3D diffusion model within the collagen apatite porosity: An insight to the nanostructure of human trabecular bone

Current advances in anisotropic structures for enhanced osteogenesis

Bone defects are a challenge to healthcare systems, as the aging population experiences an increase in bone defects. Despite the development of biomaterials for bone fillers and scaffolds, there is still an unmet need for a bone-mimetic material. Cortical bone is highly anisotropic and displays a biological liquid crystalline (LC) arrangement, giving it exceptional mechanical properties and a distinctive microenvironment. However, the biofunctions, cell-tissue interactions, and molecular mechanisms of cortical bone anisotropic structure are not well understood. Incorporating anisotropic structures in bone-facilitated scaffolds has been recognised as essential for better outcomes. Various approaches have been used to create anisotropic micro/nanostructures, but biomimetic bone anisotropic structures are still in the early stages of development. Most scaffolds lack features at the nanoscale, and there is no comprehensive evaluation of molecular mechanisms or characterisation of calcium secretion. This manuscript provides a review of the latest development of anisotropic designs for osteogenesis and discusses current findings on cell-anisotropic structure interactions. It also emphasises the need for further research. Filling knowledge gaps will enable the fabrication of scaffolds for improved and more controllable bone regeneration.

Harnessing Biofabrication Strategies to Re-Surface Osteochondral Defects: Repair, Enhance, and Regenerate

Osteochondral tissue (OC) is a complex and multiphasic system comprising cartilage and subchondral bone. The discrete OC architecture is layered with specific zones characterized by different compositions, morphology, collagen orientation, and chondrocyte phenotypes. To date, the treatment of osteochondral defects (OCD) remains a major clinical challenge due to the low self-regenerative capacity of damaged skeletal tissue, as well as the critical lack of functional tissue substitutes. Current clinical approaches fail to fully regenerate damaged OC recapitulating the zonal structure while granting long-term stability. Thus, the development of new biomimetic treatment strategies for the functional repair of OCDs is urgently needed. Here, we review recent developments in the preclinical investigation of novel functional approaches for the resurfacing of skeletal defects. The most recent studies on preclinical augmentation of OCDs and highlights on novel studies for the in vivo replacement of diseased cartilage are presented.

3D Tortuosity and Diffusion Characterization in the Human Mineralized Collagen Fibril Using a Random Walk Model

Bone tissue is mainly composed at the nanoscale of apatite minerals, collagen molecules and water that form the mineralized collagen fibril (MCF). In this work, we developed a 3D random walk model to investigate the influence of bone nanostructure on water diffusion. We computed 1000 random walk trajectories of water molecules within the MCF geometric model. An important parameter to analyse transport behaviour in porous media is tortuosity, computed as the ratio between the effective path length and the straight-line distance between initial and final points. The diffusion coefficient is determined from the linear fit of the mean squared displacement of water molecules as a function of time. To achieve more insight into the diffusion phenomenon within MCF, we estimated the tortuosity and diffusivity at different quotes in the longitudinal direction of the model. Tortuosity is characterized by increasing values in the longitudinal direction. As expected, the diffusion coefficient decreases as tortuosity increases. Diffusivity outcomes confirm the findings achieved by experimental investigations. The computational model provides insights into the relation between the MCF structure and mass transport behaviour that may contribute to the improvement of bone-mimicking scaffolds.

3D random walk model of diffusion in human Hypo- and Hyper- mineralized collagen fibrils

Bone tissue is composed at the nanoscale of apatite minerals, collagen molecules and water that form the mineralized collagen fibril (MCF). Water has a crucial role in bone biomineralization. We developed a 3D random walk model to investigate the water diffusion process within the MCF for three different scenarios, namely low, intermediate and high mineral volume fraction. The MCF geometric model is obtained after applying 6·10⁶ translational and rotational perturbations to an ordered arrangement of mineral. Subsequently, we compute 300 random trajectories of water molecules within the MCF for each mineral volume fraction. Every trajectory is constituted of up to 500 k positions of the water particle. We determined the diffusion coefficient from the linear fit of the mean squared displacement of water molecules as a function of time. We investigate changes in the diffusivity values in relation to variation of bone mineral content. The analysis performed on the random walk data, for all mineralization conditions, leads to diffusion coefficients in good agreement with the diffusivity outcomes achieved from previous experimental studies. Thus, the 3D geometrical configuration adopted in this numerical study appears suitable for modelling the MCF with different volume fractions, from hypo- to hyper-mineralized conditions. We observed that low mineral content is associated with an increase of the water diffusion, while lower values of diffusivity are determined in hypermineralized conditions. In agreement with experimental data, our results highlight the influence of the structural alterations on the mass transport properties.

Percolation networks inside 3D model of the mineralized collagen fibril

Bone is a hierarchical biological material, characterized at the nanoscale by a recurring structure mainly composed of apatite mineral and collagen, i.e. the mineralized collagen fibril (MCF). Although the architecture of the MCF was extensively investigated by experimental and computational studies, it still represents a topic of debate. In this work, we developed a 3D continuum model of the mineral phase in the framework of percolation theory, that describes the transition from isolated to spanning cluster of connected platelets. Using Monte Carlo technique, we computed overall 120 × 10⁶ iterations and investigated the formation of spanning networks of apatite minerals. We computed the percolation probability for different mineral volume fractions characteristic of human bone tissue. The findings highlight that the percolation threshold occurs at lower volume fractions for spanning clusters in the width direction with respect to the critical mineral volume fractions that characterize the percolation transition in the thickness and length directions. The formation of spanning clusters of minerals represents a condition of instability for the MCF, as it could be the onset of a high susceptibility to fracture. The 3D computational model developed in this study provides new, complementary insights to the experimental investigations concerning human MCF.

Predicting 3D moisture sorption behavior of materials from 1D investigations

Moisture in materials can be a source of future outgassing and exacerbate unwanted changes in physical and chemical properties. Here, we investigate the effect of sample size and shape on the moisture transport phenomena through a combined experimental and modeling approach. Several different materials varying in size and shape were investigated over a wide range of relative humidities (0–90%) and temperatures (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$30{-}70^{\,\circ } \hbox {C}$$\end{document}30-70∘C) using gravimetric type dynamic vapor sorption (DVS). A dynamic triple-mode sorption model, developed previously, was employed to describe the experimental results with good success; the model includes absorption, adsorption, pooling (clustering) of species, and molecular diffusion. Here we show that the full triple-mode sorption model is robust enough to predict the dynamic uptake and outgassing of 3-dimensional (3D) samples using parameters derived from quasi-1D samples. This successful demonstration on three different materials (filled polydimethylsiloxane (PDMS), unfilled PDMS, and ceramic inorganic composite) illustrates that the model is robust at describing the scale-independent physics and chemistry of moisture sorption and diffusion materials. This work demonstrates that while sorption mechanisms manifest in testing of all sample sizes, some of these mechanisms were so subtle that they were overlooked in our initial modeling and assessment, illustrating the importance of multi-scale experiments in the development of robust predictive capabilities. Our study also outlines the challenges and viable solutions for global optimization of a multi-parameter model. The ability to quantify moisture sorption and diffusion, independent of scale, using 1D lab-scale experiments enables prediction of long-term bulk materials behavior in real applications.

Uncovering a high-performance bio-mimetic cellular structure from trabecular bone

The complex cellular structure of trabecular bone possesses lightweight and superior energy absorption capabilities. By mimicking this novel high-performance structure, engineered cellular structures can be advanced into a new generation of protective systems. The goal of this research is to develop an analytical framework for predicting the critical buckling load, Young's modulus and energy absorption of a 3D printed bone-like cellular structure. This is achieved by conducting extensive analytical simulations of the bone-inspired unit cell in parallel to traverse every possible combination of its key design parameters. The analytical framework is validated using experimental data and used to evolve the most optimal cellular structure, with the maximum energy absorption as the key performance criterion. The design charts developed in this work can be used to guide the development of a futuristic engineered cellular structure with superior performance and protective capabilities against extreme loads.

A 3D Model of the Effect of Tortuosity and Constrictivity on the Diffusion in Mineralized Collagen Fibril

Bone tissue is a hierarchically structured material composed at the nanoscale by an organic matrix of collagen type I, apatite mineral and water. We considered an idealized 3D geometrical model of the mineralized collagen fibril in order to analyze the influence of structural factors, i.e. tortuosity, constrictivity, on the water effective diffusivity. The average values of the factors investigated in the diffusivity are computed on 5000 iterations by means of the Montecarlo method. The input parameters of the numerical model are the geometrical dimensions of the apatite mineral, collagen fibrils and their spatial orientation obtained with random extractions from Gaussian probability distribution functions. We analyzed the diffusion phenomenon for concentration gradients parallel to three orthogonal directions (Length, Width and Thickness) and for different scenarios, namely low, intermediate and high apatite volume fraction. For each degree of volume fraction, in the thickness direction, the tortuosity assumes greater values, up to two orders of magnitude, in comparison with the tortuous factors computed in the other directions, highlighting the anisotropy of the nanostructure. Furthermore, it was found that the tortuosity is the dominant parameter which control the effective transport properties within the mineralized collagen fibrils.