Simulation of bone tissue formation within a porous scaffold under dynamic compression

Bone Ingrowth Simulation Within the Hexanoid, a Novel Scaffold Design

The utilization of bone scaffold implants represents a promising approach for repairing substantial bone defects. In recent years, various traditional scaffold structures have been developed and, with advances in materials biology and computer technology, novel scaffold designs are now being evaluated. This study investigated the effects of a novel scaffold unit cell design (Hexanoid) through a computational framework, comparing its performance to that of four well-known scaffold designs. A finite element analysis numerical simulation and mechanical testing were conducted to analyze the dynamic bone ingrowth process and the mechanical strength of the different scaffold designs. Bone formation within the Ti-6Al-4V metal scaffolds was simulated based on the theory of bone remodeling. The outcomes of the study reveal that the novel scaffold design (Hexanoid) attains a notably elevated ultimate bone volume fraction (∼27%), it outperformed conventional unit-cell designs found in extant literature, such as cubic design with 19.1% and circular design with 16.9% in relation to the bone-to-cavity volume ratio. This novel structure also has comparable mechanical strength to that of human compact bone tissue. While the design was not optimal in every category, it provided a very satisfactory overall performance regarding certain key aspects of bone performances in comparison with the five scaffold structures evaluated. Although limitations exist in this project, similar methodologies can also be applied in the primary evaluation of new scaffold structures, resulting in improved efficiency and effectiveness. In future research, the results of this project may be integrated with clinical rehabilitation processes to offer a critical evaluation for optimization of additional novel scaffold unit-cell structure designs.

Mechanoregulation analysis of bone formation in tissue engineered constructs requires a volumetric method using time-lapsed micro-computed tomography

Bone can adapt its microstructure to mechanical loads through mechanoregulation of the (re)modeling process. This process has been investigated in vivo using time-lapsed micro-computed tomography (micro-CT) and micro-finite element (FE) analysis using surface-based methods, which are highly influenced by surface curvature. Consequently, when trying to investigate mechanoregulation in tissue engineered bone constructs, their concave surfaces make the detection of mechanoregulation impossible when using surface-based methods. In this study, we aimed at developing and applying a volumetric method to non-invasively quantify mechanoregulation of bone formation in tissue engineered bone constructs using micro-CT images and FE analysis. We first investigated hydroxyapatite scaffolds seeded with human mesenchymal stem cells that were incubated over 8 weeks with one mechanically loaded and one control group. Higher mechanoregulation of bone formation was measured in loaded samples with an area under the curve for the receiver operating curve (AUCformation) of 0.633-0.637 compared to non-loaded controls (AUCformation: 0.592-0.604) during culture in osteogenic medium (p < 0.05). Furthermore, we applied the method to an in vivo mouse study investigating the effect of loading frequencies on bone adaptation. The volumetric method detected differences in mechanoregulation of bone formation between loading conditions (p < 0.05). Mechanoregulation in bone formation was more pronounced (AUCformation: 0.609-0.642) compared to the surface-based method (AUCformation: 0.565-0.569, p < 0.05). Our results show that mechanoregulation of formation in bone tissue engineered constructs takes place and its extent can be quantified with a volumetric mechanoregulation method using time-lapsed micro-CT and FE analysis. STATEMENT OF SIGNIFICANCE: Many efforts have been directed towards optimizing bone scaffolds for tissue growth. However, the impact of the scaffolds mechanical environment on bone growth is still poorly understood, requiring accurate assessment of its mechanoregulation. Existing surface-based methods were unable to detect mechanoregulation in tissue engineered constructs, due to predominantly concave surfaces in scaffolds. We present a volumetric approach to enable the precise and non-invasive quantification and analysis of mechanoregulation in bone tissue engineered constructs by leveraging time-lapsed micro-CT imaging, image registration, and finite element analysis. The implications of this research extend to diverse experimental setups, encompassing culture conditions, and material optimization, and investigations into bone diseases, enabling a significant stride towards comprehensive advancements in bone tissue engineering and regenerative medicine.

Simulating the mechanical stimulation of cells on a porous hydrogel scaffold using an FSI model to predict cell differentiation

3D-structured hydrogel scaffolds are frequently used in tissue engineering applications as they can provide a supportive and biocompatible environment for the growth and regeneration of new tissue. Hydrogel scaffolds seeded with human mesenchymal stem cells (MSCs) can be mechanically stimulated in bioreactors to promote the formation of cartilage or bone tissue. Although in vitro and in vivo experiments are necessary to understand the biological response of cells and tissues to mechanical stimulation, in silico methods are cost-effective and powerful approaches that can support these experimental investigations. In this study, we simulated the fluid-structure interaction (FSI) to predict cell differentiation on the entire surface of a 3D-structured hydrogel scaffold seeded with cells due to dynamic compressive load stimulation. The computational FSI model made it possible to simultaneously investigate the influence of both mechanical deformation and flow of the culture medium on the cells on the scaffold surface during stimulation. The transient one-way FSI model thus opens up significantly more possibilities for predicting cell differentiation in mechanically stimulated scaffolds than previous static microscale computational approaches used in mechanobiology. In a first parameter study, the impact of the amplitude of a sinusoidal compression ranging from 1% to 10% on the phenotype of cells seeded on a porous hydrogel scaffold was analyzed. The simulation results show that the number of cells differentiating into bone tissue gradually decreases with increasing compression amplitude, while differentiation into cartilage cells initially multiplied with increasing compression amplitude in the range of 2% up to 7% and then decreased. Fibrous cell differentiation was predicted from a compression of 5% and increased moderately up to a compression of 10%. At high compression amplitudes of 9% and 10%, negligible areas on the scaffold surface experienced high stimuli where no cell differentiation could occur. In summary, this study shows that simulation of the FSI system is a versatile approach in computational mechanobiology that can be used to study the effects of, for example, different scaffold designs and stimulation parameters on cell differentiation in mechanically stimulated 3D-structured scaffolds.

Computer-aided engineering and additive manufacturing for bioreactors in tissue engineering: State of the art and perspectives

Two main challenges are currently present in the healthcare world, i.e., the limitations given by transplantation and the need to have available 3D in vitro models. In this context, bioreactors are devices that have been introduced in tissue engineering as a support for facing the mentioned challenges by mimicking the cellular native microenvironment through the application of physical stimuli. Bioreactors can be divided into two groups based on their final application: macro- and micro-bioreactors, which address the first and second challenge, respectively. The bioreactor design is a crucial step as it determines the way in which physical stimuli are provided to cells. It strongly depends on the manufacturing techniques chosen for the realization. In particular, in bioreactor prototyping, additive manufacturing techniques are widely used nowadays as they allow the fabrication of customized shapes, guaranteeing more degrees of freedom. To support the bioreactor design, a powerful tool is represented by computational simulations that allow to avoid useless approaches of trial-and-error. In the present review, we aim to discuss the general workflow that must be carried out to develop an optimal macro- and micro-bioreactor. Accordingly, we organize the discussion by addressing the following topics: general and stimulus-specific (i.e., perfusion, mechanical, and electrical) requirements that must be considered during the design phase based on the tissue target; computational models as support in designing bioreactors based on the provided stimulus; manufacturing techniques, with a special focus on additive manufacturing techniques; and finally, current applications and new trends in which bioreactors are involved.

3D printed TPMS structural PLA/GO scaffold: Process parameter optimization, porous structure, mechanical and biological properties

Bone scaffolds should have good biocompatibility and mechanical and biological properties, which are primarily by the material design, porous structure, and preparation process. In this study, we proposed polylactic acid (PLA) as the base material, graphene oxide (GO) as an enhancing filler, triply periodic minimal surface (TPMS) as a porous structure, and fused deposition modeling (FDM) 3D printing as a preparation technology to develop a TPMS structural PLA/GO scaffold and evaluate their porous structures, mechanical properties, and biological properties towards bone tissue engineering. Firstly, the influence of the FDM 3D printing process parameters on the forming quality and mechanical properties of PLA was studied by orthogonal experimental design, based on which the process parameters were optimized. Then, GO was composited with PLA, and PLA/GO nanocomposites were prepared by FDM. The mechanical tests showed that GO can effectively improve the tensile and compression strength of PLA; only by adding 0.1% GO the tensile and compression modulus was increased by 35.6% and 35.8%, respectively. Then, TPMS structural (Schwarz-P, Gyroid) scaffold models were designed and TPMS structural PLA/0.1%GO nanocomposite scaffolds were prepared by FDM. The compression test showed that the TPMS structural scaffolds had higher compression strength than the Grid structure; This was owing to the fact that the continuous curved structure of TMPS alleviated stress concentration and had a more uniform stress bearing. Moreover, cell culture indicated bone marrow stromal cells (BMSCs) showed better adhesion, proliferation, and osteogenic differentiation behaviors on the TPMS structural scaffolds as the continuous surface structure of TPMS had better connectivity and larger specific surface area. These results suggest that the TPMS structural PLA/GO scaffold has potential application in bone repair. This article suggests the feasibility of co-designing the material, structure, and technology for achieving the good comprehensive performance of polymer bone scaffolds.

In silico modelling of long bone healing involving osteoconduction and mechanical stimulation

A lot of evidence has shown the importance of stimulating cell mechanically during bone repair. In this study, we modeled the challenging fracture healing of a large bone defect in tibial diaphysis. To fill the fracture gap, we considered the implantation of a porous osteoconductive biomaterial made of poly-lactic acid wrapped by a hydrogel membrane mimicking osteogenic properties of the periosteum. We identified the optimal loading case that best promotes the formation and differentiation into bone tissue. Our results support the idea that a patient's rehabilitation program should be adapted to reproduce optimal mechanical stimulations.

A review on design of scaffold for osteoinduction: Toward the unification of independent design variables

Biophysical stimulus quantifies the osteoinductivity of the scaffold concerning the mechanoregulatory mathematical models of scaffold-assisted cellular differentiation. Consider a set of independent structural variables ($) that comprises bulk porosity levels ([Formula: see text]) and a set of morphological features of the micro-structure ([Formula: see text]) associated with scaffolds, i.e., [Formula: see text]. The literature suggests that biophysical stimulus ([Formula: see text]) is a function of independent structural variables ($). Limited understanding of the functional correlation between biophysical stimulus and structural features results in the lack of the desired osteoinductivity in a scaffold. Consequently, it limits their broad applicability to assist bone tissue regeneration for treating critical-sized bone fractures. The literature indicates the existence of multi-dimensional independent design variable space as a probable reason for the general lack of osteoinductivity in scaffolds. For instance, known morphological features are the size, shape, orientation, continuity, and connectivity of the porous regions in the scaffold. It implies that the number of independent variables ([Formula: see text]) is more than two, i.e., [Formula: see text], which interact and influence the magnitude of [Formula: see text] in a unified manner. The efficiency of standard engineering design procedures to analyze the correlation between dependent variable ([Formula: see text]) and independent variables ($) in 3D mutually orthogonal Cartesian coordinate system diminishes proportionally with the increase in the number of independent variables ([Formula: see text]) (Deb in Optimization for engineering design-algorithms and examples, PHI Learning Private Limited, New Delhi, 2012). Therefore, there is an immediate need to devise a framework that has the potential to quantify the micro-structural's morphological features in a unified manner to increase the prospects of scaffold-assisted bone tissue regeneration.

Mechanical performance of additively manufactured cobalt-chromium-molybdenum auxetic meta-biomaterial bone scaffolds

Auxetic meta-biomaterials offer unconventional strain behaviour owing to their negative Poisson's ratio (-υ) leading to deformation modes and mechanical properties different to traditional cellular biomaterials. This can lead to favourable outcomes for load-bearing tissue engineering constructs such as bone scaffolds. Emerging early-stage studies have shown the potential of auxetic architecture in increasing cell proliferation and tissue reintegration owing to their -υ. However, research on the development of CoCrMo auxetic meta-biomaterials including bone scaffolds or implants is yet to be reported. In this regard, this paper proposes a potential framework for the development of auxetic meta-biomaterials that can be printed on demand while featuring porosity requirements suitable for load-bearing bone scaffolds. Overall, the performance of five CoCrMo auxetic meta-biomaterial scaffolds characterised under two scenarios for their potential to offer near-zero and high negative Poisson's ratio is demonstrated. Ashby's criterion followed by prototype testing was employed to evaluate the mechanical performance and failure modes of the auxetic meta-biomaterial scaffolds under uniaxial compression. The best performing scaffold architectures are identified through a multi-criteria decision-making procedure combining 'analytic hierarchy process' (AHP) and 'technique for order of preference by similarity to ideal solution' (TOPSIS). The results found the Poisson's ratio for the meta-biomaterial architectures to be in the range of -0.1 to -0.24 at a porosity range of 73-82%. It was found that the meta-biomaterial scaffold (AX1) that offered the highest auxeticity also showed the highest elastic modulus, yield, and ultimate strength of 1.66 GPa, 56 MPa and 158 MPa, respectively. The study demonstrates that the elastic modulus, yield stress, and Poisson's ratio of auxetic meta-biomaterials are primarily influenced by the underlying meta-cellular architecture followed by relative density offering a secondary influence.

BEM evaluation of surface octahedral strains and internal strain gradients in 3D-printed scaffolds used for bone tissue regeneration

Most of the mechnoregulatory computational models appearing so far in tissue engineering for bone healing predictions, utilize as regulators for cell differentiation mainly the octahedral volume strains and the interstitial fluid velocity calculated at any point of the fractured bone area and controlled by empirical constants concerning these two parameters. Other stimuli like the electrical and chemical signaling of bone constituents are covered by those two regulatory fields. It is apparent that the application of the same mechnoregulatory computational models for bone healing predictions in scaffold-aided regeneration is questionable since the material of a scaffold disturbs the signaling pathways developed in the environment of bone fracture. Thus, the goal of the present work is to evaluate numerically two fields developed in the body of two different compressed scaffolds, which seem to be proper for facilitating cell sensing and improving cell viability and cell seeding efficiency. These two fields concern the surface octahedral strains that the cells attached to the scaffold can experience and the internal strain gradients that create electrical pathways due to flexoelectric phenomenon. Both fields are evaluated with the aid of the Boundary Element Method (BEM), which is ideal for evaluating with high accuracy surface strains and stresses as well as strain gradients appearing throughout the analyzed elastic domain.

Alveolar ridge preservation with fibroblast growth factor-2 modified acellular dermal matrix membrane and a bovine-derived xenograft: An experimental in vivo study

OBJECTIVE

To investigate the effect of a bone substitute material combined with fibroblast growth factor-2 (FGF-2) loaded barrier membrane on the preservation of alveolar ridge after tooth extraction.

MATERIAL AND METHODS

Four dogs were included. Six extraction sockets of each animal received the 3 treatments and were randomly divided into three groups. Group A: negative control; Group B: bovine xenografts + membrane; and Group C: bovine xenografts + FGF-2-loaded membrane. CBCT and histological analysis were performed to evaluate changes in the width and height of alveolar ridges and extraction socket bone healing 8 weeks post-extraction.

RESULTS

CBCT showed that the alveolar bone in Group A was significantly thinner than that in Group B and Group C at 1 and 3 mm apically from the alveolar crest. The alveolar width at 1 mm in Group C (60.99 ± 15.36%) was significantly thicker than that in Group B (39.75 ± 30.18%). Histomorphmetrical measurements showed that the buccal alveolar width at 1 mm was significantly thicker in Groups B and C than in Group A. Additionally, buccal bone height and lingual bone width at 1 mm in Group C (87.06 ± 10.34%, 89.09 ± 10.56%) were significantly greater than in Group A (53.48 ± 23.94%, 82.72 ± 12.59%).

CONCLUSION

The present findings indicate that application of bovine bone combined with barrier membrane with or without FGF-2 over tooth sockets can effectively reduce ridge absorption, especially in terms of ridge width and FGF-2 modified membrane seems to improve the outcomes obtained with membrane alone.

Multiphysics simulation of a compression-perfusion combined bioreactor to predict the mechanical microenvironment during bone metastatic breast cancer loading experiments

Incurable breast cancer bone metastasis causes widespread bone loss, resulting in fragility, pain, increased fracture risk, and ultimately increased patient mortality. Increased mechanical signals in the skeleton are anabolic and protect against bone loss, and they may also do so during osteolytic bone metastasis. Skeletal mechanical signals include interdependent tissue deformations and interstitial fluid flow, but how metastatic tumor cells respond to each of these individual signals remains underinvestigated, a barrier to translation to the clinic. To delineate their respective roles, we report computed estimates of the internal mechanical field of a bone mimetic scaffold undergoing combinations of high and low compression and perfusion using multiphysics simulations. Simulations were conducted in advance of multimodal loading bioreactor experiments with bone metastatic breast cancer cells to ensure that mechanical stimuli occurring internally were physiological and anabolic. Our results show that mechanical stimuli throughout the scaffold were within the anabolic range of bone cells in all loading configurations, were homogenously distributed throughout, and that combined high magnitude compression and perfusion synergized to produce the largest wall shear stresses within the scaffold. These simulations, when combined with experiments, will shed light on how increased mechanical loading in the skeleton may confer anti-tumorigenic effects during metastasis.

A comprehensive analysis of bio-inspired design of femoral stem on primary and secondary stabilities using mechanoregulatory algorithm

The coated porous section of stem surface is initially filled with callus that undergoes osseointegration process, which develops a bond between stem and bone, lessens the micromotions and transfers stresses to the bone, proximally. This phenomenon attributes to primary and secondary stabilities of the stems that exhibit trade-off the stem stiffness. This study attempts to ascertain the influence of stem stiffness on peri-prosthetic bone formation and stress shielding when in silico models of solid CoCr alloy and Ti alloy stems, and porous Ti stems (53.8 GPa and 31.5 GPa Young's moduli) were implanted. A tissue differentiation predictive mechanoregulation algorithm was employed to estimate the evolutionary bond between bone and stem interfaces with 0.5-mm- and 1-mm-thick calluses. The results revealed that the high stiffness stems yielded higher stress shielding and lower micromotions than that of low stiffness stems. Contrarily, bone formation around solid Ti alloy stem and porous Ti 53.8 GPa stem was augmented in 0.5-mm- and 1-mm-thick calluses, respectively. All designs of stems exhibited different rates of bone formation, diverse initial micromotions and stress shielding; however, long-term bone formation was coherent with different stress shielding. Therefore, contemplating the secondary stability of the stems, low stiffness stem (Ti 53.8 GPa) gave superior biomechanical performance than that of high stiffness stems.

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.

Mathematical and computational models for bone tissue engineering in bioreactor systems

Research into cellular engineered bone grafts offers a promising solution to problems associated with the currently used auto- and allografts. Bioreactor systems can facilitate the development of functional cellular bone grafts by augmenting mass transport through media convection and shear flow-induced mechanical stimulation. Developing successful and reproducible protocols for growing bone tissue in vitro is dependent on tuning the bioreactor operating conditions to the specific cell type and graft design. This process, largely reliant on a trial-and-error approach, is challenging, time-consuming and expensive. Modelling can streamline the process by providing further insight into the effect of the bioreactor environment on the cell culture, and by identifying a beneficial range of operational settings to stimulate tissue production. Models can explore the impact of changing flow speeds, scaffold properties, and nutrient and growth factor concentrations. Aiming to act as an introductory reference for bone tissue engineers looking to direct their experimental work, this article presents a comprehensive framework of mathematical models on various aspects of bioreactor bone cultures and overviews modelling case studies from literature.

The Importance of Controlled Mismatch of Biomechanical Compliances of Implantable Scaffolds and Native Tissue for Articular Cartilage Regeneration

Scaffolds for articular cartilage repair have to be optimally biodegradable with simultaneous promotion of hyaline cartilage formation under rather complex biomechanical and physiological conditions. It has been generally accepted that scaffold structure and composition would be the best when it mimics the structure of native cartilage. However, a reparative construct mimicking the mature native tissue in a healing tissue site presents a biological mismatch of reparative stimuli. In this work, we studied a new recombinant human type III collagen-polylactide (rhCol-PLA) scaffolds. The rhCol-PLA scaffolds were assessed for their relative performance in simulated synovial fluids of 1 and 4 mg/mL sodium hyaluronate with application of model-free analysis with Biomaterials Enhanced Simulation Test (BEST). Pure PLA scaffold was used as a control. The BEST results were compared to the results of a prior in vivo study with rhCol-PLA. Collectively the data indicated that a successful articular cartilage repair require lower stiffness of the scaffold compared to surrounding cartilage yet matching the strain compliance both in static and dynamic conditions. This ensures an optimal combination of load transfer and effective oscillatory nutrients supply to the cells. The results encourage further development of intelligent scaffold structures for optimal articular cartilage repair rather than simply trying to imitate the respective original tissue.

A finite element analysis for monitoring the healing progression of fixator-bone system under three loading conditions

BACKGROUND

Unilateral external fixators are widely used in orthopedics to stabilize fractured bones and in the treatment of limb deformities. The main value for evaluation of mechanical stability of the external fixator is fixator stiffness. The fixator stiffness is an important factor as it will influence the biomechanical environment to which fixator and regenerating tissues are exposed.

OBJECTIVE

The main objective of this work was to monitor the transmission of stress and the change of displacement generated in fixator-bone system under three loading conditions during healing process.

METHODS

In this study, a finite element model with changing Young's modulus of the callus is established, finite element analysis was used to investigating stress and deformation of fixator-bone system caused by axial load, torsional load and bending load during three healing stages.

RESULTS

The results reveal that at different healing stages, stress distribution between the fixator and fractured bone is different, the position of displacement is mainly concentrated in the fracture site and proximal bone and with the increase of healing time, the deformation decreased.

CONCLUSIONS

This work helps orthopedic doctors to monitor the progression of fracture healing and determine the appropriate time for removal of a fixation device and provide useful information.

Micromechanical study of the load transfer in a polycaprolactone-collagen hybrid scaffold when subjected to unconfined and confined compression

Scaffolds are used in diverse tissue engineering applications as hosts for cell proliferation and extracellular matrix formation. One of the most used tissue engineering materials is collagen, which is well known to be a natural biomaterial, also frequently used as cell substrate, given its natural abundance and intrinsic biocompatibility. This study aims to evaluate how the macroscopic biomechanical stimuli applied on a construct made of polycaprolactone scaffold embedded in a collagen substrate translate into microscopic stimuli at the cell level. Eight poro-hyperelastic finite element models of 3D printed hybrid scaffolds from the same batch were created, along with an equivalent model of the idealized geometry of that scaffold. When applying an 8% confined compression at the macroscopic level, local fluid flow of up to 20 [Formula: see text]m/s and octahedral strain levels mostly under 20% were calculated in the collagen substrate. Conversely unconfined compression induced fluid flow of up to 10 [Formula: see text]m/s and octahedral strain from 10 to 35%. No relevant differences were found amongst the scaffold-specific models. Following the mechanoregulation theory based on Prendergast et al. (J Biomech 30:539-548, 1997. https://doi.org/10.1016/S0021-9290(96)00140-6 ), those results suggest that mainly cartilage or fibrous tissue formation would be expected to occur under unconfined or confined compression, respectively. This in silico study helps to quantify the microscopic stimuli that are present within the collagen substrate and that will affect cell response under in vitro bioreactor mechanical stimulation or even after implantation.

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.

An Attempt to Predict the Preferential Cellular Orientation in Any Complex Mechanical Environment

Cells respond to their mechanical environment in different ways: while their response in terms of differentiation and proliferation has been widely studied, the question of the direction in which cells align when subject to a complex mechanical loading in a 3D environment is still widely open. In the present paper, we formulate the hypothesis that the cells orientate in the direction of unitary stretch computed from the right Cauchy-Green tensor in a given mechanical environment. The implications of this hypothesis are studied in different simple cases corresponding to either the available in vitro experimental data or physiological conditions, starting from finite element analysis results to computed preferential cellular orientation. The present contribution is a first step to the formulation of a deeper understanding of the orientation of cells within or at the surface of any 3D scaffold subject to any complex load. It is believed that these initial preferential directions have strong implications as far as the anisotropy of biological structures is concerned.

Influence of Additive Manufactured Scaffold Architecture on the Distribution of Surface Strains and Fluid Flow Shear Stresses and Expected Osteochondral Cell Differentiation

Scaffolds for regenerative medicine applications should instruct cells with the appropriate signals, including biophysical stimuli such as stress and strain, to form the desired tissue. Apart from that, scaffolds, especially for load-bearing applications, should be capable of providing mechanical stability. Since both scaffold strength and stress–strain distributions throughout the scaffold depend on the scaffold’s internal architecture, it is important to understand how changes in architecture influence these parameters. In this study, four scaffold designs with different architectures were produced using additive manufacturing. The designs varied in fiber orientation, while fiber diameter, spacing, and layer height remained constant. Based on micro-CT (μCT) scans, finite element models (FEMs) were derived for finite element analysis (FEA) and computational fluid dynamics (CFD). FEA of scaffold compression was validated using μCT scan data of compressed scaffolds. Results of the FEA and CFD showed a significant impact of scaffold architecture on fluid shear stress and mechanical strain distribution. The average fluid shear stress ranged from 3.6 mPa for a 0/90 architecture to 6.8 mPa for a 0/90 offset architecture, and the surface shear strain from 0.0096 for a 0/90 offset architecture to 0.0214 for a 0/90 architecture. This subsequently resulted in variations of the predicted cell differentiation stimulus values on the scaffold surface. Fluid shear stress was mainly influenced by pore shape and size, while mechanical strain distribution depended mainly on the presence or absence of supportive columns in the scaffold architecture. Together, these results corroborate that scaffold architecture can be exploited to design scaffolds with regions that guide specific tissue development under compression and perfusion. In conjunction with optimization of stimulation regimes during bioreactor cultures, scaffold architecture optimization can be used to improve scaffold design for tissue engineering purposes.

Use of nanoscale mechanical stimulation for control and manipulation of cell behaviour

The ability to control cell behaviour, cell fate and simulate reliable tissue models in vitro remains a significant challenge yet is crucial for various applications of high throughput screening e.g. drug discovery. Mechanotransduction (the ability of cells to convert mechanical forces in their environment to biochemical signalling) represents an alternative mechanism to attain this control with such studies developing techniques to reproducibly control the mechanical environment in techniques which have potential to be scaled. In this review, the use of techniques such as finite element modelling and precision interferometric measurement are examined to provide context for a novel technique based on nanoscale vibration, also known as "nanokicking". Studies have shown this stimulus to alter cellular responses in both endothelial and mesenchymal stem cells (MSCs), particularly in increased proliferation rate and induced osteogenesis respectively. Endothelial cell lines were exposed to nanoscale vibration amplitudes across a frequency range of 1-100 Hz, and MSCs primarily at 1 kHz. This technique provides significant potential benefits over existing technologies, as cellular responses can be initiated without the use of expensive engineering techniques and/or chemical induction factors. Due to the reproducible and scalable nature of the apparatus it is conceivable that nanokicking could be used for controlling cell behaviour within a wide array of high throughput procedures in the research environment, within drug discovery, and for clinical/therapeutic applications.

STATEMENT OF SIGNIFICANCE

The results discussed within this article summarise the potential benefits of using nanoscale vibration protocols for controlling cell behaviour. There is a significant need for reliable tissue models within the clinical and pharma industries, and the control of cell behaviour and stem cell differentiation would be highly beneficial. The full potential of this method of controlling cell behaviour has not yet been realised.

A Mechanobiology-based Algorithm to Optimize the Microstructure Geometry of Bone Tissue Scaffolds

Complexity of scaffold geometries and biological mechanisms involved in the bone generation process make the design of scaffolds a quite challenging task. The most common approaches utilized in bone tissue engineering require costly protocols and time-consuming experiments. In this study we present an algorithm that, combining parametric finite element models of scaffolds with numerical optimization methods and a computational mechano-regulation model, is able to predict the optimal scaffold microstructure. The scaffold geometrical parameters are perturbed until the best geometry that allows the largest amounts of bone to be generated, is reached. We study the effects of the following factors: (1) the shape of the pores; (2) their spatial distribution; (3) the number of pores per unit area. The optimal dimensions of the pores have been determined for different values of scaffold Young's modulus and compression loading acting on the scaffold upper surface. Pores with rectangular section were predicted to lead to the formation of larger amounts of bone compared to square section pores; similarly, elliptic pores were predicted to allow the generation of greater amounts of bone compared to circular pores. The number of pores per unit area appears to have rather negligible effects on the bone regeneration process. Finally, the algorithm predicts that for increasing loads, increasing values of the scaffold Young's modulus are preferable. The results shown in the article represent a proof-of-principle demonstration of the possibility to optimize the scaffold microstructure geometry based on mechanobiological criteria.

Biomechanical forces in the skeleton and their relevance to bone metastasis: biology and engineering considerations

Bone metastasis represents the leading cause of breast cancer related-deaths. However, the effect of skeleton-associated biomechanical signals on the initiation, progression, and therapy response of breast cancer bone metastasis is largely unknown. This review seeks to highlight possible functional connections between skeletal mechanical signals and breast cancer bone metastasis and their contribution to clinical outcome. It provides an introduction to the physical and biological signals underlying bone functional adaptation and discusses the modulatory roles of mechanical loading and breast cancer metastasis in this process. Following a definition of biophysical design criteria, in vitro and in vivo approaches from the fields of bone biomechanics and tissue engineering that may be suitable to investigate breast cancer bone metastasis as a function of varied mechano-signaling will be reviewed. Finally, an outlook of future opportunities and challenges associated with this newly emerging field will be provided.

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.

Investigation of the in vitro culture process for skeletal-tissue-engineered constructs using computational fluid dynamics and experimental methods

The in vitro culture process via bioreactors is critical to create tissue-engineered constructs (TECs) to repair or replace the damaged tissues/organs in various engineered applications. In the past, the TEC culture process was typically treated as a black box and performed on the basis of trial and error. Recently, computational fluid dynamics (CFD) has demonstrated its potential to analyze the fluid flow inside and around the TECs, therefore, being able to provide insight into the culture process, such as information on the velocity field and shear stress distribution that can significantly affect such cellular activities as cell viability and proliferation during the culture process. This paper briefly reviews the CFD and experimental methods used to investigate the in vitro culture process of skeletal-type TECs in bioreactors, where mechanical deformation of the TEC can be ignored. Specifically, this paper presents CFD modeling approaches for the analysis of the velocity and shear stress fields, mass transfer, and cell growth during the culture process and also describes various particle image velocimetry (PIV) based experimental methods to measure the velocity and shear stress in the in vitro culture process. Some key issues and challenges are also identified and discussed along with recommendations for future research.

Micro-computed tomography based computational fluid dynamics for the determination of shear stresses in scaffolds within a perfusion bioreactor

Perfusion bioreactors are known to exert shear stresses on cultured cells, leading to cell differentiation and enhanced extracellular matrix deposition on scaffolds. The influence of the scaffold's porous microstructure is investigated for a polycaprolactone (PCL) scaffold with a regular microarchitecture and a silk fibroin (SF) scaffold with an irregular network of interconnected pores. Their complex 3D geometries are imaged by micro-computed tomography and used in direct pore-level simulations of the entire scaffold-bioreactor system to numerically solve the governing mass and momentum conservation equations for fluid flow through porous media. The velocity field and wall shear stress distribution are determined for both scaffolds. The PCL scaffold exhibited an asymmetric distribution with peak and plateau, while the SF scaffold exhibited a homogenous distribution and conditioned the flow more efficiently than the PCL scaffold. The methodology guides the design and optimization of the scaffold geometry.

Combining micro computed tomography and three-dimensional registration to evaluate local strains in shape memory scaffolds

Appropriate mechanical stimulation of bony tissue enhances osseointegration of load-bearing implants. Uniaxial compression of porous implants locally results in tensile and compressive strains. Their experimental determination is the objective of this study. Selective laser melting is applied to produce open-porous NiTi scaffolds of cubic units. To measure displacement and strain fields within the compressed scaffold, the authors took advantage of synchrotron radiation-based micro computed tomography during temperature increase and non-rigid three-dimensional data registration. Uniaxial scaffold compression of 6% led to local compressive and tensile strains of up to 15%. The experiments validate modeling by means of the finite element method. Increasing the temperature during the tomography experiment from 15 to 37°C at a rate of 4 K h(-1), one can locally identify the phase transition from martensite to austenite. It starts at ≈ 24°C on the scaffolds bottom, proceeds up towards the top and terminates at ≈ 34°C on the periphery of the scaffold. The results allow not only design optimization of the scaffold architecture, but also estimation of maximal displacements before cracks are initiated and of optimized mechanical stimuli around porous metallic load-bearing implants within the physiological temperature range.

Predicting the elastic properties of selective laser sintered PCL/β-TCP bone scaffold materials using computational modelling

This study assesses the ability of finite element (FE) models to capture the mechanical behaviour of sintered orthopaedic scaffold materials. Individual scaffold struts were fabricated from a 50:50 wt% poly-ε-caprolactone (PCL)/β-tricalcium phosphate (β-TCP) blend, using selective laser sintering. The tensile elastic modulus of single struts was determined experimentally. High resolution FE models of single struts were generated from micro-CT scans (28.8 μm resolution) and an effective strut elastic modulus was calculated from tensile loading simulations. Three material assignment methods were employed: (1) homogeneous PCL elastic constants, (2) composite PCL/β-TCP elastic constants based on rule of mixtures, and (3) heterogeneous distribution of micromechanically-determined elastic constants. In comparison with experimental results, the use of homogeneous PCL properties gave a good estimate of strut modulus; however it is not sufficiently representative of the real material as it neglects the β-TCP phase. The rule of mixtures method significantly overestimated strut modulus, while there was no significant difference between strut modulus evaluated using the micromechanically-determined elastic constants and experimentally evaluated strut modulus. These results indicate that the multi-scale approach of linking micromechanical modelling of the sintered scaffold material with macroscale modelling gives an accurate prediction of the mechanical behaviour of the sintered structure.

Modelling and Tissue Engineering of Three Layers of Calvarial Bone as a Biomimetic Scaffold

In this Study, a New Zealand Rabbit Parietal Bone Was Cross-Sectioned, and Parameters such as Entire Thickness and the Thicknesses of the Compact and Spongy Tables Were Morphometrically Measured by Imagej Software. the Pore Size of the Cancellous Table Was Also Analysed, and a Calvarial Bone Model Was Created. Based upon a Natural Model for Bone Repair, a Nano-Structured Scaffold Was Designed Using Bioglass and Gelatin (BG) as its Main Components. the Scaffold Was Prepared Using Layer Solvent Casting Combined with Freeze-Drying, Layering Techniques, and other Commonly Used Techniques. the Fabricated BG Scaffolds Were Made with Different Percentages of Nanoparticles, and the 10% and 30% Constructions Were Found to Be Respectively Similar to Compact and Spongy Bone. we Fabricated Three Lamellar Scaffolds with Two Compact Layers on the outside and One Spongy Layer in the Middle to Mimic the Composition and Structure of Natural Bone. the Chemical, Physical, and Biological Tests (including Cell Seeding on Scaffold and MTT Assay) that Evaluated this Scaffold Examined its Capacity to Promote Bone Repair. Fabricated Scaffolds Implanted in Rabbit Calvaria and Evaluated the Bone Repair by X-Ray. this Mimetic BG Scaffold Could Be an Excellent Candidate for a Synthetic Calvarial Bone Graft.

Finite element method (FEM), mechanobiology and biomimetic scaffolds in bone tissue engineering

Techniques of bone reconstructive surgery are largely based on conventional, non-cell-based therapies that rely on the use of durable materials from outside the patient's body. In contrast to conventional materials, bone tissue engineering is an interdisciplinary field that applies the principles of engineering and life sciences towards the development of biological substitutes that restore, maintain, or improve bone tissue function. Bone tissue engineering has led to great expectations for clinical surgery or various diseases that cannot be solved with traditional devices. For example, critical-sized defects in bone, whether induced by primary tumor resection, trauma, or selective surgery have in many cases presented insurmountable challenges to the current gold standard treatment for bone repair. The primary purpose of bone tissue engineering is to apply engineering principles to incite and promote the natural healing process of bone which does not occur in critical-sized defects. The total market for bone tissue regeneration and repair was valued at $1.1 billion in 2007 and is projected to increase to nearly $1.6 billion by 2014.Usually, temporary biomimetic scaffolds are utilized for accommodating cell growth and bone tissue genesis. The scaffold has to promote biological processes such as the production of extra-cellular matrix and vascularisation, furthermore the scaffold has to withstand the mechanical loads acting on it and to transfer them to the natural tissues located in the vicinity. The design of a scaffold for the guided regeneration of a bony tissue requires a multidisciplinary approach. Finite element method and mechanobiology can be used in an integrated approach to find the optimal parameters governing bone scaffold performance.In this paper, a review of the studies that through a combined use of finite element method and mechano-regulation algorithms described the possible patterns of tissue differentiation in biomimetic scaffolds for bone tissue engineering is given. Firstly, the generalities of the finite element method of structural analysis are outlined; second, the issues related to the generation of a finite element model of a given anatomical site or of a bone scaffold are discussed; thirdly, the principles on which mechanobiology is based, the principal theories as well as the main applications of mechano-regulation models in bone tissue engineering are described; finally, the limitations of the mechanobiological models and the future perspectives are indicated.