Fractal dimension and white matter changes in multiple sclerosis
Introduction
Multiple sclerosis (MS) is a chronic inflammatory and neurodegenerative disease of the central nervous system (CNS) (Steinman, 2001). Several pathological processes affect white matter (WM) diffusely, including areas without classical demyelinating plaques, the so-called normal-appearing white matter (NAWM). The underlying histopathological changes of NAWM are not well known, but some identified processes are microscopic inflammatory cell infiltration, microglial activation, blood-vessel sclerosis, Wallerian degeneration of axons, astrocytic proliferation, and microscopic demyelinated and remyelinated areas (Allen and McKeown, 1979, Trapp et al., 1998). NAWM abnormalities become more pronounced with increasing physical and cognitive disability and may develop for many months or even years prior to focal-lesion development (Miller et al., 2003). Thus, the detection of markers corresponding to NAWM abnormalities is clinically relevant because these abnormalities contribute to tissue damage and to the increase of long-term clinical disability, regardless of the presence of typical macroscopic MS lesions (Filippi et al., 1995, Filippi et al., 1999, Loevner et al., 1995).
A magnetic resonance (MR) technique sensitive for detecting and quantifying the subtle neuropathological changes taking place in the NAWM is the magnetization transfer ratio (MTR). Low MTR has been associated with the main pathological changes on clinically isolated syndrome (CIS) and relapsing–remitting MS (RRMS) patients (Filippi et al., 1995, Filippi et al., 1998, Griffin et al., 2002, Loevner et al., 1995). In addition, MTR abnormalities detected in the NAWM have recently been associated with disability in other forms of MS (Ramio-Torrenta et al., 2006). However, focal lesions had been described as the predominant pathological feature in CIS patients instead of diffuse NAWM alterations (Brex et al., 2001). The lack of MTR sensitivity to the subtle NAWM pathological changes taking place in these patients and the appearance of difficulties in the standardization of this technique preclude the generalization of its use. Another approach for studying NAWM is magnetic resonance spectroscopy (MRS). Several studies using MRS in patients with MS have shown a decrease in the N-acetyl aspartate peak both in MS plaques as well as in NAWM (Miller et al., 2003), suggesting that axonal disruption contributes to the abnormalities in the NAWM.
Images representing morphologically complex objects may be described and categorized using fractal analysis approaches on the value of the fractal dimension, with widespread applications in the field of neuroscience (Fernández and Jelinek, 2001). Fractal dimension (FD) is a quantitative measure of morphological complexity, and it has been stated as a good descriptor of the complex shape of cerebral structures such as the WM and grey matter (GM) in humans (Blanton et al., 2001, Free et al., 1996, Kiselev et al., 2003, Liu et al., 2003, Thompson et al., 1996). Moreover, brain FD is altered by the presence of diseases such as psychiatric disorders (Bullmore et al., 1994, Ha et al., 2005), epilepsy (Cook et al., 1995), and even age-related WM abnormalities (Kedzia et al., 1997, Takahashi et al., 2004, Zhang et al., in press). FD analysis provides complementary information to classical brain atrophy quantification in terms of surface (Ha et al., 2005, Zhang et al., in press) and internal shape complexity (Zhang et al., 2006, Zhang et al., in press).
The aim of our study was to assess the usefulness of FD as a measurement of visible and non-visible WM abnormalities in conventional MR sequences of patients with MS. Indeed, we sought to develop a simple method for identifying additional changes of WM abnormalities in MS in order to provide a useful test for monitoring disease. We found a decrease of the WM FD in patients with MS compared to healthy controls (HC), even in sections without the presence of MS plaques.
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Patients
A total of 60 cases and 17 gender- and age-matched healthy controls (HC) were recruited in the MS centre of the University of Navarra (Spain). All subjects gave their informed consent according to the Helsinki Declaration before being included in the study, which was approved by the local Research Ethics Committee. Twenty-one patients suffered CIS, 31 RRMS, four secondary progressive MS (SPMS), and four primary progressive MS (PPMS) (McDonald et al., 2001). Patients with an active relapse, or
Results
We compared the FD of the WM border between HC and MS patients. We found that patients with MS had a decrease of the FD of the WM border compared to HC (p < 0.001; Fig. 3A). In addition, we attained the same decrease in the FD of the WM border for all subtypes of MS (p < 0.05 in all cases; Fig. 3B). To evaluate the influence of the presence of macroscopic MS lesions and the NAWM abnormalities on the FD calculation, we quantified the FD in patients with and without visible MS lesions at the
Discussion
One prominent finding of this study was that WM FD is decreased in patients with MS, both at the grey–white matter boundary (WM border) and at the internal structure of the WM (WM skeleton) of the entire brain. Such decrease in the FD was an early event in the disease and was influenced not only by the presence of MS plaques but also by changes in the NAWM. Indeed, the implementation of a simple approach, such as determining the FD on a single slice of WM segmented from a conventional MR image,
Acknowledgments
We would like to thank Diego Maza, from the Department of Physics of the University of Navarra for his helpful comments. This work was supported by Junta de Andalucía (CVI-302) to FJER, and the Spanish Ministry of Health (FIS PI051201) and Fundacion Uriach to PV. JS was a fellow of the Spanish Ministry of Health (FIS CM#05/00222), NVM of the Basque Country Government and JG of the Navarra Government. The authors have no conflicting financial interests.
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