Fractals in the Neurosciences: A Translational Geographical Approach

The chapter presents three new fractal indices (fractal fragmentation index, fractal tentacularity index, and fractal anisotropy index) and normalized Kolmogorov complexity with proven applicability in geographic research, developed by the authors, and the possibility of their future use in neuroscience. The research demonstrates the relevance of fractal analysis in different fields and the basic concepts and principles of fractal geometry being sufficient for the development of models relevant to the studied reality. Also, the research highlighted the need to continue interdisciplinary research based on known fractal indicators, as well as the development of new analysis methods with the translational potential between fields.

ComsystanJ: A collection of Fiji/ImageJ2 plugins for nonlinear and complexity analysis in 1D, 2D and 3D

Complex systems such as the global climate, biological organisms, civilisation, technical or social networks exhibit diverse behaviours at various temporal and spatial scales, often characterized by nonlinearity, feedback loops, and emergence. These systems can be characterized by physical quantities such as entropy, information, chaoticity or fractality rather than classical quantities such as time, velocity, energy or temperature. The drawback of these complexity quantities is that their definitions are not always mathematically exact and computational algorithms provide estimates rather than exact values. Typically, evaluations can be cumbersome, necessitating specialized tools. We are therefore introducing ComsystanJ, a novel and user-friendly software suite, providing a comprehensive set of plugins for complex systems analysis, without the need for prior programming knowledge. It is platform independent, end-user friendly and extensible. ComsystanJ combines already known algorithms and newer methods for generalizable analysis of 1D signals, 2D images and 3D volume data including the generation of data sets such as signals and images for testing purposes. It is based on the framework of the open-source image processing software Fiji and ImageJ2. ComsystanJ plugins are macro recordable and are maintained as open-source software. ComsystanJ includes effective surrogate analysis in all dimensions to validate the features calculated by the different algorithms. Future enhancements of the project will include the implementation of parallel computing for image stacks and volumes and the integration of artificial intelligence methods to improve feature recognition and parameter calculation.

The Spatial-Temporal Dimension of Oncological Prevalence and Mortality in Romania

The objective of this study was to identify spatial disparities in the distribution of cancer hotspots within Romania. Additionally, the research aimed to track prevailing trends in cancer prevalence and mortality according to a cancer type. The study covered the timeframe between 2008 and 2017, examining all 3,181 territorial administrative units. The analysis of spatial distribution relied on two key parameters. The first parameter, persistence, measured the duration for which cancer prevalence exceeded the 75th percentile threshold. Cancer prevalence refers to the total number of individuals in a population who have been diagnosed with cancer at a specific time point, including both newly diagnosed cases (occurrence) and existing cases. The second parameter, the time continuity of persistence, calculated the consecutive months during which cancer prevalence consistently surpassed the 75th percentile threshold. Notably, persistence of elevated values was also evident in lowland regions, devoid of any discernible direct connection to environmental conditions. In conclusion, this work bears substantial relevance to regional health policies, by aiding in the formulation of prevention strategies, while also fostering a deeper comprehension of the socioeconomic and environmental factors contributing to cancer.

A new fractal index to classify forest fragmentation and disorder

Context

Forest loss and fragmentation pose extreme threats to biodiversity. Their efficient characterization from remotely sensed data therefore has strong practical implications. Data are often separately analyzed for spatial fragmentation and disorder, but no existing metric simultaneously quantifies both the shape and arrangement of fragments.

Objectives

We present a fractal fragmentation and disorder index (FFDI), which advances a previously developed fractal index by merging it with the Rényi information dimension. The FFDI is designed to work across spatial scales, and to efficiently report both the fragmentation of images and their spatial disorder.

Methods

We validate the FFDI with 12,600 synthetic hierarchically structured random map (HRM) multiscale images, as well as several other categories of fractal and non-fractal test images (4880 images). We then apply the FFDI to satellite imagery of forest cover for 10 distinct regions of the Romanian Carpathian Mountains from 2000–2021.

Results

The FFDI outperformed its two individual components (fractal fragmentation index and Rényi information dimension) in resolving spatial patterns of disorder and fragmentation when tested on HRM classes and other image types. The FFDI thus offers a clear advantage when compared to the individual use of fractal fragmentation index and the Information Dimension, and provided good classification performance in an application to real data.

Conclusions

This work improves on previous characterizations of landscape patterns. With the FFDI, scientists will be able to better monitor and understand forest fragmentation from satellite imagery. The FFDI may also find wider applicability in biology wherever image analysis is used.

Directionally Sensitive Fractal Radiomics Compatible With Irregularly Shaped Magnetic Resonance Tumor Regions of Interest: Association With Osteosarcoma Chemoresistance

BACKGROUND

Computational analysis of routinely acquired MRI has potential to improve the tumor chemoresistance prediction and to provide decision support in precision medicine, which may extend patient survival. Most radiomic analytical methods are compatible only with rectangular regions of interest (ROIs) and irregular tumor shape is therefore an important limitation. Furthermore, the currently used analytical methods are not directionally sensitive.

PURPOSE

To implement a tumor analysis that is directionally sensitive and compatible with irregularly shaped ROIs.

STUDY TYPE

Retrospective.

SUBJECTS

A total of 54 patients with histopathologic diagnosis of primary osteosarcoma on tubular long bones and with prechemotherapy MRI.

FIELD STRENGTH/SEQUENCE

A 1.5 T, T2-weighted-short-tau-inversion-recovery-fast-spin-echo.

ASSESSMENT

A model to explore associations with osteosarcoma chemo-responsiveness included MRI data obtained before OsteoSa MAP neoadjuvant cytotoxic chemotherapy. Osteosarcoma morphology was analyzed in the MRI data by calculation of the nondirectional two-dimensional (2D) and directional and nondirectional one-dimensional (1D) Higuchi dimensions (Dh). MAP chemotherapy response was assessed by histopathological necrosis.

STATISTICAL TESTS

The area under the receiver operating characteristic (ROC) curve (AUC) evaluated the association of the calculated features with the actual chemoresponsiveness, using tumor histopathological necrosis (95%) as the endpoint. Least absolute shrinkage and selection operator (LASSO) machine learning and multivariable regression were used for feature selection. Significance was set at <0.05.

RESULTS

The nondirectional 1D Dh reached an AUC of 0.88 in association with the 95% tumor necrosis, while the directional 1D analysis along 180 radial lines significantly improved this association according to the Hanley/McNeil test, reaching an AUC of 0.95. The model defined by variable selection using LASSO reached an AUC of 0.98. The directional analysis showed an optimal predictive range between 90° and 97° and revealed structural osteosarcoma anisotropy manifested by its directionally dependent textural properties.

DATA CONCLUSION

Directionally sensitive radiomics had superior predictive performance in comparison to the standard nondirectional image analysis algorithms with AUCs reaching 0.95 and full compatibility with irregularly shaped ROIs.

EVIDENCE LEVEL

3 TECHNICAL EFFICACY: Stage 1.

Determination of Heart Rate Changes using Simulated Head Up Tilt Test for Syncope Patient Assessment

Home-based self-training can be beneficial to neurocardiogenic patients, particularly for those who experience a decreased heart rate during the clinical head up tilt test (HUT). Many patients, however, may not be able to attend a clinic and/or attend clinics which lack HUT devices. Individualized heart rate prediction based on a simulated HUT (sHUT) model may address this gap in clinical practice. The proposed sHUT model aims to predict whether home-based self-training is an appropriate beneficial intervention based on the calculated decrease in heart rate from the model. The results obtained with the model are in agreement with previous clinical findings with greater than 80% accuracy in identifying patients who could benefit from home training. The predicted home-based training efficacy of syncope against the control group had a corresponding p-value of p<0.0001. Based on these results, physicians may be able to recommend home training as part of online or telemedicine consultation.Clinical Relevance- The simulated Head Up Tilt model predicts the patient-specific efficacy of tilt-training for patients at home diagnosed with syncope.

High inter-observer reliability in standardized ultrasound measurements of subcutaneous adipose tissue in children aged three to six years

BACKGROUND

A procedure to measure subcutaneous adipose (SAT) using brightness-mode ultrasound has recently been standardized and applied to various groups of adults including underweight, overweight and obese adults. High reliability of this procedure was found in each of the examined groups. The purpose of this study was to determine inter-observer reliability of the standardized brightness-mode ultrasound measurement of uncompressed SAT in three to six-year-old children.

METHODS

Three experienced observers independently captured the ultrasound images at the eight standardized measurement sites in each of the 20 children and evaluated their images using an interactive software that detects the SAT contour and automatically measures multiple thicknesses in each image; the mean of these represents SAT thickness at a given site. The children were aged 4.9 ± 1.0 years; their body mass index ranged from 13.6-17.7 kgm- 2. Sound speed was set to 1450 ms- 1 for SAT.

RESULTS

SAT thickness sums with fibrous structures included (DI) ranged from 25.7-86.4 mm, mean DI was 48.1 ± 15.5 mm. For DI, resulting from 160 measurements by each observer, the intra-class correlation coefficient was 0.998 (95% confidence interval 0.980-0.999), standard error of the estimate was 1.1 mm, and 95% limits of agreement were within ±2.1 mm. The median difference in DI was 0.8 mm, i.e. about 1.9% of mean DI.

CONCLUSIONS

Inter-observer results in children are comparable to previously described high reliability in adults. This method, which provides a technical thickness measurement accuracy of about 0.1 to 0.2 mm, enables monitoring of subcutaneous adipose tissue in children with a similarly high reliability as was obtained in adults previously.

TRIAL REGISTRATION

German Institute of Medical Documentation and Information, German Clinical Trials Register (DRKS) ID: DRKS00010089; Date 24/02/2016.

Relative Body Weight and Standardised Brightness-Mode Ultrasound Measurement of Subcutaneous Fat in Athletes: An International Multicentre Reliability Study, Under the Auspices of the IOC Medical Commission

INTRODUCTION

Fat is a metabolic fuel, but excess body fat is ballast mass, and therefore, many elite athletes reduce body fat to dangerously low levels. Uncompressed subcutaneous adipose tissue (SAT) thickness measured by brightness-mode ultrasound (US) provides an estimate of body fat content.

METHODS

The accuracy for determining tissue borders is about 0.1-0.2 mm and reliability (experienced measurers) was within ± 1.4 mm (95% limit of agreement, LOA). We present here inter- and intra-measurer scores of three experienced US measurers from each of the centres C1 and C2, and of three novice measurers from each of the centres C3-C5. Each of the five centres measured 16 competitive adult athletes of national or international level, except for one centre where the number was 12. The following sports were included: artistic gymnastics, judo, pentathlon, power lifting, rowing, kayak, soccer, tennis, rugby, basketball, field hockey, water polo, volleyball, American football, triathlon, swimming, cycling, long-distance running, mid-distance running, hurdles, cross-country skiing, snowboarding, and ice hockey. SAT contour was detected semi-automatically: typically, 100 thicknesses of SAT at a given site (i.e., in a given image), with and without fibrous structures, were measured.

RESULTS

At SAT thickness sums DI (of eight standardised sites) between 6.0 and 70.0 mm, the LOA of experienced measurers was 1.2 mm, and the intra-class correlation coefficient ICC was 0.998; novice measurers: 3.1 mm and 0.988. Intra-measurer differences were similar. The median DI value of all 39 female participants was 51 mm (11% fibrous structures) compared to 17 mm (18%) in the 37 male participants.

DISCUSSION

DI measurement accuracy and precision enables detection of fat mass changes of approximately 0.2 kg. Such reliability has not been reached with any other method. Although females' median body mass index and mass index were lower than those of males, females' median DI was three times higher, and their percentage of fibrous structures was lower. The standardised US method provides a highly accurate and reliable tool for measuring SAT and thus changes in body fat, but training of measurers is important.

GIRK1 triggers multiple cancer-related pathways in the benign mammary epithelial cell line MCF10A

Excessive expression of subunit 1 of GIRK1 in ER+ breast tumors is associated with reduced survival times and increased lymph node metastasis in patients. To investigate possible tumor-initiating properties, benign MCF10A and malign MCF7 mammary epithelial cells were engineered to overexpress GIRK1 neoplasia associated vital parameters and resting potentials were measured and compared to controls. The presence of GIRK1 resulted in resting potentials negative to the controls. Upon GIRK1 overexpression, several cellular pathways were regulated towards pro-tumorigenic action as revealed by comparison of transcriptomes of MCF10AGIRK1 with the control (MCF10AeGFP). According to transcriptome analysis, cellular migration was promoted while wound healing and extracellular matrix interactions were impaired. Vital parameters in MCF7 cells were affected akin the benign MCF10A lines, but to a lesser extent. Thus, GIRK1 regulated cellular pathways in mammary epithelial cells are likely to contribute to the development and progression of breast cancer.

Sinoatrial Beat to Beat Variability Assessed by Contraction Strength in Addition to the Interbeat Interval

Beat to beat variability of cardiac tissue or isolated cells is frequently investigated by determining time intervals from electrode measurements in order to compute scale dependent or scale independent parameters. In this study, we utilize high-speed video camera recordings to investigate the variability of intervals as well as mechanical contraction strengths and relative contraction strengths with nonlinear analyses. Additionally, the video setup allowed us simultaneous electrode registrations of extracellular potentials. Sinoatrial node tissue under control and acetylcholine treated conditions was used to perform variability analyses by computing sample entropies and Higuchi dimensions. Beat to beat interval variabilities measured by the two recording techniques correlated very well, and therefore, validated the video analyses for this purpose. Acetylcholine treatment induced a reduction of beating rate and contraction strength, but the impact on interval variability was negligible. Nevertheless, the variability analyses of contraction strengths revealed significant differences in sample entropies and Higuchi dimensions between control and acetylcholine treated tissue. Therefore, the proposed high-speed video camera technique might represent a non-invasive tool that allows long-lasting recordings for detecting variations in beating behavior over a large range of scales.

Age is reflected in the Fractal Dimensionality of MRI Diffusion Based Tractography

Fractal analysis is a widely used tool to analyze the geometrical complexity of biological structures. The geometry of natural objects such as plants, clouds, cellular structures, blood vessel, and many others cannot be described sufficiently with Euclidian geometric properties, but can be represented by a parameter called the fractal dimension. Here we show that a specific estimate of fractal dimension, the correlation dimension, is able to describe changes in the structural complexity of the human brain, based on data from magnetic resonance diffusion imaging. White matter nerve fiber bundles, represented by tractograms, were analyzed with regards to geometrical complexity, using fractal geometry. The well-known age-related change of white matter tissue was used to verify changes by means of fractal dimension. Structural changes in the brain were successfully be observed and quantified by fractal dimension and compared with changes in fractional anisotropy.

Standardized Ultrasound Measurement of Subcutaneous Fat Patterning: High Reliability and Accuracy in Groups Ranging from Lean to Obese

A recently standardized ultrasound technique for measuring subcutaneous adipose tissue (SAT) was applied to normal-weight, overweight and obese persons. Eight measurement sites were used: upper abdomen, lower abdomen, erector spinae, distal triceps, brachioradialis, lateral thigh, front thigh and medial calf. Fat compression was avoided. Fat patterning in 38 participants (body mass index: 18.6-40.3 kgm^-2; SAT thickness sums from eight sites: 12-245 mm) was evaluated using a software specifically designed for semi-automatic multiple thickness measurements in SAT (sound speed: 1450 m/s) that also quantifies embedded fibrous structures. With respect to ultrasound intra-observer results, the correlation coefficient ρ = 0.999 (p < 0.01), standard error of the estimate = 1.1 mm and 95% of measurements were within ±2.2 mm. For the normal-weight subgroup, the median measurement deviation was 0.43 mm (1.1% of mean thickness), and for the obese/overweight subgroup it was 0.89 mm (0.5%). The eight sites used here are suggested to represent inter-individual differences in SAT patterning. High measurement accuracy and reliability can be obtained in all groups, from lean to overweight and obese, provided that measurers are trained appropriately.

Tug-of-war lacunarity-A novel approach for estimating lacunarity

Modern instrumentation provides us with massive repositories of digital images that will likely only increase in the future. Therefore, it has become increasingly important to automatize the analysis of digital images, e.g., with methods from pattern recognition. These methods aim to quantify the visual appearance of captured textures with quantitative measures. As such, lacunarity is a useful multi-scale measure of texture's heterogeneity but demands high computational efforts. Here we investigate a novel approach based on the tug-of-war algorithm, which estimates lacunarity in a single pass over the image. We computed lacunarity for theoretical and real world sample images, and found that the investigated approach is able to estimate lacunarity with low uncertainties. We conclude that the proposed method combines low computational efforts with high accuracy, and that its application may have utility in the analysis of high-resolution images.

Subcutaneous fat patterning in athletes: selection of appropriate sites and standardisation of a novel ultrasound measurement technique: ad hoc working group on body composition, health and performance, under the auspices of the IOC Medical Commission

BACKGROUND

Precise and accurate field methods for body composition analyses in athletes are needed urgently.

AIM

Standardisation of a novel ultrasound (US) technique for accurate and reliable measurement of subcutaneous adipose tissue (SAT).

METHODS

Three observers captured US images of uncompressed SAT in 12 athletes and applied a semiautomatic evaluation algorithm for multiple SAT measurements.

RESULTS

Eight new sites are recommended: upper abdomen, lower abdomen, erector spinae, distal triceps, brachioradialis, lateral thigh, front thigh, medial calf. Obtainable accuracy was 0.2 mm (18 MHz probe; speed of sound: 1450 m/s). Reliability of SAT thickness sums (N=36): R(2)=0.998, SEE=0.55 mm, ICC (95% CI) 0.998 (0.994 to 0.999); observer differences from their mean: 95% of the SAT thickness sums were within ± 1 mm (sums of SAT thicknesses ranged from 10 to 50 mm). Embedded fibrous tissues were also measured.

CONCLUSIONS

A minimum of eight sites is suggested to accommodate inter-individual differences in SAT patterning. All sites overlie muscle with a clearly visible fascia, which eases the acquisition of clear images and the marking of these sites takes only a few minutes. This US method reaches the fundamental accuracy and precision limits for SAT measurements given by tissue plasticity and furrowed borders, provided the measurers are trained appropriately.

Learning discriminative classification models for grading anal intraepithelial neoplasia

Grading intraepithelial neoplasia is crucial to derive an accurate estimate of pre-cancerous stages and is currently performed by pathologists assessing histopathological images. Inter- and intra-observer variability can significantly be reduced, when reliable, quantitative image analysis is introduced into diagnostic processes. On a challenging dataset, we evaluated the potential of learning a classifier to grade anal intraepitelial neoplasia. Support vector machines were trained on images represented by fractal and statistical features. We show that pursuing a learning-based grading strategy yields highly reliable results. Compared to existing methods, the proposed method outperformed them by a significant margin.

Automated Texture Analysis and Determination of Fibre Orientation of Heart Tissue: A Morphometric Study

The human heart has a heterogeneous structure, which is characterized by different cell types and their spatial configurations. The physical structure, especially the fibre orientation and the interstitial fibrosis, determines the electrical excitation and in further consequence the contractility in macroscopic as well as in microscopic areas. Modern image processing methods and parameters could be used to describe the image content and image texture. In most cases the description of the texture is not satisfying because the fibre orientation, detected with common algorithms, is biased by elements such as fibrocytes or endothelial nuclei. The goal of this work is to figure out if cardiac tissue can be analysed and classified on a microscopic level by automated image processing methods with a focus on an accurate detection of the fibre orientation. Quantitative parameters for identification of textures of different complexity or pathological attributes inside the heart were determined. The focus was set on the detection of the fibre orientation, which was calculated on the basis of the cardiomyocytes’ nuclei. It turned out that the orientation of these nuclei corresponded with a high precision to the fibre orientation in the image plane. Additionally, these nuclei also indicated very well the inclination of the fibre.

Pyramidal fractal dimension for high resolution images

Fractal analysis (FA) should be able to yield reliable and fast results for high-resolution digital images to be applicable in fields that require immediate outcomes. Triggered by an efficient implementation of FA for binary images, we present three new approaches for fractal dimension (D) estimation of images that utilize image pyramids, namely, the pyramid triangular prism, the pyramid gradient, and the pyramid differences method (PTPM, PGM, PDM). We evaluated the performance of the three new and five standard techniques when applied to images with sizes up to 8192 × 8192 pixels. By using artificial fractal images created by three different generator models as ground truth, we determined the scale ranges with minimum deviations between estimation and theory. All pyramidal methods (PM) resulted in reasonable D values for images of all generator models. Especially, for images with sizes ≥1024×1024 pixels, the PMs are superior to the investigated standard approaches in terms of accuracy and computation time. A measure for the possibility to differentiate images with different intrinsic D values did show not only that the PMs are well suited for all investigated image sizes, and preferable to standard methods especially for larger images, but also that results of standard D estimation techniques are strongly influenced by the image size. Fastest results were obtained with the PDM and PGM, followed by the PTPM. In terms of absolute D values best performing standard methods were magnitudes slower than the PMs. Concluding, the new PMs yield high quality results in short computation times and are therefore eligible methods for fast FA of high-resolution images.

Is a two-dimensional generalization of the Higuchi algorithm really necessary?

Fractal dimensions of data series, particularly time series can be estimated very well by using Higuchi's algorithm. Without phase space constructions, the fractal dimension of a one-dimensional data stream is calculated. Higuchi's method is well accepted and widely applied, because it is very reliable and easy to implement. A generalization of the genuine 1D algorithm to two dimensions would be desirable in order to investigate digital images. In this study, we propose several 2D generalization algorithms and evaluate differences between them. Additionally, a comparison to previously published pseudo 2D generalizations, and to the Fourier and the Blanket method are presented. The algorithms were tested on artificially generated grey value and red-green-blue colour images. It turned out that the proposed 2D generalized Higuchi algorithms are very robust, but differences in between the generalizations as well as differences to the pseudo 2D algorithms are astonishingly small.

IQM: an extensible and portable open source application for image and signal analysis in Java

Image and signal analysis applications are substantial in scientific research. Both open source and commercial packages provide a wide range of functions for image and signal analysis, which are sometimes supported very well by the communities in the corresponding fields. Commercial software packages have the major drawback of being expensive and having undisclosed source code, which hampers extending the functionality if there is no plugin interface or similar option available. However, both variants cannot cover all possible use cases and sometimes custom developments are unavoidable, requiring open source applications. In this paper we describe IQM, a completely free, portable and open source (GNU GPLv3) image and signal analysis application written in pure Java. IQM does not depend on any natively installed libraries and is therefore runnable out-of-the-box. Currently, a continuously growing repertoire of 50 image and 16 signal analysis algorithms is provided. The modular functional architecture based on the three-tier model is described along the most important functionality. Extensibility is achieved using operator plugins, and the development of more complex workflows is provided by a Groovy script interface to the JVM. We demonstrate IQM's image and signal processing capabilities in a proof-of-principle analysis and provide example implementations to illustrate the plugin framework and the scripting interface. IQM integrates with the popular ImageJ image processing software and is aiming at complementing functionality rather than competing with existing open source software. Machine learning can be integrated into more complex algorithms via the WEKA software package as well, enabling the development of transparent and robust methods for image and signal analysis.

Fractal analysis of cervical intraepithelial neoplasia

INTRODUCTION

Cervical intraepithelial neoplasias (CIN) represent precursor lesions of cervical cancer. These neoplastic lesions are traditionally subdivided into three categories CIN 1, CIN 2, and CIN 3, using microscopical criteria. The relation between grades of cervical intraepithelial neoplasia (CIN) and its fractal dimension was investigated to establish a basis for an objective diagnosis using the method proposed.

METHODS

Classical evaluation of the tissue samples was performed by an experienced gynecologic pathologist. Tissue samples were scanned and saved as digital images using Aperio scanner and software. After image segmentation the box counting method as well as multifractal methods were applied to determine the relation between fractal dimension and grades of CIN. A total of 46 images were used to compare the pathologist's neoplasia grades with the predicted groups obtained by fractal methods.

RESULTS

Significant or highly significant differences between all grades of CIN could be found. The confusion matrix, comparing between pathologist's grading and predicted group by fractal methods showed a match of 87.1%. Multifractal spectra were able to differentiate between normal epithelium and low grade as well as high grade neoplasia.

CONCLUSION

Fractal dimension can be considered to be an objective parameter to grade cervical intraepithelial neoplasia.

An efficient finite element approach for modeling fibrotic clefts in the heart

Advanced medical imaging technologies provide a wealth of information on cardiac anatomy and structure at a paracellular resolution, allowing to identify microstructural discontinuities which disrupt the intracellular matrix. Current state-of-the-art computer models built upon such datasets account for increasingly finer anatomical details, however, structural discontinuities at the paracellular level are typically discarded in the model generation process, owing to the significant costs which incur when using high resolutions for explicit representation. In this study, a novel discontinuous finite element (dFE) approach for discretizing the bidomain equations is presented, which accounts for fine-scale structures in a computer model without the need to increase spatial resolution. In the dFE method, this is achieved by imposing infinitely thin lines of electrical insulation along edges of finite elements which approximate the geometry of discontinuities in the intracellular matrix. Simulation results demonstrate that the dFE approach accounts for effects induced by microscopic size scale discontinuities, such as the formation of microscopic virtual electrodes, with vast computational savings as compared to high resolution continuous finite element models. Moreover, the method can be implemented in any standard continuous finite element code with minor effort.

Distribution of decidual natural killer cells and macrophages in the neighbourhood of the trophoblast invasion front: a quantitative evaluation

STUDY QUESTION

Do decidual natural killer (dNK) cells and decidual macrophages (dMph) become enriched in the vicinity of the trophoblast invasion front?

SUMMARY ANSWER

Morphometric image analysis and areal cell density calculations, which excluded observer bias, showed an enrichment of decidual leukocytes in the neighbourhood of the trophoblast invasion front.

WHAT IS KNOWN ALREADY

In previous studies, the number of decidual leukocytes was visually counted in medium- or high power fields. These methods, however, cannot reveal the exact spatial relationship between leukocytes and invasive trophoblast cells, and are therefore prone to subjective errors. Thus, a more objective approach is required.

STUDY DESIGN, SIZE, DURATION

Applying a new method of morphometric image analysis, leukocyte populations were studied in human tissue fragments derived from first trimester placentation sites (n = 7) as well as in co-cultures of first trimester decidual tissue with placental villi of the same pregnancy representing an appropriate in vitro model of trophoblast invasion (n = 15).

PARTICIPANTS/MATERIALS, SETTINGS, METHODS

First trimester decidual tissue was obtained from women undergoing elective terminations of pregnancy at 7-10 weeks of gestational age. Tissue sections were double-stained immunohistochemically for markers of dNK cells or dMph on one hand, and for invasive extravillous trophoblast cells on the other. To analyse the distribution of leukocytes, distinct cell compartments as well as cell neighbourhood areas were defined. Finally, relative areal cell densities were calculated and these data were compared with those of an in vitro model of trophoblast invasion as well as with tissue fragments derived from decidua parietalis without trophoblast cells.

MAIN RESULTS AND THE ROLE OF CHANCE

At first trimester placentation sites, a higher density of dNK cells as well as of dMph was found in close proximity to the invasive trophoblast (P ≤ 0.01), compared with the average areal cell density of decidual leukocytes in the tissue with exclusion of the trophoblast. The highest areal cell density of leukocytes was determined up to a distance of 20 μm from the trophoblast cells, whereas in more distant regions it was even lower than average, indicating a migration of these leukocytes towards the trophoblast invasion front. In the three-dimensional co-culture model, however, we found an enrichment of dMph (P ≤ 0.01) but not of dNK cells (P > 0,05) in the neighbourhood of the invasive trophoblast.

LIMITATIONS, REASONS FOR CAUTION

The morphometric image analysis depends on intense immunohistochemical staining that is free of background and cross-reactivity.

WIDER IMPLICATIONS OF THE FINDINGS

The presented method will be useful not only for the investigation of recurrent miscarriage but also in the fields of tumour immunology and inflammation.

STUDY FUNDING/COMPETING INTEREST(S)

The study was supported by the European Commission (Network of Excellence 'The Control of Embryo Implantation (EMBIC)', FP6-512040, lead researcher: P.S.), and by the Franz Lanyar Foundation of the Medical University of Graz, Austria (Grant #347). None of the authors declared a conflict of interests.

Beat to beat variability of embryonic chick heart cells under septic conditions: application and evaluation of entropy as well as fractal measures

Extracardiac factors of heart rate variability have commonly been investigated using linear and nonlinear methods for a long time. Recently, intracardiac mechanisms on an electrophysiological basis have been found to be also important. This work is focused on the evaluation of complex measures of temporal signals gained with microelectrode measurements of embryonic chick heart aggregates. Septic conditions were mimicked in vitro by lipopolysaccharide (LPS) administration in order to investigate the influence on beat to beat variability. Surrogate data analysis revealed high statistical significances for normalized complexity measures.

Xanthohumol ameliorates atherosclerotic plaque formation, hypercholesterolemia, and hepatic steatosis in ApoE-deficient mice

SCOPE

Xanthohumol (XN), a prenylated antioxidative and anti-inflammatory chalcone from hops, exhibits positive effects on lipid and glucose metabolism. Based on its favorable biological properties, we investigated whether XN attenuates atherosclerosis in western-type diet-fed apolipoprotein-E-deficient (ApoE⁻/⁻) mice.

METHODS AND RESULTS

XN supplementation markedly reduced plasma cholesterol concentrations, decreased atherosclerotic lesion area, and attenuated plasma concentrations of the proinflammatory cytokine monocyte chemoattractant protein 1. Decreased hepatic triglyceride and cholesterol content, activation of AMP-activated protein kinase, phosphorylation and inactivation of acetyl-CoA carboxylase, and reduced expression levels of mature sterol regulatory element-binding protein (SREBP)-2 and SREBP-1c mRNA indicate reduced lipogenesis in the liver of XN-fed ApoE⁻/⁻ mice. Concomitant induction of hepatic mRNA expression of carnitine palmitoyltransferase-1a in ApoE⁻/⁻ mice-administered XN suggests increased fatty acid beta-oxidation. Fecal cholesterol concentrations were also markedly increased in XN-fed ApoE⁻/⁻ mice compared with mice fed western-type diet alone.

CONCLUSION

The atheroprotective effects of XN might be attributed to combined beneficial effects on plasma cholesterol and monocyte chemoattractant protein 1 concentrations and hepatic lipid metabolism via activation of AMP-activated protein kinase.

Electroanatomical characterization of atrial microfibrosis in a histologically detailed computer model

Fibrosis is thought to play an important role in the formation and maintenance of atrial fibrillation (AF). The propensity of fibrosis to increase AF vulnerability depends not only on its amount, its texture plays a crucial role as well. While the detection of fibrotic tissue patches in the atria with extracellular recordings is feasible based on the analysis of electrogram fractionation, as used in clinical practice to identify ablation targets, the classification of fibrotic texture is a more challenging problem. This study seeks to establish a method for the electroanatomical characterization of the fibrotic textures based on the analysis of electrogram fractionation. The proposed method exploits the dependence of fractionation patterns on the incidence direction of wavefronts which differs significantly as a function of texture. A histologically detailed computer model of the right atrial isthmus was developed for testing the method. A stimulation protocol was conceived which generated various incidence directions for any given recording site where electrograms were computed. A classification method is derived then for discriminating three types of fibrosis, no fibrosis (control), diffuse, and patchy fibrosis. Simulation results showed that electrogram fractionation and amplitudes and their dependence upon incidence direction allow a robust discrimination between different classes of fibrosis. Finally, to minimize the technical effort, sensitivity analysis was performed to identify a minimum number of incidence directions required for robust classification.

Quantitating the subtleties of microglial morphology with fractal analysis

It is well established that microglial form and function are inextricably linked. In recent years, the traditional view that microglial form ranges between “ramified resting” and “activated amoeboid” has been emphasized through advancing imaging techniques that point to microglial form being highly dynamic even within the currently accepted morphological categories. Moreover, microglia adopt meaningful intermediate forms between categories, with considerable crossover in function and varying morphologies as they cycle, migrate, wave, phagocytose, and extend and retract fine and gross processes. From a quantitative perspective, it is problematic to measure such variability using traditional methods, but one way of quantitating such detail is through fractal analysis. The techniques of fractal analysis have been used for quantitating microglial morphology, to categorize gross differences but also to differentiate subtle differences (e.g., amongst ramified cells). Multifractal analysis in particular is one technique of fractal analysis that may be useful for identifying intermediate forms. Here we review current trends and methods of fractal analysis, focusing on box counting analysis, including lacunarity and multifractal analysis, as applied to microglial morphology.

Fractal dimension and vessel complexity in patients with cerebral arteriovenous malformations

The fractal dimension (FD) can be used as a measure for morphological complexity in biological systems. The aim of this study was to test the usefulness of this quantitative parameter in the context of cerebral vascular complexity. Fractal analysis was applied on ten patients with cerebral arteriovenous malformations (AVM) and ten healthy controls. Maximum intensity projections from Time-of-Flight MRI scans were analyzed using different measurements of FD, the Box-counting dimension, the Minkowski dimension and generalized dimensions evaluated by means of multifractal analysis. The physiological significance of this parameter was investigated by comparing values of FD first, with the maximum slope of contrast media transit obtained from dynamic contrast-enhanced MRI data and second, with the nidus size obtained from X-ray angiography data. We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity. Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD. The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs.

Lack of acyl-CoA:diacylglycerol acyltransferase 1 reduces intestinal cholesterol absorption and attenuates atherosclerosis in apolipoprotein E knockout mice

Triacylglycerols (TG) are the major storage molecules of metabolic energy and fatty acids in several tissues. The final step in TG biosynthesis is catalyzed by acyl-CoA:diacylglycerol acyltransferase (DGAT) enzymes. Lack of whole body DGAT1 is associated with reduced lipid-induced inflammation. Since one major component of atherosclerosis is chronic inflammation we hypothesized that DGAT1 deficiency might ameliorate atherosclerotic lesion development. We therefore crossbred Apolipoprotein E-deficient (ApoE(-/-)) mice with Dgat1(-/-) mice. ApoE(-/-) and ApoE(-/-)Dgat1(-/-) mice were fed Western-type diet (WTD) for 9weeks and thereafter examined for plaque formation. The mean atherosclerotic lesion area was substantially reduced in ApoE(-/-)Dgat1(-/-) compared with ApoE(-/-) mice in en face and aortic valve section analyses. The reduced lesion size was associated with decreased cholesterol uptake and absorption by the intestine, reduced plasma TG and cholesterol concentrations and increased cholesterol efflux from macrophages. The expression of adhesion molecules was reduced in aortas of ApoE(-/-)Dgat1(-/-) mice, which might be the reason for less migration capacities of monocytes and macrophages and the observed decreased amount of macrophages within the plaques. From our results we conclude that the lack of DGAT1 is atheroprotective, implicating an additional application of DGAT1 inhibitors with regard to maintaining cholesterol homeostasis and attenuating atherosclerosis.

Higuchi dimension of digital images

There exist several methods for calculating the fractal dimension of objects represented as 2D digital images. For example, Box counting, Minkowski dilation or Fourier analysis can be employed. However, there appear to be some limitations. It is not possible to calculate only the fractal dimension of an irregular region of interest in an image or to perform the calculations in a particular direction along a line on an arbitrary angle through the image. The calculations must be made for the whole image. In this paper, a new method to overcome these limitations is proposed. 2D images are appropriately prepared in order to apply 1D signal analyses, originally developed to investigate nonlinear time series. The Higuchi dimension of these 1D signals is calculated using Higuchi's algorithm, and it is shown that both regions of interests and directional dependencies can be evaluated independently of the whole picture. A thorough validation of the proposed technique and a comparison of the new method to the Fourier dimension, a common two dimensional method for digital images, are given. The main result is that Higuchi's algorithm allows a direction dependent as well as direction independent analysis. Actual values for the fractal dimensions are reliable and an effective treatment of regions of interests is possible. Moreover, the proposed method is not restricted to Higuchi's algorithm, as any 1D method of analysis, can be applied.

A 2D-computer model of atrial tissue based on histographs describes the electro-anatomical impact of microstructure on endocardiac potentials and electric near-fields

In experiments with cardiac tissue, local conduction is described by waveform analysis of the derivative of the extracellular potential Φ(e) and by the loop morphology of the near-field strength E (the components of the electric field parallel and very close to the tissue surface). The question arises whether the features of these signals can be used to quantify the degree of fibrosis in the heart. A computer model allows us to study the behavior of electric signals at the endocardium with respect to known configurations of microstructure which can not be detected during the electrophysiological experiments. This work presents a 2D-computer model with sub-cellular resolution of atrial micro-conduction in the rabbit heart. It is based on the monodomain equations and digitized histographs from tissue slices obtained post-experimentum. It could be shown that excitation spread in densely coupled regions produces uniform and anisotropic conduction. In contrast, zones with parallel fibers separated by uncoupling interstitial space or connective tissue may show uniform or complex signals depending on pacing site. These results suggest that the analysis of Φ(e) and E combined with multi-site pacing could be used to characterize the type and the size of fibrosis.

Measurement of cell death by oxidative stress in three-dimensional spheroids from trophoblast and in fragments of decidua tissue

We report a new morphometric method for measurement of the amount of cell death in three-dimensional multicellular spheroids of the trophoblast-like cell line AC1-M59 and of cultured pieces of decidua tissue (decidua spheroids) in response to a cytotoxic agent. The viability of the spheroids was assessed by adding propidium iodide to the culture medium at the end of the toxic treatment. On fluorescence and brightfield images of serial cryosections the areas of propidium iodide fluorescence and the entire corresponding spheroids were measured by applying digital image processing and ratiometrical quantification. As an example, we evaluated the cytotoxic effect of hydrogen peroxide on both types of spheroids. The relative potency of hydrogen peroxide to induce tissue damage was assessed quantitatively for determination of the minimal concentration that leads to an increase in cytotoxicity. The method presented suggests general applicability for in vitro determination of toxicity against tissues.

Automatically generated, anatomically accurate meshes for cardiac electrophysiology problems

Significant advancements in imaging technology and the dramatic increase in computer power over the last few years broke the ground for the construction of anatomically realistic models of the heart at an unprecedented level of detail. To effectively make use of high-resolution imaging datasets for modeling purposes, the imaged objects have to be discretized. This procedure is trivial for structured grids. However, to develop generally applicable heart models, unstructured grids are much preferable. In this study, a novel image-based unstructured mesh generation technique is proposed. It uses the dual mesh of an octree applied directly to segmented 3-D image stacks. The method produces conformal, boundary-fitted, and hexahedra-dominant meshes. The algorithm operates fully automatically with no requirements for interactivity and generates accurate volume-preserving representations of arbitrarily complex geometries with smooth surfaces. The method is very well suited for cardiac electrophysiological simulations. In the myocardium, the algorithm minimizes variations in element size, whereas in the surrounding medium, the element size is grown larger with the distance to the myocardial surfaces to reduce the computational burden. The numerical feasibility of the approach is demonstrated by discretizing and solving the monodomain and bidomain equations on the generated grids for two preparations of high experimental relevance, a left ventricular wedge preparation, and a papillary muscle.

Synthetic LXR agonist attenuates plaque formation in apoE-/- mice without inducing liver steatosis and hypertriglyceridemia

Liver X receptors (LXRs) are important regulators of cholesterol and lipid metabolism. LXR agonists have been shown to limit the cellular cholesterol content by inducing reverse cholesterol transport, increasing bile acid production, and inhibiting intestinal cholesterol absorption. Most of them, however, also increase lipogenesis via sterol regulatory element-binding protein-1c (SREBP1c) and carbohydrate response element-binding protein activation resulting in hypertriglyceridemia and liver steatosis. We report on the antiatherogenic properties of the steroidal liver X receptor agonist N,N-dimethyl-3beta-hydroxy-cholenamide (DMHCA) in apolipoprotein E (apoE)-deficient mice. Long-term administration of DMHCA (11 weeks) significantly reduced lesion formation in male and female apoE-null mice. Notably, DMHCA neither increased hepatic triglyceride (TG) levels in male nor female apoE-deficient mice. ATP binding cassette transporter A1 and G1 and cholesterol 7alpha-hydroxylase mRNA abundances were increased, whereas SREBP1c mRNA expression was unchanged in liver, and even decreased in macrophages and intestine. Short-term treatment revealed even higher changes on mRNA regulation. Our data provide evidence that DMHCA is a strong candidate as therapeutic agent for the treatment or prevention of atherosclerosis, circumventing the negative side effects of other LXR agonists.

Three-dimensional models of individual cardiac histoanatomy: tools and challenges

There is a need for, and utility in, the acquisition of data sets of cardiac histoanatomy, with the vision of reconstructing individual hearts on the basis of noninvasive imaging, such as MRI, enriched by reference to detailed atlases of serial histology obtained from representative samples. These data sets would be useful not only as a repository of knowledge regarding the specifics of cardiac histoanatomy, but could form the basis for generation of individualized high-resolution cardiac structure-function models. The current article presents a step in this general direction: it illustrates how whole-heart noninvasive imaging can be combined with whole-heart histology in an approach to achieve automated construction of histoanatomically detailed models of cardiac 3D structure and function at hitherto unprecedented resolution and accuracy (based on 26.4 x 26.4 x 24.4 microm MRI voxel size, and enriched by histological detail). It provides an overview of the tools used in this quest and outlines challenges posed by the approach in the light of applications that may benefit from the availability of such data and tools.

The influence of edge detection algorithms on the estimation of the fractal dimension of binary digital images

The boundary of a fractal object, represented in a two-dimensional space, is theoretically a line with an infinitely small width. In digital images this boundary or contour is limited to the pixel resolution of the image and the width of the line commonly depends on the edge detection algorithm used. The Minkowski dimension was evaluated by using three different edge detection algorithms (Sobel, Roberts, and Laplace operator). These three operators were investigated because they are very widely used and because their edge detection result is very distinct concerning the line width. Very common fractals (Sierpinski carpet and Koch islands) were investigated as well as the binary images from a cancer invasion assay taken with a confocal laser scanning microscope. The fractal dimension is directly proportional to the width of the contour line and the fact, that in practice very often the investigated objects are fractals only within a limited resolution range is considered too.

Fractal dimension of K1735 mouse melanoma clones and spheroid invasion in vitro

An in vitro tumour-host confrontation method to investigate the invasion behaviour of cancer has been applied to K1735 mouse melanomas. Fluorescently labelled spheroids of cancer cells and host cells were confronted and the temporal course of cancer invasion into the host was investigated using confocal laser scanning microscopy. To improve the quantitative data of this method, the boundary images of the fluorescently labelled confrontation pairs were treated as fractals. The physical and mathematical framework for determination of the fractal capacity dimension is widely used in biology and medicine and has proved to be a very useful tool for describing the cancer invasion process. The fractal capacity dimension determination was carried out by dilation of the binary boundaries of the objects, which were treated as an estimate of the Minkowski-Bouligand dimension. The fractal dimension correlated well with the degree of invasion of the K1735-M2 clone. Control experiments, with host-host confrontations and various K1735 clones with reduced invasiveness, support these results.

Cross-talk reduction in confocal images of dual fluorescence labelled cell spheroids

Dual fluorescence labelling is an advanced method to separate two individual specimens in a biological system using confocal microscopy. An inherent problem of this method is fluorescence channel cross-talk, which causes problems for the exact spatial determination and separation of the specimens. Using a parallel fluorescence detection and an image processing technique, based on an image subtraction method, we have developed a very straight forward method for correcting the dual channel fluorescence images. We successfully applied this method to a 3-dimensional cancer spheroid invasion assay and controlled the cross-talk compensation efficiency by a quality parameter.

Optical multisite monitoring of cell excitation phenomena in isolated cardiomyocytes

An especially designed setup which consists of an inverted fluorescence microscope, an argon ion laser and a photodiode array system permits membrane potential monitoring in isolated guinea-pig ventricular cardiomyocytes, stained with the voltage-sensitive dye di-4-ANEPPS, which responds linearly with relative fluorescence changes (delta F/F) approximately -8% per 100 mV. About a dozen measuring spots covering a single cell were simultaneously monitored with a spatial and temporal resolution of 15 microns and about 20 microseconds, respectively. In general, the rising phases of the action potentials within a single cell were highly synchronized (i.e. all upstroke velocities peaked within about 20 microseconds); however, in one cell (out of 25 examined) significant (P < 0.05) time lags exceeding the signal-dependent time resolution were also found. Experiments, simultaneously performed with our optical system and a widely used patch-clamp setup, revealed a slowed and delayed response of the clamp amplifier depending on the cell access resistance. Optical monitoring during whole-cell voltage-clamping demonstrated the influence of graduated series resistance compensation. When field stimulation was used, our results clearly demonstrated the spatially dependent polarization of the cell membrane during the stimulus, as well as a highly synchronized upstroke development. Slight differences in the maximum upstroke velocities within a single cell were also found and were basically in agreement with mathematical models.

Di-4-ANEPPS causes photodynamic damage to isolated cardiomyocytes

Action potential recordings from isolated guinea pig ventricular cells in the whole-cell recording mode were used to study the toxic and photodynamic properties of the voltage-sensitive fluorescent dye di-4-ANEPPS. Staining of the cardiomyocytes with di-4-ANEPPS (30 or 60 microM; 10 min) did not alter the action potential shape. When the stained cells were illuminated (1W/cm2) severe effects on the action potential were observed. There was a prolongation of the action potential duration, occurrence of early afterdepolarizations, reduction of the membrane resting potential and eventually inexcitability. Addition of the antioxidant catalase (100 IU/ml) to the extracellular solution delayed the onset of these effects, suggesting that reactive-oxygen-intermediates take part in di-4-ANEPPS induced photodynamic damage. Since di-4-ANEPPS is a very important tool for optical membrane potential recordings in heart tissue and single cardiomyocytes catalase might be useful in suppressing photodynamic damage during optical potential recordings.