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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    • "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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    ABSTRACT: Most technical analysis tools focus traditionally on the simple and exponential moving average technique. This study looks at the performance of an optimized fractal adaptive moving average strategy over different frequency intervals, where the Euro/US Dollar currency pair is analyzed due to the increased correlation between the Euro Index and EUR/USD, and the Dollar Index and EUR/USD over the last year compared to the last 15 years. The optimized strategy is evaluated against a buy-and-hold strategy over the 2000- 2015 period, using annualized returns, annualized risk and Sharpe performance measure. Due to the existence of different number of long and short trades in every trading scenario, this paper proposes the use of a new measure called the Sharpe/Total trades ratio which takes into account the number of trades when evaluating the different trading strategies. Findings strongly support the use of the adaptive fractal moving average model over the naïve buy-and-hold strategy where the former yielded higher annualized returns, lower annualized risk, a higher Sharpe value, although it was subject to more trades than the buy-and-hold strategy. The best market timing strategy occurred when using 131 daily fractal data with a Sharpe/Total trades ratio of 0.31%.
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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.
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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.
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