Simulation of tissue differentiation in a scaffold as a function of porosity, Young's modulus and dissolution rate: Application of mechanobiological models in tissue engineering

Computational simulation methodologies for mechanobiological modelling: a cell-centred approach to neointima development in stents

The design of medical devices could be very much improved if robust tools were available for computational simulation of tissue response to the presence of the implant. Such tools require algorithms to simulate the response of tissues to mechanical and chemical stimuli. Available methodologies include those based on the principle of mechanical homeostasis, those which use continuum models to simulate biological constituents, and the cell-centred approach, which models cells as autonomous agents. In the latter approach, cell behaviour is governed by rules based on the state of the local environment around the cell; and informed by experiment. Tissue growth and differentiation requires simulating many of these cells together. In this paper, the methodology and applications of cell-centred techniques--with particular application to mechanobiology--are reviewed, and a cell-centred model of tissue formation in the lumen of an artery in response to the deployment of a stent is presented. The method is capable of capturing some of the most important aspects of restenosis, including nonlinear lesion growth with time. The approach taken in this paper provides a framework for simulating restenosis; the next step will be to couple it with more patient-specific geometries and quantitative parameter data.

Apatite-coated porous poly(lactic-co-glycolic acid) microspheres as an injectable bone substitute

Previously, we developed an apatite-coated non-porous poly(lactic-co-glycolic acid) (PLGA) microsphere (ANPM) as an injectable bone substitute. We hypothesized that an apatite-coated porous PLGA microsphere (APPM) would have enhanced osteogenic potential compared to that of an ANPM. To test the hypothesis, critical-sized bone defects were made in mouse calvaria, and APPMs and ANPMs were implanted in the defects for 8 weeks. New bone formed around both types of bone substitutes implanted in mouse calvarial defects. Importantly, the portion of bone-like tissue area in the implant cross-sectional area was significantly higher in the APPM group than in the ANPM group (36.9% versus 14.6%, P < 0.001). Fluorochrome-labeling analysis showed that bone regeneration occurred in the pores of implanted APPMs. The results show that APPM may be useful as a bone substitute in orthopedic applications.

On stiffness of scaffolds for bone tissue engineering-a numerical study

Tissue scaffolds are typically designed and fabricated to match native bone properties. However, it is unclear if this would lead to the best tissue ingrowth outcome within the scaffold as neo-tissue keeps changing the stiffness of entire construct. This paper presents a numerical method to address this issue for design optimization and assessment of tissue scaffolds. The elasticity tensors of two different types of bones are weighted by different multipliers before being used as the targets in scaffold design. A cost function regarding the difference between the effective elasticity tensor, calculated by the homogenization technique, and the target tensor, is minimized by using topology optimization procedure. It is found that different stiffnesses can lead to different remodeling results. The comparison confirms that bone remodeling is at its best when the scaffold elastic tensor matches or is slightly higher than the elastic properties of the host bone.

Poroviscoelastic modeling of liver biomechanical response in unconfined compression

Mechanistic modeling approaches are important for understanding how fluid and solid components of the liver interact during impact trauma. This study uses poroviscoelasticity (PVE) theory to simulate liver biomechanical response in unconfined compression stress relaxation experiments, for variable ramp strain rates ranging from 0.001 to 0.1 s(-1). Specimens included 17 ex vivo porcine liver samples tested in a humidified temperature-controlled chamber. Liver response was modeled using ABAQUS, and best-fit parameters were determined using non-linear least-squares algorithms. The PVE model was able to capture the behavior of porcine liver in unconfined compression, with regression analyses for the ramp phase demonstrating high correlation between model and experiment (R(2) > 0.993, slope > 0.833, p < 0.05). The advantage of PVE modeling over traditional viscoelastic modeling is the ability to examine interstitial fluid pressure as a contributor to tissue mechanical response. This strategy creates new opportunities for quantifying an injury mechanism (burst injury) that is common in blunt abdominal trauma, and will lead to advancement of high-fidelity virtual crash test dummies, and improved vehicle safety.

Influence of high insertion torque on implant placement: an anisotropic bone stress analysis

The aim of this study was to evaluate the influence of the high values of insertion torques on the stress and strain distribution in cortical and cancellous bones. Based on tomography imaging, a representative mathematical model of a partial maxilla was built using Mimics 11.11 and Solid Works 2010 softwares. Six models were built and each of them received an implant with one of the following insertion torques: 30, 40, 50, 60, 70 or 80 Ncm on the external hexagon. The cortical and cancellous bones were considered anisotropic. The bone/implant interface was considered perfectly bonded. The numerical analysis was carried out using Ansys Workbench 10.0. The convergence of analysis (6%) drove the mesh refinement. Maximum principal stress (σmax) and maximum principal strain (εmax) were obtained for cortical and cancellous bones around to implant. Pearson's correlation test was used to determine the correlation between insertion torque and stress concentration in the periimplant bone tissue, considering the significance level at 5%. The increase in the insertion torque generated an increase in the σmax and εmax values for cortical and cancellous bone. The σmax was smaller for the cancellous bone, with greater stress variation among the insertion torques. The εmax was higher in the cancellous bone in comparison to the cortical bone. According to the methodology used and the limits of this study, it can be concluded that higher insertion torques increased tensile and compressive stress concentrations in the periimplant bone tissue.

Mechano-regulation of mesenchymal stem cell differentiation and collagen organisation during skeletal tissue repair

A number of mechano-regulation theories have been proposed that relate the differentiation pathway of mesenchymal stem cells (MSCs) to their local biomechanical environment. During spontaneous repair processes in skeletal tissues, the organisation of the extracellular matrix is a key determinant of its mechanical fitness. In this paper, we extend the mechano-regulation theory proposed by Prendergast et al. (J Biomech 30(6):539-548, 1997) to include the role of the mechanical environment on the collagen architecture in regenerating soft tissues. A large strain anisotropic poroelastic material model is used in a simulation of tissue differentiation in a fracture subject to cyclic bending (Cullinane et al. in J Orthop Res 20(3):579-586, 2002). The model predicts non-union with cartilage and fibrous tissue formation in the defect. Predicted collagen fibre angles, as determined by the principal decomposition of strain- and stress-type tensors, are similar to the architecture seen in native articular cartilage and neoarthroses induced by bending of mid-femoral defects in rats. Both stress and strain-based remodelling stimuli successfully predicted the general patterns of collagen fibre organisation observed in vivo. This provides further evidence that collagen organisation during tissue differentiation is determined by the mechanical environment. It is envisioned that such predictive models can play a key role in optimising MSC-based skeletal repair therapies where recapitulation of the normal tissue architecture is critical to successful repair.

Processing of polycaprolactone and polycaprolactone-based copolymers into 3D scaffolds, and their cellular responses

Synthetic polymers have attracted much attention in tissue engineering due to their ability to modulate biomechanical properties. This study investigated the feasibility of processing poly(epsilon-caprolactone) (PCL) homopolymer, PCL-poly(ethylene glycol) (PEG) diblock, and PCL-PEG-PCL triblock copolymers into three-dimensional porous scaffolds. Properties of the various polymers were investigated by dynamic thermal analysis. The scaffolds were manufactured using the desktop robot-based rapid prototyping technique. Gross morphology and internal three-dimensional structure of scaffolds were identified by scanning electron microscopy and micro-computed tomography, which showed excellent fusion at the filament junctions, high uniformity, and complete interconnectivity of pore networks. The influences of process parameters on scaffolds' morphological and mechanical characteristics were studied. Data confirmed that the process parameters directly influenced the pore size, porosity, and, consequently, the mechanical properties of the scaffolds. The in vitro cell culture study was performed to investigate the influence of polymer nature and scaffold architecture on the adhesion of the cells onto the scaffolds using rabbit smooth muscle cells. Light, scanning electron, and confocal laser microscopy showed cell adhesion, proliferation, and extracellular matrix formation on the surface as well as inside the structure of both scaffold groups. The completely interconnected and highly regular honeycomb-like pore morphology supported bridging of the pores via cell-to-cell contact as well as production of extracellular matrix at later time points. The results indicated that the incorporation of hydrophilic PEG into hydrophobic PCL enhanced the overall hydrophilicity and cell culture performance of PCL-PEG copolymer. However, the scaffold architecture did not significantly influence the cell culture performance in this study.

Assessment of a mechano-regulation theory of skeletal tissue differentiation in an in vivo model of mechanically induced cartilage formation

Mechanical cues are known to regulate tissue differentiation during skeletal healing. Quantitative characterization of this mechano-regulatory effect has great therapeutic potential. This study tested an existing theory that shear strain and interstitial fluid flow govern skeletal tissue differentiation by applying this theory to a scenario in which a bending motion applied to a healing transverse osteotomy results in cartilage, rather than bone, formation. A 3-D finite element mesh was created from micro-computed tomography images of a bending-stimulated callus and was used to estimate the mechanical conditions present in the callus during the mechanical stimulation. Predictions regarding the patterns of tissues--cartilage, fibrous tissue, and bone--that formed were made based on the distributions of fluid velocity and octahedral shear strain. These predictions were compared to histological sections obtained from a previous study. The mechano-regulation theory correctly predicted formation of large volumes of cartilage within the osteotomy gap and many, though not all patterns of tissue formation observed throughout the callus. The results support the concept that interstitial fluid velocity and tissue shear strain are key mechanical stimuli for the differentiation of skeletal tissues.

Corroboration of mechanobiological simulations of tissue differentiation in an in vivo bone chamber using a lattice-modeling approach

It is well established that the mechanical environment modulates tissue differentiation, and a number of mechanoregulatory theories for describing the process have been proposed. In this study, simulations of an in vivo bone chamber experiment were performed that allowed direct comparison with experimental data. A mechanoregulation theory for mesenchymal stem cell differentiation based on a combination of fluid flow and shear strain (computed using finite element analysis) was implemented to predict tissue differentiation inside mechanically controlled bone chambers inserted into rat tibae. To simulate cell activity, a lattice approach with stochastic cell migration, proliferation, and selected differentiation was adopted; because of its stochastic nature, each run of the simulation gave a somewhat different result. Simulations predicted the load-dependency of the tissue differentiation inside the chamber and a qualitative agreement with histological data; however, the full variability found between specimens in the experiment could not be predicted by the mechanoregulation algorithm. This result raises the question whether tissue differentiation predictions can be linked to genetic variability in animal populations.

Nanohydroxyapatite/poly(ester urethane) scaffold for bone tissue engineering

Biodegradable viscoelastic poly(ester urethane)-based scaffolds show great promise for tissue engineering. In this study, the preparation of hydroxyapatite nanoparticles (nHA)/poly(ester urethane) composite scaffolds using a salt-leaching-phase inverse process is reported. The dispersion of nHA microaggregates in the polymer matrix were imaged by microcomputed X-ray tomography, allowing a study of the effect of the nHA mass fraction and process parameters on the inorganic phase dispersion, and ultimately the optimization of the preparation method. How the composite scaffold's geometry and mechanical properties change with the nHA mass fraction and the process parameters were assessed. Increasing the amount of nHA particles in the composite scaffold decreased the porosity, increased the wall thickness and consequently decreased the pore size. The Young's modulus of the poly(ester urethane) scaffold was improved by 50% by addition of 10 wt.% nHA (from 0.95+/-0.5 to 1.26+/-0.4 MPa), while conserving poly(ester urethane) viscoelastic properties and without significant changes in the scaffold macrostructure. Moreover, the process permitted the inclusion of nHA particles not only in the poly(ester urethane) matrix, but also at the surface of the scaffold pores, as shown by scanning electron microscopy. nHA/poly(ester urethane) composite scaffolds have great potential as osteoconductive constructs for bone tissue engineering.

Bilayered scaffolds for osteochondral tissue engineering

Osteoarthritis (OA) is a prevalent degenerative joint disease that places a significant burden on the socioeconomic efficacy of communities around the world. Tissue engineering repair of articular cartilage in synovial joints represents a potential OA treatment strategy superior to current surgical techniques. In particular, osteochondral tissue engineering, which promotes the simultaneous regeneration of articular cartilage and underlining subchondral bone, may be a clinically relevant approach toward impeding OA progression. The unique and complex functional demands of the two contrasting tissues that comprise osteochondral tissue require the use of bilayered scaffolds to promote individual growth of both on a single integrated implant. This paper reviews the three current bilayered scaffold strategies applied to solve this challenging problem, with a focus on the need for an innovative approach to design and fabrication of new optimized scaffold combinations to reinforce materials science as an important element of osteochondral tissue engineering.

Potential and bottlenecks of bioreactors in 3D cell culture and tissue manufacturing

Over the last decade, we have witnessed an increased recognition of the importance of 3D culture models to study various aspects of cell physiology and pathology, as well as to engineer implantable tissues. As compared to well-established 2D cell-culture systems, cell/tissue culture within 3D porous biomaterials has introduced new scientific and technical challenges associated with complex transport phenomena, physical forces, and cell-microenvironment interactions. While bioreactor-based 3D model systems have begun to play a crucial role in addressing fundamental scientific questions, numerous hurdles currently impede the most efficient utilization of these systems. We describe how computational modeling and innovative sensor technologies, in conjunction with well-defined and controlled bioreactor-based 3D culture systems, will be key to gain further insight into cell behavior and the complexity of tissue development. These model systems will lay a solid foundation to further develop, optimize, and effectively streamline the essential bioprocesses to safely and reproducibly produce appropriately scaled tissue grafts for clinical studies.

Experimental-computational evaluation of human bone marrow stromal cell spreading on trabecular bone structures

The clinical application of macro-porous scaffolds for bone regeneration is significantly affected by the problem of insufficient cell colonization. Given the wide variety of different scaffold structures used for tissue engineering it is essential to derive relationships for cell colonization independent of scaffold architecture. To study cell population spreading on 3D structures decoupled from nutrient limitations, an in vitro culture system was developed consisting of thin slices of human trabecular bone seeded with Human Bone Marrow Stromal Cells, combined with dedicated microCT imaging and computational modeling of cell population spreading. Only the first phase of in vitro scaffold colonization was addressed, in which cells migrate and proliferate up to the stage when the surface of the bone is covered as a monolayer, a critical prerequisite for further tissue formation. The results confirm the model's ability to represent experimentally observed cell population spreading. The key advantage of the computational model was that by incorporating complex 3D structure, cell behavior can be characterized quantitatively in terms of intrinsic migration parameters, which could potentially be used for predictions on different macro-porous scaffolds subject to additional experimental validation. This type of modeling will prove useful in predicting cell colonization and improving strategies for skeletal tissue engineering.

Computer-aided design and finite-element modelling of biomaterial scaffolds for bone tissue engineering

Scaffold biomaterials for tissue engineering can be produced in many different ways depending on the applications and the materials used. Most research into new biomaterials is based on an experimental trial-and-error approach that limits the possibility of making many variations to a single material and studying its interaction with its surroundings. Instead, computer simulation applied to tissue engineering can offer a more exhaustive approach to test and screen out biomaterials. In this paper, a review of the current approach in biomaterials designed through computer-aided design (CAD) and through finite-element modelling is given. First we review the approach used in tissue engineering in the development of scaffolds and the interactions existing between biomaterials, cells and mechanical stimuli. Then, scaffold fabrication through CAD is presented and characterization of existing scaffolds through computed images is reviewed. Several case studies of finite-element studies in tissue engineering show the usefulness of computer simulations in determining the mechanical environment of cells when seeded into a scaffold and the proper design of the geometry and stiffness of the scaffold. This creates a need for more advanced studies that include aspects of mechanobiology in tissue engineering in order to be able to predict over time the growth and differentiation of tissues within scaffolds. Finally, current perspectives indicate that more efforts need to be put into the development of such advanced studies, with the removal of technical limitations such as computer power and the inclusion of more accurate biological and genetic processes into the developed algorithms.

Computational modelling of the mechanical environment of osteogenesis within a polylactic acid-calcium phosphate glass scaffold

A computational model based on finite element method (FEM) and computational fluid dynamics (CFD) is developed to analyse the mechanical stimuli in a composite scaffold made of polylactic acid (PLA) matrix with calcium phosphate glass (Glass) particles. Different bioreactor loading conditions were simulated within the scaffold. In vitro perfusion conditions were reproduced in the model. Dynamic compression was also reproduced in an uncoupled fluid-structure scheme: deformation level was studied analyzing the mechanical response of scaffold alone under static compression while strain rate was studied considering the fluid flow induced by compression through fixed scaffold. Results of the model show that during perfusion test an inlet velocity of 25 microm/s generates on scaffold surface a fluid flow shear stress which may stimulate osteogenesis. Dynamic compression of 5% applied on the PLA-Glass scaffold with a strain rate of 0.005 s(-1) has the benefit to generate mechanical stimuli based on both solid shear strain and fluid flow shear stress on large scaffold surface area. Values of perfusion inlet velocity or compression strain rate one order of magnitude lower may promote cell proliferation while values one order of magnitude higher may be detrimental for cells. FEM-CFD scaffold models may help to determine loading conditions promoting bone formation and to interpret experimental results from a mechanical point of view.

A mathematical approach to bone tissue engineering

Tissue engineering is becoming consolidated in the biomedical field as one of the most promising strategies in tissue repair and regenerative medicine. Within this discipline, bone tissue engineering involves the use of cell-loaded porous biomaterials, i.e. bioscaffolds, to promote bone tissue regeneration in bone defects or diseases such as osteoporosis, although it has not yet been incorporated into daily clinical practice. The overall success of a particular bone tissue engineering application depends strongly on scaffold design parameters, which do away with long and expensive clinical protocols. Computer simulation is a useful tool that may reduce animal experiments and help to identify optimal patient-specific designs after concise model validation. In this paper, we present a novel mathematical approach to bone regeneration within scaffolds, based on a multiscale framework. Results are presented over an actual scaffold microstructure, showing the potential of computer simulation, and how it can aid in the task of making bone tissue engineering a reality in clinical practice.

Rheological properties of cross-linked hyaluronan-gelatin hydrogels for tissue engineering

Hydrogels that mimic the natural extracellular matrix (ECM) are used in three-dimensional cell culture, cell therapy, and tissue engineering. A semi-synthetic ECM based on cross-linked hyaluronana offers experimental control of both composition and gel stiffness. The mechanical properties of the ECM in part determine the ultimate cell phenotype. We now describe a rheological study of synthetic ECM hydrogels with storage shear moduli that span three orders of magnitude, from 11 to 3 500 Pa, a range important for engineering of soft tissues. The concentration of the chemically modified HA and the cross-linking density were the main determinants of gel stiffness. Increase in the ratio of thiol-modified gelatin reduced gel stiffness by diluting the effective concentration of the HA component.

"May the force be with you": 14th Samuel Haughton lecture

This paper presents the 14th Samuel Haughton lecture delivered on the 26th of January 2008. The lecture began by describing Haughton's research on animal mechanics. Haughton opposed Charles Darwin's theory of natural selection using the argument that the skeleton obeys the 'principle of least action' and therefore must have been designed with that principle in mind. In the course of his research he dissected many animals, including albatrosses, cassowaries, llamas, tigers, jackals and jaguars. He took anatomical measurements and did calculations to prove that muscle attachment sites were optimally located. The relationship between optimality and evolution continues to be studied. Computer simulations show optimality is difficult to achieve. This is because, even if optimality could be defined, the gene recombinations required to evolve an optimal phenotype may not exist. The drive towards optimality occurs under gravitational forces. Simulations to predict mechano-regulation of tissue differentiation and remodelling have been developed and tested. They have been used to design biomechanically optimized scaffolds for regenerative medicine and to identify the mechanoregularory mechanisms in osteoporosis. It is proposed that an important development in bioengineering will be the discovery of algorithms that can be used for the prediction of mechano-responsiveness in biological tissues.

A finite element study of mechanical stimuli in scaffolds for bone tissue engineering

Mechanical stimuli are one of the factors that affect cell proliferation and differentiation in the process of bone tissue regeneration. Knowledge on the specific deformation sensed by cells at a microscopic level when mechanical loads are applied is still missing in the development of biomaterials for bone tissue engineering. The objective of this study was to analyze the behavior of the mechanical stimuli within some calcium phosphate-based scaffolds in terms of stress and strain distributions in the solid material phase and fluid velocity, fluid pressure and fluid shear stress distributions in the pores filled of fluid, by means of micro computed tomographed (CT)-based finite element (FE) models. Two samples of porous materials, one of calcium phosphate-based cement and another of biodegradable glass, were used. Compressive loads equivalent to 0.5% of compression applied to the solid material phase and interstitial fluid flows with inlet velocities of 1, 10 and 100 microm/s applied to the interconnected pores were simulated, changing also the inlet side and the viscosity of the medium. Similar strain distributions for both materials were found, with compressive and tensile strain maximal values of 1.6% and 0.6%, respectively. Mean values were consistent with the applied deformation. When 10 microm/s of inlet fluid velocity and 1.45 Pas viscosity, maximal values of fluid velocity were 12.76 mm/s for CaP cement and 14.87 mm/s for glass. Mean values were consistent with the inlet ones applied, and mean values of shear stress were around 5 x 10(-5)Pa. Variations on inlet fluid velocity and fluid viscosity produce proportional and independent changes in fluid velocity, fluid shear stress and fluid pressure. This study has shown how mechanical loads and fluid flow applied on the scaffolds cause different levels of mechanical stimuli within the samples according to the morphology of the materials.