Computers in Biology and Medicine 64 (2015) 179–186

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Fractal dimension analysis of cerebellum in Chiari Malformation type I Engin Akar a,n, Sadık Kara a, Hidayet Akdemir b, Adem Kırış c a b c

Institute of Biomedical Engineering, Fatih University, Istanbul, Turkey Department of Neurosurgery, Medicana International Hospital, Istanbul, Turkey Department of Radiology, Mehmet Akif Ersoy Cardio-Thoracic Surgery Training and Research Hospital, Istanbul, Turkey

art ic l e i nf o

a b s t r a c t

Article history: Received 18 May 2015 Accepted 26 June 2015

Chiari Malformation type I (CM-I) is a serious neurological disorder that is characterized by hindbrain herniation. Our aim was to evaluate the usefulness of fractal analysis in CM-I patients. To examine the morphological complexity features of this disorder, fractal dimension (FD) of cerebellar regions were estimated from magnetic resonance images (MRI) of 17 patients with CM-I and 16 healthy control subjects in this study. The areas of white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF) were calculated and the corresponding FD values were computed using a 2D box-counting method in both groups. The results indicated that CM-I patients had significantly higher (po 0.05) FD values of GM, WM and CSF tissues compared to control group. According to the results of correlation analysis between FD values and the corresponding area values, FD and area values of GM tissues in the patients group were found to be correlated. The results of the present study suggest that FD values of cerebellar regions may be a discriminative feature and a useful marker for investigation of abnormalities in the cerebellum of CM-I patients. Further studies to explore the changes in cerebellar regions with the help of 3D FD analysis and volumetric calculations should be performed as a future work. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Chiari Malformation Magnetic resonance imaging Fractal dimension White matter Gray matter Cerebrospinal fluid

1. Introduction As a serious pathological condition described by Professor Hans Chiari in 1891 [1], Chiari Malformation type I (CM-I) is characterized by the downward displacement of cerebellar tonsils, which are rounded structures located at the bottom of each cerebellar hemisphere, into the spinal canal [2,3]. Radiologically, descent of the cerebellar tonsils more than 5 mm into the cervical canal through the foramen magnum leads to the diagnosis of CM-I [4]. Although the brainstem and the fourth ventricle may be smaller or slightly deformed, they are in their normal position. Most CM-I patients involve syringomyelia, which is an abnormal dilatation of spinal canal creating a small cavity that can involve a collection of cerebrospinal fluid (CSF) [5]. CM-I may arise from several reasons, including altered CSF circulation dynamics that disrupt the equilibrium of intracranial pressure [2], incomplete development of occipital bones and small posterior cranial fossa (PCF) that results in an overcrowding of cerebellum [6–8].

n Correspondence to: Institute of Biomedical Engineering Fatih University 34500, Büyükçekmece Istanbul, TURKEY. Tel.: þ90 212 8663300 2643; fax: þ 90 212 8663412. E-mail address: [email protected] (E. Akar).

http://dx.doi.org/10.1016/j.compbiomed.2015.06.024 0010-4825/& 2015 Elsevier Ltd. All rights reserved.

Patients with CM-I may show several symptoms with various degrees of severity. The most frequent symptom is the headache in the back of the head. Another common condition is the pain in neck and shoulders [9,10]. A list of secondary signs include dysarthria, a condition that affects speech quality of a person [11]; balance and gait problems [12]; nystagmus, a condition involving repetitive, involuntary eye movements that cause limited vision [13]; and sleep apnea [14]. An important consideration of this anomaly is that a wide variety of its signs and symptoms may result in misdiagnoses with some other neurological diseases including, migraine and multiple sclerosis (MS) [6] due to an absence of a particular diagnostic test that associates the symptoms of CM-I with its anatomical conditions [11]. Midline sagittal T1 weighted magnetic resonance imaging (MRI) provides the best viewpoint for displaying herniation [15]. Computed tomography and neurological tests are additional diagnostic methods that may be used for the identification of CM-I [16]. Another common examination method is the use of a phasecontrast (PC) cine MRI that allows the assessment of CSF flow and velocity [6,17,18]. Treatment of CM-I is achieved by a surgical operation called posterior fossa decompression [19]. Strong debate on the pathophysiology of this syndrome creates a disagreement on particular aspects of surgical process [11]. Restoration of CSF flow is the primary goal of the surgeons who consider CSF flow blockage to

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be the actual cause of CM-I symptoms [20,21]. On the other hand, if surgeons believe that the small size of the posterior fossa is the major reason for CM-I symptomatology, their surgical approach will intend to enlarge the PCF region. Many studies have been performed so far to investigate the neurological characteristics of CM-I syndrome. The Majority of these previous studies were related to assessment of the morphological properties of the cerebellum and nearby regions, such as the brainstem and fourth ventricle. Sagittal MRI slices of brain were generally used to measure the morphological characteristics of the PCF. These measurements can be classified into linear and volumetric measurements. Linear measurements involve the length of tonsillar descent, which can be calculated by taking the distance between the cerebellar tips and a line drawn from the basion to the opisthion, and the length of the clivus and supraocciput. On the other hand, total volumes of the posterior fossa, CSF and brain are other type of measurements for the volumetric evaluation of CM-I [6–8,22–24]. Furthermore, there are additional studies investigating CSF flow and velocity in order to figure out the effects of CSF flow patterns on the severity of CM-I symptoms [20,21,25]. Great deal of observations and efforts have been performed until now to enlighten this anomaly; nevertheless, the exact mechanisms of CMI pathophysiology are still unclear. Therefore, new features have to be found and new methods have to be employed in order to get a more clear understanding of this anomaly. The fractal geometry introduced by Mandelbrot in 1982 [26] is a concept to describe continuous spatial or temporal phenomena that are not differentiable. Fractal objects having fractal properties that contain self-similarity, numerous quantity of details and scale invariance may be found anywhere in nature, such as plants, trees, snowflakes and coastlines. The FD analysis approaches may be employed to describe and classify the structural details in complex objects by producing a single numeric value. This value, as a quantitative measure of morphological complexity, has been used to examine a wide range of objects in biology and medicine [27– 29]. Additionally, FD analysis has been proposed as a new method and widely used in the field of neuroscience to measure object complexity and to examine structural variations in some conditions and disorders, such as gender differences [30], identification of early stage atherosclerosis [31], epilepsy [32], schizophrenia [33,34], age-related micro-structural white matter (WM) changes [35], detection of tumors [36,37], multiple sclerosis [38], Alzheimer's disease [39], stroke [40], and cerebellar degeneration [41]. Besides, dynamic changes of neural system morphology during brain growth or degeneration can be quantified by employing fractal analysis [42–44]. Furthermore, it has been demonstrated that fractal approaches are suitable for studying shape complexity of cerebral structures including WM, gray matter (GM), and WM tracts [38,41,44]. The purpose of the present study is to compute the FD value of cerebellar WM, GM and CSF tissues for an investigation of structural differences between patients with CMI and healthy controls. Segmentation of brain MRI is an important step in the analysis of brain images for the purpose of understanding the influence of several conditions such as neurodegeneration, epilepsy and trauma on brain structures. Different methods have been proposed to automatically segment the brain MR images into different clusters of tissues. These methods can be classified into several categories such as classification-based segmentation, contourbased segmentation, region-based segmentation and knowledgebased segmentation [45]. A simple technique is the use of thresholding algorithm which splits an image into different classes using threshold intensity values [46]. Besides that, other classificationbased methods include statistical classification based approaches such as Markov random field [47], expectation maximization [48] and clustering based methods like fuzzy-c means [49].

Additionally, edge based methods and active contours approach [50] can be regarded as the examples of contour-based segmentation methods. Moreover, region-based techniques involve methods based on watershed [51], region growing and split-and-merge [52] algorithms. On the other hand, there are a number of software packages, which automatically perform a set of image processing routines such as bias field correction, skull splitting and automated segmentation. Statistical Parametric Mapping (SPM), FMRIB's Software Library (FSL) are some of these packages and they have been widely used in neuroimaging studies [38,40,41,57,61]. We hypothesized that the altered physical conditions of CM-I, such as tonsillar descent and overcrowding of cerebellum, may lead to the variations in morphological complexities of cerebellar tissues such as GM, WM and CSF. Since FD value is a convenient numeric descriptor for morphological complexity of structural details in brain tissues and it has been widely used in differential diagnostic studies, we have chosen this method to investigate structural complexity variations of cerebellum between healthy controls and patients with CM-I. To the best knowledge of the authors, this is one of the first studies that uses FD analysis to evaluate structural cerebellar complexity in CM-I patients. The aim of the present study is to make an effort to contribute the redefinition of the anomaly, which is still in progress, and assist the diagnosis, treatment and management of patients with this syndrome.

2. Materials and methods 2.1. Patients and MR acquisition Data used in this study were obtained from MRI records of the department of Radiology, Mehmet Akif Ersoy Cardio-Thoracic Surgery Training and Research Hospital and Medicana International Hospital, İstanbul, from 2013 to 2014. Brain images of 16 healthy subjects (8 males and 8 females, 16–50 years age range) and 17 CM-I patients (7 males and 10 females, 16–55 years age range) were used in this study (Table 1). No statistically significant differences were found in gender and groups as a result of a chi-square analysis (p ¼0.732). Brain MRI of subjects, who were diagnosed as CM-I anomaly by an experienced radiologist and by a neurosurgeon, were included in the patient group in this study. On the other hand, having any neurological and psychiatric conditions other than CM-I was accepted as exclusion criteria for MRI data of patients. The experimental procedures of the study were approved by the Ethical Committee of Fatih University. Three-dimensional T1-weighted human MR brain images were acquired from a Siemens Symphony Magnetom Aera 1.5 T MR scanner (Erlangen, Germany). The image parameters include: 24

Table 1 Demographical and Clinical data of subjects (mean 7std.dev.).

Age Gender (M/F) GM area WM area CSF area GM FD WM FD CSF FD

Patients

Controls

p-Value

37.94 7 10.57 7/10 897.8 7 134.92 394.16 7125.55 405.517 102.01 1.687 0.07 1.577 0.07 1.377 0.13

37.56 7 9.21 8/8 649.797 65.61 487.82 7 79.37 393.25 7 55.05 1.56 70.05 1.497 0.06 1.167 0.06

0.914 – o 0.001n 0.016n 0.673 o 0.001n 0.001n o 0.001n

M/F: male/female, GM area: area of cerebellar gray matter (mm2), WM area: area of cerebellar white matter (mm2), CSF area: area of cerebrospinal fluid (mm2), GM FD: gray matter fractal dimension, WM FD: white matter fractal dimension, CSF FD, cerebrospinal fluid fractal dimension. n

Less than the significance p-Value of 0.05.

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contiguous 5 mm sagittal slices; flip angle 901, echo time 9.8 ms, repetition time 511 ms, FOV 25 cm, and matrix size 512  512. 2.2. Image processing The image processing consists of four phases which are depicted in the Fig. 1. In the present study, midline-sagittal MRI slices were used for the area and FD value calculations. A graphical user interface (GUI) application was developed based on MATLAB 8.2s to facilitate the filtering, manual extraction of cerebellum and the other image processing operations. First, using a 3  3 default kernel, a 2D median filtering was implemented on each slice that contained the interested cerebellum part in order to improve the signal to noise ratio. Secondly, a manual extraction process was performed to separate the region that covered the overall cerebellum from the whole brain image in order to create mask images. Fig. 2(b) and (c) displays the manual extraction process and extracted cerebellum image, respectively. In the following step; GM, WM and CSF segmentation process was performed using the SPM8 package (Wellcome Department of Imaging Neuroscience, London, UK). Before starting segmentation process, sagittal slices were registered using SPM utilities to create the resulted image file in nifti Filtering of MR images Manual extraction of cerebellum tissue Segmentation of GM

Segmentation of WM

Segmentation of CSF

Masking

[53] format. Default templates, which are modified versions of the ICBM Tissue Probabilistic Atlas available at LONI [54], and default parameters were used for all segmentation operations in this study. Three different output files for GM, WM and CSF were produced by the SPM application. Using the MATLAB based graphical user interface, these output files were loaded slice by slice to fulfill the masking operation. In this step, using the previously extracted cerebellum region, the segmented cerebellum was separated from the other brain tissues. As a result, the GM, WM and CSF tissues that composed the cerebellum were obtained (Fig. 2(d)–(f)). The area estimation was accomplished by counting the pixels in the corresponding image and multiplying the pixel count by the length of each pixel in mm for both vertical and horizontal axis and the result was displayed in mm2 unit. 2.3. Fractal dimension analysis In this study, the FD of segmented GM, WM and CSF for cerebellum was calculated using the box-counting method. This method has been used in many studies because of its robustness, accuracy and easy implementation [26,27]. In addition, the FD of structures, which do not own strict self-similarity, such as brain, can be evaluated by means of this method [57]. To compute the FD, the region of interest was divided into a grid of boxes. Each box in the grid had an equal edge length in pixel size. The number of nonempty boxes was counted as the box-size was progressively growing. Fig. 3 illustrates two iterations of the box-counting method. In Fig. 3(a) and (b), the cerebellar WM image was divided into the boxes of size 4 and 8 pixels, respectively. Similar procedures were applied to the cerebellar GM image in Fig. 3(c) and (d). FD of a fractal can be derived from the following power law relationship [26]: NðrÞα

Measurement of Area & FD

181

1 r FD

ð1Þ

where NðrÞ denotes the number of boxes that contained one or more pixel values which are different than zero and r denotes the box-size.

Fig. 1. Steps of image processing.

a

b

c

d

e

f

Fig. 2. Segmentation of GM, WM and CSF regions from a Chiari patient. (a) MR T1-weighted head image in the mid-sagittal region. (b) Manual selection of cerebellum tissue with surrounding CSF. (c) Extracted cerebellum tissue with surrounding CSF to use as a mask. (d) Segmented cerebellar GM, (e) segmented cerebellar WM, (f) segmented CSF surrounding cerebellum after the mask in (c) was applied on the GM, WM and CSF segmentation result images from SPM8 application.

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Fig. 3. FD calculation procedure based on box-counting method on SPM segmented MR images (data from a Chiari patient were used). Segmented images were covered by a grid of boxes (of size r) and number of boxes (N) having at least one pixel with a value greater than zero was counted in (a)WM image, r ¼ 4, N ¼243 and (b) r¼ 8, N ¼ 81. (c) GM image, r ¼4, N ¼ 296 and (d) r¼ 8, N ¼96.

By rewriting the Eq. (1), the following line formula can be achieved: lnðNðrÞÞ ¼ FD  lnðr

1

ÞþC

ð2Þ

where C is a constant. The slope of the line can be used to estimate the FD value. Since brain images are not pure fractals, a suitable range of box sizes has to be chosen. When the smaller box-sizes are selected, higher FD values will be obtained; whereas bigger box-sizes will result in smaller FD value [57]. Linearity is disrupted when the inconvenient ranges of box-sizes are selected in the linear regression analysis, which is performed to estimate the FD. Therefore, the range of box-sizes producing the highest correlation coefficient R2 can be taken as the proper box-size range (Fig. 4). In this study, a full-slope analysis, which evaluated all possible values starting from three to the number of total box-sizes, was performed to determine the appropriate box-size range. According to the results of this analysis, different values of box-size range were used for each FD calculation, instead of using a constant value. Implementation details of the FD computation method, along with the slope analysis, and its

sample applications to calculate the FD of brain MR images can also be found at [55,56].

2.4. Statistical analysis Independent samples t-tests were used to compare the differences between CM-I patients and control groups. The data follows a normal distribution under the null hypothesis, stating that “no significant differences were found in the cerebellar features between patients and controls”. Bivariate correlation analysis was applied using Pearson's method to investigate the correlations between the FD values and the corresponding areas in each group. Using this method, the correlation between cerebellar GM FD values and GM areas, between cerebellar WM FD values and WM areas and finally, between CSF FD values and CSF areas were calculated. The significance level for all results was accepted as po 0.05. The statistical software packages SPSS version 20.0 (SPSS Inc., Chicago, Illinois) were used to perform all statistical analyses.

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The mild slope of the regression line shows that the FD value of cerebellar WM was not found to be significantly correlated (R2 ¼ 0.113) to the WM area. Similarly, the FD of cerebellar CSF did not show a significant correlation (R2 ¼ 0.007) with the CSF area (Fig. 6(c)). Besides, bivariate correlation analysis also indicated that there was no significant relationship (p40.05) between areas and FD values of WM and CSF tissues neither in patients nor in controls.

4. Discussion

Fig. 4. Illustration of slope analysis for selecting the appropriate box size range. The ln(Number of nonempty boxes) is displayed in the y-axis and ln(inverse of box size) is displayed in the x-axis. Linear regression analysis were performed using the data (blue diamond) The green dashed line represents the whole data and the red solid line represents the selected range of data (from 2 to 16 pixels in this case). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

3. Results In this study, areas of cerebellar WM, GM and CSF were calculated and the corresponding FD values were quantified for 17 CM-I patients and 16 controls using a 2D box-counting method. The clinical and demographical data of patients and controls are listed in Table 1. The mean area of cerebellar GM for patients was 897.87 134.92 mm2 and 649.79 765.61 mm2 for healthy controls. Average cerebellar WM areas for patients and controls were 394.16 7125.55 mm2 and 487.82 779.37 mm2, respectively. GM areas of CM-I patients were found significantly higher (po 0.001) than those of control subjects (Fig. 5(a)). Whereas, lower values (p ¼0.016) were observed for the cerebellar WM areas of patients compared to controls (Fig. 5(c)). The average areas of CSF surrounding the cerebellum for patients and controls were 405.51 7102.01 mm2 and 393.25 755.05 mm2, respectively. These results indicated that CSF areas were insignificantly different (p ¼0.673) between two groups (Fig. 5(f)). The estimated FD values for cerebellar GM, WM and CSF are listed in Table 1. Mean cerebellar GM FD values for patients were found to be 1.6870.07; corresponding FD values for WM in controls were 1.5670.05. Average cerebellar WM FD values for patients and controls were 1.5770.07 and 1.4970.06, respectively. The FD values of GM for the patients were significantly higher (po0.001) than the FD values of healthy controls (Fig. 5(b)). Similarly, FD values for WM in patients were found to be significantly larger (p¼0.001) than the average FD values in controls. (Fig. 5(d)). The mean FD value for cerebellar CSF were 1.3770.13 in patients and 1.1670.06 in controls, which means that patients had significantly higher values compared to controls (Fig. 5(f)) even though the areas for CSF in two groups were not different. A correlation analysis between the FD values and the area values in CM-I patients and control subjects was performed. The correlation between the FD value and the area of cerebellar GM for all patients and control subjects is shown in Fig. 6(a). A high correlation is indicated by the blue regression line (R2 ¼0.624) between the GM FD value and GM area. A separation of GM data for CM-I patients and healthy controls can be observed from the plot. This means that higher FD values and larger GM areas were observed for CM-I patients, whereas control group had smaller FD values and smaller GM areas. In addition, according to the results of Pearson's tests, only the patients group had a strong correlation between GM area and FD value (p¼0.025). In Fig. 6(b), the correlation between the area of cerebellar WM and the FD value of WM for patients and controls.

CM-I is an anatomical hindbrain abnormality having various symptoms because of the obstruction of CSF circulation and compression of hindbrain tissues such as the cerebellum, brainstem, and spinal nerve [2]. Experimental and clinical evidences indicated that the herniation of cerebellar tonsils may be resulted from an inadequate development of the occipital bone and as well as a small PCF allowing less space for the cerebellum and brainstem [6]. Therefore, diagnosis of this anomaly is made with the help of imaging modalities, such as MRI and cine PC MRI scanning, which are used for visualizing tonsillar herniation and flow properties of CSF. In some previous studies related to assessment of CM-I, morphometric analysis of the PCF was performed [6,23]. These studies provided significant evidence for hindbrain overcrowding as a result of MRI assessment. Additionally, compression of the CSF spaces due to tonsillar herniation was reported as a common radiological finding. According to those results, PCF and CSF volumes were found to be significantly smaller than those of control subjects. However, no differences were observed in brain volume in CM-I patients. In some other studies, CSF flow characteristics were investigated using the Cine PC MRI [25] and intra-operative ultrasound with color Doppler flow imaging [58]. It has been reported that CM-I patients had higher magnitude peak pressure in CSF [25]. Although the previous studies have provided valuable information, it has been reported that there are still some unclear issues, which require additional studies to redefine the disorder for a couple of reasons [6,11,17,23,59,60]. First, it has been stated that herniation size is not sufficient as the unique diagnosis measure [11,17], because some patients having a herniation size of less than 5 mm show CM-I symptoms [6], whereas some other patients with a herniation that is far more than 5 mm do not show any symptoms [59]. Second, according to previous studies [6,11], CM-I can be misdiagnosed as other disorders such as multiple sclerosis, fibromyalgia, migraine and spinal cord tumors, therefore more discriminative characteristics have to be discovered for the differential diagnosis. Third, the pathophysiology of CM-I has to be understood more clearly in order to perform more successful treatments and make convenient patient management plans [11,23,60]. In order to elucidate potential pathophysiological characteristics in CM-I patients, morphological complexity of cerebellar substructures was investigated in patients and the results were compared with healthy controls' findings in this study. To the best of our knowledge, this is the first study to use the FD analysis on cerebellar WM, GM and CSF tissues to evaluate the morphological complexity properties in CM-I patients. Therefore, in addition to the area calculations of these cerebellar regions, their FD values based on a 2D box counting method were estimated. First, we found that patients have larger cerebellar GM areas compared to controls. In contrast to some studies, which reported reduced volumes of the PCF in CM-I patients [6–8,23], when compared to healthy subjects, we have found an increase in cerebellar GM areas of patients. This might be caused by a calculation difference in our study because we performed the analysis on a single slice in the mid-sagittal region. Besides, the increased GM areas may be related to the accumulation of the tissues in midline cerebellar region due to the lateral

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Fig. 5. Comparison of FD values of cerebellar GM, WM and CSF between patients and controls. (a) Comparison of GM area. (b) Comparison of GM FD. (c) Comparison of WM area. (d) Comparison of WM FD. (e) Comparison of CSF area. (f) Comparison of CSF.

compression of cerebellum. Secondly, the FD values of cerebellar GM were also found to be higher in patients than those in controls. A larger FD value implies a more complex object structure, whereas a decrease in the FD value may imply a degradation in the complexity of the structure, as the FD value is a numerical indicator of morphological complexity [41]. Therefore, larger FD results may indicate that patients have more complex cerebellar GM tissues in

midline sagittal region. This finding is in line with a previous study that reported increased FD values of cerebral GM tissues in MS due to the cellular changes and the presence of the inflammatory component as an indication of higher morphological complexity [61]. Another considerable finding in this study was the significant difference in FD values of WM region between patients with CM-I and healthy controls. Patients exhibited increased FD values in

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Fig. 6. Correlation between the FD and area values of cerebellar GM, WM and CSF. Red circles represent the patient data and green diamonds represent the control data. Blue lines displayed in the plots with R2 values resulted from the linear correlation analysis. Squared correlation coefficients show the strength of relationships (a) Scatter plot of GM FD and GM area values, blue regression line indicates a significant correlation (R2 ¼ 0.624). (b) Scatter plot of WM FD and area values. (c) Scatter plot of CSF FD and area values, blue line indicates a weak correlation (R2 ¼ 0.007). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

cerebellar WM, which may imply a more complex WM tissue structure similarly as in cerebellar GM, compared to those of controls. On the other hand, a reduction in the average area values of cerebellar WM tissues was found in CM-I patients. We believe that this result is consistent with the results of the past studies, which reported an overcrowding and compression of hindbrain tissues due to the reduced PCF volume [6–8,23]. A relatively small PCF in patients may have a negative effect on the development of cerebellar WM. Interestingly, this result may also suggest that CM-I affects the WM tissue differently from it affects the GM, since the mean GM area in patients were found to be significantly higher than that of healthy controls. Another interesting point is

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that while the cerebellar WM areas were found to be smaller, WM FD values were still estimated larger in patients. Therefore, it may be inferred that cerebellar WM tissue is properly developed in CM-I patients, although its size is relatively smaller. As a consequence, it may be suggested in the light of these findings that CM-I anomaly has effects on the cerebellar structures because of a different geometry of the PCF, cranio-cervical junction and distinct CSF flow dynamics and all of these situations may lead to higher FD complexity values in patients. Similar to complexity results in cerebellar GM and WM, the mean FD value of CSF spaces, which are located surrounding the cerebellum, in CM-I patients was also estimated to be significantly higher than that of control subjects. However, a significant difference was not found in mean cerebellar CSF volumes between patients and control subjects although some previous studies [6,23] reported compressed CSF spaces due to the descent of cerebellar tonsils. These results may indicate that CM-I patients have more complex CSF structures in midline sagittal region compared to healthy controls, although CSF areas in both groups were not significantly different. Additionally, these results support the usefulness of FD analysis, since it exposed variations in tissues even on a single MRI slice. In this study, there were some limitations, which prevented us making comprehensive evaluations on CM-I anomaly. First, the number of subjects in both groups was relatively small. Therefore, the analyses used in this study should be repeated using larger populations to verify the usefulness and the significance of our results. This situation also impeded us to calculate the gender difference of FD values in patients. Additionally, the MRI data used in this study were obtained from already existing past records. As a consequence, the symptoms of patients could not be achieved; therefore, we could not perform a correlation analysis between our results and potential CM-I symptoms. In conclusion, the results obtained for cerebellar FD values in CM-I patients support our hypothesis that variations in physical conditions of CM-I such as tonsillar descent and overcrowding of cerebellum may lead to variations in morphological complexities of GM, WM and CSF regions between patients and controls. As a future work, this study can be extended by including entire brain tissues into the analysis based on 3D FD estimation and volumetric calculations. In addition, future studies are needed to confirm these results in larger populations and to compare CM-I anomaly with other disorders such as MS, fibromyalgia, migraine, spinal cord tumors and Chiari Malformation type II, which is a less frequent and clinically more evident type of Chiari anomaly. Further studies are also needed to correlate the results of fractal analysis with the findings of PCF morphometry and CSF flow studies as well as the symptom list of CM-I patients.

Conflict of interest statement None.

Acknowledgements This study was supported by the Fatih University Research and Development Management Office under project number P58011501_B. References [1] H. Chiari, Über Veränderungen des Kleinhirns infolge von Hydrocephalie des Grosshirns, Deutsche medicinische Wochenschrift, Berlin (1891) 1172–1175. [2] C. Cai, W.J. Oakes, Hindbrain herniation syndromes: the Chiari Malformations (I and II), Semin. Pediatr. Neurol. 4 (3) (1997) 179–191.

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