The Complexity and Fractal Geometry of Nuclear Medicine Images

Grizzi, Fabio; Castello, Angelo; Qehajaj, Dorina; Russo, Carlo; Lopci, Egesta

doi:10.1007/s11307-018-1236-5

Cited by 18 publications

(20 citation statements)

References 62 publications

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“…Fractal analysis is applicable in different fields of neuroscience 6,7,14 , including neuroimaging (MRI of brain and computed tomography) [15][16][17][18][19][20][21][22][23][24] , computational studies of neurons 8, [23][24][25][26] , and fractal analysis of vascular network of brain structures [27][28][29] . A skeletonizing technique is one of the digital image pre-processing procedures which reveals the framework of the structure -its digital skeleton 12,30,31 .…”

Section: Introductionmentioning

confidence: 99%

Characterization of white matter branching in human cerebella: quantitative morphological assessment and fractal analysis of skeletonized MR images

Maryenko

Stepanenko

2021

Biomed. Res. Ther.

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Introduction: The aim of the present study was to investigate branching characteristics of the human cerebellar white matter by the means of findings obtained from the quantitative morphological assessment and fractal analysis of the skeletonized MR images of the human cerebellum. Methods: Thirty individuals with no apparent brain pathology (15 males and 15 females, ranging from 18 - 30 years of age) participated in this study. Their normal T2-weighted MR images of the cerebellar vermis (midsagittal plane) were examined. The skeletonizing procedure and subsequent quantitative morphological assessment of the acquired skeletonized MR images were performed. The following parameters were determined: the number of branches, the number of junctions, the amount of end-point voxels, junction voxels and slab voxels, the average and maximum branch lengths, the longest-shortest patch length, and the number of triple and quadruple points. Additionally, the individual branches of the obtained digital skeletons of the cerebellar white matter were examined and the following parameters were assessed: branch length variability, Euclidean distance, and branch length/Euclidean distance ratio. A fractal analysis was performed using the box counting method prior to and after the MR image skeletonizing procedure. The values of the fractal dimensions (FD) of both skeletonized and non-skeletonized MR images were calculated. Results: It was established that the cerebella, which had the maximum values of the FD, possessed a large number of small branches approximately equal in length and which were connected by numerous junctions, forming numerous endpoints. Those cerebella, which had higher values of the average branch length and greater branch length variability, showed lower values of the FD. The key characteristics of the digital skeleton that determined the values of the FD of the cerebellum and its skeletonized MR images were the number of branches and the number of junctions that had the strongest correlational relationships with the FD of the skeletonized MR images. We submitted a proposition to consider the number of branches and amount of junctions as a diagnostic criterion in the determination of normal values of the FD. Conclusions: The obtained data can be used as diagnostic criteria in assessment of the morphofunctional state of the cerebellum using magnetic resonance imaging (MRI) technique.

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Section: Introductionmentioning

confidence: 99%

Characterization of white matter branching in human cerebella: quantitative morphological assessment and fractal analysis of skeletonized MR images

Maryenko

Stepanenko

2021

Biomed. Res. Ther.

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“…Values of fractal dimension, defined on two-dimensional images, vary from 1 to 2 [3,4,16]. For fractal analysis in morphology, neuroscience (including neuroimaging) use different methods of fractal analysis [3,4,7,8,9,19], among which the most commonly used methods are box counting [1,2,10,11,15,23,24] and pixel dilatation [14,17]. The caliper method is also sometimes used [13,20].…”

Section: Introductionmentioning

confidence: 99%

Fractal dimension of external linear contour of human cerebellum (magnetic resonance imaging study)

Maryenko

Stepanenko

2021

Rep. of Morph.

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Fractal analysis is a method of mathematical analysis, which provides quantitative assessment of the spatial configuration complexity of the anatomical structures and may be used as a morphometric method. The purpose of the study was to determine the values of the fractal dimension of the outer linear contour of human cerebellum by studying the magnetic resonance images of the brain using the authors’ modification of the caliper method and compare to the values determined using the box counting method. Brain magnetic resonance images of 30 relatively healthy persons aged 18-30 years (15 men and 15 women) were used in the study. T2-weighted digital magnetic resonance images were studied. The midsagittal MR sections of the cerebellar vermis were investigated. The caliper method in the author’s modification was used for fractal analysis. The average value of the fractal dimension of the linear contour of the cerebellum, determined using the caliper method, was 1.513±0.008 (1.432÷1.600). The average value of the fractal dimension of the linear contour of the cerebellum, determined using the box counting method, was 1.530±0.010 (1.427÷1.647). The average value of the fractal dimension of the cerebellar tissue as a whole, determined using the box counting method, was 1.760±0.006 (1.674÷1.837). The values of the fractal dimension of the outer linear contour of the cerebellum, determined using the caliper method and the box counting method were not statistically significantly different. Therefore, both methods can be used for fractal analysis of the linear contour of the cerebellum. Fractal analysis of the outer linear contour of the cerebellum allows to quantify the complexity of the spatial configuration of the outer surface of the cerebellum, which is difficult to estimate using traditional morphometric methods. The data obtained from this study and the methodology of the caliper method of fractal analysis in the author’s modification can be used for morphometric investigations of the human cerebellum in morphological studies, as well as in assessment of cerebellar MR images for diagnostic purposes.

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“…Fractal dimension (FD) is a new method for measuring the irregularity and complexity of an object. It was initially introduced as a description of self-similar objects [11] and was subsequently utilized in a variety of scientific disciplines [12,13]. FD is more suitable for the analysis of nonlinear and nonstationary physiological data, such as EEG [13].…”

Section: Introductionmentioning

confidence: 99%

Effects of Continuous Positive Airway Pressure on Sleep EEG Characteristics in Patients with Primary Central Sleep Apnea Syndrome

Zhang

Chen

Wang

et al. 2021

Canadian Respiratory Journal

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This study aimed to investigate the effects of continuous positive airway pressure (CPAP) on the electroencephalographic (EEG) characteristics of patients with primary central sleep apnea syndrome (CSAS). Nine patients with primary CSAS were enrolled in this study. The raw sleep EEG data were analyzed based on two main factors: fractal dimension (FD) and zero-crossing rate of detrended FD. Additionally, conventional EEG spectral analysis in the delta, theta, alpha, and beta bands was conducted using a fast Fourier transform. The FD in patients with primary CSAS who underwent CPAP treatment was significantly decreased during nonrapid eye movement (NREM) sleep but increased during rapid eye movement (REM) sleep ( p < 0.05 ). Regarding the EEG spectral analysis, the alpha power increased, while the delta/alpha ratio decreased during REM sleep in patients with CSAS ( p < 0.05 ). In conclusion, CPAP treatment can reduce FD in NREM sleep and increase FD during REM sleep in patients with primary CSAS. FD may be used as a new biomarker of EEG stability and improvement in brain function after CPAP treatment for primary CSAS.

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The Complexity and Fractal Geometry of Nuclear Medicine Images

Cited by 18 publications

References 62 publications

Characterization of white matter branching in human cerebella: quantitative morphological assessment and fractal analysis of skeletonized MR images

Characterization of white matter branching in human cerebella: quantitative morphological assessment and fractal analysis of skeletonized MR images

Fractal dimension of external linear contour of human cerebellum (magnetic resonance imaging study)

Effects of Continuous Positive Airway Pressure on Sleep EEG Characteristics in Patients with Primary Central Sleep Apnea Syndrome

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