Lacunarity analysis: A general technique for the analysis of spatial patterns

Potential of hybrid adaptive filtering in inflammatory lesion detection from capsule endoscopy images

A new feature extraction technique for the detection of lesions created from mucosal inflammations in Crohn’s disease, based on wireless capsule endoscopy (WCE) images processing is presented here. More specifically, a novel filtering process, namely Hybrid Adaptive Filtering (HAF), was developed for efficient extraction of lesion-related structural/textural characteristics from WCE images, by employing Genetic Algorithms to the Curvelet-based representation of images. Additionally, Differential Lacunarity (DLac) analysis was applied for feature extraction from the HAF-filtered images. The resulted scheme, namely HAF-DLac, incorporates support vector machines for robust lesion recognition performance. For the training and testing of HAF-DLac, an 800-image database was used, acquired from 13 patients who undertook WCE examinations, where the abnormal cases were grouped into mild and severe, according to the severity of the depicted lesion, for a more extensive evaluation of the performance. Experimental results, along with comparison with other related efforts, have shown that the HAF-DLac approach evidently outperforms them in the field of WCE image analysis for automated lesion detection, providing higher classification results, up to 93.8% (accuracy), 95.2% (sensitivity), 92.4% (specificity) and 92.6% (precision). The promising performance of HAF-DLac paves the way for a complete computer-aided diagnosis system that could support physicians’ clinical practice.

Mechanical properties of the tumor stromal microenvironment probed in vitro and ex vivo by in situ-calibrated optical trap-based active microrheology

One of the hallmarks of the malignant transformation of epithelial tissue is the modulation of stromal components of the microenvironment. In particular, aberrant extracellular matrix (ECM) remodeling and stiffening enhances tumor growth and survival and promotes metastasis. Type I collagen is one of the major ECM components. It serves as a scaffold protein in the stroma contributing to the tissue's mechanical properties, imparting tensile strength and rigidity to tissues such as those of the skin, tendons, and lungs. Here we investigate the effects of intrinsic spatial heterogeneities due to fibrillar architecture, pore size and ligand density on the microscale and bulk mechanical properties of the ECM. Type I collagen hydrogels with topologies tuned by polymerization temperature and concentration to mimic physico-chemical properties of a normal tissue and tumor microenvironment were measured by in situ-calibrated Active Microrheology by Optical Trapping revealing significantly different microscale complex shear moduli at Hz-kHz frequencies and two orders of magnitude of strain amplitude that we compared to data from bulk rheology measurements. Access to higher frequencies enabled observation of transitions from elastic to viscous behavior that occur at ~200Hz to 2750Hz, which largely was dependent on tissue architecture well outside the dynamic range of instrument acquisition possible with SAOS bulk rheology. We determined that mouse melanoma tumors and human breast tumors displayed complex moduli ~5-1000 Pa, increasing with frequency and displaying a nonlinear stress-strain response. Thus, we show the feasibility of a mechanical biopsy in efforts to provide a diagnostic tool to aid in the design of therapeutics complementary to those based on standard histopathology.

Detecting Spatiotemporal Dynamic Landscape Patterns Using Remote Sensing and the Lacunarity Index: A Case Study of Haikou City, China

Quantifying the landscape pattern and its dynamics is essential for the monitoring and assessment of the ecological consequences of urbanization. As one of the Special Economic Zones, Haikou is one of the fastest growing regions among all Chinese cities, owing to rapid real estate development. Using a GIS-based land-use dataset from 1986, 1996, and 2000, in combination with a lacunarity index, we attempt to quantify the spatial pattern in the Haikou metropolitan area. After the landscape structure changes over the periods 1986–96 and 1996–2000 are analyzed, a Markov conversion matrix is applied in order to study the sources and destinations of landscape dynamic changes. The lacunarity index is calculated in order to measure the landscape dynamics, with respect to several major land-use types, at a range of spatial scales. The findings indicate that the leapfrog development of real estate and the rapid economic growth of Haikou City have had a great impact on the dynamic landscape patterns. From 1986 to 1996 urban land expanded dramatically and clustered, while cropland was encroached upon and fragmented. From 1996 to 2000, after the government had implemented the strict cropland protection measures, urban expansion and cropland misuse were controlled to a large degree, and a lot of cropland was reclaimed in certain areas. We investigate the dynamic landscape pattern and process, and their implications in policy and economic development.

Unique fractal evaluation and therapeutic implications of mitochondrial morphology in malignant mesothelioma

Malignant mesothelioma (MM), is an intractable disease with limited therapeutic options and grim survival rates. Altered metabolic and mitochondrial functions are hallmarks of MM and most other cancers. Mitochondria exist as a dynamic network, playing a central role in cellular metabolism. MM cell lines display a spectrum of altered mitochondrial morphologies and function compared to control mesothelial cells. Fractal dimension and lacunarity measurements are a sensitive and objective method to quantify mitochondrial morphology and most importantly are a promising predictor of response to mitochondrial inhibition. Control cells have high fractal dimension and low lacunarity and are relatively insensitive to mitochondrial inhibition. MM cells exhibit a spectrum of sensitivities to mitochondrial inhibitors. Low mitochondrial fractal dimension and high lacunarity correlates with increased sensitivity to the mitochondrial inhibitor metformin. Lacunarity also correlates with sensitivity to Mdivi-1, a mitochondrial fission inhibitor. MM and control cells have similar sensitivities to cisplatin, a chemotherapeutic agent used in the treatment of MM. Neither oxidative phosphorylation nor glycolytic activity, correlated with sensitivity to either metformin or mdivi-1. Our results suggest that mitochondrial inhibition may be an effective and selective therapeutic strategy in mesothelioma, and identifies mitochondrial morphology as a possible predictor of response to targeted mitochondrial inhibition.

Strongly enhanced light trapping in a two-dimensional silicon nanowire random fractal array

We report on the unconventional optical properties exhibited by a two-dimensional array of thin Si nanowires arranged in a random fractal geometry and fabricated using an inexpensive, fast and maskless process compatible with Si technology. The structure allows for a high light-trapping efficiency across the entire visible range, attaining total reflectance values as low as 0.1% when the wavelength in the medium matches the length scale of maximum heterogeneity in the system. We show that the random fractal structure of our nanowire array is responsible for a strong in-plane multiple scattering, which is related to the material refractive index fluctuations and leads to a greatly enhanced Raman scattering and a bright photoluminescence. These strong emissions are correlated on all length scales according to the refractive index fluctuations. The relevance and the perspectives of the reported results are discussed as promising for Si-based photovoltaic and photonic applications.

Use of adaptive hybrid filtering process in Crohn's disease lesion detection from real capsule endoscopy videos

The aim of this Letter is to present a new capsule endoscopy (CE) image analysis scheme for the detection of small bowel ulcers that relate to Crohn's disease. More specifically, this scheme is based on: (i) a hybrid adaptive filtering (HAF) process, that utilises genetic algorithms to the curvelet-based representation of images for efficient extraction of the lesion-related morphological characteristics, (ii) differential lacunarity (DL) analysis for texture feature extraction from the HAF-filtered images and (iii) support vector machines for robust classification performance. For the training of the proposed scheme, namely HAF-DL, an 800-image database was used and the evaluation was based on ten 30-second long endoscopic videos. Experimental results, along with comparison with other related efforts, have shown that the HAF-DL approach evidently outperforms the latter in the field of CE image analysis for automated lesion detection, providing higher classification results. The promising performance of HAF-DL paves the way for a complete computer-aided diagnosis system that could support the physicians' clinical practice.

The Quantitative Criteria Based on the Fractal Dimensions, Entropy, and Lacunarity for the Spatial Distribution of Cancer Cell Nuclei Enable Identification of Low or High Aggressive Prostate Carcinomas

Background: Tumor grading, PSA concentration, and stage determine a risk of prostate cancer patients with accuracy of about 70%. An approach based on the fractal geometrical model was proposed to eliminate subjectivity from the evaluation of tumor aggressiveness and to improve the prediction. This study was undertaken to validate classes of equivalence for the spatial distribution of cancer cell nuclei in a larger, independent set of prostate carcinomas.

Methods: The global fractal capacity D₀, information D₁ and correlation D₂ dimension, the local fractal dimension (LFD) and the local connected fractal dimension (LCFD), Shannon entropy H and lacunarity λ were measured using computer algorithms in digitalized images of both the reference set (n = 60) and the test set (n = 208) of prostate carcinomas.

Results: Prostate carcinomas were re-stratified into seven classes of equivalence. The cut-off D₀-values 1.5450, 1.5820, 1.6270, 1.6490, 1.6980, 1.7640 defined the classes from C1 to C7, respectively. The other measures but the D₁ failed to define the same classes of equivalence. The pairs (D₀, LFD), (D₀, H), (D₀, λ), (D₁, LFD), (D₁, H), (D₁, λ) characterized the spatial distribution of cancer cell nuclei in each class. The co-application of those measures enabled the subordination of prostate carcinomas to one out of three clusters associated with different tumor aggressiveness. For D₀ < 1.5820, LFD < 1.3, LCFD > 1.5, H < 0.7, and λ > 0.8, the class C1 or C2 contains low complexity low aggressive carcinomas exclusively. For D₀ > 1.6980, LFD > 1.7644, LCFD > 1.7051, H > 0.9, and λ < 0.7, the class C6 or C7 contains high complexity high aggressive carcinomas.

Conclusions: The cut-off D₀-values defining the classes of equivalence were validated in this study. The cluster analysis suggested that the number of the subjective Gleason grades and the number of the objective classes of equivalence could be decreased from seven to three without a loss of clinically relevant information. Two novel quantitative criteria based on the complexity and the diversity measures enabled the identification of low or high aggressive prostate carcinomas and should be verified in the future multicenter, randomized studies.

Fractal and Lacunarity Analyses: Quantitative Characterization of Hierarchical Surface Topographies

Biomimetic hierarchical surface structures that exhibit features having multiple length scales have been used in many technological and engineering applications. Their surface topographies are most commonly analyzed using scanning electron microscopy (SEM), which only allows for qualitative visual assessments. Here we introduce fractal and lacunarity analyses as a method of characterizing the SEM images of hierarchical surface structures in a quantitative manner. Taking femtosecond laser-irradiated metals as an example, our results illustrate that, while the fractal dimension is a poor descriptor of surface complexity, lacunarity analysis can successfully quantify the spatial texture of an SEM image; this, in turn, provides a convenient means of reporting changes in surface topography with respect to changes in processing parameters. Furthermore, lacunarity plots are shown to be sensitive to the different length scales present within a hierarchical structure due to the reversal of lacunarity trends at specific magnifications where new features become resolvable. Finally, we have established a consistent method of detecting pattern sizes in an image from the oscillation of lacunarity plots. Therefore, we promote the adoption of lacunarity analysis as a powerful tool for quantitative characterization of, but not limited to, multi-scale hierarchical surface topographies.

Enhanced Classification of Interstitial Lung Disease Patterns in HRCT Images Using Differential Lacunarity

The analysis and interpretation of high-resolution computed tomography (HRCT) images of the chest in the presence of interstitial lung disease (ILD) is a time-consuming task which requires experience. In this paper, a computer-aided diagnosis (CAD) scheme is proposed to assist radiologists in the differentiation of lung patterns associated with ILD and healthy lung parenchyma. Regions of interest were described by a set of texture attributes extracted using differential lacunarity (DLac) and classical methods of statistical texture analysis. The proposed strategy to compute DLac allowed a multiscale texture analysis, while maintaining sensitivity to small details. Support Vector Machines were employed to distinguish between lung patterns. Training and model selection were performed over a stratified 10-fold cross-validation (CV). Dimensional reduction was made based on stepwise regression (F-test, p value < 0.01) during CV. An accuracy of 95.8 ± 2.2% in the differentiation of normal lung pattern from ILD patterns and an overall accuracy of 94.5 ± 2.1% in a multiclass scenario revealed the potential of the proposed CAD in clinical practice. Experimental results showed that the performance of the CAD was improved by combining multiscale DLac with classical statistical texture analysis.

Characterization of human retinal vessel arborisation in normal and amblyopic eyes using multifractal analysis

AIM

To characterize the human retinal vessel arborisation in normal and amblyopic eyes using multifractal geometry and lacunarity parameters.

METHODS

Multifractal analysis using a box counting algorithm was carried out for a set of 12 segmented and skeletonized human retinal images, corresponding to both normal (6 images) and amblyopia states of the retina (6 images).

RESULTS

It was found that the microvascular geometry of the human retina network represents geometrical multifractals, characterized through subsets of regions having different scaling properties that are not evident in the fractal analysis. Multifractal analysis of the amblyopia images (segmented and skeletonized versions) show a higher average of the generalized dimensions (Dq ) for q=0, 1, 2 indicating a higher degree of the tree-dimensional complexity associated with the human retinal microvasculature network whereas images of healthy subjects show a lower value of generalized dimensions indicating normal complexity of biostructure. On the other hand, the lacunarity analysis of the amblyopia images (segmented and skeletonized versions) show a lower average of the lacunarity parameter Λ than the corresponding values for normal images (segmented and skeletonized versions).

CONCLUSION

The multifractal and lacunarity analysis may be used as a non-invasive predictive complementary tool to distinguish amblyopic subjects from healthy subjects and hence this technique could be used for an early diagnosis of patients with amblyopia.

Multi-dimensional complete ensemble empirical mode decomposition with adaptive noise applied to laser speckle contrast images

Laser speckle contrast imaging (LSCI) is a noninvasive full-field optical technique which allows analyzing the dynamics of microvascular blood flow. LSCI has attracted attention because it is able to image blood flow in different kinds of tissue with high spatial and temporal resolutions. Additionally, it is simple and necessitates low-cost devices. However, the physiological information that can be extracted directly from the images is not completely determined yet. In this work, a novel multi-dimensional complete ensemble empirical mode decomposition with adaptive noise (MCEEMDAN) is introduced and applied in LSCI data recorded in three physiological conditions (rest, vascular occlusion and post-occlusive reactive hyperaemia). MCEEMDAN relies on the improved complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and our algorithm is specifically designed to analyze multi-dimensional data (such as images). Over the recent multi-dimensional ensemble empirical mode decomposition (MEEMD), MCEEMDAN has the advantage of leading to an exact reconstruction of the original data. The results show that MCEEMDAN leads to intrinsic mode functions and residue that reveal hidden patterns in LSCI data. Moreover, these patterns differ with physiological states. MCEEMDAN appears as a promising way to extract features in LSCI data for an improvement of the image understanding.

Lacunarity analysis of atomic configurations: application to ethanol-water mixtures

Lacunarity analysis is a scale-dependent method quantifying the translational invariance in patterns. In this work it is used to characterize the distribution of several subsets of atoms in molecular systems. Binary clusters and one-component (ethanol or water) hydrogen-bonded clusters of ethanol-water mixtures with 0-100mol% ethanol content were analyzed. Molecular dynamics simulations created the configurations, and all were in good agreement with the respective experimental x-ray diffraction data. Lacunarity analysis revealed that the placement of the one-component clusters at low concentration can be described by a multifractal distribution, especially in the case of ethanol. Most of the cases these clusters are not isolated entities, but form islands in binary clusters.

Lung cancer-a fractal viewpoint

Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed.

Radiochemotherapy-induced changes of tumour vascularity and blood supply estimated by dynamic contrast-enhanced CT and fractal analysis in malignant head and neck tumours

OBJECTIVE

To investigate radiochemotherapy (RChT)-induced changes of transfer coefficient (K(trans)) and relative tumour blood volume (rTBV) estimated by dynamic contrast-enhanced CT (DCE-CT) and fractal analysis in head and neck tumours (HNTs).

METHODS

DCE-CT was performed in 15 patients with inoperable HNTs before RChT, and after 2 and 5 weeks. The dynamics of K(trans) and rTBV as well as lacunarity, slope of log(lacunarity) vs log(box size), and fractal dimension were compared with tumour behaviour during RChT and in the 24-month follow-up.

RESULTS

In 11 patients, an increase of K(trans) and/or rTBV after 20 Gy followed by a decrease of both parameters after 50 Gy was noted. Except for one local recurrence, no tumour residue was found during the follow-up. In three patients with partial tumour reduction during RChT, a decrease of K(trans) accompanied by an increase in rTBV between 20 and 50 Gy was detected. In one patient with continuous elevation of both parameters, tumour progressed after RChT. Pre-treatment difference in intratumoral heterogeneity with its decline under RChT for the responders vs non-responders was observed.

CONCLUSION

Initial growth of K(trans) and/or rTBV followed by further reduction of both parameters along with the decline of the slope of log(lacunarity) vs log(box size) was associated with positive radiochemotherapeutic response. Increase of K(trans) and/or rTBV under RChT indicated a poor outcome.

ADVANCES IN KNOWLEDGE

The modification of K(trans) and rTBV as measured by DCE-CT may be applied for the assessment of tumour sensitivity to chose RChT regimen and, consequently, to reveal clinical impact allowing individualization of RChT strategy in patients with HNT.

Analysis of microvascular perfusion with multi-dimensional complete ensemble empirical mode decomposition with adaptive noise algorithm: Processing of laser speckle contrast images recorded in healthy subjects, at rest and during acetylcholine stimulation

Laser speckle contrast imaging (LSCI) is a full-field imaging modality to monitor microvascular blood flow. It is able to give images with high temporal and spatial resolutions. However, when the skin is studied, the interpretation of the bidimensional data may be difficult. This is why an averaging of the perfusion values in regions of interest is often performed and the result is followed in time, reducing the data to monodimensional time series. In order to avoid such a procedure (that leads to a loss of the spatial resolution), we propose to extract patterns from LSCI data and to compare these patterns for two physiological states in healthy subjects: at rest and at the peak of acetylcholine-induced perfusion peak. For this purpose, the recent multi-dimensional complete ensemble empirical mode decomposition with adaptive noise (MCEEMDAN) algorithm is applied to LSCI data. The results show that the intrinsic mode functions and residue given by MCEEMDAN show different patterns for the two physiological states. The images, as bidimensional data, can therefore be processed to reveal microvascular perfusion patterns, hidden in the images themselves. This work is therefore a feasibility study before analyzing data in patients with microvascular dysfunctions.

Spatial characterization of landscapes through multifractal analysis of DEM

Landscape evolution is driven by abiotic, biotic, and anthropic factors. The interactions among these factors and their influence at different scales create a complex dynamic. Landscapes have been shown to exhibit numerous scaling laws, from Horton's laws to more sophisticated scaling of heights in topography and river network topology. This scaling and multiscaling analysis has the potential to characterise the landscape in terms of the statistical signature of the measure selected. The study zone is a matrix obtained from a digital elevation model (DEM) (map 10 × 10 m, and height 1 m) that corresponds to homogeneous region with respect to soil characteristics and climatology known as "Monte El Pardo" although the water level of a reservoir and the topography play a main role on its organization and evolution. We have investigated whether the multifractal analysis of a DEM shows common features that can be used to reveal the underlying patterns and information associated with the landscape of the DEM mapping and studied the influence of the water level of the reservoir on the applied analysis. The results show that the use of the multifractal approach with mean absolute gradient data is a useful tool for analysing the topography represented by the DEM.

Image-based three-dimensional analysis to characterize the texture of porous scaffolds

The aim of the present study is to characterize the microstructure of composite scaffolds for bone tissue regeneration containing different ratios of chitosan/gelatin blend and bioactive glasses. Starting from realistic 3D models of the scaffolds reconstructed from micro-CT images, the level of heterogeneity of scaffold architecture is evaluated performing a lacunarity analysis. The results demonstrate that the presence of the bioactive glass component affects not only macroscopic features such as porosity, but mainly scaffold microarchitecture giving rise to structural heterogeneity, which could have an impact on the local cell-scaffold interaction and scaffold performances. The adopted approach allows to investigate the scale-dependent pore distribution within the scaffold and the related structural heterogeneity features, providing a comprehensive characterization of the scaffold texture.

Could magnetic resonance provide in vivo histology?

The diagnosis of a suspected tumor lesion faces two basic problems: detection and identification of the specific type of tumor. Radiological techniques are commonly used for the detection and localization of solid tumors. Prerequisite is a high intrinsic or enhanced contrast between normal and neoplastic tissue. Identification of the tumor type is still based on histological analysis. The result depends critically on the sampling sites, which given the inherent heterogeneity of tumors, constitutes a major limitation. Non-invasive in vivo imaging might overcome this limitation providing comprehensive three-dimensional morphological, physiological, and metabolic information as well as the possibility for longitudinal studies. In this context, magnetic resonance based techniques are quite attractive since offer at the same time high spatial resolution, unique soft tissue contrast, good temporal resolution to study dynamic processes and high chemical specificity. The goal of this paper is to review the role of magnetic resonance techniques in characterizing tumor tissue in vivo both at morphological and physiological levels. The first part of this review covers methods, which provide information on specific aspects of tumor phenotypes, considered as indicators of malignancy. These comprise measurements of the inflammatory status, neo-vascular physiology, acidosis, tumor oxygenation, and metabolism together with tissue morphology. Even if the spatial resolution is not sufficient to characterize the tumor phenotype at a cellular level, this multiparametric information might potentially be used for classification of tumors. The second part discusses mathematical tools, which allow characterizing tissue based on the acquired three-dimensional data set. In particular, methods addressing tumor heterogeneity will be highlighted. Finally, we address the potential and limitation of using MRI as a tool to provide in vivo tissue characterization.

3D lacunarity in multifractal analysis of breast tumor lesions in dynamic contrast-enhanced magnetic resonance imaging

Dynamic contrast-enhanced magnetic resonance (DCE-MR) of the breast is especially robust for the diagnosis of cancer in high-risk women due to its high sensitivity. Its specificity may be, however, compromised since several benign masses take up contrast agent as malignant lesions do. In this paper, we propose a novel method of 3D multifractal analysis to characterize the spatial complexity (spatial arrangement of texture) of breast tumors at multiple scales. Self-similar properties are extracted from the estimation of the multifractal scaling exponent for each clinical case, using lacunarity as the multifractal measure. These properties include several descriptors of the multifractal spectra reflecting the morphology and internal spatial structure of the enhanced lesions relatively to normal tissue. The results suggest that the combined multifractal characteristics can be effective to distinguish benign and malignant findings, judged by the performance of the support vector machine classification method evaluated by receiver operating characteristics with an area under the curve of 0.96. In addition, this paper confirms the presence of multifractality in DCE-MR volumes of the breast, whereby multiple degrees of self-similarity prevail at multiple scales. The proposed feature extraction and classification method have the potential to complement the interpretation of the radiologists and supply a computer-aided diagnosis system.

On the fractal geometry of DNA by the binary image analysis

The multifractal analysis of binary images of DNA is studied in order to define a methodological approach to the classification of DNA sequences. This method is based on the computation of some multifractality parameters on a suitable binary image of DNA, which takes into account the nucleotide distribution. The binary image of DNA is obtained by a dot-plot (recurrence plot) of the indicator matrix. The fractal geometry of these images is characterized by fractal dimension (FD), lacunarity, and succolarity. These parameters are compared with some other coefficients such as complexity and Shannon information entropy. It will be shown that the complexity parameters are more or less equivalent to FD, while the parameters of multifractality have different values in the sense that sequences with higher FD might have lower lacunarity and/or succolarity. In particular, the genome of Drosophila melanogaster has been considered by focusing on the chromosome 3r, which shows the highest fractality with a corresponding higher level of complexity. We will single out some results on the nucleotide distribution in 3r with respect to complexity and fractality. In particular, we will show that sequences with higher FD also have a higher frequency distribution of guanine, while low FD is characterized by the higher presence of adenine.

Capsule endoscopy image analysis using texture information from various colour models

Wireless capsule endoscopy (WCE) is a novel imaging technique that is gradually gaining ground as it enables the non-invasive and efficacious visualization of the digestive track, and especially the entire small bowel including its middle part. However, the task of reviewing the vast amount of images produced by a WCE examination is a burden for the physicians. To tackle this major drawback, an innovative scheme for discriminating endoscopic images related to one of the most common intestinal diseases, ulceration, is presented here. This new approach focuses on colour-texture features in order to investigate how the structure information of healthy and abnormal tissue is distributed on RGB, HSV and CIE Lab colour spaces. The WCE images are pre-processed using bidimensional ensemble empirical mode decomposition so as to facilitate differential lacunarity analysis to extract the texture patterns of normal and ulcerous regions. Experimental results demonstrated promising classification performance (mean accuracy>95%), exhibiting a high potential towards automatic WCE image analysis.

Reproducibility of 2D and 3D fractal analysis techniques for the assessment of spatial heterogeneity of regional blood flow in rectal cancer

PURPOSE

To characterize the two-dimensional (2D) and three-dimensional (3D) fractal properties of rectal cancer regional blood flow assessed by using volumetric helical perfusion computed tomography (CT) and to determine its reproducibility.

MATERIALS AND METHODS

Institutional review board approval and informed consent were obtained. Ten prospective patients (eight men, two women; mean age, 72.3 years) with rectal adenocarcinoma underwent two repeated volumetric helical perfusion CT studies (four-dimensional adaptive spiral mode, 11.4-cm z-axis coverage) without intervening treatment within 24 hours, with regional blood flow derived by using deconvolution analysis. Two-dimensional and 3D fractal analyses of the rectal tumor were performed, after segmentation from surrounding structures by using thresholding, to derive fractal dimension and fractal abundance. Reproducibility was quantitatively assessed by using Bland-Altman statistics. Two-dimensional and 3D lacunarity plots were also generated, allowing qualitative assessment of reproducibility. Statistical significance was at 5%.

RESULTS

Mean blood flow was 63.50 mL/min/100 mL ± 8.95 (standard deviation). Good agreement was noted between the repeated studies for fractal dimension; mean difference was -0.024 (95% limits of agreement: -0.212, 0.372) for 2D fractal analysis and -0.024 (95% limits of agreement: -0.307, 0.355) for 3D fractal analysis. Mean difference for fractal abundance was -0.355 (95% limits of agreement: -0.869, 1.579) for 2D fractal analysis and -0.043 (95% limits of agreement: -1.154, 1.239) for 3D fractal analysis. The 95% limits of agreement were narrower for 3D than 2D analysis. Lacunarity plots also visually confirmed close agreement between repeat studies.

CONCLUSION

Regional blood flow in rectal cancer exhibits fractal properties. Good reproducibility was achieved between repeated studies with 2D and 3D fractal analysis.

Cellular modeling of cancer invasion: integration of in silico and in vitro approaches

Cancer invasion is one of the hallmarks of cancer and a prerequisite for cancer metastasis. However, the invasive process is very complex, depending on multiple correlated intrinsic and environmental factors, and thus is difficult to study experimentally in a fully controlled way. Therefore, there is an increased demand for interdisciplinary integrated approaches combining laboratory experiments with multiscale in silico modeling. In this review, we will summarize current computational techniques applicable to model cancer invasion in silico, with a special focus on a class of individual-cell-based models developed in our laboratories. We also discuss their integration with traditional and novel in vitro experimentation, including new invasion assays whose design was inspired by computational modeling.

Water droplet spreading and recoiling upon contact with thick-compact maltodextrin agglomerates

BACKGROUND

The food and pharmaceutical industries handle a number of compounds in the form of agglomerates which must be put into contact with water for rehydration purposes. In this work, liquid-solid interaction between water and maltodextrin thick-compact agglomerates was studied at different constituent particle sizes for two compression forces (75 and 225 MPa).

RESULTS

Rapid droplet spreading was observed which was similar in radius to the expected one for ideal, flat surfaces. Contact angle determinations reported oscillations of this parameter throughout the experiments, being indicative of droplet recoiling on top of the agglomerate. Recoiling was more frequent in samples obtained at 225 MPa for agglomerate formation. Agglomerates obtained at 75 MPa exhibited more penetration of the water. Competition between dissolution of maltodextrin and penetration of the water was, probably, the main mechanism involved in droplet recoiling. Micrographs of the wetting marks were characterized by means of image analysis and the measurements suggested more symmetry of the wetting mark at higher compression force.

CONCLUSION

Differences found in the evaluated parameters for agglomerates were mainly due to compaction force used. No significant effect of particle size in recoiling, penetration of water into the agglomerate, surface texture and symmetry was observed.

Abnormal pattern detection in Wireless Capsule Endoscopy images using nonlinear analysis in RGB color space

In recent years, an innovative method has been developed for the non-invasive observation of the gastrointestinal tract (GT), namely Wireless Capsule Endoscopy (WCE). WCE especially enables a detailed inspection of the entire small bowel and identification of its clinical lesions. However, the foremost disadvantage of this technological breakthrough is the time consuming task of reviewing the vast amount of images produced. To address this, a novel technique for distinguishing pathogenic endoscopic images related to ulcer, the most common disease of GT, is presented here. Towards this direction, the Bidimensional Ensemble Empirical Mode Decomposition was applied to RGB color images of the small bowel acquired by a WCE system in order to extract their Intrinsic Mode Functions (IMFs). The IMFs reveal differences in structure from their finest to their coarsest scale, providing a new analysis domain. Additionally, lacunarity analysis was employed as a method to quantify and extract the texture patterns of the ulcer regions and the normal mucosa, respectively, in order to discriminate the abnormal from the normal images. Experimental results demonstrated promising classification accuracy (>95%), exhibiting a high potential towards WCE-based analysis.

Multifractal and lacunarity analysis of microvascular morphology and remodeling

OBJECTIVE

Classical measures of vessel morphology, including diameter and density, are employed to study microvasculature in endothelial membrane labeled mice. These measurements prove sufficient for some studies; however, they are less well suited for quantifying changes in microcirculatory networks lacking hierarchical structure. We demonstrate that automated multifractal analysis and lacunarity may be used with classical methods to quantify microvascular morphology.

METHODS

Using multifractal analysis and lacunarity, we present an automated extraction tool with a processing pipeline to characterize 2D representations of 3D microvasculature. We apply our analysis on four tissues and the hyaloid vasculature during remodeling.

RESULTS

We found that the vessel networks analyzed have multifractal geometries and that kidney microvasculature has the largest fractal dimension and the lowest lacunarity compared to microvasculature networks in the cortex, skin, and thigh muscle. Also, we found that, during hyaloid remodeling, there were differences in multifractal spectra reflecting the functional transition from a space filling vasculature which nurtures the lens to a less dense vasculature as it regresses, permitting unobstructed vision.

CONCLUSION

Multifractal analysis and lacunarity are valuable additions to classical measures of vascular morphology and will have utility in future studies of normal, developing, and pathological tissues.

Fractal dimension of color fractal images

Fractal dimension is a very useful metric for the analysis of the images with self-similar content, such as textures. For its computation there exist several approaches, the probabilistic algorithm being accepted as the most elegant approach. However, all the existing methods are defined for 1-D signals or binary images, with extension to grayscale images. Our purpose is to propose a color version of the probabilistic algorithm for the computation of the fractal dimension. To validate this new approach, we also propose an extension of the existing algorithm for the generation of probabilistic fractals, in order to obtain color fractal images. Then we show the results of our experiments and conclude this paper.

Lacunarity analysis: a promising method for the automated assessment of melanocytic naevi and melanoma

The early diagnosis of melanoma is critical to achieving reduced mortality and increased survival. Although clinical examination is currently the method of choice for melanocytic lesion assessment, there is a growing interest among clinicians regarding the potential diagnostic utility of computerised image analysis. Recognising that there exist significant shortcomings in currently available algorithms, we are motivated to investigate the utility of lacunarity, a simple statistical measure previously used in geology and other fields for the analysis of fractal and multi-scaled images, in the automated assessment of melanocytic naevi and melanoma. Digitised dermoscopic images of 111 benign melanocytic naevi, 99 dysplastic naevi and 102 melanomas were obtained over the period 2003 to 2008, and subject to lacunarity analysis. We found the lacunarity algorithm could accurately distinguish melanoma from benign melanocytic naevi or non-melanoma without introducing many of the limitations associated with other previously reported diagnostic algorithms. Lacunarity analysis suggests an ordering of irregularity in melanocytic lesions, and we suggest the clinical application of this ordering may have utility in the naked-eye dermoscopic diagnosis of early melanoma.

Drosophila serotonergic varicosities are not distributed in a regular manner

Neurons of the brain form complex tree-like structures that are critical for function. Here we examine the spatial pattern of serotonergic varicosities, the synaptic sites of serotonin release in the central nervous system (CNS). These varicosities are thought to form largely nonjunctional-type connections that partition in a grid-like manner in order to distribute evenly the neuromodulatory neurotransmitter serotonin. We describe the neuropil distribution of serotonergic varicosities in the brain and ventral nerve cord (VNC) of the larval Drosophila CNS. In the brain, we find evidence for avoidance between varicosities at distances lower than 1.75 microm. However, in the VNC, we find a clustered distribution. A similar clustered pattern is found in the Xenopus brain. This pattern produces many varicosities that are clustered together but also includes some varicosities that are very isolated. These isolated varicosities are not found along particular topological sections of the neurite tree or in particular locations in the CNS. In addition, the pattern breaks down when serotonergic branches of adjacent segments invade each other's territory. The pattern is similar to those described by a power law.

Progression of emphysema in a 12-month hyperpolarized 3He-MRI study: lacunarity analysis provided a more sensitive measure than standard ADC analysis

RATIONALE AND OBJECTIVES

Inhaled hyperpolarized (3)He magnetic resonance (MR) imaging has been used to measure alveolar size in patients with emphysema. The aim of this study was to test the hypothesis that (3)He MR images could be used to develop a biomarker of emphysema progression.

MATERIALS AND METHODS

Twelve healthy controls and 18 patients with emphysema (eight current smokers, 10 ex-smokers) were imaged at baseline and 6 and 12 months. An additional nine subjects with alpha-1 antitrypsin deficiency (four with emphysema, six without symptoms) were also imaged at baseline and at 6 months. Each subject was imaged at two lung volumes: functional residual capacity (FRC) and FRC plus 15% of total lung capacity. Means and standard deviations of apparent diffusion coefficients (ADCs) were calculated from coronal images of the entire lung and correlated with pulmonary function test results. The lacunarity hypothesis was tested and calculated from the data using a range of 2 x 2 x 2 to 6 x 6 x 6 voxels, and the average was calculated.

RESULTS

There was no change in the mean ADC at either lung volume in any subject over the 6- or 12-month period. FRC and residual volume increased over the 12 months, suggesting air trapping. The lacunarity of images collected at FRC increased at 6 and 12 months in smokers only (P = .063 and P = .023, respectively).

CONCLUSIONS

The mean ADC calculated from MR images of the lungs with helium was not sufficiently sensitive to detect changes over a 12-month period. However, lacunarity captured more of the spatial information in the images and detected emphysema progress in the smokers.

Assessment of the spatial pattern of colorectal tumour perfusion estimated at perfusion CT using two-dimensional fractal analysis

The aim was to evaluate the feasibility of fractal analysis for assessing the spatial pattern of colorectal tumour perfusion at dynamic contrast-enhanced CT (perfusion CT). Twenty patients with colorectal adenocarcinoma underwent a 65-s perfusion CT study from which a perfusion parametric map was generated using validated commercial software. The tumour was identified by an experienced radiologist, segmented via thresholding and fractal analysis applied using in-house software: fractal dimension, abundance and lacunarity were assessed for the entire outlined tumour and for selected representative areas within the tumour of low and high perfusion. Comparison was made with ten patients with normal colons, processed in a similar manner, using two-way mixed analysis of variance with statistical significance at the 5% level. Fractal values were higher in cancer than normal colon (p < or = 0.001): mean (SD) 1.71 (0.07) versus 1.61 (0.07) for fractal dimension and 7.82 (0.62) and 6.89 (0.47) for fractal abundance. Fractal values were lower in 'high' than 'low' perfusion areas. Lacunarity curves were shifted to the right for cancer compared with normal colon. In conclusion, colorectal cancer mapped by perfusion CT demonstrates fractal properties. Fractal analysis is feasible, potentially providing a quantitative measure of the spatial pattern of tumour perfusion.