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 microm 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 x 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.     

Model simulation and analysis of perfusion culture of mammalian cells at high cell density.

Rate equations recently proposed by the authors for growth, death, consumption of nutrients, and formation of lactic acid, ammonium, and monoclonal antibody of hybridoma cells are used to simulate and analyze the behavior of perfusion cultures. Model simulations are in good agreement with experimental results from three different cell lines under varied perfusion and cell bleed rates except for cultures with very low viability. Analysis of simulations and experimental results indicates that in perfusion cultures with a complete cell separation cell bleed rate is a key parameter that strongly affects all the process variables, whereas the perfusion rate mainly affects the total and viable cell concentrations and the volumetric productivity of monoclonal antibody. Growth rate, viability, and specific perfusion rate of cells are only a function of the cell bleed rate. This also applies to cultures with partial cell separation in the permeate if the effective cell bleed rate is considered. It is suggested that the (effective) cell bleed rate of a perfusion culture should be carefully chosen and controlled separately from the perfusion rate. In general, a low cell bleed rate that warrants a reasonable cell viability appears to be desirable for the production of antibodies. Furthermore, model simulations indicate the existence of an optimum initial glucose concentration in the feed. For the cell lines considered, the initial glucose concentration used in normal cell culture media is obviously too high. The initial glutamine concentration can also be reduced to a certain extent without significantly impairing the growth and antibody production but considerably reducing the ammonia concentration. The mathematical model can be used to predict these optimum conditions and may also be used for process design.     

Computational modeling of combined cell population dynamics and oxygen transport in engineered tissue subject to interstitial perfusion

This work presents a computational model of tissue growth under interstitial perfusion inside a tissue engineering bioreactor. The model accounts both for the cell population dynamics, using a model based on cellular automata, and for the hydrodynamic microenvironment imposed by the bioreactor, using a model based on the Lattice-Boltzmann equation and the convection-diffusion equation. The conditions of static culture versus perfused culture were compared, by including the population dynamics along with oxygen diffusion, convective transport and consumption. The model is able to deal with arbitrary complex geometries of the spatial domain; in the present work, the domain modeled was the void space of a porous scaffold for tissue-engineered cartilage. The cell population dynamics algorithm provided results which qualitatively resembled population dynamics patterns observed in experimental studies, and these results were in good quantitative agreement with previous computational studies. Simulation of oxygen transport and consumption showed the fundamental contribution of convective transport in maintaining a high level of oxygen concentration in the whole spatial domain of the scaffold. The model was designed with the aim to be computationally efficient and easily expandable, i.e. to allow straightforward implementability of further models of complex biological phenomena of increasing scientific interest in tissue engineering, such as chemotaxis, extracellular matrix deposition and effect of mechanical stimulation.     

Effects of oxygen transport on 3-d human mesenchymal stem cell metabolic activity in perfusion and static cultures: experiments and mathematical model

Human mesenchymal stem cells (hMSCs) have unique potential to develop into functional tissue constructs to replace a wide range of tissues damaged by disease or injury. While recent studies have highlighted the necessity for 3-D culture systems to facilitate the proper biological, physiological, and developmental processes of the cells, the effects of the physiological environment on the intrinsic tissue development characteristics in the 3-D scaffolds have not been fully investigated. In this study, experimental results from a 3-D perfusion bioreactor system and the static culture are combined with a mathematical model to assess the effects of oxygen transport on hMSC metabolism and proliferation in 3-D constructs grown in static and perfusion conditions. Cells grown in the perfusion culture had order of magnitude higher metabolic rates, and the perfusion culture supports higher cell density at the end of cultivation. The specific oxygen consumption rate for the constructs in the perfusion bioreactor was found to decrease from 0.012 to 0.0017 micromol/10(6) cells/h as cell density increases, suggesting intrinsic physiological change at high cell density. BrdU staining revealed the noneven spatial distribution of the proliferating cells in the constructs grown under static culture conditions compared to the cells that were grown in the perfusion system. The hypothesis that the constructs in static culture grow under oxygen limitation is supported by higher Y(L/G) in static culture. Modeling results show that the oxygen tension in the static culture is lower than that of the perfusion unit, where the cell density was 4 times higher. The experimental and modeling results show the dependence of cell metabolism and spatial growth patterns on the culture environment and highlight the need to optimize the culture parameters in hMSC tissue engineering.     

Computational modeling of combined cell population dynamics and oxygen transport in engineered tissue subject to interstitial perfusion

This work presents a computational model of tissue growth under interstitial perfusion inside a tissue engineering bioreactor. The model accounts both for the cell population dynamics, using a model based on cellular automata, and for the hydrodynamic microenvironment imposed by the bioreactor, using a model based on the Lattice–Boltzmann equation and the convection-diffusion equation. The conditions of static culture versus perfused culture were compared, by including the population dynamics along with oxygen diffusion, convective transport and consumption. The model is able to deal with arbitrary complex geometries of the spatial domain; in the present work, the domain modeled was the void space of a porous scaffold for tissue-engineered cartilage. The cell population dynamics algorithm provided results which qualitatively resembled population dynamics patterns observed in experimental studies, and these results were in good quantitative agreement with previous computational studies. Simulation of oxygen transport and consumption showed the fundamental contribution of convective transport in maintaining a high level of oxygen concentration in the whole spatial domain of the scaffold. The model was designed with the aim to be computationally efficient and easily expandable, i.e. to allow straightforward implementability of further models of complex biological phenomena of increasing scientific interest in tissue engineering, such as chemotaxis, extracellular matrix deposition and effect of mechanical stimulation.     

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.     

Comparative chondrogenesis of human cells in a 3D integrated experimental–computational mechanobiology model

We present an integrated experimental–computational mechanobiology model of chondrogenesis. The response of human articular chondrocytes to culture medium perfusion, versus perfusion associated with cyclic pressurisation, versus non-perfused culture, was compared in a pellet culture model, and multiphysic computation was used to quantify oxygen transport and flow dynamics in the various culture conditions. At 2 weeks of culture, the measured cell metabolic activity and the matrix content in collagen type II and aggrecan were greatest in the perfused+pressurised pellets. The main effects of perfusion alone, relative to static controls, were to suppress collagen type I and GAG contents, which were greatest in the non-perfused pellets. All pellets showed a peripheral layer of proliferating cells, which was thickest in the perfused pellets, and most pellets showed internal gradients in cell density and matrix composition. In perfused pellets, the computed lowest oxygen concentration was 0.075 mM (7.5% tension), the maximal oxygen flux was 477.5 nmol/m²/s and the maximal fluid shear stress, acting on the pellet surface, was 1.8 mPa (0.018 dyn/cm²). In the non-perfused pellets, the lowest oxygen concentration was 0.003 mM (0.3% tension) and the maximal oxygen flux was 102.4 nmol/m²/s. A local correlation was observed, between the gradients in pellet properties obtained from histology, and the oxygen fields calculated with multiphysic simulation. Our results show up-regulation of hyaline matrix protein production by human chondrocytes in response to perfusion associated with cyclic pressurisation. These results could be favourably exploited in tissue engineering applications.     

Modeling,simulations, and optimization of smooth muscle cell tissue engineering for the production of vascular grafts

The paper presents a transient, continuum, two-phase model of the tissue engineering in fibrous scaffolds, including transport equations for the flowing culture medium, nutrient and cell concentration with transverse and in-plane diffusion and cell migration, a novel feature of local in-plane transport across a phenomenological pore and innovative layer-by-layer cell filling approach. The model is successfully validated for the smooth muscle cell tissue engineering of a vascular graft using crosslinked, electrospun gelatin fiber scaffolds for both static and dynamic cell culture, the latter in a dynamic bioreactor with a rotating shaft on which the tubular scaffold is attached. Parametric studies evaluate the impact of the scaffold microstructure, cell dynamics, oxygen transport, and static or dynamic conditions on the rate and extent of cell proliferation and depth of oxygen accessibility. An optimized scaffold of 75% dry porosity is proposed that can be tissue engineered into a viable and still fully oxygenated graft of the tunica media of the coronary artery within 2 days in the dynamic bioreactor. Such scaffold also matches the mechanical properties of the tunica media of the human coronary artery and the suture retention strength of a saphenous vein, often used as a coronary artery graft.     

Membrane transport models with fast and slow reactions: General analytical solution for a single relaxation

Summary Membrane transport models are usually expressed on the basis of chemical kinetics. The states of a transporter are related by rate constants, and the time-dependent changes of these states are given by linear differential equations of first order. To calculate the time-dependent transport equation, it is necessary to solve a system of differential equations which does not have a general analytical solution if there are more than five states. Since transport measurements in a complex system rarely provide all the time constants because some of them are too rapid, it is more appropriate to obtain approximate analytical solutions, assuming that there are fast and slow reaction steps. The states of the fast steps are related by equilibrium constants, thus permitting the elimination of their differential equations and leaving only those for the slow steps. With a system having only two slow steps, a single differential equation is obtained and the state equations have a single relaxation. Initial conditions for the slow reactions are determined after the perturbation which redistribute the states related by fast reactions. Current and zero-trans uptake equations are calculated. Curve fitting programs can be used to implement the general procedure and obtain the model parameters.     

Model-based analysis and design of a microchannel reactor for tissue engineering

Recently developed perfusion micro-bioreactors offer the promise of more physiologic in vitro systems for tissue engineering. Successful application of such bioreactors will require a method to characterize the bioreactor environment required to elicit desired cell function. We present a mathematical model to describe nutrient/growth factor transport and cell growth inside a microchannel bioreactor. Using the model, we first show that the nature of spatial gradients in nutrient concentration can be controlled by both design and operating conditions and are a strong function of cell uptake rates. Next, we extend our model to investigate the spatial distributions of cell-secreted soluble autocrine/paracrine growth factors in the bioreactor. We show that the convective transport associated with the continuous cell culture and possible media recirculation can significantly alter the concentration distribution of the soluble signaling molecules as compared to static culture experiments and hence needs special attention when adapting static culture protocols for the bioreactor. Further, using an unsteady state model, we find that spatial gradients in nutrient/growth factor concentrations can bring about spatial variations in the cell density distribution inside the bioreactor, which can result in lowered working volume of the bioreactor. Finally, we show that the nutrient and spatial limitations can dramatically affect the composition of a co-cultured cell population. Our results are significant for the development, design, and optimization of novel micro-channel systems for tissue engineering.     

Optimization of flowrate for expansion of human embryonic stem cells in perfusion microbioreactors

Microfluidic systems create significant opportunities to establish highly controlled microenvironmental conditions for screening pluripotent stem cell fate. However, since cell fate is crucially dependent on this microenvironment, it remains unclear as to whether continual perfusion of culture medium supports pluripotent stem cell maintenance in feeder-free, chemically defined conditions, and further, whether optimum perfusion conditions exist for subsequent use of human embryonic stem cell (hESCs) in other microfludic systems. To investigate this, we designed microbioreactors based on resistive flow to screen hESCs under a linear range of flowrates. We report that at low rates (conditions where glucose transport is convection-limited with Péclet number <1), cells are affected by apparent nutrient depletion and waste accumulation, evidenced by reduced cell expansion and altered morphology. At higher rates, cells are spontaneously washed out, and display morphological changes which may be indicative of early-stage differentiation. However, between these thresholds exists a narrow range of flowrates in which hESCs expand comparably to the equivalent static culture system, with regular morphology and maintenance of the pluripotency marker TG30 in >95% of cells over 7 days. For MEL1 hESCs the optimum flowrate also coincided with the time-averaged medium exchange rate in static cultures, which may therefore provide a good first estimate of appropriate perfusion rates. Overall, we demonstrate hESCs can be maintained in microbioreactors under continual flow for up to 7 days, a critical outcome for the future development of microbioreactor-based screening systems and assays for hESC culture.     

Quantitative Microdialysis: Analysis of Transients and Application to Pharmacokinetics in Brain

The behavior of a microdialysis probe in vivo is mathematically described. A diffusion-reaction model is developed that not only accounts for transport of substances through tissues and probe membranes but also accounts for transport across the microvasculature and metabolism. Time-dependent equations are presented both for the effluent microdialysate concentration and for concentration profiles about the probe. The analysis applies either to measuring the tissue pharmacokinetics of drugs administered systemically, or for sampling of endogenously produced substances from tissue. In addition, an expression is developed for the transient concentration about the probe when it is used as an infusion device. All mathematical expressions are found to be a sum of an algebraic and an integral term. Theoretical prediction of time-dependent probe behavior in brain has been compared with experimental data for acetaminophen administered at 15 mg/kg to rats by intravenous bolus. Plasma and whole striatal tissue samples were used to describe plasma kinetics and to estimate a capillary permeability-area product of 0.07 min-1. Theoretical prediction of transient effluent dialysate concentrations exhibited close agreement with experimental data over 60 min. Terminal decline of the dialysate effluent concentration was slightly overestimated but theoretical concentrations still lay within the 95% confidence interval of the experimental data at 112 min. Microvasculature transport and metabolism play major roles in determining microdialysate transient responses. Extraction fraction (recovery) has been shown to be a declining function in time for five probe operating conditions. High rates of metabolism and/or capillary transport affect the time required to approach steady-state extraction, shortening the time as the rates increase. Conversely, for substances characterized by low permeabilities and negligible metabolism, experimental situations exist that are predicted to have very slow approaches to microdialysis steady state.     

Dynamic culture of droplet‐confined cell arrays

Responding to the need of creating an accurate and controlled microenvironment surrounding the cell while meeting the requirements for biological processes or pharmacological screening tests, we aimed at designing and developing a microscaled culture system suitable for analyzing the synergic effects of extracellular matrix proteins and soluble environments on cell phenotype in a high‐throughput fashion. We produced cell arrays deposing micrometer‐scale protein islands on hydrogels using a robotic DNA microarrayer, constrained the culture media in a droplet‐like volume and developed a suitable perfusion system. The droplet‐confined cell arrays were used either with conventional culture methods (batch operating system) or with automated stable and constant perfusion (steady‐state operating system). Mathematical modeling assisted the experimental design and assessed efficient mass transport and proper fluidodynamic regimes. Cells cultured on arrayed islands (500 μm diameter) maintained the correct phenotype both after static and perfused conditions, confirmed by immunostaining and gene expression analyses through total RNA extraction. The mathematical model, validated using a particle tracking experiment, predicted the constant value of velocities over the cell arrays (less than 10% variation) ensuring the same mass transport regime. BrdU analysis on an average of 96 cell spots for each experimental condition showed uniform expression inside each cell island and low variability in the data (average of 13%). Perfused arrays showed longer doubling times when compared with static cultures. In addition, perfused cultures showed a reduced variability in the collected data, allowing to detect statistically significant differences in cell behavior depending on the spotted ECM protein. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Flow cytometric cell cycle analysis of muscle precursor cells cultured within 3D scaffolds in a perfusion bioreactor

It has been widely demonstrated that perfusion bioreactors improve in vitro three‐dimensional (3D) cultures in terms of high cell density and uniformity of cell distribution; however, the studies reported in literature were primarily based on qualitative analysis (histology, immunofluorescent staining) or on quantitative data averaged on the whole population (DNA assay, PCR). Studies on the behavior, in terms of cell cycle, of a cell population growing in 3D scaffolds in static or dynamic conditions are still absent. In this work, a perfusion bioreactor suitable to culture C₂C₁₂ muscle precursor cells within 3D porous collagen scaffolds was designed and developed and a method based on flowcytometric analyses for analyzing the cell cycle in the cell population was established. Cells were extracted by enzymatic digestion of the collagen scaffolds after 4, 7, and 10 days of culture, and flow cytometric live/dead and cell cycle analyses were performed with Propidium Iodide. A live/dead assay was used for validating the method for cell extraction and staining. Moreover, to investigate spatial heterogeneity of the cell population under perfusion conditions, two stacked scaffolds in the 3D domain, of which only the upstream layer was seeded, were analyzed separately. All results were compared with those obtained from static 3D cultures. The live/dead assay revealed the presence of less than 20% of dead cells, which did not affect the cell cycle analysis. Cell cycle analyses highlighted the increment of cell fractions in proliferating phases (S/G₂/M) owing to medium perfusion in long‐term cultures. After 7–10 days, the percentage of proliferating cells was 8–12% for dynamic cultures and 3–5% for the static controls. A higher fraction of proliferating cells was detected in the downstream scaffold. From a general perspective, this method provided data with a small standard deviation and detected the differences between static and dynamic cultures and between upper and lower scaffolds. Our methodology can be extended to other cell types to investigate the influence of 3D culture conditions on the expression of other relevant cell markers. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

RWPV bioreactor mass transport: earth-based and in microgravity

Mass transport and mixing of perfused scalar quantities in the NASA Rotating Wall Perfused Vessel bioreactor are studied using numerical models of the flow field and scalar concentration field. Operating conditions typical of both microgravity and ground-based cell cultures are studied to determine the expected vessel performance for both flight and ground-based control experiments. Results are presented for the transport of oxygen with cell densities and consumption rates typical of colon cancer cells cultured in the RWPV. The transport and mixing characteristics are first investigated with a step change in the perfusion inlet concentration by computing the time histories of the time to exceed 10% inlet concentration. The effects of a uniform cell utilization rate are then investigated with time histories of the outlet concentration, volume average concentration, and volume fraction starved. It is found that the operating conditions used in microgravity produce results that are quite different then those for ground-based conditions. Mixing times for microgravity conditions are significantly shorter than those for ground-based operation. Increasing the differential rotation rates (microgravity) increases the mixing and transport, while increasing the mean rotation rate (ground-based) suppresses both. Increasing perfusion rates enhances mass transport for both microgravity and ground-based cases, however, for the present range of operating conditions, above 5-10 cc/min there are diminishing returns as much of the inlet fluid is transported directly to the perfusion exit. The results show that exit concentration is not a good indicator of the concentration distributions in the vessel. In microgravity conditions, the NASA RWPV bioreactor with the viscous pump has been shown to provide an environment that is well mixed. Even when operated near the theoretical minimum perfusion rates, only a small fraction of the volume provides less than the required oxygen levels.     

Three-dimensional cell seeding and growth in radial-flow perfusion bioreactor for in vitro tissue reconstruction

Radial-flow perfusion bioreactor systems have been designed and evaluated to enable direct cell seeding into a three-dimensional (3-D) porous scaffold and subsequent cell culture for in vitro tissue reconstruction. However, one of the limitations of in vitro regeneration is the tissue necrosis that occurs at the central part of the 3-D scaffold. In the present study, tubular poly-L-lactic acid (PLLA) porous scaffolds with an optimized pore size and porosity were prepared by the lyophilization method, and the effect of different perfusion conditions on cell seeding and growth were compared with those of the conventional static culture. The medium flowed radially from the lumen toward the periphery of the tubular scaffolds. It was found that cell seeding under a radial-flow perfusion condition of 1.1 mL/cm2 x min was effective, and that the optimal flow rate for cell growth was 4.0 mL/cm2 x min. At this optimal rate, the increase in seeded cells in the perfusion culture over a period of 5 days was 7.3-fold greater than that by static culture over the same period. The perfusion cell seeding resulted in a uniform distribution of cells throughout the scaffold. Subsequently, the perfusion of medium and hence the provision of nutrients and oxygen permitted growth and maintenance of the tissue throughout the scaffold. The perfusion seeding/culture system was a much more effective strategy than the conventional system in which cells are seeded under a static condition and cultured in a bioreactor such as a spinner flask.     

Design of well and groove microchannel bioreactors for cell culture

Microfluidic bioreactors have been shown valuable for various cellular applications. The use of micro-wells/grooves bioreactors, in which micro-topographical features are used to protect sensitive cells from the detrimental effects of fluidic shear stress, is a promising approach to culture sensitive cells in these perfusion microsystems. However, such devices exhibit substantially different fluid dynamics and mass transport characteristics compared to conventional planar microchannel reactors. In order to properly design and optimize these systems, fluid and mass transport issues playing a key role in microscale bioreactors should be adequately addressed. The present work is a parametric study of micro-groove/micro-well microchannel bioreactors. Operation conditions and design parameters were theoretically examined via a numerical model. The complex flow pattern obtained at grooves of various depths was studied and the shear protection factor compared to planar microchannels was evaluated. 3D flow simulations were preformed in order to examine the shear protection factor in micro-wells, which were found to have similar attributes as the grooves. The oxygen mass transport problem, which is coupled to the fluid mechanics problem, was solved for various groove geometries and for several cell types, assuming a defined shear stress limitation. It is shown that by optimizing the groove depth, the groove bioreactor may be used to effectively maximize the number of cells cultured within it or to minimize the oxygen gradient existing in such devices. Moreover, for sensitive cells having a high oxygen demand (e.g., hepatocytes) or low endurance to shear (e.g., human embryonic stem cells), results show that the use of grooves is an enabling technology, since under the same physical conditions the cells cannot be cultured for long periods of time in a planar microchannel. In addition to the theoretical model findings, the culture of human foreskin fibroblasts in groove (30 microm depth) and well bioreactors (35 microm depth) was experimentally examined at various flow rates of medium perfusion and compared to cell culture in regular flat microchannels. It was shown that the wells and the grooves enable a one order of magnitude increase in the maximum perfusion rate compared to planar microchannels. Altogether, the study demonstrates that the proper design and use of microgroove/well bioreactors may be highly beneficial for cell culture assays.     

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.     

猪十二指肠组织灌流培养与静态培养比较

组织灌流培养和静态培养是肠道组织体外培养最常见的两种方法,但目前尚不清楚这两种培养方法哪种更适合用于体外胃肠激素分泌的研究.以猪十二指肠组织为研究对象,首先比较L-精氨酸下两种体外培养方法对组织胆囊收缩素(Cholecystokinin,CCK)分泌和组织活性乳酸脱氢酶(Lactate dehydrogenase,LD...