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

Novel substitution technique in intermittent infusion hemodiafiltration (I-HDF) therapy using back filtration as substitution

An infusion of dialysate into the blood compartment across the membrane using back filtration in dialysis therapy provides a stabilizing blood pressure and a membrane flushing during treatment. We devised a method to flush the membrane effectively and tried to find the optimum infusion patterns for intermittent infusion hemodiafiltration (I-HDF) from the aspect of solute removal by computing the pressure distribution in a diafilter. Bovine blood experiments were performed under following three modes: control HD in which no intentional filtration was involved, and two I-HDF in which back filtration was made either under counter current or under parallel flow. The inner surface of the hollow fiber before and after the experiment was observed using FE-SEM. According to the computation of the pressure distribution, a large amount of normal filtration occurs near the blood inlet in control HD. In addition, when the back filtration is performed under parallel flow, the amount of backfiltration near the blood inlet is 3.43 times higher than that in the case of counter current. Clearance (C_L) of inulin remained at the highest level when the back filtration was performed under parallel flow. Near the blood inlet where the fouling was significantly formed, many macropores remained on the membrane when the backfiltration was performed under parallel flow. The degree of fouling showed a distribution along with the blood flow and the pressure distribution. Furthermore, the more effective recovery of C_L can be expected by introducing the backfiltration under parallel flow to which fouling was significantly formed.

Determinants of Hemodialysis Performance: Modeling Fluid and Solute Transport in Hollow-Fiber Dialyzers

Hemodialysis constitutes the lifeline of patients with end stage renal disease, yet the parameters that affect hemodialyzer performance remain incompletely understood. We developed a computational model of mass transfer and solute transport in a hollow-fiber dialyzer to gain greater insight into the determinant factors. The model predicts fluid velocity, pressure, and solute concentration profiles for given geometric characteristics, membrane transport properties, and inlet conditions. We examined the impact of transport and structural parameters on uremic solute clearance by varying parameter values within the constraints of standard clinical practice. The model was validated by comparison with published experimental data. Our results suggest solute clearance can be significantly altered by changes in blood and dialysate flow rates, fiber radius and length, and net ultrafiltration rate. Our model further suggests that the main determinant of the clearance of unreactive solutes is their diffusive permeability. The clearance of protein-bound toxins is also strongly determined by blood hematocrit and plasma protein concentrations. Results from this model may serve to optimize hemodialyzer operating conditions in clinical practice to achieve better clearance of pathogenic uremic solutes.

The course of hematocrit value along the length of a dialyzer's fiber: Hemoconcentration modeling and validation methods

OBJECTIVES

Contemporary therapies for chronic kidney disease patients encompass a wide range of hemodialysis treatments, most of which rely greatly on dialyzers and hemofilters. The filtration process taking place in these devices with respect to the hemodynamic characteristics of the flow, has not yet been fully investigated. This study aims at improving the understanding of hemodynamics in a dialyzer by employing experimental methods and mathematical models.

METHODS

A semiempirical model has been formulated based on the principles of hemodynamics, considering the dominant phenomena of filtration-backfiltration and the corresponding driving forces. An in vitro hemodialysis circuit was accordingly assembled for experimental data acquisition, and subsequently for model validation. The circuit consisted of two dialyzers arranged in sequential order, in pursuance of increasing the number of sampling points. Fresh, heparinized porcine blood was used throughout the course of this study. Pressure and flow data obtained from in vitro investigations with the hemodialysis circuit were used as an input for the semiempirical model.

FINDINGS

The model predicted a substantial divergence in the course of hematocrit value along the length of the hollow fibers, which is corroborated by the experimental data. Particularly in certain operational conditions, hematocrit rose from 25% at the inlet to 65% halfway along the dialyzers' length, to end at 30% at the outlet.

CONCLUSION

Validation of the model's predictions with experimental data demonstrated a very good agreement, confirming the model's accuracy. Potential implementation of the model in clinical practice in the future might contribute greatly to an improved hemodialysis experience.

Combined In Silico and In Vitro Approach Predicts Low Wall Shear Stress Regions in a Hemofilter that Correlate with Thrombus Formation In Vivo

A major challenge in developing blood-contacting medical devices is mitigating thrombogenicity of an intravascular device. Thrombi may interfere with device function or embolize from the device to occlude distant vascular beds with catastrophic consequences. Chemical interactions between plasma proteins and bioengineered surface occur at the nanometer scale; however, continuum models of blood predict local shear stresses that lead to platelet activation or aggregation and thrombosis. Here, an iterative approach to blood flow path design incorporating in silico, in vitro, and in vivo experiments predicted the occurrence and location of thrombi in an implantable hemofilter. Low wall shear stress (WSS) regions identified by computational fluid dynamics (CFD) predicted clot formation in vivo. Revised designs based on CFD demonstrated superior performance, illustrating the importance of a multipronged approach for a successful design process.

Middle molecule elimination in expanded haemodialysis: only convective transport?

Background

New high-retention onset dialysers have shown improved efficacy in the elimination of uraemic toxins, and their depurative capacity has been compared with high convective volumes of online haemodiafiltration. Haemodialysis (HD) using high-flux membranes leads to convective transport by internal filtration [direct filtration (DF)/backfiltration (BF)] and allows the removal of middle molecules (MMs). The aim of this study was to assess solute transport mechanisms in expanded HD (HDx).

Methods

In 14 4-h HDx sessions with Theranova-500 dialysers under similar dialysis conditions (blood flow 400 mL/min, dialysate flow 700 mL/min, dialysate temperature 35.5°C), pressures at the inlet and outlet of both dialyser compartments (P _bi, P _bo, P _di and P _do) were collected hourly to estimate DF/BF volumes by semi-empirical methods. Uraemic toxins with various molecular weights were measured pre-dialysis, at 1 h (pre-filter and post-filter) and post-dialysis to calculate molecules' reduction over time and dialyser in vivo clearances.

Results

Ultrafiltration was 1.47 ± 0.9 L and Kt/V 1.74 ± 0.3. Hydrodynamic data (P _bi: 259 ± 39, P _bo: 155 ± 27, P _di: 271 ± 30, P _do: 145 ± 29 mmHg and oncotic pressure 22.0 ± 3.5 mmHg) allowed the estimation of DF/BF rates. DF flow ranged from 29.5 ± 4.2 to 31.3 ± 3.9 mL/min and BF flow ranged from 25.1 ± 2.3 to 23.4 ± 2.6 mL/min. The highest calculated DF volume was 7506.8 ± 935.3 mL/session. Diffusive clearances (K _d) of all solutes were higher than their convective transport (all P < 0.001) except for prolactin (23 kDa) clearances, which showed no differences. Total clearances of all solutes were correlated with their K _d (ρ = 0.899-0.987, all P < 0.001) and Kt/V correlated with all reduction rates (ρ = 0.661-0.941, P = 0.010 to <0.001). DF flow was only associated with urea (ρ = -0.793, P = 0.001), creatinine (ρ = -0.675, P = 0.008) and myoglobin clearance (ρ = 0.653, P = 0.011).

Conclusion

Results suggest that diffusive transport is a main mechanism of MM elimination in HDx. HDx offers an efficient depuration of MM without the need for high convective volumes.

Quantification of Internal Filtration in Hollow Fiber Hemodialyzers with Medium Cut-Off Membrane

Background: Inadequate removal of molecules between 5 and 50 KDa may cause long-term complication in chronic hemodialysis. Medium cut-off (MCO) is a new class of membranes with enhanced sieving properties and negligible albumin loss. MCO membrane makes it possible to perform expanded hemodialysis (HDx), a technique based on high internal filtration (IF).The present study is designed to quantify IF in 2 MCO dialyzers (Theranova 400 and 500, Baxter, Deerfield, USA) using a nuclear imaging technique previously validated. Methods: Blood and dialysate compartment pressure drop along with transmembrane pressure; they were measured in a closed in vitro circuit with human blood (blood flow [QB] = 300 and 400 mL/min; dialysate flow 500 mL/min; net ultrafiltration rate 0 mL/min). A non-diffusible marker molecule (albumin macro-aggregates labeled with 99Tc metastable) was injected in the blood compartment and nuclear emission was recorded by a gamma camera. Relative variations in the concentration of the marker molecule along the length of the filter were used to calculate local cross filtration. Results: Based on marker concentration profiles, IF was estimated. For Theranova 400, IF were 29.7 and 41.6 mL/min for QB of 300 and 400 mL/min. For Theranova 500, IF were 31.6 and 53.1 mL/min for QB of 300 and 400 mL/min respectively. Conclusions: MCO membrane provides significant amounts of IF due to the particular combination between hydraulic permeability of the membrane and reduced inner diameter of the fibers. High IF combined with enhanced sieving profile of MCO membrane leads to improved removal of a wider spectrum of uremia retention molecules in HDx, without requiring complex equipment.

Original article submission: Platelet stress accumulation analysis to predict thrombogenicity of an artificial kidney

An implantable artificial kidney using a hemofilter constructed from an array of silicon membranes to provide ultrafiltration requires a suitable blood flow path to ensure stable operation in vivo. Two types of flow paths distributing blood to the array of membranes were evaluated: parallel and serpentine. Computational fluid dynamics (CFD) simulations were used to guide the development of the blood flow paths. Pressure data from animal tests were used to obtain pulsatile flow conditions imposed in the transient simulations. A key consideration for stable operation in vivo is limiting platelet stress accumulation to avoid platelet activation and thrombus formation. Platelet stress exposure was evaluated by CFD particle tracking methods through the devices to provide distributions of platelet stress accumulation. The distributions of stress accumulation over the duration of a platelet lifetime for each device revealed that stress accumulation for the serpentine flow path exceeded levels expected to cause platelet activation while the accumulated stress for the parallel flow path was below expected activation levels.

Internal filtration in a high-flux dialyzer quantified by mean transit time of an albumin-bound indicator

Internal filtration in high-flux (HF) dialyzers significantly contributes to convective solute removal of molecules with poor diffusibility, but it is difficult to quantify. The aim of this study was to present the theory and to develop a method for measuring internal filtration and backfiltration in HF dialyzers, which also could be applied to patient studies. In a series of lab-bench experiments, the mean transit times (τd) of indocyanine green (ICG) passing the dialyzer were optically measured under different operating conditions and compared with mean transit times calculated from the known volume of the blood compartment (τV) using a mathematical model. τd was always larger than τV. The relative difference in mean transit times (1 - τV/τd) was related to the average cumulative filtration rate (Qfil). The internal filtration fraction Fb = Qfil/Qb was largely independent of blood flow (Qb) and not different from theoretical predictions obtained from a mathematical model. The dispersion of a nondiffusible indicator such as ICG can be used to quantify the magnitude of internal filtration and backfiltration in HF dialyzers using available technology. This information could be useful for testing the HF dialyzers in everyday situations.