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T1-induced apparent time dependence of diffusion coefficient measured with stimulated echo due to exchange with myelin water
Hong-Hsi Lee1, Dmitry S. Novikov1, and Els Fieremans1

1Center for Biomedical Imaging, New York University, New York, NY, United States

Synopsis

For diffusion measurements, stimulated-echo acquisition mode (STEAM) has been widely used. To enhance sensitivity to microstructure, previous studies used STEAM to vary the diffusion time by changing the mixing time tM. Here we show that varying tM results in an “apparent” STEAM-measured diffusivity dependence on tM, irrespective of genuine microstructure-specific time dependence. This effect is caused by T1-relaxation and water exchange between myelin water and "free" water (intra- and extra-axonal water). We propose a modified Kärger model considering diffusion+T1-relaxation+exchange, and demonstrate that exchange-induced tM-dependence explains ~20-50% of the total diffusion time dependence, and should be considered while using STEAM.

Purpose

Stimulated-echo acquisition mode (STEAM) has been widely used for diffusion measurements [1]. To enhance the sensitivity to microstructure, previous studies attempted to vary diffusion time Δ in a wide range [2,3], achieved by changing mixing time tM in STEAM sequence. Here we show that varying tM results in an “apparent” STEAM-measured diffusivity dependence on tM, irrespective of the genuine microstructure-specific time dependence D(t). This extra tM dependence is caused by T1-relaxation and water exchange between myelin water and "free" water (intra- and extra-axonal water) [3]. We develop a theoretical framework for this effect based on solving a modified K¨arger model incorporating longitudinal relaxation [4-6]. Furthermore, we demonstrate exchange-induced tM-dependence in human brain white matter (WM), and subsequently correct for it, revealing the genuine D(t) dependence. Exchange-induced tM-dependence explains ~20-50% of the total diffusion time dependence, and should be considered when interpreting diffusion experiments using STEAM.

Theory

For human brain WM, we proposed a diffusion+relaxation+exchange model shown in Fig.1a, where Mf and Mm are magnetizations of ”free” and myelin water. It is the K¨arger model [4,5] for a two-component magnetization M(MfMm), but with a modified initial condition for the evolution during the tM interval: the observed signal comes only from the “free” pool, i.e. the initial condition (10), and the measurement (at t>tM) projects the evolution back onto the “free” pool, because of short myelin water T2TE (Fig.1b) [7]. The result is that the apparent diffusion coefficient (ADC) in the free water acquires tM-dependence even if both compartment diffusivities are constant---in stark contrast to the regular K¨arger model, where exchange does not lead to extra time-dependence [4,5].

In this model (Fig.1a), myelin water has diffusivity Dm, longitudinal relaxation time Tm1, and free water has Df and Tf1, respectively. The exchange rates are rm (from myelin to free) and rf (from free to myelin), conforming to the detailed balance [4,5].

For this modified K¨arger model, the Bloch-Torrey equation is given by [6]tM=(D2iγgrRLRE)M,(1) where M=(MfMm),D=(Df00Dm),RL=(1/Tf1001/Tm1), and RE=(rfrmrfrm).

Solving Eq.(1) with the initial condition (10) based on previous discussion, the non-diffusion weighted signal [6]Sb=0=f+eλ+tM+feλtM,(2) where f++f=1. Sb=0 is normalized to 1 for tM=0. Fitting parameters (f+,λ+,λ) are combinations of tissue parameters (Tf1,Tm1,rf,rm), shown in Fig.1c. The myelin water residence time τm=1/rm is roughly estimated by 1/rfrm. Without water exchange (rf=rm=0), Eq.(2) degenerates to a mono-exponential decay S0=eλtM.

Solving for the signal at finite q and expanding up to q2, we get our main result: the ADC measured via STEAM DTI is given by Dapp=Df(DfDm)f+1τtM+(1+τtM)e2tM/τ1+f+fe2tM/τtMΔδ/3,(3) where τ=2/(λ+λ), and δ is diffusion gradient pulse width. To stabilize our fitting, we fixed myelin diffusivities: axial Dm0.5μm2/ms and radial Dm0.2μm2/ms [8]. The case of Dm=Dm=0 is also shown to discuss the influence of Dm on corrections.

We also applied models for time-dependent diffusion [3,9,10] to the measured Dapp and the calculated Df after correction for exchange (Table 1).

Materials and Methods

Diffusion measurements were performed on five healthy subjects (4males/1female, 23-27y/o) using a 3T Siemens Prisma scanner with a 64-channel head coil. We used a STEAM sequence provided by the vendor (Siemens WIP 511E). TE/TR=100/11900ms, resolution=(2.7mm)3, FOV=(221mm)2. For each Δ, we acquired three b=0 images and b=500s/mm2 images along 20 diffusion gradient directions. We varied Δ=71550ms and tM=5.5-484.5ms, and fixed δ=8ms. A series of WM regions-of-interest (ROIs) were created based on the JHU DTI WM atlases (anatomical WM ROI) (Fig.2) [11]. The axial and radial diffusivities were averaged over each ROI and corrected for each subject by using Eq.(3).

Results

Fig.2 shows for each ROI bi-exponential decay of the b=0 signal Sb=0, instead of mono-exponential, with respect to tM (Eq.(2)) with two time scales 1/λ+~65ms and 1/λ~830ms, and the estimated myelin residence time is τm160ms (Table 1a), consistent with previous studies [12], manifesting effects of water exchange and T1-relaxation.

The uncorrected ADC (Dapp,Dapp) and calculated free water diffusivities (Df,Df), based on Eq.(3), with respect to Δ, are both shown in Figs.3 and 4. The fitting parameters of time dependence models are shown in Table 1b-c. In general, ~20-50% of the diffusion time dependence, indicated by strength of restrictions (A,A), is contributed to exchange.

Discussion and Conclusion

Varying tM in STEAM introduces a tM-dependent diffusion in human brain WM, caused by water exchange between myelin water and "free" water with different T1 values. In WM, ~20-50% of the "diffusion time" dependence results from this effect.

Remarkably, STEAM provides an “orthogonal” contrast to monopolar pulsed-gradient spin-echo (PGSE); hence, using both sequences, or providing the correction described above based on the Sb=0 signal, may enable simultaneous mapping of microstructural and relaxational tissue parameters.

Acknowledgements

We would like to thank Thorsten Feiweier for developing the advanced diffusion WIP sequence and Jelle Veraart for assistance with image processing. Research was supported by the National Institute of Neurological Disorders and Stroke of the National Institutes of Health under award number R01NS088040.

References

[1] Merboldt, K.D., et al. JMR 64(3),479-486 (1985).

[2] Assaf, Y., et al. MRM 59:1347-1354 (2008).

[3] Fieremans, E., et al. NI 129,414-427 (2016).

[4] K¨arger, J. Adv. Colloid Interface Sci. 23,129-148 (1985).

[5] Fieremans, E., et al. NMR Biomed. 23,711-724 (2010).

[6] Stanisz, G.J., et al. MRM 39,223-233 (1998).

[7] Whittal, K.P., et al. MRM 37,34-43 (1997).

[8] Andrews, T.J., et al. MRM 56,381-385 (2006).

[9] Novikov, D.S., et al. PNAS 111,5088-5093 (2014).

[10] Burcaw, L.M., et al. NI 114,18-37 (2015).

[11] Mori, S., et al. MRI atlas of human white matter. Elsevier (2005).

[12] Rioux, J.A., et al. MRM 75(6),2265-2277 (2016).

Figures

Fig.1. (a) A modified K¨arger model (two-component model) for the brain WM, composed of myelin water and “free” water, and its corresponding tissue parameters [4,5]. (b) In a STEAM sequence, myelin water magnetization Mm decays away at t=TE/2 and t=tM+TE since myelin water T2 TE [7]. Therefore, signal is generally contributed by free water. (c) The three fitting parameters (λ+,λ,f+) in Eq.(2) are combinations of the four tissue parameters (Tf1,Tm1,rf,rm) in Fig.1a.

Fig.2. Signal Sb=0 in b=0 images decays with mixing time tM in a bi-exponential fashion, manifested by the curve, instead of a straight line, in a semi-log plot. The bi-exponential decay conforms to Eq.(2), indicating the effect of T1-relaxation and water exchange. Table 1a shows corresponding fitting parameters. WM ROIs are shown in the right column. One subject’s parametric maps are shown in the lower row. ACR (red)= anterior corona radiata, SCR (yellow)= superior corona radiata, PCR (green)= posterior corona radiata, PLIC (magenta)= posterior limb of the internal capsule, Genu (blue) and Splenium (cyan) of the corpus callosum.

Fig.3. Measured axial diffusivity Dapp (black circle) in each WM ROI is corrected based on Eq.(3) and parameters in Table 1a. Assuming that axial diffusivities of the myelin water Dm is negligible, Df would be over-corrected (red square), especially at long diffusion time Δ. Using a typical value of Dm~0.5μm2/ms [8], corrected Df (blue triangle) does not show the over-correction and gradually approaches bulk diffusivity at long Δ. Curves in each subfigure are fits based on DD+2AΔ [3,9], where D is bulk diffusivity, and A is strength of restrictions. Figures of D vs. 1/Δ are shown in the right column.

Fig.4. Measured radial diffusivity D (black circle) in each WM ROI is corrected based on Eq.(3) and parameters in Table 1a. Assuming that radial diffusivities of the myelin water Dm is negligible, the correction for D is large (red square). By using Dm~0.2μm2/ms [8], corrections are smaller (blue triangle). Curves in each subfigure are fits based on DD+Aln(Δ/δ)Δ [3,9], where D is bulk diffusivity, and A is strength of restrictions. Figures of D vs. 1/Δ are shown in the right column. Corrected D increases nonlinearly with 1/Δ, indicating that time dependence model for D is applicable to corrected data.

Table 1. (a) Parameters obtained by fitting Eq.(2) to Sb=0. (b) Parameters (D,A) obtained by fitting the time dependence of axial diffusivities DD+2AΔ [3,9], with or without corrections based on Eq.(3) and Dm = 0.5 μm2/ms. (c) Parameters obtained by fitting the time dependence of radial diffusivities DD+Aln(Δ/δ)Δ [3,9], with or without corrections based on Eq.(3) and Dm = 0.2 μm2/ms. The % change of diffusion time dependence with and without corrections for water exchange is estimated by the % change of strength (A, A) of restrictions.

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