Fractal Dimension Analysis of High-Resolution X-Ray Phase Contrast Micro-Tomography Images at Different Threshold Levels in a Mouse Spinal Cord

Laura Maugeri,Inna Bukreeva,Mauro Dinuzzo,Michela Fratini,Charles Nicaise,Marta Moraschi,Federico Giove,Alessia Cedola,Fabio Mangini

doi:10.3390/condmat3040048

Abstract

Fractal analysis is a powerful method for the morphological study of complex systems that is increasingly applied to biomedical images. Spatial resolution and image segmentation are crucial for the discrimination of tissue structures at the multiscale level. In this work, we have applied fractal analysis to high-resolution X-ray phase contrast micro-tomography (XrPCμT) images in both uninjured and injured tissue of a mouse spinal cord. We estimated the fractal dimension (FD) using the box-counting method on tomographic slices segmented at different threshold levels. We observed an increased FD in the ipsilateral injured hemicord compared with the contralateral uninjured tissue, which was almost independent of the chosen threshold. Moreover, we found that images exhibited the highest fractality close to the global histogram threshold level. Finally, we showed that the FD estimate largely depends on the image histogram regardless of tissue appearance. Our results demonstrate that the pre-processing of XrPCμT images is critical to fractal analysis and the estimation of FD.

Highlights

Fractal analysis is increasingly popular in many different fields among natural and life sciences, such as, for example, materials science [1] and neuroscience [2,3,4,5,6,7,8,9,10]
Irregularly shaped biological organisms and tissues are better characterized by fractal dimension (FD) than by traditional morphometric measures based on Euclidean geometry
We have shown that high-resolution XrPCμT images of mouse spinal cord tissue are fractal across a wide range of threshold levels used for binarization

Summary

Introduction

Fractal analysis is increasingly popular in many different fields among natural and life sciences, such as, for example, materials science [1] and neuroscience [2,3,4,5,6,7,8,9,10]. Fractal geometry features have been found in the morphology of tissue and in the vascular pattern around tumor cells [11,12] as well as in brain [2,3,13] and bone [14,15] structures and in protein aggregates [16]. All these systems cannot be considered “true” geometrical fractals as they do not scale to infinity but rather at many biologically relevant scales. Fractal analysis has been utilized to detect structural changes in white matter (WM) [4,20,21] and grey matter (GM) [5,22,23] in a variety of clinical settings [2,3,7,8]

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