The R₁ of macro-molecular protons (MP) is an important determinant of MT and T₁ contrast in human brain tissues, through its effect on MT between MP and water protons (WP). Since MP have a short T₂ and can not be observed directly, there is substantial uncertainty in the actual value of their R₁ (R_1,MP). This uncertainty hampers quantitative interpretation of MT and T₁ contrast. To address this, we developed a novel approach to extract R_1,MP from joint analysis of MT and inversion recovery (IR) data using a 2-pool model of exchange. The analysis assumed constant values for R_1,MP and R_1,WP across brain tissues, and constrained the saturation level of MP magnetization by inversion and MT pulses.

The 2-pool model analysis (1) followed here involved fitting the saturation level S_WP(t) of the WP signal measured at time t after an inversion or MT pulse to the equation:$$S_{WP}(t)=1-M_z(t)/M_z(\infty)= a_1 e^{-\lambda_1t}+a_2e^{-\lambda_2t}\quad[1]$$MT and IR data were fitted jointly, resulting in one set of rates (λ₁,λ₂) common to both experiments, and two sets of amplitudes (a₁,a₂), one for each experiment. The rates depend on the R₁’s and exchange rates k_WM, k_MW between WP and MP and vice-versa according to:$$\lambda_{1,2}=\frac{1}{2}\big(R_{1,WP}+R_{1,MP}+k_{WM}+k_{MW}\pm\sqrt{(R_{1,MP}-R_{1,WP}+k_{MW}-k_{WM})^2+4k_{MW}k_{WM}}\big)\quad [2]$$The amplitudes are related to the initial saturation levels S_WP(0), S_MP(0) according to:$$a_{1,2}=\frac{S_{WP}(0)(R_{1,WP}+k_{WM}-\lambda_{2,1})-S_{MP}(0)k_{WM}}{\lambda_1-\lambda_2}\quad[3]$$Our approach to determine a global R_1,MP and R_1,WP was as follows: based on initial estimates for R_1,MP and R_1,WP, the k_WM, k_MW, and the S_MP(0) values for IR and MT were extracted from Eq.[2-3] for each pixel. The values for S_MP(0) in both experiments then were required to obey a-priori determined constraints: both to be smaller than 1.0, and the IR-saturation to be between 70 and 100% of the MT-saturation, as is indicated in Fig 1. The R_1,MP and R_1,WP were then iteratively adjusted to have most pixels obey these constraints.

IR and MT experiments (n=10) were performed at both 3T and 7T, under an IRB approved protocol. Delay dependent pulsed MT was performed with a composite (2) MT pulse (6ms, 833Hz B₁, 16 sub-pulses) that nearly completely saturated the MP-pool (S_MP(0)~1). IR used an adiabatic inversion (5.1ms, 833Hz B₁). Delays (t) of (10, 72, 138, 258, 600) and (9, 71, 147, 283 and 1200) ms were used for MT and IR respectively. Images were acquired with EPI (1.7mm resolution, acceleration 2, 5 slices of 2mm thickness and 1.5mm spacing), TE 30ms at 3T, 24ms at 7T, TR 3s for MT, 4s for IR, 20 repetitions for MT, 14 for IR, four reference scans without MT or inversion pulse to measure $$$M_z(\infty)$$$.Values of 4.0/s and 2.0/s were found for R_1,MP at 3T and 7T respectively (Fig.1). Corresponding values for R_1,WP were 0.40/s and 0.35/s. Estimated accuracies for these parameters are 10% for R_1,MP and 20% for R_1,WP. The values for R_1,MP are within the reported range of estimates based on the tissue fraction of MP, and modeling IR based on fast exchange (i.e. 5/s at 1.2T (3), 3.7/s at 3T (4), 2-3/s at 3T and 2-2.3/s at 7T (5). Our estimates for R_1,MP will aid in quantitative interpretation of MT and T₁ contrast, and their dependence on RF pulse parameters and field strength.