transmission based APT-MRI technique using multiple transmission coils has been demonstrated that substantially increased the saturation pulse duration (89).

d. Unevenly-segmented RF irradiation for efficient CEST imaging

Conventional CEST MRI typically consists of a long RF irradiation module followed by fast image acquisition to obtain the steady-state CEST contrast. Because of lengthy RF irradiation and relaxation recovery, it is not efficient to acquire multi-slice CEST images (90). Sun et al. proposed an unevenly segmented RF labeling scheme to enhance CEST imaging sensitivity (91). It includes a long primary RF irradiation sandwiched between a repetitive secondary short RF irradiation module and fast image readout for each saturation block. In this way, the steady-state CEST effect created by the primary irradiation is refreshed by short secondary irradiation during multi-slice excitations, and efficiency of signal acquisition can be significantly improved. This approach clearly demonstrated a significant sensitivity benefit per unit time over the conventional method.

e. Multi-echo CEST MRI for sensitive CEST imaging

For CEST imaging of slow and intermediate chemical exchange, signal averaging is often needed in order to augment CEST sensitivity. Because T₂ signal decay is normalized during the CEST asymmetry calculation, the magnitude of the CEST effect is independent of echo time. It has been shown that a multi-echo EPI readout can yield the same CEST effect as the conventional single-echo acquisition. Moreover, the sensitivity of multi-echo CEST imaging was significantly higher than that of conventional single-echo CEST-EPI acquisition (92). Notably, both SNR and CNR from multi-echo CEST imaging were substantially higher than those obtained by conventional single-echo acquisition, which may facilitate in vivo CEST imaging by virtue of substantially improved sensitivity gain.

f. Image readout

There has been a variety of MRI acquisition methods tailored to improve sensitivity and efficiency of CEST imaging. One approach is using a long selective saturation strategy combined with rapid acquisition with relaxation enhancement (RARE) pulse sequences for PARACEST imaging under long T₁ relaxation conditions (93). Alternatively, a fast low-angle shot (FLASH) readout after short selective saturation periods could enhance PARACEST detection under short T₁ relaxation conditions (93). Three-dimensional CEST imaging with gradient- and spin-echo (GRASE) readout that combines the turbo spin-echo (TSE) and EPI along with 2D sensitivity encoding (SENSE) accelerations enabled significant reduction in the CEST acquisition time (94). Recently, Shah et al. integrated the single-shot steady-state free precession (SSFP) readout with CEST RF irradiation, and demonstrated comparable results with EPI readout but with substantially fewer distortion artifacts (95). More recently, keyhole and compressed sensing (CS) CEST MRI have been demonstrated, which may further enhance fast CEST imaging (96-99).

5. Quantitative CEST (qCEST) MRI

The experimentally measured CEST effect involves complex physical and chemical variables, not only parameters of interest such as CEST agent concentration, pH and temperature, but also relaxation rate and other experimental conditions. Development of qCEST analysis is necessary to augment conventional CEST-weighted MRI and to fully characterize the underlying CEST systems (49,50,75,100-102).

a. QUEST and QUESP for quantification of the CEST effect

Equation 5 describes CESTR as a function of saturation RF irradiation time (TS) (53). If T_1w can be independently determined, the labile proton ratio-weighted exchange rate can be solved by fitting CESTR as a function of saturation time (i.e., QUEST). This was further simplified with a linear fitting procedure—the reciprocal linear QUEST (RL-QUEST) method (103). In addition, the CEST system can also be quantified by using the RF power dependence of the labeling coefficient (i.e., QUESP). These methods have shown to be successful in determining a self-consistent proton exchange rate. Briefly, QUEST can be more accurate than QUESP owing to the easier measurement of saturation time than that of saturation power, especially with B₁ inhomogeneity, while QUESP has the advantage of not being limited by the demand for precision in labile proton ratio measurement (100). Recently, Randtke et al. developed QUESPT, which measures the CEST effects as a function of saturation time and saturation power, and has the potential to mitigate fitting bias (102). Note that QUEST, QUESP and QUESPT become less effective in quantifying high exchange rate cases due to the overestimation of the saturation efficiency. The Hanes-Woolf linear QUESP (HW-QUESP) method, however, was shown to produce accurate estimates of fast exchange rates because it includes a wide range of saturation power in both the x- and y-values of the plot (102).

b. QUEST with ratiometric analysis (QUESTRA) for improved quantification of the CEST MRI effect

The saturation time-dependent QUEST analysis assumes negligible direct RF saturation. However, it has been shown that a time-dependent CEST effect is governed by T_1ρ (longitudinal relaxation rate in the rotating frame), instead of the intrinsic T₁ (68,69). Sun extended the QUEST approach with ratiometric analysis (QUESTRA), which normalizes the magnetization transfer ratio (MTR) at labile frequency by MTR at reference frequency (78)

$$\begin{array}{cc}\hfill \mathrm{QUESTRA}\left(\mathrm{TS}\right)& =[1-\left(\frac{{\mathrm{MTR}}_{\mathrm{label}}\left(\mathrm{TS}\right)}{{\mathrm{MTR}}_{\mathrm{lavel}\_\mathrm{ss}}}\right)]∕[1-\left(\frac{{\mathrm{MTR}}_{\mathrm{ref}}\left(\mathrm{TS}\right)}{{\mathrm{MTR}}_{\mathrm{ref}\_\mathrm{ss}}}\right)]\hfill \\ \hfill & ={\mathrm{e}}^{-{\mathrm{f}}_{\mathrm{s}}\cdot {\mathrm{k}}_{\mathrm{sw}}\cdot \mathrm{TS}}\hfill \end{array}$$ [15]

where MTR_{label_ss} and MTR_{ref_ss} are the steady-state MTR for the label and reference scans, respectively. Because the label and reference scans experience similar direct RF saturation effects, the QUESTRA solution eliminates the confounding spillover effect with little dependence on T₁, T₂, RF irradiation power and chemical shift.

c. RF power-dependent qCEST MRI analysis

Optimization of the B₁-dependent CEST effect has benefited qCEST analysis (63). To account for the semisolid magnetization transfer (MT) effect, a dual 2-pool model was formulated based on the empirical quantitative solution of pH-sensitive in vivo APT MRI, which allowed simultaneous determination of labile amide proton concentration and exchange rates at normal and ischemic pH (75). In addition, it has been shown that the optimal RF power, which varies with the exchange rate, has a lesser degree of dependence on the labile proton concentration (50). Under circumstances of multiple RF irradiation levels, the labile proton ratio and exchange rate can be determined independently (49). In addition, Zu et al. resolved the labile proton ratio and exchange rate using the chemical exchange rotation transfer (CERT) approach, which formulates CEST measurement as a function of the flip angle of the irradiation pulse (80,104,105).

d. Omega plot for quantification of the PARACEST MRI effect

Dixon et al. proposed the omega plot for quantifying PARACEST MRI. The labile proton signal intensity is shown to be (106)

$$\frac{{\mathrm{M}}_{\mathrm{ss}}^{\mathrm{w}}}{{\mathrm{M}}_0^{\mathrm{w}}-{\mathrm{M}}_{\mathrm{ss}}^{\mathrm{w}}}=\frac{{\mathrm{k}}_{\mathrm{sw}}{\mathrm{R}}_{1\mathrm{w}}}{{\mathrm{f}}_{\mathrm{s}}}(\frac{1}{{\mathrm{k}}_{\mathrm{sw}}^2}+\frac{1}{{\omega }_1^2})$$ [16]

where ${\mathrm{M}}_{\mathrm{ss}}^{\mathrm{w}}$ is steady, the steady-state signal at the labile proton frequency. By plotting $\frac{{\mathrm{M}}_{\mathrm{ss}}^{\mathrm{w}}}{{\mathrm{M}}_0^{\mathrm{w}}-{\mathrm{M}}_{\mathrm{ss}}^{\mathrm{w}}}\mathrm{vs}.1∕{\omega }_1^2$, the exchange rate can be determined without a priori knowledge of the labile proton ratio and relaxation rate. A phantom study confirmed that the exchange rates estimated from the omega plots were in good agreement with those from the solution of Bloch-McConnell equations at slow exchanging rates. Fast exchanging protons, however, experience incomplete saturation, which introduces measurement inaccuracy. In this case, the Hanes-Woolf QUESP solution may be an alternative approach to minimize such systematic errors (102).

The concomitant RF spillover effect can be corrected to improve the omega plot analysis. It has been shown that the RF spillover effect can be reasonably estimated, and the RF spillover factor-corrected omega plot analysis can be extended for DIACEST MRI as (51,107)

$$\frac{1}{{\mathrm{CESTR}}_{\sigma }}\approx \left(1+\frac{{\mathrm{R}}_{1\mathrm{w}}}{{\mathrm{f}}_{\mathrm{s}}\cdot {\mathrm{k}}_{\mathrm{sw}}}\right)+\frac{{\mathrm{k}}_{\mathrm{sw}}\cdot ({\mathrm{R}}_{2\mathrm{s}}+{\mathrm{k}}_{\mathrm{sw}})\left(1-\frac{{\mathrm{f}}_{\mathrm{s}}\cdot {\mathrm{k}}_{\mathrm{sw}}}{{\mathrm{R}}_{1\mathrm{w}}+{\mathrm{f}}_{\mathrm{s}}\cdot {\mathrm{k}}_{\mathrm{sw}}}\right)\left(1+\frac{{\mathrm{R}}_{1\mathrm{w}}}{{\mathrm{f}}_{\mathrm{s}}\cdot {\mathrm{k}}_{\mathrm{sw}}}\right)}{{\omega }_1^2}.$$ [17]

Both the labile proton exchange rate and ratio can be solved with ${\mathrm{k}}_{\mathrm{sw}}=\frac{\sqrt{{\mathrm{R}}_{2\mathrm{s}}^2+4\cdot {\mathrm{C}}_1∕({\mathrm{C}}_0-1)}-{\mathrm{R}}_{2\mathrm{s}}}{2}$ and ${\mathrm{f}}_{\mathrm{s}}=\frac{{\mathrm{R}}_{1\mathrm{w}}}{{\mathrm{k}}_{\mathrm{sw}}\cdot ({\mathrm{C}}_0-1)}$, where C₀ and C₁ are the intercept and slope of the modified omega plot analysis.

e. Ratiometric pH MRI

The ratiometric CEST MRI compares the CEST effects from multiple labile protons of the same molecule. The normalization calculation makes the ratiometric measurement independent of CEST agent concentration, resulting in substantial simplification of qCEST analysis (108,109). Sheth et al. investigated a PARACEST contrast agent (Yb-DO3A-oAA) to measure extracellular pH (67,110). Figure 6 shows excellent linearity between the CEST effects, and the pH exhibited good dynamic range (67). Recently, iopamidol, a food and drug administration (FDA)-approved CT contrast agent, has demonstrated potential for pH imaging (111). Longo et al. demonstrated that iopamidol pH MRI can monitor renal pH changes in acute renal injury (112,113). Alternative iodinated CT agents (iopromide) for pH imaging have also been evaluated (114). More recently, a method for endogenous ratiometric CEST MRI has been developed for in vivo pH imaging by comparing amide and amine exchangeable groups (66,115).

Fig. 6.

CEST ratio-pH correlation for Yb-DO3A-oAA at 300 MHz magnetic field strength. (a) The % CEST effects of the amide (filled circles) and amine (unfilled circles) of 100 mM Yb-DO3A-oAA were measured at 37 °C using 20 μT saturation power. (b) The log10 of a ratio of CEST showed an excellent correlation with pH (R² = 0.99).

6. Artifacts And Post-Processing

Because the CEST effect is typically small, CEST MRI is prone to field inhomogeneity artifacts. In addition, conventional asymmetry analysis is subject to lipid signal contamination and contributions from asymmetric MT and NOE, which have to be considered when measuring the in vivo CEST effect.

a. Field inhomogeneity

The CEST effect is sensitive to field inhomogeneity (116-121). B₀ inhomogeneity can be measured using a conventional field map (122). B₀ shift can also be determined by fitting the direct water saturation with Bloch-McConnell (77) or Lorentzian line models (64,65,123), or a water saturation shift referencing the (WASSR) approach (122,124,125). B₀ inhomogeneity-induced CEST artifacts can be corrected by aligning the interpolated Z-spectrum based on B₀ shift. WASSR correction can be achieved with partial Z-spectral sampling in segments around the label and reference frequencies to shorten the scan time (84,126). Moreover, B₀ inhomogeneity correction can also be rectified with a model-based algorithm. Sun et al. showed that the MT asymmetry calculation is given by (75)

$${\mathrm{MTR}}_{\mathrm{asym}}={\mathrm{CESTR}}^{\prime }+\Delta \mathrm{MTR}$$ [19]

where CESTR′ represents CESTR with B₀ field inhomogeneity contamination, and ΔMTR is the MTR offset due to a field inhomogeneity-induced MTR shift. Taking into account field inhomogeneity-modulated experimental factors, the corrected PTR can be shown to be CESTR = η · CESTR′ = η ·(MTR_asym − ΔMTR), where η is the modulation factor: $\eta =\frac{\alpha ({\mathrm{B}}_1,\Delta {\omega }_{\mathrm{s}})\cdot (1-\sigma ({\mathrm{B}}_1,\Delta {\omega }_{\mathrm{s}}))}{\alpha ({\mathrm{B}}_1,\Delta {\omega }_{\mathrm{s}}+\Delta \omega )\cdot (1-\sigma ({\mathrm{B}}_1,\Delta {\omega }_{\mathrm{s}}+\Delta \omega ))}$. The compensated CESTR is given as

$$\mathrm{CESTR}=\frac{\alpha ({\mathrm{B}}_1,\Delta {\omega }_{\mathrm{s}})\cdot (1-\sigma ({\mathrm{B}}_1,\Delta {\omega }_{\mathrm{s}}))}{\alpha ({\mathrm{B}}_1,\Delta {\omega }_{\mathrm{s}}+\Delta \omega )\cdot (1-\sigma ({\mathrm{B}}_1,\Delta {\omega }_{\mathrm{s}}+\Delta \omega ))}\times [{\mathrm{MTR}}_{\mathrm{asym}}-\frac{4\Delta {\omega }_{\mathrm{s}}{\omega }_1^2{\mathrm{T}}_{1\mathrm{w}}{\mathrm{T}}_{2\mathrm{w}}^3\Delta \omega }{(1+\Delta {\omega }_{\mathrm{ref}}^2{\mathrm{T}}_{2\mathrm{w}}^2+{\omega }_1^2{\mathrm{T}}_{1\mathrm{w}}{\mathrm{T}}_{2\mathrm{w}})(1+\Delta {\omega }_{\mathrm{lavel}}^2{\mathrm{T}}_{2\mathrm{w}}^2+{\omega }_1^2{\mathrm{T}}_{1\mathrm{w}}{\mathrm{T}}_{2\mathrm{w}})}].$$ [20]

Recently, Song et al. proposed a new CEST phase mapping scheme based on length and offset varied saturation (LOVARS). Figure 7 displays the LOVARS scheme as applied to the imaging of 9L gliosarcomas in mice. The WASSR map (Fig. 7b) shows substantial B₀ variation, which distorts the MTR_asym map (Fig. 7c). The LOVARS phases show a large difference between the two ROIs (Fig. 7d), despite their similar MTR_asym magnitudes in the uncorrected CEST map (Fig. 7c). With either fast Fourier transform (FFT) (Fig. 7e) or the general linear model (GLM) (Fig. 7f), the thresholded imaginary component map (Fig. 7g) contains the same information as that obtained by conventional MTR_asym correction, but with the superiority of higher CNR and less sensitivity to field inhomogeneity (127).

Fig. 7.

In vivo demonstration of the LOVARS scheme as applied to the imaging of 9L gliosarcomas in mice. (a) T2-weighted image; (b) B₀ shift map; (c) uncorrected MTR_asym map; (d) LOVARS time domain data (top) with phase (middle) and magnitude (bottom) traces determined through FFT with ROIs as marked in (c); (e) LOVARS phase map calculated using FFT; (f) LOVARS phase map calculated using GLM; (g) thresholded LOVARS imaginary component map.

b. Filtering of CEST MRI

To improve quantitative interpretation of CEST contrast maps, Liu et al. proposed an MRI segmentation technique based on two resonance frequency offsets and the normalized magnetization ratio (NOMAR) filtering, which is defined as (128)

$$\mathrm{NOMAR}(\Delta {\omega }_1∕\Delta {\omega }_2)=\frac{1-\mathrm{MTR}\left(\Delta {\omega }_1\right)}{1-\mathrm{MTR}\left(\Delta {\omega }_2\right)}.$$ [18]

c. Lipid Artifacts

Amide proton transfer (APT) imaging is a specific form of CEST imaging that probes amide protons from endogenous proteins/peptides. Because the lipid chemical shift (-3.5 ppm) is situated approximately equal to the reference frequency for endogenous amide protons (3.5 ppm), conventional asymmetry analysis is prone to lipid contamination. This lipid artifact is particularly prominent in the CEST-EPI sequence due to a chemical shift-induced pixel change along the phase encoding direction. Sun et al. developed a lipid signal suppression method using a chemical shift-selective refocusing pulse (129). For multi-slice acquisition, a fat suppression pulse should be positioned immediately prior to the EPI readout to minimize lipid contamination (91). Notably, although a lipid-induced voxel shift is less problematic in non-EPI-based sequences due to higher phase encoding bandwidth, lipid suppression is still important to distinguish confounding asymmetric saturation transfer effects, such as NOE from lipids (130).

d. Quantitative in vivo CEST MRI

In vivo CEST MRI has been applied to study a number of disorders, including acute stroke, tumors, MS, and renal injury (22,43,123,131-136). However, endogenous APT MRI can be confounded by concomitant T₁, T₂, MT and NOE changes, and in vivo qCEST MRI provides important diagnostic value (137-142).

Because T₁, T₂ and semisolid MT changes during acute stroke are relatively small, in vivo qCEST MRI analysis has been applied to quantify tissue acidosis during acute stroke (143-145). Reasonably homogeneous labeling coefficient and spillover factor maps were calculated from an empirical solution (Eq. 6). Note that the in vivo MTR_asym is negative due to the baseline shift of the ΔMTR’_asym. The routine pH-weighted MTR_asym map shows significant regional differences between cerebral WM and GM that is attributable to the concomitant RF irradiation effects and does not reflect pH. However, the tissue pH map derived from qCEST analysis accurately represents tissue acidification in the ischemic lesion. Recently, Zaiss et al. proposed an MT ratio (MTR_Rex) analysis using the inverse Z-spectrum to eliminate spillover and semisolid MT effects (72). Conventional APT contrast (Fig. 8a) is contaminated by DS and T₁ effects (Figs. 8d, e). By correcting the spillover with MTR_Rex (Fig. 8b), and correcting the T₁ using the apparent exchange-dependent relaxation (AREX) evaluation (Fig. 8c), a pH map can be calculated (Fig. 8f) that will show significantly improved contrast between ischemic and normal regions (Fig. 8g).

Fig. 8.

(a) Conventional APT contrast is contaminated by (d) spillover and (e) T₁ effects. With correction of spillover by (b) MTR_Rex and correction of T₁ by the (c) AREX evaluation, (f) an absolute pH map can be calculated, which shows (g) significantly higher contrast between the stroke area and normal tissue.

7. Conclusion

CEST MRI is a sensitive imaging method that can characterize the chemical and biological properties of intracellular and extracellular domains of the tissue. However, the conventional CEST-weighted MRI method is limited by its dependence on experimental conditions. The emerging qCEST analysis method enables simultaneous determination of labile proton ratio and exchange rate, and is expected to provide an invaluable paradigm for in vivo imaging. Along with innovative acquisition, optimization and quantification methods, CEST MRI opens the way to an unbiased measure of important biological information for clinical translation.

Table of abbreviations

APT(R)

Amide Proton Transfer (Ratio)

AREX

Apparent Exchange-dependent Relaxation

CERT

Chemical Exchange Rotation Transfer

CEST(R)

Chemical Exchange Saturation Transfer (Ratio)

qCEST

Quantitative CEST

CNR

Contrast-to-Noise Ratio

CS

Compressed Sensing

CTR

Combined Transfer Rate

CW

Continuous Wave

DIACEST

Diamagnetic CEST

D(W)S

Direct Water Saturation

EPI

Echo Planar Imaging

FFT

Fast Fourier Transform

FISP

Fast Imaging with Steady Precession

FLASH

Fast Low-angle SHot

FWHM

Full Width at Half Maximum

GLM

General Linear Model

GM

Gray Matter

GRASE

Gradient And Spin-Echo

LOVARS

Length and Offset VARied saturation

MT(R)

Magnetization Transfer (Ratio)

MTR_asym

Magnetization Transfer Ratio Asymmetry

MTR_Rex

Spillover-correct Magnetization Transfer Ratio Yielding R_ex

NOE

Nuclear Overhauser Effect

NOMAR

NOrmalized MAgnetization Ratio

NSA

Number of Signal Average

PARACEST

Paramagnetic CEST

PTR

Proton Transfer Rate

QUESP

QUantification of Exchange as a function of Saturation Power

QUEST(RA)

QUantification of Exchange as a function of Saturation Time (Ratiometric Analysis)

RARE

Rapid Acquisition with Relaxation Enhancement

rCEST(R)

Ratiometric CESTR (Ratio)

RF

RadioFrequency

RL-QUEST

Reciprocal Linear-QUEST

SAR

Specific Absorption Rate

SENSE

SENSitivity Encoding

SL

Spin Locking

SNR_put

Signal-to-Noise Ratio per unit time

SSFP

Steady-State Free Precession

TE

Echo Time

TR

Repetition Time

TS

Saturation RF irradiation time

TSE

Turbo Spin-Echo

WASSR

WAter Saturation Shift Referencing

WSP

Weak Saturation Pulse

Table of mathematical notations

A, Γ

Peak and full width half maximum (FWHM) of a Lorentzian line shape

α

Labeling coefficient or excitation pulse flip angle

CESTR′

CESTR with B₀ field inhomogeneity contamination

ΔMTR

MTR offset due to a field inhomogeneity-induced MTR shift

Δω_w,s

Frequency difference between the labeling RF and the labile proton resonance

η

Field inhomogeneity-modulated experimental factor of CESTR

Ω

Frequency offset of spin-lock pulse

f_s

Labile proton concentration with respect to bulk water

γ

Gyromagnetic ratio

I_ref, I_label

Image intensity with RF irradiation applied at the reference and labile proton frequency

k_sw, k_ws

Chemical exchange rate of protons, from pool s (w) to pool w (s)

L₁

Proton transfer rate

L₂

Lorentzian function representing MTR′_asym

${\mathrm{M}}_0^{\mathrm{w},\mathrm{s}}$

Equilibrium magnetizations for bulk water (w) and solute pool (s)

${\mathrm{M}}_{\mathrm{x},\mathrm{y},\mathrm{z}}^{\mathrm{w},\mathrm{s}}$

Bulk water and solute magnetizations along x, y and z directions

${\mathrm{M}}_{\mathrm{ss}}^{\mathrm{w}}$

Steady-state signal at the labile proton frequency

R_1w,s, R_2w,s

Longitudinal and transverse relaxation rates of bulk water and labile groups

R_1ρ

Longitudinal relaxation rate in the rotating frame

R_ex

Chemical exchange relaxation rate

σ

Spillover factor

T_1w

Longitudinal relaxation rate of water proton

T_1ρ

T₁ relaxation time in the rotating frame

T_2w

Transverse relaxation rate of water proton

Θ

Lock angle of the water magnetization

ω₁

Irradiation RF power