Oxygen gradients in tissue-engineered PEGT/PBT cartilaginous constructs: measurement and modeling

The supply of oxygen within three-dimensional tissue-engineered (TE) cartilage polymer constructs is mainly by diffusion. Oxygen consumption by cells results in gradients in the oxygen concentration. The aims of this study were, firstly, to identify the gradients within TE cartilage polymer constructs and, secondly, to predict the profiles during in vitro culture. A glass microelectrode system was adapted and used to penetrate cartilage and TE cartilaginous constructs, yielding reproducible measurements with high spatial resolution. Cartilage polymer constructs were cultured for up to 41 days in vitro. Oxygen concentrations, as low as 2-5%, were measured within the center of these constructs. At the beginning of in vitro culture, the oxygen gradients were steeper in TE constructs in comparison to native tissue. Nevertheless, during the course of culture, oxygen concentrations approached the values measured in native tissue. A mathematical model was developed which yields oxygen profiles within cartilage explants and TE constructs. Model input parameters were assessed, including the diffusion coefficient of cartilage (2.2 x 10(-9)) + (0.4 x 10(-9) m(2) s(-1)), 70% of the diffusion coefficient of water and the diffusion coefficient of constructs (3.8 x 10(-10) m(2) s(-1)). The model confirmed that chondrocytes in polymer constructs cultured for 27 days have low oxygen requirements (0.8 x 10(-19) mol m(-3) s(-1)), even lower than chondrocytes in native cartilage. The ability to measure and predict local oxygen tensions offers new opportunities to obtain more insight in the relation between oxygen tension and chondrogenesis.     

Osteochondral tissue coculture: An in vitro and in silico approach

Osteochondral tissue engineering aims to regenerate functional tissue-mimicking physiological properties of injured cartilage and its subchondral bone. Given the distinct structural and biochemical difference between bone and cartilage, bilayered scaffolds, and bioreactors are commonly employed. We present an osteochondral culture system which cocultured ATDC5 and MC3T3-E1 cells on an additive manufactured bilayered scaffold in a dual-chamber perfusion bioreactor. Also, finite element models (FEM) based on the microcomputed tomography image of the manufactured scaffold as well as on the computer-aided design (CAD) were constructed; the microenvironment inside the two FEM was studied and compared. In vitro results showed that the coculture system supported osteochondral tissue growth in terms of cell viability, proliferation, distribution, and attachment. In silico results showed that the CAD and the actual manufactured scaffold had significant differences in the flow velocity, differentiation media mixing in the bioreactor and fluid-induced shear stress experienced by the cells. This system was shown to have the desired microenvironment for osteochondral tissue engineering and it can potentially be used as an inexpensive tool for testing newly developed pharmaceutical products for osteochondral defects.     

An experimental and numerical study on the transverse deformations in tensile test of tendons

The transverse deformations of tendons assessed in tensile tests seems to constitute a controversial issue in literature. On the one hand, large positive variations of the Poisson’s ratio have been reported, indicating volume reduction under tensile states. On the other hand, negative values were also observed, pointing out an auxetic material response. Based on these experimental observations, the following question is raised: Are these large and discrepant transverse deformations intrinsically related to the constitutive response of tendons or they result from artifacts of the mechanical test setup? In order to provide further insights to this question, an experimental and numerical study on the transverse kinematics of tendons was carried out. Tensile experiments were performed in branches of deep digital flexor tendons of domestic porcine, where the transverse displacements were measured by two high-speed, high-accuracy optical digital micrometers placed transversely to one another. Aiming at a better understanding of the effects of the mechanical test setup in the transverse measurements, a three-dimensional finite element model is proposed to resemble the tensile experiment. The main achieved results strongly support the following hypotheses regarding tensile tests of tendons: the clamping region considerably affects the kinematics of the specimen even at a large distance from the clamps; the transverse deformations are mainly ruled by stiff fibers embedded in a soft matrix; the generalization of the Poisson’s ratio to draw conclusions about changes in volume of tendons may lead to misinterpretations.     

Combined measurement and modeling of specimen-specific knee mechanics for healthy and ACL-deficient conditions

Quantifying the mechanical environment at the knee is crucial for developing successful rehabilitation and surgical protocols. Computational models have been developed to complement in vitro studies, but are typically created to represent healthy conditions, and may not be useful in modeling pathology and repair. Thus, the objective of this study was to create finite element (FE) models of the natural knee, including specimen-specific tibiofemoral (TF) and patellofemoral (PF) soft tissue structures, and to evaluate joint mechanics in intact and ACL-deficient conditions. Simulated gait in a whole joint knee simulator was performed on two cadaveric specimens in an intact state and subsequently repeated following ACL resection. Simulated gait was performed using motor-actuated quadriceps, and loads at the hip and ankle. Specimen-specific FE models of these experiments were developed in both intact and ACL-deficient states. Model simulations compared kinematics and loading of the experimental TF and PF joints, with average RMS differences [max] of 3.0° [8.2°] and 2.1° [8.4°] in rotations, and 1.7 [3.0] and 2.5 [5.1] mm in translations, for intact and ACL-deficient states, respectively. The timing of peak quadriceps force during stance and swing phase of gait was accurately replicated within 2° of knee flexion and with an average error of 16.7% across specimens and pathology. Ligament recruitment patterns were unique in each specimen; recruitment variability was likely influenced by variations in ligament attachment locations. ACL resections demonstrated contrasting joint mechanics in the two specimens with altered knee motion shown in one specimen (up to 5 mm anterior tibial translation) while increased TF joint loading was shown in the other (up to 400 N).     

Synthesis rates and binding kinetics of matrix products in engineered cartilage constructs using chondrocyte-seeded agarose gels

Large-sized cartilage constructs suffer from inhomogeneous extracellular matrix deposition due to insufficient nutrient availability. Computational models of nutrient consumption and tissue growth can be utilized as an efficient alternative to experimental trials to optimize the culture of large constructs; models require system-specific growth and consumption parameters. To inform models of the [bovine chondrocyte]−[agarose gel] system, total synthesis rate (matrix accumulation rate+matrix release rate) and matrix retention fractions of glycosaminoglycans (GAG), collagen, and cartilage oligomeric matrix protein (COMP) were measured either in the presence (continuous or transient) or absence of TGF-β3 supplementation. TGF-β3's influences on pyridinoline content and mechanical properties were also measured. Reversible binding kinetic parameters were characterized using computational models. Based on our recent nutrient supplementation work, we measured glucose consumption and critical glucose concentration for tissue growth to computationally simulate the culture of a human patella-sized tissue construct, reproducing the experiment of Hung et al. (2003). Transient TGF-β3 produced the highest GAG synthesis rate, highest GAG retention ratio, and the highest binding affinity; collagen synthesis was elevated in TGF-β3 supplementation groups over control, with the highest binding affinity observed in the transient supplementation group; both COMP synthesis and retention were lower than those for GAG and collagen. These results informed the modeling of GAG deposition within a large patella construct; this computational example was similar to the previous experimental results without further adjustments to modeling parameters. These results suggest that these nutrient consumption and matrix synthesis models are an attractive alternative for optimizing the culture of large-sized constructs.     

Specimen-specific modeling of hip fracture pattern and repair

Hip fracture remains a major health problem for the elderly. Clinical studies have assessed fracture risk based on bone quality in the aging population and cadaveric testing has quantified bone strength and fracture loads. Prior modeling has primarily focused on quantifying the strain distribution in bone as an indicator of fracture risk. Recent advances in the extended finite element method (XFEM) enable prediction of the initiation and propagation of cracks without requiring a priori knowledge of the crack path. Accordingly, the objectives of this study were to predict femoral fracture in specimen-specific models using the XFEM approach, to perform one-to-one comparisons of predicted and in vitro fracture patterns, and to develop a framework to assess the mechanics and load transfer in the fractured femur when it is repaired with an osteosynthesis implant. Five specimen-specific femur models were developed from in vitro experiments under a simulated stance loading condition. Predicted fracture patterns closely matched the in vitro patterns; however, predictions of fracture load differed by approximately 50% due to sensitivity to local material properties. Specimen-specific intertrochanteric fractures were induced by subjecting the femur models to a sideways fall and repaired with a contemporary implant. Under a post-surgical stance loading, model-predicted load sharing between the implant and bone across the fracture surface varied from 59%:41% to 89%:11%, underscoring the importance of considering anatomic and fracture variability in the evaluation of implants. XFEM modeling shows potential as a macro-level analysis enabling fracture investigations of clinical cohorts, including at-risk groups, and the design of robust implants.     

丝纤维支架材料的制备技术及其应用研究进展

丝纤维特别是丝素蛋白和蜘蛛丝蛋白作为具有良好生物相容性的高分了生物材料在组织工程和生物医学领域里有着广泛的应用。本文阐述了近年来在组织工程研究中所涉及的利用丝纤维进行支架材料制备、细胞培养和体内植入检测手段等方面的研究概况。     

Nutrient gradients in engineered cartilage: metabolic kinetics measurement and mass transfer modeling

Since tissue-engineered cartilage is avascular, both nutrient supply and metabolic waste removal rely on diffusion. As a result, gradients of nutrients and wastes exist through the construct. Previous models usually calculate gradients of oxygen, glucose, and lactic acid separately, without taking into account the complex interdependence between concentrations of these substrates and rates of metabolism. In this study, these interactions were experimentally examined and incorporated into diffusion models. One-dimensional diffusion-reaction models were developed for three typical culture conditions, that is, static culture, perfusion culture, and suspended culture. The profiles of oxygen, glucose, lactic acid, and pH in the cultured constructs were calculated simultaneously using measured metabolic rates. The maximum construct size and cell density which could be supported before nutrients were depleted in the construct center was identified; a function predicting the relationship between construct dimension and the maximum viable cell density was developed. For constructs incubated under static culture the model demonstrated that the gradients which developed through the medium could not be neglected. Perfusion cultures could support a considerably higher cell density than static cultures, while for batch cultures in a rotating bioreactor, the volume of medium also influences the maximum cell density that could be supported. This study provides useful guidance for design of engineered cartilage constructs.     

Cohesive finite element modeling of age-related toughness loss in human cortical bone

Although the age-related loss of bone quality has been implicated in bone fragility, a mechanistic understanding of the relationship is necessary for developing diagnostic and treatment modalities in the elderly population at risk of fracture. In this study, a finite element based cohesive zone model is developed and applied to human cortical bone in order to capture the experimentally shown rising crack growth behavior and age-related loss of bone toughness. The cohesive model developed here is based on a traction–crack opening displacement relationship representing the fracture processes in the vicinity of a propagating crack. The traction–displacement curve, defining the cohesive model, is composed of ascending and descending branches that incorporate material softening and nonlinearity. The results obtained indicate that, in contrast to initiation toughness, the finite element simulations of crack growth in compact tension (CT) specimens successfully capture the rising R-curve (propagation toughness) behavior and the age-related loss of bone toughness. In close correspondence with the experimentally observed decrease of 14–15% per decade, the finite element simulation results show a decrease of 13% in the R-curve slope per decade. The success of the simulations is a result of the ability of cohesive models to capture and predict the parameters related to bone fracture by representing the physical processes occurring in the vicinity of a propagating crack. These results illustrate that fracture mechanisms in the process zone control bone toughness and any modification to these would cause age-related toughness loss.     

Analytical and numerical approaches to coexistence of strains in a two-strain SIS model with diffusion

This article introduces a two-strain spatially explicit SIS epidemic model with space-dependent transmission parameters. We define reproduction numbers of the two strains, and show that the disease-free equilibrium will be globally stable if both reproduction numbers are below one. We also introduce the invasion numbers of the two strains which determine the ability of each strain to invade the single-strain equilibrium of the other strain. The main question that we address is whether the presence of spatial structure would allow the two strains to coexist, as the corresponding spatially homogeneous model leads to competitive exclusion. We show analytically that if both invasion numbers are larger than one, then there is a coexistence equilibrium. We devise a finite element numerical method to numerically confirm the stability of the coexistence equilibrium and investigate various competition scenarios between the strains. Finally, we show that the numerical scheme preserves the positive cone and converges of first order in the time variable and second order in the space variables.     

丝素蛋白在电纺丝法构建组织工程支架中的应用进展

丝素蛋白是天然高分子纤维蛋白,具有良好的物理和机械力学性能及生物相容性,因而在组织工程领域有着广阔的应用前景。文中对丝素蛋白的化学组成、分子结构特点、提取方法以及利用静电纺丝技术在组织工程化支架构建中的应用作了概述。总结了丝素蛋白在用于组织工程材料上的性能和优势以及在人工血管、皮肤、骨组织等工程化支架方面的应用情况,探讨了丝素蛋白支架对细胞在其上生长、增殖和功能的影响,同时对丝素蛋白在组织工程化食道支架及其他再生医学上的应用前景进行了展望。     

Finite element modeling of the breakage behavior of agricultural biomass pellets under different heights during handling and storage

It is very important to determine the amount of mechanical damage to biomass pellets during handling, transportation, and storage. However, it is difficult to determine the amount of damage to biomass pellets caused by existing external forces. However, a useful method is the finite element methods, which can be used in different engineering fields to simulate the posture of the material under defined boundary conditions. In this research, a drop test simulation of biomass pellet samples was performed by using the finite element method. An experimental study (compressive test) was carried out to measure some mechanical properties of the sample and use the obtained data in the finite element method simulation. The stress–strain curve of different biomass pellets was determined. Yield strength, Poisson’s ratio, ultimate strength and modulus of elasticity, and stress were identified. In the end, the maximum equivalent stress, highest contact force (generated normal force from target surface at impact), and shape of deformation of samples at impact were obtained from simulation results. The drop scenario was created with 25 steps after the impact site, and the FEM simulation was solved. The maximum stress value was 9.486 MPa, and the maximum generated force was 485.31 N. at step 8 of the FEM simulation. When the stress magnitudes were assessed, simulation outputs indicated that simulation stress values are inconsistent with experimental data.     

Enhancement of cell growth in tissue-engineering constructs under direct perfusion: Modeling and simulation

Perfusion bioreactors improve mass transfer in cell-scaffold constructs. We developed a mathematical model to simulate nutrient flow through cellular constructs. Interactions among cell proliferation, nutrient consumption, and culture medium circulation were investigated. The model incorporated modified Contois cell-growth kinetics that includes effects of nutrient saturation and limited cell growth. Nutrient uptake was depicted through the Michaelis-Menton kinetics. To describe the culture medium convection, the fluid flow outside the cell-scaffold construct was described by the Navier-Stokes equations, while the fluid dynamics within the construct was modeled by Brinkman's equation for porous media flow. Effects of the media perfusion were examined by including time-dependant porosity and permeability changes due to cell growth. The overall cell volume was considered to consist of cells and extracellular matrices (ECM) as a whole without treating ECM separately. Numerical simulations show when cells were cultured subjected to direct perfusion, they penetrated to a greater extent into the scaffold and resulted in a more uniform spatial distribution. The cell amount was increased by perfusion and ultimately approached an asymptotic value as the perfusion rates increased in terms of the dimensionless Peclet number that accounts for the ratio of nutrient perfusion to diffusion. In addition to enhancing the nutrient delivery, perfusion simultaneously imposes flow-mediated shear stress to the engineered cells. Shear stresses were found to increase with cell growth as the scaffold void space was occupied by the cell and ECM volumes. The macro average stresses increased from 0.2 mPa to 1 mPa at a perfusion rate of 20 microm/s with the overall cell volume fraction growing from 0.4 to 0.7, which made the overall permeability value decrease from 1.35 x 10(-2)cm(2) to 5.51 x 10(-4)cm(2). Relating the simulation results with perfusion experiments in literature, the average shear stresses were below the critical value that would induce the chondrocyte necrosis.     

Engineered bone culture in a perfusion bioreactor: a 2D computational study of stationary mass and momentum transport

Successful bone cell culture in large implants still is a challenge to biologists and requires a strict control of the physicochemical and mechanical environments. This study analyses from the transport phenomena viewpoint the limiting factors of a perfusion bioreactor for bone cell culture within fibrous and porous large implants (2.5 cm in length, a few cubic centimetres in volume, 250 μm in fibre diameter with approximately 60% porosity).

A two-dimensional mathematical model, based upon stationary mass and momentum transport in these implants is proposed and numerically solved. Cell oxygen consumption, in accordance theoretically with the Michaelis–Menten law, generates non linearity in the boundary conditions of the convection diffusion equation. Numerical solutions are obtained with a commercial code (Femlab® 3.1; Comsol AB, Stockholm, Sweden). Moreover, based on the simplification of transport equations, a simple formula is given for estimating the length of the oxygen penetration within the implant.

Results show that within a few hours of culture process and for a perfusion velocity of the order of 10^? 4 m s^? 1, the local oxygen concentration is everywhere sufficiently high to ensure a suitable cell metabolism. But shear stresses induced by the fluid flow with such a perfusion velocity are found to be locally too large (higher than 10^? 3 Pa). Suitable shear stresses are obtained by decreasing the velocity at the inlet to around 2 × 10^? 5 m s^? 1. But consequently hypoxic regions (low oxygen concentrations) appear at the downstream part of the implant.

Thus, it is suggested here that in the determination of the perfusion flow rate within a large implant, a compromise between oxygen supply and shear stress effects must be found in order to obtain a successful cell culture.     

Growth and differentiation of alveolar bone cells in tissue-engineered constructs and monolayer cultures

The ability to enhance bone regeneration by implanting autologous osteoblasts in combination with an appropriate scaffold would be of great clinical interest. The aim of our study was to compare the growth and differentiation of alveolar bone cells in tissue-engineered constructs and in monolayer cultures, as the basis for developing procedures for routine preparation of bone-like tissue constructs. Alveolar bone tissue was obtained from four human donors and explant cultures of the cells were established. Expanded cells were seeded on macroporous hydroxyapatite granules, and cultured in medium supplemented with osteogenic differentiation factors for up to 3 weeks. Control monolayer cultures were established in parallel, and cultured in media with or without osteogenic supplements. Cell proliferation, alkaline phosphatase (AP) activity and gene expression of AP, osteopontin and osteocalcin were determined under different culture conditions at weekly intervals. Cells in tissue constructs exhibited growth patterns similar to those in control monolayer cultures: enhanced proliferation was noted during the first 2 weeks of cultivation, followed by a decrease in cell numbers. AP activity at 3 weeks was higher in all cultures in osteogenic medium than in control medium. Gene expression levels were stable in monolayer cultures in both types of media whereas, in tissue constructs, they exhibited patterns of osteogenic differentiation. Light and scanning electron microscopy examination of the cell-seeded constructs showed uniform cell distribution, as well as cell attachment and growth into the interior region of the hydroxyapatite granules. Our results show that bone-like constructs with viable cells exhibiting differentiated phenotype can be prepared by cultivation of alveolar-bone cells on the tested hydroxyapatite granules.     

Excitability and isometric contractile properties of mammalian skeletal muscle constructs engineered in vitro

Summary Our purpose was to engineer three-dimensional skeletal muscle tissue constructs from primary cultures of adult rat myogenic precursor cells, and to measure their excitability and isometric contractile properties. The constructs, termed myooids, were muscle-like in appearance, excitability, and contractile function. The myooids were 12 mm long and ranged in diameter from 0.1 to 1 mm. The myooids were engineered with synthetic tendons at each end to permit the measurement of isometric contractile properties. Within each myooid the myotubes and fibroblasts were supported by an extracellular matrix generated by the cells themselves, and did not require a preexisting scaffold to define the size, shape, and general mechanical properties of the resulting structure. Once formed, the myooids contracted spontaneously at approximately 1 Hz, with peak-to-peak force amplitudes ranging from 3 to 30 μN. When stimulated electrically the myooids contracted to produce force. The myooids (n=14) had the following mean values: diameter of 0.49 mm, rheobase of 1.0 V/mm, chronaxie of 0.45 ms, twitch force of 215 μN, maximum isometric force of 440 μN, resting baseline force of 181 μN, and specific force of 2.9kN/m². The mean specific force was approximately 1% of the specific force generated by control adult rat muscle. Based on the functional data, the myotubes in the myooids appear to remain arrested in an early developmental state due to the absence of signals to promote expression of adult myosin isoforms.     

Tissue engineering of human cartilage in bioreactors using single and composite cell-seeded scaffolds

Chondrocytes isolated from human fetal epiphyseal cartilage were seeded under mixed conditions into 15-mm-diameter polyglycolic acid (PGA) scaffolds and cultured in recirculation column bioreactors to generate cartilage constructs. After seeding, the cell distributions in thick (4.75 mm) and thin (2.15 mm) PGA disks were nonuniform, with higher cell densities accumulating near the top surfaces. Composite scaffolds were developed by suturing together two thin PGA disks after seeding to manipulate the initial cell distribution before bioreactor culture. The effect of medium flow direction in the bioreactors, including periodic reversal of medium flow, was also investigated. The quality of the tissue-engineered cartilage was assessed after 5 weeks of culture in terms of the tissue wet weight, glycosaminoglycan (GAG), total collagen and collagen type II contents, histological analysis of cell, GAG and collagen distributions, and immunohistochemical analysis of collagen types I and II. Significant enhancement in construct quality was achieved using composite scaffolds compared with single PGA disks. Operation of the bioreactors with periodic medium flow reversal instead of unidirectional flow yielded further improvements in tissue weight and GAG and collagen contents with the composite scaffolds. At harvest, the constructs contained GAG concentrations similar to those measured in ex vivo human adult articular cartilage; however, total collagen and collagen type II levels were substantially lower than those in adult tissue. This study demonstrates that the location of regions of high cell density in the scaffold coupled with application of dynamic bioreactor operating conditions has a significant influence on the quality of tissue-engineered cartilage.     

Mathematical modeling of cell growth in a 3D scaffold and validation of static and dynamic cultures

Tissue engineering, an immensely important field in contemporary clinical practices, aims at the repair or replacement of damaged tissues. The mathematical model proposed herein shows the distribution and growth of cells in their characteristic time in a 3D scaffold model. This study contributes to the progress of simulation techniques in static and dynamic cultures of bone tissue. Brinkman, nutrient transport, and cell growth equations are brought together to quantify the growth behavior of cells. However, when a static culture is being studied, the Brinkman equation is eliminated. The model was validated by experimental cell culture using 3‐(4,5‐dimethylthiazol‐2‐yl)‐2,5‐diphenyltetrazolium bromide assay and scanning electron microscopy. Then, static and dynamic cultures were compared to assess the cell density and cell distribution in the scaffold. Cell counting after 21 days of cell culture showed that the number of cells increased 42‐fold in static and 53.5‐fold in dynamic cultures, which was in good agreement with our model estimations (37‐fold increase in the number of cells in static and 49‐fold increase in dynamic cultures). In conclusion, our mathematical model could predict cell distribution and growth in the scaffold.