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

Evaluation of rabbit adipose derived stem cells fate in perfused multilayered silk fibroin composite scaffold for Osteochondral repair

Development of osteochondral tissue engineering approaches using scaffolds seeded with stem cells in association with mechanical stimulations has been recently considered as a promising technique for the repair of this tissue. In this study, an integrated and biomimetic trilayered silk fibroin (SF) scaffold containing SF nanofibers in each layer was fabricated. The osteogenesis and chondrogenesis of stem cells seeded on the fabricated scaffolds were investigated under a perfusion flow. 3-Dimethylthiazol-2,5-diphenyltetrazolium bromide assay showed that the perfusion flow significantly enhanced cell viability and proliferation. Analysis of gene expression by stem cells revealed that perfusion flow had significantly upregulated the expression of osteogenic and chondrogenic genes in the bone and cartilage layers and downregulated the hypertrophic gene expression in the intermediate layer of the scaffold. In conclusion, applying flow perfusion on the prepared integrated trilayered SF-based scaffold can support osteogenic and chondrogenic differentiation for repairing osteochondral defects.

Perfusion of MC3T3E1 Preosteoblast Spheroids within Polysaccharide-Based Hydrogel Scaffolds: An Experimental and Numerical Study at the Bioreactor Scale

The traditional 3D culture systems in vitro lack the biological and mechanical spatiotemporal stimuli characteristic to native tissue development. In our study, we combined porous polysaccharide-based hydrogel scaffolds with a bioreactor-type perfusion device that generates favorable mechanical stresses while enhancing nutrient transfers. MC3T3E1 mouse osteoblasts were seeded in the scaffolds and cultivated for 3 weeks under dynamic conditions at a perfusion rate of 10 mL min^-1. The spatial distribution of the cells labeled with superparamagnetic iron oxide nanoparticles was visualized by MRI. Confocal microscopy was used to assess cell numbers, their distribution inside the scaffolds, cell viability, and proliferation. The oxygen diffusion coefficient in the hydrogel was measured experimentally. Numerical simulations of the flow and oxygen transport within the bioreactor were performed using a lattice Boltzmann method with a two-relaxation time scheme. Last, the influence of cell density and spheroid size on cell oxygenation was investigated. The cells spontaneously organized into spheroids with a diameter of 30-100 μm. Cell viability remained unchanged under dynamic conditions but decreased under static culture. The cell proliferation (Ki67 expression) in spheroids was not observed. The flow simulation showed that the local fluid velocity reached 27 mm s^-1 at the height where the cross-sectional area of the flow was the smallest. The shear stress exerted by the fluid on the scaffolds may locally rise to 100 mPa, compared with the average value of 25 mPa. The oxygen diffusion coefficient in the hydrogel was 1.6×10-9 m² s^-1. The simulation of oxygen transport and consumption confirmed that the cells in spheroids did not suffer from hypoxia when the bioreactor was perfused at 10 mL min^-1, and suggested the existence of optimal spheroid size and spacing for appropriate oxygenation. Collectively, these findings enabled us to define the optimal conditions inside the bioreactor for an efficient in vitro cell organization and survival in spheroids, which are paramount to future applications with organoids.

Effects of Elasticity on Cell Proliferation in a Tissue-Engineering Scaffold Pore

Scaffolds engineered for in vitro tissue engineering consist of multiple pores where cells can migrate along with nutrient-rich culture medium. The presence of the nutrient medium throughout the scaffold pores promotes cell proliferation, and this process depends on several factors such as scaffold geometry, nutrient medium flow rate, shear stress, cell-scaffold focal adhesions and elastic properties of the scaffold material. While numerous studies have addressed the first four factors, the mathematical approach described herein focuses on cell proliferation rate in elastic scaffolds, under constant flux of nutrients. As cells proliferate, the scaffold pores radius shrinks and thus, in order to sustain the nutrient flux, the inlet applied pressure on the upstream side of the scaffold pore must be increased. This results in expansion of the elastic scaffold pore, which in turn further increases the rate of cell proliferation. Considering the elasticity of the scaffold, the pore deformation allows further cellular growth beyond that of inelastic conditions. In this paper, our objectives are as follows: (i) Develop a mathematical model for describing fluid dynamics, scaffold elasticity and cell proliferation for scaffolds consist of identical nearly cylindrical pores; (ii) Solve the models and then simulate cellular proliferation within an elastic pore. The simulation can emulate real life tissue growth in a scaffold and offer a solution which reduces the numerical burdens. Lastly, our results demonstrated are in qualitative agreement with experimental observations reported in the literature.

Generation and evaluation of input values for computational analysis of transport processes within tissue cultures

Techniques for tissue culture have seen significant advances during the last decades and novel 3D cell culture systems have become available. To control their high complexity, experimental techniques and their Digital Twins (modelling and computational tools) are combined to link different variables to process conditions and critical process parameters. This allows a rapid evaluation of the expected product quality. However, the use of mathematical simulation and Digital Twins is critically dependent on the precise description of the problem and correct input parameters. Errors here can lead to dramatically wrong conclusions. The intention of this review is to provide an overview of the state‐of‐the‐art and remaining challenges with respect to generating input values for computational analysis of mass and momentum transport processes within tissue cultures. It gives an overview on relevant aspects of transport processes in tissue cultures as well as modelling and computational tools to tackle these problems. Further focus is on techniques used for the determination of cell‐specific parameters and characterization of culture systems, including sensors for on‐line determination of relevant parameters. In conclusion, tissue culture techniques are well‐established, and modelling tools are technically mature. New sensor technologies are on the way, especially for organ chips. The greatest remaining challenge seems to be the proper addressing and handling of input parameters required for mathematical models. Following Good Modelling Practice approaches when setting up and validating computational models is, therefore, essential to get to better estimations of the interesting complex processes inside organotypic tissue cultures in the future.

A 3D Mathematical Model of Coupled Stem Cell-Nutrient Dynamics in Myocardial Regeneration Therapy

Stem cell therapy is a promising treatment for the regeneration of myocardial tissue injured by an ischemic event. Mathematical modeling of myocardial regeneration via stem cell therapy is a challenging task, since the mechanisms underlying the processes involved in the treatment are not yet fully understood. Many aspects must be accounted for, such as the spread of stem cells and nutrients, chemoattraction, cell proliferation, stages of cell maturation, differentiation, angiogenesis, stochastic effects, just to name a few. In this paper we propose a 3D mathematical model with a free boundary that aims to provide a qualitative description of some main aspects of the stem cell regenerative therapy in a simplified scenario. The paper mainly focuses on the description of the shrinking of the necrotic core during treatment. The stem cell and nutrients dynamics are described through coupled reaction-diffusion problems. Proliferation, chemoattraction, tissue regeneration and nutrient consumption are included in the model.

Modelling-informed cell-seeded nerve repair construct designs for treating peripheral nerve injuries

Millions of people worldwide are affected by peripheral nerve injuries (PNI), involving billions of dollars in healthcare costs. Common outcomes for patients include paralysis and loss of sensation, often leading to lifelong pain and disability. Engineered Neural Tissue (EngNT) is being developed as an alternative to the current treatments for large-gap PNIs that show underwhelming functional recovery in many cases. EngNT repair constructs are composed of a stabilised hydrogel cylinder, surrounded by a sheath of material, to mimic the properties of nerve tissue. The technology also enables the spatial seeding of therapeutic cells in the hydrogel to promote nerve regeneration. The identification of mechanisms leading to maximal nerve regeneration and to functional recovery is a central challenge in the design of EngNT repair constructs. Using in vivo experiments in isolation is costly and time-consuming, offering a limited insight on the mechanisms underlying the performance of a given repair construct. To bridge this gap, we derive a cell-solute model and apply it to the case of EngNT repair constructs seeded with therapeutic cells which produce vascular endothelial growth factor (VEGF) under low oxygen conditions to promote vascularisation in the construct. The model comprises a set of coupled non-linear diffusion-reaction equations describing the evolving cell population along with its interactions with oxygen and VEGF fields during the first 24h after transplant into the nerve injury site. This model allows us to evaluate a wide range of repair construct designs (e.g. cell-seeding strategy, sheath material, culture conditions), the idea being that designs performing well over a short timescale could be shortlisted for in vivo trials. In particular, our results suggest that seeding cells beyond a certain density threshold is detrimental regardless of the situation considered, opening new avenues for future nerve tissue engineering.

Optimization of Oxygen Delivery Within Hydrogels

The field of tissue engineering has been continuously evolving since its inception over three decades ago with numerous new advancements in biomaterials and cell sources and widening applications to most tissues in the body. Despite the substantial promise and great opportunities for the advancement of current medical therapies and procedures, the field has yet to capture wide clinical translation due to some remaining challenges, including oxygen availability within constructs, both in vitro and in vivo. While this insufficiency of nutrients, specifically oxygen, is a limitation within the current frameworks of this field, the literature shows promise in new technological advances to efficiently provide adequate delivery of nutrients to cells. This review attempts to capture the most recent advances in the field of oxygen transport in hydrogel-based tissue engineering, including a comparison of current research as it pertains to the modeling, sensing, and optimization of oxygen within hydrogel constructs as well as new technological innovations to overcome traditional diffusion-based limitations. The application of these findings can further the advancement and development of better hydrogel-based tissue engineered constructs for future clinical translation and adoption.

Pulsating fluid flow affects pre-osteoblast behavior and osteogenic differentiation through production of soluble factors

Bone mass increases after error-loading, even in the absence of osteocytes. Loaded osteoblasts may produce a combination of growth factors affecting adjacent osteoblast differentiation. We hypothesized that osteoblasts respond to a single load in the short-term (minutes) by changing F-actin stress fiber distribution, in the intermediate-term (hours) by signaling molecule production, and in the long-term (days) by differentiation. Furthermore, growth factors produced during and after mechanical loading by pulsating fluid flow (PFF) will affect osteogenic differentiation. MC3T3-E1 pre-osteoblasts were either/not stimulated by 60 min PFF (amplitude, 1.0 Pa; frequency, 1 Hz; peak shear stress rate, 6.5 Pa/s) followed by 0-6 h, or 21/28 days of post-incubation without PFF. Computational analysis revealed that PFF immediately changed distribution and magnitude of fluid dynamics over an adherent pre-osteoblast inside a parallel-plate flow chamber (immediate impact). Within 60 min, PFF increased nitric oxide production (5.3-fold), altered actin distribution, but did not affect cell pseudopodia length and cell orientation (initial downstream impact). PFF transiently stimulated Fgf2, Runx2, Ocn, Dmp1, and Col1⍺1 gene expression between 0 and 6 h after PFF cessation. PFF did not affect alkaline phosphatase nor collagen production after 21 days, but altered mineralization after 28 days. In conclusion, a single bout of PFF with indirect associated release of biochemical factors, stimulates osteoblast differentiation in the long-term, which may explain enhanced bone formation resulting from mechanical stimuli.

Bioengineering a cryogel-derived bioartificial liver using particle image velocimetry defined fluid dynamics

Bioartificial Liver (BAL) devices are extracorporeal systems designed to support or recover hepatic function in patients with liver failure. The design of an effective BAL remains an open challenge since it requires a complex co-optimisation of cell colonisation, biomaterial scaffold and BAL fluid dynamics. Building on previous evidence of suitability as a blood perfusion device for detoxification, the current study investigated the use of RGD-containing p(HEMA)-alginate cryogels as BAL scaffolds. Cryogels were modified with alginate to reduce protein fouling and functionalised with an RGD-containing peptide to increase hepatocyte adhesion. A novel approach for characterisation of the internal flow through the porous matrix was developed by employing Particle Image Velocimetry (PIV) to visualise flow inside cryogels. Based on PIV results, which showed the laminar nature of flow inside cryogel pores, a multi-layered bioreactor composed of spaced cryogel discs was designed to improve blood/hepatocyte mass exchange. The stacked bioreactor showed a significantly higher production of albumin and urea compared to the column version, with improved cell colonisation and proliferation over time. The cell-free cryogel-based device was tested for safety in a bile-duct ligation model of liver cirrhosis. Thus, a stacked bioreactor prototype was developed based on a surface-engineered cryogel design with optimised fluid dynamics for BAL use.

A Hybrid Model of Cartilage Regeneration Capturing the Interactions Between Cellular Dynamics and Porosity

To accelerate the development of strategies for cartilage tissue engineering, models are necessary to investigate the interactions between cellular dynamics and the local microenvironment. We use a discrete framework to capture the individual behavior of cells, modeling experiments where cells are seeded in a porous scaffold or hydrogel and over the time course of a month, the scaffold slowly degrades while cells divide and synthesize extracellular matrix constituents. The movement of cells and the ability to proliferate is a function of the local porosity, defined as the volume fraction of fluid in the surrounding region. A phenomenological approach is used to capture a continuous profile for the degrading scaffold and accumulating matrix, which will then change the local porosity throughout the construct. We parameterize the model by first matching total cell counts in the construct to chondrocytes seeded in a polyglycolic acid scaffold (Freed et al. in Biotechnol Bioeng 43:597-604, 1994). We investigate the influence of initial scaffold porosity on the total cell count and spatial profiles of cell and ECM in the construct. Cell counts were higher at day 30 in scaffolds of lower initial porosity, and similar cell counts were obtained using different models of scaffold degradation and matrix accumulation (either uniform or cell-specific). Using this modeling framework, we study the interplay between a phenomenological representation of scaffold architecture and porosity as well as the potential continuous application of growth factors. We determine parameter regimes where large cellular aggregates occur, which can hinder matrix accumulation and cellular proliferation. The developed modeling framework can easily be extended and can be used to identify optimal scaffolds and culture conditions that lead to a desired distribution of extracellular matrix and cell counts throughout the construct.

Applications of Computer Modeling and Simulation in Cartilage Tissue Engineering

BACKGROUND

Advances in cartilage tissue engineering have demonstrated noteworthy potential for developing cartilage for implantation onto sites impacted by joint degeneration and injury. To supplement resource-intensive in vivo and in vitro studies required for cartilage tissue engineering, computational models and simulations can assist in enhancing experimental design.

METHODS

Research articles pertinent to cartilage tissue engineering and computer modeling were identified, reviewed, and summarized. Various applications of computer modeling for cartilage tissue engineering are highlighted, limitations of in silico modeling are addressed, and suggestions for future work are enumerated.

RESULTS

Computational modeling can help better characterize shear stresses generated by bioreactor fluid flow, refine scaffold geometry, customize the mechanical properties of engineered cartilage tissue, and model rates of cell growth and dynamics. Thus, results from in silico studies can help resourcefully enhance in vitro and in vivo studies; however, the limitations of these studies, such as the underlying assumptions and simplifications applied in each model, should always be addressed and justified where applicable. In silico models should also seek validation and verification when possible.

CONCLUSION

Future studies may adopt similar approaches to supplement in vitro trials and further investigate effects of mechanical stimulation on chondrocyte and stem cell dynamics. Additionally, as precision medicine, machine learning, and powerful open-source software become more popular and accessible, applications of multi-scale and multiphysics computational models in cartilage tissue engineering are expected to increase.

A parameterised mathematical model to elucidate osteoblast cell growth in a phosphate-glass microcarrier culture

Tissue engineering has the potential to augment bone grafting. Employing microcarriers as cell-expansion vehicles is a promising bottom-up bone tissue engineering strategy. Here we propose a collaborative approach between experimental work and mathematical modelling to develop protocols for growing microcarrier-based engineered constructs of clinically relevant size. Experiments in 96-well plates characterise cell growth with the model human cell line MG-63 using four phosphate glass microcarrier materials. Three of the materials are doped with 5 mol% TiO₂ and contain 0%, 2% or 5% CoO, and the fourth material is doped only with 7% TiO₂ (0% CoO). A mathematical model of cell growth is parameterised by finding material-specific growth coefficients through data-fitting against these experiments. The parameterised mathematical model offers more insight into the material performance by comparing culture outcome against clinically relevant criteria: maximising final cell number starting with the lowest cell number in the shortest time frame. Based on this analysis, material 7% TiO₂ is identified as the most promising.

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.

Curvature- and fluid-stress-driven tissue growth in a tissue-engineering scaffold pore

Cell proliferation within a fluid-filled porous tissue-engineering scaffold depends on a sensitive choice of pore geometry and flow rates: regions of high curvature encourage cell proliferation, while a critical flow rate is required to promote growth for certain cell types. When the flow rate is too slow, the nutrient supply is limited; when it is too fast, cells may be damaged by the high fluid shear stress. As a result, determining appropriate tissue-engineering-construct geometries and operating regimes poses a significant challenge that cannot be addressed by experimentation alone. In this paper, we present a mathematical theory for the fluid flow within a pore of a tissue-engineering scaffold, which is coupled to the growth of cells on the pore walls. We exploit the slenderness of a pore that is typical in such a scenario, to derive a reduced model that enables a comprehensive analysis of the system to be performed. We derive analytical solutions in a particular case of a nearly piecewise constant growth law and compare these with numerical solutions of the reduced model. Qualitative comparisons of tissue morphologies predicted by our model, with those observed experimentally, are also made. We demonstrate how the simplified system may be used to make predictions on the design of a tissue-engineering scaffold and the appropriate operating regime that ensures a desired level of tissue growth.

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

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

Modelling mesenchymal stromal cell growth in a packed bed bioreactor with a gas permeable wall

A mathematical model was developed for mesenchymal stromal cell (MSC) growth in a packed bed bioreactor that improves oxygen availability by allowing oxygen diffusion through a gas-permeable wall. The governing equations for oxygen, glucose and lactate, the inhibitory waste product, were developed assuming Michaelis-Menten kinetics, together with an equation for the medium flow based on Darcy's Law. The conservation law for the cells includes the effects of inhibition as the cells reach confluence, nutrient and waste product concentrations, and the assumption that the cells can migrate on the scaffold. The equations were solved using the finite element package, COMSOL. Previous experimental results collected using a packed bed bioreactor with gas permeable walls to expand MSCs produced a lower cell yield than was obtained using a traditional cell culture flask. This mathematical model suggests that the main contributors to the observed low cell yield were a non-uniform initial cell seeding profile and a potential lag phase as cells recovered from the initial seeding procedure. Lactate build-up was predicted to have only a small effect at lower flow rates. Thus, the most important parameters to optimise cell expansion in the proliferation of MSCs in a bioreactor with gas permeable wall are the initial cell seeding protocol and the handling of the cells during the seeding process. The mathematical model was then used to identify and characterise potential enhancements to the bioreactor design, including incorporating a central gas permeable capillary to further enhance oxygen availability to the cells. Finally, to evaluate the issues and limitations that might be encountered scale-up of the bioreactor, the mathematical model was used to investigate modifications to the bioreactor design geometry and packing density.

Numerical optimization of cell colonization modelling inside scaffold for perfusion bioreactor: A multiscale model

Part of clinically applicable bone graft substitutes are developed by using mechanical stimulation of flow-perfusion into cell-seeded scaffolds. The role of fluid flow is crucial in driving the nutrient to seeded cells and in stimulating cell colonization. A common numerical approach is to use a multiscale model to link some physical quantities (wall shear stress and inlet flow rate) that act at different scales. In this study, a multiscale model is developed in order to determine the optimal inlet flow rate to cultivate osteoblast-like cells seeded in a controlled macroporous biomaterial inside a perfusion bioreactor system. We focus particularly on the influence of Wall Shear Stress on cell colonization to predict cell colonization at the macroscale. Results obtained at the microscale are interpolated at the macroscale to determine the optimal flow rate. For a macroporous scaffold made of interconnected pores with pore diameters of above 350 μm and interconnection diameters of 150 μm, the model predicts a cell colonization of 325% after a 7-day-cell culture with a constant inlet flow rate of 0.69 mL·min^-1. Furthermore, the strength of this protocol is the possibility to adapt it to most porous biomaterials and dynamic cell culture systems.

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

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

Efficient Computational Design of a Scaffold for Cartilage Cell Regeneration

Due to the sensitivity of mammalian cell cultures, understanding the influence of operating conditions during a tissue generation procedure is crucial. In this regard, a detailed study of scaffold based cell culture under a perfusion flow is presented with the aid of mathematical modelling and computational fluid dynamics (CFD). With respect to the complexity of the case study, this work focuses solely on the effect of nutrient and metabolite concentrations, and the possible influence of fluid-induced shear stress on a targeted cell (cartilage) culture. The simulation set up gives the possibility of predicting the cell culture behavior under various operating conditions and scaffold designs. Thereby, the exploitation of the predictive simulation into a newly developed stochastic routine provides the opportunity of exploring improved scaffold geometry designs. This approach was applied on a common type of fibrous structure in order to increase the process efficiencies compared with the regular used formats. The suggested topology supplies a larger effective surface for cell attachment compared to the reference design while the level of shear stress is kept at the positive range of effect. Moreover, significant improvement of mass transfer is predicted for the suggested topology.

A poroelastic mixture model of mechanobiological processes in biomass growth: theory and application to tissue engineering

In this article we propose a novel mathematical description of biomass growth that combines poroelastic theory of mixtures and cellular population models. The formulation, potentially applicable to general mechanobiological processes, is here used to study the engineered cultivation in bioreactors of articular chondrocytes, a process of Regenerative Medicine characterized by a complex interaction among spatial scales (from nanometers to centimeters), temporal scales (from seconds to weeks) and biophysical phenomena (fluid-controlled nutrient transport, delivery and consumption; mechanical deformation of a multiphase porous medium). The principal contribution of this research is the inclusion of the concept of cellular "force isotropy" as one of the main factors influencing cellular activity. In this description, the induced cytoskeletal tensional states trigger signalling transduction cascades regulating functional cell behavior. This mechanims is modeled by a parameter which estimates the influence of local force isotropy by the norm of the deviatoric part of the total stress tensor. According to the value of the estimator, isotropic mechanical conditions are assumed to be the promoting factor of extracellular matrix production whereas anisotropic conditions are assumed to promote cell proliferation. The resulting mathematical formulation is a coupled system of nonlinear partial differential equations comprising: conservation laws for mass and linear momentum of the growing biomass; advection-diffusion-reaction laws for nutrient (oxygen) transport, delivery and consumption; and kinetic laws for cellular population dynamics. To develop a reliable computational tool for the simulation of the engineered tissue growth process the nonlinear differential problem is numerically solved by: (1) temporal semidiscretization; (2) linearization via a fixed-point map; and (3) finite element spatial approximation. The biophysical accuracy of the mechanobiological model is assessed in the analysis of a simplified 1D geometrical setting. Simulation results show that: (1) isotropic/anisotropic conditions are strongly influenced by both maximum cell specific growth rate and mechanical boundary conditions enforced at the interface between the biomass construct and the interstitial fluid; (2) experimentally measured features of cultivated articular chondrocytes, such as the early proliferation phase and the delayed extracellular matrix production, are well described by the computed spatial and temporal evolutions of cellular populations.

Responses of MSCs to 3D Scaffold Matrix Mechanical Properties under Oscillatory Perfusion Culture

Both fluid shear stress and matrix stiffness are implicated in bone metabolism and functional adaptation, but the synergistic action of these mechanical cues on the biological behaviors of mesenchymal stem cells (MSCs) is still not well-known. In the present work, a homemade oscillatory flow device was applied to investigate the effects of matrix stiffness on MSCs survival, distribution, and osteogenic differentiation in three-dimensional (3D) conditions. Furthermore, the flow field and cell growth in this bioreactor were theoretically simulated. The results demonstrated that oscillatory shear stress significantly increased the viability and distribution uniformity of MSCs throughout the scaffold after culture for 3 weeks. Compared to static culture, oscillatory shear stress could promote the collagen secretion, mineral deposits, and osteogenic differentiation of MSCs. The findings obtained from this work indicate that the oscillatory perfusion not only provides a higher survival rate and a more uniform distribution of cells but also facilitates osteogenic differentiation of MSCs. Oscillating perfusion bioreactor culture of MSCs in 3D scaffold with optimal matrix stiffness could offer an easy-to-use but efficient bioreactor for bone tissue engineering.

A mathematical model of tissue-engineered cartilage development under cyclic compressive loading

In this work a coupled model of solute transport and uptake, cell proliferation, extracellular matrix synthesis and remodeling of mechanical properties accounting for the impact of mechanical loading is presented as an advancement of a previously validated coupled model for free-swelling tissue-engineered cartilage cultures. Tissue-engineering constructs were modeled as biphasic with a linear elastic solid, and relevant intrinsic mechanical stimuli in the constructs were determined by numerical simulation for use as inputs of the coupled model. The mechanical dependent formulations were derived from a calibration and parametrization dataset and validated by comparison of normalized ratios of cell counts, total glycosaminoglycans and collagen after 24-h continuous cyclic unconfined compression from another dataset. The model successfully fit the calibration dataset and predicted the results from the validation dataset with good agreement, with average relative errors up to 3.1 and 4.3 %, respectively. Temporal and spatial patterns determined for other model outputs were consistent with reported studies. The results suggest that the model describes the interaction between the simultaneous factors involved in in vitro tissue-engineered cartilage culture under dynamic loading. This approach could also be attractive for optimization of culture protocols, namely through the application to longer culture times and other types of mechanical stimuli.

Modeling the fluid-dynamics and oxygen consumption in a porous scaffold stimulated by cyclic squeeze pressure

The architecture and dynamic physical environment of tissues can be recreated in-vitro by combining 3D porous scaffolds and bioreactors able to apply controlled mechanical stimuli on cells. In such systems, the entity of the stimuli and the distribution of nutrients within the engineered construct depend on the micro-structure of the scaffolds. In this work, we present a new approach for optimizing computational fluid-dynamics (CFD) models for the investigation of fluid-induced forces generated by cyclic squeeze pressure within a porous construct, coupled with oxygen consumption of cardiomyocytes. A 2D axial symmetric macro-scaled model of a squeeze pressure bioreactor chamber was used as starting point for generating time dependent pressure profiles. Subsequently the fluid movement generated by the pressure fields was coupled with a complete 3D micro-scaled model of a porous protein cryogel. Oxygen transport and consumption inside the scaffold was evaluated considering a homogeneous distribution of cardiomyocytes throughout the structure, as confirmed by preliminary cell culture experiments. The results show that a 3D description of the system, coupling a porous geometry and time dependent pressure driven flow with fluid-structure-interaction provides an accurate and meaningful description of the microenvironment in terms of shear stress and oxygen distribution than simple stationary 2D models.

A triphasic constrained mixture model of engineered tissue formation under in vitro dynamic mechanical conditioning

While it has become axiomatic that mechanical signals promote in vitro engineered tissue formation, the underlying mechanisms remain largely unknown. Moreover, efforts to date to determine parameters for optimal extracellular matrix (ECM) development have been largely empirical. In the present work, we propose a two-pronged approach involving novel theoretical developments coupled with key experimental data to develop better mechanistic understanding of growth and development of dense connective tissue under mechanical stimuli. To describe cellular proliferation and ECM synthesis that occur at rates of days to weeks, we employ mixture theory to model the construct constituents as a nutrient-cell-ECM triphasic system, their transport, and their biochemical reactions. Dynamic conditioning protocols with frequencies around 1 Hz are described with multi-scale methods to couple the dissimilar time scales. Enhancement of nutrient transport due to pore fluid advection is upscaled into the growth model, and the spatially dependent ECM distribution describes the evolving poroelastic characteristics of the scaffold-engineered tissue construct. Simulation results compared favorably to the existing experimental data, and most importantly, distinguish between static and dynamic conditioning regimes. The theoretical framework for mechanically conditioned tissue engineering (TE) permits not only the formulation of novel and better-informed mechanistic hypothesis describing the phenomena underlying TE growth and development, but also the exploration/optimization of conditioning protocols in a rational manner.

Creation of a Hybrid Scaffold with Dual Configuration of Aligned and Random Electrospun Fibers

A novel hybrid construct was developed by combining aligned fibers (AFs) and random fibers (RFs) to form a scaffolding system. Homogeneous fiber-based structures were fabricated by electrospinning, which produced both random and aligned fiber mats depending on the collection method. The upper part of the scaffold contained an AF layer, which possessed a well-organized configuration that provided uniaxial topographic guidance. For mechanical stability and support, the lower part of the scaffold was composed of an RF layer. Despite the presence of randomly distributed RFs, desirable alignment and differentiation could be achieved in cultured C2C12 myoblasts by controlling the density of AF layer. The fibrous structure of the hybrid scaffold also exhibited high porosity and therefore reasonable permeability. Owing to the structural stability provided by the underlying RFs, the cell-laden fibrous scaffolds were amenable to physical manipulation, such as multilayering. Collectively, the morphological features and manipulable architecture of the developed scaffolds suggest that they would perform well in practical applications.

A dynamic perfusion bioreactor approach for engineering respiratory tissues in-vitro

In vitro culture of respiratory tissues poses many challenges due to the intrinsic complexity of the respiratory system. Multiple cellular phenotypes comprise the respiratory epithelium and operate under dynamic, gas-interchanging conditions that should be replicated for near-physiologic cultivation of functional tissues in vitro. A novel biomimetic perfusion bioreactor system has been proposed to reconstitute key functional conditions of the human lung. This portable system consists of several biologically-inspired components: (i) a 3-dimensional (3-D) elastomeric soft tissue scaffold construct, (ii) a mechanical actuator, (iii) a perfusion system and (iv) gaseous exchange capabilities. These integrated components operate synergistically to create a unique, dynamic air-liquid interface (ALI) environment that allows controlled application of physiological and pathological strain while complementing standard cell culture techniques. This system holds potential for engineering 3-D tissues to meet growing demand for a range of applications, from more ethical and efficient pharmaceutical screening to clinical graft transplants.

A mathematical model and computational framework for three-dimensional chondrocyte cell growth in a porous tissue scaffold placed inside a bi-directional flow perfusion bioreactor

The in vitro chondrocyte cell culture for cartilage tissue regeneration in a perfusion bioreactor is a complex process. Mathematical modeling and computational simulation can provide important insights into the culture process, which would be helpful for selecting culture conditions to improve the quality of the developed tissue constructs. However, simulation of the cell culture process is a challenging task due to the complicated interaction between the cells and local fluid flow and nutrient transport inside the complex porous scaffolds. In this study, a mathematical model and computational framework has been developed to simulate the three-dimensional (3D) cell growth in a porous scaffold placed inside a bi-directional flow perfusion bioreactor. The model was developed by taking into account the two-way coupling between the cell growth and local flow field and associated glucose concentration, and then used to perform a resolved-scale simulation based on the lattice Boltzmann method (LBM). The simulation predicts the local shear stress, glucose concentration, and 3D cell growth inside the porous scaffold for a period of 30 days of cell culture. The predicted cell growth rate was in good overall agreement with the experimental results available in the literature. This study demonstrates that the bi-directional flow perfusion culture system can enhance the homogeneity of the cell growth inside the scaffold. The model and computational framework developed is capable of providing significant insight into the culture process, thus providing a powerful tool for the design and optimization of the cell culture process.

Computational modelling of the scaffold-free chondrocyte regeneration: a two-way coupling between the cell growth and local fluid flow and nutrient concentration

The in vitro chondrocyte cell culture process in a perfusion bioreactor provides enhanced nutrient supply as well as the flow-induced shear stress that may have a positive influence on the cell growth. Mathematical and computational modelling of such a culture process, by solving the coupled flow, mass transfer and cell growth equations simultaneously, can provide important insight into the biomechanical environment of a bioreactor and the related cell growth process. To do this, a two-way coupling between the local flow field and cell growth is required. Notably, most of the computational and mathematical models to date have not taken into account the influence of the cell growth on the local flow field and nutrient concentration. The present research aimed at developing a mathematical model and performing a numerical simulation using the lattice Boltzmann method to predict the chondrocyte cell growth without a scaffold on a flat plate placed inside a perfusion bioreactor. The model considers the two-way coupling between the cell growth and local flow field, and the simulation has been performed for 174 culture days. To incorporate the cell growth into the model, a control-volume-based surface growth modelling approach has been adopted. The simulation results show the variation of local fluid velocity, shear stress and concentration distribution during the culture period due to the growth of the cell phase and also illustrate that the shear stress can increase the cell volume fraction to a certain extent.

Influence of the scaffold geometry on the spatial and temporal evolution of the mechanical properties of tissue-engineered cartilage: insights from a mathematical model

The production of tissue-engineered cartilage in vitro with inhomogeneous mechanical properties is a problem yet to be solved. Different geometries have been studied to overcome this caveat; however, the reported measurements are limited to average values of some properties and qualitative measures of spatial distributions. We will apply a coupled model to extend knowledge about the introduction of a macrochannel in a scaffold by calculating spatiotemporal patterns for several interest variables related to the remodeling of the mechanical properties. Model parameters were estimated based on experimental data on the temporal patterns of glycosaminoglycans, collagen and compressive Young's modulus for channel-free constructs. The model reproduced the experimental data trends in both geometries, with experimental-numerical correlations between 0.84 and 0.97. The channel had a higher impact on the reduction in spatial heterogeneities and delay of saturation of core properties than in the improvement of average properties. Despite the possible improvement of cell densities for longer periods than 56 days, it is estimated that it will not cause further significant improvements of the mechanical properties. The degrees of spatial heterogeneity of the Young's modulus and permeability in the channeled geometry are 23 and 27 % of the channel-free values. While the average Young's modulus values are in the range of native cartilage, the permeabilities are one to three degrees of magnitude higher than the native cartilage, suggesting that limiting factors such as scaffold porosity and initial permeability are more relevant than scaffold geometry to effectively decrease the tissue permeability.

Modelling and simulation of the chondrocyte cell growth, glucose consumption and lactate production within a porous tissue scaffold inside a perfusion bioreactor

Mathematical and numerical modelling of the tissue culture process in a perfusion bioreactor is able to provide insight into the fluid flow, nutrients and wastes transport, dynamics of the pH value, and the cell growth rate. Knowing the complicated interdependence of these processes is essential for optimizing the culture process for cell growth. This paper presents a resolved scale numerical simulation, which allows one not only to characterize the supply of glucose inside a porous tissue scaffold in a perfusion bioreactor, but also to assess the overall culture condition and predict the cell growth rate. The simulation uses a simplified scaffold that consists of a repeatable unit composed of multiple strands. The simulation results explore some problematic regions inside the simplified scaffold where the concentration of glucose becomes lower than the critical value for the chondrocyte cell viability and the cell growth rate becomes significantly reduced.

Modeling of time dependent localized flow shear stress and its impact on cellular growth within additive manufactured titanium implants

Bone augmentation implants are porous to allow cellular growth, bone formation and fixation. However, the design of the pores is currently based on simple empirical rules, such as minimum pore and interconnects sizes. We present a three-dimensional (3D) transient model of cellular growth based on the Navier-Stokes equations that simulates the body fluid flow and stimulation of bone precursor cellular growth, attachment, and proliferation as a function of local flow shear stress. The model's effectiveness is demonstrated for two additive manufactured (AM) titanium scaffold architectures. The results demonstrate that there is a complex interaction of flow rate and strut architecture, resulting in partially randomized structures having a preferential impact on stimulating cell migration in 3D porous structures for higher flow rates. This novel result demonstrates the potential new insights that can be gained via the modeling tool developed, and how the model can be used to perform what-if simulations to design AM structures to specific functional requirements.

Applying shear stress to endothelial cells in a new perfusion chamber: hydrodynamic analysis

Perfusion bioreactors have been proved to be an impartible part of vascular tissue engineering due to its broad range of applications as a means to distribute nutrients within porous scaffold along with providing appropriate physical and mechanical stimuli. To better understand the mechanical phenomena inside a bioreactor, computational fluid dynamics (CFD) was adopted followed by a validation technique. The fluid dynamics of the media inside the bioreactor was modeled using the Navier-Stokes equation for incompressible fluids while convection through the scaffold was described by Brinkman's extension of Darcy's law for porous media. Flow within the reactor determined the orientation of endothelial cells on the scaffold. To validate flow patterns, streamlines and shear stresses, colorimetry technique was used following attained results from CFD. Our bioreactor was modeled to simulate the optimum condition and flow patterns over scaffold to culture ECs for in vitro experimentation. In such experiments, cells were attached firmly without significant detachment and more noticeably elongation process was triggered even shortly after start up.

Prediction of cell growth rate over scaffold strands inside a perfusion bioreactor

Mathematical and computational modeling of the dynamic process where tissue scaffolds are cultured in perfusion bioreactors is able to provide insight into the cell and tissue growth which can facilitate the design of tissue scaffolds and selection of optimal operating conditions. To date, a resolved-scale simulation of cell growth in the culture process, by taking account of the influences of the supply of nutrients and fluid shear stress on the cells, is not yet available in the literature. This paper presents such a simulation study specifically on cartilage tissue regeneration by numerically solving the momentum, scalar transport and cell growth equations, simultaneously, based on the lattice Boltzmann method. The simulation uses a simplified scaffold that consists of two circular strands placed in tandem inside a microchannel, with the object of identifying the effect of one strand on the other. The results indicate that the presence of the front strand can reduce the cell growth rate on the surface of the rear strand, depending on the distance between them. As such, the present study allows for investigation into the influence of the scaffold geometry on the cell growth rate within scaffolds, thus providing a means to improve the scaffold design and the culture process.

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.

Bulk stress distributions in the pore space of sphere-packed beds under Darcy flow conditions

In this paper, bulk stress distributions in the pore space of columns packed with spheres are numerically computed with lattice Boltzmann simulations. Three different ideally packed and one randomly packed configuration of the columns are considered under Darcy flow conditions. The stress distributions change when the packing type changes. In the Darcy regime, the normalized stress distribution for a particular packing type is independent of the pressure difference that drives the flow and presents a common pattern. The three parameter (3P) log-normal distribution is found to describe the stress distributions in the randomly packed beds within statistical accuracy. In addition, the 3P log-normal distribution is still valid when highly porous scaffold geometries rather than sphere beds are examined. It is also shown that the 3P log-normal distribution can describe the bulk stress distribution in consolidated reservoir rocks like Berea sandstone.

In silico prediction of the cell proliferation in porous scaffold using model of effective pore

The mathematical prediction of cell proliferation in porous scaffold still remains a challenge. The analysis of existing models and experimental data confirms a need for a new solution, which takes into account cells" development on the scaffold pore walls as well as some additional parameters such as the pore size, cell density in cellular layers, the thickness of the growing cell layer and others. The simulations, presented below, are based on three main approaches. The first approach takes into account multilayer cell growth on the pore walls of the scaffold. The second approach is a simulation of cell proliferation in a discrete process as a continuous one. The third one is the representation of scaffold structure as a system of cylindrical channels. Oxygen (nutrient) mass transfer is realized inside these channels. The model, described below, proposes the new solution to time dependent description of cell proliferation in porous scaffold and optimized trophical conditions for tissue development.

Whole organ and tissue reconstruction in thoracic regenerative surgery

Development of novel prognostic, diagnostic, and treatment options will provide major benefits for millions of patients with acute or chronic respiratory dysfunction, cardiac-related disorders, esophageal problems, or other diseases in the thorax. Allogeneic organ transplant is currently available. However, it remains a trap because of its dependency on a very limited supply of donated organs, which may be needed for both initial and subsequent transplants. Furthermore, it requires lifelong treatment with immunosuppressants, which are associated with adverse effects. Despite early clinical applications of bioengineered organs and tissues, routine implementation is still far off. For this review, we searched the PubMed, MEDLINE, and Ovid databases for the following keywords for each tissue or organ: tissue engineering, biological and synthetic scaffold/graft, acellular and decelluar(ized), reseeding, bioreactor, tissue replacement, and transplantation. We identified the current state-of-the-art practices in tissue engineering with a focus on advances during the past 5 years. We discuss advantages and disadvantages of biological and synthetic solutions and introduce novel strategies and technologies for the field. The ethical challenges of innovation in this area are also reviewed.

Engineering parameters in bioreactor's design: a critical aspect in tissue engineering

Bioreactors are important inevitable part of any tissue engineering (TE) strategy as they aid the construction of three-dimensional functional tissues. Since the ultimate aim of a bioreactor is to create a biological product, the engineering parameters, for example, internal and external mass transfer, fluid velocity, shear stress, electrical current distribution, and so forth, are worth to be thoroughly investigated. The effects of such engineering parameters on biological cultures have been addressed in only a few preceding studies. Furthermore, it would be highly inefficient to determine the optimal engineering parameters by trial and error method. A solution is provided by emerging modeling and computational tools and by analyzing oxygen, carbon dioxide, and nutrient and metabolism waste material transports, which can simulate and predict the experimental results. Discovering the optimal engineering parameters is crucial not only to reduce the cost and time of experiments, but also to enhance efficacy and functionality of the tissue construct. This review intends to provide an inclusive package of the engineering parameters together with their calculation procedure in addition to the modeling techniques in TE bioreactors.

Oxygen consumption in T-47D cells immobilized in alginate

OBJECTIVES

Encapsulation or entrapment of cells is increasingly being used in a wide variety of scientific studies for tissue engineering and development of novel medical devices. The effect on cell metabolism of such systems is, in general, not well characterized. In this work, a simple system for monitoring respiration of cells embedded in 3-D alginate cultures was characterized.

MATERIALS AND METHODS

T-47D cells were cultured in alginate gels. Oxygen concentration curves were recorded within cell-gel constructs using two different sensor systems, and cell viability and metabolic state were characterized using confocal microscopy and commercially available stains.

RESULTS

At sufficient depth within constructs, recorded oxygen concentration curves were not significantly influenced by influx of oxygen through cell-gel layers and oxygen consumption rate could be calculated simply by dividing oxygen loss in the system per time, by the number of cells. This conclusion was supported by a 3-D numeric simulation. For the T-47D cells, the oxygen consumption rate was found to be 61 ± 6 fmol/cell/h, 3-4 times less than has previously been found for these cells, when grown exponentially in monolayer culture.

CONCLUSIONS

The experimental set-up presented here may be varied in multiple ways by changing the cell-gel construct 3-D microenvironment, easily allowing investigation of a variety of factors on cell respiration.

Porohyperviscoelastic model simultaneously predicts parenchymal fluid pressure and reaction force in perfused liver

Porohyperviscoelastic (PHVE) modeling gives a simplified continuum approximation of pore fluid behavior within the parenchyma of liver tissue. This modeling approach is particularly applicable to tissue engineering of artificial livers, where the inherent complexity of the engineered scaffolds prevents the use of computational fluid dynamics. The objectives of this study were to simultaneously predict the experimental parenchymal fluid pressure (PFP) and compression response in a PHVE liver model. The model PFP matched the experimental measurements (318 Pa) to within 1.5%. Linear regression of both phases of compression, ramp, and hold, demonstrated a strong correlation between the model and the experimental reaction force (p<0.5). The ability of this PVE model to accurately predict both fluid and solid behavior is important due to the highly vascularized nature of liver tissue and the mechanosensitivity of liver cells to solid matrix and fluid flow properties.

Mathematical model of growth factor driven haptotaxis and proliferation in a tissue engineering scaffold

Motivated by experimental work (Miller et al. in Biomaterials 27(10):2213-2221, 2006, 32(11):2775-2785, 2011) we investigate the effect of growth factor driven haptotaxis and proliferation in a perfusion tissue engineering bioreactor, in which nutrient-rich culture medium is perfused through a 2D porous scaffold impregnated with growth factor and seeded with cells. We model these processes on the timescale of cell proliferation, which typically is of the order of days. While a quantitative representation of these phenomena requires more experimental data than is yet available, qualitative agreement with preliminary experimental studies (Miller et al. in Biomaterials 27(10):2213-2221, 2006) is obtained, and appears promising. The ultimate goal of such modeling is to ascertain initial conditions (growth factor distribution, initial cell seeding, etc.) that will lead to a final desired outcome.

2-D coupled computational model of biological cell proliferation and nutrient delivery in a perfusion bioreactor

Tissue engineering aims to regenerate, repair or replace organs or tissues which have become defective due to trauma, disease or age related degeneration. This engineering may take place within the patient's body or tissue can be regenerated in a bioreactor for later implantation into the patient. Regeneration of soft tissue is one of the most demanding applications of tissue engineering. Producing proper nutrient supply, uniform cell distribution and high cell density are the important challenges. Many experimental models exist for tissue growth in a bioreactor. It is important to put experiments into a theoretical framework. Mathematical modelling in terms of physical and biochemical mechanisms is the best tool to understand experimental results. In this work a mathematical model of convective and diffusive transport of nutrients and cell evolution in a perfusion bioreactor is developed. A cell-seeded porous scaffold is placed in a perfusion bioreactor and fluid delivers the nutrients to the cells for their growth. The model describes the key features of the tissue engineering processes which includes the interaction between the cell growth, variation of material permeability due to cell proliferation, flow of fluid through the material and delivery of nutrients to the cells. The fluid flow through the porous scaffold is modelled by Darcy's law, and the delivery of nutrients to the cells is modelled by the advection-diffusion equation. A non-linear reaction diffusion system is used to model the cell growth. The growth of cells is modelled by logistic growth. COMSOL (a commercial finite element solver) is used to numerically solve the model. The results show that the distribution of cells and total cell number in the scaffold does not depend on the initial cell density but depend on the material permeability.