A general linear relaxometry model of R1 using imaging data

Abstract

Purpose: The longitudinal relaxation rate (R1 ) measured in vivo depends on the local microstructural properties of the tissue, such as macromolecular, iron, and water content. Here, we use whole brain multiparametric in vivo data and a general linear relaxometry model to describe the dependence of R1 on these components. We explore a) the validity of having a single fixed set of model coefficients for the whole brain and b) the stability of the model coefficients in a large cohort.

Methods: Maps of magnetization transfer (MT) and effective transverse relaxation rate (R2 *) were used as surrogates for macromolecular and iron content, respectively. Spatial variations in these parameters reflected variations in underlying tissue microstructure. A linear model was applied to the whole brain, including gray/white matter and deep brain structures, to determine the global model coefficients. Synthetic R1 values were then calculated using these coefficients and compared with the measured R1 maps.

Results: The model's validity was demonstrated by correspondence between the synthetic and measured R1 values and by high stability of the model coefficients across a large cohort.

Conclusion: A single set of global coefficients can be used to relate R1 , MT, and R2 * across the whole brain. Our population study demonstrates the robustness and stability of the model.

Keywords: 3T; MT; PD; PD*; R1; R2*; T1; T2*; longitudinal relaxation; magnetization transfer; quantitative; relaxometry; transverse relaxation; water content.

Figure 1

Illustration of the linear relaxometry model that is constructed on a per-subject basis. The three model coefficients are the least squares solution to the matrix equation R₁ = Mβ.

Figure 2

Exemplary single subject data from the cohort using a masking threshold of 30% on the tissue probabilities. The global β coefficients for this subject were: 0.2692 s⁻¹, 0.3979 s⁻¹/p.u., and 0.0011. The Pearson coefficient of the model in this subject was 0.96. (a) Measured R₁ map. (b) R₁ map synthesized using the model coefficients. (c) Spatial map of the model residuals (ie, the difference between the measured and synthesized R₁ maps). (d) Synthesized R₁ values plotted against the measured R₁ values across the whole brain illustrates the high correspondence between the two R₁ measures.

Figure 3

Residuals from the linear model were significantly lower and contained far fewer anatomical structure and bias field effects when MT (a) rather than MTR (b) was used as a surrogate for macromolecules.

Figure 4

Normalized residuals expressed in percent units from the linear model incorporating free water and macromolecular content (a) were reduced by also including an iron term (b). (c) The difference highlights iron-rich structures, such as the pallidum and dentate nucleus, in which the residuals were particularly reduced.