Abstract
Traditional histology is the gold standard for tissue studies, but it is intrinsically reliant on two-dimensional (2D) images. Study of volumetric tissue samples such as whole hearts produces a stack of misaligned and distorted 2D images that need to be reconstructed to recover a congruent volume with the original sample's shape. In this paper, we develop a mathematical framework called Transformation Diffusion (TD) for stack alignment refinement as a solution to the heat diffusion equation. This general framework does not require contour segmentation, is independent of the registration method used, and is trivially parallelizable. After the first stack sweep, we also replace registration operations by operations in the space of transformations, several orders of magnitude faster and less memory-consuming. Implementing TD with operations in the space of transformations produces our Transformation Diffusion Reconstruction (TDR) algorithm, applicable to general transformations that are closed under inversion and composition. In particular, we provide formulas for translation and affine transformations. We also propose an Approximated TDR (ATDR) algorithm that extends the same principles to tensor-product B-spline transformations. Using TDR and ATDR, we reconstruct a full mouse heart at pixel size 0.92µm×0.92µm, cut 10µm thick, spaced 20µm (84G). Our algorithms employ only local information from transformations between neighboring slices, but the TD framework allows theoretical analysis of the refinement as applying a global Gaussian low-pass filter to the unknown stack misalignments. We also show that reconstruction without an external reference produces large shape artifacts in a cardiac specimen while still optimizing slice-to-slice alignment. To overcome this problem, we use a pre-cutting blockface imaging process previously developed by our group that takes advantage of Brewster's angle and a polarizer to capture the outline of only the topmost layer of wax in the block containing embedded tissue for histological sectioning.
Highlights
Traditional histology, the study of tissue microarchitecture, originated in the 17th c. with first applications of microscopy to animal-derived samples by Marcello Malpighi
In this paper we propose a mathematical framework for histology reconstruction called Transformation Diffusion (TD) that tackles several of the limitations of the methods we discuss above
We propose a general algorithm called Transformation Diffusion Reconstruction (TDR) that is valid for transformations that are closed under inversion and composition, and provide specific formulas for the cases of translation and affine transformations
Summary
Traditional histology, the study of tissue microarchitecture, originated in the 17th c. with first applications of microscopy to animal-derived samples by Marcello Malpighi. With first applications of microscopy to animal-derived samples by Marcello Malpighi. Traditional histology, the study of tissue microarchitecture, originated in the 17th c. It has become the gold standard for structural description of cells and tissue, serving important functions in clinical diagnosis of pathologies. One of the main limitations of traditional histology is the fact that the acquired 2D images cannot be directly stacked to reconstruct a consistent 3D volume with the original sample shape due to a series of tissue transformations. Histological processing for wax-embedding reduces tissue volume by 48% compared to ex vivo MRI (Burton et al, 2014), and produces non-affine deformations. The process of recovering the sample’s original 3D shape, generally referred to as 3D histology reconstruction or congruencing, has received a fair amount of attention in the field since Wilhelm His’ studies of human embryos in 1880, with significant mathematical and computing improvements in the last decades
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
