A MATLAB tool for computing the spherical harmonic fractal dimension of the cerebral cortex

Fractal dimension (FD) has become a very useful tool in neuroscience with a wide range of applications in characterizing several neurodegenerative diseases. The most commonly used method for computing the FD of brain tissues is box-counting. This technique performs very well on 2D images and 3D volumes; however, it presents several drawbacks when processing cortical surfaces in 3D. In this study, we present a MATLAB program for computing the FD of 3D surfaces based on spherical harmonics. We developed a novel MATLAB program, called UJA-SHFD, based on a spherical harmonics FD algorithm which overcomes the limitations of the classical box-counting algorithm when processing 3D surfaces. Moreover, spherical-harmonic-based FD (SHFD) enables the processing of both global (providing a single FD value for the entire surface) and local level assessments in each cortical surface vertex. UJA-SHFD has been specifically designed and tested for processing cortical surfaces obtained from the FreeSurfer software suite. Nevertheless, the program can also process any kind of surface in the Wavefront OBJ format. UJA-SHFD can be used both through a graphical user interface and at the command line. The present study demonstrates the usefulness of UJA-SHFD through its application to a neuroimaging study looking at the progression of brain atrophy in Alzheimer’s disease. UJA-SHFD is a novel MATLAB program with the goal of developing neuroimaging analyses of FD computation for the investigation of brain morphological changes in neurodegenerative and neuropsychiatric disorders. The MATLAB source code of UJA-SHFD is freely available.