Progress toward a potentially implantable, enzyme-based glucose sensor.

Our efforts toward the development of a potentially implantable, enzyme-based glucose sensor have concentrated on understanding in sufficient detail the most important component, the enzyme-containing membrane. We describe here some features that this membrane must have to operate as a constituent of a chronically implanted sensor. A model of reaction and diffusion within the membrane is outlined and methods of membrane characterization are reviewed.

Increases in mass transfer-area coefficients and urea Kt/V with increasing dialysate flow rate are greater for high-flux dialyzers.

The hemodialyzer mass transfer-area coefficient (K(o)A) for urea increases with increasing dialysate flow rate (Q(d)). The magnitude of the increase in K(o)A varies depending on the particular dialyzer under consideration; however, dialyzer properties that govern this phenomenon have not been established. We hypothesized that Q(d)-dependent increases in K(o)As are influenced by the water permeability of the dialysis membrane. We evaluated in vitro the effect of blood flow rate (Q(b)) and Q(d) on urea and creatinine K(o)As for two low-flux (Polyflux 6L and 8L) and two high-flux (Polyflux 14S and 17S) dialyzers containing Polyamide S membranes with similar membrane surface areas. Additional experiments were also performed on high-flux dialyzers containing Polyamide S membranes with very large surface areas (Polyflux 21S and 24S). K(o)As, calculated from the mean of blood- and dialysate-side clearances, were determined at zero net ultrafiltration for three different Q(b) and Q(d) combinations: Q(b) of 300 mL/min and Q(d) of 500 mL/min; Q(b) of 450 mL/min and Q(d) of 500 mL/min; and Q(b) of 450 mL/min and Q(d) of 800 mL/min. Urea and creatinine K(o)As were independent of the Q(b) but increased when Q(d) was increased from 500 to 800 mL/min. These increases in both urea and creatinine K(o)As were greater for high-flux than low-flux dialyzers (P < 0.0001). As expected, urea and creatinine K(o)As also increased with increasing membrane surface area. We conclude that dialysis membrane water permeability (or flux) is a dialyzer property that influences the dependence of small-solute K(o)As and clearance on Q(d). Whether this phenomenon is caused by enhanced internal filtration for dialyzers containing high-flux membranes requires further study.

Effect of dialysis membranes and middle molecule removal on chronic hemodialysis patient survival.

The type of dialysis membrane used for routine therapy has been recently shown to correlate with the survival of chronic hemodialysis patients. We examined whether this effect of dialysis membrane could be explained by differences in dialyzer removal of middle molecules using data from the 1991 Case Mix Adequacy Study of the United States Renal Data System. The sample analyzed included patients who had been treated by hemodialysis for 1 year or more, who were dialyzed with the 19 most commonly used dialyzers in 1991, and for whom delivered urea Kt/V could be calculated from predialysis and postdialysis blood urea nitrogen concentrations. Vitamin B12 (1,355 daltons) was used as a marker for middle molecules, and the clearance of vitamin B12 was estimated based on in vitro data. After adjustments for case mix, comorbidities, and urea Kt/V, the relative risk of mortality for a 10% higher calculated total cleared volume of vitamin B12 was 0.953 (P < 0.0001 v 1.000). Similar results were obtained when middle molecule removal was adjusted for body size. We conclude that both small and middle molecule removal indices appear to be independently associated with the risk of mortality in chronic hemodialysis patients. Differences in mortality when using different types of dialysis membrane may be explained by differences in middle molecule removal.

The hemodialysis membranes: a historical perspective, current state and future prospect.

Transport and biocompatibility characteristics are two important considerations when choosing hemodialysis membranes. Dialyzer performance depends on clearances of small solutes, middle molecules, and oncotically active proteins. Although complement and neutrophil activation have become the gold standards for biocompatibility testing of dialysis membranes, alterations of other cellular and noncellular blood elements as a result of blood-membrane interactions are also important. Because of concerns about middle molecule transport and biocompatibility, the original cellophane membrane has been gradually replaced by modified cellulosic membranes and synthetic membranes for clinical use. Recent studies suggest that the choice of dialysis membrane influences the clinical outcome of patients in several areas, including intradialytic acute anaphylactoid reactions, beta 2-microglobulin associated amyloidosis, recovery from acute renal failure, and mortality of chronic hemodialysis patients. However, the relative contributions of middle molecule transport, biocompatibility, and other factors in determining these differences in outcome are unclear. Future development of hemodialysis membranes should focus on improving biocompatibility and enhancing clearances of small solutes and middle molecules, while minimizing the loss of larger plasma proteins.

Flow distributions in hollow fiber hemodialyzers using magnetic resonance Fourier velocity imaging.

Distribution of flow within the hollow fibers and the dialysate compartment of hemodialyzers is difficult to measure; previous work has suggested that flow distributions may be non uniform. Magnetic resonance Fourier velocity imaging was used to determine flow distributions within the hollow fibers and dialysate compartment of three commercial hemodialyzers (CA170, CT190, and F60A). Distilled water was pumped without pulsatility through the hollow fibers and the outflow was circulated in a countercurrent direction through the dialysate compartment. Steady state flow distributions were determined simultaneously in both directions using input flow rates of 300 and 600 ml/min. Flow distributions within the hollow fibers were relatively uniform in most hemodialyzer cross sections, approximately Gaussian, and similar for all hemodialyzers. Flow distributions in the dialysate compartment were non uniform and skewed to high flow rates. High flow in the dialysate compartment was largely outside the fiber bundle for the CA170 and CT190 hemodialyzers. Local regions containing both low flow within the hollow fibers and high flow in the dialysate compartment were observed for the F60A hemodialyzer, and these regions became more prominent at a flow rate of 600 ml/min. The results of this study demonstrate that flow distributions within the hollow fibers and dialysate compartment of hemodialyzers can be simultaneously determined using magnetic resonance Fourier velocity imaging. It is concluded that the distribution of flow within the hollow fibers of hemodialyzers is relatively uniform but in the dialysate compartment it is not uniform and depends upon hemodialyzer design.

Single compartment models for evaluating beta 2-microglobulin clearance during hemodialysis.

Methods for evaluating dialyzer clearance of beta 2-microglobulin during clinical hemodialysis have not been well established. The authors show, theoretically, that the postdialysis-to-predialysis concentration ratio, a parameter often used to estimate dialyzer clearance of beta 2-microglobulin, depends on KdT/V (the dialyzer clearance times the treatment time divided by the distribution volume for beta 2-microglobulin) and the ultrafiltration rate, assuming that a single compartment kinetic model is valid. They also show that adjustment of the postdialysis concentration of beta 2-microglobulin for changes in its volume of distribution does not entirely correct for fluid removal when the adjusted postdialysis-to-predialysis concentration ratio is significantly below one. These considerations suggest that estimates of dialyzer clearance of beta 2-microglobulin using single compartment models are more reliable than those using only the postdialysis-to-predialysis concentration ratio. To illustrate these constructs, the authors compared experimental estimates of beta 2-microglobulin clearance during clinical hemodialysis using single compartment models with those measured directly from the arteriovenous concentration difference across the dialyzer. First-use low flux and high flux-dialyzers and those reprocessed with Renalin were studied. Single compartment estimates of beta 2-microglobulin clearance for low flux dialyzers were similar to those measured directly across the dialyzer, but single compartment estimates of beta 2-microglobulin clearance for high flux dialyzers exceeded (p < 0.001) those measured directly across the dialyzer, independent of whether fluid removal during hemodialysis was assumed to be removed entirely from the extracellular compartment or proportionally from both intracellular and extracellular compartments. The authors conclude that accurate estimates of beta 2-microglobulin clearance for high flux dialyzers will require kinetic models that are more complex than those assuming a uniform distribution of beta 2-microglobulin in a single, well-mixed compartment.

Hematocrit as an indicator of blood volume and a predictor of intradialytic morbid events.

Hematocrit (H) levels can change during hemodialysis, and these changes in H are inversely related to changes in blood volume (BV). The objectives of this study were to determine whether mean arterial pressure (MAP) decreases with decreasing BV and rising H during hemodialysis, and to determine the relationship between dialysis induced intravascular volume depletion and intradialytic morbid events (IME), defined as hypotension, cramping, or lightheadedness that led to dialysis staff intervention. We monitored H continuously using a noninvasive optical technique in 93 hemodialysis sessions in 16 patients. IME occurred in 48 sessions. MAP decreased with increasing H in 10 of 16 patients (P < 0.05), but the relationship between MAP and H varied among the patients. The rate of BV change during sessions without morbidity (5.6 +/- 3.6 [SD] %/hr) was lower (P < 0.001) than that preceding IME in the other sessions (12.2 +/- 5.5 [SD] %/hr). Twelve of 16 patients who exhibited recurrent IME during this study experienced these events when H reached a patient specific threshold. It is concluded that MAP decreases with decreasing BV and increasing H in many patients on hemodialysis, and that a high rate of BV change often indicates that IME are forthcoming. It is further hypothesized that a patient specific H threshold is indicative of a critical BV level below which certain patients experience IME.

Interpreting peritoneal membrane osmotic reflection coefficients using a distributed model of peritoneal transport.

The relationship between the osmotic reflection coefficient for the peritoneal membrane and that for peritoneal capillaries was derived theoretically using a distributed model of peritoneal transport. The distributed model predicted that the osmotic reflection coefficient for the peritoneal membrane was equal to that for peritoneal capillaries only when the capillary wall was the dominant diffusive solute transport resistance. Under these conditions, moreover, all peritoneal capillaries equally contributed to transperitoneal ultrafiltration. If, on the other hand, interstitial tissue was the dominant diffusive solute transport resistance, then the osmotic reflection coefficient for the peritoneal membrane was lower than that for peritoneal capillaries and only superficial capillaries participated in transperitoneal ultrafiltration. Previous experiments have demonstrated that the capillary wall is not the dominant diffusive solute transport resistance for small osmotic solutes across the peritoneal membrane; thus osmotic reflection coefficients for the peritoneal membrane are likely several times less than those for peritoneal capillaries.

Efficacy of local dipyridamole therapy in a porcine model of arteriovenous graft stenosis.

Perivascular delivery of antiproliferative drugs has been proposed as an approach to prevent neointimal hyperplasia associated with hemodialysis polytetrafluoroethylene (PTFE) grafts. We examined this approach to deliver dipyridamole in a porcine graft model. PTFE grafts were implanted between the carotid artery and external jugular vein bilaterally in pigs. During the surgery or 1 week post-graft placement, dipyridamole (0.26-52 mg) alone or incorporated in microspheres was mixed with an injectable polymeric gel and applied to the graft-arterial and graft-venous anastomoses on one side, whereas the contralateral control graft received no treatment. Three or four weeks after operation, the grafts and adjacent vessels were explanted en bloc and cross-sections of the anastomoses were examined histologically. The degree of neointimal hyperplasia was quantified by planimetry. In separate experiments, dipyridamole was extracted from the explanted tissues and assayed by spectrofluorometry. The normalized median hyperplasia areas of the treated and control graft-venous anastomoses were 0.45 (25th-75th percentile, 0.30-0.86) and 0.24 (0.21-0.30), respectively (N=7; P=0.08). The median hyperplasia areas of the treated and control graft-arterial anastomoses were 0.12 (0.07-0.39) and 0.11 (0.09-0.13), respectively (N=7; P=0.31). The dipyridamole levels in the vascular walls around the anastomoses were at or above the in vitro inhibitory concentrations for approximately 3 weeks. These results suggest that the local perivascular sustained delivery of dipyridamole, even at high dosages, was ineffective in inhibiting neointimal hyperplasia associated with PTFE grafts in a porcine model.

Determining ultrafiltration properties of the peritoneum.

Peritoneal solute reflection coefficients have previously been determined by simply comparing the time dependence of the solute concentration in the dialysis solution with that predicted by mathematical models. The present study theoretically examines the experimental conditions required to determine the solute reflection coefficient from the dependence of the dialysate concentration on time. Optimal experimental conditions are first derived using an approximate mathematical model that permits simple interpretation; these predictions are confirmed by numerical computation using a more rigorous model. It is demonstrated that the peritoneal solute reflection coefficient can be determined when solute transport is in the blood to dialysate direction only during a hypertonic exchange. When solute transport is in the dialysate to blood direction, the solute reflection coefficient can be determined using a hypotonic dialysis solution only for solutes that diffuse slowly across the peritoneum. Reliable determinations of the peritoneal solute reflection coefficient can only be obtained when using these experimental conditions.

Evaluation of peritoneal membrane pore models.

Pore models of peritoneal fluid and solute transport are reviewed and critiqued. Although several pore models of the peritoneal membrane have been previously formulated, a model containing three distinct pore sizes is required to accurately simulate both the molecular size dependence of solute transport and the time dependence of fluid transport during peritoneal dialysis in man. Nevertheless, certain observations from peritoneal dialysis experiments using animals do not agree with predictions from the three-pore model. These discrepancies suggest that the three-pore model of peritoneal transport based exclusively on capillary physiology is incomplete. Moreover, our inability to accurately estimate peritoneal reflection coefficients for small osmotic solutes questions whether lymph flow rates from the peritoneal cavity calculated using the three-pore model are reliable. Further experimental and theoretical studies are needed to obtain a better understanding of peritoneal transport physiology.

Solute fluxes in different treatment modalities.

The principles governing solute flux or transport in different artificial kidney treatment modalities are reviewed. Solute clearance profiles were calculated for identical artificial kidney membranes during haemodialysis, haemofiltration and haemodiafiltration. It was shown that the clearance of small solutes depends largely on the dialysate flow rate and is similar when using either haemodialysis or haemodiafiltration. In contrast, clearance of middle molecules, especially low-molecular-weight proteins, depends largely on convective transport induced by high ultrafiltration rates and is maximized when using either haemofiltration or haemodiafiltration. Optimal fluxes for both small solutes and middle molecules can be achieved by using postdilution haemodiafiltration. Recent work has shown that use of the reduction in plasma concentration, even after normalization for changes in extracellular volume during therapy, is not an exact measure of beta2-microglobulin (and other low-molecular-weight proteins) clearance. It is proposed that beta2-microglobulin clearance be reported in future studies instead of the normalized reduction in beta2-microglobulin plasma concentration. Additional studies are necessary to determine the effects of postdialysis rebound on the calculated clearance for beta2-microglobulin and other high-molecular-mass uraemic toxins.

Evaluation of peritoneal membrane permeability.

Total removal of fluid and solutes during peritoneal dialysis depends on both the dialysis prescription (ie, the number, length, and timing of the dwells and the volume and contents of the dialysis solution) and the permeability of the peritoneal membrane. Peritoneal membrane permeability determines the rate of solute equilibration between body fluids and the solution within the peritoneal cavity and is, therefore, a significant determinant of the solute removal rate. The relationship between fluid removal during peritoneal dialysis and the properties of the peritoneal membrane is more complex; peritoneal ultrafiltration is inversely related to the permeability of the peritoneal membrane to osmotic solutes but is directly related to the hydraulic conductivity of the peritoneal membrane. The peritoneal equilibration test (PET) is widely used as the standard method for evaluating peritoneal membrane permeability, and results from the PET can be used to determine the type of peritoneal dialysis therapy optimal for the permeability characteristics of the patient's peritoneal membrane. Simple extrapolations from the PET can only provide qualitative estimates of the dialysis dose required for various types of peritoneal dialysis. More accurate estimates of the required dialysis dose can be provided by mathematical models of peritoneal fluid and solute transport, but these models require calculation of the permeability-area product or mass transfer-area coefficient of the peritoneal membrane. Although the latter approach shows promise for improving peritoneal dialysis prescriptions, determination of the delivered dose of peritoneal dialysis can, at present, only be assessed by directly measuring total 24-hour solute and fluid removal.

Molecular charge influences transperitoneal macromolecule transport.

The influence of molecular charge on macromolecule transport during peritoneal dialysis was assessed by determining transperitoneal transport rates for fluorescent-labeled macromolecules (molecular radii from 15 to 40 A) that differed only in molecular charge: neutral dextran, anionic dextran sulfate and cationic diethylaminoethyl (DEAE) dextran. The test macromolecules were infused into the bloodstream of unanesthetized New Zealand White rabbits at a constant rate, and isotonic dialysis solution (40 ml/kg) was instilled into the peritoneal cavity. Blood and dialysate samples were taken hourly over a four hour dwell. Transperitoneal transport rates were assessed by calculating both the dialysate to plasma concentration ratio at four hours and the permeability-area product for the peritoneum, the latter parameter determined from the increase in the dialysate concentration with time. Transport rates for DEAE dextran were less (P < 0.05) than those for both neutral dextran and dextran sulfate; transport rates for neutral dextran and dextran sulfate were not different. Moreover, transperitoneal transport rates for fluorescent-labeled DEAE dextran were not affected by adding unlabeled DEAE dextran to the intravenous infusion solution, an observation suggesting that low transport rates for DEAE dextran were not due to its binding to plasma protein. We conclude that molecular charge is a determinant of transperitoneal macromolecule transport.

Unilateral nephrectomy and glomerular solute transport in the dog.

The influence of compensatory hyperfunction that occurs following unilateral nephrectomy on glomerular solute transport was determined in awake, unanesthetized dogs by renal clearance studies. Two groups of dogs were studied using different test solutes: group I (N = 5) using inulin, iothalamate, creatinine and sodium p-aminohippurate; and group II (N = 6) using creatinine, neutral dextran (3000 to 50,000 daltons) and sodium p-aminohippurate. Compensatory hyperfunction, as assessed by the increase in creatinine clearance per kidney, was 43 +/- 7% and 39 +/- 11% in the group I and II dogs, respectively. The inulin to creatinine and iothalamate to creatinine clearance ratios in the group I dogs were 0.93 +/- 0.07 and 1.00 +/- 0.04 before unilateral nephrectomy. The respective values after unilateral nephrectomy of 0.86 +/- 0.04 and 0.89 +/- 0.05 were lower but not statistically different. In the group II dogs, dextran to creatinine clearance ratios (dextran fractional clearance) over the molecular weight range studied also did not change significantly following unilateral nephrectomy. The magnitude of the change in dextran fractional clearance following unilateral nephrectomy was qualitatively consistent with that predicted by previous models of glomerular macromolecular transport based on membrane pore theory. A lack of quantitative agreement with these models, however, precluded a calculation of the changes in glomerular functional parameters following unilateral nephrectomy. Significant alterations in fractional clearance for neutral macromolecules do not occur following unilateral nephrectomy in the dog.

Peritoneal solvent drag reflection coefficients are within the physiological range.

Previous estimates of the peritoneal solvent drag reflection coefficient (sigma) are widely disparate; some are outside the range expected for a semipermeable membrane (i.e., between 0 and 1). We have evaluated a novel method for determining sigma in a rabbit model of peritoneal dialysis. Test solute was infused intravenously, and sequential 2-hour isotonic and hypertonic exchanges (40 ml/kg) were performed in random order. Test solute was also added to the instilled hypertonic dialysis solution to inhibit transperitoneal solute diffusion during this exchange. Eight experiments were performed with creatinine as test solute and glucose as osmotic solute, and six experiments were performed with glucose as test solute and mannitol as osmotic solute. When using isotonic dialysis solution, the dialysate/plasma concentration ratio (D/P) for both test solutes increased throughout the exchange (p < 0.001). When using hypertonic dialysis solution, D/P creatinine was initially near 1 and decreased during the 1st hour of the exchange (p < 0.05); D/P glucose (as test solute) was initially 0.82 +/- (SEM) 0.07 and did not change during the exchange. The peritoneal diffusive permeability-area product (PA) was determined by fitting a mathematical model to the time dependence of the dialysate test solute concentration during the isotonic exchange using PA as an adjustable parameter, and sigma was determined in like manner during the hypertonic exchange using sigma as an adjustable parameter (and assuming a PA value equal to that during the isotonic exchange). The creatinine PA (1.37 +/- 0.28 ml/min) was higher than that for glucose (0.62 +/- 0.07 ml/min) as expected based on their solution diffusion coefficients. Creatinine and glucose sigma values were 0.38 +/- 0.06 and 0.43 +/- 0.05, respectively. We conclude that peritoneal sigma values for creatinine and glucose are within the physiological range.

The effect of convection on bidirectional peritoneal solute transport: predictions from a distributed model.

A distributed model of the peritoneum has been proposed as an alternative to the standard membrane model for describing peritoneal solute transport. The effect of convection on bidirectional peritoneal solute transport is studied theoretically using the distributed model. Approximate analytical and exact numerical solutions to the distributed model yield predictions similar to those when using a membrane model of peritoneal solute transport. Difficulties in interpretation of the membrane transport parameters may arise, however, when interstitial tissue, not the capillary wall, is the dominant diffusive solute transport resistance. Under such conditions the effect of convection on peritoneal solute transport is dependent on the transport direction. Moreover, predictions from the distributed model are similar to those for a membrane model containing two transport barriers in series. Thus, both the distributed model and a membrane model containing two serial transport barriers equivalently describe the effect of convection on bidirectional peritoneal solute transport.

Convection does not govern plasma to dialysate transport of protein.

The dependence of protein clearance on molecular size during peritoneal dialysis can be explained by assuming that either convection or diffusion is the major mechanism governing plasma to dialysate transport of protein. If convection is the predominant transport mechanism, then plasma-to-dialysate transport rates for protein should not decrease when the protein concentration in the instilled dialysis solution is increased. In the present study, plasma-to-dialysate transport rates for fluorescein-labeled protein tracers, alpha-lactalbumin and immunoglobulin G (IgG), were determined during a six hour isotonic exchange (25 ml/kg) in New Zealand White rabbits. The protein tracers were continuously infused into the bloodstream to keep plasma concentrations relatively constant, and transperitoneal transport rates were determined either with or without tracer protein added to the instilled dialysis solution. Plasma-to-dialysate transport rates were greater for alpha-lactalbumin than for IgG as expected based on the molecular size of these proteins. Transport rates for both alpha-lactalbumin and IgG decreased when tracer protein was added to the instilled dialysis solution. The present observations do not support convection as the major mechanism governing plasma to dialysate transport of protein during peritoneal dialysis.

Characterization of molecular transport in artificial kidneys.

Transport characterizations of artificial kidneys require the use of multiple marker molecules of various sizes, including small solutes, middle molecules, and albumin. Previous approaches for evaluating hemodialyzer transport performance are reviewed. New data obtained from in vitro experiments comparing 5 low molecular weight proteins of approximately the same molecular size as markers for middle molecule transport also are described. Sieving coefficients for marker low molecular weight proteins may vary substantially for a given artificial kidney membrane. Furthermore, sieving coefficients for marker proteins that do not absorb significantly to the membrane are comparable to those for polydisperse dextrans. These observations suggest that other protein properties besides molecular size are important determinants of protein sieving coefficients across artificial kidney membranes. We conclude that low molecular weight proteins can behave differently from one another and generalizations about artificial kidney membrane transport from data obtained on a single protein may be problematic, and that both low molecular weight proteins and polydisperse dextrans are useful markers of middle molecular transport across artificial kidney membranes.