Hemofiltration system

Field of the Invention

0001The present invention is directed to a system of blood filtration, and more particularly supervisory control systems and an adaptive control systems for controlling the continuous filtration of fluid and/or soluble waste from the blood of a patient based on one or more monitored patient parameters and fluid flow rates.

General Background of the Invention

0002For various reasons, including illness, injury or surgery, patients may require replacement or supplementation of their natural renal function in order to remove excess fluid or fluids containing dissolved waste products from their blood. Several procedures known for this purpose are dialysis, hemodialysis, hemofiltration, hemodiafiltration and ultrafiltration; another related procedure is plasmapheresis. The specific procedure employed depends upon the needs of the particular patient. For example, dialysis is used to remove soluble waste and solvent from blood; hemofiltration is used to remove plasma water from blood; hemodiafiltration is used to remove both unwanted solute (soluble waste) and plasma water from blood; ultrafiltration is a species of hemofiltration; and plasmapheresis is used to remove blood plasma by means of a plasmapheresis filter. Because the replacement of renal function may affect nutrition, erythropoiesis, calcium-phosphorus balance and solvent and solute clearance from the patient, it is imperative that there be accurate control of the procedure utilized. The accurate control of the rate of removal of intravascular fluid volume is also important to maintain proper fluid balance in the patient and prevent hypotension.

0003Various systems have been proposed to monitor and control renal replacement procedures. For example, <patcit id="pcit0001" dnum="US4132644A"><text>U.S. Patent No. 4,132,644</text></patcit> discloses a dialysis system in which the weight of dialyzing liquid in a closed liquid container is indicated by a scale. After the dialyzing liquid flows through the dialyzer, the spent liquid is returned to the same container and the weight is again indicated. Since the container receives the original dialyzing liquid plus ultrafiltrate, the amount of ultrafiltrate removed from the patient is equal to the increase in total weight in the container. This system is not driven by a weight measuring device and does not offer precise control of the amount of liquids used in the procedure.

0004<patcit id="pcit0002" dnum="US4204957A"><text>U.S. Patent No. 4,204,957</text></patcit> discloses an artificial kidney system which utilizes weight measurement to control the supply of substitute fluid to a patient. In this system, the patient's blood is pumped through a filter and the filtrate from the blood is discharged to a measuring vessel associated with a weighing device. A second measuring vessel containing substitute fluid is associated with a second weighing device and is connected to the purified blood line. By means of a pump, the substitute fluid and the purified blood are pumped back to the patient. The first and second weighing devices are coupled to one another by a measuring system in such a way that a fixed proportion of substitute is supplied to the purified blood stream from the second measuring vessel depending an the weight of the filtrate received in the first measuring vessel. This system does not utilize circulating dialysate fluid in the blood filtration.

0005<patcit id="pcit0003" dnum="US4767399A"><text>U.S. Patent No. 4,767,399</text></patcit> discloses a system for performing continuous arteriovenous hemofiltration (CAVH). The disclosed system relies upon utilizing a volumetric pump to withdraw a desired amount of fluid from the patient's blood and return a selected amount of fluid volume to the patient.

0006<patcit id="pcit0004" dnum="US4923598A"><text>U.S. Patent No. 4,923,598</text></patcit> discloses an apparatus for hemodialysis and hemofiltration which comprises an extracorporeal blood circuit including a dialyzer and/or filter arrangement. The system determines fluid withdrawal per unit time and total amount of fluid withdrawn by utilizing flow sensors in conjunction with an evaluating unit located upstream and downstream of the dialyzer or filter arrangement in the blood circuit.

0007<patcit id="pcit0005" dnum="US4728433A"><text>U.S. Patent No. 4,728,433</text></patcit> discloses a system for regulating ultrafiltration by differential weighing. The system includes a differential weighing receptacle having an inlet chamber and an outlet chamber which allows a fixed amount of fresh dialysate, by weight, to flow through the hemodialyzer. This system operates in a sequence of weighing cycles during which the amount of ultrafiltrate removed from the blood may be calculated. Additionally, the ultrafiltration rate for each weighing cycle may be calculated. This system provides a mechanism for determining and regulating the amount of ultrafiltrate removed from the blood while delivering dialysate to the patient in alternating fill and drain cycles of the inlet and outlet chambers of the differential weighing receptacle.

0008For certain patients, renal replacement procedures may extend over hours or even days. In general, current systems for monitoring and controlling renal replacement procedures lack the flexibility and accuracy required to perform such procedures on neonates. This is mainly due to the absence of a satisfactory automatic control of the pumps employed. Because of the patient risk involved in using such equipment, health care personnel measure the fluid removed from the patient on an hourly basis. The continuing need to monitor the fluid removed leads to a significant increase in nursing care and thus increases the cost of the therapy. Therefore, there is a need to improve the level of autonomy for the systems such that the procedure is less time consuming for medical personnel, and consequently less costly. However, the enhanced autonomy must not come at the expense of patient safety.

0009Some conventional renal function replacement/supplementation systems possess an elementary level of supervisory control that simply detects the presence of a fault condition, sounds an alarm, and de-energizes the system pumps to halt the procedure. If the hemofilter clots while the pumps are de-energized, the tubing and hemofilter must be replaced with a concomitant increase in the chance of infection for the patient. Furthermore, the hemofiltration procedure is delayed with a possibly negative impact upon the patient's health.

0010Due to the time-varying nature of the renal function replacement/supplementation system, the dynamics of fluid pumping may change over time. For example, the characteristics of system components such as tubing, filter, and connectors may vary slowly over time due to aging or as occlusion of the path for fluid flow. As the flow path becomes constricted, the pumping rate of the pump must be altered to compensate for the increased flow resistance. Furthermore, the replacement of a tubing set requires a rapid change adjustment of the pumping rates that may be difficult to initially establish as a relatively constant value due to short-term transient variations. Current systems for monitoring and controlling renal replacement procedures lack the ability to autonomously correct these time-dependent flow rate variations with high accuracy, rapid response, and minimal overshoot or transient variations following correction.

0011The need exists for a multipurpose renal function replacement/supplementation system which is accurate, reliable, capable of continuous, long-term operation, and which can be used effectively on adult, pediatric and neonatal patients. Further, the need exists for a feedback control system for controlling the multipurpose renal function replacement/supplementation system that accurately regulates the transfer of fluid and monitors the overall behavior of the system to improve patient care and provide greater autonomy.

0012<patcit id="pcit0006" dnum="WO9806875A"><text>WO98/06875</text></patcit> discloses a multipurpose hemofiltration system for the removal of fluid and/or soluble waste from the blood of a patient. The system and method are equally applicable to adult, paediatric and neonatal patients. The system continuously monitors the weight of infusate in a first reservoir and drained fluid in a second reservoir and compares those weights to corresponding predetermined computed weights. When necessary, the pumping rates of the infusate, drained fluid and blood are adjusted in order to achieve a preselected amount of fluid removal from the patient's blood in a preselected time period. Application of this system and method provide repeatable and highly precise results.

0013<nplcit id="ncit0001" npl-type="b"><text>Nordio M et al: "Projection and Simulation Results of an Adaptive Fuzzy Control Molule for Blood Pressure and Blook Volume durig Hemodialysis" ASAIO Journal, US, J.. Lippincott Co. Hagerstown, MD, vol. 40, no. 3, 1 July 1994 (1994-07-01), pages 686-690</text></nplcit>, XP000498259 ISSN: 1058-2916 describes use of a fuzzy logic method to mathematically translate empirical measures to correct UF rates and sodium dialysate concentration when patient parameters such as blood volume and blood pressure are not within certain limits during hemodialysis.

0014The present invention is direct to a control system for controlling the pumping rate of at least one pump for pumping fluid in a medical system, said control system comprising a sensor for measuring the flow rate of liquid in a medical system generated by at least one pump, the flow rate sensor providing flow rate data signals correlated to the fluid flow rate, and a controller operably connectable to the at least one pump in a medical system and operably connected to the flow rate sensor, the controller receiving the flow rate data signals and generating an output signal for adjusting the pumping rate of fluid generated by the at least one pump, the controller providing the output signal for the at least one pump on a periodic ongoing basis, characterised in that the controller is an adaptive controller, the controller using an adaptive law to generate a set of controller parameters for correcting time-dependent deviations of the flow rate from a predetermined flow rate, and using a control law to generate the output signal from the set of controller parameters for adjusting the pumping rate of fluid generated by the at least one pump to achieve the predetermined flow rate.

0015As used herein the term "hemofiltration" is to be broadly construed to include hemodialysis, hemofiltration, hemodiafiltration, ultrafiltration and plasmapheresis processes. As used herein, the term "infusate" is defined to include dialysate fluid or any other replacement fluids which may be supplied to the patient as a part of the hemofiltration procedures.

0016In a preferred embodiment, the system of the present invention includes a hemofilter, a blood pump for pumping blood from a patient through the hemofilter and back to the patient, and suitable tubing for carrying the pumped blood to and from the patent. The system further includes a first reservoir for maintaining a supply of infusate, a first weighing means for continuously monitoring the weight of the infusate and generating weight data signals correlated to the monitored weight, and a first pump for pumping the infusate from the first reservoir to the hemofilter or appropriate blood tubing access port. A second reservoir receives drained fluid (e.g., spent infusate or ultrafiltrate, including the fluids and solutes removed from the blood) from the hemofilter, and a second weighing means monitors the weight of the drained fluid and generates weight data signals correlated to the monitored weight. A second pump pumps the drained fluid from the hemofilter to the second reservoir. The system also includes a computerized controller operably connected to the blood pump, the infusate pump, the drain pump and the first and second weighing means.

0017The computer controller is, by initial selection of the operator, interfaced with one or more of the various monitoring systems that are operably connected to the patient. These monitoring systems, which are well known in the art, generate and output data signals corresponding to the monitored patient parameters, and the computer controller receives such data signals. During the hemofiltration operation, the interfaced parameters are constantly monitored; however, the controller only responds to specific parameter data that corresponds to the patient parameters selected by the operator. The patient parameters which may be monitored and interfaced with the computer controller include the following: arterial pressure, central venous pressure, pulmonary arterial pressure, mean arterial pressure, capillary wedge pressure, systemic vascular resistance, cardiac output, O₂ and CO₂ content and saturation (expired, venous or arterial), blood pressure, heart rate, patient weight, external infusion rates, and hematocrit. Numerous of these parameters may be monitored and corresponding output data signals generated in known manner utilizing an indwelling intravenous or intra-arterial catheter. The remaining parameters are monitored and data signals are generated by means well known in the art. The operator will select one or more of the above parameters to interface with the controller which will then periodically, but on an ongoing basis during treatment, interrogate at predetermined intervals the parameter data signals that are continuously generated by the interfaced monitoring system(s). The controller then evaluates the parameter data and in response thereto, when necessary, the controller generates control signals which automatically adjust the pumping rates of the infusate, drained fluid and blood pumps so as to achieve a preselected amount of fluid removal from the patient's blood for patient benefit and safety.

0018It will be appreciated that the system of the present invention may utilize a combination of monitoring and responding to the infusate and drained fluid weight data signals along with one or more of the other patient parameters interfaced to the controller.

0019By way of specific examples, in connection with monitoring the patient's weight, the computer controller may be interfaced with a bed scale which provides continuous values for the patient's weight. In response to the overall patient weight data signals, the computer controller may control the infusate and/or drained fluid pumps to achieve a predesigned protocol for decreasing or increasing the patient's weight over time. The increase or decrease in patient's weight can be accomplished in either a linear or non-linear manner with respect to time by appropriate pump control. Similarly, the computer may be interfaced with a continuous read-out device of the patient's O₂ saturation and the controller will receive, evaluate and respond to the O₂ saturation data by controlling the infusate, drained fluid and blood pumping rates accordingly to optimize patient oxygenation.

0020In connection with all of the above-described monitored parameters, the computer controller will receive data signals corresponding and relating to each particular selected parameter from an appropriate signal generating device or source operably connected to the patient. The controller will then, after periodic interrogation, compare the interrogated values with predetermined desired values and will automatically make the appropriate, predetermined changes in the infusate, drained fluid and blood pumping rates in response to the monitored signals. Furthermore, more than one of the above-referenced parameters can be continuously monitored simultaneously and the computer may be programmed with a hierarchy to consider one or more specific parameters rather than others and will respond with the appropriate and desired adjustments in infusate, drained fluid and blood pumping rates based on those selected parameters.

0021The computer controller is designed and programmed to adjust the pumping rates (pump speed) of the infusate, drained fluid and blood pumps so as to provide a linear response or a non-linear (curvilinear) response to the observed changes in the selected monitored parameters. In this regard, "linear" is defined to mean a fixed, non-exponential change, and "non-linear" or "curvilinear" means anything other than linear. The selection of linear versus non-linear response profile is made by the operator of the system depending on the needs of the patient. For example, in certain situations it may be desirable to have an initially fast fluid removal rate that decreases over time. In that case a curvilinear or exponential response would be utilized. In other circumstances, consistent or constant fluid removal over time is desired, and so a linear response profile is selected. It is further contemplated that at the election of the operator the computer controller may combine linear and curvilinear response signals so as to tailor the pump rates to achieve a desired response profile. For example, a non-linear initial response period for fast initial fluid removal, followed by a linear response period for ongoing fluid removal at a consistent rate.

0022In the combination embodiment, the computer controller incorporates the adaptive control system for controlling the pumping rate of at least one of the system infusate, drained fluid and blood pumps. The adaptive controller is operably connected to each pump to be adaptively controlled and to its associated flow rate sensor. The adaptive control system receives flow rate data signals correlated to the fluid flow rate from a sensor, such as a flowmeter or weight scale, measuring the flow rate of fluid generated by the pump being controlled. The adaptive controller calculates a controller parameter vector using an adaptive law to generate a set of controller parameters for correcting time-dependent deviations of the flow rate from a predetermined flow rate. Based on the controller parameters, the adaptive controller then uses a control law to generate an output signal for adjusting the pumping rate of fluid generated by the pump to achieve the predetermined flow rate. Finally, the controller provides the output signal to the pump on a periodic ongoing basis for adjusting the fluid flow rate. In one aspect, the adaptive controller may use parameter projections to limit the range of the output signal for maintaining the pump in a linear regime of pump operation.

0023A method is disclosed in which, blood from a patient is pumped through a hemofilter and a supply of infusate, which is maintained in a first reservoir, is pumped from the first reservoir through the hemofilter, countercurrent to the blood. The weight of infusate in the first reservoir is continuously monitored and data signals correlated to that weight are generated. Drained fluid (e.g., spent infusate) is pumped from the hemofilter and is received in a second reservoir. The weight of the drained fluid in the second reservoir is continuously monitored and weight data signals correlated thereto are generated. The signals correlated to the weight of infusate and drained fluid are interrogated at regular intervals (for example every minute) by a system controller and are compared to corresponding predetermined computed weights in the memory of the controller. The controller determines the amount and rate of fluid withdrawal from the patient's blood. If those values differ from preselected, preprogrammed desired values, the controller generates control signals which independently adjust the pumping rates of the infusate and drained fluid pumps so as to achieve the desired amount of fluid removal. The control signals may also control the blood pumping rate.

0024In an alternative method, independent of or in addition to the infusate and drained fluid weight monitoring and pump control, the computer controller may be interfaced with one or more of the previously discussed monitoring systems. In this method, the controller will receive, evaluate and respond to the selected patient parameter data by generating appropriate, responsive control signals by which the infusate, drained fluid and blood pumping rates are controlled to achieve the desired amount of fluid removal. This may be accomplished in combination with or independent of the infusate and drained fluid weight monitoring.

0025In an alternative mode of operation, flow rate data signals for the fluid flow generated by a pump in a hemofiltration system and patient parameter data signals, such as heart rate and blood pressure, are supplied to a supervisory controller. Flow rate data signals are derived from the rate change in weight of either infusate or drained fluid or from the blood flow rate. The signals are analyzed utilizing fuzzy logic based on at least one predetermined supervisory rule and an output signal is provided to the appropriate pump to adjust, as necessary on a periodic ongoing basis, the flow rate of fluid generated by that pump.

0026In yet another alternative mode of operation, flow rate data signals for the fluid flow generated by a pump in a hemofiltration system are supplied to an adaptive controller. Flow rate data signals are derived from the rate change in weight of either infusate or drained fluid or from the blood flow rate. A set of controller parameters is generated from the flow rate signals for use in correcting time-dependent deviations in flow rate from a predetermined flow rate. The signals and parameters are analyzed using a control law to generate an output signal. The output signal is provided to the adaptively controlled pump on a periodic ongoing basis.

0027The advantages of the system of the present invention are achieved at least in part due to the adaptive system controller which implements closed-loop, feedback control that precisely and accurately adjusts and controls the pumping rates. Further features and advantages of the system and apparatus of the present invention will become apparent with reference to the Figure and the detailed description which follows.

Brief Description of the Drawings

0028<ul id="ul0001" list-style="none" compact="compact"><li><figref idref="f0001">Fig. 1</figref> is a diagrammatic representation of one embodiment of the system of the present invention; a variation is shown in phantom.</li><li><figref idref="f0002">Fig. 2</figref> is a diagrammatic representation of an alternative embodiment of the system of the present invention.</li><li><figref idref="f0003">Fig.3</figref> diagrammatically illustrates the hierarchical control architecture for a hemofiltration system.</li><li><figref idref="f0004">Fig. 4</figref> diagrammatically illustrates the fuzzy logic process performed by the supervisory controller of <figref idref="f0003">Fig. 3</figref>.</li><li><figref idref="f0004">Fig. 5</figref> represents the supervisory control architecture implemented in the supervisory controller.</li><li><figref idref="f0003">Fig. 6A</figref> is a set of membership functions for blood pressure data signals that are input into the fuzzy logic control system.</li><li><figref idref="f0003">Fig. 6B</figref> is a set of input membership functions for heart rate data signals that are input into the fuzzy logic control system.</li><li><figref idref="f0003">Fig. 6C</figref> is a set of output membership functions for signals representing changes in ultrafiltration rate that are output from the fuzzy logic control system.</li><li><figref idref="f0005">Fig. 7A</figref> is a graphical representation of the tracking error of a blood pump for an ultrafiltration simulation.</li><li><figref idref="f0005">Fig. 7B</figref> is a graphical representation of the control voltage for an ultrafiltration simulation.</li><li><figref idref="f0005">Fig. 7C</figref> is a graphical representation of the controller parameters for an ultrafiltration simulation.</li><li><figref idref="f0006">Fig. 8A</figref> is a graphical representation of the tracking error of a blood pump for an ultrafiltration simulation.</li><li><figref idref="f0006">Fig. 8B</figref> is a graphical representation of the tracking error of a drain pump for an ultrafiltration simulation.</li><li><figref idref="f0006">Fig. 8C</figref> is a graphical representation of the tracking error of a first replacement pump for an ultrafiltration simulation.</li><li><figref idref="f0006">Fig. 8D</figref> is a graphical representation of the tracking error of a second replacement pump for an ultrafiltration simulation.</li><li><figref idref="f0007">Fig. 9A</figref> is a graphical representation of the tracking error of a drain pump for an ultrafiltration simulation.</li><li><figref idref="f0007">Fig. 9B</figref> is a graphical representation of the control voltage for an ultrafiltration simulation.</li><li><figref idref="f0007">Fig. 9C</figref> is a graphical representation of the controller parameters for an ultrafiltration simulation.</li><li><figref idref="f0008">Fig. 10A</figref> is a graphical representation of the heart rate for an ultrafiltration simulation.</li><li><figref idref="f0008">Fig. 10B</figref> is a graphical representation of the blood pressure for an ultrafiltration simulation.</li><li><figref idref="f0008">Fig. 10C</figref> is a graphical representation of the desired drain flow rate calculated by fuzzy system I for an ultrafiltration simulation.</li><li><figref idref="f0009">Fig. 11A</figref> is a graphical representation of the heart rate for an ultrafiltration simulation.</li><li><figref idref="f0009">Fig. 11B</figref> is a graphical representation of the blood pressure for an ultrafiltration simulation.</li><li><figref idref="f0009">Fig. 11C</figref> is a graphical representation of the desired drain flow rate calculated by fuzzy system II for an ultrafiltration simulation.</li><li><figref idref="f0010">Fig. 12A</figref> is a graphical representation of the heart rate for an ultrafiltration simulation.</li><li><figref idref="f0010">Fig. 12B</figref> is a graphical representation of the blood pressure for an ultrafiltration simulation.</li><li><figref idref="f0010">Fig. 12C</figref> is a graphical representation of the desired drain flow rate calculated by fuzzy system III for an ultrafiltration simulation.</li><li><figref idref="f0011">Fig. 13A</figref> is a graphical representation of the heart rate for an ultrafiltration simulation.</li><li><figref idref="f0011">Fig. 13B</figref> is a graphical representation of the blood pressure for an ultrafiltration simulation.</li><li><figref idref="f0011">Fig. 13C</figref> is a graphical representation of the desired drain flow rate calculated by fuzzy system IV for an ultrafiltration simulation.</li><li><figref idref="f0012">Fig. 14A</figref> is a graphical representation of the heart rate for an ultrafiltration simulation.</li><li><figref idref="f0012">Fig. 14B</figref> is a graphical representation of the blood pressure for an ultrafiltration simulation.</li><li><figref idref="f0012">Fig. 14C</figref> is a graphical representation of the desired drain flow rate calculated by FSIII for an ultrafiltration simulation.</li><li><figref idref="f0012">Fig. 14D</figref> is a graphical representation of the blood pump flow rate for an ultrafiltration simulation.</li></ul>

Detailed Description of the Invention

0029<figref idref="f0001">Fig. 1</figref> shows a diagrammatic representation of a preferred embodiment of the system of the present invention. The portion of <figref idref="f0001">Fig. 1</figref> shown in phantom represents an alternative embodiment of the present invention which will be described hereinbelow. Hemofiltration system 10 is operated and controlled by a suitable controller designated generally as 12. Controller 12 may be a programmable computer having a display 13 and is operably connected to various components of hemofiltration system 10, as will be described in greater detail hereinafter.

0030In operation, blood is pumped from a patient (not shown), which may be an adult, pediatric or neonatal patient, through a suitable catheter (not shown) and input tubing 14 by means of a blood pump 16. Blood pump 16, which is preferably of the roller type, is operably connected to controller 12 by line 18. One suitable blood pump is the RS-7800 Minipump manufactured by Renal Systems, Minneapolis, MN. Input tubing 14 through which the patient's blood is pumped preferably includes a pressure transducer 20 upstream of pump 16. Pressure transducer 20 is operably connected to controller 12 via line 21. Means are included downstream of blood pump 16 for accessing input tubing 14 to enable the injection or infusion of desired fluids, including medications and anticlotting compounds such as heparin, into the patient's blood. The injection or infusion of such fluids to the blood may be accomplished in any suitable manner; <figref idref="f0001">Fig. 1</figref> shows diagrammatically a syringe and tube arrangement 22, but it will be appreciated that other means could be employed for the same purpose.

0031The patient's blood is pumped through hemofilter 24 by blood pump 16. Filters of the type suitable for use in the system of the present invention are readily available; one example of a suitable hemofilter is the Diafilter manufactured by AMICON, Denvers, MA. Where the present system is used to perform plasmapheresis, a suitable plasmapheresis filter such as the Plasmaflo manufactured by Parker Hannifin, Irvine, CA can be employed.

0032Input tubing 14 includes a second pressure transducer 26 slightly upstream of hemofilter 24. Pressure transducer 26 is operably connected to controller 12 via line 28. The patient's blood exits hemofilter 24, passes through output tubing 30 and is returned to the patient via any suitable means such as a venous catheter arrangement (not shown). Output tubing 30 preferably includes a suitable blood flow detector 31 which verifies that there is blood flow in the system and an air bubble/foam control device such as air bubble clamp 32 to prevent the passage of air bubbles to the patient. Blood flow detector 31 and air bubble clamp 32 may be operably connected (not shown) to controller 12 or directly to the pumps to interlock all pumps upon detection of any air bubbles in the blood or upon the cessation of blood flow. A suitable foam-bubble detector is the RS-3220A manufactured by Renal Systems. Output tubing 30 also preferably includes a pressure transducer 34 immediately downstream of hemofilter 24. Pressure transducer 34 is operably connected to controller 12 via line 36.

0033A first reservoir 50 maintains a supply of suitable dialysate or other fluid, referred to herein generally as infusate 52. The infusate-containing reservoir 50 is supported by a weighing device such as electronic scale 54 which is operably connected to controller 12 via line 56. Infusate 52 is pumped from reservoir 50 via tubing 58 by means of infusate pump 60, which is preferably of the roller variety. A suitable pump for this purpose is a 31/2" Roller Pump manufactured by PEMCO, Cleveland, OH. Infusate pump 60 is operably connected to controller 12 via line 62 and pumps infusate 52 through hemofilter 24 countercurrent to the blood pumped therethrough. In accordance with known principles, infusate 52 may extract certain components (fluids and/or soluble waste) from the blood passing through hemofilter 24. The fluid drained from hemofilter 24 includes spent infusate and the components removed from the blood, which are referred to herein as drained fluid 76. In an alternative embodiment wherein system 10 is used as a fluid or plasma replacement system, e.g., to perform plasmapheresis, the infusate (which may be blood plasma) from reservoir 50 is pumped via tubing 59 (shown in phantom) to blood output tubing 30 or via tubing 59a (also shown in phantom) to input tubing 14, thereby replacing the fluid volume removed from the blood. In this embodiment, the drained fluid 76 from hemofilter or plasmapheresis filter 24 does not include any spent infusate since the infusate is pumped directly to blood output tubing 30 or input tubing 14 and supplied to the patient.

0034The drained fluid 76 is pumped from hemofilter 24 through outlet tubing 64 by means of drain pump 66, which is preferably a roller-type pump, and may be the same as infusate pump 60. Drain pump 66 is operably connected to controller 12 via line 68. Output tubing 64 preferably includes a pressure transducer 70 downstream of hemofilter 24, but upstream of drain pump 66. Pressure transducer 70 is operably connected to controller 12 via line 72. Output tubing 64 also preferably includes a blood leak detector 67 which detects the presence of blood in the drained fluid 76, as may occur if hemofilter 24 ruptures. A suitable blood leak detector is sold by COBE, Lakewood, Co as model 500247000. Blood leak detector 67 may be operably connected (not shown) to controller 12 or directly to the pumps to interlock all pumps upon the detection of blood in the drained fluid. Drained fluid 76 pumped from hemofilter 24 is pumped into a second reservoir 74 which collects the drained fluid. Second reservoir 74 is supported by a weighing device such as electronic scale 78, which is operably connected to controller 12 via line 80.

0035Scales 54 and 78, which may be model 140 CP sold by SETRA of Acton, MA continuously generate weight data signals correlated to the weight of infusate and drained fluid contained in reservoirs 50 and 74, respectively. Those weight data signals are continuously fed to controller 12, to which the scales are linked through an interface having a data protocol, such as an RS-232 interface. It will be appreciated that a single scale could be utilized in place of the two scales whereby the weight differential between reservoir 50 and 74 is monitored and a corresponding data signal is generated. Pressure transducers 20, 26, 34 and 70 all continuously measure the pressure at their respective locations in hemofiltration system 10 and generate pressure data signals correlated thereto which are fed to controller 12. A suitable type of pressure transducer is model number 042-904-10 sold by COBE of Lakewood, CO. When certain predetermined alarm or danger conditions exist in the system 10, as represented by the pressure data signals, the controller will either adjust the infusate, drained fluid, or blood pumping rate, or a combination thereof, or will shut the system down entirely.

0036Controller 12 is preferably a programmable computer that is capable of sending and receiving signals from auxiliary equipment including pressure transducers 20, 26, 34 and 70, first and second scales 54 and 78, respectively, and blood pump 16, infusate pump 60, and drain pump 66. In operation, controller 12 interrogates, at regular intervals, the weight data signals generated by first and second scales 54 and 78. From these signals, controller 12 determines the weight of infusate and drained fluid in the first and second reservoirs 50 and 74 at that point in time, and compares those weights to corresponding predetermined computed weights which have been programmed into and are stored by controller 12. By monitoring the weight of infusate in reservoir 50 and the weight of drained fluid in reservoir 74 at regular intervals, the rate of change of those weights and the rate of hemofiltration can be calculated by the computer portion of controller 12. When the weights deviate from the predetermined computed weights and/or the rate of hemofiltration deviates from a preselected, preprogrammed desired rate, controller 12 generates control signals which control or adjust the rates at which blood pump 16, infusate pump 60 and drain pump 66 are operated, as necessary, to adjust the hemofiltration rate to the desired rate, or to stop the pumps when preselected limits have been reached. This is accomplished in a continuous manner; i.e., continuous weight data signal generation, periodic interrogation of those weight data signals and computation of the required weight and/or rate information, comparison to predetermined computed values and automatic adjustment of the pumping rates of the pumps, as necessary, to achieve the desired amount and/or rate of hemofiltration.

0037Controller 12 is programmed so that infusate pump 60 and drain pump 66 are operated only when blood pump 16 is being operated. In the case when ultrafiltration is being performed, the pumping rate of drain pump 66 must equal the pumping rate of infusate pump 60 plus the desired ultrafiltration rate.

0038Controller 12 continuously receives pressure data signals from pressure transducers 20, 26, 34 and 70 and is programmed to generate alarm signals when high and low pressure limits are exceeded at any of the monitored locations. Furthermore, an alarm signal is generated when the pressure differential across hemofilter 24 exceeds a predetermined upper limit, as monitored specifically by pressure transducers 26, 34 and 70. Additionally, controller 12 may stop the pumps when preselected pressure limits (high or low) are exceeded, as for example may occur if the system tubing becomes occluded or ruptures or if pump occlusion occurs. Finally, controller 12 may signal when the infusate level in reservoir 50 reaches a predetermined lower limit and when the drained fluid level in reservoir 76 reaches a predetermined upper limit. Hemofiltration system 10 may also include suitable blood warmer and infusate warmer devices (not shown) to adjust and/or maintain the blood and infusate temperatures at desired levels, Such devices may also generate alarm signals when the fluid temperatures are outside of preselected limits.

0039Display 13 offers updated display of measured and computed parameters such as pressures, pressure differentials, temperatures, flow rates and amounts of infusate, drain and ultrafiltration, and alarm conditions. Controller 12 generates both visual and audible alarms and all the pumps are interlocked to prevent operation thereof under alarm conditions. Users have the option of disabling or unabling the alarms (the audible part of the alarm and its interlock with the pumps) to perform a procedure under close supervision. A printer (not shown) is operably connected (not shown) to controller 12 to generate a hard copy of procedural data currently displayed or stored at regular intervals, at the completion of a procedure or at any desired time.

0040Hemofiltration system 10 can be operated in one of two modes: 1) a manual mode wherein the pumping rates of blood pump 16, infusate pump 60 and drain pump 66 are provided by controller 12 when fixed voltages are applied; and 2) an automatic mode wherein the pumps are controlled by controller 12 when the desired hemofiltration amount or rate has been programmed into the controller. The automatic mode allows the system to be paused and later continued without losing previously measured and computed data.

0041<figref idref="f0002">Fig. 2</figref> shows a diagrammatic representation of several alternative embodiments of the hemofiltration system 10 of the present invention. Because of the commonality of many of the system components in <figref idref="f0002">Fig. 2</figref> vis-a-vis the system depicted in <figref idref="f0001">Fig. 1</figref>, like reference numerals are intended to indicate like components. Furthermore, the system components in <figref idref="f0002">Figs. 2</figref> operate in the same manner as the corresponding system components shown in <figref idref="f0001">Fig. 1</figref> and described hereinabove. Input tubing 14 further includes a flowmeter or flow probe 27 slightly upstream of hemofilter 24. The flow probe 27 is operably connected to controller 12 via line 29. A suitable flow probe 27 is an ultrasonic flow probe manufactured by Transonic Systems, Inc. Other suitable types of flowmeters include a bearingless rotary flowmeter, a Doppler flowmeter, and a differential electromagnetic flowmeter.

0042The hemofiltration system of <figref idref="f0002">Fig. 2</figref> further includes interfaces between controller 12 and monitoring systems which generate parameter data signals corresponding to selected patient parameters such as blood gas 100, hematocrit 110, patient heart rate 120, patient blood pressure 130 and numerous other patient parameters (designated generally as 140), which other parameters may be one or more of the following: arterial pressure, central venous pressure, pulmonary arterial pressure, mean arterial pressure, capillary wedge pressure, systemic vascular resistance, cardiac output, end tidal O₂ and CO₂, core and peripheral body temperature, and patient weight. While the blood gas sensor 100 and hematocrit sensor 110 are shown as being connected to the input tubing 14, these parameters can also be monitored by means associated directly with the patient rather than via tubing 14. In fact, whereas venous O₂ saturation could be measured as indicated, arterial O₂ saturation would require the monitor to be located elsewhere. The overall patient weight parameter can be monitored utilizing a standard patient bed scale (not shown) as is well known in the art.

0043During the hemofiltration procedure, one or more of the various patient parameters will be monitored continuously and the controller will, at the selection of the operator, be responsive to selected parameter data supplied to the controller. The parameter data may be evaluated and responded to by the controller independent of the infusate and drained fluid weight data signals; i.e., the system may operate and respond based on one or more of the selected parameters and not the weight data signals; or the system may respond to a combination of the weight data signals and one or more selected specific parameters.

0044One or more independent patient infusion pumps 150 may be interfaced with computer controller 12 to supply data signals correlated to the infusion to the patient of intravenous fluids, medications, parenteral nutrition and/or blood products. The controller 12 may evaluate this data and make modifications to the infusate, drained fluid and blood pumping rates so as to compensate for the extraneous fluid being delivered to the patient by means of the infusion pumps. In this regard, the overall fluid balance in the patient can be managed concurrent with the hemofiltration procedure.

0045In an alternative embodiment wherein system 10 is used to perform an ultrafiltration procedure or hemodialysis procedure, the infusate (which may be one or more replacement fluids such as a calcium replacement fluid or a bicarbonate replacement fluid) from reservoir 50 is pumped via tubing 59 (shown in phantom) to blood outlet tubing 30 or via tubing 59a (also shown in phantom) to input tubing 14, thereby offsetting substances and fluid volume removed from the blood. In this embodiment, the drained fluid 76 from hemofilter 24 does not include any spent infusate since the infusate is pumped directly to blood output tubing 30 and supplied to the patient. In yet another alternative embodiment, a distinct replacement fluid may be provided by a system having more than one infusate pump 60. For example, infusate pump 60 may be a first infusate pump for delivering a first replacement fluid to blood outlet tubing 30 via tubing 59 and the system 10 may further include a second infusate pump (not shown) for delivering a second replacement fluid to blood outlet tubing 30 via a length of tubing (not shown but similar to tubing 59).

0046<figref idref="f0003">Fig. 3</figref> represents a hierarchal control architecture that may be implemented by the computer controller 12 of <figref idref="f0002">Fig. 2</figref> for controlling the pumping rates in the hemofiltration system 10 to perform an ultrafiltration or hemodialysis procedure, referred to hereinafter collectively as an ultrafiltration procedure. Because of the commonality of many of the system components in <figref idref="f0003">Fig. 3</figref>, vis-a-vis the system depicted in <figref idref="f0001">Figs. 1</figref> and <figref idref="f0002">2</figref>, like reference numerals are intended to indicate like components. Furthermore, the system components in <figref idref="f0003">Fig. 3</figref> operate in the same manner as the corresponding system components shown in <figref idref="f0001">Figs. 1</figref> and <figref idref="f0002">2</figref> and described hereinabove. The heirarchal control architecture disclosed herein is further described in "Intelligent Contol of Continuous Venovenous Hemofiltration, Efrain O. Morales, Master's Thesis, University of Cincinnati, Department of Electrical &amp; Computer Engineering and Computer Science, and in "Hierarchical Adaptive and Supervisory Control of Continuous Venovenous Hemofiltration," Efrain O. Morales, Marios M. Polycarpou, Nat Hemasilpin, and John. J. Bissler, submitted to IEEE Transactions on Control Systems Technology, to be published, both of which are hereby incorporated by reference in their entirety.

0047Referring to <figref idref="f0003">Fig. 3</figref>, the supervisory controller 160 controls a blood pump 16, a drain pump 66, and a pair of infusate pumps 60, namely a bicarbonate replacement pump 60a and a calcium replacement pump 60b. Pumps 60a, 60b provide replacement fluids to replace fluid volume removed from the patient during the ultrafiltration procedure. The actual weight ω_rep1(n), ω_rep2 (n) of each replacement fluid supplied to the patient is respectively monitored by an electronic scale 54a, 54b (where each scale is similar to scale 54 shown in <figref idref="f0002">Fig. 2</figref>) with a frequency of a sample period n. In a typical ultrafiltration procedure, the sample period is on the order of one second. The actual weight ω_dra(n) of the drained fluid is monitored by an electronic scale 78. The ultrafiltration rate is calculated as the difference between the rate change in drained fluid weight and the rate change in the replacement fluid weight. The actual flow q_blo(n) from blood pump 16 is indicated by a flow probe 27.

0048Blood pump 16 is controlled by an adaptive pump controller 162, implemented in the controller 12, which receives a desired fluid flow rate <maths id="math0001"><math display="inline"><msubsup><mi mathvariant="normal">q</mi><mi>blo</mi><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced></math><img file="EP1514562B1_D0001.tif" /></maths> calculated by the supervisory controller 160 as a reference command input. The pump controller 162 is operably connected to the blood pump 16 via line 18 for transmitting a voltage u_blo(n) which corresponds to the desired pumping rate and which is proportional to <maths id="math0002"><math display="inline"><msubsup><mi mathvariant="normal">q</mi><mi>blo</mi><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced><mn mathvariant="normal">.</mn></math><img file="EP1514562B1_D0002.tif" /></maths> The actual flow q_blo(n) measure by the flow probe 27 is provided as a feedback signal via line 29 to the supervisory controller 160 and to the pump controller 162. The pump controller 162 further provides a controller parameter vector θ_blo, indicative of the tracking performance, to the supervisory controller 160.

0049Drain pump 66 is controlled by an adaptive pump controller 170, implemented in the controller 12, which receives a desired weight signal <maths id="math0003"><math display="inline"><msubsup><mi mathvariant="normal">ω</mi><mi>dra</mi><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced></math><img file="EP1514562B1_D0003.tif" /></maths> calculated by the supervisory controller 160 as a reference command input. The pump controller 170 is operably connected to the drain pump 66 via line 68 for transmitting a voltage u_dra(n) which corresponds to the desired pumping rate and is proportional to the rate change of <maths id="math0004"><math display="inline"><msubsup><mi mathvariant="normal">ω</mi><mi>dra</mi><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced></math><img file="EP1514562B1_D0004.tif" /></maths> The actual weight ω_dra(n) measured by the scale 78 is provided as a feedback signal via line 80 to the supervisory controller 160 and to the pump controller 170. The pump controller 170 further provides a controller parameter vector θ_dra, indicative of the tracking performance, to the supervisory controller 160.

0050Bicarbonate replacement pump 60a and calcium replacement pump 60b are controlled by a respective adaptive pump controller 180a, 180b, both implemented in the controller 12, which receives a desired weight signal <maths id="math0005"><math display="inline"><msubsup><mi mathvariant="normal">ω</mi><mi>dra</mi><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced></math><img file="EP1514562B1_D0005.tif" /></maths><maths id="math0006"><math display="inline"><msubsup><mi mathvariant="normal">ω</mi><mrow><mi>rep</mi><mo>⁢</mo><mn>2</mn></mrow><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced></math><img file="EP1514562B1_D0006.tif" /></maths> calculated by the supervisory controller 160 as a reference command input. The pump controller 162 is operably connected via a respective line 62a, 62b (similar to line 62 shown in <figref idref="f0002">Fig. 2</figref>) to the respective pump 60a, 60b for transmitting a respective voltage u_rep1(n), u_rep2(n) which corresponds to the desired pumping rate and is proportional to the rate change of <maths id="math0007"><math display="inline"><msubsup><mi mathvariant="normal">ω</mi><mrow><mi>rep</mi><mo>⁢</mo><mn mathvariant="normal">1</mn></mrow><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced><mo>,</mo></math><img file="EP1514562B1_D0007.tif" /></maths><maths id="math0008"><math display="inline"><msubsup><mi mathvariant="normal">ω</mi><mrow><mi>rep</mi><mo>⁢</mo><mn>2</mn></mrow><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced><mo>,</mo></math><img file="EP1514562B1_D0008.tif" /></maths> respectively. The actual weight ω_rep1(n), ω_rep2(n) measured by the respective scale 54a, 54b is provided as a feedback signal via line 56a, 56b, respectively, to the supervisory controller 160 and to the respective pump controller 180a, 180b. Each pump controller 180a, 180b further provides a respective controller parameter vector θ_rep1, θ_rep2 indicative of the tracking performance between desired and actual flow rates, to the supervisory controller 160.

0051The supervisory controller 160 uses a parameter projection feature to remove an input saturation nonlinearity, such that the pumps 16, 60a, 60b, 66 can each be viewed as a linear system. The adaptation of the controller parameters enables enhanced tracking of the pump controllers 162, 170, 180a, 180b in the presence of time variations in flow due to, for example, changes in tubing diameters and wear, changes in hemofilter characteristics, or changes in flow resistance in the blood line.

0052If the respective applied voltage u_dra(n), u_rep1(n), u_rep2(n) is limited to the linear regime of pump operation, the replacement pumps 60a, 60b and the drain pump 66 are each adequately modeled by a time-varying auto-regressive moving average (ARMA) adaptive control algorithm. The adaptive control algorithm can be expressed as:<maths id="math0009"><math display="block"><mi mathvariant="normal">ω</mi><mfenced><mi mathvariant="normal">n</mi></mfenced><mo mathvariant="normal">-</mo><msubsup><mi mathvariant="normal">b</mi><mn mathvariant="normal">1</mn><mo mathvariant="normal">*</mo></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo>⁢</mo><mi mathvariant="normal">ω</mi><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo mathvariant="normal">+</mo><msubsup><mi mathvariant="normal">b</mi><mn mathvariant="normal">2</mn><mo mathvariant="normal">*</mo></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo>⁢</mo><mi mathvariant="normal">ω</mi><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">2</mn></mfenced><mo mathvariant="normal">=</mo><msubsup><mi mathvariant="normal">a</mi><mn mathvariant="normal">0</mn><mo mathvariant="normal">*</mo></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo mathvariant="normal">+</mo><msubsup><mi mathvariant="normal">a</mi><mn mathvariant="normal">1</mn><mo mathvariant="normal">*</mo></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo>⁢</mo><mi mathvariant="normal">u</mi><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced></math><img file="EP1514562B1_D0009.tif" /></maths> that relates the actual weights ω_dra(n), ω_rep1(n), ω_rep2(n) and the corresponding applied voltages u_dra(n), u_rep1(n), u_rep2(n). A unique set of respective system parameters <maths id="math0010"><math display="inline"><msubsup><mi mathvariant="normal">a</mi><mn>0</mn><mo mathvariant="normal">*</mo></msubsup><mo>,</mo></math><img file="EP1514562B1_D0010.tif" /></maths><maths id="math0011"><math display="inline"><msubsup><mi mathvariant="normal">a</mi><mn mathvariant="normal">1</mn><mo mathvariant="normal">*</mo></msubsup><mo>,</mo></math><img file="EP1514562B1_D0011.tif" /></maths><maths id="math0012"><math display="inline"><msubsup><mi mathvariant="normal">b</mi><mn mathvariant="normal">1</mn><mo mathvariant="normal">*</mo></msubsup><mo>,</mo></math><img file="EP1514562B1_D0012.tif" /></maths><maths id="math0013"><math display="inline"><msubsup><mi mathvariant="normal">b</mi><mn>2</mn><mo mathvariant="normal">*</mo></msubsup></math><img file="EP1514562B1_D0013.tif" /></maths> is ascribed to each pump 60a, 60b, 66. The system parameters <maths id="math0014"><math display="inline"><msubsup><mi mathvariant="normal">a</mi><mn>0</mn><mo mathvariant="normal">*</mo></msubsup><mo>,</mo></math><img file="EP1514562B1_D0014.tif" /></maths><maths id="math0015"><math display="inline"><msubsup><mi mathvariant="normal">a</mi><mn mathvariant="normal">1</mn><mo mathvariant="normal">*</mo></msubsup><mo>,</mo></math><img file="EP1514562B1_D0015.tif" /></maths><maths id="math0016"><math display="inline"><msubsup><mi mathvariant="normal">b</mi><mn mathvariant="normal">1</mn><mo mathvariant="normal">*</mo></msubsup><mo>,</mo></math><img file="EP1514562B1_D0016.tif" /></maths> are unknown time-varying parameters assumed to vary slowly in the absence of disturbances and <maths id="math0017"><math display="inline"><msubsup><mi mathvariant="normal">a</mi><mn>1</mn><mo mathvariant="normal">*</mo></msubsup><mo>,</mo></math><img file="EP1514562B1_D0017.tif" /></maths> is assumed to be positive since the pump motor never turns the rollers in a reverse direction. The bias parameter <maths id="math0018"><math display="inline"><msubsup><mi mathvariant="normal">a</mi><mn>0</mn><mo mathvariant="normal">*</mo></msubsup></math><img file="EP1514562B1_D0018.tif" /></maths> is included in the equation because it is possible for a pump to induce no fluid flow for a non-zero voltage.

0053Employing a direct adaptive control scheme, designed to track the desired weight signal ω^*(n), the control voltage is determined from:<maths id="math0019"><math display="block"><mi mathvariant="normal">u</mi><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo mathvariant="normal">=</mo><msup><mi mathvariant="normal">θ</mi><mi mathvariant="normal">T</mi></msup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo>⁢</mo><mi mathvariant="normal">φ</mi><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced></math><img file="EP1514562B1_D0019.tif" /></maths><maths id="math0020"><math display="block"><msup><mi mathvariant="normal">θ</mi><mi mathvariant="normal">T</mi></msup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo mathvariant="normal">:</mo><mo mathvariant="normal">=</mo><mfenced open="[" close="]"><msub><mi mathvariant="normal">θ</mi><mn mathvariant="normal">1</mn></msub><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo>⁢</mo><msub><mi mathvariant="normal">θ</mi><mn mathvariant="normal">2</mn></msub><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo>⁢</mo><msub><mi mathvariant="normal">θ</mi><mn mathvariant="normal">3</mn></msub><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo>⁢</mo><msub><mi mathvariant="normal">θ</mi><mn mathvariant="normal">4</mn></msub><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced></mfenced></math><img file="EP1514562B1_D0020.tif" /></maths><maths id="math0021"><math display="block"><msup><mi mathvariant="normal">φ</mi><mi mathvariant="normal">T</mi></msup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo mathvariant="normal">:</mo><mo mathvariant="normal">=</mo><mfenced open="[" close="]"><mn mathvariant="normal">1</mn><mo mathvariant="normal">-</mo><mi mathvariant="normal">ω</mi><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo mathvariant="normal">-</mo><mi mathvariant="normal">ω</mi><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">2</mn></mfenced><mo>⁢</mo><msup><mi mathvariant="normal">ω</mi><mo mathvariant="normal">*</mo></msup><mfenced><mi mathvariant="normal">n</mi></mfenced></mfenced><mo mathvariant="normal">,</mo></math><img file="EP1514562B1_D0021.tif" /></maths> where θ(n) is a vector whose components are the controller parameters generated by an adaptive law and φ(n) is a regressor vector, where |φ(n)| ≥ 1 for all n ≥ 0. If e(n) := ω(n) - ω'(n) denotes the tracking error for the accumulated fluid weight, then the tracking error satisfies:<maths id="math0022"><math display="block"><mi mathvariant="normal">e</mi><mfenced><mi mathvariant="normal">n</mi></mfenced><mo mathvariant="normal">=</mo><msubsup><mi mathvariant="normal">a</mi><mn mathvariant="normal">1</mn><mo mathvariant="normal">*</mo></msubsup><mo>⁢</mo><msup><mfenced><mi mathvariant="normal">θ</mi><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo mathvariant="normal">-</mo><msup><mi mathvariant="normal">θ</mi><mo mathvariant="normal">*</mo></msup></mfenced><mi mathvariant="normal">T</mi></msup><mo>⁢</mo><mi mathvariant="normal">φ</mi><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo mathvariant="normal">,</mo></math><img file="EP1514562B1_D0022.tif" /></maths> where θ* represents the unknown "optimal" parameter vector<maths id="math0023"><math display="block"><msup><mi mathvariant="normal">θ</mi><mo>*</mo></msup><mo>=</mo><mfrac><mn>1</mn><msup><msub><mi>a</mi><mn>1</mn></msub><mo>*</mo></msup></mfrac><mo>⁢</mo><msup><mfenced open="[" close="]"><mtable><mtr><mtd><mo>-</mo><msup><msub><mi>a</mi><mn>0</mn></msub><mo>*</mo></msup></mtd><mtd><mo>-</mo><msup><msub><mi>b</mi><mn>1</mn></msub><mo>*</mo></msup></mtd><mtd><mo>-</mo><msup><msub><mi>b</mi><mn>2</mn></msub><mo>*</mo></msup></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mi>T</mi></msup></math><img file="EP1514562B1_D0023.tif" /></maths>

0054Although the dependence of θ^* on sample time n is not explicit, θ^* will vary slowly with time, which is one of the main motivations for the utilization of on-line parameter estimation and adaptive control techniques. In general, the derivation of provably stable adaptive control algorithms for linear time-varying systems is complex. Due to the slowly time-varying nature of the pump dynamics, standard adaptive control methods with θ^* constant were found to be satisfactory for the present invention.

0055Pumps in an ultrafiltration system typically exhibit saturation behavior at the lower and upper end of the operation. Specifically, below a certain voltage level the rollers of the pump cease to rotate and fluid flow ceases. Similarly, there is a maximum allowable control voltage, typically specified by the pump manufacturer. Due to saturation in the control signal for pumps, the standard adaptive control must be modified such that the inequality u, ≤ θ^T(n)φ(n)≤ u_h holds, where the positive constants u, and u_h are, respectively, the minimum and maximum allowable control voltages. To address the time-varying parametric uncertainty and input saturations, the following normalized gradient adaptive law with planar projections apply: <maths id="math0024"><math display="block"><mi mathvariant="normal">θ</mi><mfenced><mi>n</mi></mfenced><mo>=</mo><mi mathvariant="normal">θ</mi><mo>⁢</mo><mfenced><mi>n</mi><mo>-</mo><mn>1</mn></mfenced><mo>-</mo><mfrac><mrow><mi mathvariant="normal">γ</mi><mo>⁢</mo><msup><mn>0</mn><mi>e</mi></msup><mfenced><mi>n</mi></mfenced></mrow><msup><mfenced open="|" close="|"><mi mathvariant="normal">φ</mi><mo>⁢</mo><mfenced><mi>n</mi><mo>-</mo><mn>1</mn></mfenced></mfenced><mn>2</mn></msup></mfrac><mo>⁢</mo><mi mathvariant="normal">φ</mi><mo>⁢</mo><mfenced><mi>n</mi><mo>-</mo><mn>1</mn></mfenced><mo>-</mo><mi>p</mi><mfenced><mi>n</mi></mfenced></math><img file="EP1514562B1_D0024.tif" /></maths><maths id="math0025"><math display="block"><mi>p</mi><mfenced><mi>n</mi></mfenced><mo>:</mo><mo>=</mo><mi mathvariant="normal">I</mi><mo>⁢</mo><mfenced><msup><mi mathvariant="normal">μ</mi><mi>T</mi></msup><mfenced><mi>n</mi></mfenced><mo>⁢</mo><mi mathvariant="normal">φ</mi><mo>⁢</mo><mfenced><mi>n</mi><mo>-</mo><mn>1</mn></mfenced><mo>,</mo><msub><mi>u</mi><mi>l</mi></msub></mfenced><mo>⁢</mo><mfenced open="[" close="]"><mfrac><mrow><msup><mi mathvariant="normal">μ</mi><mi>T</mi></msup><mfenced><mi>n</mi></mfenced><mo>⁢</mo><mi mathvariant="normal">φ</mi><mo>⁢</mo><mfenced><mi>n</mi><mo>-</mo><mn>1</mn></mfenced><mo>-</mo><msub><mi>u</mi><mi>l</mi></msub></mrow><msup><mfenced open="|" close="|"><mi mathvariant="normal">φ</mi><mo>⁢</mo><mfenced><mi>n</mi><mo>-</mo><mn>1</mn></mfenced></mfenced><mn>2</mn></msup></mfrac></mfenced><mo>⁢</mo><mi mathvariant="normal">φ</mi><mo>⁢</mo><mfenced><mi>n</mi><mo>-</mo><mn>1</mn></mfenced><mo>+</mo><mi mathvariant="normal">I</mi><mo>⁢</mo><mfenced><msub><mi>u</mi><mi>h</mi></msub><mo>,</mo><msup><mi mathvariant="normal">μ</mi><mi>T</mi></msup><mfenced><mi>n</mi></mfenced><mo>⁢</mo><mi mathvariant="normal">φ</mi><mo>⁢</mo><mfenced><mi>n</mi><mo>-</mo><mn>1</mn></mfenced></mfenced><mo>⁢</mo><mfenced open="[" close="]"><mfrac><mrow><msup><mi mathvariant="normal">μ</mi><mi>T</mi></msup><mfenced><mi>n</mi></mfenced><mo>⁢</mo><mi mathvariant="normal">φ</mi><mo>⁢</mo><mfenced><mi>n</mi><mo>-</mo><mn>1</mn></mfenced><mo>-</mo><msub><mi>u</mi><mi>h</mi></msub></mrow><msup><mfenced open="|" close="|"><mi mathvariant="normal">φ</mi><mo>⁢</mo><mfenced><mi>n</mi><mo>-</mo><mn>1</mn></mfenced></mfenced><mn>2</mn></msup></mfrac></mfenced><mo>⁢</mo><mi mathvariant="normal">φ</mi><mo>⁢</mo><mfenced><mi>n</mi><mo>-</mo><mn>1</mn></mfenced></math><img file="EP1514562B1_D0025.tif" /></maths><maths id="math0026"><math display="block"><mi mathvariant="normal">μ</mi><mfenced><mi>n</mi></mfenced><mo>:</mo><mo>=</mo><mi mathvariant="normal">θ</mi><mo>⁢</mo><mfenced><mi>n</mi><mo>-</mo><mn>1</mn></mfenced><mo>-</mo><mfrac><mrow><mi mathvariant="normal">γ</mi><mo>⁢</mo><msup><mn>0</mn><mi>e</mi></msup><mfenced><mi>n</mi></mfenced></mrow><msup><mfenced open="|" close="|"><mi mathvariant="normal">φ</mi><mo>⁢</mo><mfenced><mi>n</mi><mo>-</mo><mn>1</mn></mfenced></mfenced><mn>2</mn></msup></mfrac><mo>⁢</mo><mi mathvariant="normal">φ</mi><mo>⁢</mo><mfenced><mi>n</mi><mo>-</mo><mn>1</mn></mfenced></math><img file="EP1514562B1_D0026.tif" /></maths> where adaptive step-size γ₀ is chosen such that it satisfies <maths id="math0027"><math display="inline"><mn mathvariant="normal">0</mn><mo mathvariant="normal"><</mo><msub><mi mathvariant="normal">γ</mi><mn mathvariant="normal">0</mn></msub><mo mathvariant="normal"><</mo><mn mathvariant="normal">2</mn><mo>⁢</mo><msup><mfenced open="[" close="]"><msub><mi>sup</mi><mi mathvariant="normal">n</mi></msub><mo>⁢</mo><msubsup><mi mathvariant="normal">a</mi><mn mathvariant="normal">1</mn><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced></mfenced><mrow><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo mathvariant="normal">,</mo></math><img file="EP1514562B1_D0027.tif" /></maths> where an upper bound of <maths id="math0028"><math display="inline"><msubsup><mi mathvariant="normal">a</mi><mn mathvariant="normal">1</mn><mo mathvariant="normal">*</mo></msubsup></math><img file="EP1514562B1_D0028.tif" /></maths> is assumed to be known. The indicator function I(·,·) is defined as:<maths id="math0029"><math display="block"><mi mathvariant="normal">I</mi><mfenced><msub><mi mathvariant="normal">x</mi><mn mathvariant="normal">1</mn></msub><msub><mi mathvariant="normal">x</mi><mn mathvariant="normal">2</mn></msub></mfenced><mo mathvariant="normal">:</mo><mo mathvariant="normal">=</mo><mrow><mo mathvariant="normal">{</mo><mtable><mtr><mtd><mn mathvariant="normal">1</mn></mtd><mtd><mi>if</mi><mspace width="1em" /><msub><mi mathvariant="normal">x</mi><mn mathvariant="normal">1</mn></msub><mo mathvariant="normal"><</mo><msub><mi mathvariant="normal">x</mi><mn mathvariant="normal">2</mn></msub></mtd></mtr><mtr><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mi>otherwise</mi></mtd></mtr></mtable></mrow></math><img file="EP1514562B1_D0029.tif" /></maths> The projection term p(n) guarantees that the controller parameters θ(n) will be projected onto the hyperplane θ^Tφ(n-1) -u_l = 0 if µ^T(n)φ(n-1) < u_l. Similarly, the controller parameters θ(n) will be projected onto the hyperplane θ^Tφ(n-1) -u_h = 0 if µ^T(n)φ(n-1) > u_b. Thus the parameter estimates θ(n) are adapted such that the control voltage is restricted to a value between u_l and u_h.

0056If the applied voltage u_blo(n) is limited to the linear regime of pump operation, the blood pump 16 is adequately modeled by on ARMA adaptive control algorithm, that may be expressed as:<maths id="math0030"><math display="block"><msub><mi mathvariant="normal">q</mi><mi>blo</mi></msub><mfenced><mi mathvariant="normal">n</mi></mfenced><mo mathvariant="normal">+</mo><msubsup><mi mathvariant="normal">b</mi><mn mathvariant="normal">1</mn><mi>blo</mi></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo>⁢</mo><msub><mi mathvariant="normal">q</mi><mi>blo</mi></msub><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo mathvariant="normal">=</mo><msubsup><mi mathvariant="normal">a</mi><mn mathvariant="normal">0</mn><mi>blo</mi></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo mathvariant="normal">+</mo><msubsup><mi mathvariant="normal">a</mi><mn mathvariant="normal">1</mn><mi>blo</mi></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo>⁢</mo><msub><mi mathvariant="normal">u</mi><mi>blo</mi></msub><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mn mathvariant="normal">.</mn></math><img file="EP1514562B1_D0030.tif" /></maths> that relates the actual flow q_blo(n) and the applied voltage u_blo(n) at the n^th sample time. The system parameters <maths id="math0031"><math display="inline"><msubsup><mi mathvariant="normal">a</mi><mn>0</mn><mi>blo</mi></msubsup><mo>,</mo></math><img file="EP1514562B1_D0031.tif" /></maths><maths id="math0032"><math display="inline"><msubsup><mi mathvariant="normal">a</mi><mn>1</mn><mi>blo</mi></msubsup><mo>,</mo></math><img file="EP1514562B1_D0032.tif" /></maths><maths id="math0033"><math display="inline"><msubsup><mi mathvariant="normal">b</mi><mn>1</mn><mi>blo</mi></msubsup></math><img file="EP1514562B1_D0033.tif" /></maths> are assumed to vary slowly over time in the absence of disturbances and <maths id="math0034"><math display="inline"><msubsup><mi mathvariant="normal">a</mi><mn>1</mn><mi>blo</mi></msubsup></math><img file="EP1514562B1_D0034.tif" /></maths> is assumed to be positive.

0057A minimum applied voltage is chosen as a value slightly above the voltage for which the rollers of the blood pump 16 can overcome friction and rotate. If the applied voltage never falls below the minimum voltage, the blood flow is never static during the ultrafiltration procedure and the possibility of clotting is reduced. The minimum voltage will depend upon the properties of the tubing used. A typical minimum voltage is 0.3 volts. A maximum voltage will be provided by the pump manufacturer. A typical maximum voltage is 3.2 volts.

0058The control law is expressed by <maths id="math0035"><math display="inline"><msub><mi mathvariant="normal">u</mi><mi>blo</mi></msub><mfenced><mi mathvariant="normal">n</mi></mfenced><mo mathvariant="normal">=</mo><msubsup><mi mathvariant="normal">θ</mi><mi>blo</mi><mi mathvariant="normal">T</mi></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced><mo>⁢</mo><msub><mi mathvariant="normal">φ</mi><mi>blo</mi></msub><mfenced><mi mathvariant="normal">n</mi></mfenced><mo mathvariant="normal">,</mo></math><img file="EP1514562B1_D0035.tif" /></maths> where θ_blo(n) is a vector consisting of the three controller parameters, as known for a direct adaptive control scheme, and φ_blo(n) is given by:<maths id="math0036"><math display="block"><msubsup><mi mathvariant="normal">θ</mi><mi>blo</mi><mi mathvariant="normal">T</mi></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo mathvariant="normal">=</mo><mfenced open="[" close="]"><mn mathvariant="normal">1</mn><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">q</mi><mi>blo</mi></msub><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mfenced><mo>⁢</mo><msubsup><mi mathvariant="normal">q</mi><mi>blo</mi><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced></mfenced><mn mathvariant="normal">.</mn></math><img file="EP1514562B1_D0036.tif" /></maths> The desired fluid flow <maths id="math0037"><math display="inline"><msubsup><mi mathvariant="normal">q</mi><mi>blo</mi><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced></math><img file="EP1514562B1_D0037.tif" /></maths> is the output of a low-pass filter<maths id="math0038"><math display="block"><msub><mi>L</mi><mi mathvariant="italic">blo</mi></msub><mfenced><mi>z</mi></mfenced><mo>=</mo><mn>0.2514</mn><mo>⁢</mo><mfrac><mrow><mi>z</mi><mo>+</mo><mn>0.99</mn></mrow><mrow><mi>z</mi><mo>-</mo><mn>0.5</mn></mrow></mfrac></math><img file="EP1514562B1_D0038.tif" /></maths> which provides a smooth response to required changes in the desired flow rate. For example, the blood pump 16 start-up will be smooth so that the catheter will not draw against the vessel wall.

0059<figref idref="f0004">Fig. 4</figref> generically illustrates the fuzzy logic process that may be implemented in a microprocessor, such as by supervisory controller 160 implemented in computer controller 12, for decision-making to control a process, such as an ultrafiltration procedure. As is familiar from fuzzy logic theory, a fuzzy logic control system 190 generally comprises a fuzzifier 192, an inference engine 194, and a defuzzifier 196 for controlling a plant 198. The fuzzifier 192 accepts one or more discrete input data signals 200 and forms a fuzzy set by assigning degrees of membership in a set of input membership functions. The inference engine 194 makes one or more fuzzy inferences from the input signals 200 based on a fuzzy rule base 202. The defuzzifier 196 defuzzifies the fuzzy inferences based upon a set of output membership functions and provides a discrete output control signal 204 to the plant 198. The fuzzy rule base 202 comprises expert knowledge regarding the operational protocol of the system being controlled and comprises sets of "if-then" rules for controlling the plant 198. The defuzzifier 196 may apply various mathematical techniques known in the art of fuzzy logic to defuzzify the fuzzy inferences. The plant 198 may supply feedback signals 206, relating to performance of the plant 198, to the fuzzy logic control system 190 for use by the inference engine 194.

0060Fuzzification and defuzzification compose the interface needed between measured physical quantities (inputs 200 and outputs 204) and the fuzzy inference engine 194. The resulting mathematical relation is a fuzzy system. The fuzzy system accepts as inputs crisp values, forms fuzzy sets from these values, makes an inference from the specified rule base 202, and provides a crisp output by defuzzifying the inferred fuzzy output.

0061In the present case, the plant 168 is the hemofiltration system 10, the fuzzy logic control system 190 is implemented by software in the computer controller 12 for controlling the pumps 16, 60a, 60b, 66, and the input data signals 200 are the patient heart rate 120 and the patient blood pressure 130. The patient heart rate 120 is typically measured in beats per minute (bpm) and the patient blood pressure 130 is typically measured in millimeters of mercury (mmHg). Relying upon the expert clinical knowledge of a physician, an exemplary fuzzy rule base 202 for modifying the ultrafiltration rate based upon the heart rate 120 (R_h) and the blood pressure 130 (P_b) has the following set of Supervisory Rules: <dl id="dl0001" compact="compact"><dt>Supervisory Rule (1):</dt><dd>If R_h is high and P_b is normal or low, then decrease ultrafiltration. Wait 10 minutes.</dd><dt>Supervisory Rule (2):</dt><dd>If P_b is low and R_h is normal or high, then decrease ultrafiltration. Wait 10 minutes.</dd><dt>Supervisory Rule (3):</dt><dd>If both P_b and R_h are low then provide the user with a choice between a decrease or increase of the ultrafiltration rate. Wait 5 minutes.</dd><dt>Supervisory Rule (4):</dt><dd>If both P_b and R_h are high for 30 consecutive minutes, then provide the user with a choice between a decrease or increase of the ultrafiltration rate.</dd><dt>Supervisory Rule (5):</dt><dd>If P_b is high and R_h is low for 60 consecutive minutes, then increase ultrafiltration.</dd><dt>Supervisory Rule (6):</dt><dd>The lowest possible value of ultrafiltration is 0 ml./hr. The highest possible value of the ultrafiltration rate is 30% above that of the ultrafiltration rate specified by the physician, and can thus be changed during the ultrafiltration procedure if so desired.</dd><dt>Supervisory Rule (7):</dt><dd>If an increase in ultrafiltration occurs such that the filtered fraction (proportional to the ratio of the desired drained rate to the desired blood flow rate) is greater than 20%, increase the blood pump flow such that the filtered fraction equals 0.2.</dd></dl> Supervisory Rules 1-5 were implemented using fuzzy logic techniques while Supervisory Rules 6 and 7 were incorporated into the supervisory algorithm based on standard switching (crisp) logic methods. The instructions to wait in Supervisory Rules 1-5 are local to each rule. For example, if the ultrafiltration is decreased because Supervisory Rule 1 is satisfied, Supervisory Rule 1 cannot operate again until 10 minutes have lapsed. However, the ultrafiltration rate may be modified if one of Supervisory Rules 2-7 is subsequently triggered. Other sets of Supervisory Rules would be apparent to one of ordinary skill in the art and the Supervisory Rules may be so varied without departing from the scope and spirit of the present invention. For example, a time-independent set of Supervisory Rules is formulated below.

0062High and low thresholds of heart rate (R_high, R_low) and blood pressure (P_high, P_low) are specified to the supervisory controller 160 based on the size and cardiovascular state of the patient. These thresholds are used by the supervisory controller 160 to characterize the magnitudes of the heart rate 120 and the blood pressure 130 according to the following inequalities. If R_low<R_h<R_high, then the heart rate 120 is deemed normal. If R_low >R_h, then the heart rate 120 is characterized as being low, and if R_h>R_high then the heart rate 120 is high. Similar inequalities apply to characterize the blood pressure 130. The thresholds may be changed during the ultrafiltration procedure to respond to changes in the patient's cardiovascular state.

0063<figref idref="f0004">Fig. 5</figref> diagrammatically illustrates the supervisory controller 160 according to the principles of the present invention in which time has been eliminated as an input parameter. The supervisory controller 160 comprises four separate fuzzy systems 210, 220, 230, 240 that a switch logic 250 activates based upon whether the heart rate 120 and blood pressure 130 are low, normal, or high. Only one of the fuzzy systems 210, 220, 230, 240 may be active at a given time. The switch logic 250 also performs the operation of waiting the required duration before or after a supervisory adjustment to the ultrafiltration as required by the Supervisor Rules.

0064<figref idref="f0003">Figs. 6A and 6B</figref> are two sets of input membership functions defined for the input data signals of heart rate 120 and blood pressure 130, respectively, provided to the supervisory controller 160. <figref idref="f0003">Fig. 6C</figref> is a set of output membership functions defined for the output data signal connoting the change 135 in ultrafiltration rate for use in defuzzifying the fuzzy inferences made by fuzzy systems 210, 220, 230, 240. Points on each membership function represent the degree of confidence, ranging between 0 and 1, that any single input data signal 120, 130 or output control signal 135 belongs to a particular fuzzy region. Due to overlaps, one input data signal 120, 130 or output data signal 135 may belong to more than one membership function. The membership functions may be varied to have differing gradations as understood by one of ordinary skill in the art of fuzzy logic.

0065Each individual input membership function and output membership function is defined as a distinct curve having a center and a full-width. In the example of this description, individual membership functions are chosen from curves having characteristic shapes such as a triangular (T) function, a right trapezoidal (RT) function, a left trapezoidal (LT) function, or a constant value (C) function. Alternative characteristic shapes could be selected depending upon the desired response without departing from the spirit and scope of the present invention.

0066With reference to <figref idref="f0003">Figs. 6A-C</figref>, Table 1 summarizes the input and output membership functions for the following universe of discourse:<maths id="math0039"><math display="block"><mtable><mtr><mtd><msub><mi mathvariant="normal">U</mi><mn mathvariant="normal">1</mn></msub><mo mathvariant="normal">=</mo><mrow><mo mathvariant="normal">(</mo><mo mathvariant="normal">-</mo><mi mathvariant="normal">∞</mi><mo mathvariant="normal">,</mo><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>low</mi></msubsup><mo mathvariant="normal">]</mo></mrow></mtd><mtd><msub><mi mathvariant="normal">U</mi><mn mathvariant="normal">2</mn></msub><mo>=</mo><mfenced><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>low</mi></msubsup><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>high</mi></msubsup></mfenced></mtd><mtd><msub><mi mathvariant="normal">U</mi><mn mathvariant="normal">3</mn></msub><mo>=</mo><mrow><mo>[</mo><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>high</mi></msubsup><mo>,</mo><mo>+</mo><mi>∞</mi><mo>)</mo></mrow></mtd></mtr></mtable></math><img file="EP1514562B1_D0039.tif" /></maths><maths id="math0040"><math display="block"><mtable><mtr><mtd><msub><mi mathvariant="normal">V</mi><mn mathvariant="normal">1</mn></msub><mo mathvariant="normal">=</mo><mrow><mo mathvariant="normal">(</mo><mo mathvariant="normal">-</mo><mi mathvariant="normal">∞</mi><mo mathvariant="normal">,</mo><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>low</mi></msubsup><mo mathvariant="normal">]</mo></mrow></mtd><mtd><msub><mi mathvariant="normal">V</mi><mn mathvariant="normal">2</mn></msub><mo>=</mo><mfenced><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>low</mi></msubsup><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>high</mi></msubsup></mfenced></mtd><mtd><msub><mi mathvariant="normal">V</mi><mn mathvariant="normal">3</mn></msub><mo>=</mo><mrow><mo>[</mo><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>high</mi></msubsup><mo>,</mo><mo>+</mo><mi>∞</mi><mo>)</mo></mrow></mtd></mtr></mtable></math><img file="EP1514562B1_D0040.tif" /></maths><maths id="math0041"><math display="block"><msub><mi mathvariant="normal">Y</mi><mn mathvariant="normal">1</mn></msub><mo mathvariant="normal">=</mo><mrow><mo mathvariant="normal">(</mo><mo mathvariant="normal">-</mo><mn mathvariant="normal">0.2</mn><mo>⁢</mo><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo mathvariant="normal">*</mo></msubsup><mo mathvariant="normal">,</mo><mo mathvariant="normal">-</mo><mn mathvariant="normal">0.05</mn><mo>⁢</mo><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo mathvariant="normal">*</mo></msubsup><mo mathvariant="normal">]</mo></mrow><mspace width="5em" /><msub><mi mathvariant="normal">Y</mi><mn>2</mn></msub><mo mathvariant="normal">=</mo><mrow><mo mathvariant="normal">(</mo><mo>+</mo><mn mathvariant="normal">0.05</mn><mo>⁢</mo><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo mathvariant="normal">*</mo></msubsup><mo mathvariant="normal">,</mo><mo>+</mo><mn mathvariant="normal">0.2</mn><mo>⁢</mo><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo mathvariant="normal">*</mo></msubsup><mo mathvariant="normal">]</mo></mrow></math><img file="EP1514562B1_D0041.tif" /></maths> where <maths id="math0042"><math display="inline"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced></math><img file="EP1514562B1_D0042.tif" /></maths> is the desired ultrafiltration rate at the time the supervisory controller 160 is activated. <tables id="tabl0001" num="0001"><table frame="all"><title><b>Table 1</b></title><tgroup cols="5"><colspec colnum="1" colname="col1" colwidth="21mm" /><colspec colnum="2" colname="col2" colwidth="20mm" /><colspec colnum="3" colname="col3" colwidth="12mm" /><colspec colnum="4" colname="col4" colwidth="32mm" /><colspec colnum="5" colname="col5" colwidth="26mm" /><thead valign="top"><row valign="middle"><entry align="center">Name</entry><entry align="center">Defined in</entry><entry align="center">Type</entry><entry align="center">Centroid</entry><entry align="center">Width</entry></row></thead><tbody><row valign="middle"><entry align="center"><maths id="math0043"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">11</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0043.tif" /></maths>(R_h)</entry><entry align="center">U₁</entry><entry align="center">RT</entry><entry align="center">0.85 <maths id="math0044"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0044.tif" /></maths></entry><entry align="center">0.15 <maths id="math0045"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0045.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0046"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>12</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0046.tif" /></maths>(R_h)</entry><entry align="center">U₁</entry><entry align="center">T</entry><entry align="center">0.925 <maths id="math0047"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0047.tif" /></maths></entry><entry align="center">0.15 <maths id="math0048"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0048.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0049"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">13</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0049.tif" /></maths>(R_h)</entry><entry align="center">U₁</entry><entry align="center">T</entry><entry align="center"><maths id="math0050"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0050.tif" /></maths></entry><entry align="center">0.15 <maths id="math0051"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0051.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0052"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>2</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0052.tif" /></maths>(R_h)</entry><entry align="center">U₂</entry><entry align="center">C</entry><entry align="center">½(<maths id="math0053"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0053.tif" /></maths> - <maths id="math0054"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0054.tif" /></maths>)</entry><entry align="center">(<maths id="math0055"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0055.tif" /></maths> - <maths id="math0056"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0056.tif" /></maths>)</entry></row><row valign="middle"><entry align="center"><maths id="math0057"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>31</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0057.tif" /></maths>(R_h)</entry><entry align="center">U₃</entry><entry align="center">T</entry><entry align="center"><maths id="math0058"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0058.tif" /></maths></entry><entry align="center">0.15 <maths id="math0059"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0059.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0060"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>32</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0060.tif" /></maths>(R_h)</entry><entry align="center">U₃</entry><entry align="center">T</entry><entry align="center">0.925 <maths id="math0061"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0061.tif" /></maths></entry><entry align="center">0.15 <maths id="math0062"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0062.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0063"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>33</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0063.tif" /></maths>(R_h)</entry><entry align="center">U₃</entry><entry align="center">LT</entry><entry align="center">0.85 <maths id="math0064"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0064.tif" /></maths></entry><entry align="center">0.15 <maths id="math0065"><math display="block"><msubsup><mi mathvariant="normal">R</mi><mi mathvariant="normal">h</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0065.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0066"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>11</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0066.tif" /></maths>(P_b)</entry><entry align="center">V₁</entry><entry align="center">RT</entry><entry align="center">0.85 <maths id="math0067"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0067.tif" /></maths></entry><entry align="center">0.15 <maths id="math0068"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0068.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0069"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>12</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0069.tif" /></maths>(P_b)</entry><entry align="center">V₁</entry><entry align="center">T</entry><entry align="center">0.925 <maths id="math0070"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0070.tif" /></maths></entry><entry align="center">0.15 <maths id="math0071"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0071.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0072"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>13</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0072.tif" /></maths>(P_b)</entry><entry align="center">V₁</entry><entry align="center">T</entry><entry align="center"><maths id="math0073"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0073.tif" /></maths></entry><entry align="center">0.15 <maths id="math0074"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0074.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0075"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>2</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0075.tif" /></maths>(P_b)</entry><entry align="center">V₂</entry><entry align="center">C</entry><entry align="center">½ (<maths id="math0076"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0076.tif" /></maths><maths id="math0077"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0077.tif" /></maths>)</entry><entry align="center"><maths id="math0078"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0078.tif" /></maths><maths id="math0079"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>low</mi></msubsup></math><img file="EP1514562B1_D0079.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0080"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>31</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0080.tif" /></maths>(P_b)</entry><entry align="center">V₃</entry><entry align="center">T</entry><entry align="center"><maths id="math0081"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0081.tif" /></maths></entry><entry align="center">0.15 <maths id="math0082"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0082.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0083"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>32</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0083.tif" /></maths>(P_b)</entry><entry align="center">V₃</entry><entry align="center">T</entry><entry align="center">0.925 <maths id="math0084"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0084.tif" /></maths></entry><entry align="center">0.15 <maths id="math0085"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0085.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0086"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>33</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0086.tif" /></maths>(P_b)</entry><entry align="center">V₃</entry><entry align="center">LT</entry><entry align="center">0.85 <maths id="math0087"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0087.tif" /></maths></entry><entry align="center">0.15 <maths id="math0088"><math display="block"><msubsup><mi mathvariant="normal">P</mi><mi mathvariant="normal">b</mi><mi>high</mi></msubsup></math><img file="EP1514562B1_D0088.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0089"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>11</mn><mi mathvariant="normal">y</mi></msubsup></math><img file="EP1514562B1_D0089.tif" /></maths>(Δ)</entry><entry align="center">Y₁</entry><entry align="center">T</entry><entry align="center">-0.2<maths id="math0090"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo>*</mo></msubsup></math><img file="EP1514562B1_D0090.tif" /></maths></entry><entry align="center">0.15<maths id="math0091"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo>*</mo></msubsup></math><img file="EP1514562B1_D0091.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0092"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>12</mn><mi mathvariant="normal">y</mi></msubsup></math><img file="EP1514562B1_D0092.tif" /></maths>(Δ)</entry><entry align="center">Y₁</entry><entry align="center">T</entry><entry align="center">-0.125<maths id="math0093"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo>*</mo></msubsup></math><img file="EP1514562B1_D0093.tif" /></maths></entry><entry align="center">0.15<maths id="math0094"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo>*</mo></msubsup></math><img file="EP1514562B1_D0094.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0095"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>13</mn><mi mathvariant="normal">y</mi></msubsup></math><img file="EP1514562B1_D0095.tif" /></maths>(Δ)</entry><entry align="center">Y₁</entry><entry align="center">T</entry><entry align="center">-0.05<maths id="math0096"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo>*</mo></msubsup></math><img file="EP1514562B1_D0096.tif" /></maths></entry><entry align="center">0.15<maths id="math0097"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo>*</mo></msubsup></math><img file="EP1514562B1_D0097.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0098"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>21</mn><mi mathvariant="normal">y</mi></msubsup></math><img file="EP1514562B1_D0098.tif" /></maths>(Δ)</entry><entry align="center">Y₂</entry><entry align="center">T</entry><entry align="center">0.05<maths id="math0099"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo>*</mo></msubsup></math><img file="EP1514562B1_D0099.tif" /></maths></entry><entry align="center">0.15<maths id="math0100"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo>*</mo></msubsup></math><img file="EP1514562B1_D0100.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0101"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>22</mn><mi mathvariant="normal">y</mi></msubsup></math><img file="EP1514562B1_D0101.tif" /></maths>(Δ)</entry><entry align="center">Y₂</entry><entry align="center">T</entry><entry align="center">0.125<maths id="math0102"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo>*</mo></msubsup></math><img file="EP1514562B1_D0102.tif" /></maths></entry><entry align="center">0.15<maths id="math0103"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo>*</mo></msubsup></math><img file="EP1514562B1_D0103.tif" /></maths></entry></row><row valign="middle"><entry align="center"><maths id="math0104"><math display="block"><msubsup><mi mathvariant="normal">µ</mi><mn>23</mn><mi mathvariant="normal">y</mi></msubsup></math><img file="EP1514562B1_D0104.tif" /></maths>(Δ)</entry><entry align="center">Y₂</entry><entry align="center">T</entry><entry align="center">0.2<maths id="math0105"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo>*</mo></msubsup></math><img file="EP1514562B1_D0105.tif" /></maths></entry><entry align="center">0.15<maths id="math0106"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo>*</mo></msubsup></math><img file="EP1514562B1_D0106.tif" /></maths></entry></row></tbody></tgroup></table></tables>

0067The inputs to the fuzzy systems are the patient heart rate and blood pressure. The output of each fuzzy system 210, 220, 230, 240 is derived by combining the singleton fuzzifier, the fuzzy inferences from each invoked rule, and the center-average defuzzifier. The output of the fuzzy systems, Δ(n), is a recommended change 135 to the ultrafiltration rate. The change is implemented by keeping the replacement fluid flows constant and adding Δ(n) to the drain flow rate. That is, once a change in ultrafiltration Δ(n) is calculated at sample time n, it is applied as follows:<maths id="math0107"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mrow><mi>rep</mi><mo>⁢</mo><mn mathvariant="normal">1</mn></mrow><mo mathvariant="normal">*</mo></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">+</mo><mn mathvariant="normal">1</mn></mfenced><mo mathvariant="normal">=</mo><msubsup><mi mathvariant="normal">q</mi><mrow><mi>rep</mi><mo>⁢</mo><mn mathvariant="normal">1</mn></mrow><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced></math><img file="EP1514562B1_D0107.tif" /></maths><maths id="math0108"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mrow><mi>rep</mi><mo>⁢</mo><mn mathvariant="normal">2</mn></mrow><mo mathvariant="normal">*</mo></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo>+</mo><mn>1</mn></mfenced><mo>=</mo><msubsup><mi mathvariant="normal">q</mi><mrow><mi>rep</mi><mo>⁢</mo><mn mathvariant="normal">2</mn></mrow><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced></math><img file="EP1514562B1_D0108.tif" /></maths><maths id="math0109"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mi>dra</mi><mo mathvariant="normal">*</mo></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo mathvariant="normal">+</mo><mn mathvariant="normal">1</mn></mfenced><mo mathvariant="normal">=</mo><msubsup><mi mathvariant="normal">q</mi><mi>dra</mi><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced><mo mathvariant="normal">+</mo><mi mathvariant="normal">Δ</mi><mfenced><mi mathvariant="normal">n</mi></mfenced></math><img file="EP1514562B1_D0109.tif" /></maths><maths id="math0110"><math display="block"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo mathvariant="normal">*</mo></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo>+</mo><mn>1</mn></mfenced><mo>=</mo><msubsup><mi mathvariant="normal">q</mi><mi>dra</mi><mo mathvariant="normal">*</mo></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo>+</mo><mn>1</mn></mfenced><mo>-</mo><msubsup><mi mathvariant="normal">q</mi><mrow><mi>rep</mi><mo>⁢</mo><mn>1</mn></mrow><mo mathvariant="normal">*</mo></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo>+</mo><mn>1</mn></mfenced><mo>-</mo><msubsup><mi mathvariant="normal">q</mi><mrow><mi>rep</mi><mo>⁢</mo><mn>2</mn></mrow><mo mathvariant="normal">*</mo></msubsup><mo>⁢</mo><mfenced><mi mathvariant="normal">n</mi><mo>+</mo><mn>1</mn></mfenced><mo>,</mo></math><img file="EP1514562B1_D0110.tif" /></maths> resulting in an ultrafiltration rate changed by Δ(n) between sample time n and sample time n + 1. The output membership functions may change from sample time to sample time because they are dependent on <maths id="math0111"><math display="inline"><msubsup><mi mathvariant="normal">q</mi><mi>ult</mi><mo mathvariant="normal">*</mo></msubsup><mfenced><mi mathvariant="normal">n</mi></mfenced><mo>,</mo></math><img file="EP1514562B1_D0111.tif" /></maths> and thus the fuzzy system mappings built upon these may also change. This feature was designed such that the ultrafiltration system may be used for any size patient. For example, a neonate requires much smaller changes in flow rates than an adult, a fact reflected by the width of some membership functions being dependent upon the desired ultrafiltration rate.

0068Fuzzy system 210 (FSI) applies where the heart rate 120 is high and/or the blood pressure 130 is low, as defined in Supervisory Rules 1 and 2, to output a negative number to add to the ultrafiltration rate. Fuzzy system 210 comprises three fuzzy subsystems 210a, 210b, 210c (FSIA, FSIB, FSIC). The switch logic 250 activates fuzzy system 210 if the heart rate 120 is high and the blood pressure 130 is high or low, or if the heart rate 120 is high or low and the blood pressure 130 is low. The switch logic 250 also disables the selection of fuzzy system 210 for 10 minutes and chooses which fuzzy subsystem 210a, 210b, 210c will calculate the decrease in the drain flow rate.

0069The switch logic 250 activates fuzzy subsystem 210a if R_h is high and P_b is normal. The fuzzy rule base for fuzzy subsystem 210a is: <ul id="ul0002" list-style="none" compact="compact"><li>FSIA Rule (1): If R_h is <maths id="math0112"><math display="inline"><msubsup><mi mathvariant="normal">μ</mi><mn mathvariant="normal">31</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0112.tif" /></maths> then Δ is <maths id="math0113"><math display="inline"><msubsup><mi mathvariant="normal">μ</mi><mn mathvariant="normal">13</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0113.tif" /></maths>.</li><li>FSIA Rule (2): If R_h is <maths id="math0114"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">32</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0114.tif" /></maths> then Δ is <maths id="math0115"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">12</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0115.tif" /></maths>.</li><li>FSIA Rule (3): If R_h is <maths id="math0116"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">33</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0116.tif" /></maths> then Δ is <maths id="math0117"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">11</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0117.tif" /></maths>.</li></ul> The switch logic 250 activates fuzzy subsystem 210b if R_b is normal and P_b is high. The fuzzy rule base for fuzzy subsystem 210b is: <ul id="ul0003" list-style="none" compact="compact"><li>FSIB Rule (1): If P_b is <maths id="math0118"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>11</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0118.tif" /></maths> then Δ is <maths id="math0119"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>11</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0119.tif" /></maths></li><li>FSIB Rule (2): If P_b is <maths id="math0120"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>22</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0120.tif" /></maths> then Δ is <maths id="math0121"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>12</mn><mi mathvariant="normal">y</mi></msubsup></math><img file="EP1514562B1_D0121.tif" /></maths></li><li>FSIB Rule (3): If P_b is <maths id="math0122"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>33</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0122.tif" /></maths> then Δ is <maths id="math0123"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">13</mn><mi mathvariant="normal">y</mi></msubsup></math><img file="EP1514562B1_D0123.tif" /></maths></li></ul> The switch logic 250 activates subsystem fuzzy subsystem 210c if R_h is high and P_b is low. The fuzzy rule base for fuzzy subsystem 210c is: <ul id="ul0004" list-style="none" compact="compact"><li>FSIC Rule (1,1): If P_b is <maths id="math0124"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>11</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0124.tif" /></maths> and R_h is <maths id="math0125"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">31</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0125.tif" /></maths> then A is <maths id="math0126"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>11</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0126.tif" /></maths></li><li>FSIC Rule (1, 2): If P_b is <maths id="math0127"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>11</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0127.tif" /></maths> and R_h is <maths id="math0128"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">32</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0128.tif" /></maths> then Δ is <maths id="math0129"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>11</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0129.tif" /></maths>.</li><li>FSIC Rule (1,3): If P_b is <maths id="math0130"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>11</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0130.tif" /></maths> and R_h is <maths id="math0131"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>33</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0131.tif" /></maths> then Δ is <maths id="math0132"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>11</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0132.tif" /></maths></li><li>FSIC Rule (2,1): If P_b is <maths id="math0133"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>12</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0133.tif" /></maths> and R_h is <maths id="math0134"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">31</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0134.tif" /></maths> then Δ is <maths id="math0135"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>12</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0135.tif" /></maths></li><li>FSIC Rule (2,2): If P_b is <maths id="math0136"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>12</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0136.tif" /></maths> and R_h is <maths id="math0137"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">32</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0137.tif" /></maths> then Δ is µ<maths id="math0138"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">12</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0138.tif" /></maths></li><li>FSIC Rule (2,3): If P_b is <maths id="math0139"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">12</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0139.tif" /></maths> and R_h is <maths id="math0140"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">33</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0140.tif" /></maths> then Δ is <maths id="math0141"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>11</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0141.tif" /></maths></li><li>FSIC Rule (3,1): If P_b is <maths id="math0142"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>13</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0142.tif" /></maths> and R_h is <maths id="math0143"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">31</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0143.tif" /></maths> then Δ is <maths id="math0144"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">13</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0144.tif" /></maths></li><li>FSIC Rule (3,2): If P_b is <maths id="math0145"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>13</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0145.tif" /></maths> and R_h is <maths id="math0146"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">32</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0146.tif" /></maths> then Δ is <maths id="math0147"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">12</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0147.tif" /></maths></li><li>FSIC Rule (3,3): If P_b is <maths id="math0148"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>13</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0148.tif" /></maths> and R_h is <maths id="math0149"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">33</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0149.tif" /></maths> then Δ is <maths id="math0150"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">11</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0150.tif" /></maths></li></ul>

0070The switch logic 250 activates fuzzy system 220 (FSII) if the heart rate 120 and blood pressure 130 are low, as defined in Supervisory Rule 3, to calculate the change 135 in ultrafiltration rate and disables fuzzy system 220 for 10 minutes. Fuzzy system 220 comprises two fuzzy subsystems 220a, 220b (FSIIA, FSIIB). Since the direction of the change 135 in ultrafiltration rate is indeterminate, the switch logic 250 must query the user whether the ultrafiltration rate should be increased or decreased. The user selects fuzzy subsystem 220a to increase the ultrafiltration rate. The fuzzy rule base for fuzzy subsystem 220a is: <ul id="ul0005" list-style="none" compact="compact"><li>Rule (1): If R_h is <maths id="math0151"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">11</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0151.tif" /></maths> then Δ is <maths id="math0152"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>23</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0152.tif" /></maths></li><li>Rule (2): If R_h is <maths id="math0153"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">12</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0153.tif" /></maths> then Δ is <maths id="math0154"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>22</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0154.tif" /></maths></li><li>Rule (3): If R_h is <maths id="math0155"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">13</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0155.tif" /></maths> then Δ is <maths id="math0156"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">21</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0156.tif" /></maths></li></ul> Alternatively, the user selects fuzzy subsystem 220b to decrease the ultrafiltration rate. The fuzzy rule base for fuzzy subsystem 220b is: <ul id="ul0006" list-style="none" compact="compact"><li>Rule (1): If P_b is <maths id="math0157"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">11</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0157.tif" /></maths> then Δ is <maths id="math0158"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">11</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0158.tif" /></maths></li><li>Rule (2): If P_b is <maths id="math0159"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">12</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0159.tif" /></maths> then Δ is <maths id="math0160"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">12</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0160.tif" /></maths></li><li>Rule (3): If P_b is <maths id="math0161"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">13</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0161.tif" /></maths> then Δ is <maths id="math0162"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">13</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0162.tif" /></maths></li></ul>

0071The switch logic 250 activates fuzzy system 230 (FSIII) if the heart rate 120 and blood pressure 130 are both high for 30 consecutive minutes, as defined in Supervisor Rule 4, to calculate the change 135 in ultrafiltration rate. Fuzzy system 230 comprises two fuzzy subsystems 230a, 230b (FSIIIA, FSIIIB). Since the direction of the change 135 in ultrafiltration rate is indeterminate, the user is queried whether the ultrafiltration rate should be increased or decreased. The user manually selects fuzzy subsystem 230a to decrease the ultrafiltration rate. The fuzzy rule base for fuzzy subsystem 230a is: <ul id="ul0007" list-style="none" compact="compact"><li>Rule (1): If P_b is <maths id="math0163"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">31</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0163.tif" /></maths> then Δ is <maths id="math0164"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">21</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0164.tif" /></maths></li><li>Rule (2): If P_b is <maths id="math0165"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>32</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0165.tif" /></maths> then Δ is <maths id="math0166"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>22</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0166.tif" /></maths></li><li>Rule (3): If P_b is <maths id="math0167"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>33</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0167.tif" /></maths> then Δ is <maths id="math0168"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>23</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0168.tif" /></maths></li></ul> The user selects fuzzy subsystem 230b to increase the ultrafiltration rate. The fuzzy rule base for fuzzy subsystem 230b is: <ul id="ul0008" list-style="none" compact="compact"><li>Rule (1): If R_h is <maths id="math0169"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">31</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0169.tif" /></maths> then Δ is <maths id="math0170"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">13</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0170.tif" /></maths></li><li>Rule (2): If R_h is <maths id="math0171"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>32</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0171.tif" /></maths> then Δ is <maths id="math0172"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">12</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0172.tif" /></maths></li><li>Rule (3): If R_h is <maths id="math0173"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>33</mn><mi mathvariant="normal">u</mi></msubsup></math><img file="EP1514562B1_D0173.tif" /></maths> then Δ is <maths id="math0174"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">11</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0174.tif" /></maths></li></ul>

0072Finally, fuzzy system 230 (FS IV) calculates increases in ultrafiltration rate as a consequence of improvement in the patient's condition. The switch logic activates fuzzy system 240 if R_h is low and P_b is high. The fuzzy rule base for fuzzy subsystem 240 is: <ul id="ul0009" list-style="none" compact="compact"><li>Rule (1): If P_b is <maths id="math0175"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">31</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0175.tif" /></maths> then Δ is <maths id="math0176"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">21</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0176.tif" /></maths></li><li>Rule (2): If P_b is <maths id="math0177"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">32</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0177.tif" /></maths> then Δ is <maths id="math0178"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn mathvariant="normal">22</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0178.tif" /></maths></li><li>Rule (3): If P_b is <maths id="math0179"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>33</mn><mi mathvariant="normal">v</mi></msubsup></math><img file="EP1514562B1_D0179.tif" /></maths>then Δ is <maths id="math0180"><math display="inline"><msubsup><mi mathvariant="normal">µ</mi><mn>23</mn><mi mathvariant="normal">y</mi></msubsup><mn>.</mn></math><img file="EP1514562B1_D0180.tif" /></maths></li></ul> The supervisory controller 160 also adjusts the filtered fraction such that the filtered fraction is always less than or equal to 20%, as prescribed by Supervisory Rule 7.

0073In another aspect, the supervisory control system 160 also validates the measured flow rates by comparing those flow rates with prediction errors based on the pump model. The supervisory control system 180 must ignore inaccurate fluid weight measurements, which are the result of, for example, inadvertent bumps to the electronic scales 54, 78, while accurately detecting significant leaks in the fluid pathways or a disconnected tubing. In the latter instances, the supervisory control system 160 halts the ultrafiltration procedure and triggers audible and visual alarms.

0074The prediction error for the drain pump 66 and the infusate pump 60 is defined as the difference in the measured accumulated fluid weight and the predicted weight forecast by the pump model. The tracking error is defined as the difference in the predicted fluid weight and the desired fluid weight. For the blood pump 16, fluid flow rates are measured by flow probe 27 and the prediction error and the tracking error are referenced with respect to fluid flow rate.

0075If, for a given minimum number of consecutive sample periods, the prediction error is greater than a positive constant provided by the pump model and the tracking error is greater than a second positive constant also provided by the pump model, the supervisory controller 160 triggers a supervisory action. If only the prediction error or only the tracking error is large, the parameter estimates by the supervisory controller 160 are not yet tuned to the hemofiltration system 10. If both errors are large and are of the same sign, the pumps 16, 60a, 60b, 66 of the hemofiltration system 10 are halted. If the prediction error and the tracking error are large and of opposite sign, the parameter estimates by the supervisory controller 160 are marginally tuned to the undisturbed hemofiltration system 10, and either an inaccurate measurement or a sudden drastic change in the dynamics of the hemofiltration system 10 has likely occurred. A drastic change in the pump dynamics can only be caused by a significant system fault such as a tubing leak. If an inconsistent weight or flow is sensed for any pump 16, 60a, 60b, 66 for more than a predetermined number of consecutive samples, the supervisory controller 160 disables the hemofiltration system 10 and triggers audible and visual alarms.

0076Implementation of either or both of the aforementioned adaptive control or supervisory control can increase the autonomy of a hemofiltration system. Various advantages follow from the enhanced autonomy. For example, the continuous monitoring and control reduces medical costs and improves the quality of medical care by reducing the need for intermittent supervision of the ultrafiltration procedure by clinical staff. Further details of the invention will be described in the following examples.

0077The following examples are simulated ultrafiltation procedures performed with an ultrafiltration system having adaptive controll and supervisory controll, as described above, wherein either tap water or expired blood functioned as a virtual patient. Since the pump model utilized is based on actual fluid weights or flows and not from pump roller angular speeds, the control performance is independent of the fluid's rheology. While the range of achievable flows may change, the type of fluid used for the simulations is irrelevant from the point of view of flow tracking.

0078A sampling period of n=1.75 seconds was used in these examples. This specific sampling period was selected after some initial experimentation, taking into consideration the fact that the instantaneous pump flow is impulsive and only the average flow is of interest. Too small a sampling period may give large variations in flow from sample to sample, resulting in a control signal that varies too rapidly, causing a non-smooth operation. On the other hand, a sampling time of more than a few seconds may result in slow response and large tracking errors.

0079At the beginning of the simulation in each example, all tubing segments were primed with water, or 150 mEq/L sodium chloride solution if blood is used in the example, to eliminate air bubbles in the lines. A source of measurement noise for the drained weight is the evaporation of drained fluid, which can be prevented by sealing the drain container. Other sources of measurement noise include the swinging of replacement fluid bags due to air drafts, which introduces uncertainty in the weight measurements. Placing the bags and the scales inside an enclosure minimizes this uncertainty and enables the practical use of the scales' accuracy (±0.5 gr) as the sole source of uncertainty in the weight measurements. Flow measurements are taken by an ultrasonic flow-probe (Transonic Systems, Inc.) which is calibrated by the manufacturer for the fluid being used. The accuracy of the flow-probe is ±7% of the measured value, which is a source of blood flow error but not of ultrafiltration error.

0080The simulation flow rates for the blood, drain, and replacement pumps are chosen to be consistent with those typically used with a neonate as the patient. Ultrafiltration is beneficial to smaller patients if small flow rates and a small extracorporeal blood line volume are used. The type and size of tubing and connectors for the blood line are chosen according to the magnitude of the flow rates needed. These components determine the ARMA equation parameters for each pump, which in general will vary in time as the physical characteristics of the components vary over time. Values of adaptive step-size γ₀, maximum voltage u_h, and minimum voltage u₁, for purposes of the simulations in the example, are given in Table 2. <tables id="tabl0002" num="0002"><table frame="all"><title>Table 2</title><tgroup cols="4"><colspec colnum="1" colname="col1" colwidth="26mm" /><colspec colnum="2" colname="col2" colwidth="10mm" /><colspec colnum="3" colname="col3" colwidth="17mm" /><colspec colnum="4" colname="col4" colwidth="17mm" /><thead valign="top"><row><entry>Pump</entry><entry>γ₀</entry><entry>u₁ [volts]</entry><entry>u_h [volts]</entry></row></thead><tbody><row><entry>Drain</entry><entry>0.1</entry><entry align="char" char="." charoff="11">0.6</entry><entry>10.0</entry></row><row><entry>Replacement 1</entry><entry>0.1</entry><entry align="char" char="." charoff="11">0.2</entry><entry>10.0</entry></row><row><entry>Replacement 2</entry><entry>0.1</entry><entry align="char" char="." charoff="11">0.4</entry><entry>5.0</entry></row><row><entry>Blood</entry><entry>-</entry><entry align="char" char="." charoff="11">0.3</entry><entry>3.2</entry></row></tbody></tgroup></table></tables>

Example 1

0081For a ultrafiltration procedure simulated with a container full of blood as the "patient", the tracking error, the control voltage and the controller parameters are shown in <figref idref="f0005">Figs. 7A, 7B, and 7C</figref>, respectively. The tracking error goes to zero within thirty seconds, while the voltage remains steady. A large negative blood pump tracking error at the beginning of the ultrafiltration procedure is tolerated because the patient will not be adversely affected by a slow blood clearance of a few seconds. A large positive tracking error could result in decreased tissue perfusion, and the patient may or may not react adversely to the decrease of nutrients reaching various tissues. Hence, a transiently large negative error at the beginning of the ultrafiltration procedure is tolerated in exchange for preventing tracking overshoot.

Example 2

0082A ultrafiltration procedure lasting approximately one hour, with the blood flow rate set at 40.0 ml/min, the drain flow rate set to 230.0 ml/hr, and both replacement flow rates set to 100.0 ml/hr simulates an ultrafiltration procedure performed on a neonate. Typical flow rate and weight tracking errors of a simulation utilizing water as a substitute for all fluids are shown in <figref idref="f0006">Figs. 8A, 8B, 8C and 8D</figref>. The blood pump tracking error at the beginning of this simulation differs in character from the beginning of the simulation shown in <figref idref="f0005">Figs. 7A-7C</figref> because the flowmeter low pass filter choices provided by the manufacturer were not identical for this time period in the two simulations. Given the precise duration of the procedure, the expected ultrafiltration was 30.1 ml. The ultrafiltration measured by comparing the initial (269.3 ± 0.5 gr) and final weight (241.0 ± 0.5 gr) of the "patient" was 28.3 ± 0.7 gr, which results in a difference of 1.7 ± 0.7 ml from the desired ultrafiltration. The expected ultrafiltration measured by comparing the initial and final weights of drain and replacement fluids was 28.4 ± 1.2 ml. The expected ultrafiltration rate is calculated from the initial weights for the drain and replacement containers 0.0 ± 0.5 gr, 345.2 ± 0.5 gr, and 341.3 ± 0.5 gr, respectively, and the corresponding final weights 230.5 ± 0.5 gr, 243.4 ± 0.5 gr, and 241.0 ± 0.5 gr, respectively, as [(230.5 ± 0.5) - (0.0 ± 0.5)] - [345.2 ± 0.5) - (243.4 ± 0.5)] - [341.3 ± 0.5) - (241.0 ± 0.5)] = 28.4 ± 1.2 gr.

Example 3

0083<figref idref="f0007">Figs. 9A, 9B, and 9C</figref> present a simulation where the scale is bumped twice and a tubing leak occurs. Threshold values for determining an incongruent weight change are given in Table 3. <tables id="tabl0003" num="0003"><table frame="all"><title>Table 3</title><tgroup cols="4"><colspec colnum="1" colname="col1" colwidth="26mm" /><colspec colnum="2" colname="col2" colwidth="39mm" /><colspec colnum="3" colname="col3" colwidth="41mm" /><colspec colnum="4" colname="col4" colwidth="62mm" /><thead valign="top"><row><entry>Pump</entry><entry>Maximum Tracking Error</entry><entry>Maximum Prediction Error</entry><entry>Minimum No. of Samples for Validating An Incongruent Measurement of Flow</entry></row></thead><tbody><row><entry>Blood</entry><entry align="center">20 ml/min</entry><entry align="center">20 ml/min</entry><entry align="center">5</entry></row><row><entry>Drain</entry><entry align="center">3 gr</entry><entry align="center">3 gr</entry><entry align="center">5</entry></row><row><entry>Replacement 1</entry><entry align="center">3 gr</entry><entry align="center">3 gr</entry><entry align="center">5</entry></row><row><entry>Replacement 2</entry><entry align="center">3 gr</entry><entry align="center">3 gr</entry><entry align="center">5</entry></row></tbody></tgroup></table></tables> A brief disturbance of a large magnitude is introduced at a n=10 (by placing a large weight on the scale and removing it), and the supervisory controller does not react. At n=60, a similar, smaller disturbance is introduced for a brief period, and again, the supervisory controller does not respond. At n=90, a similar small disturbance is introduced, but for a prolonged period. This simulates a leak in the tubing, and is a much smaller disturbance than is generally encountered when leaks occur during actual ultrafiltration procedures. The controller detects the incongruent weight change and decides, in this case, to discontinue ultrafiltration.

Example 4

0084<figref idref="f0008">Figs. 10A, 10B, and 10C</figref> show simulated patient data and the desired drain rate for a simulation of ultrafiltration performed on a neonate. The patient heart rate and blood pressure are generated with computer software. The blood flow rate is set to 40 ml/min, and the replacement rates are both set to 100 ml/min. The thresholds for the heart rate are chosen as 90 bpm and 105 bpm, and the thresholds for the blood pressure are chosen as 70 mmHg and 95 mmHg. At the beginning of the simulation, R_h and P_b are within their normal ranges. Around n=40, R_h rises to above the threshold while P_b stays normal. The supervisory controller makes a correction due to the high heart rate and waits for a reaction. During an actual ultrafiltration procedure, the supervisory controller would wait about 10 minutes before taking any other actions because of a high heart rate. For purposes of the simulation, the wait is shortened to about 30 seconds. The switch logic once again activates FSIA 30 seconds after the first correction since the patient's heart rate remains high. The supervisory controller waits 30 more seconds, and the switch logic rechecks R_h and P_b. This time, the heart rate is high and the blood pressure is low, so the switch logic activates FSIC. The fuzzy subsystem FISC decreases the ultrafiltration rate at about n=100, and shortly thereafter R_h and P_b begin to return to normal. Since the patient parameters return to normal before the supervisory controller checks if the reactivation of FSI is necessary, no further corrections are made.

Example 5

0085<figref idref="f0009">Figs. 11A, 11B and 11C</figref> show a simulation where the heart rate and blood pressure are both low and the user has specified a decrease of ultrafiltration when queried by the supervisory controller. The blood flow rate is set to 40 ml/min, and the replacement rates are both set to 100 ml/min. The minimum and maximum thresholds for the heart rate are chosen as 90 bpm and 105 bpm, and the minimum and maximum thresholds for the blood pressure are chosen as 70 mmHg and 95 mmHg. At the beginning of the simulation, R_h and P_b are within their normal ranges. At about n=80, R_h and P_b drop below their respective low thresholds, and FSIIB calculates an ultrafiltration rate decrease. The switch logic forces FSII to wait 10 seconds (5 minutes for an actual ultrafiltration procedure) before another adjustment is made. Since the patient parameters never return to their respective normal ranges, the supervisory controller lowers the drain rate until the ultrafiltration rate is zero.

Example 6

0086<figref idref="f0010">Figs. 12A, 12B and 12C</figref> show a simulation where the patient parameters are both high and the user specifies an increase of the ultrafiltration rate. The blood flow rate is set to 40 ml/min, and the replacement rates are both set to 100 ml/min. The thresholds for the heart rate are chosen as 90 bpm and 105 bpm, and the thresholds for the blood pressure are chosen as 70 mmHg and 95 mmHg. At the beginning of the simulation, R_h and P_b are within their normal ranges. At about n=60, both the patient heart rate and blood pressure rise above their respective upper thresholds. After 20 seconds (30 minutes in an actual ultrafiltration procedure), the condition for activating FSII is met and the ultrafiltration rate is increased. Since the patient parameters never return to their respective normal ranges, the supervisory controller raises the drain rate until the ultrafiltration rate is 30% above the rate initially given. At this point, the hemofiltrator alerts the user that the maximum ultrafiltration rate has been set as the desired rate.

Example 7

0087<figref idref="f0011">Figs. 13A, 13B and 13C</figref> present a simulation where the patient is getting well enough to increase the ultrafiltration rate. The blood flow rate is set to 40 ml/min, and the replacement rates are both set to 100 ml/min. The thresholds for the heart rate are chosen as 90 bpm and 105 bpm, and the thresholds for the blood pressure are chosen as 70 mmHg and 95 mmHg. At the beginning of the simulation, R_h and P_b are within their normal ranges. Once the heart rate and blood pressure are in the favorable regions, the supervisory controller waits 120 seconds (about 60 minutes in an actual ultrafiltration procedure) to detect transient behavior before increasing the drain pump flow rate. Since the heart rate and the blood pressure return to their normal ranges, no further adjustments are made.

Example 8

0088<figref idref="f0012">Figs. 14A, 14B and 14C</figref> depict a simulation where the supervisory controller adjusts the ultrafiltration due to a high filtered fraction. The patient parameters are both high for an extended period of time and the initial ultrafiltration rate of 132.6 ml/hr is increased to 172.4 ml/hr by increasing the drain rate from 332.6 ml/hr to 372.4 ml/hr. The latter flow rate would give a filtered fraction of 22.2% if the blood pumping were held at 40.0 ml/min. In order to bring the filtered fraction down to 20%, the blood pump flow rate must be increased to 44.3 ml/min.

0089The supervisory control system and the adaptive control system described above are not limited to use in a ultrafiltration procedure, but may find application in other medical systems that employ a pump for transferring a fluid, such as a heart-lung machine. Other suitable medical applications would be apparent to one of ordinary skill in the art.