PROCEDURE FOR THE DETERMINATION OF THE KT/V PARAMETER DURING THE KIDNEY SPARE REPLACEMENTS BASED ON A NONLINEAR FIT PROCEDURE

The invention relates to a method to determine the Kt/V parameter in kidney substitution treatment.

Dialysis adequacy is the topic that has got and gets more attention when one thinks about patient outcome. In order to estimate dialysis adequacy one needs a parameter establishing a relation between dialysis dosage and patient outcome. The most accepted parameter to estimate the quantity of dialysis delivered or dosage is the Kt/V, where K is the effective clearance for urea, t is the treatment time and V is the urea distribution volume which matches the total body water.

The NCDS (National Cooperative Dialysis Study) and the HEMO study found, after analyzing a large patient group, that morbidity and mortality in end stage renal disease (ESRD) was strongly correlated with the Kt/V value or dialysis dose. Data obtained from these studies resulted in guidelines regarding hemodialysis treatments, which demand a minimum dose of Kt/V=1.2 generally and 1.4 for diabetics respectively (DOQI guidelines). It is worthy to point out that a morbidity decrease not only improves the patient well-being, but also reduces significantly the medical costs as the patient requires less care.

The need of a reliable and cost effective method to monitor the Kt/V and by extension control dialysis adequacy and morbidity, is therefore easily understood.

In the Kt/V calculation, the main problems are K and V estimation along with the multi-compartment urea kinetics. V can be estimated by bioimpedance, anthropometric measurements or applying the urea kinetic model (UKM), all these methods have a certain degree of error. K can be estimated so far by measuring the urea blood concentration before and after the treatment or by monitoring inlet and outlet conductivity changes in the dialysate side.

Blood samples method is the reference one. After taking the blood samples and applying either UKM or Daugirdas formula a single pool Kt/V (spKt/V) is estimated, further, Daugirdas second generation formulas should be used to get an equilibrated Kt/V (eKt/V) which accounts for the urea rebound caused by the fact that urea kinetic's does not follow a single pool model but a multi-compartment one. This method has two main problems: it is not possible to know whether the treatment is adequate or not before it finishes, therefore it is not possible to perform any action to improve the situation; it is not an easy to apply method: sampling time is very important to get an accurate value, and the medical staff must send the samples to the lab, wait for the results and calculate Kt/V values with the help of a computer. These facts result on a monthly basis Kt/V measurements in best case, which means that in worst case scenario a patient might be under-dialyzed for one whole month.

Conductivity methods are based on the observation that sodium clearance is almost equal to urea clearance and that the relationship between dialysate conductivity and dialysate sodium concentration can be considered linear on the temperature range of interest. Therefore it is possible to get urea clearance by measuring the sodium diffusion transport through the membrane in the dialyzer.

It is important to introduce the concept of Dialysance, as it slightly differs from Clearance:

• Clearance is defined as the ratio between transport rate and concentration multiplied by flow, and it is applicable when the diffusing substance is on the blood side but not on the dialysate, that is the case for urea.
• Dialysance is defined as the ratio between transport rate and concentration gradient multiplied by flow, and it is applicable when the diffusing substance is in both dialyzer sides. When one applies conductivity methods to measure urea Clearance, one actually measures sodium Dialysance (Depner T, Garred L. Solute transport mechanisms in dialysis. Hörl W, Koch K, Lindsay R, Ronco C, Winchester JF, editors. Replacement of renal function by dialysis, 5^th ed. Kluwer academic publishers, 2004:73-91).
• During conductivity based clearance measurements, a dialysate inlet conductivity different to the blood one is produced, which results in a net transfer of sodium either from blood to dialysate or from dialysate to blood due to the generated gradient. There are currently several methods which are applied in the industry:
  • In a first method in a first step a conductivity profile is determined and in a second step the conductivity profile is used for integration of conductivity peaks (Polaschegg HD, Levin NW. Hemodialysis machines and monitoris. Hörl W, Koch K, Lindsay R, Ronco C, Winchester JF, editors. Replacement of renal function by dialysis, 5th ed. Kluwer academic publishers, 2004:414-418). The main advantages of such approaches are: they are relatively easy to implement and cost effective as they only need an extra conductivity/temperature sensor downstream the dialyzer; they offer Kt/V measurements during the treatment allowing the medical staff to react and perform some actions in case the treatment is not going as it should. However, conductivity based methods have also some limitations: they can induce some sodium load in the patient during the measurement; they are not useful to obtain other interesting parameters like nPCR or TRU; the maximum measurement frequency offered so far by the industry is about 20 minutes, that means that in worst case scenario the patient could be under-dialyzed for 20 minutes; and, although there are some publications and patents regarding it, so far, conductivity methods haven't been applied with enough reliability to hemofiltration or hemodiafiltration treatments.

Another method to estimate hemodialysis adequacy is by direct measurement of the waste products (urea) concentration in the effluent dialysate, this method assumes that the evolution of urea concentration over the time in the dialysate side is proportional to the one in the blood, therefore the slope of the line obtained after applying the natural logarithm to the registered concentration values over the time will be the same on both sides: dialysate and blood, and by definition such slope is K/V, which multiplied by the therapy time results on the Kt/V value.

There are two methods available to measure online the concentration of waste products in effluent dialysate: Urea sensors and UV spectrophotometry.

The limitations of the urea sensors are well known. Recent works carried out by Fridolin I. et al (I. Fridolin, M. Magnusson, L.-G. Lindberg. On-line monitoring of solutes in dialysate using absorption of ultraviolet radiation: Technique description. The International Journal of Artificial Organs. Vol. 25, no. 8, 2002, pp. 748-761) and Uhlin F. (Uhlin F. Haemodialysis treatment monitored online by ultra violet absorbance. Linköping University Medical Dissertations n° 962. Department of Medicine and Care Division of Nursing Science & Department of Biomedical Engineering. 2006.) have shown that UV spectrophotometry is a reliable and cost affordable method to monitor waste products in effluent dialysate. Additionally the European Patent EP1083948B1 describes a sensor coupled with the dialysate flow system of a dialysis machine, which is actually an UV spectrophotometer measuring UV absorbance of UV absorbing products in spent dialysate.

The author has found that the above referenced works have however some limitations:

• The logarithmic linearization of the timely exponential decay of the concentration of waste products on spent dialysate leads to a linear least squares fitting procedure. Recent experiences showed that the Kt/V values obtained by said procedure are about 10% lower than the Kt/V values obtained by means of blood samples.
• The clearance and consequently the Kt/V value during a dialysis treatment strongly depend on the counter current effect between patient blood and dialysis fluid, thus changes on the blood and/or dialysate flow will affect the treatment clearance and Kt/V. Said flow changes also affect the timely exponential decay of waste products on spent dialysate, however due to the inherent noise of the measurement and the relative low gain that the exponential decay has, it is almost impossible to recognize these flow changes by analyzing the decaying concentration curve, specially if the changes are not dramatic.
• From the kinetics point of view is it possible to say that the human body has two compartments, intracellular (IC) and extracellular (EC). At the beginning of any kidney substitution treatment, the machine clears the EC, creating a gradient effect between IC and EC, which forces the waste products from the IC diffuse and/or convect into the EC. General speaking the clearing capabilities of any dialyzer are higher than the existing clearance between IC and EC, therefore the second will limit the clearance of the first. Such situation results in the fact that the timely decrease of the blood urea concentration during a dialysis treatment does not follow a simple exponential decay, but a double exponential decay, wherein one of the exponential factors depends on the clearance between IC and EC, and the other depends on the dialyzer clearance.

The inherent assumption of a single exponential decay of the above referenced works leads to noticeable inaccuracies when one compares the result of the measuring with the Kt/V obtained by means of blood samples.

FIG. 3 depicts the body compartments which are important from the kinetics point of view and the relations among them. The clearance k_IC-EC between IC and EC controls the diffusion and convection of waste products from IC into EC. As long as the solutes are in the EC, which comprises interstitial fluid and blood, they can be cleared from the body either by the residual renal function (RRF) or the dialysis treatment. The clearance due to the treatment is represented on the draw as K_D. The UV sensor is coupled with the dialysate outlet.

The aim of this invention is to provide a reliable method, which in combination with any device able to continuously measure any dialysis related waste product, overcomes the above listed problems. Said measuring device may be coupled at any position of the flow system of a dialysis machine.

This problem is solved by a method with the features described in claim 1. Preferred embodiments of the invention are described in the claims 2 to 20.

Further goals, advantages, features and possibilities of use of this invention arise out of the subsequent description of the embodiments of the invention. Therefore every described or depict feature of its own or in arbitrary meaningful combination forms the subject matter of the invention even independent of its summary in the claims or its reference to other claims.

It shows:

FIG 1

Depicts a portion of a conventional dialysis machine plus a slight modification to host a sensor coupled with the dialysate circuit,

FIG 2

Depicts a standalone measuring device coupled with a dialysis machine,

FIG 3

Depicts the body compartments regarding urea kinetics and the relationships among them,

FIG 4

Graph depicting the absorbance measured during a real treatment (dotted) together with a fitted line (solid) modelled using a single exponential function,

FIG 5

Graph depicting the absorbance measured during a real treatment (dotted) together with a fitted line (solid) modelled using a double exponential function and

FIG 6

Graph depicting the absorbance measured during a real treatment (dotted) together with a fitted line (solid) modelled by splitting the whole dataset in 12 subsets and applying a single exponential fitting procedure to each of them.

• FIG. 1 shows a draw of the dialysate circuit of a conventional dialysis machine plus a slight modification to host a sensor coupled with the dialysate circuit. The blood from a patient is taken out into an extracorporeal circuit, it flows through the tube 32 into the blood chamber 30 of a dialyzer and returns to the patient through the tube 31. The flow rate of the blood circuit is controlled by the blood pump 33. The dialysis fluid is made of several concentrates and water, therefore the machine disclosed in figure 1 comprises a water inlet 12, two concentrates inlets 16 and 18 and two concentrate pumps 17 and 19. The water flow together with the concentrates flow define the final properties of the dialysis fluid. The conduit 20 takes the dialysis fluid to the dialysate chamber 29 of the dialyzer, which is separated from the blood chamber 30 by a semipermeable membrane. The dialysis fluid it is pumped into the dialyzer by the pump 21. A second pump 34 sucks the dialysis fluid and any ultrafiltrate removed from the blood. A bypass line 35 is arranged between the pumps 21 and 34. Several valves 26, 27 and 28 are arranged to control the dialysate flow. The conduit 36 leads the spent dialysate to a UV-sensor 37 measuring its light absorbance, the UV-sensor 37 is connected by an interface with the computer 14 which processes the measured data, the result of the data processing is displayed and/or printed by the device 15, which is connected with the computer 14 by an interface. The conduit 36 leads the spent dialysate after its measurement by the sensor 37 to the drain system 13. The dotted lines 22, 24 and 25 represent an adaptation of the disclosed apparatus for hemodiafiltration treatments. The substitution fluid comes from a substitution fluid source 11, flows through the line 22 and is pumped in the blood lines of the patient by the pump 23. In case of post dilution hemodiafiltration the conduit 24 leads the substitution fluid to the venous line of the extracorporeal blood system; in case of pre dilution hemodiafiltration the conduit 25 leads the substitution fluid to the arterial line of the extracorporeal blood system; and in case of pre-post dilution hemodiafiltration both conduits 24 and 25 are used. The computer 14 controls all the elements shown on the figure by means of proper interfaces, said interfaces are not drawn for the sake of simplicity. The computer 14 gathers information about other parameters of the dialysis machine, like for example blood flow, dialysate flow and/or therapy time, these parameters together with the measured data are processed, the result tunes the Kt/V measuring functionality to assess deviations. Eventually the UV-sensor 16 can be substituted by an Urea-sensor, in this case will the urea concentration in spent dialysate measured instead of the light absorbance. The disclosed dialysis machine is provided with several other means as is conventional. These other means are not disclosed, since they are not relevant for the operation of the present invention.
• FIG. 2 shows another embodiment where the measuring unit is build in a stand alone device 3 coupled with the effluent dialysate of a dialysis machine 1. An interface 3 between the standalone device and the dialysis machine allows a bidirectional data communication required to minimize the deviation of the Kt/V measuring function.

As described above, the current algorithms linearize the exponential decay of waste products concentration in spent dialysate, apply a linear regression, and work out the Kt/V value. However it is possible to apply a non linear regression procedure to directly model the measured data avoiding the linearization step, such approach significantly improves the measurement accuracy.

The practical application of said non linear fitting procedure comprises a measuring unit coupled with the flow system of a dialysis machine and a software implementation of the non linear regression procedure. The software algorithm keeps a collection of measurements delivered by the measuring unit, when the data collection has at least two values, the algorithm performs successive iterations to minimize the difference between the experimental or measured data and the fitted function. Every time a new value arrives to the data collection the procedure is repeated increasing the accuracy of the model. FIG. 4 shows a graph with successive measurements together with the modelled function which best fits the experimental data.

The modelled function in the preferred embodiment is a single exponential decay of the form:

A collection of data pairs absorbance-time are the input for the fitting procedure. The outputs are A_o and K/V. The latter multiplied by the treatment time gives the Kt/V value.

It is possible to apply the above described method to any model handing a factor, which meets the Kt/V value or any other dialysis adequacy parameter either directly or by means of mathematical operations, which require as input said modelled factor.

It is also possible to split the data in subcollections, fit each of them individually and apply a mathematical operation with all the partial results to work out the final parameter. In the above described embodiment, where an UV-Spectrophotometer is coupled with the effluent dialysate of a dialysis machine, the whole treatment data may be divided in 4 subcollections, the fitting procedure hands a K/V factor for each of the four collections, said factors multiplied by the time that each subcollection lasts result on four partial Kt/V values, which after addition deliver the Kt/V value for the whole treatment.

The number of subcollections considered by the algorithm depends on empiric data, the purpose is to maximize the accuracy of the measuring system.

Due to the double compartment nature of the human body the timely decay of waste products concentration in blood and/or spent dialysate do not actually follow a single exponential function but a double exponential function of the form. Ct=a⋅e-b⋅t+c⋅e-d⋅t

Where one of the factors describes the diffusion and/or convection of waste products between ICM and ECM, and the other between ECM and dialysis machine.

This fact reveals that the method published by Uhlin et al has an inherent error, and could also explain the deviations reported by the same author.FIG. 4 shows a plot of a timely decrease of waste products absorbance (concentration) in spent dialysate together with a best fitted line using a single exponential model. In this case it is possible to see that, while during most of the treatment the fitted line (solid) is slightly above or follows the actual line (dotted), at the beginning it is clearly below and at the end is again slightly below.FIG. 5 shows the same data but fitted with a double exponential model, in this case the fitted line (dotted) perfectly follows the actual absorbance line (solid). Because of mathematical reasons it is not possible to fuse the factors b and d of the equation 2 in one common factor that could eventually match the ratio K/V like in the single exponential model. However it is possible to split the measured or actual line in many pieces, fit a single exponential model and add the resulting partial Kt/Vs into the Kt/V value for the whole treatment in a subcollections like fashion (see above).FIG. 6 shows again the same data set, after splitting it in twelve pieces and fitting individually each of the pieces using a single exponential model. In that case even using an imperfect model the fitted line (solid) perfectly follows the actual absorbance line (dotted).

Alternatively to the exponential non linear fitting procedure, it is also possible to fit a line using a linear regression with each data subset. The slope of said fitted line matches the K/V ratio as well, which multiplied by the time range of the analyzed data subset results on a partial Kt/V. The whole Kt/V is calculated as described above, by adding up all the obtained partial Kt/Vs. The slight accuracy loss can be compensated by the fact that this procedure is much easier to compute than the previous one.

The number of pieces into which the data is split depends on empiric data, the author has found that a number of pieces between eight and twelve maximize the accuracy of the method.

The described method together with a measuring unit, able to measure the concentration and/or absorbance of any waste product in dialysate, coupled with the flow system of a kidney substitution treatment machine is able to measure the Kt/V value or other adequacy parameters with high accuracy and reproducibility.

As commented above, the clearance and consequently the Kt/V value during a dialysis treatment strongly depend on the counter current effect between patient blood and dialysis fluid, thus changes on the blood and/or dialysate flow will affect the treatment clearance and by extension the Kt/V and/or other adequacy parameters. A measuring unit, coupled with the flow system of a dialysis machine and able to continuously measure concentration of waste products in spent dialysate, will reflect in its output, changes on the slope of the timely exponential decay every time that any parameter able to affect the treatment clearance changes, like for example changes on blood flow and/or dialysate flow. Due to the inherent noise of the measurement and the relative low slope that the exponential decay has, it is almost impossible to recognize these flow changes by analyzing the decaying concentration curve, especially if the changes are not dramatic.

However if there is a data interface between the measuring unit and the dialysis machine, because either the measuring unit is integrated on the dialysis machine or, if the measuring unit is a stand alone device, there is a external data interface connecting it with the dialysis machine, any change on any parameter able to affect the clearance can be tracked and the Kt/V function algorithm may use a subcollection like fashion as explained above to split the treatment data in pieces having constant parameters, fit each piece individually, work out partial Kt/V values and add them up to get the Kt/V value or other adequacy parameters for the whole treatment.

In one of the preferred embodiments the UV sensor measures every 3 minutes, of course the measurement frequency could be higher, but it has been found that a measurement frequency of 3 minutes delivers enough data, about 80 measurements in a 4 hours treatment, to measure the Kt/V with enough reliability and accuracy. If the treatment conditions are kept constant, meaning that there are no blood and/or dialysate flow changes during the dialysis, each of the above mentioned twelve data subsets will include about seven measurements. Therefore twelve partial Kt/Vs will be calculated for each of the subsets and the final whole Kt/V will be the result of adding the partial Kt/Vs up. If the dialysis parameters that may affect the clearance are changed, like for example blood and/or dialysate flow, the timestamp of the change will be tracked and the current subset will be close even if it does not contain yet seven measurements. The machine will wait for a dead time until to start a new subset. The dead time is required because of two reasons: The dialysis procedure is a slow system with an important inertia, the new conditions require some time to be stable; the UV sensor is coupled with the out flowing dialysate, therefore the effect of the changes needs some time to flow from the filter to the position of the UV sensor. The latter results on a shifted absorbance curve at the sensor position when comparing it with an hypothetic absorbance curve directly measured at dialyzer outlet. In the following table the first absorbance measurement happened at time 5.1 minutes, however the time considered in the first data subset it is not from 5.1 to 23.3 but 0 to 23.3. Even though there is no data available, during the first 5.1 minutes of treatment the patient is of course treated, so the results are better if the first K/V factor is extrapolated to the whole treatment time, starting at time 0. Similar situation happens when a change on the dialysis condition, a bypass or a sequential period force the start of a new data subset.

The algorithm may work as shown in the following example:

A kidney substitution treatment machine together with a measuring unit, able to measure the concentration and/or absorbance of any waste product in dialysate, coupled with the flow system of said kidney substitution treatment machine and integrated on the hardware of said kidney substitution treatment machine, or alternatively integrated on a standalone device connected through a external data interface with said kidney substitution treatment machine and coupled with the out flowing dialysate of said kidney substitution treatment machine; that implement an algorithm able to recognize changes on the parameters, which may affect the clearance during a kidney substitution treatment, by analysis of the slope of the timely exponential decay of the concentration of waste products, or by splitting the measured data according to the changes of said parameters; are able to measure the Kt/V value or other adequacy parameters with high accuracy and reproducibility.

During bypass periods the patient is not treated, therefore the data measured during bypass can not be used by the Kt/V measuring functionality. The interface between measuring unit and machine lets the system know about said bypass periods. The data measured during these periods will not be considered and will not affect the accuracy of the function.

During sequential dialysis the dialysate flow is stopped and the weight of the patient is reduced keeping the constant blood osmolarity, meaning that the patient is dried but not dialyzed, therefore the sensor lectures during a sequential period should not be considered by the Kt/V functionality. The interface between measuring unit and machine lets the system know about said sequential periods. The data measured during these periods will not be considered and will not affect the accuracy of the function.

In one of the preferred embodiments during a bypass or a sequential period the UV sensor stops measuring and the current subset is interrupted but not closed, when said period is over the machine waits for a dead time to both let the system stabilize and let the changes arrive from the dialyzer to the position in the flow system where the sensor is coupled. After the dead time the machine may start a procedure to recognize if the absorbance signal has a constant and slow decrease, the fulfilling of this last condition means that the system is stabilized after the bypass and/or sequential period, and the subset which was interrupted can carry on.

The algorithm may work as shown in the following example:

A kidney substitution treatment machine together with a measuring unit, able to measure the concentration and/or absorbance of any waste product in dialysate, coupled with the flow system of said kidney substitution treatment machine and integrated on the hardware of said kidney substitution treatment machine, or alternatively integrated on a standalone device connected through a external data interface with said kidney substitution treatment machine and coupled with the out flowing dialysate of said kidney substitution treatment machine; that implement an algorithm able to recognize bypass or sequential periods by analysis of the sensor's output signal, or by management of the different events happening in the machine; are able to measure the Kt/V value or other adequacy parameters with high accuracy and reproducibility.