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The fractal dimension (FD) is a quantitative parameter that characterizes the morphometric variability of the human brain. In this study, we investigate spherical harmonic\u2010based FD (SHFD), thickness, and local gyrification index (LGI) to assess whether they identify cortical surface abnormalities toward the conversion to AD. We study 33 AD patients, 122 mild cognitive impairment (MCI) patients (50 MCI converters and 29 MCI nonconverters), and 32 healthy controls (HC). SHFD, thickness, and LGI methodology allowed us to perform not only global level but also local level assessments in each cortical surface vertex. First, we found that global SHFD decreased in AD and future MCI converters compared to HC, and in MCI converters compared to MCI nonconverters. Second, we found that local white matter SHFD was reduced in AD compared to HC and MCI mainly in medial temporal lobe. Third, local white\u2010matter SHFD was significantly reduced in MCI converters compared to MCI nonconverters in distributed areas, including the medial frontal lobe. Thickness and LGI metrics presented a reduction in AD compared to HC. Thickness was significantly reduced in MCI converters compared to healthy controls in entorhinal cortex and lateral temporal. In summary, SHFD was the only surface measure showing differences between MCI individuals that will convert or remain stable in the next 4\u00a0years. We suggest that SHFD may be an optimal complement to thickness loss analysis in monitoring longitudinal changes in preclinical and clinical stages of AD.<jats:italic>Hum Brain Mapp 38:5905\u20135918, 2017<\/jats:italic>. \u00a9<jats:bold>2017 Wiley Periodicals, Inc.<\/jats:bold><\/jats:p>","DOI":"10.1002\/hbm.23773","type":"journal-article","created":{"date-parts":[[2017,8,31]],"date-time":"2017-08-31T10:10:35Z","timestamp":1504174235000},"page":"5905-5918","source":"Crossref","is-referenced-by-count":55,"title":["Complexity analysis of cortical surface detects changes in future Alzheimer's disease converters"],"prefix":"10.1002","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7579-8350","authenticated-orcid":false,"given":"Juan","family":"Ruiz de Miras","sequence":"first","affiliation":[{"name":"Computer Science Department University of Ja\u00e9n Ja\u00e9n Spain"},{"name":"Gordon Center for Medical Imaging, Division of Nuclear Medicine and Molecular Imaging, Department of Radiology Massachusetts General Hospital and Harvard Medical School Boston Massachusetts"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8743-5239","authenticated-orcid":false,"given":"V\u00edctor","family":"Costumero","sequence":"additional","affiliation":[{"name":"Gordon Center for Medical Imaging, Division of Nuclear Medicine and Molecular Imaging, Department of Radiology Massachusetts General Hospital and Harvard Medical School Boston Massachusetts"},{"name":"Department of Methodology University of Valencia Valencia Spain"},{"name":"Department of Basic and Clinical Psychology and Psychobiology Jaume I University Castell\u00f3 de la Plana Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vicente","family":"Belloch","sequence":"additional","affiliation":[{"name":"ERESA Medical Group Valencia Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joaqu\u00edn","family":"Escudero","sequence":"additional","affiliation":[{"name":"Department of Neurology General Hospital of Valencia Valencia Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C\u00e9sar","family":"\u00c1vila","sequence":"additional","affiliation":[{"name":"Department of Basic and Clinical Psychology and Psychobiology Jaume I University Castell\u00f3 de la Plana Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jorge","family":"Sepulcre","sequence":"additional","affiliation":[{"name":"Gordon Center for Medical Imaging, Division of Nuclear Medicine and Molecular Imaging, Department of Radiology Massachusetts General Hospital and Harvard Medical School Boston Massachusetts"},{"name":"Athinoula A. 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