Department of Biophysics and Department of Nephrology, Pitié-Salpétrière University Hospital, Paris, France
Correspondence and offprint requests to: T. Petitclerc MD, Department of Nephrology, CHU Pitié-Salpétrière, 83 boulevard de l'Hôpital, F-75651 Paris, France.
Abstract
On-line monitoring of dialysate conductivity is now a standard equipment (called `Diascan®') of the dialysis monitor Integra® (Hospal, Italy). From the record of the dialysate conductivity at the dialyser inlet and outlet, the Diascan® calculates the values of patient's plasma conductivity and of ionic dialysance which is a weighed average of the dialysances of all ions of quantitative importance in plasma and dialysate. Because there is an equivalence between the transfer characteristics of urea and electrolytes, the ionic dialysance reflects the urea clearance corrected for recirculation. Because the conductivity of a solution is related to the concentrations of the ions and thus to the effective osmolality, the plasma conductivity is a reflection of the plasma sodium concentration. The determination of ionic dialysance and plasma conductivity by the Diascan® module is fully automatic and totally inexpensive, does not require any blood or dialysate sampling and therefore can be repeated every 15 or 30 min during each dialysis session. Some clinical applications of conductivity modelling are presented: (i) the repeated measurement of ionic dialysance allows the quantification of the dialysis dose actually delivered to the patient from the beginning of the session; (ii) the measurement of ionic dialysance with blood lines in normal and reversed positions permits the easy estimation of the blood flow rate in the vascular access of the haemodialysed patient; (iii) the on-line monitoring of ionic dialysance allows the development of new methods of haemodialysis with simultaneous infusion of ions; (iv) the on-line monitoring of ionic dialysance and patient's plasma conductivity facilitates the automatic optimization of the dialysate conductivity for each individual patient.
Keywords: conductivity modelling; dialysate sodium; dialysis efficiency; haemodialysis; ionic dialysance; on-line monitoring; vascular access flow
Introduction
On-line monitoring of dialysate conductivity, based on conductivity modelling, is a major field of research in the Hemodialysis Unit of the Nephrology Department headed by Prof. Claude Jacobs until September 1998. The aim of this paper is to present an update of the theoretical aspects of conductivity modelling and to summarize recent clinical applications of its implementation in a dialysis monitor.
Conductivity modelling
Conductivity modelling is based on the quantification of ionic mass transfer through the dialyser membrane and on the substitution of concentration measurements by conductivity measurements.
Ionic mass transfer through the dialyser membrane
In case of a merely diffusive solute (non-ionic substance with a zero reflection coefficient), solute mass transfer J from blood to dialysate in the absence of ultrafiltration is proportional to the difference between blood (cB) and dialysate (cD) concentrations at the dialyser inlet according to:
![]() | (1) |
where coefficient D0 is called `dialysance' of the solute [1]. For a solute absent from the dialysate which is delivered to the dialyser (cD=0), the dialyser clearance J/cB is equal to its dialysance D0.
Actually the total transfer J is a combination of diffusive transfer, convective transfer due to ultrafiltration and, for ionic substances, electrical transfer relative to the transmembrane gradient of electric potential due to the GibbsDonnan effect. Under these conditions, the transfer J is not proportional to (cB-cD). The ratio J/(cB-cD) also called dialysance by some authors [2] is not independent of cB and cD. Therefore it is not useful.
Kinetic modelling detailed in the Appendix shows that the mass transfer through the dialyser membrane could be written:
![]() | (2) |
where QF is the ultrafiltration rate and where D and are two coefficients independent of cB and cD and called `dialysance' and `GibbsDonnan coefficient' respectively.
For a solute absent from the dialysate delivered to the dialyser (cD=0), equation (2) shows that the dialysance (D), taking into account ultrafiltration and Donnan ratio, is identical to the dialyser clearance C1=J/cB of this solute, like the dialysance (D0) in the absence of ultrafiltration (QF=0) and of GibbsDonnan effect (=1).
The dialysate concentration (cDout) at the dialyser outlet is (see Appendix):
![]() | (3) |
Possible access recirculation accounts for the discrepancy between the blood concentration (cP) of the patient and the blood concentration (cB) at the dialyser inlet. Mathematical modelling shows that equations (2) and (3) can be written [3]:
![]() | (4) |
![]() | (5) |
where the value (Deff) of effective dialysance of the patient (dialysance corrected for access recirculation) is related to the dialysance (D) of the dialyser (dialysance without recirculation) and to the access recirculation ratio (R) by the following relation [3]:
![]() | (6) |
Equation (5) shows that cP represents the concentration of solute that is free to diffuse (not trapped by Donnan effect) and is called `effective concentration' of the solute.
From concentration measurement to conductivity measurement
Because the conductivity of a solution is related to the concentrations of the ions, it is possible to substitute conductivity measurements () for concentration measurements (c). As shown in the Appendix, equation (5) becomes:
![]() | (7) |
where effP and Dionic are called `effective plasma conductivity' of the patient and `ionic dialysance' respectively. Effective plasma conductivity is related only to the effective concentrations of ions in plasma. Thus
effP is different from the actual value of patient's plasma conductivity and cannot be directly measured in plasma. However, the concept of ionic dialysance (Dionic) and of effective plasma conductivity (
effP) is of great interest because Dionic and
effP can be estimated from dialysate conductivity measurements alone, without the need for conductivity measurements in plasma.
For the determination of effP and Dionic values, the value X of
D prescribed for the patient is changed by about ±1 mS/cm during 2 min, defining an X' value of
D. Equation (7) is written for each pair (X, Y) and (X', Y') of
D and
Dout measured at the two levels of
D. Assuming that the changes in ionic dialysance (Dionic) and patient's effective plasma conductivity (
effP) are negligible during the short time period required for all measurements of X, X', Y and Y' (about 5 min), Dionic and
effP can be calculated by the following equations:
![]() | (8) |
![]() | (9) |
For QF=0, equation (8) is similar to Polashegg's equation, which does not take into account ultrafiltration [4].
On-line conductivity monitoring
The Diascan® is a standard module in the dialysis monitor Integra® (Hospal, Italy). This module consists of (i) the implementation in the dialysis machine of a conductivity probe at the dialysate outlet of the dialyser; (ii) appropriate software.
Each 30 min, the Diascan® software records values X and Y of the dialysate conductivity at the dialyser inlet and outlet, changes the conductivity of the dialysate delivered by the dialysis machine during about 2 min, records values X' and Y' and then calculates the values of ionic dialysance and effective plasma conductivity using equations (8) and (9). This determination of ionic dialysance and of effective plasma conductivity is easy, totally inexpensive, and does not require any blood flow measurement or any blood or dialysate sampling. It should be pointed out that only value Dionic taking into account recirculation can be calculated by the Diascan®, but the value of recirculation ratio (R) cannot be calculated.
The following are some applications of the Diascan® developed in the Nephrology Department headed by Prof. Claude Jacobs at the Pitié-Salpétrière Hospital of Paris.
Monitoring dialysis efficiency
Ions of quantitative importance in the plasma and in the dialysate are small molecular weight ions and therefore have transfer characteristics through the dialyser membrane similar to that of urea. Thus the ionic dialysance (weighed average of the dialysances of all ions) should be near to that of urea, which is equal to urea clearance in a single-pass dialysis, because urea is absent from the dialysate delivered to the dialyser.
Actually the ionic dialysance is slightly, but significantly, lower (by about 5%) than urea clearance [5]. However, the strong correlation (r2=0.88) between ionic dialysance and urea clearance substantiates the ionic dialysance as a reflection of the delivered dialysis dose Kt. A decrease in ionic dialysance immediately detected during the session may indicate an insufficient delivery of dialysis dose and must raise questions in the physician about its aetiology [6]:
Because the ionic dialysance measurement can be frequently repeated (each 15 or 30 min), the record of ionic dialysance during each dialysis session is an excellent quality assurance parameter of the effective dialysis dose (Kt) actually delivered to the patient.
Monitoring of vascular access flow
Vascular access complications always account for a large part of the morbidity and cost of haemodialysis treatment. The monitoring of vascular access flow rate is of great interest in the early detection of dysfunction. Because the recirculation ratio induced by temporarily reversing the blood lines is dependent on the blood flow rate in the vascular access, several non-invasive techniques have recently been proposed to estimate access flow by measuring the recirculation ratio using different methods. Ultrasound dilution, conductivity dilution or haemoglobin dilution provide non-invasive measurements of access flow by injecting a saline bolus [8].
Because the ionic dialysance value calculated from conductivity modelling takes into account recirculation, the vascular access flow (QA) can be estimated from the ionic dialysance values (D) and (Drev) recorded with blood lines in normal and reversed positions respectively:
![]() | (10) |
where QF is the ultrafiltration rate [9].
There is a strong correlation (r2=0.86) between the value of access flow calculated from relation (10) and the value measured by ultrasound dilution technique (HD01 monitor®, Transonic Systems Inc., Ithaca, NY), which has proved to be very accurate. Thus the record of ionic dialysance values at normal and reversed positions of the blood lines provides a valuable estimation of access flow. It is entirely non-invasive, easy to perform (no need of bolus injection and of accurate measurement of dialyser blood flow), and totally inexpensive because the Diascan® is standard equipment in the Integra® dialysis monitor.
DuoCart biofiltration
To minimize precipitation of calcium and magnesium carbonates in the hydraulic circuit of dialysis monitors, it has been proposed to separate bicarbonate and divalent ions (calcium and magnesium) in the dialysate, using a buffer-free dialysate with simultaneous infusion of sodium bicarbonate in post-dilution mode (acetate-free biofiltration) [10]. DuoCart biofiltration is a new haemodialysis method that also allows the separation of bicarbonate and divalent ions. The dialysate contains only sodium chloride and bicarbonate obtained from two separate powder cartridges. The ionic complement is simultaneously infused back to the patient with glucose, using one 2-l bag of a specially designed sterile and pyrogen-free solution. In order to avoid the risk of an inadequate reinjection with regard to the dialyser clearance of reinfused ions, especially potassium, the reinjection rate should be adjusted to the value of the ionic dialysance measured each 30 min.
Using a reinfusion solution containing 58 mmol/l K, 44.5 mmol/l Ca, 14.7 mmol/l Mg, and 20 g/l glucose, with a flow rate equal to 1/27 of the value of ionic dialysance, the changes in plasma concentrations during 15 dialysis sessions (duration, 213±38 min; blood flow, 238±26 ml/min; ultrafiltration, 0.96±0.36 l/h) were similar to those observed during conventional bicarbonate dialysis [11]. The reinfused solution volume ranged from 1196 to 1454 ml, corresponding to a reinfusion rate of 6.2±0.4 ml/min. Specially designed software for automatically adjusting the reinfusion flow rate from the value of ionic dialysance measured by the Diascan® each 30 min is now implemented in a dialysis monitor Integra® specially equipped to receive, in addition to the sodium bicarbonate cartridge (BiCart®, Gambro, Sweden), a cartridge of sodium chloride (SelectCart®, Gambro, Sweden) instead of the usual liquid concentrate.
Like acetate-free biofiltration, this method separates bicarbonate and divalent ions and hopefully will offer the same advantages: total absence of acetate, no chemical limitation in bicarbonate supply of the patient, and easier cleaning of the dialysis monitor. However, the method offers several additional advantages. The powder form of the dialysate associated with a sterile and pyrogen-free solution is of interest for the improvement of the bacterial dialysate conditions, such as the absence of glucose in the dialysate and the absence of calcium carbonate precipitation. In combination with the absence of acetate, these conditions might improve dialysate biocompatibility. The storage of the dialysate as two cartridges along with a 2-l bag of reinfusion solution can also ease the burden of the nursing staff. Regarding membrane biocompatibility, the alkaline pH of the dialysate (pH>8) due to the absence of CO2 (extemporaneously produced from acetic acid in conventional bicarbonate haemodialysis) might also reduce bradykinin release following the contact phase with the dialysis membrane, and which is responsible for the early hypersensibility reaction, particularly in patients treated with ACE inhibitors. The personalization of potassium and calcium supply for the individual patient only needs a change in the composition of reinfusion solution. The calcium-free dialysate is adapted to the potential use of citrate anticoagulation in patients at high risk of bleeding. The volume of reinfusion (<2 l) does not require the use of an expensive high-permeability membrane. The cost of reinfusionone 2-l bag containing simple solutescould be low and is much lower than the cost of reinfusion (68 l of sodium bicarbonate) required in acetate-free biofiltration.
Monitoring of sodium balance
The effective plasma conductivity is a reflection of osmotically active solutes in the extracellular fluid and therefore of plasma sodium. Because the Diascan® provides automatically, each 30 min, the value of effective plasma conductivity of the patient, the dialysate conductivity can be automatically adjusted using a feedback loop in an attempt to reach a target value of effective plasma conductivity. By reaching at the end of each dialysis session both the value of dry weight and that of effective plasma conductivity fixed by the physician, the exact amounts of water and sodium accumulated since the previous session can be accurately removed during the session: the sodium-water balance is thus truly regulated, avoiding chronic sodiumwater overload.
Plasma conductivity cannot be continuously measured by the Diascan® because this measurement requires a transient change in dialysate conductivity. Consequently the implementation of the feedback loop requires the determination of the relationship between dialysate conductivity and change in plasma conductivity for predicting the variation of the plasma conductivity during the time between two measures. This determination requires the elaboration of a kinetic model of sodium transfer. Because the osmotic distribution volume of sodium is that of total body water, this kinetic modelling can be based on a single-pool model.
Diacontrol® is a specific software specially designed for the Integra® dialysis monitor. From the values of ionic dialysancea reflection of sodium dialysanceand of plasma conductivity measured by the Diascan®, Diacontrol® determines automatically the optimal dialysate conductivity for each individual patient in order to reach the desired value of the effective plasma conductivity at the end of the session (Figure 1). For an expected value of the patient's effective conductivity at 14.0 mS/cm, the actual value was 13.98±0.04 mS/cm (number of sessions, 40). For an expected value of the patient's conductivity fixed at a range 1414.2 mS/cm, the mean value of the absolute difference between expected and actual values was lower than 0.05 mS/cm (48 sessions), roughly equivalent to 0.5 mmol/l in terms of plasma sodium concentration. These preliminary results are in agreement with, and actually better than, those obtained with a version developed on the previous dialysis monitor Monitral® (Hospal, Italy) [12].
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Appendix
Ionic mass transfer through the dialyser membrane
We assume that, in the presence of ultrafiltration and/or GibbsDonnan effect, the total transfer J is again a linear function of cB and cD:
![]() |
where D and D' are two coefficients independent of cB and cD and which have been called by Ross `generalized clearances' [14].
Equations for solute conservation in blood and dialysate are respectively:
![]() |
![]() |
where Q stands for flow rate, subscripts B, D and F stand for blood, dialysate and ultrafiltration respectively and where cBout and cDout are the concentrations of blood and dialysate at the dialyser outlet.
The electrically negative plasma proteins, which cannot pass through the dialyser membrane, are responsible for a transmembrane gradient of electrical potential which leads to retention of the cations and ejection of the anions from the plasma. Consequently the value cDeq of cD which allows the stability of dialysate concentrations into the dialyser (cD=cDout) is not equal to cB. The ratio =cDeq/cB is called GibbsDonnan coefficient. The coefficient (
) is equal to 1 for a non-ionic solute and is different from 1 by less than 10% for a monovalent ion in clinical haemodialysis situations.
By definition of , for cD=
cB, the dialysate concentrations at the dialyser inlet (cD) and outlet (cDout) are equal. Thus equation (c) yields:
![]() |
![]() |
![]() |
Consequently equation (a) becomes:
![]() |
Combining equation (c) and (g) and solving for cDout yields the following:
![]() |
From concentration measurement to conductivity measurement
If Dj is the effective dialysance of a dialyser for a given ion (j), the dialysate concentration cDout,j of the ion (j) at the dialyser outlet can be written from equation (5):
![]() |
where cD,j and cP,j are the concentrations of the ion (j) in the inlet dialysate and in the patient's plasma respectively, and where j is the Donnan coefficient for the given ion (j) (
j<1 for a cation and
j>1 for an anion).
The relation between the partial conductivity j related to the ion (j) in the solution and its molar concentration cj is as follows:
j=zj F uj cj where F is the Faraday (96500 Coulombs) and where zj and uj are the valence and the electric mobility of the ion (j) in a given solution (zj uj>0 for anions and cations). Assuming the mobility of a given ion is the same in plasma and in dialysate and multiplying the two sides of equation (i) by zj F uj yields:
![]() |
The conductivity of a given solution is the sum of the partial conductivity
j related to each ion (j):
![]() |
Consequently:
![]() |
The ionic dialysance (Dionic) is defined as the average of Deff,j/j weighed by conductivity gradient at the dialyser inlet (
j
P,j-
D,j) of each ion (j):
![]() |
We define the effective plasma conductivity (effP) of the patient as:
![]() |
Therefore:
![]() |
Equation (k) can be written:
![]() |
Acknowledgments
This work was carried out with the collaboration of Hospal R&D Int. (Lyon, France).
References