First Order Logic with Fuzzy Semantics for Describing and Recognizing Nerves in Medical Images

TL;DR

The paper tackles the problem of robustly describing and recognizing nerve fiber bundles in medical images where anatomical descriptions are inherently imprecise. It introduces a first-order fuzzy logic framework that encodes spatial entities, relations, and quantifiers with fuzzy satisfaction degrees, and implements a segmentation/recognition algorithm by evaluating knowledge-driven queries on imaging data. Key contributions include concrete semantic definitions, dilation-based spatial operators, and directional predicates, demonstrated on pelvic nerves in both adult and pediatric subjects. The approach is explainable and knowledge-driven, enabling 3D patient-specific surgical planning by integrating anatomical knowledge with diffusion and anatomical MRI data.

Abstract

This article deals with the description and recognition of fiber bundles, in particular nerves, in medical images, based on the anatomical description of the fiber trajectories. To this end, we propose a logical formalization of this anatomical knowledge. The intrinsically imprecise description of nerves, as found in anatomical textbooks, leads us to propose fuzzy semantics combined with first-order logic. We define a language representing spatial entities, relations between these entities and quantifiers. A formula in this language is then a formalization of the natural language description. The semantics are given by fuzzy representations in a concrete domain and satisfaction degrees of relations. Based on this formalization, a spatial reasoning algorithm is proposed for segmentation and recognition of nerves from anatomical and diffusion magnetic resonance images, which is illustrated on pelvic nerves in pediatric imaging, enabling surgeons to plan surgery.

Figures (6)

• Figure 1: Sacral plexus illustration according to Gray Gray, plate 828.
• Figure 2: Interpretation in the concrete domain of the region anterior to the obturator muscle (muscle contours are shown in red). Slices in three orthogonal directions are displayed.
• Figure 3: Interpretation of the predicate "crossing" in the concrete domain.
• Figure 4: Example of the whole set of fibers computed from dMRI using a tractography algorithm.
• Figure 5: Illustration of the L5-S3 pelvic fiber recognition result for a healthy adult. Left: 3D representation. Right, from top to bottom: dMRI axial slice, T2 MRI axial slice, T2 MRI sagittal slice.