Optimisation of solute transport in dialysers using a three-dimensional finite volume model

Dialyser manufacturers only provide limited information about mass removal under well-defined flow and solute conditions in commercially available dialysers for hemodialysis. This computational study aimed at assessing the solute transport efficiency in a dialyser for different geometries (fiber lengths and diameters).

A three-dimensional finite volume model of a single fiber in a high flux polysulphone dialyser (Fresenius F60) was developed. Different equations describe blood and dialysate flow (Navier–Stokes), radial filtration flow (Darcy) and solute transport (convection–diffusion). Fluid and membrane properties were derived from in vitro and in vivo tests as well as from literature data. Urea (MW60) was used as marker to simulate small molecule removal, while middle molecule transport was modelled using vitamin B12 (MW1355) and inulin (MW5200). Keeping the fluid velocity in a single fiber constant, fiber diameter and length were changed in a wide range for evaluation of solute removal efficiency. Clearances were found enhanced by 13% (urea), 50% (vitamin B12) and 89% (inulin) for a fiber twice as long as a standard one and by 5.5% (vitamin B12) and 21% (inulin) for a fiber diameter of 150 μm instead of 200 μm. The impact of fiber dimensions was more pronounced for the middle molecules compared to urea.     

Mathematical Model of a Countercurrent Flow Multi-fibre Dialyser

Summary The closed form solution to a distributed parameter mathematical model of a countercurrent flow dialyser is presented. The model consisting of a bundle of hollow fibres in a shell accounts for axial convection and radial diffusion. The proposed model relates the fractional removal of a solute to mass transfer parameters such as Sherwood number, length Peclet number and system geometry. Excellent agreement with experimental beer dialysis data is demonstrated for the removal of alcohol using 8-lm thick 200-lm diameter cuprophane hollow-fibre membrane fibres. Potentially, this model could be very helpful in designing new processes involving dialysis. For example, removal efficiency better than 90% is achievable in systems operating with a Sherwood number of 2.0, length Peclet number of 5 · 105, unit tube-side/shell-side volumetric flow and length-to-diameter ratio of 5000. Results were obtained in this work from only the first eigenvalue and the case of no solute in the incoming dialysate stream.     

Effect of nitroprusside on peritoneal dialysis clearances.

We have studied the effect of intraperitoneal nitroprusside on small (urea) and middle (vitamin B12) molecule dialysis clearances in patients maintained on chronic peritoneal dialysis. Clearances were measured in six patients during the addition of 6 mg of nitroprusside to three and seven consecutive, hourly two-liter exchanges during the course of a routine dialysis treatment. Results indicate that clearances of urea and B12 both increased about 35 percent with the addition of the vasodilator for three exchanges. Clearances immediately returned to baseline values when administration of the vasodilator was discontinued. Addition of the drug to seven consecutive exchanges resulted in a sustained 35 percent increment in clearances. We conclude that addition of 6 mg of nitroprusside to peritoneal dialysis solution can result in a significant increment in both small and middle molecule clearances. Maintenance of the higher clearances requires sustained administration of the drug, which can be tolerated for at least six exchanges with no adverse side effects.     

Preparation and in vitro analysis of microencapsulated genetically engineered E. coli DH5 cells for urea and ammonia removal

This article describes a novel method of urea and ammonia removal using microencapsulated, genetically engineered Escherichia coli DH5 cells. Optimization of bacterial cell encapsulation was carried out. The optimal method consists of alginate 2.00% (w/v) at a flow rate of 0.0724 mL/min and a coaxial air flow rate of 2.00 L/min. This produces spherical, alginate-poly-L-lysine-alginate (APA) microcapsules of an average 500 +/- 45 mum diameter. Increasing the concentration of alginate from 1.00% to 1.75% improves the quality of the microcapsules, while cell viability remains unaffected. The APA microcapsules are mechanically stable up to 210-rpm agitation with no bacterial cell leakage. The in vitro performance of urea and ammonia removal by encapsulated bacteria is assessed. One hundred milligrams of bacterial cells in APA microcapsules, in their log phase state of growth, can lower 87.89 +/- 2.25% of the plasma urea within 20 min and 99.99% in 30 min. The same amount of encapsulated bacteria can also lower ammonia from 975.14 +/- 70.15 muM/L to 81.151 +/- 7.37 muM/L in 30 min. There are no significant differences in depletion profiles by free and encapsulated bacteria for urea and ammonia removal. This novel approach using microencapsulated, genetically engineered E. coli cells is significantly more efficient than presently available methods of urea and ammonia removal. For instance, it is 30 times more efficient than the standard urease-ammonium adsorbent system. (c) 1995 John Wiley & Sons, Inc.     

The Action of Pitressin on Solute Permeability of the Rabbit Nephron in Vivo

The isotopic equilibration of urea, thiourea, and inulin between urine and plasma was determined in rabbits in the presence or absence of antidiuretic hormone (ADH). Animals were anesthetized with ethanol and permitted to reach steady state after completion of surgery. Tracer was then administered by intraarterial infusion in such a manner that a high constant specific activity in plasma was rapidly attained. Urine flow was kept independent of ADH by addition of mannitol. Urea/creatinine clearance ratios and the accumulation of urea in renal medulla and papilla also remained unaffected by ADH. Under these conditions, thiourea and inulin at all times approached equilibrium, at similar rates. In the absence of ADH, urea also equilibrated at a rate similar to that of inulin. The addition of ADH, however, significantly prolonged the delay before urinary urea reached the high constant specific activity of plasma urea. These observations are interpreted in terms of a specific effect of the hormone on the solute permeability of the nephron.     

Disposable Membrane Insert for the Kiil Dialyser

The use of a presterilized, disposable, mesh-supported membrane envelope in the Watson Marlow Kiil dialyser results in a 12% improvement in urea and creatinine clearance. Priming volume, uptake volume, and ultrafiltration rate are unchanged. Residual blood volume remains small. Blood flow resistance is increased. The envelope therefore offers considerable advantages over conventional assembly for dialysis with a blood pump.     

Clinical Evaluation of a Disposable Artificial Kidney

The in-vivo performance of a new disposable parallel flow countercurrent type of artificial kidney has been compared with that of the modified four-layered Kiil dialyser. The dialysance of urea and endogenous creatinine in the former was significantly better than in the latter for similar blood flow rates, and, moreover, unlike the dialysance with the Kiil dialyser it continued to improve over 12 hours. Among 100 disposable artificial kidneys tested no failure occurred from blood leaks despite the use of high negative pressures in the dialysate compartment. No pyrogen reactions were observed.These new artificial kidneys were ready for use in less than one-seventh of the time taken to prepare the conventional Kiil dialyser. Other advantages are their low priming volumes, the lack of a pump in the blood line, and the reduced risk of infection.     

Transient solute diffusion in articular cartilage

The one-dimensional transient diffusion of glucose, inulin and dextran into adult bovine knee articular cartilage was determined for transport times of 1, 5, 15 and 60 min, and 4, 12, 24 and 48 h. The apparent diffusion coefficient and apparent interface partition coefficient were calculated from the concentration-depth profiles within the tissue using a theoretical model for non-steady state solute diffusion. The diffusion coefficient was found to decrease with both solute size and transport time. The partition coefficient also decreased with solute size but increased with transport time. Neither coefficient was dependent on normal tissue fluid or proteoglycan content variations.     

Further Observations on Asymmetrical Solute Movement across Membranes

The permeability of frog skin under the influence of urea hyperosmolarity has been studied. Flux ratio asymmetry has been demonstrated again for tracer mannitol. The inhibitors DNP, CN^-, and ouabain have been used to eliminate active sodium transport and it was found that urea hyperosmolarity produces asymmetrical mannitol fluxes on frog skins having no short-circuit current. These findings suggest that flux ratio asymmetry is due to solute interaction and is unrelated to sodium transport. Studies with a synthetic membrane show clearly that bulk flow of fluid can produce a "solvent drag" effect and change flux ratios. When bulk flow is blocked and solute gradients allowed their full expression, then solute interaction "solute drag" is easily demonstrable in a synthetic system.     

Countercurrent exchange in the inner renal medulla: Vasa recta-descending limb system

A model of countercurrent exchange has been developed to simulate transport of salt, urea and water among vasa recta and descending limbs of the loop of Henle in the inner medulla. These vessels are abstracted as three concentric cylinders: the inne one represents descending vasa recta, the middle one represents ascending vasa recta and the outer one represents descending limbs. The capillary plexus, which connects the ascending and descending vasa recta, is modeled as a series of well-mixe compartments. Multicomponent transport equations for the sytem are derived from steady state mass balances and simple passive flux relations. The resulting set of nonlinear equations are solved numerically by an iterative Gauss-Seidel algorithm with under-relaxation. Simulations yield the salt and urea concentrations as well as volume flow rates in all tubes and compartments. The simulations indicate that solute concentrations can increase monotonically toward the papillae even if all transport processes within the exchanger are passive and source fluxes decrease monotonically toward the papillae.     

Two outer membrane transport systems for vitamin B12 in Salmonella typhimurium.

The involvement of an outer membrane transport component for vitamin B12 uptake in Salmonella typhimurium, analogous to the btuB product in Escherichia coli, was investigated. Mutants of S. typhimurium selected for resistance to bacteriophage BF23 carried mutations at the btuB locus (butBS) (formerly called bfe, at the analogous map position as the E. coli homolog) and were defective in high-affinity vitamin B12 uptake. The cloned E. coli btuB gene (btuBE) hybridized to S. typhimurium genomic DNA and restored vitamin B12 transport activity to S. typhimurium btuBS mutants. An Mr-60,000 protein in the S. typhimurium outer membrane was repressed by growth with vitamin B12 and was eliminated in a btuBS mutant. The btuBS product thus appears to play the same role in vitamin B12 transport by S. typhimurium as does the E. coli btuBE product. A second vitamin B12 transport system that is not present in E. coli was found by cloning a fragment of S. typhimurium DNA that complemented btuB mutants for vitamin B12 utilization. In addition to this plasmid with a 6-kilobase insert of S. typhimurium DNA, vitamin B12 utilization by E. coli btuB strains required the btuC and btuD products, necessary for transport across the cytoplasmic membrane, but not the btuE or tonB product. The plasmid conferred low levels of vitamin B12-binding and energy-dependent transport activity but not susceptibility to phage BF23 or utilization of dicyanocobinamide. The cloned S. typhimurium DNA encoding this new transport system did not hybridize to the btuBE gene or to E. coli chromosomal DNA and therefore does not carry the S. typhimurium btuBS locus. Increased production of an Mr -84,000 polypeptide associated with the outer membrane was seen. The new locus appears to be carried on the large plasmid in most S. typhimurium strains. Thus S. typhimurium possesses both high- and low-affinity systems for uptake of cobalamins across the outer membrane.     

TonB-Dependent Transporter FhuA in Planar Lipid Bilayers: Partial Exit of Its Plug from the Barrel

TonB-dependent transporters (TBDTs), which transport iron-chelating siderophores and vitamin B(12) across the outer membrane of Gram-negative bacteria, share a conserved architecture of a 22-stranded β-barrel with an amino-terminal plug domain occluding the barrel. We previously reported that we could induce TBDTs to reversibly open in planar lipid bilayers via the use of urea and that these channels were responsive to physiological concentrations of ligands. Here we report that in the presence of urea, trypsin can cleave the amino-terminal 67 residues of the plug of the TonB-dependent transporter FhuA, as assessed by gel shift and mass spectrometry assays. On the bilayer, trypsin treatment in the presence of urea resulted in the induced conductance no longer being reversed upon removal of urea, suggesting that urea opens intact FhuA channels by pulling the plug at least partly out of the barrel and that removal of the urea then allows reinsertion of the plug into the barrel. When expressed separately, the FhuA plug domain was found to be a mostly unfolded structure that was able to occlude isolated FhuA β-barrels inserted into the membrane. Thus, although folded in the barrel, the plug need not be folded upon exiting the barrel. The rate of insertion of the β-barrels into the membrane was tremendously increased in the presence of an osmotic gradient provided by either urea or glycerol. Negative staining electron microscopy showed that FhuA in a detergent solution formed vesicles, thus explaining why an osmotic gradient promoted the insertion of FhuA into membranes.     

Effect of cobalamin derivatives on DNA synthesis in cells of Propionibacterium freudenreichii subsp. shermanii

The increase of DNA-synthesis rate (according incorporation [8-14C]adenine) in B12-deficient cells Propionibacterium shermanii as a result of different cobalamines adding into the cell suspension including metoxyethyladenile analog of adenozilcobalamin and some components of vitamin B12 molecule has been found. The DNA-synthesis rate in B12-deficient cells is nearly twice lower as compared with one in B12-normal cells. Considerable stimulative effect (80-100%) was provided with coenzyme forms of cobalamin. The data confirm the participation of vitamin B12 in DNA-synthesis in Propionibacterium cells.     

Application of a fiber-matrix model to transport in renal tubules

The effects of tight junction structure on water and solute fluxes across proximal tubular epithelium were examined with fiber-matrix equations previously derived by Curry and Michel (1980. Microvascular Research. 20:96-99). Using plausible estimates of tight junction fiber length and width the model predicts solute (Ps) and water permeability (Lp) coefficients that agree with the measured values. When fiber-matrix and pore models were compared for physiologically relevant ranges of matrix void fraction (80-98%) and pore radii (0-20 A), the fiber-matrix model predicted a 10-fold higher Lp/Ps ratio. Lp/Ps was most sensitive to small changes in tight junction structure when void fractions exceeded 90%. Void fractions of 96.5% and 97.1% predicted previously measured values for Lp and solute permeabilities in rat and rabbit proximal tubules. These values are consistent with void fractions and permeabilities of artificial membranes. The fiber-matrix tight junction model was incorporated into a model of reabsorption from the rat proximal tubule developed by Weinstein (1984). American Journal of Physiology. 247:F848-F862.) A void fraction of 98% predicted the experimental results for isosmotic reabsorption driven by active transport. Changing void fraction over the range of 97-99% produced a 50-75% change in predicted volume reabsorption with active transport. According to the fiber-matrix model: (a) solute permeabilities alone cannot be used to predict Lp, (b) previously measured solute permeabilities in the proximal tubule are compatible with significant water reabsorption through a water-permeable tight junction, and (c) hydraulic and solute permeabilities may be sensitive to small changes in tight junction fiber length and diameter or ionic strength within the tight junction.     

Role of pancreatic enzymes in the intraluminal transport and ileal absorption of vitamin B 12 (Cb 1)

The present paper outlines the classical concepts of transport and absorption of vitamin B12 and discusses findings which provide new insight into the important role of pancreatic enzymes in the absorption of the vitamin B12. In vivo experiments with healthy subjects and patients with exocrine pancreatic insufficiency demonstrate that the pancreatic enzymes do not activate "the precursor" intrinsic factor molecule but solely dissociate vitamin from the inactive R type proteins with a consequent coupling to the biologically active intrinsic factor.     

Osmotic water flow in leaky epithelia

I review three currently unsolved and controversial problems in understanding solute-linked water transport in epithelia. 1. Values of osmotic water permeability (Posm) calculated from steady-state osmotic flow in response to a gradient of a probe molecule tend to be underestimates, because of three unstirred-layer (USL) effects. These are: dissipation of the probe's gradient by diffusion in USL's; reduction of the probe's gradient, due to the sweeping-away effect of water flow generated by the probe itself; and solute polarization (creation of an opposing gradient of an initially symmetrically distributed solute by the sweeping-away effect). These errors increase with probe permeability, USL thickness, Posm, and concentration ratio of symmetrically distributed solute to probe, and vary inversely as the fractional area available for water flow (e.g., lateral intercellular space width). The form of an osmotic transient, and the possibility of extracting a true Posm value from the transient, depend on the relative values of three time constants: those for solute diffusion in USL's, for solute polarization by water flow in USL's and for measuring water flow. Sweeping-away effects cause major underestimates (by one or more orders of magnitude) in epithelial Posm determinations, as shown by apparent streaming potentials during osmotic flow and by transiently reversed flows after removal of the proble. True Posm values for leaky epithelia probably exceed 10(-3) or 10(-2) cm/sec.osm. The necessary conditions for resolving osmotic transients are set out. 2. I illustrate the difficulties in deciding what fraction of transepithelial water flow is via the cells, and what fraction via the junctions. There is no existing method for answering this question. 3. Controversies about the validity, or need for modification, of the standing-gradient theory are discussed. Progress in this field requires new methods: to resolve osmotic transients; to separate transcellular and transjunctional water flows; and to measure solute concentrations in lateral intercellular spaces directly.     

Transport of vitamin B12 in Escherichia coli: cloning of the btuCD region.

The transport of vitamin B12 in Escherichia coli requires a specific vitamin B12 receptor protein in the outer membrane and the tonB gene product. In addition, the btuC gene, located at min 38 on the genetic map, has been found to influence vitamin B12 uptake or utilization. The btuC function is required for the growth response to vitamin B12 when the outer membrane transport process (btuB or tonB function) is defective. However, even in a wild-type strain, btuC is required for proper transport of vitamin B12. Additional mutations in the vicinity of btuC were isolated as lac fusions that produced a phenotype similar to that of a btuC mutant. The btuC region was cloned by selection for complementation of a btuC mutation. Complementation testing with plasmids carrying various deletions or transposon Tn1000 insertions demonstrated that the new mutations defined a separate, independently expressed locus, termed btuD. The coding regions for both genes were identified on a 3.4-kilobase HindIII-HincII fragment and were 800 to 1,000 base pairs in length. They were separated by a 600- to 800-base-pair region. The gene order in this portion of the chromosome map was found to be pps-zdh-3::Tn10-btuD-btuC-pheS. Expression of beta-galactosidase in the btuD-lac fusion-bearing strains, whether proficient or defective in vitamin B12 transport, was not regulated by the presence of vitamin B12 in the growth medium.     

Performance of a hollow fibre beaker device for continuous enzymic reactions

The performance of the beaker-type hollow fibre dialyser as a continuous enzymatic reactor has been examined for two operational modes: (A) enzyme inside the fibres and substrate outside the fibres, (B) enzyme outside the fibres and substrate inside the fibres. On the basis of simple mathematical models, it is demonstrated that the superiority of mode (B) over (A) appears as the system approaches membrane permeation control. This conclusion is confirmed experimentally in the hydrolysis of urea.     

Simultaneous convective and diffusive mass transfers in a hemodialyser

The mass transfer in a hemodialyser in the presence of combined dialysis and ultrafiltration has been calculated by integration of mass fluxes across the boundary layers in blood and dialysate phase taking into account the partial rejection of solute as well as changes in local blood flow and ultrafiltration flux along the membrane. Clearances of creatinin, vitamin B12, and myoglobin have been calculated as a function of blood and ultrafiltrate flow rate and were found to be in good agreement with in vitro measurements. The data suggest the following empirical correlation for the hemodiafiltration clearance.     

The N-terminal domain of a TonB-dependent transporter undergoes a reversible stepwise denaturation

Gram-negative bacteria contain a family of outer membrane transport proteins that function in the uptake of rare nutrients, such as iron and vitamin B(12). These proteins are termed TonB-dependent because transport requires an interaction with the inner-membrane protein TonB. Using a combination of site-directed spin labeling and chemical denaturation, we examined the site-specific unfolding of regions of the Escherichia coli vitamin B(12) transporter, BtuB. The data indicate that a portion of the N-terminal region of the protein, which occupies the lumen of the BtuB barrel, denatures prior to the unfolding of the barrel and that the free energy of folding for the N-terminus is smaller than that typically seen for globular proteins. Moreover, the data indicate that the N-terminal domain does not unfold in a single event but unfolds in a series of independent steps. The unfolding of the N-terminus is reversible, and removal of denaturant restores the native fold of the protein. These data are consistent with proposed transport mechanisms that involve a transient rearrangement or unfolding of the N-terminus of the protein, and they provide evidence of a specific protein conformation that might be an intermediate accessed during transport.