Prediction of permeability of regular scaffolds for skeletal tissue engineering: a combined computational and experimental study

Continuum Modeling and Simulation in Bone Tissue Engineering

Bone tissue engineering is currently a mature methodology from a research perspective. Moreover, modeling and simulation of involved processes and phenomena in BTE have been proved in a number of papers to be an excellent assessment tool in the stages of design and proof of concept through in-vivo or in-vitro experimentation. In this paper, a review of the most relevant contributions in modeling and simulation, in silico, in BTE applications is conducted. The most popular in silico simulations in BTE are classified into: (i) Mechanics modeling and scaffold design, (ii) transport and flow modeling, and (iii) modeling of physical phenomena. The paper is restricted to the review of the numerical implementation and simulation of continuum theories applied to different processes in BTE, such that molecular dynamics or discrete approaches are out of the scope of the paper. Two main conclusions are drawn at the end of the paper: First, the great potential and advantages that in silico simulation offers in BTE, and second, the need for interdisciplinary collaboration to further validate numerical models developed in BTE.

Lattice and continuum modelling of a bioactive porous tissue scaffold

A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. We derive a model on a square grid lattice to demonstrate the importance of explicitly modelling the network structure of the porous scaffold and compare results from this model with those from a modified continuum model from the literature. We capture two-way coupling between cell growth and fluid flow by allowing cells to block pores, and by allowing the shear stress of the fluid to affect cell growth and death. We explore a range of parameters for both models and demonstrate quantitative and qualitative differences between predictions from each of these approaches, including spatial pattern formation and local oscillations in cell density present only in the lattice model. These differences suggest that for some parameter regimes, corresponding to specific cell types and scaffold geometries, the lattice model gives qualitatively different model predictions than typical continuum models. Our results inform model selection for bioactive porous tissue scaffolds, aiding in the development of successful tissue engineering experiments and eventually clinically successful technologies.

A computational fluid dynamics approach to determine white matter permeability

Glioblastomas represent a challenging problem with an extremely poor survival rate. Since these tumour cells have a highly invasive character, an effective surgical resection as well as chemotherapy and radiotherapy is very difficult. Convection-enhanced delivery (CED), a technique that consists in the injection of a therapeutic agent directly into the parenchyma, has shown encouraging results. Its efficacy depends on the ability to predict, in the pre-operative phase, the distribution of the drug inside the tumour. This paper proposes a method to compute a fundamental parameter for CED modelling outcomes, the hydraulic permeability, in three brain structures. Therefore, a bidimensional brain-like structure was built out of the main geometrical features of the white matter: axon diameter distribution extrapolated from electron microscopy images, extracellular space (ECS) volume fraction and ECS width. The axons were randomly allocated inside a defined border, and the ECS volume fraction as well as the ECS width maintained in a physiological range. To achieve this result, an outward packing method coupled with a disc shrinking technique was implemented. The fluid flow through the axons was computed by solving Navier-Stokes equations within the computational fluid dynamics solver ANSYS. From the fluid and pressure fields, an homogenisation technique allowed establishing the optimal representative volume element (RVE) size. The hydraulic permeability computed on the RVE was found in good agreement with experimental data from the literature.

A Perfusion Bioreactor System for Cell Seeding and Oxygen-Controlled Cultivation of Three-Dimensional Cell Cultures

Bioreactor systems facilitate three-dimensional (3D) cell culture by coping with limitations of static cultivation techniques. To allow for the investigation of proper cultivation conditions and the reproducible generation of tissue-engineered grafts, a bioreactor system, which comprises the control of crucial cultivation parameters in independent-operating parallel bioreactors, is beneficial. Furthermore, the use of a bioreactor as an automated cell seeding tool enables even cell distributions on stable scaffolds. In this study, we developed a perfusion microbioreactor system, which enables the cultivation of 3D cell cultures in an oxygen-controlled environment in up to four independent-operating bioreactors. Therefore, perfusion microbioreactors were designed with the help of computer-aided design, and manufactured using the 3D printing technologies stereolithography and fused deposition modeling. A uniform flow distribution in the microbioreactor was shown using a computational fluid dynamics model. For oxygen measurements, microsensors were integrated in the bioreactors to measure the oxygen concentration (OC) in the geometric center of the 3D cell cultures. To control the OC in each bioreactor independently, an automated feedback loop was developed, which adjusts the perfusion velocity according to the oxygen sensor signal. Furthermore, an automated cell seeding protocol was implemented to facilitate the even distribution of cells within a stable scaffold in a reproducible way. As proof of concept, the human mesenchymal stem cell line SCP-1 was seeded on bovine cancellous bone matrix of 1 cm³ and cultivated in the developed microbioreactor system at different oxygen levels. The oxygen control was capable to maintain preset oxygen levels ±0.5% over a cultivation period of several days. Using the automated cell seeding procedure resulted in evenly distributed cells within a stable scaffold. In summary, the developed microbioreactor system enables the cultivation of 3D cell cultures in an automated and thus reproducible way by providing up to four independently operating, oxygen-controlled bioreactors. In combination with the automated cell seeding procedure, the bioreactor system opens up new possibilities to conduct more reproducible experiments to investigate optimal cultivation parameters and to generate tissue-engineering grafts in an oxygen-controlled environment.

Effect of scaffold architecture on cell seeding efficiency: A discrete phase model CFD analysis

Within perfusion cell culture systems, scaffold architecture is able to control important biological parameters such as permeability and fluid flow-induced shear stress. As well, one of the main factors affecting the final fate of this process as well as optimal cell differentiation and proliferation in these systems is initial adhesion of cells to scaffolds. In this study, the effect of scaffold architecture on the adhesion of the cells was computationally investigated. For this purpose, four scaffold models including double-diamond, gyroid, FR-D, and Schwarz-primitive were designed using triply periodic minimal surface (TPMS) geometry with a constant porosity of 80%. As well, the inlet velocity of zero to simulate static cell culture and three different inlet velocities for modeling the dynamic cell culture conditions were also selected. The results showed that cell culture efficiency of scaffolds could be changed up to seven times from architecture to architecture under the same conditions. The efficiency of cell culture in scaffolds with tortuous architecture was also reported higher than those with relatively straight microchannels. In terms of culture methods, unlike dynamic cell culture model in which almost a homogeneous cell distribution was observed in static cell culture simulation, more cells adhered, but they had agglomerated in the scaffold entrance regions and had failed to reach all regions. The results of this study shed more light on the selection and design of scaffold architecture for optimal cell culture in tissue engineering.

Computational Design and Optimization of Nerve Guidance Conduits for Improved Mechanical Properties and Permeability

Nerve guidance conduits (NGCs) are tubular tissue engineering scaffolds used for nerve regeneration. The poor mechanical properties and porosity have always compromised their performances for guiding and supporting axonal growth. Therefore, in order to improve the properties of NGCs, the computational design approach was adopted to investigate the effects of different NGC structural features on their various properties, and finally design an ideal NGC with mechanical properties matching human nerves and high porosity and permeability. Three common NGC designs, namely hollow luminal, multichannel, and microgrooved, were chosen in this study. Simulations were conducted to study the mechanical properties and permeability. The results show that pore size is the most influential structural feature for NGC tensile modulus. Multichannel NGCs have higher mechanical strength but lower permeability compared to other designs. Square pores lead to higher permeability but lower mechanical strength than circular pores. The study finally selected an optimized hollow luminal NGC with a porosity of 71% and tensile modulus of 8 MPa to achieve multiple design requirements. The use of computational design and optimization was shown to be promising in future NGC design and nerve tissue engineering research.

Mechanical performance of additively manufactured meta-biomaterials

Additive manufacturing (AM) (=3D printing) and rational design techniques have enabled development of meta-biomaterials with unprecedented combinations of mechanical, mass transport, and biological properties. Such meta-biomaterials are usually topologically ordered and are designed by repeating a number of regular unit cells in different directions to create a lattice structure. Establishing accurate topology-property relationships is of critical importance for these materials. In this paper, we specifically focus on AM metallic meta-biomaterials aimed for application as bone substitutes and orthopaedic implants and review the currently available evidence regarding their mechanical performance under quasi-static and cyclic loading conditions. The topology-property relationships are reviewed for regular beam-based lattice structures, sheet-based lattice structures including those based on triply periodic minimal surface, and graded designs. The predictive models used for establishing the topology-property relationships including analytical and computational models are covered as well. Moreover, we present an overview of the effects of the AM processes, material type, tissue regeneration, biodegradation, surface bio-functionalization, post-manufacturing (heat) treatments, and loading profiles on the quasi-static mechanical properties and fatigue behavior of AM meta-biomaterials. AM meta-biomaterials exhibiting unusual mechanical properties such as negative Poisson's ratios (auxetic meta-biomaterials), shape memory behavior, and superelasitcity as well as the potential applications of such unusual behaviors (e.g. deployable implants) are presented too. The paper concludes with some suggestions for future research. STATEMENT OF SIGNIFICANCE: Additive manufacturing enables fabrication of meta-biomaterials with rare combinations of topological, mechanical, and mass transport properties. Given that the micro-scale topological design determines the macro-scale properties of meta-biomaterials, establishing topology-property relationships is the central research question when rationally designing meta-biomaterials. The interest in understanding the relationship between the topological design and material type on the one hand and the mechanical properties and fatigue behavior of meta-biomaterials on the other hand is currently booming. This paper presents and critically evaluates the most important trends and findings in this area with a special focus on the metallic biomaterials used for skeletal applications to enable researchers better understand the current state-of-the-art and to guide the design of future research projects.

Mechanical behaviours and mass transport properties of bone-mimicking scaffolds consisted of gyroid structures manufactured using selective laser melting

Bone scaffolds created in porous structures manufactured using selective laser melting (SLM) are widely used in tissue engineering, since the elastic moduli of the scaffolds are easily adjusted according to the moduli of the tissues, and the large surfaces the scaffolds provide are beneficial to cell growth. SLM-built gyroid structures composed of 316L stainless steel have demonstrated superior properties such as good corrosion resistance, strong biocompatibility, self-supported performance, and excellent mechanical properties. In this study, gyroid structures of different volume fraction were modelled and manufactured using SLM; the mechanical properties of the structures were then investigated under quasi-static compression loads. The elastic moduli and yield stresses of the structures were calculated from stress-strain diagrams, which were developed by conducting quasi-static compression tests. In order to estimate the discrepancies between the designed and as-produced gyroid structures, optical microscopy and micro-CT scanner were used to observe the structures' micromorphology. Since good fluidness is conducive to the transport of nutrients, computational fluid dynamics (CFD) values were used to investigate the pressure and flow velocity of the channel of the three kinds of gyroid structures. The results show that the sizes of the as-produced structures were larger than their computer aided design (CAD) sizes, but the manufacturing errors are within a relatively stable range. The elastic moduli and yield stresses of the structures improved as their volume fractions increased. Gyroid structure can match the mechanical properties of human bone by changing the porosity of scaffold. The process of compression failure showed that 316L gyroid structures manufactured using SLM demonstrated high degrees of toughness. The results obtained from CFD simulation showed that gyroid structures have good fluidity, which has an accelerated effect on the fluid in the middle of the channel, and it is suitable for transport nutrients. Therefore, we could predict the scaffold's permeability by conducting CFD simulation to ensure an appropriate permeability before the scaffold being manufactured. SLM-built gyroid structures that composed of 316L stainless steel were suitable to be designed as bone scaffolds in terms of mechanical properties and mass-transport properties, and had significant promise.

Architectural Design of 3D Printed Scaffolds Controls the Volume and Functionality of Newly Formed Bone

The successful regeneration of functional bone tissue in critical-size defects remains a significant clinical challenge. To address this challenge, synthetic bone scaffolds are widely developed, but remarkably few are translated to the clinic due to poor performance in vivo. Here, it is demonstrated how architectural design of 3D printed scaffolds can improve in vivo outcomes. Ceramic scaffolds with different pore sizes and permeabilities, but with similar porosity and interconnectivity, are implanted in rabbit calvaria for 12 weeks, and then the explants are harvested for microcomputed tomography evaluation of the volume and functionality of newly formed bone. The results indicate that scaffold pores should be larger than 390 µm with an upper limit of 590 µm to enhance bone formation. It is also demonstrated that a bimodal pore topology-alternating large and small pores-enhances the volume and functionality of new bone substantially. Moreover, bone formation results indicate that stiffness of new bone is highly influenced by the scaffold's permeability in the direction concerned. This study demonstrates that manipulating pore size and permeability in a 3D printed scaffold architecture provides a useful strategy for enhancing bone regeneration outcomes.

Additively manufactured porous metallic biomaterials

Additively manufactured (AM, =3D printed) porous metallic biomaterials with topologically ordered unit cells have created a lot of excitement and are currently receiving a lot of attention given their great potential for improving bone tissue regeneration and preventing implant-associated infections.

Current Trends in Metallic Orthopedic Biomaterials: From Additive Manufacturing to Bio-Functionalization, Infection Prevention, and Beyond

There has been a growing interest in metallic biomaterials during the last five years, as recent developments in additive manufacturing (=3D printing), surface bio-functionalization techniques, infection prevention strategies, biodegradable metallic biomaterials, and composite biomaterials have provided many possibilities to develop biomaterials and medical devices with unprecedented combinations of favorable properties and advanced functionalities. Moreover, development of biomaterials is no longer separated from the other branches of biomedical engineering, particularly tissue biomechanics, musculoskeletal dynamics, and image processing aspects of skeletal radiology. In this editorial, I will discuss all the above-mentioned topics, as they constitute some of the most important trends of research on metallic biomaterials. This editorial will, therefore, serve as a foreword to the papers appearing in a special issue covering the current trends in metallic biomaterials.

Mesenchymal stem cell cultivation in electrospun scaffolds: mechanistic modeling for tissue engineering

Tissue engineering is a multidisciplinary field of research in which the cells, biomaterials, and processes can be optimized to develop a tissue substitute. Three-dimensional (3D) architectural features from electrospun scaffolds, such as porosity, tortuosity, fiber diameter, pore size, and interconnectivity have a great impact on cell behavior. Regarding tissue development in vitro, culture conditions such as pH, osmolality, temperature, nutrient, and metabolite concentrations dictate cell viability inside the constructs. The effect of different electrospun scaffold properties, bioreactor designs, mesenchymal stem cell culture parameters, and seeding techniques on cell behavior can be studied individually or combined with phenomenological modeling techniques. This work reviews the main culture and scaffold factors that affect tissue development in vitro regarding the culture of cells inside 3D matrices. The mathematical modeling of the relationship between these factors and cell behavior inside 3D constructs has also been critically reviewed, focusing on mesenchymal stem cell culture in electrospun scaffolds.

3D bioprinting of tissues and organs for regenerative medicine

3D bioprinting is a pioneering technology that enables fabrication of biomimetic, multiscale, multi-cellular tissues with highly complex tissue microenvironment, intricate cytoarchitecture, structure-function hierarchy, and tissue-specific compositional and mechanical heterogeneity. Given the huge demand for organ transplantation, coupled with limited organ donors, bioprinting is a potential technology that could solve this crisis of organ shortage by fabrication of fully-functional whole organs. Though organ bioprinting is a far-fetched goal, there has been a considerable and commendable progress in the field of bioprinting that could be used as transplantable tissues in regenerative medicine. This paper presents a first-time review of 3D bioprinting in regenerative medicine, where the current status and contemporary issues of 3D bioprinting pertaining to the eleven organ systems of the human body including skeletal, muscular, nervous, lymphatic, endocrine, reproductive, integumentary, respiratory, digestive, urinary, and circulatory systems were critically reviewed. The implications of 3D bioprinting in drug discovery, development, and delivery systems are also briefly discussed, in terms of in vitro drug testing models, and personalized medicine. While there is a substantial progress in the field of bioprinting in the recent past, there is still a long way to go to fully realize the translational potential of this technology. Computational studies for study of tissue growth or tissue fusion post-printing, improving the scalability of this technology to fabricate human-scale tissues, development of hybrid systems with integration of different bioprinting modalities, formulation of new bioinks with tuneable mechanical and rheological properties, mechanobiological studies on cell-bioink interaction, 4D bioprinting with smart (stimuli-responsive) hydrogels, and addressing the ethical, social, and regulatory issues concerning bioprinting are potential futuristic focus areas that would aid in successful clinical translation of this technology.

Relevant biological processes for tissue development with stem cells and their mechanistic modeling: A review

A potential alternative for tissue transplants is tissue engineering, in which the interaction of cells and biomaterials can be optimized. Tissue development in vitro depends on the complex interaction of several biological processes such as extracellular matrix synthesis, vascularization and cell proliferation, adhesion, migration, death, and differentiation. The complexity of an individual phenomenon or of the combination of these processes can be studied with phenomenological modeling techniques. This work reviews the main biological phenomena in tissue development and their mathematical modeling, focusing on mesenchymal stem cell growth in three-dimensional scaffolds.

Design and Structure-Function Characterization of 3D Printed Synthetic Porous Biomaterials for Tissue Engineering

3D printing is now adopted for use in a variety of industries and functions. In biomedical engineering, 3D printing has prevailed over more traditional manufacturing methods in tissue engineering due to its high degree of control over both macro- and microarchitecture of porous tissue scaffolds. However, with the improved flexibility in design come new challenges in characterizing the structure-function relationships between various architectures and both mechanical and biological properties in an assortment of clinical applications. Presently, the field of tissue engineering lacks a comprehensive body of literature that is capable of drawing meaningful relationships between the designed structure and resulting function of 3D printed porous biomaterial scaffolds. This work first discusses the role of design on 3D printed porous scaffold function and then reviews characterization of these structure-function relationships for 3D printed synthetic metallic, polymeric, and ceramic biomaterials.

Influence of Inherent Surface and Internal Defects on Mechanical Properties of Additively Manufactured Ti6Al4V Alloy: Comparison between Selective Laser Melting and Electron Beam Melting

Additive manufacture (AM) appears to be the most suitable technology to produce sophisticated, high quality, lightweight parts from Ti6Al4V alloy. However, the fatigue life of AM parts is of concern. In our study, we focused on a comparison of two techniques of additive manufacture—selective laser melting (SLM) and electron beam melting (EBM)—in terms of the mechanical properties during both static and dynamic loading. All of the samples were untreated to focus on the influence of surface condition inherent to SLM and EBM. The EBM samples were studied in the as-built state, while SLM was followed by heat treatment. The resulting similarity of microstructures led to comparable mechanical properties in tension, but, due to differences in surface roughness and specific internal defects, the fatigue strength of the EBM samples reached only half the value of the SLM samples. Higher surface roughness that is inherent to EBM contributed to multiple initiations of fatigue cracks, while only one crack initiated on the SLM surface. Also, facets that were formed by an intergranular cleavage fracture were observed in the EBM samples.

THE USE OF COMPUTATIONAL FLUID DYNAMICS IN THE OPTIMIZATION OF AIR-IMPEDANCE ELECTROSPUN STRUCTURES FOR TISSUE ENGINEERING

Electrospinning is a viable method for dermal tissue engineering scaffold fabrication. Grafts using air-impedance electrospinning possess the ability to significantly increase cellular infiltration. However, current air-impedance methods lack precise control over flow properties through the collecting mandrel and are unable to accurately control fiber deposition in an organized and well-distributed manner. This study focusses on the use of computational fluid dynamics (CFD) and its application to air-impedance structures to optimize the deposition of the resulting dermal graft. Air-impedance structures were created from a range of air pressures to determine the optimal pressure for fiber collection. Initial results showed a pressure of 11[Formula: see text]psi (1.3[Formula: see text]scfm), which led to increased cellular penetration, but created uneven structures. This inlet flow rate was implemented as the primary boundary condition for CFD simulations. CFD software was used to gather data on fluid flow characteristics for a variety of mandrel geometries. Results showed that a mandrel with increased length and offset pore geometry provided the highest uniformity of flow along the length of the model over the other mandrel lengths, geometries, and pore alignments based largely on pressure and velocity analysis. This mandrel was manufactured and used for validation of CFD data via scaffold analysis and cellular infiltration studies. Scaffold characterization confirmed a significant advantage in the creation of structures fabricated with the optimized air-impedance mandrel by effectively doubling the efficiency of production via larger usable scaffold area. The results indicate that CFD validation is a valuable technique to optimize air impedance scaffolds in silico and has proven to be a useful tool in the fabrication of tissue engineering scaffolds.

Computationally designed lattices with tuned properties for tissue engineering using 3D printing

Tissue scaffolds provide structural support while facilitating tissue growth, but are challenging to design due to diverse property trade-offs. Here, a computational approach was developed for modeling scaffolds with lattice structures of eight different topologies and assessing properties relevant to bone tissue engineering applications. Evaluated properties include porosity, pore size, surface-volume ratio, elastic modulus, shear modulus, and permeability. Lattice topologies were generated by patterning beam-based unit cells, with design parameters for beam diameter and unit cell length. Finite element simulations were conducted for each topology and quantified how elastic modulus and shear modulus scale with porosity, and how permeability scales with porosity cubed over surface-volume ratio squared. Lattices were compared with controlled properties related to porosity and pore size. Relative comparisons suggest that lattice topology leads to specializations in achievable properties. For instance, Cube topologies tend to have high elastic and low shear moduli while Octet topologies have high shear moduli and surface-volume ratios but low permeability. The developed method was utilized to analyze property trade-offs as beam diameter was altered for a given topology, and used to prototype a 3D printed lattice embedded in an interbody cage for spinal fusion treatments. Findings provide a basis for modeling and understanding relative differences among beam-based lattices designed to facilitate bone tissue growth.

The Use of Finite Element Analyses to Design and Fabricate Three-Dimensional Scaffolds for Skeletal Tissue Engineering

Computational modeling has been increasingly applied to the field of tissue engineering and regenerative medicine. Where in early days computational models were used to better understand the biomechanical requirements of targeted tissues to be regenerated, recently, more and more models are formulated to combine such biomechanical requirements with cell fate predictions to aid in the design of functional three-dimensional scaffolds. In this review, we highlight how computational modeling has been used to understand the mechanisms behind tissue formation and can be used for more rational and biomimetic scaffold-based tissue regeneration strategies. With a particular focus on musculoskeletal tissues, we discuss recent models attempting to predict cell activity in relation to specific mechanical and physical stimuli that can be applied to them through porous three-dimensional scaffolds. In doing so, we review the most common scaffold fabrication methods, with a critical view on those technologies that offer better properties to be more easily combined with computational modeling. Finally, we discuss how modeling, and in particular finite element analysis, can be used to optimize the design of scaffolds for skeletal tissue regeneration.

Challenges in engineering large customized bone constructs

The ability to treat large tissue defects with customized, patient-specific scaffolds is one of the most exciting applications in the tissue engineering field. While an increasing number of modestly sized tissue engineering solutions are making the transition to clinical use, successfully scaling up to large scaffolds with customized geometry is proving to be a considerable challenge. Managing often conflicting requirements of cell placement, structural integrity, and a hydrodynamic environment supportive of cell culture throughout the entire thickness of the scaffold has driven the continued development of many techniques used in the production, culturing, and characterization of these scaffolds. This review explores a range of technologies and methods relevant to the design and manufacture of large, anatomically accurate tissue-engineered scaffolds with a focus on the interaction of manufactured scaffolds with the dynamic tissue culture fluid environment. Biotechnol. Bioeng. 2017;114: 1129-1139. © 2016 Wiley Periodicals, Inc.

Estimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations

In this paper, a comprehensive framework is proposed to estimate the anisotropic permeability matrix in trabecular bone specimens based on micro-computed tomography (microCT) imaging combined with pore-scale fluid dynamics simulations. Two essential steps in the proposed methodology are the selection of (i) a representative volume element (RVE) for calculation of trabecular bone permeability and (ii) a converged mesh for accurate calculation of pore fluid flow properties. Accurate estimates of trabecular bone porosities are obtained using a microCT image resolution of approximately 10 μm. We show that a trabecular bone RVE in the order of 2 × 2 × 2 mm³ is most suitable. Mesh convergence studies show that accurate fluid flow properties are obtained for a mesh size above 125,000 elements. Volume averaging of the pore-scale fluid flow properties allows calculation of the apparent permeability matrix of trabecular bone specimens. For the four specimens chosen, our numerical results show that the so obtained permeability coefficients are in excellent agreement with previously reported experimental data for both human and bovine trabecular bone samples. We also identified that bone samples taken from long bones generally exhibit a larger permeability in the longitudinal direction. The fact that all coefficients of the permeability matrix were different from zero indicates that bone samples are generally not harvested in the principal flow directions. The full permeability matrix was diagonalized by calculating the eigenvalues, while the eigenvectors showed how strongly the bone sample's orientations deviated from the principal flow directions. Porosity values of the four bone specimens range from 0.83 to 0.86, with a low standard deviation of ± 0.016, principal permeability values range from 0.22 to 1.45 ⋅ 10 ^-8 m², with a high standard deviation of ± 0.33. Also, the anisotropic ratio ranged from 0.27 to 0.83, with high standard deviation. These results indicate that while the four specimens are quite similar in terms of average porosity, large variability exists with respect to permeability and specimen anisotropy. The utilized computational approach compares well with semi-analytical models based on homogenization theory. This methodology can be applied in bone tissue engineering applications for generating accurate pore morphologies of bone replacement materials and to consistently select similar bone specimens in bone bioreactor studies.

Post Processing and Biological Evaluation of the Titanium Scaffolds for Bone Tissue Engineering

Nowadays, post-surgical or post-accidental bone loss can be substituted by custom-made scaffolds fabricated by additive manufacturing (AM) methods from metallic powders. However, the partially melted powder particles must be removed in a post-process chemical treatment. The aim of this study was to investigate the effect of the chemical polishing with various acid baths on novel scaffolds' morphology, porosity and mechanical properties. In the first stage, Magics software (Materialise NV, Leuven, Belgium) was used to design a porous scaffolds with pore size equal to (A) 200 µm, (B) 500 µm and (C) 200 + 500 µm, and diamond cell structure. The scaffolds were fabricated from commercially pure titanium powder (CP Ti) using a SLM50 3D printing machine (Realizer GmbH, Borchen, Germany). The selective laser melting (SLM) process was optimized and the laser beam energy density in range of 91-151 J/mm³ was applied to receive 3D structures with fully dense struts. To remove not fully melted titanium particles the scaffolds were chemically polished using various HF and HF-HNO₃ acid solutions. Based on scaffolds mass loss and scanning electron (SEM) observations, baths which provided most uniform surface cleaning were proposed for each porosity. The pore and strut size after chemical treatments was calculated based on the micro-computed tomography (µ-CT) and SEM images. The mechanical tests showed that the treated scaffolds had Young's modulus close to that of compact bone. Additionally, the effect of pore size of chemically polished scaffolds on cell retention, proliferation and differentiation was studied using human mesenchymal stem cells. Small pores yielded higher cell retention within the scaffolds, which then affected their growth. This shows that in vitro cell performance can be controlled to certain extent by varying pore sizes.

Is trabecular bone permeability governed by molecular ordering-induced fluid viscosity gain? Arguments from re-evaluation of experimental data in the framework of homogenization theory

It is generally agreed on that trabecular bone permeability, a physiologically important quantity, is governed by the material׳s (vascular or intertrabecular) porosity as well as by the viscosity of the pore-filling fluids. Still, there is less agreement on how these two key factors govern bone permeability. In order to shed more light onto this somewhat open issue, we here develop a random homogenization scheme for upscaling Poiseuille flow in the vascular porosity, up to Darcy-type permeability of the overall porous medium "trabecular bone". The underlying representative volume element of the macroscopic bone material contains two types of phases: a spherical, impermeable extracellular bone matrix phase interacts with interpenetrating cylindrical pore channel phases that are oriented in all different space directions. This type of interaction is modeled by means of a self-consistent homogenization scheme. While the permeability of the bone matrix equals to zero, the permeability of the pore phase is found through expressing the classical Hagen-Poiseuille law for laminar flow in the format of a "micro-Darcy law". The upscaling scheme contains pore size and porosity as geometrical input variables; however, they can be related to each other, based on well-known relations between porosity and specific bone surface. As two key results, validated through comprehensive experimental data, it appears (i) that the famous Kozeny-Carman constant (which relates bone permeability to the cube of the porosity, the square of the specific surface, as well as to the bone fluid viscosity) needs to be replaced by an again porosity-dependent rational function, and (ii) that the overall bone permeability is strongly affected by the pore fluid viscosity, which, in case of polarized fluids, is strongly increased due to the presence of electrically charged pore walls.

Human periosteal-derived cell expansion in a perfusion bioreactor system: proliferation, differentiation and extracellular matrix formation

Perfusion bioreactor systems have shown to be a valuable tool for the in vitro development of three-dimensional (3D) cell-carrier constructs. Their use for cell expansion, however, has been much less explored. Since maintenance of the initial cell phenotype is essential in this process, it is imperative to obtain insight into the bioreactor-related variables determining cell fate. Therefore, this study investigated the influence of fluid flow-induced shear stress on the proliferation, differentiation and matrix deposition of human periosteal-derived cells in the absence of additional differentiation-inducing stimuli; 120 000 cells were seeded on additive manufactured 3D Ti6Al4V scaffolds and cultured for up to 28 days at different flow rates in the range 0.04-6 ml/min. DNA measurements showed, on average, a three-fold increase in cell content for all perfused conditions in comparison to static controls, whereas the magnitude of the flow rate did not have an influence. Contrast-enhanced nanofocus X-ray computed tomography showed substantial formation of an engineered neotissue in all perfused conditions, resulting in a filling (up to 70%) of the total internal void volume, and no flow rate-dependent differences were observed. The expression of key osteogenic markers, such as RunX2, OCN, OPN and Col1, did not show any significant changes in comparison to static controls after 28 days of culture, with the exception of OSX at high flow rates. We therefore concluded that, in the absence of additional osteogenic stimuli, the investigated perfusion conditions increased cell proliferation but did not significantly enhance osteogenic differentiation, thus allowing for this process to be used for cell expansion. Copyright © 2014 John Wiley & Sons, Ltd.

A novel scaffold geometry for chondral applications: theoretical model and in vivo validation

A theoretical model of the 3D scaffold internal architecture has been implemented with the aim to predict the effects of some geometrical parameters on total porosity, Young modulus, buckling resistance and permeability of the graft. This model has been adopted to produce porous poly-caprolacton based grafts for chondral tissue engineering applications, best tuning mechanical and functional features of the scaffolds. Material prototypes were produced with an internal geometry with parallel oriented cylindrical pores of 200 μm of radius (r) and an interpore distance/pores radius (d/r) ratio of 1. The scaffolds have been then extensively characterized; progenitor cells were then used to test their capability to support cartilaginous matrix deposition in an ectopic model. Scaffold prototypes fulfill both the chemical-physical requirements, in terms of Young's modulus and permeability, and the functional needs, such as surface area per volume and total porosity, for an enhanced cellular colonization and matrix deposition. Moreover, the grafts showed interesting chondrogenic potential in vivo, besides offering adequate mechanical performances in vitro, thus becoming a promising candidate for chondral tissues repair. Finally, a very good agreement was found between the prediction of the theoretical model and the experimental data. Many assumption of this theoretical model, hereby applied to cartilage, may be transposed to other tissue engineering applications, such as bone substitutes.

Modeling mechanical signals on the surface of µCT and CAD based rapid prototype scaffold models to predict (early stage) tissue development

In the field of tissue engineering, mechano-regulation theories have been applied to help predict tissue development in tissue engineering scaffolds in the past. For this, finite element models (FEMs) were used to predict the distribution of strains within a scaffold. However, the strains reported in these studies are volumetric strains of the material or strains developed in the extracellular matrix occupying the pore space. The initial phase of cell attachment and growth on the biomaterial surface has thus far been neglected. In this study, we present a model that determines the magnitude of biomechanical signals on the biomaterial surface, enabling us to predict cell differentiation stimulus values at this initial stage. Results showed that magnitudes of the 2D strain--termed surface strain--were lower when compared to the 3D volumetric strain or the conventional octahedral shear strain as used in current mechano-regulation theories. Results of both µCT and CAD derived FEMs from the same scaffold were compared. Strain and fluid shear stress distributions, and subsequently the cell differentiation stimulus, were highly dependent on the pore shape. CAD models were not able to capture the distributions seen in the µCT FEM. The calculated mechanical stimuli could be combined with current mechanobiological models resulting in a tool to predict cell differentiation in the initial phase of tissue engineering. Although experimental data is still necessary to properly link mechanical signals to cell behavior in this specific setting, this model is an important step towards optimizing scaffold architecture and/or stimulation regimes.

Current trends in the design of scaffolds for computer-aided tissue engineering

Advances introduced by additive manufacturing have significantly improved the ability to tailor scaffold architecture, enhancing the control over microstructural features. This has led to a growing interest in the development of innovative scaffold designs, as testified by the increasing amount of research activities devoted to the understanding of the correlation between topological features of scaffolds and their resulting properties, in order to find architectures capable of optimal trade-off between often conflicting requirements (such as biological and mechanical ones). The main aim of this paper is to provide a review and propose a classification of existing methodologies for scaffold design and optimization in order to address key issues and help in deciphering the complex link between design criteria and resulting scaffold properties.

Mechanical modulation of nascent stem cell lineage commitment in tissue engineering scaffolds

Taking inspiration from tissue morphogenesis in utero, this study tests the concept of using tissue engineering scaffolds as delivery devices to modulate emergent structure-function relationships at early stages of tissue genesis. We report on the use of a combined computational fluid dynamics (CFD) modeling, advanced manufacturing methods, and experimental fluid mechanics (micro-piv and strain mapping) for the prospective design of tissue engineering scaffold geometries that deliver spatially resolved mechanical cues to stem cells seeded within. When subjected to a constant magnitude global flow regime, the local scaffold geometry dictates the magnitudes of mechanical stresses and strains experienced by a given cell, and in a spatially resolved fashion, similar to patterning during morphogenesis. In addition, early markers of mesenchymal stem cell lineage commitment relate significantly to the local mechanical environment of the cell. Finally, by plotting the range of stress-strain states for all data corresponding to nascent cell lineage commitment (95% CI), we begin to "map the mechanome", defining stress-strain states most conducive to targeted cell fates. In sum, we provide a library of reference mechanical cues that can be delivered to cells seeded on tissue engineering scaffolds to guide target tissue phenotypes in a temporally and spatially resolved manner. Knowledge of these effects allows for prospective scaffold design optimization using virtual models prior to prototyping and clinical implementation. Finally, this approach enables the development of next generation scaffolds cum delivery devices for genesis of complex tissues with heterogenous properties, e.g., organs, joints or interface tissues such as growth plates.

A survey of methods for the evaluation of tissue engineering scaffold permeability

The performance of porous scaffolds for tissue engineering (TE) applications is evaluated, in general, in terms of porosity, pore size and distribution, and pore tortuosity. These descriptors are often confounding when they are applied to characterize transport phenomena within porous scaffolds. On the contrary, permeability is a more effective parameter in (1) estimating mass and species transport through the scaffold and (2) describing its topological features, thus allowing a better evaluation of the overall scaffold performance. However, the evaluation of TE scaffold permeability suffers of a lack of uniformity and standards in measurement and testing procedures which makes the comparison of results obtained in different laboratories unfeasible. In this review paper we summarize the most important features influencing TE scaffold permeability, linking them to the theoretical background. An overview of methods applied for TE scaffold permeability evaluation is given, presenting experimental test benches and computational methods applied (1) to integrate experimental measurements and (2) to support the TE scaffold design process. Both experimental and computational limitations in the permeability evaluation process are also discussed.

Noninvasive real-time monitoring by alamarBlue(®) during in vitro culture of three-dimensional tissue-engineered bone constructs

Bone tissue engineering (TE) aims to develop reproducible and predictive three-dimensional (3D) TE constructs, defined as cell-seeded scaffolds produced by a controlled in vitro process, to heal or replace damaged and nonfunctional bone. To control and assure the quality of the bone TE constructs, a prerequisite for regulatory authorization, there is a need to develop noninvasive analysis techniques to evaluate TE constructs and to monitor their behavior in real time during in vitro culturing. Most analysis techniques, however, are limited to destructive end-point analyses. This study investigates the use of the nontoxic alamarBlue(®) (AB) reagent, which is an indicator for metabolic cell activity, for monitoring the cellularity of 3D TE constructs in vitro as part of a bioreactor culturing processes. Within the field of TE, bioreactors have a huge potential in the translation of TE concepts to the clinic. Hence, the use of the AB reagent was evaluated not only in static cultures, but also in dynamic cultures in a perfusion bioreactor setup. Hereto, the AB assay was successfully integrated in the bioreactor-driven TE construct culture process in a noninvasive way. The obtained results indicate a linear correlation between the overall metabolic activity and the total DNA content of a scaffold upon seeding as well as during the initial stages of cell proliferation. This makes the AB reagent a powerful tool to follow-up bone TE constructs in real-time during static as well as dynamic 3D cultures. Hence, the AB reagent can be successfully used to monitor and predict cell confluence in a growing 3D TE construct.

Biomaterial porosity determined by fractal dimensions, succolarity and lacunarity on microcomputed tomographic images

Porous structures are becoming more and more important in biology and material science because they help in reducing the density of the grafted material. For biomaterials, porosity also increases the accessibility of cells and vessels inside the grafted area. However, descriptors of porosity are scanty. We have used a series of biomaterials with different types of porosity (created by various porogens: fibers, beads …). Blocks were studied by microcomputed tomography for the measurement of 3D porosity. 2D sections were re-sliced to analyze the microarchitecture of the pores and were transferred to image analysis programs: star volumes, interconnectivity index, Minkowski-Bouligand and Kolmogorov fractal dimensions were determined. Lacunarity and succolarity, two recently described fractal dimensions, were also computed. These parameters provided a precise description of porosity and pores' characteristics. Non-linear relationships were found between several descriptors e.g. succolarity and star volume of the material. A linear correlation was found between lacunarity and succolarity. These techniques appear suitable in the study of biomaterials usable as bone substitutes.