Mitigating the impact of flip angle and orientation dependence in single compartment R2* estimates via 2-pool modeling

Purpose: The effective transverse relaxation rate ( $R_2^{*}$ ) is influenced by biological features that make it a useful means of probing brain microstructure. However, confounding factors such as dependence on flip angle (α) and fiber orientation with respect to the main field ( $\theta$ ) complicate interpretation. The α- and $\theta$ -dependence stem from the existence of multiple sub-voxel micro-environments (e.g., myelin and non-myelin water compartments). Ordinarily, it is challenging to quantify these sub-compartments; therefore, neuroscientific studies commonly make the simplifying assumption of a mono-exponential decay obtaining a single $R_2^{*}$ estimate per voxel. In this work, we investigated how the multi-compartment nature of tissue microstructure affects single compartment $R_2^{*}$ estimates.

Methods: We used 2-pool (myelin and non-myelin water) simulations to characterize the bias in single compartment $R_2^{*}$ estimates. Based on our numeric observations, we introduced a linear model that partitions $R_2^{*}$ into α-dependent and α-independent components and validated this in vivo at 7T. We investigated the dependence of both components on the sub-compartment properties and assessed their robustness, orientation dependence, and reproducibility empirically.

Results: $R_2^{*}$ increased with myelin water fraction and residency time leading to a linear dependence on α. We observed excellent agreement between our numeric and empirical results. Furthermore, the α-independent component of the proposed linear model was robust to the choice of α and reduced dependence on fiber orientation, although it suffered from marginally higher noise sensitivity.

Conclusion: We have demonstrated and validated a simple approach that mitigates flip angle and orientation biases in single-compartment $R_2^{*}$ estimates.