Article

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

ABSTRACT

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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    • "While the concept of fractured dimensions was emphasized in Mandelbrot (1967) where he initiated the coastline paradox, its applications range from characterizing turbulence (Mandelbrot, 1982), urban growth (Chen, 2011), human physiology (King et al., 2009) medicine (Losa, 2006) and more importantly in our case, market trends (Peters, 1991; Mandelbrot, 2004). Mandelbrot (1967) suggests that the smaller the increment of measurement, the longer the measured length becomes such that if one were to measure a stretch of coastline with a yardstick, one would get a shorter result than if the same stretch were measured with a one-foot ruler. "
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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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    • "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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