Bioartificial kidney. I. Theoretical analysis of convective flow in hollow fiber modules: application to a bioartificial hemofilter

Analytical expressions describing convective flow in a continuous arteriovenous hollow fiber hemofilter were developed. In the lumen of the hollow fiber membrane, existing analytical expressions were applied to describe velocity profiles and pressure. For flow in the shell (the extracapillary space separating the fibers), analytical expressions for the radial and axial velocity profiles and pressure distribution were derived by first finding the stream function. The expressions are based on a similarity solution. Previous analyses of ultrafiltration have either ignored osmotic pressure or assumed constant shell pressure. In this paper, the axial variation in lumen pressure, shell pressure, and osmotic pressure were accounted for. The predicted filtration rates agree well with the experimental results. This flow model is general enough to describe flow in hollow fiber membrane systems employed as bioreactors (e.g., for cell cultures and as bioartificial organs) and as separators (e.g., ultrafiltration and microfiltration) operating in the open-shell mode. The results were applied to determine the design of an optimally functioning bioartificial hemofilter for use ex vivo or in vivo.     

Modeling analysis of an intercalated-spiral alternate-dead-ended hollow fiber bioreactor for mammalian cell cultures

The model analysis of a bioreactor with two intercalated-spiral sets of hollow fibers with alternated dead ends is presented. Design equations are derived based on a model with two jumped fibers and an approximation of the fluid mechanics with a small fiber radius-to-length ratio. The performance of the bioreactor is simulated with and without cell growth utilizing a segregated radial flow model in the extracapillary space. The pressure modulus, the wall Peclet number, the Thiele modulus, and the Monod constant are used as model parameters. The results can be used to assess the proper choice of fiber permeability, fiber length, fiber spacing, and flow velocity.     

A radial flow hollow fiber bioreactor for the large-scale culture of mammalian cells

A radial flow hollow fiber bioreactor has been developed that maximizes the utilization of fiber surface for cell growth while eliminating nutrient and metabolic gradients inherent in conventional hollow fiber cartridges. The reactor consists of a central flow distributor tube surrounded by an annular bed of hollow fibers. The central flow distributor tube ensures an axially uniform radial convective flow of nutrients across the fiber bed. Cells attach and proliferate on the outer surface of the fibers. The fibers are pretreated with polylysine to facilitate cell attachment and long-term maintenance of tissuelike densities of cell mass. A mixture of air and CO(2) is fed through the tube side of the hollow fibers, ensuring direct oxygenation of the cells and maintenance of pH. Spent medium diffuses across the cell layer into the tube side of the fibers and is convected away along with the spent gas stream. The bioreactor was run as a recycle reactor to permit maximum utilization of nutrient medium. A bioreactor with a membrane surface area of 1150 cm(2) was developed and H1 cells were grown to a density of 7.3 x 10(6) cells/cm(2).     

Theoretical analysis of the effect of convective flow on solute transport and insulin release in a hollow fiber bioartificial pancreas

The bioartificial pancreas, in which transplanted pancreatic tissue or isolated cells are cultured on a hollow fiber membrane, is an attractive approach to restore physiologic insulin delivery in the treatment of diabetes. Insulin response in prototype devices has been unacceptable due to the large mass transport limitations associated with the membrane and the surrounding shell region. Although available theoretical analyses provide some insight into the combined effects of transport and reaction in the bioartificial pancreas, they cannot quantitatively account for the effects of convective recirculation flow, complex intrinsic insulin secretory kinetics, and non-uniform distribution of pancreatic cells. We have developed a detailed model for glucose and insulin transport and insulin secretion in the hollow fiber bioartificial pancreas based on the solution of the mass and momentum conservation equations describing flow and transport in the lumen, matrix, and shell. Model predictions are in good agreement with literature data obtained in a hollow fiber device with minimal radial convective flow. Although no quantitative data are available for a device with significant radial convection, model simulations demonstrate that convective recirculation flow can dramatically improve insulin response, allowing the device to accurately capture the bi-phasic insulin secretion characteristic of the normal physiologic response. Results provide fundamental insights into the coupling between kinetics and transport in the hollow fiber system and a rational basis for the design of clinical devices.     

Treatment of trichloroethylene (TCE) in a membrane biofilter

This article reports on the biodegradation of trichloroethylene (TCE) in a hollow-fiber membrane biofilter. Air contaminated with TCE was passed through microporous hollow fibers while an oxygen-free nutrient solution was recirculated through the shell side of the membrane module. The biomass was attached to the outside surface of the microporous hollow fibers by initially supplying toluene in the gas phase that flows through the fibers. While studies on TCE biodegradation were conducted, there was no toluene present in the gas phase. At 20-ppmv inlet concentration of TCE and 36-s gas-phase residence time, based on total internal volume of the hollow fibers, 30% removal efficiency of TCE was attained. At higher air flow rates or lower gas-phase residence times, lower removal efficiencies were observed. During TCE degradation, the pH of the liquid phase on the shell side of the membrane module decreased due to release of chloride ions. A mathematical model was developed to describe the synchronous aerobic/anaerobic biodegradation of TCE. (c) 1996 John Wiley & Sons, Inc.     

Mathematical model for pressure losses in the hemodialysis graft vascular circuit

Stenosis-induced thrombosis and abandonment of the hemodialysis synthetic graft is an important cause of morbidity and mortality. The graft vascular circuit is a unique low-resistance shunt that has not yet been systematically evaluated. In this study, we developed a mathematical model of this circuit. Pressure losses (deltaPs) were measured in an in vitro experimental apparatus and compared with losses predicted by equations from the engineering literature. We considered the inflow artery, arterial and venous anastomoses, graft, stenosis, and outflow vein. We found significant differences between equations and experimental results, and attributed these differences to the transitional nature of the flow. Adjustment of the equations led to good agreement with experimental data. The resulting mathematical model predicts relations between stenosis, blood flow, intragraft pressure, and important clinical variables such as mean arterial blood pressure and hematocrit. Application of the model should improve understanding of the hemodynamics of the stenotic graft vascular circuit.     

A model of plasma membrane flow and cytosis regulation in growing pollen tubes

A model of cytosis regulation in growing pollen tubes is developed and simulations presented. The authors address the question on the minimal assumptions needed to describe the pattern of exocytosis and endocytosis reported recently by experimental biologists. Biological implications of the model are also treated. Concepts of flow and conservation of membrane material are used to pose an equation system, which describes the movement of plasma membrane in the tip of growing pollen tubes. After obtaining the central equations, relations describing the rates of endocytosis and exocytosis are proposed. Two cytosis receptors (for exocytosis and endocytosis), which have different recycling rates and activation times, suffice to describe a stable growing tube. Simulations show a very good spatial separation between endocytosis and exocytosis, in which separation is shown to depend strongly on exocytic vesicle delivery. In accordance to measurements, most vesicles in the clear zone are predicted to be endocytic. Membrane flow is essential to maintain cell polarity, and bi-directional flow seems to be a natural consequence of the proposed mechanism. For the first time, a model addressing plasma membrane flow and cytosis regulation were posed. Therefore, it represents a missing piece in an integrative model of pollen tube growth, in which cell wall mechanics, hydrodynamic fluxes and regulation mechanisms are combined.     

Optimum fiber spacing in a hollow fiber bioreactor

A high surface area hollow fiber reactor was developed for mammalian cell culture. The reactor employs an interfiber gel matrix of agar or collagen for cell support. A model was developed to predict cell density as a function of fiber spacing. Optimum spacings are calculated for two sizes of Celgard hollow fibers. Ehrlich Ascites Tumor (EAT) cells were grown to an estimated density of 1.1 x 10(8) viable cells/mL in the extracapillary space-corresponding to an overall reactor density of 7 x 10(7) cells/mL. On the basis of available kinetic and diffusivity data, the model predicts that lactate accumulation may limit cell growth in the early stage of medium utilization, while oxygen delivery becomes limiting at later stages.     

Modulation of transmembrane pressure in manufacturing scale tangential flow filtration N-1 perfusion seed culture

Mammalian cells were grown to high density in a 3,000 L culture using perfusion with hollow fibers operated in a tangential flow filtration mode. The high-density culture was used to inoculate the production stage of a biomanufacturing process. At constant permeate flux operation, increased transmembrane pressures (TMPs) were observed on the final day of the manufacturing batches. Small scale studies suggested that the filters were not irreversibly fouled, but rather exposed to membrane concentration polarization that could be relieved by tangential sweeping of the hollow fibers. Studies were undertaken to analyze parameters that influence the hydrodynamic profile within hollow fibers; including filter area, cell density, recirculation flow rate, and permeate flow rate. Results indicated that permeate flow rate had the greatest influence on modulating TMP. Further evaluation showed a significant decrease in TMP when permeate flow was reduced, and this occurred without any negative effect on cell growth or viability. Hence, a 30% reduction of permeate flow rate was implemented at manufacturing scale. A stable operation was achieved as TMP was successfully reduced by 75% while preserving all critical factors for performance in the perfusion bioreactor.     

Transport mechanisms in oral transmucosal drug delivery: implications for pain management

The mechanism for the oral transmucosal delivery of fentanyl citrate (OTFC) was investigated in this work. A developed mathematical model included the following transport characteristics: dissolution of the fentanyl citrate lozenge, diffusion through the saliva and oral mucosal membrane and equilibrium between adjacent layers. An orthogonal-collocation-based solution procedure was adopted to discretize the governing equations and boundary conditions. The Mathematica® built-in function, NDSolve, was applied to integrate the equations with respect to time. Simulations were conducted with a 200 μg-dosage. A novel fabrication method, aimed at maintaining a high flux for a prolonged period of time, was proposed based on the calculated delivery rate and cumulative amount of medicament absorbed into the systemic circulation. The model allows drug manufacturers to decide when to replace the unit based on estimated drug concentrations in the saliva and the mucosal membrane. Both the model and solution strategies were validated using serum fentanyl citrate concentration collected from adult subjects. The predicted profiles, based on parameters obtained from the literature, agree well with the experimental data.     

An investigation of the diffusion-limited growth of animal cells around single hollow fibers

To compare modeling with experimental data of cell growth surrounding individual fibers, the growth profiles of hybridoma cells in the extracapillary space of single hollow fiber bioreactors were examined. Agarose was provided in the extracapillary space to provide support and minimize convection. By sacrificing bioreactors at various time intervals, the growth profiles of cells surrounding a single hollow fiber could be monitored with increasing time. Using photomicroscopy and viable staining, areas of viable and nonviable cell growth were examined at various stages of development ranging from initial seeding to stable growth conditions. Cells were found to act as nucleation sites for the growth of individual colonies within the agarose. Profiles at stable growth conditions resulted in a thick cell mass near the surface of the fiber wall followed by cell colonies of decreasing size with increasing radial distance. A simplified theoretical model for cell growth was developed using mass balance equations for substrate penetration into individual cell colonies as well as away from the wall of a single fiber. The resulting profiles derived from theory were compared with experiments and found to be in good agreement for entering oxygen concentrations of 5% and 20%. (c) 1992 John Wiley & Sons, Inc.     

Effect of harvesting protocol on performance of a hollow fiber bioreactor.

In this study, a bioreactor subject to Starling flow in closed shell batch harvest mode was compared to two forms of additional forced extracapillary (EC) space convection including EC circulation and EC cycling. Despite the presence of Starling flow as the dominant EC convection mechanism in the batch harvest system, the bioreactor start up was fairly good. However, the antibody productivity of the batch harvest system fell off rapidly after day 20 resulting in only 4.5 g of antibody produced. EC circulation with flow parallel to the fibers had a slightly better start up than the batch harvest. However, the antibody productivity also dropped after day 20 with EC circulation, resulting in only 7.5 g of antibody produced. EC cycling with flow both parallel and perpendicular to the fibers resulted in a start up similar to that of EC circulation. However, in contrast to the other two systems, antibody productivity in the EC cycling system was stable over the 60-day experiment resulting in the production of 23 g of antibody. These results demonstrate the importance of inducing the proper flow distribution in the EC space to allow consistent and stable production in hollow fiber bioreactors.     

Continuous modeling of metabolic networks with gene regulation in yeast and in vivo determination of rate parameters

A continuous model of a metabolic network including gene regulation to simulate metabolic fluxes during batch cultivation of yeast Saccharomyces cerevisiae was developed. The metabolic network includes reactions of glycolysis, gluconeogenesis, glycerol and ethanol synthesis and consumption, the tricarboxylic acid cycle, and protein synthesis. Carbon sources considered were glucose and then ethanol synthesized during growth on glucose. The metabolic network has 39 fluxes, which represent the action of 50 enzymes and 64 genes and it is coupled with a gene regulation network which defines enzyme synthesis (activities) and incorporates regulation by glucose (enzyme induction and repression), modeled using ordinary differential equations. The model includes enzyme kinetics, equations that follow both mass-action law and transport as well as inducible, repressible, and constitutive enzymes of metabolism. The model was able to simulate a fermentation of S. cerevisiae during the exponential growth phase on glucose and the exponential growth phase on ethanol using only one set of kinetic parameters. All fluxes in the continuous model followed the behavior shown by the metabolic flux analysis (MFA) obtained from experimental results. The differences obtained between the fluxes given by the model and the fluxes determined by the MFA do not exceed 25% in 75% of the cases during exponential growth on glucose, and 20% in 90% of the cases during exponential growth on ethanol. Furthermore, the adjustment of the fermentation profiles of biomass, glucose, and ethanol were 95%, 95%, and 79%, respectively. With these results the simulation was considered successful. A comparison between the simulation of the continuous model and the experimental data of the diauxic yeast fermentation for glucose, biomass, and ethanol, shows an extremely good match using the parameters found. The small discrepancies between the fluxes obtained through MFA and those predicted by the differential equations, as well as the good match between the profiles of glucose, biomass, and ethanol, and our simulation, show that this simple model, that does not rely on complex kinetic expressions, is able to capture the global behavior of the experimental data. Also, the determination of parameters using a straightforward minimization technique using data at only two points in time was sufficient to produce a relatively accurate model. Thus, even with a small amount of experimental data (rates and not concentrations) it was possible to estimate the parameters minimizing a simple objective function. The method proposed allows the obtention of reasonable parameters and concentrations in a system with a much larger number of unknowns than equations. Hence a contribution of this study is to present a convenient way to find in vivo rate parameters to model metabolic and genetic networks under different conditions.     

A numerical and experimental study of mass transfer in the artificial kidney

To develop a more efficient and optimal artificial kidney, many experimental approaches have been used to study mass transfer inside, outside, and cross hollow fiber membranes with different kinds of membranes, solutes, and flow rates as parameters. However, these experimental approaches are expensive and time consuming. Numerical calculation and computer simulation is an effective way to study mass transfer in the artificial kidney, which can save substantial time and reduce experimental cost. This paper presents a new model to simulate mass transfer in artificial kidney by coupling together shell-side, lumen-side, and transmembrane flows. Darcy's equations were employed to simulate shell-side flow, Navier-Stokes equations were employed to simulate lumen-side flow, and Kedem-Katchalsky equations were used to compute transmembrane flow. Numerical results agreed well with experimental results within 10% error. Numerical results showed the nonuniform distribution of flow and solute concentration in shell-side flow due to the entry/exit effect and Darcy permeability. In the shell side, the axial velocity in the periphery is higher than that in the center. This numerical model presented a clear insight view of mass transfer in an artificial kidney and may be used to help design an optimal artificial kidney and its operation conditions to improve hemodialysis.     

A Theoretical Model of Pattern Formation in Coral Reefs

We present a mathematical model of the growth of coral subject to unidirectional ocean currents using concepts of porous-media flow and nonlinear dynamics in chemical systems. Linear stability analysis of the system of equations predicts that the growth of solid (coral) structures will be aligned perpendicular to flow, propagating against flow direction. Length scales of spacing between structures are selected based on chemical reaction and flow rates. In the fully nonlinear system, autocatalysis in the chemical reaction accelerates growth. Numerical analysis reveals that the nonlinear growth creates sharp fronts of high solid fraction that, as predicted by the linear stability, advance against the predominating flow direction. The findings of regularly spaced growth areas oriented perpendicular to flow are qualitatively supported on both a colonial and a regional reef scale. Received 1 October 2001; accepted 22 May 2002.     

Large eddy simulation of the unsteady flow-field in an idealized human mouth-throat configuration

The present study concerns the simulation and analysis of the flow field in the upper human respiratory system in order to gain an improved understanding of the complex flow field with respect to the process affecting drug delivery for medical treatment of the human air system. For this purpose, large eddy simulation (LES) is chosen because of its powerful performance in the transitional range of laminar and turbulent flow fields. The average gas velocity in a constricted tube is compared with experimental data (Ahmed and Giddens, 1983) and numerical data from Reynolds-averaged Navier-Stokes (RANS) equations coupled with low Reynolds number (LRN) κ-ω model (Zhang and Kleinstreuer, 2003) and LRN shear-stress transport κ-ω model (Jayaraju et al., 2007), for model validation. The present study emphasizes on the instantaneous flow field, where the simulations capture different scales of secondary vortices in different flow zones including recirculation zones, the laryngeal jet zone, the mixing zone, and the wall shear layer. It is observed that the laryngeal jet tail breaks up, and the unsteady motion of laryngeal jet is coupled with the unsteady distribution of secondary vortices in the jet boundary. The present results show that it is essential to study the unsteady flow field since it strongly affects the particle flow in the human upper respiratory system associated with drug delivery for medical treatment.     

An integrated fluid–structure interaction and thrombosis model for type B aortic dissection

False lumen thrombosis (FLT) in type B aortic dissection has been associated with the progression of dissection and treatment outcome. Existing computational models mostly assume rigid wall behavior which ignores the effect of flap motion on flow and thrombus formation within the FL. In this study, we have combined a fully coupled fluid–structure interaction (FSI) approach with a shear-driven thrombosis model described by a series of convection–diffusion reaction equations. The integrated FSI-thrombosis model has been applied to an idealized dissection geometry to investigate the interaction between vessel wall motion and growing thrombus. Our simulation results show that wall compliance and flap motion can influence the progression of FLT. The main difference between the rigid and FSI models is the continuous development of vortices near the tears caused by drastic flap motion up to 4.45 mm. Flap-induced high shear stress and shear rates around tears help to transport activated platelets further to the neighboring region, thus speeding up thrombus formation during the accelerated phase in the FSI models. Reducing flap mobility by increasing the Young’s modulus of the flap slows down the thrombus growth. Compared to the rigid model, the predicted thrombus volume is 25% larger using the FSI-thrombosis model with a relatively mobile flap. Furthermore, our FSI-thrombosis model can capture the gradual effect of thrombus growth on the flow field, leading to flow obstruction in the FL, increased blood viscosity and reduced flap motion. This model is a step closer toward simulating realistic thrombus growth in aortic dissection, by taking into account the effect of intimal flap and vessel wall motion.

     

Detection and characterization of heparin-binding proteins with a gel overlay procedure.

The binding of 125I-labeled derivatives of heparin has been used by several investigators to identify heparin-binding fragments of different heparin-binding proteins. In this report we utilize the procedure described by J.W. Smith and D.J. Knauer (1987, Anal. Biochem. 160, 105-114) to produce 125I-fluorescein-heparin. Using this derivative, we compare the use of gel overlay procedures with "Western blot" procedures for the detection of heparin-binding proteins following polyacrylamide gel electrophoresis in the presence of sodium dodecyl sulfate. We show that the gel overlay procedure is a relatively simple and sensitive method for visualizing heparin-binding proteins. In addition, we use the procedure to characterize the heparin-binding properties of heparin-binding growth factor 1 (acidic fibroblast growth factor) with synthetic peptide competitors and site-directed mutants of the growth factor.     

Protamine immobilization and heparin adsorption on the protamine-bound cellulose fiber membrane

Immobilization of protamine to the inner lumen of cellulose hollow fibers has been shown useful in preventing both heparin- and protamine-induced complications during an extracorporeal blood circulation procedure. The current study examined the effects of variables on the immobilization of protamine to cyanogen bromide (CNBr)-activated cellulose hollow fibers. The degree of protamine immobilization was controlled by three independent parameters: the amount of CNBr used during the activation process, the duration of the coupling process, and the protamine concentration in the coupling solution. By the adjustment of these parameters, cellulose fibers containing desired amounts of immobilized protamine (ranging from 1 to 20 mg of immobilized protamine per gram of dry fibers) were readily prepared.Heparin adsorption to the protamine-bound cellulose fibers was also examined. The adsorption isotherm followed a Langmuir adsorption model. The amount of heparin adsorbed was dependent on both the heparin concentration in the substrate solution and the protamine loading on the fibers. The Langmuir adsorption constant K was estimated to be 0.37 +/- 0.06 mL/mg, whereas the saturation capacity Q(s) of the protamine-bound fibers increased with increasing the protamine loading.     

Heparin and the phenotype of adult human vascular smooth muscle cells

Summary To study mechanisms controlling growth and phenotype in human vascular smooth muscle cells, we established culture conditions under which these cells proliferate rapidly and achieve life-spans of 50–60 population doublings. In medium containing heparin and heparin-binding growth factors, growth rate and life-span of human vascular smooth muscle cells increased more than 50% relative to cultures with neither supplement, and more than 20% compared to cultures supplemented only with heparin-binding growth factors. In contrast to observations made in rat vascular smooth muscle cells, smooth muscle-specific α-actin in the human cells was expressed only in the presence of heparin and colocalized with β/γ nonmuscle actins in stress fibers, not in adhesion plaques. Heparin, in the presence of heparin-binding growth factors, also caused more than 170% stimulation of tracer glucosamine incorporation into hyaluronic acid and a 7.5-fold increase in hyaluronic acid accumulation. In comparison, total sulfate incorporation into sulfated glycosaminoglycans increased by less than 40%. In light of our previous findings that heparin suppresses collagen gene expression, we conclude that heparin induces human vascular smooth muscle cells exposed to heparin-binding growth factors to remodel their extracellular matrix by altering the relative rates of hyaluronic acid (HA) and collagen synthesis. The resulting hyaluronic-acid-rich, collagen-poor matrix may enhance infiltration of CD44/hyaluronate-receptor-bearing T-lymphocytes and monocytes into the vascular wall, an early event in atherogenesis.