Fractal dimension analysis for quantifying cerebellar morphological change of multiple system atrophy of the cerebellar type (MSA-C)

Abstract

Multiple system atrophy of the cerebellar type (MSA-C) is a degenerative neurological disease of the central nervous system. This study aims to demonstrate that the morphological changes of cerebellar structure, specifically, the cerebellum white matter (CBWM) and cerebellum gray matter (CBGM) from T1-weighted magnetic resonance (MR) images, can be quantified by three-dimensional (3D) fractal dimension (FD) analysis, which is a measure of complexity. Twenty-three MSA-C patients and twenty-one normal subjects participated in this study. The results of this study show that MSA-C patients presented significantly lower FD values compared to the control group, and that morphological change in the CBWM dominates the cerebellar degeneration. In addition, the FD analysis method is superior to conventional volumetric methods in quantifying the structural changes of WM and GM because it exhibits smaller variances and less gender effect. Since a decrease of cerebellar FD value indicates degeneration of the cerebellar structure, this study further suggests that the morphological changes of cerebellar structures (CBGM and CBWM) can be characterized by FD analysis.

Introduction

Multiple system atrophy (MSA) is a form of sporadic spinocerebellar degeneration characterized by varying degrees of parkinsonism, cerebellar ataxia, and autonomic dysfunction (Wenning et al., 2002, Wenning et al., 2004, Papp et al., 1989, Soma et al., 2006). The onset of this disease usually occurs about age sixty, and progresses relentlessly until death an average of 9 years later (Wenning et al., 1994). Gait ataxia is the most typical early symptom of this disease. Other clinical features include dysarthria, unintentional movement, and parkinsonian or other extrapyramidal symptoms (Berciano, 1982). Neuropathologically, glial inclusion formation is the most prominent pathological feature of MSA (Papp et al., 1989). Other features include variable neuronal loss and gliosis in the putamen, substantia nigra, pontine nuclei, cerebellar cortex, inferior olive, and intermediolateral column of the spinal cord (Soma et al., 2006).

MSA can be categorized into two main subtypes depending on its dominant clinical features: MSA-C (cerebellar) and MSA-P (parkinsonism) (Papp et al., 1989, Gilman et al., 1999). MSA-C is more common than MSA-P in Japan and Taiwan, while MSA-P is more common than MSA-C in the United States. Overall, MSA-C is the most common subtype of MSA, and has been labeled as olivopontocerebellar atrophy (OPCA) (Graham and Oppenheimer, 1969, Kuriyama et al., 2005). Many investigators have reported that the main pathological changes of MSA-C are the loss of neurons in the ventral portion of the pons, inferior olives, and cerebellar cortex. Its fundamental lesions occur in the arcuate, pontine, inferior olivary, pontobulbar nuclei, and the cerebellar cortex (Pemde et al., 1995, Konagaya et al., 2002, Lee et al., 2004a).

Magnetic resonance imaging (MRI) is a widely used tool for clinicians to evaluate degenerative disorders of the brain and spinal cord (Horimoto et al., 2000, Brenneis et al., 2007), motor function impairment (Baloh et al., 2003), seizure source (Free et al., 1996, Woermann et al., 2001) and tumor growth (Pereira et al., 2000, Iftekharuddin et al., 2000). The ‘putaminal hyperintense rim’ and ‘hot cross bun’ signs are the two main MRI indicators of MSA. A hyperintense rim at the lateral edge of the dorsolateral putamen appears in 34.5% of MSA patients, and a ‘hot cross bun’ sign in the pontine basis (PB) appears in 63.3% of MSA subjects. These putaminal and pontine abnormalities became more prominent as MSA-P or MSA-C progress. The atrophy of the cerebellar vermis and PB are significantly correlated, particularly with the interval following the appearance of cerebellar symptoms in MSA-C. MSA patients also exhibit atrophy of the corpus callosum (Watanabe et al., 2002).

This study aims to demonstrate that the morphological changes in the cerebellar structure (the cerebellum white matter (CBWM) and cerebellum gray matter (CBGM)) can be characterized by 3D fractal dimension (FD) analysis. The FD analysis method condenses all of the structural details of an irregular object into a single numeric value. This value can then serve as a quantitative measure of morphological complexity (Ha et al., 2005, Esteban et al., 2007), which makes FD analysis a convenient tool for this MSA-C study. Neuroscience has used FD analysis to quantify shape complexity and morphological change analysis for years (Fernández and Jelinek, 2001, Shan et al., 2006, Free et al., 1996, Zhang et al., 2007, Sandu et al., 2008, Cutting and Garvin, 1987 Oct). Because FD analysis is based on a logarithmic scale, small increases in the FD value correspond to large increase in complexity (Smith et al., 1989). Shan et al. suggested that the FD index is a compact measure of structural complexity, and can be used as a summary index of structure irregularity (Shan et al., 2006). They further proposed that fractal geometry can be used to describe the abnormalities of cortical morphology in patients with neurological disorders. Liu et al. reported that the FD value of a normal brain cortex is stable and has a low variance (Liu et al., 2003). Kiselev et al. demonstrated the self-similar fractal structure of the cerebral cortex, which has an FD value 2.80 ± 0.05 (Kiselev et al., 2003). FD analysis can also quantify dynamic changes of the structural or functional complexity of the neural system during the process of brain development or degeneration (Free et al., 1996, Liu et al., 2003, Lee et al., 2004b, Esteban et al., 2007). Researchers have also applied FD measurement in many image analyses of central nervous system disorders such as schizophrenia (Sandu et al., 2008), tumor detection (Zook and Iftekharuddin, 2005, Iftekharuddin et al., 2000, Pereira et al., 2000), respiration system analysis (Peng et al., 2002), multiple sclerosis (Esteban et al., 2007), medulloblastoma (Shan et al., 2006), epilepsy (Cook, 1995), obsessive–compulsive disorder (Ha et al., 2005), and age-related WM abnormalities (Zhang et al., 2007). Since FD analysis can serve as a quantitative measure of morphological complexity by summarizing the structural details of an irregular object into a single value (Ha et al., 2005, Esteban et al., 2007), this study hypothesizes that it can be a convenient tool for the study of MSA-C.

In addition to 3D FD values, this study calculates the volumes of CBGM and CBWM. The analyses below illustrate the advantages of the 3D FD method using data from MSA-C patients and normal subjects. The FD method is superior to the conventional volumetric method in that it exhibits much smaller standard deviations and less gender effect. The FD values of the CBWM and CBGM of MSA-C patients were significantly smaller than those in the control group. FD results also reveal that morphological changes in the CBWM dominate the cerebellar degeneration.