Abstract:
Methods and apparatuses for determining a fluid parameter in a vessel by altering a property of the fluid, sensing the difference in the property after the fluid is altered, particularly as related to the property in an unaltered portion of the fluid.

Description:
RELATED APPLICATIONS 
   This patent application is a continuation of U.S. patent application Ser. No. 10/238,164 filed Sept. 10, 2002 now U.S. Pat. No. 6,614,212; which is a continuation of U.S. patent application Ser. No. 09/563,107 filed May 2, 2000, now U.S. Pat. No. 6,452,371; which is a continuation of U.S. patent application Ser. No. 09/220,139 filed Dec. 23, 1998, now U.S. Pat. No. 6,075,367; which is a continuation of U.S. patent application Ser. No. 08/876,445 filed Jun. 16, 1997, now U.S. Pat. No. 5,900,726; which was a continuation of U.S. patent application Ser. No. 08/486,982 filed Jun. 7, 1995, now U.S. Pat. No. 5,644,240; which was a continuation-in-part of U.S. patent application Ser. No. 08/332,647 filed Nov. 1, 1994, now U.S. Pat. No. 5,510,716; which was a continuation of U.S. patent application Ser. No. 07/954,584 filed Sept. 30, 1992, now abandoned. 

   FIELD OF THE INVENTION 
   This invention relates to measurement of multiple hemodynamic variables. More particularly, this invention relates to measurement of the hemodynamic variables during a medical procedure or for diagnostic purposes using a differential conductivity monitor to measure or detect at least one of recirculation efficiency, flow rate or the presence of air bubbles. 
   BACKGROUND OF THE INVENTION 
   In many medical situations it is desirable to quantitatively determine, or measure, various hemodynamic parameters, such as the recirculation rate or the recirculation efficiency of a biological or medical fluid to increase the benefits of, or decrease the time required for, a therapeutic treatment, or for diagnostic purposes. For example, hemodialysis (herein “dialysis”) is an inconvenient, expensive, and uncomfortable medical procedure. It is, therefore, widely recognized as desirable to minimize the amount of time required to complete the procedure and to achieve a desired level of treatment. 
   In dialysis, a joint is typically surgically created between a vein and an artery of a patient undergoing dialysis. The joint provides a blood access site where an inlet line to a dialysis apparatus and an outlet line from the dialysis apparatus are connected. The inlet line draws blood to be treated from the patient, while the outlet line returns blood to the patient. 
   The joint may be an arteriovenous fistula, which is a direct connection of one of the patient&#39;s veins to one of the patient&#39;s arteries. Alternatively the joint may be a synthetic or animal organ graft connecting the vein to the artery. As used herein, the term “fistula” refers to any surgically created or implanted joint between one of the patient&#39;s veins and one of the patient&#39;s arteries, however created. 
   In the fistula a portion of the treated blood returned to the patient by the outlet line may recirculate. Recirculating treated blood will co-mingle with untreated blood being withdrawn from the patient by the inlet line. This recirculated, and the resulting co-mingling of treated and untreated blood, is dependent, in part, on the rate at which blood is withdrawn from and returned to the patient. The relationship is typically a direct, but non-linear relationship. It can be readily appreciated that the dialysis apparatus will operate most effectively, and the desired level of treatment achieved in the shortest period of time, when the inlet line is drawing only untreated blood at the maximum flow rate capability of the dialysis apparatus consistent with patient safety. As a practical matter, however, as flow rate through the dialysis apparatus is increased, the proportion of recirculated treated blood in the blood being drawn through the inlet line is increased. In order to select the flow rate through the dialysis apparatus, it is desirable to know the proportion of recirculated treated blood in the blood being withdrawn from the patient by the inlet line. This proportion is referred to herein as the “recirculation ratio”. The recirculation ratio can also be defined as the ratio between the flow of recirculated blood being withdrawn from the fistula to the flow of blood being returned to the fistula. Recirculation efficiency may then be defined by the relationship:
 
 E= 1 −R   (Equation 1)
 
where
         E=Recirculation efficiency   R=Recirculation ratio
 
Alternatively, recirculation efficiency may be equivalently expressed as the ratio of blood flow being returned to the fistula, but not being recirculated, to the total blood flow being returned to the fistula. Knowing the recirculation efficiency, the dialysis apparatus operator can adjust the flow rate through the dialysis apparatus to minimize the time required to achieve the desired level of treatment.
       

   In the prior art, quantitative determination of recirculation ratio or recirculation efficiency has typically required laboratory testing, such as blood urea nitrogen tests, which take considerable amounts of time and which require withdrawing blood from the patient, which is recognized as undesirable. 
   A method and apparatus for qualitatively detecting the presence or absence of recirculation in a fistula is described in “FAM 10 Fistula Flow Studies and their Interpretation” published by Gambro, Ltd. based on research performed in 1982. The Gambro method and apparatus injects a quantity of a fluid having an optical density less than the optical density of treated blood into the dialysis apparatus outlet line. A resulting change in the optical density of the blood being drawn through the dialysis apparatus inlet line is qualitatively detected as indicative of the presence of recirculation. The Gambro method and apparatus does not quantitatively determine or measure a recirculation ratio or recirculation efficiency. 
   Devices which qualitatively determine recirculation by thermal techniques are also known. 
   A quantitative measurement of the recirculation efficiency of a bodily or medical fluid is useful in other therapeutic and diagnostic procedures as well. For example, recirculation ratios and efficiencies are useful for determining cardiac output, intervascular recirculation, recirculation in non-surgically created access sites, and dialyzer performance from either the blood side or the dialysate side of the dialyzer, or both. 
   It is known that the electrical conductivity of a fluid in a closed non-metallic conduit can be measured without contact with the fluid by inducing an alternating electrical current in a conduit loop comprising a closed electrical path of known cross sectional area and length. The magnitude of the current thus induced is proportional to the conductivity of the fluid. The induced current magnitude may then be detected by inductive sensing to give a quantitative indication of fluid conductivity. A conductivity cell for measuring the conductivity of a fluid in a closed conduit without contact with the fluid is described in U.S. Pat. No. 4,740,755 entitled “Remote Conductivity Sensor Having Transformer Coupling In A Fluid Flow Path,” issued Apr. 26, 1988 to Ogawa and assigned to the assignee of the present invention, the disclosure of which is hereby incorporated herein by reference. 
   It is further desirable to have a way of detecting the presence of air in a dialysis apparatus outlet line to minimize the probability of air being returned to a patient in the outlet line. It is further advantageous to have a means of determining a volume flow rate of fluid flowing in the inlet and outlet tube of the dialysis apparatus. 
   Air bubble detectors which detect the presence of an air bubble sonically, ultrasonically or optically are known, but a more sensitive device that is not subject to sonic or optical shadows or distortion is desirable. 
   It is further desirable to measure a flow rate of a fluid in a tube, either as a part of a recirculation monitoring procedure, or as a separately measured hemodynamic parameter. 
   It is still further desirable to provide a hemodymamic monitoring device which is capable of monitoring more than one hemodynamic parameter, in order to reduce system cost and increase system flexibility. 
   It is against this background that the differential conductivity hemodynamic monitor of the present invention developed. 
   SUMMARY OF THE INVENTION 
   A significant aspect of the present invention is a method and an apparatus for accurately measuring a volumetric flow rate of a fluid flowing in a tube. In accordance with this aspect of the invention the fluid has an electrical conductivity and a corresponding concentration of conductivity producing ions. The electrical conductivity of the fluid is altered, as by injection of a bolus of hypertonic saline solution. The altered electrical conductivity is measured and integrated over time. The integrated value is then interpreted to determine flow rate. 
   Further in accordance with this aspect of the invention, fluid conductivity is measured by flowing the fluid through a conductivity cell with a continuous path configuration, inducing an electrical current in the fluid in the conductivity cell, and sensing the first electrical current in the first fluid in the first conductivity cell. Still further in accordance with this aspect of the invention, current inducing and sensing may be performed by positioning an exciting electromagnetic coil in proximity with the conductivity cell to induce the electrical current in the continuous path of the conductivity cell, and positioning a sensing electromagnetic coil in proximity with the conductivity cell to sense the induced current. Yet further in accordance with this aspect of the invention, the effects of background conductivity are compensated for. 
   Still further in accordance with this aspect, a second fluid may be flowing in another tube, and the conductivity measuring may measure the difference between the conductivity of the first fluid in the tube and the conductivity of the second fluid in the other tube. 
   A further significant aspect of the present invention is an apparatus capable of performing a plurality of hemodynamic parameter determinations. In accordance with this aspect of the invention the apparatus measures the flow rate of a fluid in a tube and further is suitable for use as a recirculation monitor for determining a degree of recirculation of a fluid in a zone of a vessel. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic diagram of a dialysis system incorporating a differential conductivity recirculation monitor in accordance with the present invention. 
       FIG. 2  is a partial perspective view illustrating the functional elements of the differential conductivity recirculation monitor shown in FIG.  1 . 
       FIG. 3  is an electrical schematic diagram of the differential conductivity recirculation monitor shown in FIG.  2 . 
       FIG. 4  is an electrical block diagram of sensing logic usable with the differential conductivity recirculation monitor illustrated in  FIGS. 2 and 3 . 
       FIG. 5  is a graph illustrating differential conductivity versus time during a recirculation test employing the differential conductivity recirculation monitor shown in FIG.  2 . 
       FIG. 6  is a graph illustrating the integral of differential conductivity versus time during a recirculation test employing the differential conductivity recirculation monitor shown in  FIG. 2 , having substantially the same time scale as FIG.  5 . 
       FIG. 7  is a partial elevational view of a tubing set and sectional view of an excitation and sensing unit for use with the dialysis system shown in  FIG. 1 , incorporating the differential conductivity recirculation monitor in accordance with the present invention. 
       FIG. 8  is a partially diagrammatic sectional view taken substantially at line  8 — 8  in FIG.  7 . 
       FIG. 9  is a partially diagrammatic perspective view of the excitation and sensing unit of the differential conductivity recirculation monitor of the present invention. 
       FIG. 10  is a diagrammatic representation of the passage of an ideal bolus of saline and an actual bolus of saline through a conductivity cell of the present invention. 
       FIG. 11  is an illustration of the output signals from the conductivity cell of FIG.  10 . 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     FIG. 1  illustrates a dialysis system  20  incorporating a differential conductivity recirculation monitor  22  for determining and displaying recirculation efficiency in accordance with the present invention. The dialysis system  20 , which is one example of a medical system with which the present invention may be advantageously used, comprises a dialysis apparatus  24  connected to a fistula  26  surgically formed in a dialysis patient (not shown). Untreated blood is drawn from the fistula  26  through a dialyzer inlet needle  28  and a dialyzer inlet line  30 . Treated blood is returned to the fistula through a dialyzer outlet line  32  and a dialyzer outlet needle  34 . The recirculation monitor  22  is located in the dialyzer inlet and outlet lines  30  and  32  at a point intermediate between the fistula  26  and the dialysis apparatus  24 . 
   The dialysis apparatus  24  comprises a blood pump  36  typically a peristaltic pump, a dialyzer  38  having a blood compartment  40  and a dialysate compartment  42  separated by a semi-permeable membrane  44 , a bubble trap  46  and a dialysate generator  48 . Blood is drawn from the fistula  26  by the action of the blood pump  36  and passed through the blood compartment  40  of the dialyzer  38 . The membrane  44  allows transfer of impurities in the blood, such as urea and creatinine, from the blood compartment  40  to the dialysate compartment  42  of the dialyzer  38 . The dialysate compartment  42  is connected to a dialysate generator  48  which generates the dialysate, a liquid isotonic to blood, and circulates it through the dialysate compartment  42 . 
   The principles of operation of the differential conductivity recirculation detector  22  of the present invention are explained in conjunction with  FIGS. 2 and 3 . The recirculation detector  22  comprises a needle access site  50  in the dialyzer outlet line  32 . A first or outlet conductivity cell  52  is located in the dialyzer outlet line  32  downstream of the needle access site  50 . A second or inlet conductivity cell  54  is located in the dialyzer inlet line  30 . The first conductivity cell  52  comprises an upstream connection  56 , a downstream connection  58  and first and second tubing branches  60  and  62 , respectively, each of which interconnect the upstream connection  56  with the downstream connection  58 . Treated blood from the dialyzer flows in the dialyzer outlet line  32  through the needle access site  50  to the upstream connection  56 . At the upstream connection  56  the flow splits approximately equally with a portion of the treated blood flowing in each of the two tubing branches  60  and  62  of the outlet conductivity cell  52 . The flow rejoins at the downstream connection  58  and flows through the dialyzer outlet line  32  to the fistula  26  (FIG.  1 ). Similarly, the inlet conductivity cell  54  comprises an upstream connection  64 , a downstream connection  66  and third and fourth tubing branches  68  and  70 , respectively, which each connect the upstream connection  64  to the downstream connection  66 . Untreated blood from the fistula  26  flowing in the dialyzer inlet line  30 , enters the inlet conductivity cell  54  at the upstream connection  64  divides approximately equally between the third and fourth tubing branches  68  and  70  and rejoins at the downstream connection  66  to the inlet conductivity cell  54 . Each one of the tubing branches  60 ,  62 ,  68  and  70  has the same cross sectional area and length as each other one of the tubing branches. 
   The blood, or other biological or medical fluid, flowing in each conductivity cell  52  and  54  comprises an electrical circuit. The electrical circuit is a path for circulation of an electrical current from the upstream connection, through one of the tubing branches, to the downstream connection and from the downstream connection through the other one of the tubing branches to the upstream connection. 
   The outlet conductivity cell  52  and the inlet conductivity cell  54  are positioned adjacent to each other in an angular relationship resembling a pretzel so that the first tubing branch  60  of the outlet conductivity cell  52  is positioned parallel to the third tubing branch  68  of the inlet conductivity cell at an excitation location. The conductivity cells are further positioned so that the second tubing branch  62  of the outlet conductivity cell  52  crosses the fourth tubing branch  70  of the inlet conductivity cell  54  at an angle, approximately sixty degrees in the preferred embodiment, at a sensing location. An excitation coil  72  encircles the first tubing branch  60  of the outlet conductivity cell  52  and the third tubing branch  68  of the inlet conductivity cell  54  at the excitation location. A sensing coil  74  encircles the second tubing branch  62  of the outlet conductivity cell  52  and the fourth tubing branch  70  of the inlet conductivity cell  54  at the sensing location. 
   An electrical circuit, as is illustrated schematically in  FIG. 3 , is thus formed. The excitation coil  72  is inductively coupled to the outlet conductivity cell  52  and the inlet conductivity cell  54 . When a source of excitation energy  76  causes an alternating excitation current, illustrated by direction arrow  78 , to flow in the excitation coil  72  a changing magnetic field is generated which causes an electrical current, illustrated by the direction arrow  80 , to flow in the blood in the outlet conductivity cell  52  and causes another electrical current, illustrated by direction arrow  82 , to flow in the same electrical direction in the blood in the inlet conductivity cell  54 . Since the conductivity cells  52  and  54  are formed to create electrical paths of equal cross sectional area and equal path length the electrical conductance of the paths, as illustrated by the schematic resistors  84  and  86 , and thus the magnitude of the induced currents  80  and  82 , will be related to the conductivity of the blood in the respective conductivity cells  52  and  54 . 
   The induced currents  80  and  82  flowing in the outlet and inlet conductivity cells  52  and  54  generate a changing magnetic field at the sensing location that induces a sensed current, illustrated by direction arrow  88 , in the sensing coil  74 . The induced currents  80  and  82  are in opposite electrical directions so that the magnetic field at the sensing location has a magnitude proportional to the difference between the induced currents. The sensed current  88  is proportional to the magnetic field at the sensing location where the sensing coil  74  encircles the second and fourth tubing branches  62  and  70 , respectively. The sensed current  88  induced in the sensing transformer  74  is therefore proportional to a difference between the induced currents  80  and  82  in the outlet and inlet conductivity cells  52  and  54 , respectively. The induced currents  80  and  82  in the outlet and inlet conductivity cells  52  and  54 , respectively, are related to the conductivity of the fluids in those chambers. Therefore, the magnitude of the sensed current  88  induced in the sensing coil  74  will be related to the difference between the conductivities of the fluids in the outlet and inlet conductivity cells  52  and  54 . The sensed current  88  is delivered to, and interpreted by a sensing logic and display circuit  90 , which displays the recirculation efficiency. 
   It should be appreciated that the present invention will function in substantially the same way if the locations of the exciting coil  72  and sensing coil  74  are reversed. 
   Referring now to  FIGS. 1 and 2 , to use the recirculation monitor  22  to perform a recirculation test the dialysis system operator injects a bolus of a marker fluid into the treated blood in the dialyzer outlet line  32  at the needle access site  50  using a typical hypodermic needle  92 . The marker fluid may have an electrical conductivity that is higher or lower than the fluid flowing in the outlet line  32 . In the preferred embodiment a high conductivity marker fluid is used to avoid damaging blood cells. In the preferred embodiment the bolus is 1 milliliter of 24 percent hypertonic saline solution. The conductivity of the treated blood being returned to the patient through the dialyzer outlet line  32  and the outlet conductivity cell  52  of the recirculation monitor  22  is altered. This altered conductivity blood enters the fistula through the outlet needle  34 . 
   If the flow balance in the fistula  26  is such that no flow is recirculating the altered conductivity blood will exit the fistula, as illustrated by the flow circulation arrow  94 , without altering the conductivity of the blood within the fistula. If, however, the flow balance within the fistula  26  is such that blood is recirculating, as illustrated by flow circulation arrow  96 , a portion of the blood withdrawn from the fistula  26  by the pump  36  will be the altered conductivity blood. The recirculation monitor  22  measures the conductivity of the blood flowing in the outlet line  32  and the conductivity of the blood flowing in the inlet line  30  and quantitatively determines the difference between those conductivities continuously throughout the recirculation test. The sensing logic and display circuit  90  interprets the quantitative conductivity differences measured by the recirculation monitor  22  to determine recirculation efficiency. 
   The determination of recirculation efficiency will be explained by reference to  FIGS. 4 ,  5  and  6 . The outlet conductivity cell  52  and the inlet conductivity cell  54  may be thought of as signal generators generating the induced currents  80  and  82  in the outlet and inlet conductivity cells. The induced current  82  of the inlet conductivity cell  54  is inverted  98  and added  100  to the induced current  80  in the outlet conductivity cell  52 , by virtue of the physical relationships between the conductivity cells, excitation coil  72  and sensing coil  74 , to produce the sensed current  88 . 
   The sensing logic and display circuit  90  performs a zeroing operation  102 , a dialyzer outlet flow determining operation  104 , and unrecirculated flow determining operation  106 , and a dividing operation  108 , and includes a visual display device  110 , preferably a liquid crystal display. Alternatively the functions of the sensing logic and display circuit  90  may be performed by a digital computer (not shown). 
     FIG. 5  is a graph illustrating differential conductivity (reference  112 ) as a function of time (reference  114 ) during a typical recirculation test.  FIG. 6  is a graph illustrating the integral of differential conductivity (reference  116 ) as a function of time  114  during the typical recirculation test. Prior to the beginning of the recirculation test there may be some normal difference (reference  118 ) between the conductivity of the treated blood in the dialyzer outlet line  32  ( FIG. 2 ) and the untreated blood in the dialyzer inlet line  30  (FIG.  2 ). This normal conductivity difference  118  is subtracted from the sensed current  88  by the zeroing operation  102  of the sensing logic and display circuit  90  to remove the effect of the normal difference in conductivity  118  from determination of recirculation efficiency. The recirculation test begins (reference time T 1 ) when the bolus of high conductivity fluid is injected into the dialyzer outlet line  32  ( FIG. 2 ) at the needle access site  50  (FIG.  2 ). The conductivity of the treated blood in the dialyzer outlet line  32  ( FIG. 2 ) is increased. As the bolus passes through the outlet conductivity cell  52  ( FIG. 2 ) the differential conductivity  112  increases (reference  120 ) and then decreases (reference  122 ) until the normal conductivity difference  118  is reached (reference time T 2 ). The outlet flow determining operation  104  calculates the integral of conductivity from the start of the test (reference time T 1 ) until the differential conductivity returns to the normal value  118  (reference time T 2 ). The integral  116  of the conductivity increases (reference  124 ) until a first steady state value (reference  126 ) of the integral  116  is reached when the differential conductivity  112  returns to the normal value  118  (reference time T 2 ). The first steady state value  126  is stored by the outlet flow determining operation  104  and is representative of the flow of treated blood in the dialyzer outlet line  32  (FIG.  2 ). 
   After the treated blood with the altered conductivity enters the fistula  26  ( FIG. 1 ) a portion of it may recirculate and be withdrawn from the fistula  26  ( FIG. 1 ) through the dialyzer inlet line  30  (FIG.  2 ). The conductivity of the untreated blood in the inlet conductivity cell  54  is increased (reference time T 3 ), causing the differential conductivity to decrease  128  and then increase  130 , returning to the normal value of conductivity difference  118  (reference time T 4 ). The integral of differential conductivity from the beginning of the recirculation test (reference time T 1 ) until the normal value of conductivity difference  118  is reached again (reference time T 4 ) is calculated by the unrecirculated flow determining operation  106  of the sensing logic and display circuit  90 . The integral of differential conductivity  116  decreases (reference) to a second steady state value  134  (reference time T 4 . 
   The second steady state value  134  of the integral of differential conductivity is stored by the unrecirculated flow determining operation  106  of the sensing logic and display circuit  90  and is representative of the portion of the bolus of high conductivity liquid that was not recirculated. The second steady state value  134  is thus representative of the unrecirculated portion of the treated blood flow. The dividing operation divides the second steady state value  134  by the first steady state value  126  to calculate a recirculation efficiency  136 . The recirculation efficiency  136  is provided to the operator as a visual output by the display device  110 . 
   It will be apparent to those skilled in the art that the sensing logic and display circuit  90  may be implemented using analog or digital circuit devices and that other calculation algorithms may be used to calculate recirculation efficiency  138 . Further, the recirculation efficiency  138  may be calculated in real time or, alternatively, the necessary data stored and the calculations performed on the stored data. 
   Further details of the preferred embodiment of the differential conductivity recirculation monitor will be explained by reference to  FIGS. 7-11 . 
     FIG. 7  illustrates a portion of a typical disposable tubing set  140  incorporating conductivity cells  52  and  54  in accordance with the present invention. As is well known in the art, it is highly desirable for all portions of the tubing set  140  to be used with a dialysis system to be disposable, in order to prevent cross contamination and infection between patients. This is true of most blood and other biological or medical fluid processing systems. 
   Disposable tubing sets may be formed from a plurality of plastic tubes, connectors, needles and medical devices using techniques that are well known in the art. The discussion of the tubing set  140  will therefore be limited to a discussion of the differential conductivity recirculation monitor  22  ( FIG. 1 ) portion of the tubing set. 
   The dialyzer outlet line  32  is a plastic tube which extends through the needle access site  50 , into the outlet conductivity cell  52 . The outlet conductivity cell  52  comprises a plastic conduit loop and includes the upstream connection  56 , elongated divided first and second tubing branches  60  and  62 , and the downstream connector  58 . The downstream connector  58  has mounted in it an extension of the dialyzer outlet line  32 , which is mounted through a connector  142  to the outlet needle  34 . 
   The dialyzer inlet needle  28  is connected through a connector  144 , to the dialyzer inlet line  30 . The dialyzer inlet line  30  is connected to the inlet conductivity cell  54 , which includes the upstream connection  64 , elongated divided third and fourth tubing branches  68  and  70  respectively, and downstream connector  66 . The dialyzer inlet line  30  extends from the downstream connector  66  to the dialyzer apparatus  24  (FIG.  1 ). 
   In the preferred embodiment the portion of the dialyzer outlet line  32  between the dialyzer outlet needle  34  and the downstream connector  58  of the outlet conductivity cell  52  and the portion of the dialyzer inlet line  30  between the dialyzer inlet needle  28  and the upstream connector  64  of the inlet conductivity cell  54  must be sufficiently long so that the bolus of marker fluid passes completely through the outlet conductivity cell before any altered conductivity fluid from the fistula  26  enters the inlet conductivity cell. 
   The conductivity cells  52  and  54  have the overall shape of links in an ordinary chain, straight side portions  146  being joined at their ends by semicircular portions  148 . In cross-section at the excitation location, as shown in  FIG. 8 , the wall of each conductivity cell  42  and  54  defines a D, the insides of the Ds providing conduit portions  150  and  152 . A flat portion  154  of the D of the outlet conductivity cell  52  is abutted and adhered to a flat portion  156  of the D of the inlet conductivity cell  54  along one pair of semicircular portions  148  of the conductivity cells. The other pair of circular portions  148  are separated so that axes of the conductivity cells  52  and  54  define therebetween an angle of approximately sixty degrees. The flat portions  154  and  156  of the conductivity cells  52  and  54  are further joined along two of the straight portions  146  at a location along the second and fourth tubing branches  62  and  70 , respectively at the sensing location. An orientation tab  159  is formed on the inlet conductivity cell  54 . 
   Mating with tube set  140  is a tubing set acceptor  160 . As shown in  FIG. 9 , the tubing set acceptor  160  comprises a portion of an excitation and sensing unit  162  which also includes a logic circuit module  164 . The tubing set acceptor  160  comprises a portion of a first, or rear, acceptor plate  166  and a second, or front, acceptor plate  168  joined by a hinge  169  for motion between open and closed positions and provided with a latch or spring (not shown) to hold the acceptor plates in the closed position. The first acceptor  166  plate is relieved to accept into appropriately-shaped indentations  170  thereof the outlet conductivity cell  52  ( FIG. 2 ) and portions the tubing set  140  (FIG.  7 ). The second acceptor plate  168  is relieved to accept into appropriately-shaped indentations  172  thereof the inlet conductivity cell  54  and portions of the tubing set  140  (FIG.  7 ). An orientation tab recess  173  is defined by at least one of the appropriately shaped indentations  170  and  172 . The orientation tab recess  173  cooperates with the orientation tab  159  ( FIG. 7 ) of the tubing set  140  ( FIG. 7 ) to assure that the tubing set is correctly oriented when installed in the tubing set acceptor  160 . 
   The tubing set acceptor  160  is sufficiently large to support the conductivity cells  52  and  54  and enough of the dialyzer outlet line  32  and dialyzer inlet line  30  so that fluid flow patterns through the conductivity cells are substantially repeatable, being relatively unaffected by bends, curves, tubing movement, and other disturbances or variations in the positions of the outlet and inlet lines with respect to the conductivity cells during measurement. 
   The excitation coil  72  and sensing coil  74  are mounted to the tubing set acceptor  160 . The excitation coil  72  and sensing coil,  74  are positioned at right angles to each other to minimize magnetic interference between the coils. The excitation coil  72  comprises a first, or rear, and a second, or front, half core  174  and  176 , respectively. Similarly the sensing coil comprises a third, or rear, and a fourth, or front, half-core  178  and  180  respectively. The first and third half-cores  174  and  178 , respectively are mounted to the first acceptor plate  166  and the second and third half cores  176  and  180  respectively are mounted to the second acceptor plate  186 . 
   As illustrated in  FIG. 8 , each half core has a U-shaped configuration, with short legs  182  having ends  184  and connecting legs  186 . The tubing set acceptor  160  holds a portion of the tubing set  140  which includes the conductivity cells  52  and  54  in a fixed relationship with the excitation coil  72  and sensing coil  74 . 
   The first and second half cores  174  and  176  are oriented so that their ends  184  abut when the first and second acceptor plates  166  and  168  are brought to the closed position. The excitation coil  72  thus formed is in the shape of a rectangle defining a rectangular window. The third and fourth half cores  178  and  180  are similarly oriented so that their ends abut when the first and second acceptor plates  166  and  168  are brought to the closed position. The sensing coil  74  thus formed is also in the shape of a rectangular ring defining a rectangular window (not shown). When a tubing set  140  is placed in the tubing set acceptor  160  the first and third tubing branches  60  and  68  are engaged in the window of the excitation coil  72  and the second and fourth tubing branches  62  and  70  are engaged in the window of the sensing coil  74  so that the coils encircle the corresponding tubing branches. Biasing springs  188  may be provided to hold corresponding half-cores in firm contact when the acceptor plates  166  and  168  are closed. 
   The legs  182  and  186  of the coil  72  and  74  are square in cross-section. At least one connecting leg  186  of each coil  72  and  74  is transformer wire wrapped  190 . 
   The logic circuit module  164  of the excitation and sensing unit  162  may be mounted to one of the acceptor plates  168  or may be separate from the tubing set acceptor  160  with wiring interconnections (not shown) to the tubing set acceptor  160 . Further, either or both of the logic circuit module  164  or the tubing set acceptor  160  may be incorporated into the dialysis apparatus  24 . The logic circuit module houses the sensing logic and display circuit  90 , with the display device  110  and one or more manual input switches  192  to enable the operator to perform such functions as turning the recirculation monitor on and off, testing the operation of the monitor and initiating recirculation test, and may also include switches and displays associated with other hemodynamic monitoring functions. 
   Although the display device  110  and manual input switches  192  are shown in  FIG. 9  as being on a side  194  of the logic circuit module  164  adjacent to the second acceptor plate  168 , in the preferred embodiment the display device and manual input switches may be on a side  196  opposite the second acceptor plate  168 , or any other side of the logic circuit module. 
   The circuitry for conductivity measurement and calibration may suitably be as set forth in the Ogawa patent incorporated by reference above. 
   The apparatus and methods described above may optionally be adapted to measure and detect other hemodynamic parameters such as the presence of entrained air in the treated blood returned to the patient from the dialysis apparatus  24  through the dialyzer outlet line  32 . For this use it is not necessary to inject saline at the needle access site  50 . Entrained air in the blood in the form of a large bubble will cause an electrical discontinuity in the outlet conductivity cell  52  as it passes through either of the tubing branches  60 ,  62  of the outlet conductivity cell  52 . This will cause the magnitude of induced current  80  flowing in the outlet conductivity cell  52  to be greatly reduced or turned off completely, depending on the size of the bubble. Further, a plurality of small bubbles will effectively reduce the conducting volume of the blood in the tubing branches  60 ,  62  of the conductivity cell, decreasing the conductance, and therefore the induced current  80 , in the outlet conductivity cell  52 . 
   By sensing this reduction in the outlet conductivity cell  52  induced current  80  the passage of a bubble or a plurality of bubbles can be detected, and corrective action taken, if necessary, to minimize their introduction into the patient through the outlet line  32  and outlet needle  28 . Corrective action may include turning off the dialysis apparatus  24 , closing a venous clamp (not shown) and/or activating indicator or alarm devices to alert a human operator of the presence of the air bubble of bubbles. 
   In the preferred embodiment, a difference in the conductivity of the blood in the outlet conductivity cell  52  of the outlet line  32  and the blood in the inlet conductivity cell of the inlet line  30  is substantially constantly monitored. When one or more air bubbles enter the outlet conductivity cell  52 , causing the conductance, and thus the induced current  80  and resulting sensed conductivity of the fluid in the cell  52 , to decrease relative to the conductivity of the blood in the inlet conductivity cell  54 , this decrease is sensed by logic in the sensing logic and display circuit  90  of the logic circuit module  164  of the excitation and sensing unit  162 . If the conductivity of the blood in the outlet conductivity cell  52  is sufficiently lower than the conductivity of the blood in the inlet conductivity cell  54 , this conductivity difference is interpreted as the presence of entrained air in the outlet line  32 . 
   The apparatus and methods described above may optionally be adapted to measure the hemodynamic parameter of blood volumetric flow in the outlet line  32 . Blood volumetric flow rate may be measured and displayed as and incident to the measurement of a degree of recirculation, as described above, or may be measured in a separate blood volumetric flow monitoring procedure. 
   The measurement of blood volumetric flow using the differential conductivity sensor of the present apparatus will be explained by reference to  FIGS. 10 and 11 . The conductivity of a fluid is directly proportional to the concentration of conductivity producing ions in the fluid. Consider an ideal bolus  202  of hypertonic saline solution having a known volume vol and a known mass of conductivity altering ions M. The ion concentration of this ideal bolus  202  would be: 
             C   =     M   vol             (     Equation   ⁢           ⁢   2     )             
 
If this bolus were injected at the needle access site  50  into the outlet line  32 , which is a tube of known cross-sectional area a, into fluid flowing at a flow rate Q, corresponding to a velocity V, the ideal bolus would pass through the outlet line  32  in the form of a cylinder having a length L, L being defined as: 
             L   =     vol   a             (     Equation   ⁢           ⁢   3     )             
 
   As this ideal bolus  202  passes through the outlet conductivity cell  52  it would cause the conductivity cell to sense a square pulse  204  of altered differential conductivity having a magnitude proportional to the ion concentration C of the bolus and a duration t 1  proportional to the length L of the bolus  202  and the flow rate Q of the fluid. The flow rate of the fluid can then be calculated as: 
             Q   =     Va   =       La     t   1       =     M     Ct   1                   (     Equation   ⁢           ⁢   4     )             
 
Note that Ct 1  is the area under the sensed square pulse  204 .
 
   In reality the bolus  202 ′ of known volume vol and known mass of conductivity altering ions M will not take the form of a perfect cylinder, but will exhibit gradual leading edge curve  206  and trailing edge curve  208 , and will further diffuse into the fluid in the outlet line  32 . The differential conductivity pulse  204 ′ caused by the passage of the bolus  202 ′ through the outlet conductivity cell  52  will deviate substantially from a square pulse and will have gradually increasing and decreasing leading and trailing edges  210 ,  212  corresponding to the leading and trailing edges  206 ,  208  of the bolus. Furthermore, the time t 2  that the bolus  202 ′ takes to pass through the outlet conductivity cell will be longer than the time t 1  for an ideal bolus  202 . In order to determine the flow rate, Q it is necessary to determine the area under the differential conductivity curve by integrating the output over time as follows: 
             Q   =     M       ∫   0     t   2       ⁢       C   ⁡     (   t   )       ⁢     ⅆ   t                   (     Equation   ⁢           ⁢   5     )             
 
   Thus, if a bolus of saline of a known volume vol and a known concentration of conductivity altering ions C k  is injected into the needle access site  50 , the flow rate of the fluid can be determined to be: 
             Q   =         C   k     *   vol         ∫   0     t   2       ⁢       C   ⁡     (   t   )       ⁢     ⅆ   t                   (     Equation   ⁢           ⁢   6     )             
 
   When the fluid flowing in the conductivity cell  32  has a background conductivity, representing a background concentration C b  of conductivity, measured by the outlet conductivity cell  52  immediately prior to the passage of the bolus  202 ′ through the cell  52 , representing a background level of conductivity producing ions, the effect of the background level must be subtracted to obtain the correct value of flow: 
             Q   =         (       C   k     -     C   b       )     *   vol         ∫   0     t   2       ⁢       (       C   ⁡     (   t   )       -     C   b       )     ⁢     ⅆ   t                   (     Equation   ⁢           ⁢   7     )             
 
In the differential conductivity cell  22  of the preferred embodiment C b  is representative of a difference in background concentration, and hence conductivity, between the fluid in the outlet conductivity cell  52  and the fluid in the inlet conductivity cell. If, under steady state conditions, the conductivity of fluid in the outlet cell  52  is the same as the conductivity in the inlet cell, then the background concentration C b  is zero. The preferred embodiment of the present invention may optionally be provided with selectably engageable logic to analyze a differential conductivity pulse from the bolus  202 ′ of saline passing through the outlet conductivity cell  52  and generate a value indicative of the flow rate through the conductivity cell. This value may be selectively displayable on the same display device  110  as is used to display a degree of recirculation. The bolus of saline  202 ′ may optionally be the same bolus used to determine a degree of recirculation, in which case the flow rate will be determined substantially simultaneously with the degree of recirculation and displayed simultaneously of sequentially therewith.
 
   The apparatus and methods described above may optionally be further adapted to incorporate the capability of measuring or detecting more than one hemodynamic parameter into a single differential conductivity measuring apparatus. 
   The preferred embodiments of the present invention has been described by reference to determination of recirculation efficiency in a surgically created blood access site during, or in conjunction with, a hemodialysis procedure. It should be understood that the present invention is not so limited. The present invention may be used in a variety of medical and non-medical circumstances where it is desirable to determine recirculation efficiency. Further, it should be understood that the present invention may be used in a variety of medical and non-medical circumstances where it is desirable to compare the electrical conductivities of two fluids. Presently preferred embodiments of the present invention and many of its aspects, features and advantages have been described with a degree of particularity. It should be understood that this description has been made by way of preferred example, and that the invention is defined by the scope of the following claims.