Downloadable computer models for renal replacement therapy

Effect of Membrane Permeance and System Parameters on the Removal of Protein-Bound Uremic Toxins in Hemodialysis

Inadequate clearance of protein-bound uremic toxins (PBUTs) during dialysis is associated with morbidities in chronic kidney disease patients. The development of high-permeance membranes made from materials such as graphene raises the question whether they could enable the design of dialyzers with improved PBUT clearance. Here, we develop device-level and multi-compartment (body) system-level models that account for PBUT-albumin binding (specifically indoxyl sulfate and p-cresyl sulfate) and diffusive and convective transport of toxins to investigate how the overall membrane permeance (or area) and system parameters including flow rates and ultrafiltration affect PBUT clearance in hemodialysis. Our simulation results indicate that, in contrast to urea clearance, PBUT clearance in current dialyzers is mass-transfer limited: Assuming that the membrane resistance is dominant, raising PBUT permeance from 3 × 10-6 to 10-5 m s-1 (or equivalently, 3.3 × increase in membrane area from ~ 2 to ~ 6 m2) increases PBUT removal by 48% (from 22 to 33%, i.e., ~ 0.15 to ~ 0.22 g per session), whereas increasing dialysate flow rates or adding adsorptive species have no substantial impact on PBUT removal unless permeance is above ~ 10-5 m s-1. Our results guide the future development of membranes, dialyzers, and operational parameters that could enhance PBUT clearance and improve patient outcomes.

Regional citrate anticoagulation "non-shock" protocol with pre-calculated flow settings for patients with at least 6 L/hour liver citrate clearance

BACKGROUND

Regional citrate anticoagulation (RCA) for the prevention of clotting of the extracorporeal blood circuit during continuous kidney replacement therapy (CKRT) has been employed in limited fashion because of the complexity and complications associated with certain protocols. Hypertonic citrate infusion to achieve circuit anticoagulation results in variable systemic citrate- and sodium load and increases the risk of citrate accumulation and hypernatremia. The practice of "single starting calcium infusion rate for all patients" puts patients at risk for clinically significant hypocalcemia if filter effluent calcium losses exceed replacement. A fixed citrate to blood flow ratio, personalized effluent and pre-calculated calcium infusion dosing based on tables derived through kinetic analysis enable providers to use continuous veno-venous hemo-diafiltration (CVVHDF)-RCA in patients with liver citrate clearance of at least 6 L/h.

METHODS

This was a single-center prospective observational study conducted in intensive care unit patients triaged to be treated with the novel pre-calculated CVVHDF-RCA "Non-shock" protocol. RCA efficacy outcomes were time to first hemofilter loss and circuit ionized calcium (iCa) levels. Safety outcomes were surrogate of citrate accumulation (TCa/iCa ratio) and the incidence of acid-base and electrolyte complications.

RESULTS

Of 53 patients included in the study, 31 (59%) had acute kidney injury and 12 (22.6%) had the diagnosis of cirrhosis at the start of CVVHDF-RCA. The median first hemofilter life censored for causes other than clotting exceeded 70 h. The cumulative incidence of hypernatremia (Na > 148 mM), metabolic alkalosis (HCO3- > 30 mM), hypocalcemia (iCa < 0.9 mM) and hypercalcemia (iCa > 1.5 mM) were 1/47 (1%), 0/50 (0%), 1/53 (2%), 1/53 (2%) respectively and were not clinically significant. The median (25th-75th percentile) of the highest TCa/iCa ratio for every 24-h interval on CKRT was 1.99 (1.91-2.13).

CONCLUSIONS

The fixed citrate to blood flow ratio, as opposed to a titration approach, achieves adequate circuit iCa (< 0.4 mm/L) for any hematocrit level and plasma flow. The personalized dosing approach for calcium supplementation based on pre-calculated effluent calcium losses as opposed to the practice of "one starting dose for all" reduces the risk of clinically significant hypocalcemia. The fixed flow settings achieve clinically desirable steady state systemic electrolyte levels.

Improving Clearance for Renal Replacement Therapy

The adequacy of hemodialysis is now assessed by measuring the removal of a single solute, urea. The urea clearance provided by current dialysis methods is a large fraction of the blood flow through the dialyzer, and, therefore, cannot be increased much further. However, other solutes, which are less effectively cleared than urea, may contribute more to the residual uremic illness suffered by patients on hemodialysis. Here, we review a variety of methods that could be used to increase the clearance of such nonurea solutes. New clinical studies will be required to test the extent to which increasing solute clearances improves patients' health.

Regional Citrate Anticoagulation Protocol for Patients with Presumed Absent Citrate Metabolism

Background

Regional citrate anticoagulation (RCA) is not recommended in patients with shock or severe liver failure. We designed a protocol with personalized precalculated flow settings for patients with absent citrate metabolism that abrogates risk of citrate toxicity, and maintains neutral continuous KRT (CKRT) circuit calcium mass balance and normal systemic ionized calcium levels.

Methods

A single-center prospective cohort study of patients in five adult intensive care units triaged to the CVVHDF-RCA "Shock" protocol.

Results

Of 31 patients included in the study, 30 (97%) had AKI, 16 (52%) had acute liver failure, and five (16%) had cirrhosis at the start of CKRT. The median lactate was 5 mmol/L (interquartile range [IQR], 3.2-10.7), AST 822 U/L (IQR, 122-2950), ALT 352 U/L (IQR, 41-2238), total bilirubin 2.7 mg/dl (IQR, 1.0-5.1), and INR two (IQR, 1.5-2.6). The median first hemofilter life censored for causes other than clotting exceeded 70 hours. The cumulative incidence of hypernatremia (Na >148 mM), metabolic alkalosis (HCO3- >30 mM), and hypophosphatemia (P<2 mg/dl) were one out of 26 (4%), zero out of 30 (0%), and one out of 30 (3%), respectively, and were not clinically significant. Mild hypocalcemia occurred in the first 4 hours in two out of 31 patients, and corrected by hour 6 with no additional Ca supplementation beyond the per-protocol administered Ca infusion. The maximum systemic total Ca (tCa; mM)/ionized Ca (iCa; mM) ratio never exceeded 2.5.

Conclusions

The Shock protocol can be used without contraindications and is effective in maintaining circuit patency with a high, fixed ACDA infusion rate to blood flow ratio. Keeping single-pass citrate extraction on the dialyzer >0.75 minimizes the risk of citrate toxicity even in patients with absent citrate metabolism. Precalculated, personalized dosing of the initial Ca-infusion rate from a table on the basis of the patient's albumin level and the filter effluent flow rate maintains neutral CKRT circuit calcium mass balance and a normal systemic iCa level.

Mathematical models for kidney function focusing on clinical interest

We give an overview of mathematical models of renal physiology and anatomy with the clinician in mind. Beyond the past focus on issues of local transport mechanisms along the nephron and the urine concentrating mechanism, recent models have brought insight into difficult problems such as renal ischemia (oxygen and CO₂ diffusion in the medulla) or calcium and potassium homeostasis. They have also provided revealing 3D reconstructions of the full trajectories of families of nephrons and collecting ducts through cortex and medulla. The recent appearance of sophisticated whole-kidney models representing nephrons and their associated renal vasculature promises more realistic simulation of renal pathologies and pharmacological treatments in the foreseeable future.

An in silico method to predict net calcium transfer during hemodialysis

International guidelines for chronic hemodialysis patients suggest a dialysate calcium concentration between 1.25 and 1.5 mmol/L. However, it is not certain if these dialysate calcium levels result in net calcium transfer into the patient. With ubiquitous prevalence of vascular calcification in hemodialysis patients, it is pertinent to model the mass balance of calcium during dialysis. To this end, we developed a two compartmental patient model and spatiotemporal representation of dialyzer model to investigate and quantify the calcium mass balance during dialysis. The model accounts for calcium-albumin binding and varying protein concentration; the latter accounts for the Gibbs-Donnan effect. The model simulations suggest that despite a lower dialysate calcium concentration of 1.25 mmol/L, some of our patients may be loaded with calcium during dialysis. This net calcium flux from dialysate to blood side may be a potential contributor to vascular calcification, a primary cause of cardiovascular mortality in hemodialysis patients.

A novel mathematical model of protein-bound uremic toxin kinetics during hemodialysis

Protein-bound uremic toxins (PBUTs) are difficult to remove by conventional hemodialysis; a high degree of protein binding reduces the free fraction of toxins and decreases their diffusion across dialyzer membranes. Mechanistic understanding of PBUT kinetics can open new avenues to improve their dialytic removal. We developed a comprehensive model of PBUT kinetics that comprises: (1) a three-compartment patient model, (2) a dialyzer model. The model accounts for dynamic equilibrium between protein, toxin, and the protein-toxin complex. Calibrated and validated using clinical and experimental data from the literature, the model predicts key aspects of PBUT kinetics, including the free and bound concentration profiles for PBUTs and the effects of dialysate flow rate and dialyzer size on PBUT removal. Model simulations suggest that an increase in dialysate flow rate improves the reduction ratio (and removal) of strongly protein-bound toxins, namely, indoxyl sulfate and p-cresyl sulfate, while for weakly bound toxins, namely, indole-3-acetic acid and p-cresyl glucuronide, an increase in blood flow rate is advantageous. With improved dialyzer performance, removal of strongly bound PBUTs improves gradually, but marginally. The proposed model can be used for optimizing the dialysis regimen and for in silico testing of novel approaches to enhance removal of PBUTs.

Kt/Vurea and Nonurea Small Solute Levels in the Hemodialysis Study

The Hemodialysis (HEMO) Study showed that high-dose hemodialysis providing a single-pool Kt/V_urea of 1.71 provided no benefit over a standard treatment providing a single-pool Kt/V_urea of 1.32. Here, we assessed whether the high-dose treatment used lowered plasma levels of small uremic solutes other than urea. Measurements made ≥3 months after randomization in 1281 patients in the HEMO Study showed a range in the effect of high-dose treatment compared with that of standard treatment: from no reduction in the level of p-cresol sulfate or asymmetric dimethylarginine to significant reductions in the levels of trimethylamine oxide (-9%; 95% confidence interval [95% CI], -2% to -15%), indoxyl sulfate (-11%; 95% CI, -6% to -15%), and methylguanidine (-22%; 95% CI, -18% to -27%). Levels of three other small solutes also decreased slightly; the level of urea decreased 9%. All-cause mortality did not significantly relate to the level of any of the solutes measured. Modeling indicated that the intermittency of treatment along with the presence of nondialytic clearance and/or increased solute production accounted for the limited reduction in solute levels with the higher Kt/V_urea In conclusion, failure to achieve greater reductions in solute levels may explain the failure of high Kt/V_urea treatment to improve outcomes in the HEMO Study. Furthermore, levels of the nonurea solutes varied widely among patients in the HEMO Study, and achieved Kt/V_urea accounted for very little of this variation. These results further suggest that an index only on the basis of urea does not provide a sufficient measure of dialysis adequacy.

Mechanism of Prominent Trimethylamine Oxide (TMAO) Accumulation in Hemodialysis Patients

Large size, protein binding and intracellular sequestration are well known to limit dialytic removal of compounds. In studying the normal renal and dialytic handling of trimethylamine oxide (TMAO), a molecule associated with cardiovascular disease in the general population, we discovered two largely unrecognized additional limitations to sustained reduction of a solute by chronic hemodialysis. We measured solute levels and handling in subjects on chronic hemodialysis (ESRD, n = 7) and compared these with levels and clearance in normal controls (NLS, n = 6). The ESRD patients had much higher peak predialysis plasma levels of TMAO than NLS (77 ± 26 vs 2±1 μM, mean ± SD, p<0.05). For comparison, predialysis BUN levels in ESRD subjects were 45±11 mg/dl and 15±3 mg/dl in NLS. Thus TMAO levels in ESRD average about 40 fold those in NLS while BUN is 3 fold NLS. However, the fractional reduction of TMAO concentration during dialysis, was in fact greater than that of urea (86±3 vs 74±6%, TMAO vs urea, p < 0.05) and its dialytic clearance while somewhat lower than that of urea was comparable to creatinine's. Also production rates were similar (533±272 vs 606 ± 220 μ moles/day, ESRD vs NLS, p>0.05). However, TMAO has a volume of distribution about one half that of urea. Also in NLS the urinary clearance of TMAO was high (219±78 ml/min) compared to the urinary urea and creatinine clearances (55±14 and 119±21 ml/min, respectively). Thus, TMAO levels achieve multiples of normal much greater than those of urea due mainly to 1) TMAO's high clearance by the normal kidney relative to urea and 2) its smaller volume of distribution. Modelling suggests that only much more frequent dialysis would be required to lower levels Thus, additional strategies such as reducing production should be explored. Furthermore, using urea as the sole marker of dialysis adequacy may be misleading since a molecule, TMAO, that is dialyzed readily accumulates to much higher multiples of normal with urea based dialysis prescriptions.

Effect of increasing dietary fiber on plasma levels of colon-derived solutes in hemodialysis patients

BACKGROUND AND OBJECTIVES

Numerous uremic solutes are derived from the action of colon microbes. Two such solutes, indoxyl sulfate and p-cresol sulfate, have been associated with adverse outcomes in renal failure. This study tested whether increasing dietary fiber in the form of resistant starch would lower the plasma levels of these solutes in patients on hemodialysis.

DESIGN, SETTING, PARTICIPANTS, & MEASUREMENTS

Fifty-six patients on maintenance hemodialysis were randomly assigned to receive supplements containing resistant starch (n=28) or control starch (n=28) daily for 6 weeks in a study conducted between October 2010 and May 2013. Of these, 40 patients (20 in each group) completed the study and were included in the final analysis. Plasma indoxyl sulfate and p-cresol sulfate levels were measured at baseline and week 6.

RESULTS

Increasing dietary fiber for 6 weeks significantly reduced the unbound, free plasma level of indoxyl sulfate (median -29% [25th percentile, 75th percentile, -56, -12] for fiber versus -0.4% [-20, 34] for control, P=0.02). The reduction in free plasma levels of indoxyl sulfate was accompanied by a reduction in free plasma levels of p-cresol sulfate (r=0.81, P<0.001). However, the reduction of p-cresol sulfate levels was of lesser magnitude and did not achieve significance (median -28% [-46, 5] for fiber versus 4% [-28, 36] for control, P=0.05).

CONCLUSIONS

Increasing dietary fiber in hemodialysis patients may reduce the plasma levels of the colon-derived solutes indoxyl sulfate and possibly p-cresol sulfate without the need to intensify dialysis treatments. Further studies are required to determine whether such reduction provides clinical benefits.

Mathematical analysis for internal filtration of convection-enhanced high-flux hemodialyzer

Structural modifications using a conventional hemodialyzer improved the internal filtration and clearance of middle molecular weight wastes by enhanced convection effect. In this study, we employed a mathematical model describing the internal filtration rate as well as the hemodynamic and hematologic parameters in highflux dialyzer to interpret the previous reported experimental results. Conventional high-flux hemodialysis and convection-enhanced high-flux hemodialysis were configured in the mathematical forms and integrated into the iterative numerical method to predict the internal filtration phenomena inside the dialyzers during dialysis. The distributions of blood pressure, dialysate pressure, oncotic pressure, blood flow rates, dialysate flow rates, local ultrafiltration, hematocrit, protein concentration and blood viscosity along the axial length of dialyzer were calculated in order to estimate the internal filtration volume. The results show that the filtration volumes by internal filtration is two times higher in a convection-enhanced high-flux hemodialyzer than in a conventional high-flux hemodialzer and explains the experimental result of improved clearance of middle molecular size waste in convection-enhanced high-flux hemodialyzer.

Selectively increasing the clearance of protein-bound uremic solutes

BACKGROUND

The toxicity of bound solutes could be better evaluated if we could adjust the clearance of such solutes independent of unbound solutes. This study assessed whether bound solute clearances can be increased while maintaining urea clearance constant during the extended hours of nocturnal dialysis.

METHODS

Nine patients on thrice-weekly nocturnal dialysis underwent two experimental dialysis treatments 1 week apart. The experimental treatments were designed to provide the same urea clearance while providing widely different bound solute clearance. One treatment employed a large dialyzer and high dialyzate flow rate (Qd) of 800 mL/min while blood flow (Qb) was 270 mL/min. The other treatment employed a smaller dialyzer and Qd of 300 mL/min while Qb was 350 mL/min.

RESULTS

Treatment with the large dialyzer and higher Qd greatly increased the clearances of the bound solutes p-cresol sulfate (PCS: 27±9 versus 14±6 mL/min) and indoxyl sulfate (IS: 26±8 versus 14±5 mL/min) without altering the clearance of urea (204±20 versus 193±16 mL/min). Increasing PCS and IS clearances increased the removal of these solutes (PCS: 375±200 versus 207±86 mg/session; IS: 201±137 versus 153±74 mg/session), while urea removal was not different.

CONCLUSIONS

The removal of bound solutes can thus be increased by raising the dialyzate flow and dialyzer size above the low levels sufficient to achieve target Kt/V(urea) during extended treatment. Selectively increasing the clearance of bound solutes provides a potential means to test their toxicity.

Dialysis cannot be dosed

Adequate dialysis is difficult to define because we have not identified the toxic solutes that contribute most to uremic illness. Dialysis prescriptions therefore cannot be adjusted to control the levels of these solutes. The current solution to this problem is to define an adequate dose of dialysis on the basis of fraction of urea removed from the body. This has provided a practical guide to treatment as the dialysis population has grown over the past 25 years. Indeed, a lower limit to Kt/V(urea) (or the related urea reduction ratio) is now established as a quality indicator by the Centers for Medicare and Medicaid for chronic hemodialysis patients in the United States. For the present, this urea-based standard provides a useful tool to avoid grossly inadequate dialysis. Dialysis dosing, however, based on measurement of a single, relatively nontoxic solute can provide only a very limited guide toward improved treatment. Prescriptions which have similar effects on the index solute can have widely different effects on other solutes. The dose concept discourages attempts to increase the removal of such solutes independent of the index solute. The dose concept further assumes that important solutes are produced at a constant rate relative to body size, and discourages attempts to augment dialysis treatment by reducing solute production. Identification of toxic solutes would provide a more rational basis for the prescription of dialysis and ultimately for improved treatment of patients with renal failure.

Contribution of residual function to removal of protein-bound solutes in hemodialysis

BACKGROUND AND OBJECTIVES

This study evaluated the contribution of residual function to the removal of solutes for which protein binding limits clearance by hemdialysis.

DESIGN, SETTING, PARTICIPANTS, & MEASUREMENTS

Solute concentrations were measured in 25 hemodialysis patients with residual urea clearances ranging from 0.1 to 6.2 ml/min per 1.73 m2. Mathematical modeling assessed the effect of residual function on time-averaged solute concentrations.

RESULTS

Dialytic clearances of the protein-bound solutes p-cresol sulfate, indoxyl sulfate, and hippurate were reduced in proportion to the avidity of binding and averaged 8±2, 10±3, and 44±13% of the dialytic urea clearance. For each bound solute, the residual clearance was larger in relation to the residual urea clearance. Residual kidney function therefore removed a larger portion of each of the bound solutes than of urea. Increasing residual function was associated with lower plasma levels of p-cresol sulfate and hippurate but not indoxyl sulfate. Wide variation in solute generation tended to obscure the dependence of plasma solute levels on residual function. Mathematical modeling that corrected for this variation indicated that increasing residual function will reduce the plasma level of each of the bound solutes more than the plasma level of urea.

CONCLUSIONS

In comparison to urea, solutes than bind to plasma proteins can be more effectively cleared by residual function than by hemodialysis. Levels of such solutes will be lower in patients with residual function than in patients without residual function even if the dialysis dose is reduced based on measurement of residual urea clearance in accord with current guidelines.

Increasing the Clearance of Protein-Bound Solutes by Addition of a Sorbent to the Dialysate

The capacity of sorbent systems to increase solute clearances above the levels that are provided by hemodialysis has not been well defined. This study assessed the extent to which solute clearances can be increased by addition of a sorbent to the dialysate. Attention was focused on the clearance of protein-bound solutes, which are cleared poorly by conventional hemodialysis. A reservoir that contained test solutes and artificial plasma was dialyzed first with the plasma flow set at 46 +/- 3 ml/min and the dialysate flow (Q(d)) set at 42 +/- 3 ml/min using a hollow fiber kidney with mass transfer area coefficients greater than Q(d) for each of the solutes. Under these conditions, the clearance of urea (Cl(urea)) was 34 +/- 1 ml/min, whereas the clearances of the protein-bound solutes indican (Cl(ind)), p-cresol sulfate (Cl(pcs)), and p-cresol (Cl(pc)) averaged only 5 +/- 1, 4 +/- 1, and 14 +/- 1 ml/min, respectively The effect of addition of activated charcoal to the dialysate then was compared with the effect of increasing Q(d) without addition of any sorbent. Addition of charcoal increased Cl(ind), Cl(pcs), and Cl(pc) to 12 +/- 1, 9 +/- 2, and 35 +/- 4 ml/min without changing Cl(urea). Increasing Q(d) without the addition of sorbent had a similar effect on the clearance of the protein-bound solutes. Mathematical modeling predicted these changes and showed that the maximal effect of addition of a sorbent to the dialysate is equivalent to that of an unlimited increase in Q(d). These results suggest that as an adjunct to conventional hemodialysis, addition of sorbents to the dialysate could increase the clearance of protein-bound solutes without greatly altering the clearance of unbound solutes.