Mean-intercept anisotropy analysis of porous media. II. Conceptual shortcomings of the MIL tensor definition and Minkowski tensors as an alternative

Data-Driven Based Characterization of Anisotropic Mechanical Properties for Cancellous Bone From Low-Resolution CT Images

OBJECTIVES

Exploring the anisotropic mechanical behavior of cancellous bone is crucial for in-vivo bone biomechanical analysis. However, it is challenging to characterize anisotropic mechanical behaviors under low-resolution (LR) clinical CT images due to a lack of microstructural information. The data-driven method proposed in this article accurately characterizes the anisotropic mechanical properties of cancellous bone from LR clinical CT images.

METHODS

The trabecular bone cubes of sheep are used to obtain a high-resolution (HR) micro-CT and an LR clinical CT image dataset. First, an auto-encoder model is trained using HR image data. Microstructural features are extracted by the encoder. A fast super-resolution (FSR) model is trained to map LR bone cubes to the features extracted from corresponding HR samples. The pretrained FSR model is used to convert LR clinical CT images to encoded microstructural features. The features are later used to predict target histomorphological parameters, anisotropic elastic tensors, and fabric tensors based on a fully connected neural network.

RESULTS

The data-driven model accurately predicts the elastic tensor and fabric tensor of trabecular bones with LR CT images with 0.6 mm/pixel spatial resolution. It was verified that LR clinical CT images could generate microstructural information using a generative deep-learning model and an up-sampling operation.

SIGNIFICANCE

This study proves that clinical medical images of cancellous bone can be used for analysis of complex mechanical properties using a data-driven method, which is useful for real-time bone defect diagnosis and personalized bone prosthesis design in clinical application.

The local and global geometry of trabecular bone

The organization and shape of the microstructural elements of trabecular bone govern its physical properties, are implicated in bone disease, and serve as blueprints for biomaterial design. To devise fundamental structure-property relationships and design truly bone-mimicking biomaterials, it is essential to characterize trabecular bone structure from the perspective of geometry, the mathematical study of shape. Using micro-CT images from 70 donors at five different sites, we analyze the local and global geometry of human trabecular bone in detail, respectively by quantifying surface curvatures and Minkowski functionals. We find that curvature density maps provide distinct and sensitive shape fingerprints for bone from different sites. Contrary to a common assumption, these curvature maps also show that bone morphology does not approximate a minimal surface but exhibits a much more intricate curvature landscape. At the global (or integral) perspective, our Minkowski analysis illustrates that trabecular bone exhibits other types of anisotropy/ellipticity beyond interfacial orientation, and that anisotropy varies substantially within the trabecular structure. Moreover, we show that the Minkowski functionals unify several traditional morphometric indices. Our geometric approach to trabecular morphometry provides a fundamental language of shape that could be useful for bone failure prediction, understanding geometry-driven tissue growth, and the design of bone-mimicking tissue scaffolds. STATEMENT OF SIGNIFICANCE: The architecture of trabecular bone is key in determining bone properties, and is often a starting point for the design of bone-substitutes. Despite the substantial history of bone morphometry, a fundamental characterization of trabecular bone geometry is still lacking. Therefore, we introduce a robust framework to quantify local and global trabecular bone geometry, which we apply to hundreds of micro-CT scans. Our approach relies on quantifying surface curvatures and Minkowski functionals, which are the most fundamental local and global shape quantifiers. Our results show that these shape metrics are sensitive to differences between bone types and unify traditional metrics within a single mathematical framework. This geometrical framework could also be useful to design bone-mimicking scaffolds and understand geometry-driven tissue growth.

Reconstructing porous structures from FIB-SEM image data: Optimizing sampling scheme and image processing

Nano-porous materials can be imaged spatially by focused ion beam scanning electron microscopy (FIB-SEM). This method generates a stack of SEM images that has to be segmented (or reconstructed) to serve as basis for structural characterization. To this end, we apply two state-of-the-art algorithms. We study the influence of the original image's voxel size on estimates of morphological characteristics and effective permeabilities. Special attention is paid to analyzing anisotropies due to the FIB-SEM typical anisotropic sampling. Quantitative comparison of morphological descriptors and flow properties of reconstructed data is enabled by the use of synthetic FIB-SEM sets for which a ground truth is available. Moreover, in that case, reconstruction parameters can be chosen optimally, too.

Strength of bacterial adhesion on nanostructured surfaces quantified by substrate morphometry

Microbial adhesion and the subsequent formation of resilient biofilms at surfaces are decisively influenced by substrate properties, such as the topography. To date, studies that quantitatively link surface topography and bacterial adhesion are scarce, as both are not straightforward to quantify. To fill this gap, surface morphometry combined with single-cell force spectroscopy was performed on surfaces with irregular topographies on the nano-scale. As surfaces, hydrophobized silicon wafers were used that were etched to exhibit surface structures in the same size range as the bacterial cell wall molecules. The surface structures were characterized by a detailed morphometric analysis based on Minkowski functionals revealing both qualitatively similar features and quantitatively different extensions. We find that as the size of the nanostructures increases, the adhesion forces decrease in a way that can be quantified by the area of the surface that is available for the tethering of cell wall molecules. In addition, we observe a bactericidal effect, which is more pronounced on substrates with taller structures but does not influence adhesion. Our results can be used for a targeted development of 3D-structured materials for/against bio-adhesion. Moreover, the morphometric analysis can serve as a future gold standard for characterizing a broad spectrum of material structures.

Scale-free crystallization of two-dimensional complex plasmas: Domain analysis using Minkowski tensors

Experiments of the recrystallization processes in two-dimensional complex plasmas are analyzed to rigorously test a recently developed scale-free phase transition theory. The "fractal-domain-structure" (FDS) theory is based on the kinetic theory of Frenkel. It assumes the formation of homogeneous domains, separated by defect lines, during crystallization and a fractal relationship between domain area and boundary length. For the defect number fraction and system energy a scale-free power-law relation is predicted. The long-range scaling behavior of the bond-order correlation function shows clearly that the complex plasma phase transitions are not of the Kosterlitz, Thouless, Halperin, Nelson, and Young type. Previous preliminary results obtained by counting the number of dislocations and applying a bond-order metric for structural analysis are reproduced. These findings are supplemented by extending the use of the bond-order metric to measure the defect number fraction and furthermore applying state-of-the-art analysis methods, allowing a systematic testing of the FDS theory with unprecedented scrutiny: A morphological analysis of lattice structure is performed via Minkowski tensor methods. Minkowski tensors form a complete family of additive, motion covariant and continuous morphological measures that are sensitive to nonlinear properties. The FDS theory is rigorously confirmed and predictions of the theory are reproduced extremely well. The predicted scale-free power-law relation between defect fraction number and system energy is verified for one more order of magnitude at high energies compared to the inherently discontinuous bond-order metric. It is found that the fractal relation between crystalline domain area and circumference is independent of the experiment, the particular Minkowski tensor method, and the particular choice of parameters. Thus, the fractal relationship seems to be inherent to two-dimensional phase transitions in complex plasmas. Minkowski tensor analysis turns out to be a powerful tool for investigations of crystallization processes. It is capable of revealing nonlinear local topological properties, however, still provides easily interpretable results founded on a solid mathematical framework.

Characterization of maximally random jammed sphere packings. III. Transport and electromagnetic properties via correlation functions

In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral functions, hole probabilities, and local density fluctuations. From the remarkable structural features of the MRJ packings, especially its disordered hyperuniformity, exceptional physical properties can be expected. Here we employ these structural descriptors to estimate effective transport and electromagnetic properties via rigorous bounds, exact expansions, and accurate analytical approximation formulas. These property formulas include interfacial bounds as well as universal scaling laws for the mean survival time and the fluid permeability. We also estimate the principal relaxation time associated with Brownian motion among perfectly absorbing traps. For the propagation of electromagnetic waves in the long-wavelength limit, we show that a dispersion of dielectric MRJ spheres within a matrix of another dielectric material forms, to a very good approximation, a dissipationless disordered and isotropic two-phase medium for any phase dielectric contrast ratio. We compare the effective properties of the MRJ sphere packings to those of overlapping spheres, equilibrium hard-sphere packings, and lattices of hard spheres. Moreover, we generalize results to micro- and macroscopically anisotropic packings of spheroids with tensorial effective properties. The analytic bounds predict the qualitative trend in the physical properties associated with these structures, which provides guidance to more time-consuming simulations and experiments. They especially provide impetus for experiments to design materials with unique bulk properties resulting from hyperuniformity, including structural-color and color-sensing applications.