Characterization of Atrophic Changes in the Cerebral Cortex Using Fractal Dimensional Analysis

Department of Neurology, University of Texas Southwestern Medical Center, 5323 Harry Hines Blvd, Dallas, TX 75390-9129, USA. Center for BrainHealth, University of Texas at Dallas, Dallas, TX, USA.
Brain Imaging and Behavior (Impact Factor: 4.6). 06/2009; 3(2):154-166. DOI: 10.1007/s11682-008-9057-9
Source: PubMed


The purpose of this project is to apply a modified fractal analysis technique to high-resolution T1 weighted magnetic resonance images in order to quantify the alterations in the shape of the cerebral cortex that occur in patients with Alzheimer's disease. Images were selected from the Alzheimer's Disease Neuroimaging Initiative database (Control N=15, Mild-Moderate AD N=15). The images were segmented using a semi-automated analysis program. Four coronal and three axial profiles of the cerebral cortical ribbon were created. The fractal dimensions (D(f)) of the cortical ribbons were then computed using a box-counting algorithm. The mean D(f) of the cortical ribbons from AD patients were lower than age-matched controls on six of seven profiles. The fractal measure has regional variability which reflects local differences in brain structure. Fractal dimension is complementary to volumetric measures and may assist in identifying disease state or disease progression.

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    • "The FD has been shown to be more accurate than other methods (i.e., volumetric voxel-based morphometry) for the detection of WM changes in several diseases and for identifying different clinical phenotypes such as amyotrophic lateral sclerosis (Rajagopalan and others 2013) (Fig. 4), AD (King and others 2010), multiple sclerosis (Esteban and others 2007, 2009), and epilepsy (Lin and others 2007). In addition, it has been used for investigating brain development and age-related changes (King and others 2009; Li and others 2011; Mustafa and others 2012; Zhang and others 2007). In the connectomics era, the traditional diffusion tensor models have also benefited from new computational fractalbased approaches for the characterization and measurement of water molecule diffusion in vivo (Jian and others 2007). "
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    ABSTRACT: It has been ascertained that the human brain is a complex system studied at multiple scales, from neurons and microcircuits to macronetworks. The brain is characterized by a hierarchical organization that gives rise to its highly topological and functional complexity. Over the last decades, fractal geometry has been shown as a universal tool for the analysis and quantification of the geometric complexity of natural objects, including the brain. The fractal dimension has been identified as a quantitative parameter for the evaluation of the roughness of neural structures, the estimation of time series, and the description of patterns, thus able to discriminate different states of the brain in its entire physiopathological spectrum. Fractal-based computational analyses have been applied to the neurosciences, particularly in the field of clinical neurosciences including neuroimaging and neuroradiology, neurology and neurosurgery, psychiatry and psychology, and neuro-oncology and neuropathology. After a review of the basic concepts of fractal analysis and its main applications to the basic neurosciences in part I of this series, here, we review the main applications of fractals to the clinical neurosciences for a holistic approach towards a fractal geometry model of the brain.
    The Neuroscientist 02/2015; 21(1):30-43. DOI:10.1177/1073858413513928 · 6.84 Impact Factor
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    • "As shown below, FD measures are used in neuroscience to reveal gender and age structural differences in the cerebral cortex in the absence of disease and to investigate psychiatric and neurological disorders. Development and ageing of the human brain can be studied with FD and have shown increasing cortical complexity from early foetal life (Garel et al., 2001; Kedzia et al., 2002; Rybaczuk et al., 1996; Shyu et al., 2010; Wu et al., 2009) through childhood (Blanton et al., 2001) and into adulthood (Amunts et al., 1997; Free et al., 1996; Takahashi et al., 2004) until decreasing complexity is seen in late life and in Alzheimer's disease (King et al., 2009, 2010; Zhang et al., 2007). There is also a growing literature on the cortical FD in many psychiatric disorders including schizophrenia and manic depression (Bullmore et al., 1994; Ha et al., 2005; Narr et al., 2001, 2004), obsessive compulsive disorder (Ha et al., 2005), autism (Raznahan et al., 2010) and neurological disorders including stroke (Zhang et al., 2008), Williams syndrome (Thompson et al., 2005; Van Essen et al., 2006) and multiple sclerosis (Esteban et al., 2007, 2009). "
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    ABSTRACT: Fractal measures such as fractal dimension (FD) can quantify the structural complexity of the brain. These have been used in clinical neuroscience to investigate brain development, ageing and in studies of psychiatric and neurological disorders. Here, we examined associations between the FD of white matter and cognitive changes across the life course in the absence of detectable brain disease. The FD was calculated from segmented cerebral white matter MR images in 217 subjects aged about 68years, in whom archived intelligence scores from age 11years were available. Cognitive test scores of fluid and crystallised intelligence were obtained at the time of MR imaging. Significant differences were found (intracranial volume, brain volume, white matter volume and Raven's Progressive Matrices score) between men and women at age 68years and novel associations were found between FD and measures of cognitive change over the life course from age 11 to 68years. Those with greater FD were found to have greater than expected fluid abilities at age 68years than predicted by their childhood intelligence and less cognitive decline from age 11 to 68years. These results are consistent with other reports that FD measures of cortical structural complexity increase across the early life course during maturation of the cerebral cortex and add new data to support an association between FD and cognitive ageing.
    NeuroImage 04/2012; 61(3):694-701. DOI:10.1016/j.neuroimage.2012.03.088 · 6.36 Impact Factor
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    • "Most calculations of the cortical surface FD rely on the boxcounting method, which calculates regional areas for progressively lower sampling resolutions. Since the number of vertices steadily decreases, the position of these vertices can have a large impact on the FD metric and can potentially overlook relevant cortical folding information (Free et al., 1996; King et al., 2009). This concern can be addressed by aligning sulci across subjects to approximate the same cortical location for each vertex for all subjects (Thompson et al., 1996). "
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    ABSTRACT: Altered cortical surface complexity and gyrification differences may be a potentially sensitive marker for several neurodevelopmental disorders. We propose to use spherical harmonic (SPH) constructions to measure cortical surface folding complexity. First, we demonstrate that the complexity measure is accurate, by applying our SPH approach and the more traditional box-counting method to von Koch fractal surfaces with known fractal dimension (FD) values. The SPH approach is then applied to study complexity differences between 87 patients with DSM-IV schizophrenia (with stable psychopathology and treated with antipsychotic medication; 48 male/39 female; mean age=35.5 years, SD=11.0) and 108 matched healthy controls (68 male/40 female; mean age=32.1 years, SD=10.0). The global FD for the right hemisphere in the schizophrenia group was significantly reduced. Regionally, reduced complexity was also found in temporal, frontal, and cingulate regions in the right hemisphere, and temporal and prefrontal regions in the left hemisphere. These results are discussed in terms of previously published findings. Finally, the anatomical implications of a reduced FD are highlighted through comparison of two subjects with vastly different complexity maps.
    NeuroImage 02/2011; 56(3):961-73. DOI:10.1016/j.neuroimage.2011.02.007 · 6.36 Impact Factor
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