Quantification of white matter fiber orientation at tumor margins with diffusion tensor invariant gradients

Introduction: Neurosurgical planning of tumor resection seeks to minimize damage to healthy tissue during surgery. Diffusion tensor imaging (DTI) may help to resolve how the tumor has affected nearby white matter pathways, and to discriminate between fibers extending into the tumor, versus those deflected around it. Fiber orientation is usually modeled by the tensor principal eigenvector e1, enabling qualitative tumor assessment with e1 colormaps [2] and tractography [3,4]. Tumors can also affect scalar-valued functions called invariants, such as Trace (3 times mean diffusivity or “ADC”) and Fractional Anisotropy (FA) [1]. Invariants enable quantitative tumor assessment through metrics such as the Tumor Infiltration Index [5]. We seek to unify these approaches by measuring spatial gradients of invariants: vectors that estimate the surface orientation of the tumor, and that can be quantitatively compared with fiber orientation. We propose two metrics: Diffusion angle Da to quantify the angle between the fiber direction and the tumor boundary, and Diffusion fraction Df to quantify the fraction of diffusion across the tumor boundary. Theory: To the extent that changes in invariants like Trace and FA highlight tissue affected by a tumor, the gradients of the invariants (vectors pointing in the direction of fastest increase) may indicate the surface orientation of the affected tissue boundary. The relationship between the tumor and surrounding fibers can then be quantified by the angle between the invariant gradient and e1. For example, where the Trace gradient is parallel to e1, the fibers are going directly into and out of edema (in which trace is elevated [5]); where perpendicular, fibers are going around edema. Similar reasoning applies to the gradient of FA, since pathology can lower FA [5].