DETERMINING INTERNAL FILTRATION RATE WITHIN A CAPILLARY HEMODIALYZER

Abstract

The present disclosure relates to a method and a device for determining an internal filtration rate IFR within a capillary hemodialyzer.

Claims

1. A computer-implemented method for determining an internal filtration rate IBR within a capillary hemodialyzer using the dimensions of the hemodialyzer, dimensions and physical parameters of the hollow fiber membranes present in the hemodialyzer, and flow rates of blood and dialys ate through the hemodialyzer, the method comprising the steps of: i) acquiring, using a computer, data on physical properties of the hemodialyzer and of hollow fiber membranes present in the hemodialyzer, the data comprising a diameter d H of the housing of the hemodialyzer, a number N of the hollow fiber membranes present in the hemodialyzer, an effective length L of the hollow fiber membranes present in the hemodialyzer, a total surface area A.sub.tot of the hollow fiber membranes present in the hemodialyzer, an internal diameter d B of the hollow fiber membranes present in the hemodialyzer, a wall thickness ?.sub.M of the hollow fiber membranes present in the hemodialyzer, a porosity ?.sub.M of the hollow fiber membranes present in the hemodialyzer, and an ultrafiltration coefficient K.sub.UF of the hollow fiber membranes present in the hemodialyzer; ii) acquiring, using the computer, a blood flow rate Q.sub.B and a dialysis flow rate Q.sub.D through the hemodialyzer during operation of the hemodialyzer; iii) determining, using the computer, the internal filtration rate IFR of the hemodialyzer, based on the data acquired in steps i and ii, wherein the internal filtration rate IFR is determined according to $IFR = N ? d ? K {(P ? - P ? - ?_{0}) x_{i} - \frac{128 ? ?}{N ? d ?} [Q ? (\frac{x_{i}^{2}}{2} - L x_{i}) - N ? d ? [\frac{v_{2} - v_{1}}{6 L} (\frac{x_{i}^{4}}{4} - L^{3} x_{i}) + \frac{v_{1}}{2} (\frac{x_{i}^{3}}{3} - L^{2} x_{i})]] + \frac{? ?}{2 N ? f ?} [Q ? \frac{x_{i}^{2}}{2} - N ? d ? [\frac{v_{2} - v_{1}}{2 L} (\frac{x_{i}^{4}}{1 2} - \frac{L^{2}}{2} x_{i}^{2}) + v_{1} (\frac{x_{i}^{3}}{6} - \frac{L}{2} x_{i}^{2})]]}$ $? indicates text missing or illegible when filed$ wherein N refers to the number of hollow fiber membranes present in the hemodialyzer; d.sub.B refers to the internal diameter of hollow fiber membranes present in the hemodialyzer; K $K - \frac{K_{UF}}{A_{t o t} ?_{M}} ?,$ $? indicates text missing or illegible when filed$ K.sub.UF refers to the ultrafiltration coefficient of the hollow fiber membranes present in the hemodialyzer, A.sub.tot refers to the total membrane area of the hollow fiber membranes present in the hemodialyzer (A.sub.tot=N?d.sub.BL) , ?.sub.M m refers to the membrane porosity of the hollow fiber membranes present in the hemodialyzer; P.sub.,out refers to the blood pressure at hemodialyzer exit; P.sub.D,out refers to the dialysate pressure at hemodialyzer exit; ?.sub.0 refers to the average oncotic pressure; X.sub.i refers to the location of inversion point (J.sub.v(x.sub.i)=0); ?.sub.B refers to the blood viscosity; Q.sub.B refers to the blood flow rate; L refers to the effective length of hollow fiber membranes present in the hemodialyzer; v.sub.1 refers to J.sub.v(0); v.sub.2 refers to J.sub.v(L); ?.sub.D refers to the dialysate viscosity; Q.sub.D refers to the dialys ate flow rate; and $f_{R_{o}, R_{k}} \frac{? - R ?}{1 6} + \frac{?}{2} (\frac{?}{2} \ln (\frac{R_{o}}{R_{k}}) + \frac{?}{4}) - \frac{?}{8} (R_{k}^{2} - R_{o}^{2}),$ $R_{o} = \frac{d ?}{2} + ?_{M},$ $R_{k} = R_{o} + ? ?,$ $? indicates text missing or illegible when filed$ wherein d.sub.B refers to the internal diameter of the hollow fiber membranes present in the hemodialyzer, ?.sub.M refers to the wall thickness of the hollow fiber membranes present in the hemodialyzer, ?.sub.? refers to the thickness of the diffusion layer around the hollow fiber membranes present in the hemodialyzer.

2. The method of claim 1, additionally comprising the steps of: iv) acquiring, using the computer, data on a duration TD of the operation of the hemodialyzer; v) determining, using the computer, a total volume V.sub.tot of fluid exchanged through the wall of the hollow fiber membranes present in the hemodialyzer during operation of the hemodialyzer, based on the internal filtration rate IFR and the data acquired in step iv, wherein the total volume V.sub.tot is determined according to $V_{tot} = ?_{0}^{TD} IFR (t) dt .$

3. The method of claim 1, wherein data on physical properties of the hemodialyzer and of hollow fiber membranes present in the hemodialyzer are acquired from a database in operative association with a processor of the computer.

4. The method of claim 1, wherein data on physical properties of the hemodialyzer and of hollow fiber membranes present in the hemodialyzer and/or the blood flow rate and the dialysis flow rate through the hemodialyzer during operation of the hemodialyzer is acquired from an input device in operative association with a processor of the computer.

5. The method of claim 4, wherein the input device comprises a contactless reader.

6. The method of claim 4, wherein the input device comprises at least one user interface.

7. The method of claim 4, wherein the input device comprises an extracorporeal blood treatment apparatus.

8. A system comprising a) a database comprising data on physical properties of a plurality of capillary hemodialyzers and of hollow fiber membranes present therein, the data comprising a diameter d.sub.H of the housing of the hemodialyzers, a number N of the hollow fiber membranes present in the hemodialyzers, an effective length L of the hollow fiber membranes present in the hemodialyzers, a total surface area A.sub.tot of the hollow fiber membranes present in the hemodialyzers, an internal diameter d.sub.B of the hollow fiber membranes present in the hemodialyzers, a wall thickness ?.sub.M of the hollow fiber membranes present in the hemodialyzers, a porosity EM of the hollow fiber membranes present in the hemodialyzers, and an ultrafiltration coefficient KUF of the hollow fiber membranes present in the hemodialyzers; and/or b) an input device configured for providing data on physical properties of a capillary hemodialyzer and of hollow fiber membranes present in the hemodialyzer, the data comprising a diameter d H of the housing of the hemodialyzer, a number N of the hollow fiber membranes present in the hemodialyzer, an effective length L of the hollow fiber membranes present in the hemodialyzer, a total surface area A.sub.tot of the hollow fiber membranes present in the hemodialyzer, an internal diameter d.sub.B of the hollow fiber membranes present in the hemodialyzer, a wall thickness ?.sub.M of the hollow fiber membranes present in the hemodialyzer, a porosity ?.sub.M of the hollow fiber membranes present in the hemodialyzer, and an ultrafiltration coefficient K.sub.UF of the hollow fiber membranes present in the hemodialyzer; and/or for providing a blood flow rate and a dialysis flow rate through the hemodialyzer during operation of the hemodialyzer; c) an output device configured for output of data received from a computer processor in operative association with the output device; d) a computer processor programmed for communication with the database and/or the input device, and for communication with the output device, the processor programmed for a. acquiring data from the database and/or the input device, the data comprising a diameter d H of the housing of a hemodialyzer, a number N of the hollow fiber membranes present in the hemodialyzer, an effective length L of the hollow fiber membranes present in the hemodialyzer, a total surface area A.sub.tot of the hollow fiber membranes present in the hemodialyzer, an internal diameter d.sub.B of the hollow fiber membranes present in the hemodialyzer, a wall thickness ?.sub.M of the hollow fiber membranes present in the hemodialyzer, a porosity EM of the hollow fiber membranes present in the hemodialyzer, and an ultrafiltration coefficient K.sub.UF of the hollow fiber membranes present in the hemodialyzer; and/or a blood flow rate and a dialysis flow rate through the hemodialyzer during operation of the hemodialyzer, b. determining an internal filtration rate UR within a capillary hemodialyzer, based on the acquired data, wherein the internal filtration rate IFR is determined according to $IFR = N ? d ? K {(P ? - P ? - ?_{0}) x_{i} - \frac{128 ? ?}{N ? d ?} [Q ? (\frac{x_{i}^{2}}{2} - L x_{i}) - N ? d ? [\frac{v_{2} - v_{1}}{6 L} (\frac{x_{i}^{4}}{4} - L^{3} x_{i}) + \frac{v_{1}}{2} (\frac{x_{i}^{3}}{3} - L^{2} x_{i})]] + \frac{? ?}{2 N ? f ?} [Q ? \frac{x_{i}^{2}}{2} - N ? d ? [\frac{v_{2} - v_{1}}{2 L} (\frac{x_{i}^{4}}{1 2} - \frac{L^{2}}{2} x_{i}^{2}) + v_{1} (\frac{x_{i}^{3}}{6} - \frac{L}{2} x_{i}^{2})]]}$ $? indicates text missing or illegible when filed$ wherein N refers to the number of hollow fiber membranes present in the hemodialyzer; d.sub.B refers to the internal diameter of hollow fiber membranes present in the hemodialyzer; K refers to $\frac{K_{UF}}{A_{t o t} ?_{M}},$ K.sub.UF refers to the ultrafiltration coefficient of the hollow fiber membranes present in the hemodialyzer, A.sub.tot refers to the total membrane area of the hollow fiber membranes present in the hemodialyzer (A.sub.tot=N?d.sub.BL), ?.sub.M refers to the membrane porosity of the hollow fiber membranes present in the hemodialyzer; P.sub.B,out refers to the blood pressure at hemodialyzer exit; P.sub.D,out refers to the dialysate pressure at hemodialyzer exit; ?.sub.0 refers to the average oncotic pressure; X.sub.i refers to the location of inversion point (J.sub.v(x.sub.i)=0); ?.sub.B refers to the blood viscosity; Q.sub.B refers to the blood flow rate; L refers to the effective length of hollow fiber membranes present in the hemodialyzer; v.sub.1 refers to J.sub.v(0); v.sub.2 refers to J.sub.v(L); ?.sub.D refers to the dialysate viscosity; Q.sub.D refers to the dialys ate flow rate; and $f_{R_{o}, R_{k}} \frac{? - R ?}{1 6} + \frac{?}{2} (\frac{?}{2} \ln (\frac{R_{o}}{R_{k}}) + \frac{?}{4}) - \frac{?}{8} (R_{k}^{2} - R_{o}^{2}),$ $R_{o} = \frac{d ?}{2} + ?_{M},$ $R_{k} = R_{o} + ? ?,$ $? indicates text missing or illegible when filed$ wherein d.sub.B refers to the internal diameter of the hollow fiber membranes present in the hemodialyzer, ?.sub.M refers to the wall thickness of the hollow fiber membranes present in the hemodialyzer, ?.sub.? refers to the thickness of the diffusion layer around the hollow fiber membranes present in the hemodialyzer, c. optionally, determining a total volume V.sub.tot of fluid exchanged through the wall of the hollow fiber membranes present in the hemodialyzer during operation of the hemodialyzer, wherein the total volume V.sub.tot is determined according to
v.sub.tot=?.sub.0.sup.?DIFR(t)dt, d. transmitting the determined internal filtration rate IFR, and, optionally, the total volume V.sub.tot of fluid exchanged to the output device.

9. The system of claim 8, wherein the input device, the output device, and the processor are contained in a mobile communication device.

10. The system of claim 8, wherein the input device is a graphical use interface (GUI) of a mobile communication device.

11. The system of claim 8, wherein the output device is a display device.

12. A computer program for instructing a computer processor to perform the method of a. acquiring data from a database and/or an input device in operative association with the processor, the data comprising a diameter du of the housing of a hemodialyzer, a number N of the hollow fiber membranes present in the hemodialyzer, an effective length L of the hollow fiber membranes present in the hemodialyzer, a total surface area A.sub.tot of the hollow fiber membranes present in the hemodialyzer, an internal diameter d B of the hollow fiber membranes present in the hemodialyzer, a wall thickness of the hollow fiber membranes present in the hemodialyzer, a porosity EM of the hollow fiber membranes present in the hemodialyzer, and an ultrafiltration coefficient K.sub.UF of the hollow fiber membranes present in the hemodialyzer; and/or a blood flow rate and a dialysis flow rate through the hemodialyzer during operation of the hemodialyzer; b. determining an internal filtration rate UR within a capillary hemodialyzer, based on the acquired data, wherein the internal filtration rate IFR is determined according to $IFR = N ? d ? K {(P ? - P ? - ?_{0}) x_{i} - \frac{128 ? ?}{N ? d ?} [Q ? (\frac{x_{i}^{2}}{2} - L x_{i}) - N ? d ? [\frac{v_{2} - v_{1}}{6 L} (\frac{x_{i}^{4}}{4} - L^{3} x_{i}) + \frac{v_{1}}{2} (\frac{x_{i}^{3}}{3} - L^{2} x_{i})]] + \frac{? ?}{2 N ? f ?} [Q ? \frac{x_{i}^{2}}{2} - N ? d ? [\frac{v_{2} - v_{1}}{2 L} (\frac{x_{i}^{4}}{1 2} - \frac{L^{2}}{2} x_{i}^{2}) + v_{1} (\frac{x_{i}^{3}}{6} - \frac{L}{2} x_{i}^{2})]]}$ $? indicates text missing or illegible when filed$ wherein N refers to the number of hollow fiber membranes present in the hemodialyzer; d.sub.B refers to the internal diameter of hollow fiber membranes present in the hemodialyzer; K refers to $\frac{K_{UF}}{A_{t o t} ?_{M}},$ K.sub.UF refers to the ultrafiltration coefficient of the hollow fiber membranes present in the hemodialyzer, A.sub.tot refers to the total membrane area of the hollow fiber membranes present in the hemodialyzer (A.sub.tot=N?d.sub.BL), ?.sub.M refers to the membrane porosity of the hollow fiber membranes present in the hemodialyzer; P.sub.B,out refers to the blood pressure at hemodialyzer exit; P.sub.D,out refers to the dialysate pressure at hemodialyzer exit; ?.sub.0 refers to the average oncotic pressure; X.sub.i refers to the location of inversion point (J.sub.v(x.sub.i)=0); ?.sub.B refers to the blood viscosity; Q.sub.B refers to the blood flow rate; L refers to the effective length of hollow fiber membranes present in the hemodialyzer; v.sub.1 refers to J.sub.v(0); v.sub.2 refers to J.sub.v(L); ?.sub.D refers to the dialysate viscosity; Q.sub.D refers to the dialys ate flow rate; and $f_{R_{o}, R_{k}} \frac{? - R ?}{1 6} + \frac{?}{2} (\frac{?}{2} \ln (\frac{R_{o}}{R_{k}}) + \frac{?}{4}) - \frac{?}{8} (R_{k}^{2} - R_{o}^{2}),$ $R_{o} = \frac{d ?}{2} + ?_{M},$ $R_{k} = R_{o} + ? ?,$ $? indicates text missing or illegible when filed$ wherein d.sub.B refers to the internal diameter of the hollow fiber membranes present in the hemodialyzer, ?.sub.M refers to the wall thickness of the hollow fiber membranes present in the hemodialyzer, ?.sub.?refers to the thickness of the diffusion layer around the hollow fiber membranes present in the hemodialyzer; c. optionally, determining a total volume V.sub.tot of fluid exchanged through the wall of the hollow fiber membranes present in the hemodialyzer during operation of the hemodialyzer, wherein the total volume V.sub.tot is determined according to
v.sub.tot=?.sub.0.sup.?DIFR(t)dt, d. transmitting the determined internal filtration rate IFR, and, optionally, the total volume V.sub.tot of fluid exchanged to an output device in operative association with the processor.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0006] FIG. 1 shows a schematic perspective view and sectional detail views of a capillary hemodialyzer and fluid flows within the hemodialyzer;

[0007] FIG. 2 shows a comparison of experimentally determined internal filtration rates and internal filtra- tion rates determined according to the method of the present disclosure for one model of a hemodialyzer;

[0008] FIG. 3 shows a comparison of experimentally determined internal filtration rates and internal filtration rates determined according to the method of the present disclosure for another model of a hemodialyzer.

DETAILED DESCRIPTION

[0009] The present disclosure provides a computer-implemented method for determining an internal filtration rate IFR within a capillary hemodialyzer. The method comprises [0010] i) acquiring, using a computer, data on physical properties of the hemodialyzer and of hollow fibers present in the hemodialyzer; [0011] ii) acquiring, using the computer, a blood flow rate Q B and a dialysis flow rate Q D through the hemodialyzer during operation of the hemodialyzer; [0012] iii) determining, using the computer, the internal filtration rate IFR of the hemodialyzer, based on the data acquired in steps i and ii.

[0013] In one embodiment, the method additionally comprises [0014] iv) acquiring, using the computer, data on a duration TD of the operation of the hemodialyzer; [0015] v) determining, using the computer, a total volume Vtot of fluid exchanged through the wall of the hollow fiber membranes present in the hemodialyzer during operation of the hemodialyzer, based on the internal filtration rate IFR and the data acquired in step iv.

[0016] In a particular embodiment, data on physical properties of the hemodialyzer and of hollow fibers present in the hemodialyzer are acquired from a database in operative association with a processor of the computer.

[0017] In one embodiment of the method, the database comprises data on physical properties of a plurality of different hemodialyzers and of hollow fibers present in the hemodialyzers. For each hemodialyzer of the plurality of different hemodialyzers, such data may comprise a diameter d H of the housing of the hemodialyzer, a number N of the hollow fibers present in the hemodialyzer, an effective length L of the hollow fibers present in the hemodialyzer, a total surface area A.sub.tot of the hollow fibers present in the hemodialyzer, an internal diameter d.sub.B of the hollow fibers present in the hemodialyzer, a wall thickness ?.sub.M of the hollow fibers present in the hemodialyzer, a porosity ?.sub.m of the hollow fibers present in the hemodialyzer, and an ultrafiltration coefficient K.sub.UF of the hollow fibers present in the hemodialyzer.

[0018] Additionally, the database may comprise data on a blood viscosity ?.sub.B and a dialysate viscosity ?.sub.D.

[0019] In a further embodiment, data on physical properties of the hemodialyzer and of hollow fibers present in the hemodialyzer and/or the blood flow rate Q.sub.B and the dialysis flow rate Q.sub.D through the hemodialyzer during operation of the hemodialyzer is acquired from an input device in operative association with a processor of the computer.

[0020] The hemodialyzer is perfused with blood at a blood flow rate Q.sub.B and dialysate at a dialysate flow rate Q.sub.D during operation, i.e., when it is used in an external blood circuit to remove toxins from blood. The internal filtration rate IFR and the total volume V.sub.tot of fluid exchanged through the wall of the hollow fiber membranes present in the hemodialyzer vary with blood flow rate Q.sub.B and dialysate flow rate Q.sub.D through the hemodialyzer.

[0021] In one embodiment, the input device comprises a contactless reader. In a particular embodiment, the contactless reader is an optical reader which acquires data of a barcode or QR code present on a hemodialyzer. In another particular embodiment, the contactless reader is a sensor which acquires data from an RFID or NFC tag present on or in the hemodialyzer.

[0022] In a further embodiment, the input device comprises at least one user interface. In a particular embodiment, the user interface comprises a keyboard or a touchscreen. In a further embodiment of the system, the input device comprises a graphical use interface (GUI). In a particular embodiment, the input device comprises a touchscreen of a smartphone. The input device is used for manually entering data on physical properties of the hemodialyzer and of hollow fibers present in the hemodialyzer, and/or the blood flow rate Q.sub.B and the dialysis flow rate Q.sub.D through the hemodialyzer during operation of the hemodialyzer.

[0023] In another embodiment, the input device comprises an extracorporeal blood treatment apparatus. The extracorporeal blood treatment apparatus controls the parameters of an extracorporeal blood circuit comprising a hemodialyzer during operation, i.e. during the treatment of a patient.

[0024] When used as an input device for the method of the present disclosure, the extracorporeal blood treatment apparatus provides data on physical properties of the hemodialyzer and of hollow fibers present in the hemodialyzer, and/or the blood flow rate Q.sub.B and the dialysis flow rate Q.sub.D through the hemodialyzer during operation of the hemodialyzer. In one embodiment of the method, the processor acquires realtime data of the blood flow rate Q.sub.B and the dialysis flow rate Q.sub.D through a hemodialyzer during operation of the hemodialyzer and, optionally, data on the duration TD of the operation, from the extracorporeal blood treatment apparatus, i.e. during an actual treatment. In another embodiment, a blood flow rate QB and a dialysis flow rate Q.sub.D through a hemodialyzer during operation of the hemodialyzer and, optionally, a duration TD of the operation, are manually entered through the input device to simulate a treatment.

[0025] In one embodiment of the method, the data on physical properties of the hemodialyzer and of hollow fibers present in the hemodialyzer comprise a diameter d H of the housing of the hemodialyzer, a number N of the hollow fibers present in the hemodialyzer, an effective length L of the hollow fibers present in the hemodialyzer, a total surface area A.sub.tot of the hollow fibers present in the hemodialyzer, an internal diameter d.sub.B of the hollow fibers present in the hemodialyzer, a wall thickness ?.sub.M of the hollow fibers present in the hemodialyzer, a porosity ?.sub.m of the hollow fibers present in the hemodialyzer, and an ultrafiltration coefficient K.sub.UF of the hollow fibers present in the hemodialyzer.

[0026] In one embodiment of the method, the internal filtration rate IFR is determined according to

[00001] $IFR = N ? d_{B} ?_{0}^{x_{i}} J_{v} (z) dz$

with [0027] N number of hollow fibers present in the hemodialyzer; [0028] d.sub.b internal diameter of hollow fibers present in the hemodialyzer; [0029] J.sub.v(z) ultrafiltration flux through the membrane wall; [0030] x.sub.i location of inversion point (J.sub.v(x.sub.i)=0).

[0031] This equation can be rewritten as

[00002] $IFR = N ? d_{B} K ?_{0}^{x_{i}} (P_{B} (z) - P_{D} (z) - ?_{o}) dz$ $with$ $K - \frac{K_{U F}}{A_{t o t} ?_{M}},$ [0032] K.sub.UF ultrafiltration coefficient of the hollow fibers present in the hemodialyzer, [0033] A.sub.tot total membrane area of the hollow fibers present in the hemodialyzer (A.sub.tot=N?d.sub.BL), [0034] ?.sub.M membrane porosity of the hollow fibers present in the hemodialyzer; [0035] P.sub.B(z) blood pressure; [0036] P.sub.D(z) dialysate pressure; [0037] ?.sub.o average oncotic pressure;

[0038] In another embodiment of the method, the internal filtration rate IFR is determined according to

[00003] $IFR = N ? d_{B} K {(P_{B, out} - P_{D, out} - ?_{0}) x_{i} - \frac{1 2 8 ?_{B}}{N ? d_{B}^{4}} [Q_{B} (\frac{x_{i}^{2}}{2} - L x_{i}) - N ? d_{B} [\frac{v_{2} - v_{1}}{6 L} (\frac{x_{i}^{4}}{4} - L^{3} x_{i}) + \frac{v_{1}}{2} (\frac{x_{i}^{3}}{3} - L^{2} x_{i})]] + \frac{?_{D}}{2 N ? f_{R_{o}, R_{k}}} [Q_{D} \frac{x_{i}^{2}}{2} - N ? d_{B} [\frac{v_{2} - v_{1}}{2 L} (\frac{x_{i}^{4}}{1 2} - \frac{L^{2}}{2} x_{i}^{2}) + v_{1} (\frac{x_{i}^{3}}{6} - \frac{L}{2} x_{i}^{2})]]}$

with [0039] N number of hollow fibers present in the hemodialyzer; [0040] d.sub.B internal diameter of the hollow fibers present in the hemodialyzer;

[00004] $K - \frac{K_{UF}}{A_{t o t} ?_{M}},$ [0041] K.sub.UF ultrafiltration coefficient of the hollow fibers present in the hemodialyzer, [0042] A.sub.tot total membrane area of the hollow fibers present in the hemodialyzer (A.sub.tot=N?d.sub.BL), [0043] ?.sub.M membrane porosity of the hollow fibers present in the hemodialyzer; [0044] P.sub.B,out blood pressure at hemodialyzer exit; [0045] P.sub.D,out dialysate pressure at hemodialyzer exit; [0046] ?.sub.o average oncotic pressure; [0047] x.sub.i location of inversion point (J.sub.v(x.sub.i)=0); [0048] ?.sub.B blood viscosity; [0049] Q.sub.B blood flow rate; [0050] L effective length of hollow fibers present in the hemodialyzer; [0051] v.sub.1 J.sub.v(0) ; [0052] v.sub.2 J.sub.v(L); [0053] ?.sub.D dialysate viscosity; [0054] Q.sub.D dialysate flow rate;

[00005] $f_{R_{o}, R_{k}} \frac{R_{k}^{4} - R_{o}^{4}}{1 6} + \frac{R_{k}^{2}}{2} (\frac{R_{k}^{2}}{2} \ln (\frac{R_{o}}{R_{k}}) + \frac{R_{k}^{2} - R_{o}^{2}}{4}) - \frac{R_{o}^{2}}{8} (R_{k}^{2} - R_{o}^{2}),$ $R_{o} = \frac{d_{B}}{2} + ?_{M},$ $R_{k} = R_{o} + ?_{?},$ [0055] d.sub.B internal diameter of hollow fibers present in the hemodialyzer, [0056] ?.sub.M wall thickness of the hollow fibers present in the hemodialyzer, [0057] ?.sub.? half the distance between adjacent hollow fibers present in the hemodialyzer.

[0058] In a further embodiment of the method, some of the parameters in the above equation for IFR are calculated according to the following equations:

[00006] $\begin{matrix} f_{R_{o}, R_{k}} = \frac{R_{k}^{4} - R_{o}^{4}}{1 6} + \frac{R_{k}^{2}}{2} (\frac{R_{k}^{2}}{2} \ln (\frac{R_{o}}{R_{k}}) + \frac{R_{k}^{2} - R_{o}^{2}}{4}) - \frac{R_{o}^{2}}{8} (R_{k}^{2} - R_{o}^{2}) & 1. \end{matrix}$ $\begin{matrix} K = - \frac{K_{UF}}{A_{tot} ?_{M}} & 2. \end{matrix}$ $\begin{matrix} E_{1} = \frac{?_{D} d_{B} L^{3}}{1 6 f_{R_{o}, R_{k}}} - \frac{8 0 ?_{B} L^{3}}{3 d_{B}^{3}} & 3. \end{matrix}$ $\begin{matrix} E_{2} = \frac{5 ?_{D} d_{B} L^{3}}{4 8 f_{R_{o}, R_{k}}} - \frac{1 6 ?_{B} L^{3}}{d_{B}^{3}} & 4. \end{matrix}$ $\begin{matrix} R_{1} = 1 + \frac{1 2 8}{3} K \frac{?_{B} L^{2}}{d_{B}^{3}} & 5. \end{matrix}$ $\begin{matrix} R_{2} = 1 - K \frac{?_{D} d_{B} L^{2}}{6 f_{R_{o}, R_{k}}} + \frac{1 6}{9} K^{2} \frac{?_{B} ?_{D} L^{4}}{R_{1} f_{R_{o}, R_{k}} d_{B}^{2}} & 6. \end{matrix}$ $\begin{matrix} F_{1} = (P_{B, o u t} - ?_{0}) L + 6 4 \frac{?_{B} L^{2} Q_{B}}{N ? d_{B}^{4}} + \frac{?_{D} L^{2} Q_{D}}{4 N ? f_{R_{o}, R_{k}}} & 7. \end{matrix}$ $\begin{matrix} F_{2} = E_{2} - \frac{6 4}{3} \frac{E_{1} ?_{B} L^{2} K}{R_{1} d_{B}^{3}} & 8. \end{matrix}$ $\begin{matrix} B_{1} = P_{B, o u t} - P_{D, o u t} - ?_{o} + \frac{1 2 8 ?_{B} Q_{B} L}{N ? d_{B}^{4}} & 9. \end{matrix}$ $\begin{matrix} B_{2} = P_{B, o u t} - ?_{o} + \frac{1 2 8 ?_{B} Q_{B} L}{N ? d_{B}^{4}} & 10. \end{matrix}$ $\begin{matrix} D_{1} = P_{B, o u t} - P_{D, o u t} - ?_{o} + \frac{?_{D} Q_{D} L}{2 N ? f_{R_{o}, R_{k}}} & 11. \end{matrix}$ $\begin{matrix} D_{2} = P_{B, o u t} - ?_{o} + \frac{?_{D} Q_{D} L}{2 N ? f_{R_{o}, R_{k}}} & 12. \end{matrix}$ $\begin{matrix} G_{1} = F_{1} + \frac{E_{1}}{R_{1}} {KB}_{2} + \frac{F_{2}}{R_{2}} {KD}_{2} + \frac{F_{2}}{R_{2}} K^{2} \frac{?_{D} d_{B} L^{2}}{1 2 f_{R_{o}, R_{k}}} B_{2} & 13. \end{matrix}$ $\begin{matrix} G_{2} = L + \frac{E_{1}}{R_{1}} K + \frac{F_{2}}{R_{2}} K + \frac{F_{2}}{R_{2}} K^{2} \frac{?_{D} d_{B} L^{2}}{1 2 R_{1} f_{R_{o}, R_{k}}} & 14. \end{matrix}$ $\begin{matrix} P_{D, o u t} = \frac{1}{G_{2}} (G_{1} - \frac{UF}{N ? d_{B} K}) & 15. \end{matrix}$ $\begin{matrix} v_{1} = J_{v} (0) = K \frac{1}{R_{1}} (B_{1} - \frac{6 4 ?_{B} L^{2}}{3 d_{B}^{3}} v_{2}) & 16. \end{matrix}$ $\begin{matrix} v_{2} = J_{v} (L) = \frac{K}{R_{2}} (D_{1} + K \frac{?_{D} d_{B} L^{2} B_{1}}{1 2 R_{1} f_{R_{o}, R_{k}}}) & 17. \end{matrix}$ $\begin{matrix} x_{i} = \frac{v_{1}}{v_{1} - v_{2}} & 18. \end{matrix}$

with [0059] N number of hollow fibers present in the hemodialyzer; [0060] L effective length of the hollow fibers present in the hemodialyzer; [0061] d.sub.B internal diameter of the hollow fibers present in the hemodialyzer; [0062] A.sub.tot total membrane area of the hollow fibers present in the hemodialyzer (A.sub.tot=N?d.sub.BL), [0063] UF net ultrafiltration flow rate; [0064] K.sub.UF UF coefficient; [0065] Q.sub.B blood flow rate; [0066] Q.sub.D dialysate flow rate; [0067] P.sub.B,out blood pressure at dialyzer exit; [0068] P.sub.D,out dialysate pressure at dialyzer exit; [0069] ?.sub.o average oncotic pressure; [0070] ?.sub.B blood viscosity; [0071] ?.sub.D dialysate viscosity; [0072] ?.sub.M membrane porosity; [0073] ?.sub.M membrane thickness.

[0074] In one embodiment of the method, the total volume V tot of fluid exchanged through the wall of the hollow fiber membranes present in the hemodialyzer over a time period TD of operation of the hemodialyzer is determined according to

[00007] $V_{tot} = ?_{0}^{TD} IFR (t) dt$

[0075] The present disclosure also provides a system comprising [0076] a) a database comprising data on physical properties of a plurality of capillary hemodialyzers and of hollow fibers present therein; and/or [0077] b) an input device configured for providing data on physical properties of a capillary hemodialyzer and of hollow fibers present in the hemodialyzer and/or for providing a blood flow rate and a dialysis flow rate through the hemodialyzer during operation of the hemodialyzer; [0078] c) an output device configured for output of data received from a computer processor in operative association with the output device; [0079] d) a computer processor programmed for communication with the database and/or the input device, and for communication with the output device, the processor programmed for [0080] a. acquiring data from the database and/or the input device, [0081] b. determining an internal flow rate IFR within a capillary hemodialyzer, based on the acquired data, [0082] c. optionally, determining a total volume V tot of fluid exchanged through the wall of the hollow fiber membranes present in the hemodialyzer during operation of the hemodialyzer; [0083] d. transmitting the determined internal flow rate IFR, and, optionally, the total volume V tot of fluid exchanged to the output device.

[0084] In one embodiment of the system, the input device, the output device, and the processor are contained in a portable device. In one embodiment, the portable device is a portable computer, for instance, a laptop, a tablet computer, or a PDA. In a further embodiment, the portable device is a mobile communication device, for instance, a smartphone.

[0085] In one embodiment of the system, the output device is a display device. Examples of suitable display devices include monitors, computer displays, and touchscreens. In a particular embodiment, the display device is a touchscreen of a smartphone.

[0086] In one embodiment of the system, the database is present in a computer memory in operative association with the computer processor. In a further embodiment, the computer memory is contained in a portable device comprising the input device, the output device, and the processor. In another embodiment, the database is present in a remote computer memory, a network drive, or a cloud memory accessible via the internet.

[0087] The present disclosure also provides a computer program for instructing a computer processor to perform the method of [0088] a. acquiring data from a database and/or an input device in operative association with the processor; [0089] b. determining an internal filtration rate IFR within a capillary hemodialyzer, based on the acquired data; [0090] c. optionally, determining a total volume V tot of fluid exchanged through the wall of the hollow fiber membranes present in the hemodialyzer during operation of the hemodialyzer; [0091] d. transmitting the determined internal flow rate IFR, and, optionally, the total volume V.sub.tot of fluid exchanged to an output device in operative association with the processor.

[0092] In one embodiment, the computer program takes the form of a software application (app) that can be installed and run on a smartphone.

[0093] The present disclosure also provides a non-transitory computer-readable medium comprising the computer program.

[0094] It will be understood that the features mentioned above and those described hereinafter can be used not only in the combination specified but also in other combinations or on their own, without departing from the scope of the present invention.

[0095] The method of the present disclosure will now be further described in the following examples and referring to the attached drawings.

[0096] FIG. 1 shows a schematic perspective view and sectional detail views of a capillary hemodialyzer 10 and fluid flows within the hemodialyzer 10. The hemodialyzer 10 comprises a bundle 20 of hollow fiber membranes 21. In the top left corner of FIG. 1, a detail of a cross-section of the bundle is shown with several hollow fiber membranes 21, each having a membrane wall 22. Blood flow and dialysate flow through the hemodialyzer 10 are indicated by arrows. Blood enters the hemodialyzer 10 through a blood inlet located on a header of the hemodialyzer 10 at a blood flow rate Q.sub.B,in, flows through the lumen of the hollow fiber membranes 21 of the bundle 20, and leaves the hemodialyzer 10 at a blood flow rate Q.sub.B,out through a blood outlet located on another header of the hemodialyzer 10. Dialysate enters the hemodialyzer 10 through a dialysate inlet positioned near one end of the hemodialyzer 10 at a dialysate flow rate Q.sub.D,in flows through the space outside the hollow fiber membranes 21 of the bundle 20, and leaves the hemodialyzer 10 at a dialysate flow rate Q.sub.D,out through a dialysate outlet positioned near the opposite end of the hemodialyzer 10. In the top right corner of FIG. 1, a detail of a longitudinal section of one of hollow fiber membranes 21 is shown. The effective length of the hollow fiber membrane 21 is L, the internal radius of the hollow fiber membrane 21 is d.sub.B/2, the thickness of the membrane wall 22 is ?.sub.M, the distance between the longitudinal axis of one hollow fiber membrane 21 and the longitudinal axis of an adjacent hollow fiber membrane 21 is 2*R.sub.k, with R.sub.k=R.sub.o+?.sub.?, or R.sub.k=d.sub.B/2+?.sub.N+?.sub.?, R.sub.o being half the outside diameter of the hollow fiber membrane 21, and ?.sub.? being half the distance between two adjacent hollow fiber membranes 21. Blood flows in the lumen of the hollow fiber membrane 21, dialysate flows on the outside of the hollow fiber membrane 21, and ultrafiltration flux J.sub.v permeates the membrane wall 22.

EXAMPLE 1

[0097] Internal filtration rates within a hemodialyzer (Polyflux? 210H, Gambro Dialysatoren GmbH, 72379 Hechingen, Germany) were determined according to one embodiment of the method of the present disclosure, and compared to internal flow rates determined experimentally (from D. Schneditz et al.: Internal filtration, filtration fraction, and blood flow resistance in high- and low-flux dialyzers, Clin. Hemorheol. Microcirc. 58 (2014) 455-469).

[0098] The following physical properties of the hemodialyzer were used for the determination: [0099] hollow fiber inner diameter d.sub.B=215 ?m [0100] Membrane wall thickness ?.sub.M=50 ?m [0101] Membrane porosity ?.sub.M=0.7 [0102] Number of fibers N=11,640 [0103] Effective length L=270 mm [0104] Ultrafiltration coefficient K.sub.UF=85 ml/(h*mm Hg) [0105] Half distance between adjacent fibers ?.sub.?=68.2 ?m [0106] Hemodialyzer housing inner diameter d.sub.H=48.7 mm

[0107] Values for blood viscosity of ?=5.2 mPas and dialysate viscosity of ?.sub.D=0.96 mPas were used.

[0108] Internal filtration rate IFR was determined for a dialysis flow rate Q.sub.D of 500 ml/min, and blood flow rates Q.sub.B of 200 ml/min, 300 ml/min, 400 ml/min, and 500 ml/min, respectively.

[0109] The values for the following constant parameters were obtained as described above. [0110] K=0.119 ?m.sup.2s/kg [0111] R.sub.1=1.19 [0112] R.sub.2=1.01 [0113] E.sub.1=?285 MPas [0114] E.sub.2=?182 MPas [0115] F.sub.2=?159 MPas [0116] G.sub.2=0.223 m

[0117] The following table shows IFR at Q.sub.D=500 ml/min and different blood flow rates Q.sub.B.

TABLE-US-00001 Q.sub.B [ml/min] 200 300 400 500 IFR [ml/min] 15.4 23.1 30.7 38.4

[0118] FIG. 2 shows a comparison of the internal flow rates determined according to the method of the present disclosure and experimentally determined internal flow rates taken from D. Schneditz et al.: Internal filtration, filtration fraction, and blood flow resistance in high- and low-flux dialyzers, Clin. Hemorheol. Microcirc. 58 (2014) 455-469.

EXAMPLE 2

[0119] Internal filtration rates within a hemodialyzer (Theranova? 400, Gambro Dialysatoren GmbH, 72379 Hechingen, Germany) were determined according to one embodiment of the method of the present disclosure, and compared to internal flow rates determined experimentally (from A. Lorenzin et al.: Quantification of Internal Filtration in Hollow Fiber Hemodialyzers with Medium Cut-off Membrane, Blood Purif. 46 (2018) 196-204).

[0120] The following physical properties of the hemodialyzer were used for the determination: [0121] hollow fiber inner diameter d.sub.B=180 ?m [0122] Membrane wall thickness ?.sub.M=35 ?m [0123] Membrane porosity ?.sub.M=0.5 [0124] Number of fibers N=13,000 [0125] Effective length L=236 mm [0126] Ultrafiltration coefficient K.sub.UF=48 ml/(h*mm Hg) [0127] half distance between adjacent fibers ?.sub.?=41.9 ?m [0128] Hemodialyzer housing inner diameter d.sub.H=38 mm

[0129] Values for blood viscosity of ?.sub.B=5.0 mPas and dialysate viscosity of ?.sub.D=0.96 mPas were used.

[0130] Internal filtration rate IFR was determined for a dialysis flow rate Q.sub.D of 500 ml/min, and blood flow rates Q.sub.B of 300 ml/min and 400 ml/min, respectively.

[0131] The values for the following constant parameters were obtained as described above. [0132] K=0.116 ?m.sup.2s/kg [0133] R.sub.1=1.24 [0134] R.sub.2=1.04 [0135] E.sub.1=?335 MPas [0136] E.sub.2=?237 MPas [0137] F.sub.2=?206 MPas [0138] G.sub.2=0.182 m

[0139] The following table shows IFR at Q.sub.D=500 ml/min and different blood flow rates Q.sub.B.

TABLE-US-00002 Q.sub.B [ml/min] 300 400 IFR [ml/min] 26.7 41.6

[0140] FIG. 3 shows a comparison of the internal flow rates determined according to the method of the present disclosure and experimentally determined internal flow rates taken from A. Lorenzin et al.: Quantification of Internal Filtration in Hollow Fiber Hemodialyzers with Medium Cutoff Membrane, Blood Purif. 46 (2018) 196-204.

List of Reference Signs

[0141] 10 hemodialyzer [0142] 20 bundle of hollow fiber membranes [0143] 21 hollow fiber membrane [0144] 22 membrane wall [0145] L length of hollow fiber membrane [0146] ?.sub.M thickness of membrane wall [0147] d.sub.B internal diameter of hollow fiber membrane [0148] R.sub.k radius of space occupied by hollow fiber membrane

DETERMINING INTERNAL FILTRATION RATE WITHIN A CAPILLARY HEMODIALYZER

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A61M1/1605

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A61M1/1613

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G16H20/40

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A61M1/1627

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Abstract

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