The effective transverse relaxation rate ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> ) 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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>θ</mml:mi></mml:mrow> <mml:annotation>$$ \uptheta $$</mml:annotation></mml:semantics> </mml:math> ) complicate interpretation. The α- and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>θ</mml:mi></mml:mrow> <mml:annotation>$$ \uptheta $$</mml:annotation></mml:semantics> </mml:math> -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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> estimate per voxel. In this work, we investigated how the multi-compartment nature of tissue microstructure affects single compartment <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> estimates.
We used 2-pool (myelin and non-myelin water) simulations to characterize the bias in single compartment <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> estimates. Based on our numeric observations, we introduced a linear model that partitions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> 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.
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> 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.
We have demonstrated and validated a simple approach that mitigates flip angle and orientation biases in single-compartment <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> estimates.