Voxel‐Specific Eigenvalue Approach for Improved Fiber Orientation Estimation in Diffusion MRI

This study presents a novel approach to improve fiber orientation estimation in diffusion tensor imaging (DTI), a widely used MRI technique for mapping brain white matter fibers (WMFs) by analyzing water diffusion patterns. Traditional DTI estimates the diffusion tensor matrix (DT-matrix) via linear regression, which effectively detects a single fiber per voxel but fails in regions with crossing fibers. To address this limitation, multicompartment mixture models have been introduced, typically assuming fixed eigenvalues <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>.</mml:mo> <mml:mn>5</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:mn>4</mml:mn> <mml:mo>)</mml:mo></mml:mrow> <mml:annotation>$$ \left(1.5,0.4,0.4\right) $$</mml:annotation></mml:semantics> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>μ</mml:mi></mml:mrow> <mml:annotation>$$ \upmu $$</mml:annotation></mml:semantics> </mml:math> m <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msup><mml:mrow></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msup> </mml:mrow> <mml:annotation>$$ {}^2 $$</mml:annotation></mml:semantics> </mml:math> /ms based on normative WMF data. However, such fixed assumptions may lead to inaccuracies in regions with complex microstructures. In contrast, the proposed method dynamically computes the eigenvalues of the DT-matrix for each voxel, allowing for a voxel-specific characterization of diffusion properties. This adaptability accounts for spatial variability in fiber geometry, improving the accuracy of fiber orientation detection. Simulations and experiments on human and rat brain datasets demonstrate that the method achieves improved white matter reconstruction and reduced angular error compared with traditional DTI and fixed-eigenvalue models. By tailoring diffusion modeling to each voxel, this approach enhances neuroimaging analysis, refines tissue microstructure characterization, and advances the precision of diffusion MRI.