A Review of Mathematical Models for the Formation of\ud Vascular Networks

Mainly two mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former consists of the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter consists of the sprouting of new vessels from an existing capillary or post-capillary venule. Similar phenomena are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis.\ud \ud A number of mathematical approaches have analysed these phenomena. This paper reviews the different modelling procedures, with a special emphasis on their ability to reproduce the biological system and to predict measured quantities which describe the overall processes. A comparison between the different methods is also made, highlighting their specific features

Modelling the microstructure and the viscoelastic behaviour of carbon black filled rubber materials from 3D simulations

International audienceVolume fraction and spatial repartition of fillers impact the physical properties of rubber. Extended percolating networks of nano-sized fillers significantly modify the macroscopic mechanical properties of rubbers. Random models that describe the multiscale microstructure of rubber and efficient Fourier-based numerical algorithms are combined to predict the material’s mechanical properties. From TEM image analysis, various types of multiscale models were proposed and validated, accounting for the non-homogeneous distribution of fillers: in the present work, aggregates are located outside of an exclusion polymer simulated by two families of random models. The first model generates the exclusion polymer by a Boolean model of spheres. In the second model, the exclusion polymer is a mosaic model built from a Johnson-Mehl tessellation. Here the exclusion polymer and the polymer containing the filler show a similar morphology, contrary to the Boolean model. Aggregates are then described as the intersection of a Boolean model of spheres and of the complementary of the exclusion polymer. Carbon black particles are simulated by a Cox model of spheres in the aggregates. The models rely on a limited number of parameters fitted from experimental covariance and cumulative granulometry. The influence of the model parameters on percolation properties of the models is studied numerically from 3D simulations. Finally, a novel Fourier-based algorithm is proposed to estimate the viscoelastic properties of linear heterogeneous media, in the harmonic regime. The method is compared to analytical results and to a different, time-discretized FFT scheme. As shown in this work, the proposed numerical method is efficient for computing the viscoelastic response of microstructures containing rubbers and fillers

Modelling the Microstructure and the Viscoelastic Behaviour of Carbon Black Filled Rubber Materials from 3D Simulations

Volume fraction and spatial repartition of fillers impact the physical properties of rubber. Extended percolating networks of nano-sized fillers significantly modify the macroscopic mechanical properties of rubbers. Random models that describe the multiscale microstructure of rubber and efficient Fourier-based numerical algorithms are combined to predict the material’s mechanical properties. From TEM image analysis, various types of multiscale models were proposed and validated, accounting for the non-homogeneous distribution of fillers: in the present work, aggregates are located outside of an exclusion polymer simulated by two families of random models. The first model generates the exclusion polymer by a Boolean model of spheres. In the second model, the exclusion polymer is a mosaic model built from a Johnson-Mehl tessellation. Here the exclusion polymer and the polymer containing the filler show a similar morphology, contrary to the Boolean model. Aggregates are then described as the intersection of a Boolean model of spheres and of the complementary of the exclusion polymer. Carbon black particles are simulated by a Cox model of spheres in the aggregates. The models rely on a limited number of parameters fitted from experimental covariance and cumulative granulometry. The influence of the model parameters on percolation properties of the models is studied numerically from 3D simulations. Finally, a novel Fourier-based algorithm is proposed to estimate the viscoelastic properties of linear heterogeneous media, in the harmonic regime. The method is compared to analytical results and to a different, time-discretized FFT scheme. As shown in this work, the proposed numerical method is efficient for computing the viscoelastic response of microstructures containing rubbers and fillers

The impact of pre- and post-image processing techniques on deep learning frameworks: A comprehensive review for digital pathology image analysis

Recently, deep learning frameworks have rapidly become the main methodology for analyzing medical images. Due to their powerful learning ability and advantages in dealing with complex patterns, deep learning algorithms are ideal for image analysis challenges, particularly in the field of digital pathology. The variety of image analysis tasks in the context of deep learning includes classification (e.g., healthy vs. cancerous tissue), detection (e.g., lymphocytes and mitosis counting), and segmentation (e.g., nuclei and glands segmentation). The majority of recent machine learning methods in digital pathology have a pre- and/or post-processing stage which is integrated with a deep neural network. These stages, based on traditional image processing methods, are employed to make the subsequent classification, detection, or segmentation problem easier to solve. Several studies have shown how the integration of pre- and post-processing methods within a deep learning pipeline can further increase the model's performance when compared to the network by itself. The aim of this review is to provide an overview on the types of methods that are used within deep learning frameworks either to optimally prepare the input (pre-processing) or to improve the results of the network output (post-processing), focusing on digital pathology image analysis. Many of the techniques presented here, especially the post-processing methods, are not limited to digital pathology but can be extended to almost any image analysis field

The impact of pre- and post-image processing techniques on deep learning frameworks: A comprehensive review for digital pathology image analysis.

Recently, deep learning frameworks have rapidly become the main methodology for analyzing medical images. Due to their powerful learning ability and advantages in dealing with complex patterns, deep learning algorithms are ideal for image analysis challenges, particularly in the field of digital pathology. The variety of image analysis tasks in the context of deep learning includes classification (e.g., healthy vs. cancerous tissue), detection (e.g., lymphocytes and mitosis counting), and segmentation (e.g., nuclei and glands segmentation). The majority of recent machine learning methods in digital pathology have a pre- and/or post-processing stage which is integrated with a deep neural network. These stages, based on traditional image processing methods, are employed to make the subsequent classification, detection, or segmentation problem easier to solve. Several studies have shown how the integration of pre- and post-processing methods within a deep learning pipeline can further increase the model's performance when compared to the network by itself. The aim of this review is to provide an overview on the types of methods that are used within deep learning frameworks either to optimally prepare the input (pre-processing) or to improve the results of the network output (post-processing), focusing on digital pathology image analysis. Many of the techniques presented here, especially the post-processing methods, are not limited to digital pathology but can be extended to almost any image analysis field

Two and three dimensional segmentation of multimodal imagery

The role of segmentation in the realms of image understanding/analysis, computer vision, pattern recognition, remote sensing and medical imaging in recent years has been significantly augmented due to accelerated scientific advances made in the acquisition of image data. This low-level analysis protocol is critical to numerous applications, with the primary goal of expediting and improving the effectiveness of subsequent high-level operations by providing a condensed and pertinent representation of image information. In this research, we propose a novel unsupervised segmentation framework for facilitating meaningful segregation of 2-D/3-D image data across multiple modalities (color, remote-sensing and biomedical imaging) into non-overlapping partitions using several spatial-spectral attributes. Initially, our framework exploits the information obtained from detecting edges inherent in the data. To this effect, by using a vector gradient detection technique, pixels without edges are grouped and individually labeled to partition some initial portion of the input image content. Pixels that contain higher gradient densities are included by the dynamic generation of segments as the algorithm progresses to generate an initial region map. Subsequently, texture modeling is performed and the obtained gradient, texture and intensity information along with the aforementioned initial partition map are used to perform a multivariate refinement procedure, to fuse groups with similar characteristics yielding the final output segmentation. Experimental results obtained in comparison to published/state-of the-art segmentation techniques for color as well as multi/hyperspectral imagery, demonstrate the advantages of the proposed method. Furthermore, for the purpose of achieving improved computational efficiency we propose an extension of the aforestated methodology in a multi-resolution framework, demonstrated on color images. Finally, this research also encompasses a 3-D extension of the aforementioned algorithm demonstrated on medical (Magnetic Resonance Imaging / Computed Tomography) volumes

Elastic and electrical behavior of some random multiscale highly-contrasted composites

International audienceThe role of a non-uniform distribution of heterogeneities on the elastic as well as electrical properties of composites is studied numerically and compared with available theoretical results. Specifically, a random model made of embedded Boolean sets of spherical inclusions (see e.g. Jean et al, 2007) serves as the basis for building simple two-scales microstructures of ``granular''-type. Materials with ``infinitely-contrasted'' properties are considered, i.e. inclusions elastically behave as rigid particles or pores, or as perfectly-insulating or highly-conducting heterogeneities. The inclusion spatial dispersion is controlled by the ratio between the two characteristic lengths of the microstructure. The macroscopic behavior as well as the local response of composites are computed using full-field computations, carried out with the "Fast Fourier Transform" method (Moulinec and Suquet, 1994). The entire range of inclusion concentration, and dispersion ratios up to the separation of length scales are investigated. As expected, the non-uniform dispersion of inhomogeneities in multi-scale microstructures leads to increased reinforcing or softening effects compared to the corresponding one-scale model (Willot and Jeulin, 2009); these effects are however still significantly far apart from Hashin-Shtrikman bounds. Similar conclusions are drawn regarding the electrical conductivity