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Combination of MT and R₂^* measurements to distinguish between contributions of semisolids and iron to R₁

Xu Jiang¹, Erika Raven^1,2, Peter van Gelderen¹, and Jeff H. Duyn¹

¹Advanced MRI Section, LFMI, NINDS, National Institutes of Health, Bethesda, MD, United States, ²Center for Functional and Molecular Imaging, Georgetown University Medical Center, Washington, DC, United States

Synopsis

In human brain, the apparent longitudinal relaxation rate (R₁) primarily originates from magnetization transfer (MT) effects associated with the macromolecular ¹H-proton fraction (f), although in some regions the iron concentration may contribute as well (Rooney, 2007). To quantify their relative contributions at 7 T, we measured f and R₁ of water protons (R_1,WP) corrected for MT effects using a pulsed, transient MT approach (van Gelderen, 2016). The iron concentration was taken from literature and correlated with R₂^*. The results indicate that the combination of R₂^* and MT measurements may provide a sensitive means to quantify R_1,WP, f and iron concentration.

Introduction

Previous studies have shown that R₁ contrast in brain is predominantly determined by the macromolecular ¹H-proton (MP) fraction f ^1,2. Therefore, methods ^3–5 based on monitoring the longitudinal relaxation of water ¹H-protons (WPs) followed by a two pool, i.e. WPs and MPs, exchange model analysis have been used ^2,4,5 to estimate f. However, these studies generally require extensive experiments to solve for the unknown parameters in the two pool model, often requiring a number of simplifying assumptions ^3–5. These assumptions may not be correct in regions with high iron concentration. For example, iron may affect the intrinsic R₁ of WP (R_1,WP) in the absence of MT effects. Here we applied a previously introduced pulsed MT method to measure R_1,WP and correlated it with R₂^* as a surrogate of iron concentration, as well with putative iron concentrations derived from previously published histological measurements ^6,7.

Methods

Seven human subjects (ages 23-49, average age 32.3, 3 females) were scanned under an IRB approval on a 7 T Siemens scanner. The MP fraction was determined using pulsed saturation recovery experiments, followed by two pool exchange model ⁵ analysis:

$$FS_{WP}(t)=1- \frac{M_{WP}(t)}{M_{WP}(\infty)}=a_{1}e^{-\lambda_{1}t}+a_{2}e^{-\lambda_{2}t}$$[1]

$$\lambda_{1,2}=(R_{1,WP}+R_{1,MP}+k_{MW}+k_{WM}\pm\sqrt{(R_{1,MP}-R_{1,WP}+k_{MW}-k_{WM})^{2}+4k_{MW}k_{WM}})/2$$[2]

$$a_{1,2}=\pm\frac{FS_{WP}(0)(R_{1,WP}+k_{WM}-\lambda_{2,1})-FS_{MP}(0)k_{WM}}{\lambda_{1}-\lambda_{2}}$$[3]

$$(1-f)k_{WM}=fk_{MW}$$[4]

Here, M is the longitudinal magnetization, R₁ is its relaxation rate, FS is fractional saturation, λ₁ and λ₂ are fast and slow rate constants of the saturation recovery, and a₁ and a₂ are the corresponding amplitudes. k_WM and k_MW are the MT exchange rates between two pools. f is the MP fraction. An inversion recovery (IR) or a composite saturation recovery (SR) pulse, were used to differentially modulate the two pools, followed by EPI acquisition at variable delay t to sample FS_WP(t). The IR pulse was an adiabatic hyperbolic secant pulse, with a duration of 5.12 ms, an energy of 0.51 (μT)²s, a B₁ amplitude of 833 Hz and a β of 1400 s^-1 ⁸. The SR pulse had a duration of 6 ms and consisted of a train of 16 hard pulses with angles 60°, -120°, 120°, -120°, ….120°, -60°, with a B₁ amplitude of 833 Hz ². The delay times for the IR experiment were 6, 63, 144, 282 and 1200 ms, for the SR they were: 7, 127, 258, 401 and 559 ms. The field-of-view was 240x180 mm. The echo time (TE) for EPI was 24 ms. The TRs were 6 and 3 s for IR and SR experiments respectively. The use of two different preparation pulses facilitated fitting of λ₁ and λ₂, using Eq. [1], and furthermore allowed extraction of k_MW, k_WM, f, and R_1,WP, using Eqs. [2-3], with assuming R_1,MP = 2 s^-1 and FS_MP(0) = 0.93 for the SR experiment as determined previously ². R₂^* was measured using a MGRE sequence with TR of 1 s, TE of 3.2 ms, 28 even (same gradient polarity) echoes with spacing of 1.54 ms, and the same resolution and field-of-view as the EPI scans. A single exponential decay for the transverse magnetization: $$$M_{\bot}(t)=M_{\bot0}e^{-R_{2}^{*}t}$$$, was fitted to the magnitude data of different echoes, where $$$M_{\bot0}=M_{\bot}(0)$$$. Only echo times between 7.8 ms to 44.8 ms were used for the fitting, to avoid influence from the fast decaying myelin water component ⁹. Four ROI’s were hand drawn, in Caudate nucleus (CN), Putaman (PUT), Thalamus (TH) and Frontal white matter (FWM), as exemplified by Fig. 1. The iron concentration in the four ROI’s was calculated using formulae reported previously ^6,7. The subject-wise ROI-averaged correlations between R_1,WP and the iron concentration, between R_1,WP and R₂^*, and between R₂^* and the iron concentration were studied using linear regression.

Results and Discussion

Table 1 shows the fitting results of R₂^*, f and R_1,WP. Linear regression of R₂^* with the iron concentration gives: $$$R_{2}^{*}(C_{Fe})=0.218C_{Fe}+28.1$$$ with adjusted R² of 0.79, where is the fresh weight concentration of non-heme iron in parts per million (ppm). Linear regression of R_1,WP with the iron concentration gives: $$$R_{1,WP}(C_{Fe})=0.00118C_{Fe}+0.33$$$ with adjusted R² of 0.78. And linear regression of R_1,WP with R₂^* gives: $$$R_{1,WP}(R_{2}^{*})=0.00433R_{2}^{*}+0.22$$$ with adjusted R² of 0.60. These three correlations are shown in Fig. 2. The results show that R₂^* is correlated with the iron concentration, consistent with previous reported linear correlation of R₂^* with iron ^10–12. Importantly R₂^* can be used to reliably estimate R_1,WP to reduce the number of unknowns in Eqs. [1-4] and can possibly be used to facilitate the extraction of MP fraction.

Acknowledgements

This research was supported by the Intramural Research Program of the National Institutes of Health, National Institute of Neurological Disorders and Stroke (NS 002990-15).

References

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Figures

Figure 1. Example of hand drawn ROI’s (a) on Caudate Nucleus (CN) (pink), Putamen (PUT) (green), Thalamus (TH) (yellow) and Frontal White Matter (FWM) (red). ROI locations are shown superimposed on a MGRE image at echo time of 32.5 ms, together with the corresponding f (b) and R₂^* (c) maps.

Figure 2. Linear correlations between R_1,WP and iron concentration (a), between R_1,WP and R₂^* (b), and between R₂^* and iron concentration (c), with iron concentration as weight fraction.

Table 1. ROI averaged R₂^*, f and R_1,WP, averaged over all subjects (± standard deviation); all rates are reported in s^-1; Note: Caudate Nucleus (CN), Putamen (PUT), Thalamus (TH) and Frontal White Matter (FWM).

Proc. Intl. Soc. Mag. Reson. Med. 25 (2017)

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