Fractal dimension analysis of MR images reveals grey matter structure irregularities in schizophrenia
Introduction
In addition to recent demonstrations of neurocognitive impairments in schizophrenia, involving both behavioural [1] and brain mapping data [2], studies of brain morphology have consistently shown grey matter (GM) abnormalities in schizophrenia [3], [4], [5], [6], [7], [8], [9], [10], [11], in individuals at high risk for developing schizophrenia [12], [13] and in first-episode patients [14]. Other studies have shown that this is not a side-effect of medication [15]. Further evidence is given by the meta-analysis by Shapleske et al. [16] and recent overviews by Shenton [17], Chitnis and Ellison-Wright [18], and Niznikiewicz et al. [19].
Although different MRI techniques have been used, with different subgroups of patients, the majority of the studies have revealed substantial GM loss in the superior (STG) and middle temporal gyri (MTG) (including the hippocampus), middle frontal gyrus (MFG), and anterior cingulate (AC). Studies of cognitive impairment in schizophrenia have implicated the same brain areas, e.g. the link of executive and attentional working memory to the prefrontal cortex [20]; verbal memory to the hippocampus [3], [21] and loss of initiative and apathy to the anterior cingulate cortex [18].
MR morphological studies provide a measure of voxel-based differences in GM volume or density, or of differences in cortical thickness, between patients with schizophrenia and healthy control subjects. There is, however, reason to believe that also other aspects of brain morphology factors may be abnormal in schizophrenia, e.g. the gross cortical surface structure. It has been reported in other brain-related disorders, e.g. reading- and learning-disability, that an increased rate of microdysgenesis of the cortex is present, with abundance of ectopias, i.e. neurons that are out of place and microgyrification [22], [23]. Such structural abnormalities were found mostly in the perisylvian and anterior vascular border regions. Interestingly, asymmetry in the microstructure between the right and left hemispheres have also been reported [24]. Since several studies have pointed to a possible relationship between language-related learning disabilities and schizophrenia (e.g. [25], [26], [27]), it is not unreasonable to assume that architectural abnormalities may exist also in the schizophrenic brain. We therefore predicted that schizophrenia involves increased gyrification and neuronal misplacements that will result in a more rugged cortical surface than that observed in a healthy control group. Such architectural anomalies may, moreover, be more preponderant in one hemisphere, and in specific cortical regions, presumed to be affected in schizophrenia (see [16], [18]).
Previous studies of the cortical architecture of the human brain have, however, been performed only on post-mortem samples. For example, Galaburda and his colleagues [22], [28] examined the brains of five dyslexic individuals at autopsy, using standard neuropathological approaches. Obviously such an approach would require access to the brains of deceased patients, and would be difficult to correlate with, e.g. functional or cognitive data. Moreover, standard morphological MR analysis techniques will not allow for a quantification of architectural differences in the cortical surface structure. The problem facing current in vivo imaging techniques is that many organs in the human body, including the brain, have complex geometric structures, e.g. the folding pattern of the cortical sheet. Therefore, these structures cannot be characterized using only measures within classical Euclidean geometry [29]. Such complex geometry can, however, be characterized by its shape properties at different scales, i.e. by fractal geometry. More precisely, the folding pattern of the cortical sheet, e.g. Im [30] can be described in terms of its fractal dimension (FD) [31], [32], [33]. FD provides a way of quantifying the shape complexity of objects into a single numerical value, which can be compared between groups of patients, or between patients and healthy controls [34], [29], [35]. The term fractal was introduced by Mandelbrot [29] to deal with such objects that present self-similarity. This means magnifying an object into more and more details of the fine structure and the degree to which the part is similar to the whole.
The FD of the cortical folding has been studied in patients with epilepsy [36] and obsessive–compulsive disorder [37], and in children at different ages [38]. With regard to schizophrenia, Narr et al. [39] found a higher FD value for the grey matter/external cerebrospinal fluid boundaries in patients with schizophrenia compared to healthy controls, while Ha et al. [37] found reduced FD value. A problem when interpreting the results of Narr et al. [39] and Ha et al. [37] is that the first study compared first-episode schizophrenia patients, while the second study compared schizophrenia patients with obsessive–compulsive patients. Thus, it is still an open question whether schizophrenia involves increased or decreased FD values, and thus abnormality of cortical surface geometry. We therefore compared patients with mean illness duration of 8 years, with an age-matched healthy control group. We segmented grey matter from the inner white matter and the outer pial structures in order to obtain a quantification of the relationship between brain surface and volume.
Section snippets
Subjects
The samples consisted of seven patients with a DSM-IV diagnosis of schizophrenia and six healthy control subjects. Because of the small sample size, the present study should be considered as a feasibility study only. The patients were outpatients and inpatients recruited for research purposes from psychiatric clinics in Bergen and Oslo, Norway. Mean duration of the illness for the patients was 8.7 years, S.D. 8.2 years. The control subjects were recruited from the University of Bergen and
Results
The results are presented separately for the box-counting and Minkowski–Bouligand methods.
Discussion
Both the box-counting and the Minkowski–Bouligand methods showed overall higher FD values for the whole brain volume, which is in accordance with the findings by Narr et al. [39]. The results were also similar for the box-counting and Minkowski–Bouligand methods, thus whether one or the other of the methods is used when calculating the FD in brain structures seemed not a major issue. When targeting the hemispheres separately, a higher FD value was observed for the schizophrenic patients for the
Summary
The fractal dimension was used to reveal brain structure irregularities in patients with schizophrenia compared to a healthy control group. It is well known that the folding and convolutions of the cortical surface of the human brain have a complex structure, which cannot be completely characterized using traditional MR morphometry techniques and Euclidean geometry. On the other hand, the fractal dimension provides a way of quantifying the shape complexity of objects into a single numerical
Anca Larisa Sandu was born in Botosani, Romania, in 1975. She received a degree in medical bioengineering from the “Gr. T. Popa” University of Medicine and Pharmacy, Iasi, Romania, in 2001 and a MSc, from the Faculty of Physics, “Al. I. Cuza” University, in the same city, in 2003. Since 2004, she has been with the University of Bergen, Norway, where she is a doctoral student. Her research interests focus on structural MR image processing and analysis of biological signals using nonlinear
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Anca Larisa Sandu was born in Botosani, Romania, in 1975. She received a degree in medical bioengineering from the “Gr. T. Popa” University of Medicine and Pharmacy, Iasi, Romania, in 2001 and a MSc, from the Faculty of Physics, “Al. I. Cuza” University, in the same city, in 2003. Since 2004, she has been with the University of Bergen, Norway, where she is a doctoral student. Her research interests focus on structural MR image processing and analysis of biological signals using nonlinear methods.
Inge Rasmussen was born in Andøy, Norway, in 1971. He is a MSc in structural chemistry and an MD, both from the University of Tromsø, Norway. He is currently finishing his PhD in medical technology in the University of Trondheim, focussing on functional and structural MR-imaging of the brain. His research projects focus on clinically applicable functional imaging in neurosurgical patients and functional imaging in a number of psychiatric disorders.
Arvid Lundervold was born in Oslo, Norway in 1952, He has a MD degree in medicine from University of Oslo in 1982, and a PhD degree at the Faculty of Medicine, University of Bergen, Norway, in 1995. He is since 2005 professor in medical information technology at the Faculty of Medicine, University of Bergen, Norway. His research interests are in medical information technology and neuroinformatics.
Frank Kreuder was born in Duisburg, Germany, in 1968. He received his diploma in physics from the University of Aachen, Germany, in 1995 and his MD from the University of Hamburg, Germany, in 1998. He worked in the Department of Neuroradiology at the University of Luebeck, Germany. Since 2001 he is a researcher at the Centre for Neuropsychological Research, University of Trier, Germany. His current research interests include medical image processing (especially registration, reconstruction and segmentation), diffusion tensor imaging, fMRI and computational neuroanatomy.
Gesche Neckelmann was born in 1962. She has a MD degree from the University of Heidelberg, Germany, in 1990. She is legitimized specialist in neuroradiology at the Department of Radiology, Haukeland University Hospital, Bergen, Norway. She is also a member of the Bergen fMRI-Group, University of Bergen. Her research interests are in various aspects of MR imaging, including MR perfusion, fMRI, DTI, and their clinical applications.
Kenneth Hugdahl was born in Brunflo, Sweden in 1948. He received a BA degree and PhD degree from the University of Uppsala, Sweden in 1973 and 1977, respectively. Since 1984 he is professor in Biological psychology and head of the Bergen fMRI-Group at the University of Bergen, Norway. His research interests are in cognitive neuroscience and functional brain imaging, including the neurocognition of schizophrenia.
Karsten Specht was born in Remscheid, Germany, in 1969. He received a degree in physics from the Technical University Aachen, Germany, in 1997 and PhD in neuroscience from the University Magdeburg, Germany, in 2003. Since 2004, he has been with the University of Bergen, Norway, where he holds a position as senior researcher in the Section for Cognitive Neuroscience at the Department for Biological and Medical Psychology. His research interests focus on methodological aspects of MR image processing, schizophrenia, and speech processing.
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The present research was financially supported by a grant to Kenneth Hugdahl from the Alfried Krupp von Bohlen und Halbach Stiftung, Germany.