From homogeneous to fractal normal and tumorous microvascular networks in the brain

We studied normal and tumorous three-dimensional (3D) microvascular networks in primate and rat brain. Tissues were prepared following a new preparation technique intended for high-resolution synchrotron tomography of microvascular networks. The resulting 3D images with a spatial resolution of less than the minimum capillary diameter permit a complete description of the entire vascular network for volumes as large as tens of cubic millimeters. The structural properties of the vascular networks were investigated by several multiscale methods such as fractal and power- spectrum analysis. These investigations gave a new coherent picture of normal and pathological complex vascular structures. They showed that normal cortical vascular networks have scale- invariant fractal properties on a small scale from 1.4 lm up to 40 to 65 lm. Above this threshold, vascular networks can be considered as homogeneous. Tumor vascular networks show similar characteristics, but the validity range of the fractal regime extend to much larger spatial dimensions. These 3D results shed new light on previous two dimensional analyses giving for the first time a direct measurement of vascular modules associated with vessel-tissue surface exchange

Application of Fractal Dimension for Quantifying Noise Texture in Computed Tomography Images

Purpose Evaluation of noise texture information in CT images is important for assessing image quality. Noise texture is often quantified by the noise power spectrum (NPS), which requires numerous image realizations to estimate. This study evaluated fractal dimension for quantifying noise texture as a scalar metric that can potentially be estimated using one image realization. Methods The American College of Radiology CT accreditation phantom (ACR) was scanned on a clinical scanner (Discovery CT750, GE Healthcare) at 120 kV and 25 and 90 mAs. Images were reconstructed using filtered back projection (FBP/ASIR 0%) with varying reconstruction kernels: Soft, Standard, Detail, Chest, Lung, Bone, and Edge. For each kernel, images were also reconstructed using ASIR 50% and ASIR 100% iterative reconstruction (IR) methods. Fractal dimension was estimated using the differential box‐counting algorithm applied to images of the uniform section of ACR phantom. The two‐dimensional Noise Power Spectrum (NPS) and one‐dimensional‐radially averaged NPS were estimated using established techniques. By changing the radiation dose, the effect of noise magnitude on fractal dimension was evaluated. The Spearman correlation between the fractal dimension and the frequency of the NPS peak was calculated. The number of images required to reliably estimate fractal dimension was determined and compared to the number of images required to estimate the NPS‐peak frequency. The effect of Region of Interest (ROI) size on fractal dimension estimation was evaluated. Feasibility of estimating fractal dimension in an anthropomorphic phantom and clinical image was also investigated, with the resulting fractal dimension compared to that estimated within the uniform section of the ACR phantom. Results Fractal dimension was strongly correlated with the frequency of the peak of the radially averaged NPS curve, having a Spearman rank‐order coefficient of 0.98 (P‐value \u3c 0.01) for ASIR 0%. The mean fractal dimension at ASIR 0% was 2.49 (Soft), 2.51 (Standard), 2.52 (Detail), 2.57 (Chest), 2.61 (Lung), 2.66 (Bone), and 2.7 (Edge). A reduction in fractal dimension was observed with increasing ASIR levels for all investigated reconstruction kernels. Fractal dimension was found to be independent of noise magnitude. Fractal dimension was successfully estimated from four ROIs of size 64 × 64 pixels or one ROI of 128 × 128 pixels. Fractal dimension was found to be sensitive to non‐noise structures in the image, such as ring artifacts and anatomical structure. Fractal dimension estimated within a uniform region of an anthropomorphic phantom and clinical head image matched that estimated within the ACR phantom for filtered back projection reconstruction. Conclusions Fractal dimension correlated with the NPS‐peak frequency and was independent of noise magnitude, suggesting that the scalar metric of fractal dimension can be used to quantify the change in noise texture across reconstruction approaches. Results demonstrated that fractal dimension can be estimated from four, 64 × 64‐pixel ROIs or one 128 × 128 ROI within a head CT image, which may make it amenable for quantifying noise texture within clinical images

Spatial complexity of the cerebral cortex pial surface: quantitative assessment by two-dimensional fractal analysis of MRI brain scans

The objective of the current study was to evaluate the spatial complexity of the cerebral pial surface through two-dimensional fractal analysis of the external linear contour of cerebral hemispheres and to investigate the correlation between the parameters determined using Euclidean and fractal geometries. Magnetic resonance brain images were obtained from 100 individuals (44 males and 56 females, aged 18–86 years). Five magnetic resonance images were selected from the MRI dataset of each brain, comprising four tomographic sections in the coronal plane and one section in the axial plane. Fractal dimension values of the linear contour of the pial surface of cerebral hemispheres were measured using the two-dimensional box counting method. Morphometric parameters based on Euclidean geometry were also determined (perimeter, area and their derivative values). In this study, the obtained fractal dimension values were shown to be sensitive to the tortuosity of the linear contour of cerebral hemispheres, which depends on the number of gyri and sulci and the complexity of their shape. Therefore, the fractal dimension can be considered as an objective quantitative parameter characterizing the spatial complexity of the pial surface of cerebral hemispheres. The present study revealed that the Euclidean geometry-based morphometric parameters most strongly associated with the fractal dimension of the cerebral linear contour were the perimeter and the parameters calculated from perimeter values, including the perimeter-to-area ratio, shape factor, and two-dimensional gyrification index. Fractal dimension values did not exhibit strong correlations with age. The data obtained in this study can be utilized for anatomical and anthropological studies. Furthermore, they hold practical applications in clinical contexts for diagnostic purposes, such as the diagnosis of congenital cerebral malformations and postnatal cerebral maldevelopment

Structural brain complexity and cognitive decline in late life : A longitudinal study in the Aberdeen 1936 Birth Cohort

Copyright © 2014 Elsevier Inc. All rights reserved.Peer reviewedPostprin

Bessel beam illumination reduces random and systematic errors in quantitative functional studies using light-sheet microscopy

Light-sheet microscopy (LSM), in combination with intrinsically transparent zebrafish larvae, is a choice method to observe brain function with high frame rates at cellular resolution. Inherently to LSM, however, residual opaque objects cause stripe artifacts, which obscure features of interest and, during functional imaging, modulate fluorescence variations related to neuronal activity. Here, we report how Bessel beams reduce streaking artifacts and produce high-fidelity quantitative data demonstrating a fivefold increase in sensitivity to calcium transients and a 20 fold increase in accuracy in the detection of activity correlations in functional imaging. Furthermore, using principal component analysis, we show that measurements obtained with Bessel beams are clean enough to reveal in one-shot experiments correlations that can not be averaged over trials after stimuli as is the case when studying spontaneous activity. Our results not only demonstrate the contamination of data by systematic and random errors through conventional Gaussian illumination and but,furthermore, quantify the increase in fidelity of such data when using Bessel beams

Fractal and multifractal analysis of PET-CT images of metastatic melanoma before and after treatment with ipilimumab

PET/CT with F-18-Fluorodeoxyglucose (FDG) images of patients suffering from metastatic melanoma have been analysed using fractal and multifractal analysis to assess the impact of monoclonal antibody ipilimumab treatment with respect to therapy outcome. Our analysis shows that the fractal dimensions which describe the tracer dispersion in the body decrease consistently with the deterioration of the patient therapeutic outcome condition. In 20 out-of 24 cases the fractal analysis results match those of the medical records, while 7 cases are considered as special cases because the patients have non-tumour related medical conditions or side effects which affect the results. The decrease in the fractal dimensions with the deterioration of the patient conditions (in terms of disease progression) are attributed to the hierarchical localisation of the tracer which accumulates in the affected lesions and does not spread homogeneously throughout the body. Fractality emerges as a result of the migration patterns which the malignant cells follow for propagating within the body (circulatory system, lymphatic system). Analysis of the multifractal spectrum complements and supports the results of the fractal analysis. In the kinetic Monte Carlo modelling of the metastatic process a small number of malignant cells diffuse throughout a fractal medium representing the blood circulatory network. Along their way the malignant cells engender random metastases (colonies) with a small probability and, as a result, fractal spatial distributions of the metastases are formed similar to the ones observed in the PET/CT images. In conclusion, we propose that fractal and multifractal analysis has potential application in the quantification of the evaluation of PET/CT images to monitor the disease evolution as well as the response to different medical treatments.Comment: 38 pages, 9 figure

Representation Learning by Learning to Count

We introduce a novel method for representation learning that uses an artificial supervision signal based on counting visual primitives. This supervision signal is obtained from an equivariance relation, which does not require any manual annotation. We relate transformations of images to transformations of the representations. More specifically, we look for the representation that satisfies such relation rather than the transformations that match a given representation. In this paper, we use two image transformations in the context of counting: scaling and tiling. The first transformation exploits the fact that the number of visual primitives should be invariant to scale. The second transformation allows us to equate the total number of visual primitives in each tile to that in the whole image. These two transformations are combined in one constraint and used to train a neural network with a contrastive loss. The proposed task produces representations that perform on par or exceed the state of the art in transfer learning benchmarks.Comment: ICCV 2017(oral