Mathematical textbook of deformable neuroanatomies.

TLDR

The ideal textbook is built on a fixed coordinate system that compiles all known physical properties of neuroanatomies. The study presents mathematical methods to transform digital anatomical textbooks from an idealized form to individualized representations that capture normal anatomical variability. The approach uses multimodal imaging data and symbolic anatomical information to define high‑dimensional probabilistic transformations, selecting the one that aligns the textbook coordinate system with the patient’s deformable elastic anatomy. Automatic registration, segmentation, and fusion are achieved, as the textbook’s symbolic and multisensor attributes enable seamless alignment with patient data.

Abstract

Mathematical techniques are presented for the transformation of digital anatomical textbooks from the ideal to the individual, allowing for the representation of the variabilities manifest in normal human anatomies. The ideal textbook is constructed on a fixed coordinate system to contain all of the information currently available about the physical properties of neuroanatomies. This information is obtained via sensor probes such as magnetic resonance, as well as computed axial and emission tomography, along with symbolic information such as white- and gray-matter tracts, nuclei, etc. Human variability associated with individuals is accommodated by defining probabilistic transformations on the textbook coordinate system, the transformations forming mathematical translation groups of high dimension. The ideal is applied to the individual patient by finding the transformation which is consistent with physical properties of deformable elastic solids and which brings the coordinate system of the textbook to that of the patient. Registration, segmentation, and fusion all result automatically because the textbook carries symbolic values as well as multisensor features.