In this study, we propose a novel method for quantifying tortuosity in 3D voxelized objects. As a shape characteristic, tortuosity has been widely recognized as a valuable feature in image analysis, particularly in the field of medical imaging. Our proposed method extends the two-dimensional approach of the Slope Chain Code (SCC) which creates a one-dimensional representation of curves. The utility of 3D tortuosity (τ3D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _{3D}$$\\end{document}) as a shape descriptor was investigated by characterizing brain structures. The results of the τ3D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _{3D}$$\\end{document} computation on the central sulcus and the main lobes revealed significant differences between Alzheimer’s disease (AD) patients and control subjects, suggesting its potential as a biomarker for AD. We found a p<0.05\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p<0.05$$\\end{document} for the left central sulcus and the four brain lobes.