# 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 (τ_{d}) 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 (τ_{V}) using a mathematical model. τ_{d} was always larger than τ_{V}. The relative difference in mean transit times (1 − τ_{V}/τ_{d}) was related to the average cumulative filtration rate (*Q* _{fil}). The internal filtration fraction *F* _{b} = *Q* _{fil}/*Q* _{b} was largely independent of blood flow (*Q* _{b}) 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.

From the ^{*}Institute of Physiology, Medical University of Graz, Graz, Austria; and ^{†}Nephrology Section, Department of Internal Medicine, Ghent University Hospital, Gent, Belgium.

Submitted for consideration April 2013; accepted for publication in June 2013

Disclosure: The authors have no conflicts of interest to report.

Reprint Requests: Daniel Schneditz, PhD, Institute of Physiology, Medical University of Graz, Harrachgasse 21/5 8010 Graz, Austria. Email: daniel.schneditz@medunigraz.at.

High-flux (HF) dialysis has become increasingly popular because this mode of therapy provides improved removal of large and protein-bound solutes by maximizing the convective transport across the dialyzer membrane.^{1},^{2} In HF dialyzers, convective transport is inherently increased because of enhanced forward filtration at the blood inflow and concomitant backfiltration at the blood outflow, and the countercurrent arrangement of dialysate flow, even in the absence of net ultrafiltration.^{3}

Internal filtration and backfiltration are not accessible to direct quantification. Indirect approaches are based on the measurement of filtration- and backfiltration-induced changes in blood concentrations of particles confined to the blood compartment or to changes in fiber blood flow velocity using radiolabeled albumin aggregates or ultrasound flow measurements.^{4},^{5} While providing important insight into the relationship between fiber geometry and dialyzer function,^{6},^{7} these methods are limited to *in vitro* studies because of the type of tracer used or because of the experimental setup to scan the dialyzers. These studies, however, indicate the potential of indicators and blood flow measurements to quantify internal filtration and backfiltration.

Therefore, it was the aim of this study to present a technique applicable to everyday practice using a safe indicator, as well as available technology, and to develop the theoretical background for the measurement of internal filtration. This study presents the theory, the experimental setup, and the *in vitro* data to explore this new approach.

## Methods

Internal filtration was analyzed in lab-bench studies under standard operating conditions and zero net ultrafiltration using whole bovine blood for perfusion of the dialyzer blood compartment and a dialysis monitor to provide Ca^{2+}-free dialysate, as described elsewhere.^{8}

Indocyanine green (Pulsion Medical Systems SE, Feldkirchen, Germany) was used as an indicator. Two hundred fifty microliters of aqueous ICG solution was injected into the arterial dialysis line upstream of the blood pump at a concentration of 1 mg/ml. In- and outflow concentrations in chambers directly attached to the dialyzer were simultaneously measured by optical means (Crit-Line III, Hema Metrics, Kaysville, UT), with a sampling frequency of 0.5 Hz and recorded on laptop PCs for off-line analysis.

The physical characteristics of the dialyzer such as the priming volume given by the manufacturer, fiber volumes derived from fiber numbers and fiber geometries, and the dead space volumes estimated from volumes between sensor measuring sites and fiber in- or outlets are summarized in Table 1.

Measurements were done for a range of blood flows *Q* _{b} increasing in steps of 100 ml/min from 100 to 500 ml/min and returning to 100 ml/min to detect changes caused by protein deposition and fiber clotting. The dialysate flow was set to 500 ml/min. After the completion of measurements, the dialyzer blood compartment was thoroughly rinsed with dialysate to assess potential fiber clotting.

Delivered blood flows were determined by ultrasonic means (HD03; Transonic Systems Inc., Ithaca, NY) after calibration of sensors by timed collection of sample mass and measurement of sample density. Blood viscosities η and densities ρ were measured at 37°C by a capillary viscometer (Oscillating Capillary Rheometer and Density Meter, http://www.anton-paar.com/, A. Paar KG, Graz, Austria), as described previously.^{9},^{10} Hematocrit was measured by microhematocrit centrifugation (Mikro 20; Hettich, Tuttlingen, Germany).

### Mean Transit Time

The passage of ICG at the measuring site leads to a transient increase in optical density and produces a typical dilution curve (Figure 1A) from which the mean transit time τ is calculated according to well-established theory^{11},^{12}:

where *t* represents the sample time and *r*(*t*) refers to the relative change in optical density.

where *D*(*t*) is the optical density as a function of time and *D* _{0} is the baseline value before ICG injection.

The passage of indicator at the outflow is delayed because of indicator dispersion within the dialyzer blood compartment. The difference between outflow (τ_{out}) and inflow (τ_{in}) mean transit times, therefore, refers to the mean transit time across the dialyzer τ_{d} and is given as

This time is related to the blood flow *Q* _{b} and to the effective distribution volume *V* _{eff} between in- and outflow measuring sites. When τ_{d} and *Q* _{b} are known, *V* _{eff} can be calculated from this relationship.

Alternatively, when *V* is known,

the effective blood flow *Q* _{b,eff} through the dialyzer (the average dialyzer blood flow) can be calculated.

### Internal Filtration Fraction

The transit time of indicator across the dialyzer is the sum of transit time across the priming volume τ_{V} and the time delay τ_{fil} caused by the reduced fiber blood flow because of internal filtration and backfiltration:

The transit time through the priming volume *V* in the absence of internal filtration and backfiltration is given as

With Equations 4, 5, and 6, the ratio of transit time caused by filtration and backfiltration τ_{fil} to overall dialyzer transit time τ_{d} is therefore given as

which is related to average internal filtration fraction *F* _{b} relative to blood flow, and where *Q* _{fil} is the average internal filtration rate. The internal filtration fraction relative to plasma flow *F* _{p} is then given as

where *H* is the hematocrit.

### Mathematical Model

Mean transit times were computed using a previously described mathematical model.^{13} The average fiber blood flow *Q* _{f} was quantified by the integration of modeled local flow over the fractional length of the dialyzer. With fiber volume *V* _{f} known from fiber geometry provided by the manufacturer, the mean fiber transit time τ_{f} was therefore obtained as

The transit time τ_{∂} in the dead spaces *V* _{∂} between sensor sites and fiber in- and outlets was estimated as

The model was solved numerically (Berkeley Madonna v. 8.3.18, http://www.berkeleymadonna.com/) using the proprietary boundary value module to adjust for dialysate inflow pressures under the condition of zero net ultrafiltration. This approach bypassed the requirement of random correction factors and time-consuming numerical iterations used elsewhere.^{14}

### Data Analysis

Data are reported as mean ± standard deviation or as appropriate. Data were analyzed by linear regression analysis and analysis of variance (ANOVA) for the significance of regression parameters, β_{0} and β_{1}. If the intercept β_{0} in the linear regression model was not different from zero by ANOVA, the linear regression model was used with zero intercept (β_{0} = 0). A probability of <0.05 was assumed to reject the null hypothesis.

## Results

Data from 24 dilution measurements obtained in two studies using bovine blood from two animals entered final analysis. Fiber clotting was absent as judged from visual inspection of rinsed dialyzer blood compartments.

Injection of ICG into the arterial dialysis line produced characteristic dilution curves from which the mean transit time across the dialyzer was calculated as the difference between out- and inflow mean transit times (Figure 1A; Equation 3). Mean dialyzer transit times ranged from approximately 20 seconds at highest *Q* _{b} to 1 minute and 40 seconds at lowest *Q* _{b}. A comparison of experimental and modeled transit times accounting for the effects of internal filtration and backfiltration and for the transit of indicator across dead spaces showed identity (Figure 1B). The intercept β_{0} of the linear regression was not different from zero, and the slope β_{1} was not different from unity in the β_{0} = 0 regression model.

Dialyzer transit times measured under different flow conditions and plotted *versus* blood flow showed a hyperbolic relationship with an exponent close to −1 (Figure 2A). Consequently, dialyzer transit time plotted *versus* reciprocal blood flow produced a linear relationship (Figure 2B). A zero intercept linear regression model was used after confirming that β_{0} was not different from zero in the 1/*Q* _{b} model. The slope β_{1} of the linear regression (*y* = 162.0*x*, *p* < 0.001, *r* ^{2} = 1.00) refers to the average effective distribution volume *V* _{eff} (Equation 3). The absence of a systematic deviation of τ_{d} from the linear model in this relationship indicated a constant effective distribution volume, independent of experimental blood flow.

The effective distribution volume was 162.0 ± 5.4 ml. This was much larger than the priming volume (*V* = 125 ml; Table 1) provided by the manufacturer and also significantly larger than the total volume calculated from dialyzer and fiber characteristics (*V* _{t} = 151.3; Table 1). The modeled volume in excess of the physical compartment volume therefore was 162.0–151.3 = 11.7 ml. This discrepancy was used to quantify the average internal filtration rate and internal filtration fraction as described in Equations 7 and 8. The results are summarized in Table 2.

The mathematical model was used to estimate the average internal filtration rate and the average internal plasma filtration fraction (Figure 3). A comparison of modeled and experimental data showed an increase in average internal filtration rates with increasing blood flows (Figure 4A). Despite the scatter seen with experimental data, the linear regression was not different from that obtained from the mathematical model. On the contrary, modeled internal filtration fractions decreased with increasing blood flow (Figure 4B). In addition, despite this scatter seen with experimental data, the linear regression was not different from the mathematical model. The scatter seen with experimental data was due to limited time resolution of the current sensor ((2-second sampling period) and errors in manual synchronization of both sensors used in this study. These limitations need to be addressed for future applications.

## Discussion

This lab-bench study showed that ICG dilution was suitable to measure transit times with available technology in commercial dialyzers, that measured data were not different from those obtained from a mathematical model, that transit times and distribution volumes were considerably larger than expected for the reported priming volume, and that this increase was related to internal filtration and backfiltration.

Indocyanine green is an approved dye and has been used for the measurement of cardiac output, hepatic clearance, and plasma volume in numerous experimental and clinical applications.^{15–19} The use of ICG in hemodialysis is limited to a few studies even though delivery and measurement of ICG are considerably simplified in the presence of an extracorporeal circulation.^{20},^{21} Indocyanine green is a small and water-soluble molecule; however, in plasma it is strongly bound to albumin. Indocyanine green is neither cleared by the kidneys nor cleared by the dialyzer so that it qualifies for a nondiffusible indicator. Following a bolus injection into the arterial line of the extracorporeal circulation, the ICG transit across the dialyzer therefore depends on the volume between entrance and exit sites and on the blood flow through that volume. When the extracorporeal blood flow is known as in this study, the duration of the indicator transit, also known as mean transit time, can be used to calculate the volume of distribution from well-established relationships (see Equation 3).

The measurement of internal filtration and backfiltration using a nondiffusible indicator is based on volume effects of internal filtration and backfiltration (Figure 5). Under conditions of zero net ultrafiltration, the blood flow continuously falls in upstream parts of the dialyzer. After reaching a minimum close to the center of the dialyzer, the blood flow then continuously increases because of backfiltration and, under the condition of zero net ultrafiltration, finally resumes the baseline value when reaching the dialyzer exit. Because the blood flow rate is transiently decreased within the dialyzer, the average blood flow over the whole dialyzer is lower than the blood flow entering or leaving the dialyzer.

Indocyanine green transit times were measured by optical means using the Crit-Line III. This device has been developed to measure hematocrit in the extracorporeal circulation during hemodialysis for the purpose of monitoring ultrafiltration- and refilling-induced changes in hemoconcentration.^{22} The sensor in this device is sensitive to ICG and has been used to measure ICG concentration in the extracorporeal circulation for the purpose of estimating hepatic clearance, hepatosplanchnic perfusion, and absolute blood volume in clinical applications.^{21} Because the computation of mean transit times requires normalization to the area under the curve (the integral of *r*(*t*)d*t* in the denominator of Equation 1), τ is independent of absolute indicator mass or indicator concentration. Therefore, for the purpose of measuring transit times, and in contrast to aforementioned applications, it is sufficient to analyze the optical density curve without calibration or quantification of the exact amount of ICG injected into the system. For the same reason, the measurement of mean transit time is also independent of a uniform loss of indicator from the system. However, if substantial amounts of indicator are gradually lost during dialyzer transit, for example, because of increased membrane permeability and convective transport of protein into countercurrent flow of dialysate, the mean transit time τ_{out} is expected to decrease. As a consequence, calculated dialyzer transit time τ_{d} will be shorter, effective distribution volume will be smaller (Equation 3), and internal filtration and backfiltration will be underestimated. However, HF dialyzer membranes are designed to minimize protein loss (Table 1) so that the effects on computation of internal filtration and backfiltration will be minimal.

For a solute confined to blood such as ICG, the distribution volume within the dialyzer is expected to correspond to the volume occupied by blood, the so-called priming volume given by the manufacturer. This volume is related to dialyzer function. Blood clots forming in dialyzer fibers lead to a reduction in dialyzer surface area, thereby reducing dialyzer solute clearance and ultrafiltration characteristics, both of which are related to membrane surface area. Thus, the measurement of fiber bundle volume using the transit time approach has been suggested to quantify the degree of fiber clotting.^{23} Information on fiber bundle volume is especially important when dialyzers are reused.

For a diffusible solute not confined to the blood compartment and diffusing into the dialysate compartment, the distribution volume can be expected to be larger than the priming volume. This is comparable with the larger distribution volume for diffusible solutes used in organ perfusion studies.^{24},^{25}

In the current study, the distribution volume was larger than the dialyzer priming volume given by the manufacturer, even though protein-bound ICG is a nondiffusible indicator. At first sight, this increase is at odds with current understanding that ICG does not diffuse into the dialysate compartment. This is also different from the results of a previous study where fiber volume in HF dialyzers was almost always reduced.^{23}

The apparent increase in distribution volume in the HF dialyzer observed in the current study is the result of using *Q* _{b} as the reference flow (Equation 3) while in fact, internal filtration and backfiltration in dialyzers lead to a reduction in fiber blood flow which has been measured by the Doppler ultrasound technique.^{5} In the case of a dialyzer, where the volume occupied by blood is known from fiber geometry, and in absence of blood clots obstructing part of that volume, mean dialyzer transit times can therefore be used to calculate effective average blood flow (*Q* _{b,eff}, Equation 4), average internal filtration rate (*Q* _{fil}, Equation 7), average internal filtration fraction relative to blood flow (*F* _{b}, Equation 7), and when the hematocrit is also known, average internal filtration fraction relative to plasma flow (*F* _{p}, Equation 8).

The effective distribution volume was constant for the range of blood flows studied as seen from the tight linear relationship between dialyzer transit time and reciprocal blood flow (Figure 2B). Thus, the internal filtration fraction determined from transit times and assuming a constant priming volume did not depend on blood flow (Figure 4). This is consistent with the mathematical model predicting only small changes in internal filtration fraction with changing blood flow.^{8}

### What Are the Implications of This Study?

First, in the absence of fiber clotting, the dynamic distribution volume in dialyzers determined by indicator dilution exceeds the physical priming volume because of internal filtration and backfiltration. This increase may be masked in the presence of fiber clotting. Therefore, the measurement of transit time alone is not suitable to detect fiber clotting. However, when fiber clotting can be excluded such as with automated regional citrate anticoagulation,^{26} transit time is importantly related to the magnitude of internal filtration and backfiltration.

Subsequently, the measurement of transit times using ICG dilution is easily done with available technology designed for hemodialysis. This could be useful for the development and testing of dialyzers in clinical situations.

Furthermore, correspondence with experimental data shows that the mathematical model was suitable to capture important aspects of fluid exchange in permeable hollow fibers, such as internal filtration and backfiltration. Moreover, this study shows that the clinical dialyzer can serve as a model for studies regarding the microcirculation. The experimental data and the theoretical model show that microcirculatory filtration and backfiltration increase the modeled distribution volume of an unfiltered (nondiffusing) indicator. This may have consequences for the calculation of intravascular volumes in physiological studies.

And last, but not least, and to the best of our knowledge, this is the first description of the effects of filtration and backfiltration on the dispersion of a nondiffusible indicator passing a microcirculation.

## Acknowledgment

S. Eloot is working as postdoctoral fellow for the Belgian Fund of Scientific Research Flanders (FWO-Vlaanderen).

## References

*In vivo*measurement of hemodialyzer fiber bundle volume: Theory and validation. Kidney Int. 1998;54:1751–1758

**Keywords:**

hemodialysis; hollow fiber dialyzer; filtration; indicator dilution; mathematical modeling