NDT Advance Access originally published online on June 13, 2007
Nephrology Dialysis Transplantation 2007 22(10):2962-2969; doi:10.1093/ndt/gfm356
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Temperature and concentration distribution within the Genius® dialysate container
1Institute Biomedical Technology, Ghent University, Gent, Belgium, 2Renal Division, Department of Internal Medicine, Ghent University Hospital, Gent, Belgium, 3Fluid Mechanics Laboratory, Ghent University, Gent, Belgium and 4AZ Sint Blasius Hospital, Dendermonde, Belgium
Correspondence and offprint requests to: Sunny Eloot, Institute Biomedical Technology, Ghent University, Campus Heymans - Block B, De Pintelaan 185, 9000 Gent, Belgium Email: sunny.eloot{at}ugent.be
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Abstract |
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Background. The Genius® single-pass batch system, using a closed dialysate container, is increasingly applied for dialysis treatment. Although fluid separation between fresh and spent dialysate is maintained in the container during standard dialysis, dialysate mixing may occur under certain clinical conditions. An in vitro study showed that differences in dialysate temperature and solute content between fresh and spent dialysate determine the occurrence and moment of dialysate mixing.
Methods. To better understand the maintenance of separation of fresh and spent dialysate in the prevention of mixing, a mathematical model of the 75 l Genius® container was developed and the general fluid, mass and heat transfer equations were solved, simulating a dialysis session of 300 min with 1 g/l urea as starting ‘blood’ urea concentration and 36.2°C starting dialysate temperature. Boundary and initial conditions were chosen according to two different strategies applied in previous in vitro tests, with spontaneous cooling of the reservoir on the one hand and heating of the spent dialysate to maintain an equal temperature as the fresh dialysate on the other.
Results. Our simulation data show that dialysate inside the container is cooling down near the container wall in both scenarios and near the central glass tube in the setup with spontaneous cooling. In the setup with heating of spent dialysate, the upper layers are heated near the central tube. Since density stratification is maintained at each time point, solutes will rise towards warmer zones. This is halfway between the container axis and wall for spontaneous cooling and, even to a larger extent, near the central tube for simulations with heated spent dialysate. Hence, the contaminated volume in the case of heating is much larger than theoretically supposed.
Conclusions. These computer simulations unravel temperature and concentration distribution inside the container, offering insight into the complicated mixing phenomenon and indicate that temperature is a major impacting factor.
Keywords: dialysate contamination; dialysis efficiency; single-pass batch system; numerical simulations
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Introduction |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionConclusionAcknowledgementsReferences |
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The Genius® system (Fresenius Medical Care, Bad Homburg, Germany) gains interest for application in standard dialysis [1–5] as well as in extended dialysis [6,7]. Genius® dialysis is also successful for the treatment of acute renal failure [8,9] and acute intoxication [10,11] at the intensive care unit. Its success is mainly attributable to the use of ultrapure dialysate, which is not to be prepared at the bedside and makes the system user-friendly and transportable.
This single-pass batch system, originally developed by Tersteegen and Van Endert [12], differs from other currently used dialysis machines as it contains a closed container in which both fresh and spent dialysate are stored (Figure 1) [2,12,13]. During standard dialysis, adequate separation of fresh and spent dialysate is maintained [1,11]. It has been demonstrated that this separation is based on differences in density caused by differences in temperature and solute content. The warmer fresh dialysate has a lower density compared with the colder spent dialysate loaded with uraemic solutes. Based on in vitro experiments however, concerns were raised about the possibility of premature mixing in conditions with a diminished density gradient [14]. Examples of such conditions are a decreased density of spent dialysate in the absence of uraemic retention solutes and in the case the dialysate is heated inside the dialyser by blood e.g. due to fever of the patient or when starting Genius® dialysis with relatively cold fresh dialysate. Early mixing was noted during a dialysis treatment of a lithium-intoxicated patient with normal renal function in which spent dialysate was less dense [15]. As a consequence, partial recirculation of spent dialysate resulted in a decrease in dialysis efficiency. The question how the mixing starts and proceeds has until now not been solved.
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To better understand the influence of concentration and temperature on the occurrence of dialysate mixing in the container, we previously performed in vitro experiments [14]. As patient substitute, a reservoir filled with dialysate was loaded with various amounts of urea. Furthermore, temperature differences between fresh and spent dialysate were imposed by whether or not spent dialysate was heated until equal temperatures were obtained at the container inlet and outlet. The tests with heating of spent dialysate are representative for what happens during dialysis when spent dialysate is less dense. In the in vitro tests, mixing was found to occur earlier for lower concentrations of toxins in the patient's substitute and for a smaller temperature difference between the fresh and spent dialysate [14]. The limitations of this approach were, however, that concentrations and temperatures could be measured only at a discrete number of time intervals and that no insight is gained into the spatial distribution of concentration and temperature within the container.
Therefore, the present study sets out to visualise mass and heat transport inside the container in order to understand how to anticipate the transport processes inside the container avoiding early dialysate mixing. Therefore, a computer model [two-dimensional axi-symmetrical Computational Fluid Dynamics (CFD) model] was developed, describing the variation during dialysis of local temperatures and solute concentrations in the container. Model calibration was performed based on different parameter settings of the patient and dialysate, in parallel to our previous in vitro setup.
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Materials and methods |
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A two-dimensional axi-symmetrical numerical model (Fluent, Sheffield, UK) of the 75 l Genius® dialysate container was developed, describing the container in three dimensions. With CFD, the fundamental governing equations of fluid dynamics (i.e. continuity, momentum and energy equations), which are based, respectively, on the fundamental physical principles of mass conservation, Newton's second law and the law of energy conservation [16] are usually differential equations in their most general form. By replacing these differential equations with numbers which are advanced in space and/or time, a final numerical description of the complete flow field of interest is obtained.
The numerical results were calibrated for two different setups as measured during two representative in vitro tests [14]. A dialysis session of 300 min was simulated mathematically, corresponding to the in vitro tests with a ‘blood side’ urea start concentration of 30 g urea dissolved in 30 l dialysate in an open reservoir simulating a patient. Furthermore, simulations were performed for spontaneous cooling of this reservoir as well as with heating of the spent dialysate to maintain an equal temperature compared with the fresh dialysate.
Model geometry
The model geometry has a cylindrical shape with a height of 340 mm and an internal diameter of 400 mm. On the top and bottom, the container geometry describes half a sphere. The wall thickness of the container is taken equal to 40 mm, with glass material characteristics adapted so that the calculated heat loss corresponds to the observed heat loss in the previously performed in vitro experiments [14]. The central tube, containing the UV light, has a radius of 10 mm, surrounded by an inlet ring for spent dialysate of 7 mm in width and a glass wall of 3 mm thick. The inner and outer shell of the inlet tube ends 27 mm and 20 mm above the bottom of the container, respectively. The fresh dialysate outlet section at the container top and surrounding the central tube consists of a ring of 15 mm in width. Since thickness dimensions are estimated, the final model calibration is based on adjustment of the material characteristics, according to the in vitro measurements.
Governing equations
All equations are solved in the two-dimensional axi-symmetrical model that corresponds to a three-dimensional model in which the axis of the central tube functions as a symmetric rotation axis.
Fluid dynamic equations
The fluid flow is described by the unsteady incompressible continuity and momentum equations using a time step of 6 s. Since the fluid properties (density 
and dynamic viscosity µ) are temperature dependent, the energy equation was solved simultaneously.
Convection-diffusion equation
The transport of urea in the container, driven by pressure and concentration differences, is described by the convection-diffusion equation. Diffusion is the result of concentration differences, while convection is due to bulk motion of the fluid. In the case of natural convection, this motion is induced by density differences that result from concentration and temperature variations, while forced convection can take place due to mass inflow in the container. The general convection-diffusion equation is defined as:
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urea the urea density (1323 kg/m3), u the fluid velocity (m/s), and (uurea – u) the diffusional velocity of urea in the fluid (m/s), Durea the diffusion coefficient of urea in dialysate (m2/s), the total density (kg/m3), and d
urea/ds the urea mass fraction gradient in the s direction, defined as:
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| (2) |
D the dialysate density (g/l).
Fluid property equations
The fluid properties (density and viscosity) are dependent on the temperature and the solute concentration. The increase of dialysate viscosity for higher density is negligible, while the non-negligible decrease of dialysate viscosity µ (Pa·s) for higher temperatures T (°C) is described by [16]:
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The increase of dialysate density D (kg/m3) for higher temperatures T (°C) is described as a function of the density 0 (1007 kg/m3) at temperature T0 (30°C), and the volumetric thermal expansion coefficient of dialysate β (β·0 = 0.3 kg/m3/K):
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Finally, the density of the urea-dialysate mixture m (kg/m3) is calculated as a volumetric average with Vu and VD the volumes of urea and dialysate, respectively, and u the density of urea (1323 kg/m3):
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Heat transfer equations
The heat transfer inside the container is originated by conduction, as described by Fourier's law and by the mixing of warm and cold dialysate:
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Dialysate near the outer wall of the container is cooled down due to the natural (air) convection, described with Newton's law of cooling:
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Dialysate surrounding the central tube is cooled down or heated by the dialysate flowing down inside the central tube. This phenomenon is described with Fourier's law as a function of the heat conduction coefficient k for glass (1.3 W/m/K), the glass density G (2200 kg/m3) and the heat capacity of glass cpG (840 J/kg/K):
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Boundary conditions
Container
The container wall is modelled as a wall where no-slip occurs, while the container axis is defined as a symmetric axis. On top of the container, the fluid flow exit is defined as a zero outlet pressure, while the inlet is defined as a constant mass flow rate of 5 g/s of the spent dialysate. This corresponds to an overall dialysate flow of approximately 300 mL/min as used with the in vitro experiments [14].
Temperature
The temperature measurements during the in vitro test with spontaneous cooling showed an approximately constant temperature difference between the fresh and spent dialysate during the entire dialysis, i.e. 2.5°C [14]. Therefore, in the numerical model, the temperature of the spent dialysate as applied at the container inlet was calculated from the temperature of the fresh dialysate at the container outlet. For simulation of the test with heating until equal temperatures, the temperature of the spent dialysate at the container inlet was taken instantaneously equal to that of the fresh dialysate as measured at the container outlet. Furthermore, for both simulations, the fresh dialysate was characterised by a temperature of 36.2°C at the start of dialysis.
Urea concentration
pTo calculate the urea concentration in the spent dialysate, a single pool kinetic model was used to simulate concentration variation in the substitute patient [17,18], corresponding to the reservoir of 30 l with the in vitro tests. Since the urea removal from the patient also depends on the urea concentration in the dialysate at the dialyser inlet (CDi), the differential equation was solved numerically (JSim, National Simulation Resource, Seattle, USA). The dialyser outlet concentration of the dialysate (CDo) is equal to the concentration at the container inlet and can be calculated using the formula for dialysate-side dialysance D with QD the dialysate flow in the dialyser [19]:
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To obtain the concentrations and temperatures at the container outlet, a velocity-weighted integration was performed for use in further calculations.
Statistical analysis
Correlations between parameters were investigated by performing Pearson correlation analysis.
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Results |
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For each time step, temperature and solute distributions can be visualised in a cross-section of the container (Figure 2). From fitting the in vitro measured dialysate concentrations at the dialyser outlet in the single-pool model, a urea start concentration in the patient substitute of 1.13 g/l and 1.04 g/l is found for the respective tests with spontaneous cooling and with heating of the spent dialysate.
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Figure 2 shows as example, the time evolution of urea concentrations in the container for the case of spontaneous cooling at 5, 30, 60, 90, 120, 150, 180, 210 and 240 min after the start of dialysis. At these time points, urea concentration in the inflowing spent dialysate is equal to 0.60, 0.57, 0.49, 0.42, 0.35, 0.30, 0.25, 0.21 and 0.33 g/l, respectively. Initially, this concentration decreases progressively during dialysis, according to the mass balance between the patient (kinetic model) on the one hand and the dialyser on the other. However, between the 180th and 210th min, spent dialysate concentration ceases to decrease and even increases from the 210th min due to the fact that from that moment on spent dialysate enters into the dialyser. As illustrated in Figure 2, fluid separation between fresh and spent dialysate remains explicit during almost the entire dialysis session. However, above the virtual separation layer, halfway in between the container axis and the wall, fresh dialysate is contaminated by spent dialysate. This zone becomes broader as dialysis time progresses.
The numerical results of the time variation of the urea concentration in the dialysate at the container inlet and outlet, are illustrated in Figure 3 for a dialysis session with spontaneous cooling (Panel A) and with heating of spent dialysate (Panel B). Contamination of the fresh dialysate with urea concentrations above 0.01 g/l is observed at the container outlet from 183rd min on for the simulations with spontaneous cooling and from 106th min on with heating of spent dialysate. The time point at which highly contaminated dialysate (urea concentrations more than 0.1 g/l up to 0.3 g/l) leaves the container, is at 236 and 186 min, respectively. Figure 3 also shows that the outlet concentration for both scenarios is not varying smoothly, but fluctuates in time. A highly significant correlation was found between the numerical results, as calculated in the context of the present analysis, and the direct measurements obtained previously during our in vitro experiments [14] for the spontaneous cooling (n = 19, R = 0.949, P < 0.001) as well as for heating of spent dialysate (n = 19, R = 0.968, P < 0.001).
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Figure 4 illustrates the difference between the simulations with spontaneous cooling and those with heating of spent dialysate at 90 min after the dialysis start. Concentration and temperature of the inflowing spent dialysate are 0.42 g/l and 33.0°C with spontaneous cooling (Panel A) and 0.42 g/l and 35.7°C with heating of spent dialysate (Panel B). Figure 4 also shows the radial variation of the urea concentration and temperature at 200 mm above the container bottom (Figure 4C) and at 200 mm below the container top (Figure 4D).
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In both cases, the isotherms illustrate the cooling of the dialysate near the container wall as well as the mostly horizontal transition lines between different temperature layers, especially for spontaneous cooling. Furthermore, with spontaneous cooling, the temperature of the dialysate in the container surrounding the central tube is influenced by the inflowing spent dialysate. In the upper part of the container, the spent dialysate inflowing at the container top is 2.5°C cooler compared with the fresh dialysate pumped out of the container (33.0°C vs 35.5°C at the container outlet). Hence, the warmer fresh dialysate is cooled down, while the colder spent dialysate is heated while flowing downward through the central tube, until it reaches layers of the same temperature (Figure 4A). Below this point, spent dialysate starts heating the dialysate surrounding the central tube, although very locally. For the tests with heating of spent dialysate, the inflowing dialysate is warmer than the surrounding dialysate over almost the entire height of the container. This results in heat transfer towards the dialysate inside the container, with the exception of near the top where temperatures are equal.
At 90 min after dialysis start for the setup with spontaneous cooling, separation between fresh and spent dialysate is present at one-third of the container height and is well maintained, except halfway in between the container axis and wall (Figure 4A). At 200 mm above the container bottom, urea concentrations are found to increase gradually from 0.39 g/l near the central tube up to 0.60 g/l near the container wall (Figure 4C). For the simulation with heating of spent dialysate, the separation zone at the same moment is positioned higher in the container (i.e. halfway up the container height) and a urea concentration above zero is present up to the upper container part around the central glass tube (Figures 4B and D). Immediately below the separation zone, a thin layer of fresh dialysate is present near the container wall, changing into slightly contaminated dialysate (0.20 g/l) following the container wall downwards. In the bulk of the spent dialysate at 200 mm above the container bottom, urea concentrations are varying quite chaotically in between 0.3 and 0.4 g/l (Figure 4C). Identical phenomena continue to be observed also at later time points. The presence of relatively high concentrations in the central part of the container up to areas near the top is the reason why entrance of contaminated dialysate into the dialyser occurs so early in this setting.
Finally, when evaluating temperature and concentration variation over the entire volume of the container at 90 min, extreme temperature and concentration differences are 2.4°C and 0.57 g/l for the tests with spontaneous cooling, while this is only 0.7°C and 0.40 g/l, respectively, for the setup with heating of spent dialysate. Smaller temperature and concentration gradients imply that density is not changing much over the entire container volume, explaining why dialysate contamination occurs earlier in the case of heating of spent dialysate, compared with spontaneous cooling.
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Discussion |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionConclusionAcknowledgementsReferences |
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The present study sets out to unravel the temperature and concentration profiles inside the Genius® container during dialysis. The fluid separation zone is, at the same moment of the dialysis session, positioned higher in the container for the simulation with heating of spent dialysate. Above the separation layer, fresh dialysate contamination was found halfway up near the central tube and the container wall for the simulations with spontaneous cooling, while this zone was positioned along the central tube for the simulation with heating of spent dialysate.
The differences between the results for spontaneous cooling and dialysate heating (Figures 3 and 4) can be explained as follows: independent of temperature and concentration, it is the physics of nature that stratification based on density is present inside the container with the highest density at the bottom layers. Immediately after dialysate preparation, even prior to dialysis, dialysate inside the container starts to cool progressively in spite of the insulation of the container. This cooling starts near the container wall and results in a sinking of the cooler dialysate by gravity. Hence, a temperature gradient, similar to the density gradient, comes into being with at the bottom heavy cool and at the top the lighter warmer dialysate. The temperature of the dialysate near the central tube is also disturbed by heat transport to and from the inflowing colder or warmer spent dialysate in the simulations with spontaneous cooling and heating of spent dialysate, respectively. As a consequence, the mostly horizontal transition lines between the different temperature layers are disturbed near the central axis and the container wall, especially for the condition with heating (Figure 4B).
In the case of spontaneous dialysate cooling, the density decrease caused by the higher temperatures above the separation layer and in between the central tube and the container wall, is counterbalanced by a similar density increase due to relatively higher urea concentrations (Figure 2 and Figure 4A). As a consequence, contaminated fresh dialysate is observed earlier at the container outlet than theoretically expected at 250 min, when at a flow rate of 300 ml/min a total amount of 75 l dialysate has passed the container outlet (Figure 2). Furthermore, the inflowing spent dialysate, although drained at the bottom of the container, intends to migrate towards zones of equal density and raises upward along the central tube until it reaches a fluid layer with similar density (Figure 4A). Mixing however, proceeds much slower than with heating of the spent dialysate.
In the experiments where spent dialysate is heated, the spent fluid drained at the bottom of the container is warmer than the cool fresh dialysate already present at the bottom. Hence, this drained warm spent dialysate rises above the cooler and heavier fresh dialysate, unless solute content results in a higher density and can counteract this upward movement. At 90 min during dialysis, the inflowing spent dialysate with a concentration of 0.40 g/l rises towards the separation zone (see arrow in Figure 4B). Furthermore, the continuous sinking of fresh dialysate along the container wall results in a dilution of the urea concentration in the lower regions. Due to this continuous dilution by fresh dialysate, the contaminated volume is larger than expected. This clarifies why recirculation of spent dialysate occurs earlier when spent dialysate is heated at the container inlet compared with no heating [14].
The variation of density due to temperature variations and that due to concentration variations is generally known to be 0.4 g/l/°C and 0.24. Furthermore, evaluating the temperature and concentration variations over the entire volume of the container, it is obvious that temperature is the major impacting factor determining the time point of dialysate mixing. Hence, caution must be taken when performing a dialysis during which blood heats the dialysate in the dialyser. This happens whenever the patient's blood temperature exceeds the fresh dialysate temperature, such as in patients with fever or when fresh dialysate may cool down significantly during a protracted dialysis with lowered blood flow rates. It is not excluded that the temperature difference that stabilises the partitioning between the dialysate fractions disappears and eventually inverts, resulting in a situation at risk for early dialysate contamination with a decrease of dialysis adequacy. Such a situation could be avoided by using a dialysate start temperature of at least 38°C or by additionally cooling spent dialysate by using longer dialysate outlet tubings.
However, the impact of solute concentration should not be neglected, so that caution must also be taken when performing dialysis in the case of intoxication with a small waste load in the patient. Again, a solution to avoid this eventuality could be the external cooling of the spent dialysate before the inflow into the container, as can be obtained by using longer spent dialysate lines, which should allow for maintaining adequate fluid separation under any clinical condition.
Finally, it should be remarked that the Genius® system uses a double-sided roller pump that simultaneously generates blood and dialysate flow in the dialyser, so that blood inlet and dialysate outlet flows are the same. As a consequence, the ultrafiltration rate must be taken into account when estimating the theoretical duration during which a total amount of 75 l dialysate has passed the container outlet. In that way, for a pump flow rate of 300 ml/min, dialysis might be extended from 250 min (no ultrafiltration) to 264 min (1 l/h ultrafiltration).
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Conclusion |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionConclusionAcknowledgementsReferences |
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The Genius® single-pass batch system is a mobile dialysis system with numerous advantages if no mixing of fresh and spent dialysate occurs during dialysis. It was found earlier however, that mixing inside the Genius® container might happen under certain clinical conditions. To better understand the impact of temperature and solute content, both influencing density, in vitro tests were previously performed and it was found that dialysate mixing was enhanced for a spent dialysate temperature approaching the temperature of the fresh dialysate. The present numerical study offers a direct insight into the time variation and relative importance of the impacting factors determining dialysate mixing. Besides solute concentration, temperature was found to be the major impacting factor, such that care must be taken when performing non-standardised dialysis.
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Acknowledgements |
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SE was supported by the Belgian Fund for Scientific Research-Flanders (FWO Grant ‘Krediet Fernand De Waele’) and is working as a post-doctoral fellow for FWO-Flanders.
Conflict of interest statement. None declared.
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References |
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Accepted in revised form: 9. 5.07
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