Original contributionQuantitative morphologic evaluation of white matter in survivors of childhood medulloblastoma
Introduction
Survivors of pediatric brain tumors commonly have cognitive delays or deficits caused by cranial radiation therapy (CRT) administered with or without chemotherapy [1], [2], [3], [4]. The fact that CRT can cause changes in the structure of white matter (WM) [5] has been well documented. Recently, intellectual deficits have been associated with decreases in the volume of normal-appearing white matter (NAWM) [6], [7], [8]. Furthermore, diffusion tensor magnetic resonance imaging (MRI) studies have shown loss of anisotropy in WM as a result of irradiation [9]. These recent findings suggest that measurements of WM damage could be a useful index of the cumulative impact of central nervous system (CNS) insult from multiple sources [8].
WM damage could be evaluated by several methods, including volumetric studies [6], [7], [8] and diffusion tensor MRI [9]. Volumetric studies investigate quantitative relationships between volumetric changes and functions in the brain. Diffusion tensor MRI quantifies changes in WM fiber organizations. However, morphologic evaluation of WM damage has been largely restricted to visual estimation. In the present study, we applied fractal geometry to quantify WM integrity in the brain of survivors of childhood medulloblastoma.
The term fractals, which was coined by Mandelbrot [10], [11], refers to complex objects characterized by a structural pattern that is continuous but not differentiable. Unlike traditional Euclidean structures with integral dimensions, fractal structures are mathematical objects with fractional dimensions [10]. Mathematically generated fractals, such as the Koch curve or the Sierpinski triangle, have the fractal property of exact self-similarity, and this similarity extends over an infinite range of scales of measurements. Natural fractals, such as clouds, trees and snowflakes, share the same fractal property as mathematical fractals. However, natural fractals show approximate similarity, and their similarity extends over a finite range of scales. Although there is a continuing debate about the use of the term fractal to describe these natural objects [11], [12], fractal geometry [specifically, the index of fractal dimension (FD)] is a useful tool to quantify the inherent complexity of an object.
Fractal geometry has been successfully applied as a quantitative morphologic tool in geology [13]. It has also been used to describe pathological architecture in medicine [14], [15] and textures in Pattern Recognit [16]. In neuroimaging studies, fractal feature analysis has quantified the cortical complexity of different structures; for example, sulcal/gyral convolutions [17], [18], the WM skeleton in cerebella [19] and the boundary between the WM and the cerebral cortex [20], [21] have undergone FD analysis. FD analysis of sulcal/gyral convolutions showed that the FDs of all primary sulci are similar in their complexity in normal adults [18]. In a similar FD analysis of sulcal/gyral convolution of 24 normal children and adolescents (ages, 6–16 years), age-related increases of sulcal FDs were found in the left and right inferior frontal and left superior frontal regions [17]. FD analysis of the WM skeleton in the cerebella of 24 healthy young subjects also revealed a stable, narrow-range FD index of 2.57 [19]. The results of these studies suggest that the FD index, which is a compact measure of structural complexity, can be used as a summary index of structure irregularity.
Fractal geometry has also been used to describe the abnormalities of cortical morphology in patients with neurologic disorders. Bullmore et al. [21] estimated the FD indexes of the boundary between the WM and the cerebral cortex in 39 schizophrenic patients, 23 manic–depressive patients and 31 control subjects. The mean FD index in manic–depressive patients was greater than that in controls, and the mean FD index in schizophrenic patients was less than that in controls. In a study of cerebral cortical patterns in frontal lobe epilepsy, Cook et al. determined that the typical FD index of the cortical–WM interface was 1.45±0.06 in 20 normal subjects. Nine of 16 patients with frontal lobe epilepsy had an FD index less than 1.27 (lowest value, 1.17).
Several different methods can be used to characterize FD for different applications, and they are based on different theoretical formulations and assumptions, such as shape description approaches (box-counting and surface area measurements) and statistical approaches (semivariance and Fourier transform methods). Generally, shape description methods resolve and analyze the target object itself. The statistical approaches use statistical models of a certain pattern of the object. In this study, we used a box-counting method to quantify the FD of NAWM boundary because boundaries are lines on 2D images. We used a semivariance method to analyze the FD of NAWM intensity because results of Fourier-transform-based methods may be affected by the range of frequencies used, and discrepancies were found in results of previous studies [22].
In the study described here, we used fractal geometry to investigate the morphologic damage shown in T1-weighted MR images of NAWM in the brain of pediatric patients with medulloblastoma in the posterior fossa. An artificial neural network algorithm based on T1-, T2- and proton density (PD)-weighted images [26] was used to segment T1-weighted MR images of the normal cerebrum into NAWM, gray matter (GM), cerebrospinal fluid (CSF) and vessels. The FD index of WM boundary was calculated by using a box-counting method, and the FD index of WM intensity was determined by using a fractional Brownian motion (FBM) model. The purposes of our study were to devise a quantitative method to describe cortical morphology and to use the method to monitor neurotoxicity in survivors of pediatric brain tumors.
Section snippets
Patients
Participants were recruited from an ongoing study of treatment for primary medulloblastoma at St. Jude Children's Research Hospital. The MRI data of these recruited patients had already been obtained by protocol-directed MR examinations. The use of these retrospective MR data was approved, and the requirement of informed consent was waived by the Institutional Review Board. All patients who enrolled in the treatment protocol and had evaluable MR examinations within the first 3 months of therapy
Results
Fig. 1 shows an example of results from the successful segmentation of an MR image of various types of brain tissue. The accuracy and validation of this segmentation method were established previously [6], [27].
An example of linear regression model fittings of the natural logarithms of WM boundary voxels over the natural logarithms of scale factors is shown in Fig. 2A; an example of the fittings of the natural logarithms of intensity variations over the natural logarithms of scales (distances)
Discussion
In this study, we applied fractal geometry analysis to assess NAWM in the MR images of the brain of medulloblastoma survivors. This study is the first quantitative evaluation of changes in morphologic complexity in the developing brain of children who survive medulloblastoma. This study is also the first to utilize the FD index of intensity to describe variations in WM intensity in the brain.
Previous studies showed that cognitive deficits are associated with lower volumes of NAWM [8].
Acknowledgments
This work was supported, in part, by a Cancer Center Support grant (CA21765) from the National Cancer Institute and by the American Lebanese Syrian Associated Charities.
The authors thank Rhonda Simmons for her assistance in the collection and processing of MRI data, and Julia Cay Jones, Ph.D., E.L.S., and Margaret Carbaugh, medical editor, for editorial consultation.
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