ONLINE LINEARIZATION OF AN OPTICAL SENSOR

Abstract

A method and device for linearizing an optical sensor in a dialysis apparatus. The method includes introducing a sensor to the dialysate-side drain line, determining the linear range of the optical sensor, backwards extrapolating the data from the linear range and correcting the data from the non-linear range.

Claims

1.-15. (canceled)

16. A method of linearizing an optical sensor in a dialysis apparatus, comprising the steps of: introducing the optical sensor to a dialysate-side drain line of a dialysate circuit, determining a linear range of the optical sensor, recording data with the optical sensor in a linear range and a non-linear range, backwards extrapolating the recorded data recorded in the non-linear range by the data recorded in the linear range, correcting or replacing the data determined by the sensor from the non-linear range with the backwards extrapolated data for the non-linear range.

17. The method according to claim 16, wherein the backward extrapolation is implemented by non-linear regression of a regression curve.

18. The method according to claim 16, wherein the method further comprises the step of: adjusting a shunt interval and shunt duration of a shunt in the dialysate circuit.

19. The method according to claim 18, wherein determining the linear range further comprises the steps of: applying a difference of local shunt maximums as minuend and extinction signals of the optical sensor before changing to the respective shunt as subtrahend to the extinction signals before changing to the shunt as abscissa axis and determining at least one extinction or where the data is smaller than a maximum turning point.

20. The method according to claim 18, wherein the shunt has a first duration of 18 seconds and the shunt interval has a second duration longer than the first duration.

21. The method according to claim 20, wherein the first duration is 18 seconds or less and the second duration is 4 minutes.

22. The method according to claim 18, wherein the shunt intervals are distributed to be equidistant or non-equidistant in time.

23. The method according to claim 18, wherein the determination of a clearance K is carried out by calculating the extinction in the plasma, after a shunt maximum following a shunt duration between 2 and 3 minutes.

24. The method according to claim 23, wherein the determination of a dialysate-side clearance and of blood-side clearance is non-invasive.

25. The method according to claim 16, wherein the method further comprises the step of: determining a Kt/V value for checking the linearization of the optical sensor.

26. The method according to claim 25, wherein calculating the Kt/V value is carried out by determining an initial urea content and a urea concentration c(t) at a given point in time t, which were measured by a linearized optical sensor.

27. The method according to claim 25, wherein the determined Kt/V value is determined by a model for considering a rebound effect.

28. The method according to claim 25, wherein the determined Kt/V value is determined by a Single-Pool model with consideration of the urea generation during therapy.

29. The method according to claim 19, wherein the shunt maximums of the difference are stored.

30. The method according to claim 29, wherein the shunt intervals start after a predetermined duration of therapy.

31. A dialysis machine comprising: an optical sensor for measuring a current dialysis process; and a data correction unit adapted to linearize the optical sensor according to a method in accordance with claim 16.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The invention is best understood from the following detailed description when read in connection with the accompanying drawings. Included in the drawings are the following figures:

[0022] FIG. 1 shows the extinction of an optical sensor with respect to a reference device,

[0023] FIG. 2 shows the time course of extinction both for the optical sensor and for the reference device,

[0024] FIG. 3 shows a schematic representation of the invention,

[0025] FIG. 4 shows a course of extinction during therapy,

[0026] FIG. 5 shows the extinction difference of an optical sensor,

[0027] FIG. 6 shows the extinction difference of a reference measuring device,

[0028] FIG. 7A shows the dialysate-side extinction course of the reference values as well as the exponential fit of the values and FIG. 7B shows the dialysate-side extinction course of the optical sensor as well as the extrapolating exponential fit of the last nine values,

[0029] FIG. 8 shows the linearized characteristic line of the optical sensor along with the original characteristic line,

[0030] FIG. 9A shows the blood-side extinction course of the reference values as well as the extrapolated fit of the values and FIG. 9B shows the blood-side extinction course of the optical sensor as well as the extrapolating exponential fit of the last four values, and

[0031] FIG. 10 shows the linearized characteristic line of the optical sensor along with the non-linearized characteristic line.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0032] In FIG. 3 the schematic representation of the invention is illustrated. Blood which is conveyed to a dialyzer is collected from a patient 1 via the arterial tube system 2 by means of a conveying unit 3. In the dialyzer 4 the blood is freed from urinary excreted substances and excess water. Subsequently, the purified blood is returned to the patient via the venous tube system 5. The collection and the return of the blood via a joint cannula is equally imaginable. In the dialyzer 4 hollow fiber capillaries are provided which have a semipermeable membrane. The capillaries are flushed by the so-called dialysis fluid which, on the one hand, absorbs urinary excreted substances and excess water from the blood and, on the other hand, outputs especially hydrogen carbonate for treating an acidosis of the patient 1. The dialysis fluid flows through the feed line 6 to the dialyzer. At the dialysis fluid outlet of the dialyzer 4 a drain line 7 comprising at least one optical sensor 8 is arranged. The optical sensor 8 comprises at least one photodiode and preferably two photodetectors and is used for determining an absorption characteristic of a dialysate. This is preferably the absorbance or, respectively, extinction which can be measured when the dialysate includes substances which absorb light. The photodiode of the optical sensor 8 for this purpose emits narrow-band light in the UV range with the wavelengths between 200 and 350 nm being preferred. Preferably, light having a peak wavelength of from 275 and 295 nm is emitted. Alternatively, the optical sensor is designed so that it measures fluorescence, to which end it emits light for exciting optically active substances and then measures the emission.

[0033] Different options are resulting for the position of the optical sensor 8 in the drain line 7. For example, in the case of a shunt it may be located in the separated part and/or in front of a balancing device or behind a balancing device.

[0034] Frequently, the characteristic line of the optical sensor 8 is linear to a limited extent only (see FIG. 1). In order to extend the linear measuring range, according to aspects the invention it is repeatedly changed to the shunt in the course of therapy. During the shunt, the dialysis fluid flows through an appropriate valve position past the dialyzer, wherein the blood continues being conveyed through the dialyzer 4. Due to stopping (or alternatively at least reducing) the dialysis fluid flow through the dialyzer 4, at least part of the dialysis-side residual volume is at least partially saturated. I.e. substances, and especially light-absorbing substances, on the blood side pass over to the enclosed dialysate side, in other words in the dialyzer substances interacting with electromagnetic radiation pass from the blood-guiding side over to the dialysis fluid-guiding side. Of preference, shunt durations of 18 seconds are provided. Also, the reverse that substances pass from the enclosed side over to the blood side is possible.

[0035] In FIG. 4 an extinction course during a therapy is illustrated. At an interval of four minutes, it is changed to the shunt for 18 seconds at a time. The extinction signal of the optical sensor 8 (E.sub.OS) shows a short-time increase after stopping the shunt. The local maximums are referred to as E.sub.top. E.sub.Ref,DA denotes the course of extinction at the dialysis fluid outlet measured by a reference device. E.sub.Ref,BE denotes the course of extinction at the blood inlet measured by a reference device. E.sub.calc denotes the course of extinction at the blood inlet measured by an optical sensor.

[0036] Solely on the basis of the curve E.sub.OS it is not evident whether or, respectively, when the optical sensor is linear. When, however, the difference E.sub.top-E.sub.pre is applied over E.sub.pre (with E.sub.pre standing for the extinction of E.sub.OS shortly before changing to the shunt), a characteristic curve is resulting, as shown in FIG. 5. In a linear sensor the difference E.sub.top-E.sub.pre applied over E.sub.pre would be a monotonically increasing straight line (see FIG. 6). In the case of the optical sensor, the difference shows a maximum turning point, however, and then decreases again. The E.sub.pre value in the maximum turning point represents the extinction from which the optical sensor becomes non-linear. Extinctions smaller than the E.sub.pre value in the maximum turning point thus are trustworthy as regards linearity. In other words, extinctions above the maximum turning point originate from the non-linear range and there below originate from the linear range. In each of the figures, also the E.sub.top/E.sub.pre ratio is shown against E.sub.pre. In the case of the reference measuring device the ratio is constant. In the case of the optical sensor, a constancy for E.sub.pre values smaller than the E.sub.pre values in the maximum is valid. The ratio is continuously decreasing for increasing values. Thus, instead of the difference, also the ratio may be considered so as to be able to judge whether and, respectively, from when the sensor is within the linear range.

[0037] The course of the difference in FIG. 5 may be considered a downward opened parabola. As is known, a parabola is mathematically defined by three points. Thus, it is also imaginable to reduce the number of circuits in the shunt to at least three, for example at the beginning of a therapy, in the middle of a therapy and at the end of a therapy. By a subsequent square fit through said at least three points the vertex of the parabola can be determined which can be considered to be a linearity limit, as described before.

[0038] The invention provides as an alternative to restrict the implementation of the shunt changes to the non-linear range only, i.e. at the beginning of therapy. In randomly defined time intervals it is changed to the shunt and subsequently the difference is observed. As soon as a flattening or the reversal of the gradient of the curve is detected, subsequent changes to the shunt can be renounced, as the sensor is linear from this point. The range within which changing to the shunt would occur, would correspond to the right leg of the parabola in FIG. 5.

[0039] For linearization E.sub.pre values that are smaller than the E.sub.pre values in the maximum are used. Said values now are used for non-linear regression. Preferably, this is an exponential function of the formula:

E(t)=a.Math.e.sup.bt

[0040] However, also other functions such as a double exponential function, for example, are imaginable.

[0041] FIG. 7A illustrates a regression for the reference measuring device. It is clearly visible in which way the measuring data and the regression curve lie on top of each other. The extrapolated extinction at t=0 is just above 0.4. FIG. 7B illustrates a similar representation. However, here the values of the optical sensor are shown. It is evident how in this case the measured extinction values deviate from the regression curve at an extinction of about 0.2. When the last nine data are fitted and extrapolated, the extinction at t=0 just as the reference is at a value of slightly above 0.4. Thus, the reference and the fit of the optical sensor show identical curves. Hence the optical sensor 8 is online linearized during measurement.

[0042] In FIG. 8 now the characteristic line of the optical sensor linearized according to aspects of the invention is shown (E.sub.OS,korr). In addition, the original characteristic (E.sub.OS) is applied which had to be corrected.

[0043] The time interval of the changes to the shunt is variable. It may be implemented at fixedly defined intervals during the entire therapy duration, for example, wherein the times of changing to the shunt may be distributed to be equidistant or non-equidistant. Moreover, it is imaginable that changes to the shunt start as late as after or up to a particular duration of therapy.

[0044] Since the initial values (extinction at t=0) and the extinction values at the end of a therapy are known now, the Kt/V value can be corrected according to any one of the following equations.

[0045] A simplified model without considering further effects is the simplest formula for determining the Kt/V value during dialysis therapy. It takes neither the generation of urea in the patient during therapy nor the so-called rebound effect into account.

[00001]$\frac{\mathrm{Kt}}{V}=\ln \left(\frac{c_0}{c\left(t\right)}\right)$

[0046] Here K stands for the urea clearance, t stands for the duration of therapy, V stands for the urea distribution volume, co stands for the initial urea concentration and c(t) stands for the urea concentration at a given point in time t.

[0047] Another model for determining the Kt/V value is the Single-Pool model taking urea generation during therapy into account. In this model it is assumed in a simplified manner that urea is dissolved merely in a large distribution volume. As compared to the afore-mentioned model, it is considered that during therapy urea is generated in the patient's body. Moreover, the model considers that the convection occurring by ultrafiltration additionally removes urea.

[00002]$\mathrm{sp}.Math.\frac{\mathrm{Kt}}{V}=-\ln \left(-0.008.Math.t+\frac{c\left(t\right)}{c_0}\right)+\left(4-3.5.Math.\frac{c\left(t\right)}{c_0}\right).Math.\frac{\mathrm{UF}}{W}$

[0048] UF stands for the ultrafiltration volume and W stands for the patient's weight.

[0049] Another model for determining the Kt/V value considers the rebound effect (equilibrated Kt/V). In reality, the movement of urea through the body is not unrestrictedly possible, as urea is present both in the intracellular and in the extracellular space and in the intravascular space. A model considering the existence of said different spaces deviating from the Single-Pool model helps to determine a so-called equilibrated Kt/V. In this case, the backflow of urea after therapy from organs of low blood flow into the intravascular space is taken into consideration.

[00003]$e.Math.\frac{\mathrm{Kt}}{V}=\mathrm{sp}.Math.\frac{\mathrm{Kt}}{V}-\frac{0.6}{T}.Math.\mathrm{sp}.Math.\frac{\mathrm{Kt}}{V}+0.03$

[0050] In this formula, T corresponds to the entire duration of therapy.

[0051] Especially toward the end of the dialysis therapy, the extinction to be expected is low, as many light-absorbing substances have been removed already. Therefore, it is provided to implement a long shunt of about 2 to 3 minutes especially toward the end of therapy. During a shunt, the dialysis fluid flows past the dialyzer, with the blood continuing to circulate. After a certain period of time the dialysate-side residual volume in the dialyzer absorbs the substances from the blood to the extent that an at least partially diffusive equilibrium exists between the dialysate side and the blood side in the dialyzer. When it is changed to main connection again, the saturated dialysate-side residual volume is guided through the optical sensor 8, where a short-time signal change can be measured. The extinction in the maximum of the signal change corresponds to the extinction in the plasma or at least in the plasma water. For calculating the extinction in the plasma and, respectively, in the plasma water the following equation is used:

E.sub.calc=(E.sub.topE.sub.pre).Math.kE.sub.pre

wherein the factor k in the case of long shunt is 1. The clearance K can be determined according to the following equation, as is known:

[00004]$K=Q_d.Math.\frac{C_{\mathrm{DO}}}{C_{\mathrm{BI}}}$

[0052] Here Q.sub.d stands for the dialysis fluid flow and C.sub.DO as well as C.sub.BI stand for concentration-equivalent variables at the dialysis fluid outlet and the blood inlet. A concentration-equivalent variable for example is a concentration of one or more substances or an absorption characteristic such as the absorbance or, respectively, extinction or fluorescence. According to Beer-Lambert law, the extinction is proportional to the concentration of a light-absorbing substance. C.sub.DO may be determined directly by means of the optical sensor 8 (C.sub.DO=E.sub.OS). C.sub.BI is resulting from the local maximums that occur following a shunt and are calculated as afore-described (C.sub.BI=E.sub.calc).

[0053] It is obvious that blood-side extinctions are always higher than dialysate-side extinctions so that the change to the shunt limited in time up to reaching a diffusive equilibrium always or at least very frequently would take sensor signals to the non-linear range. In the worst case, the optical sensor would be in saturation, which hardly allows any informative measurements. Laboratory measurements have resulted in the fact that a shunt duration of 18 seconds is sufficient to subsequently reach 50% of the blood-side value. The risk of the optical sensor being provided in saturation is significantly reduced in this way. Related to the equation for calculating the extinction in the plasma, this means that k=2 is required. If other dialyzers or flow rates are used, the invention provides to determine the factor online. For this purpose, at first a long shunt and subsequently a short shunt are implemented, and alternatively first a short one and subsequently a long one. Finally, from both shunts the ratio

[00005]$k=\frac{{\left(E_{\mathrm{top}}-E_{\mathrm{pre}}\right)}_{\mathrm{lang}}}{{\left(E_{\mathrm{top}}-E_{\mathrm{pre}}\right)}_{\mathrm{kurz}}}$

is formed, wherein the numerator originates from the long shunt and the denominator originates from the short shunt. When, in this way the k factor is determined, by way of short shunts a blood-side value (E.sub.calc) is non-invasively determined by dialysate-side measurements. Of course, it is further also possible to select even shorter shunt times, which equally results in an adaptation of the k factor. Shorter shunt times offer the advantage that the subsequent local extinction maximums are smaller and tend to be rather within the linear range of the characteristic line of the optical sensor.

[0054] When repeatedly short shunts and at least at the end of therapy at least one long shunt are implemented, blood-side values (E.sub.calc) can be determined by determining the k factor and the equation for calculating the extinction in the plasma. It is important for this purpose to make use of extinctions which lie within the linear range of the optical sensor. This relates especially to the extinctions E.sub.top and E.sub.pre. It can be inferred from the picture in FIG. 5 which values are within the linear range. Now similarly to the preceding sections, non-linear regression curves can be drafted. FIG. 9A shows the corresponding regression for the reference and FIG. 9B shows the corresponding regression for the optical sensor. In the case of the optical sensor, the four last calculated values at the blood inlet (E.sub.calc) were considered. In this case, too, the extrapolated values with t=0 are about equal, when comparing the reference and the optical sensor to each other. In the right-hand part of the figure it is moreover clearly evident in which way the calculated values (E.sub.calc) deviate from the regression curve at the beginning of therapy. It is known that the number of regression points has a great influence on the quality of extrapolation. In order to design the extrapolation even more robust and more precise for this reason, in addition blood samples may be collected at the beginning and toward the end of therapy and may be analyzed so as to determine a Kt/V value by way of the equations 1, 2 and/or 3. Said Kt/V value then can be compared to the Kt/V value from the extrapolation and can be used to correct the latter.

[0055] FIG. 10 shows the linearized characteristic line of the optical sensor along with the non-linearized characteristic line. In the equation for non-linear regression the variable b stands for the ratio of clearance K to the distribution volume V:

[00006]$b=\frac{K}{V}$

[0056] Since b can be determined from fits (see FIGS. 7A, 7B, 9A, and 9B) and K is calculated according to the equation for calculating the clearance, the equation for calculating the variable b can be rearranged for V. In this way, the distribution volume can be determined.

[0057] Since, for the first time, retroactive correction is made, the course of the optical sensor can be corrected already during therapy, i.e. online. For this, e.g. the characteristic lines from FIG. 8 and FIG. 10 can be used. Moreover, the invention provides to store at least the maximums of the difference E.sub.top-E.sub.pre over E.sub.pre. In this way, it can be predicted with sufficiently available data for following therapies whether, respectively, from when the sensor data are within the linear range. This helps to avoid changes to the shunt at the beginning of therapy.

[0058] Alternatively, an embodiment without any additional recording of measuring values is imaginable. The characteristic line of the optical sensor 8 (or of any other sensor) is deposited on the machine and/or a data managing system. This may be realized, for example, in the form of a look-up table and may be used for adjusting the optical sensor 8 during an ongoing therapy. In this way, too, changes to the shunt can be avoided or at least reduced. Since each change to the shunt results in the fact that the blood cannot be sufficiently purified for this period, it is of advantage to carry out, during a shunt, further measurements or tests which equally require changing to the shunt so as to make efficient use of the time for multiple applications.