Method and device for monitoring a blood vessel access

0001The invention relates to a method for monitoring a vascular access during an extracorporeal blood treatment, in particular a chronic blood purification therapy such as hemodialysis, hemofiltration and hemodiafiltration, and a device for extracorporeal blood treatment, in particular for hemodialysis, hemofiltration and hemodiafiltration, with a device for monitoring the vascular access.

0002In the known methods of chronic blood purification therapy such as hemodialysis, hemofiltration and hemodiafiltration blood of the patient is passed through an extracorporeal circuit. Arteriovenous fistulas, vascular grafts or various catheters are used as access to the vascular system of the patient. Typical flows within the vascular access are in the range of 1100 ml / min. The connection of the patient with the extracorporeal circulation is usually via dialysis needles, with which the fistula or the vascular implant is punctured.

0003If, during treatment, the connection between the extracorporeal circulation and the vascular system loosens or a blood leak occurs in the extracorporeal circuit, bleeding of the patient can only be prevented if the extracorporeal blood flow is stopped within a few minutes. Therefore, extracorporeal blood circuits are generally equipped with protection systems that permanently reduce arterial and venous pressure (P_art. or P_ven.Within the system, monitor the entry of air into the extracorporeal circuit.

0004In the event of an alarm, the blood treatment is stopped, the venous clamp is closed and an audible and visual warning signal is triggered. The pressure measurement based protection system responds when the arterial or venous pressure in the extracorporeal circuit changes by more than ± 60 torr. Here, the alarm limits are chosen so that a change in position of the patient does not trigger an alarm.

0005If the connection between the patient and the machine detaches at the arterial connection, ie, at that cannula which produces the blood flow from the patient to the extracorporeal circuit, the pressure-based machine-side protection system responds quickly, as explained below. The dialysis cannula represents the highest flow resistance in the extracorporeal system. When air is drawn in via the cannula into the arterial vacuum system of the extracorporeal circuit, the flow resistance of the cannula decreases by a factor of 10 in proportion to the density difference between blood and air³, Thus, the arterial vacuum breaks down abruptly in the extracorporeal circuit.

0006In the event that the venous cannula separates from the vascular access, however, the response of the pressure-based protection system is not always guaranteed. On the venous side, the purified blood is supplied to the patient with overpressure, wherein the venous pressure is proportional to the flow rate of the blood pump. Penetration of air through the cannula in the extracorporeal circulation as it would be the case on the arterial vacuum side is thus excluded. Therefore, the flow resistance of the venous cannula does not change and the venous machine pressure decreases only by the amount of pressure in the vascular access of the patient. Thus, the venous pressure change in the extracorporeal circuit is usually too small to trigger a response of the pressure-based protection system. Only in the case that the venous cannula after slipping out of the vascular access is well below the fistula, the additional hydrostatic pressure difference between venous pressure sensor and cannula causes a machine alarm.

0007Even in the case of a blood leak in the venous tube system, it may happen that the resulting venous pressure drop is insufficient to ensure release of the existing pressure-based protection system.

0008In addition to the above method, in which the pressure in the arterial branch of the extracorporeal circuit is monitored to detect slippage of the arterial cannula and monitored independently of the pressure monitoring in the arterial branch of the pressure in the venous branch of the extracorporeal circuit to slipping out of the venous Recognize cannula, monitoring systems are known to monitor the propagating pressure pulses in the extracorporeal circuit.

0009The <patcit id="pcit0001" dnum="WO9710013A"><text>WO 97/10013</text></patcit> describes a dialysis machine with such a monitoring system that monitors the pressure pulses in the venous blood line generated in the arterial blood line by the blood pump.

0010The invention has for its object to provide a method for monitoring a vascular access during an extracorporeal blood treatment that both a safe detection of slipping out of the venous cannula from the vascular access and a reliable detection of a blood leak in the venous branch of the extracorporeal circulation allowed and a low apparative Effort required. This object is achieved with the features of claim 1.

0011Another object of the invention is to provide a device for extracorporeal blood treatment with a device for monitoring a vascular access, which detects both slipping out of the venous cannula from the vascular access and a blood leak in the venous branch of the extracorporeal circuit with high reliability and only one requires little equipment. The solution of this object is achieved according to the invention with the features of claim 6.

0012The method according to the invention can be designed as a machine-integrated protection system. Here, use is made of sensors that are already present in the known blood treatment devices. Thus, the machine-side change for implementation of the protection system is limited only to a modification of the machine control.

0013The inventive method is based on that both the pressure in the arterial branch and the pressure in the venous branch of the extracorporeal circuit is monitored to detect slipping out of the venous cannula from the vascular access or a blood leak in the venous branch of the extracorporeal circuit. From the pressure in the arterial and venous branch of the extracorporeal circuit characteristic values ​​are calculated for the state of the vascular access, which are then evaluated to detect a faulty vascular access.

0014With the method according to the invention not only a slipping out of the venous cannula and a blood leak in the venous branch of the extracorporeal circuit can be reliably detected, but also slipping out of the arterial cannula and a blood leak in the arterial branch of the extracorporeal circuit.

0015The inventive method can also be combined with other methods for detecting a faulty vascular access. This further increases the security of the monitoring system.

0016In the event that the vascular access is faulty, an acoustic and / or visual alarm is preferably given. In addition, the blood flow in the extracorporeal circuit can be interrupted to prevent blood loss. An interruption of the blood flow is possible in the known devices for extracorporeal blood treatment in that the arranged in the extracorporeal circulation blood pump stopped and / or arranged in an extracorporeal circuit safety valve, z. B. a hose clamp is closed.

0017A monitoring of the defective vascular access with the method according to the invention can be carried out not only in devices for hemodialysis, hemofiltration and hemodiafiltration, but also in the known cell separators, in which the blood of a donor in an extracorporeal circuit is subjected to centrifugation and thereby separated into its components.

0018In the following, the inventive method for monitoring a vascular access and a device for extracorporeal blood treatment with a device for monitoring the vascular access with reference to the drawings using an exemplary embodiment is explained in more detail.

Show it:

0019<dl id="dl0001"><dt>Fig. 1</dt><dd>a table showing the influences that contribute to a change of pressure in the arterial and venous branch of the extracorporeal circuit,</dd><dt>Fig. 2</dt><dd>An embodiment of an apparatus for extracorporeal blood treatment with a device for monitoring the vascular access in a simplified schematic representation,</dd><dt>Fig. 3</dt><dd>a flow chart of the monitoring device,</dd><dt>Fig. 4</dt><dd>the arterial and venous pressure as a function of the blood flow in the extracorporeal circulation,</dd><dt>Fig. 5</dt><dd>the change of the arterial and venous pressure in the extracorporeal circulation with a change of position of the patient,</dd><dt>Fig. 6</dt><dd>the pressure conditions in the extracorporeal circulation when slipping out of the venous cannula from the vascular access and</dd><dt>Fig. 7</dt><dd>the pressure conditions in the case of a blood leak in the venous branch of the extracorporeal circulation.</dd></dl>

0020During extracorporeal blood treatment, the arterial and venous pressures P_ven. + P_art. measured in the extracorporeal circuit with a frequency f and the sum P_S from venous and arterial pressure (Equation 1).<maths id="math0001" num="(Gleichung 1)"><math display="block"><msub><mi mathvariant="normal">P</mi><mi mathvariant="normal">S</mi></msub><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">P</mi><mrow><mi>ven</mi><mn mathvariant="normal">.</mn></mrow></msub><mo mathvariant="normal">+</mo><msub><mi mathvariant="normal">P</mi><mi>kind</mi></msub></math><img file="EP1584339B1_D0001.tif" /></maths><dl id="dl0002" compact="compact"><dt>P_art.:</dt><dd>Measured value of the arterial pressure in the extracorporeal circuit.</dd><dt>P_ven.:</dt><dd>Measurement of venous pressure in the extracorporeal circuit.</dd></dl>

0021In addition, the difference ΔP of venous and arterial pressure is calculated:<maths id="math0002" num="(Gleichung 2)"><math display="block"><mi mathvariant="normal">.DELTA.P</mi><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">P</mi><mrow><mi>ven</mi><mn mathvariant="normal">.</mn></mrow></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">P</mi><mrow><mi>kind</mi><mn>.</mn></mrow></msub></math><img file="EP1584339B1_D0002.tif" /></maths>

0022The change in the sum of arterial and venous pressure is given by: <maths id="math0003" num="(Gleichung 3)"><math display="block"><mi mathvariant="normal">d</mi><mfenced><msub><mi mathvariant="normal">P</mi><mi mathvariant="normal">S</mi></msub></mfenced><mo mathvariant="normal">=</mo><msub><mi mathvariant="normal">P</mi><mi>SN</mi></msub><mo mathvariant="normal">-</mo><msub><mi mathvariant="normal">P</mi><mrow><mi>SN</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mrow></msub></math><img file="EP1584339B1_D0003.tif" /></maths><dl id="dl0003" compact="compact"><dt>P_SN:</dt><dd>Current measured value of the total pressure.</dd><dt>P_SN-1:</dt><dd>Previous measured value of the total pressure.</dd></dl>

0023The change of the pressure difference is:<maths id="math0004" num="(Gleichung 4)"><math display="block"><mi mathvariant="normal">d</mi><mfenced><mi mathvariant="normal">.DELTA.P</mi></mfenced><mo mathvariant="normal">=</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><msub><mi mathvariant="normal">P</mi><mi mathvariant="normal">N</mi></msub><mo mathvariant="normal">-</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><msub><mi mathvariant="normal">P</mi><mrow><mi mathvariant="normal">N</mi><mo mathvariant="normal">-</mo><mn mathvariant="normal">1</mn></mrow></msub></math><img file="EP1584339B1_D0004.tif" /></maths><dl id="dl0004" compact="compact"><dt>.DELTA.P_N:</dt><dd>Current measured value of the pressure difference.</dd><dt>.DELTA.P_N-1:</dt><dd>Previous measured value of the pressure difference.</dd></dl>

0024An erroneous vascular access is then concluded if the following conditions are met for N consecutive measurements:<ol id="ol0001" compact="compact"><li>a) Σ N d (P_s) is negative and less than a threshold M₁ (Equation 5)</li><li>b) <b>Σ</b> N d (ΔP) is negative and less than a threshold M₂ (Equation 6)</li></ol>

0025In this case either the venous cannula has slipped out or there is a blood leak in the venous branch of the extracorporeal circuit.

0026From the table (<figref idref="f0001">FIG. 1</figref>) shows which influences contribute to the change of venous and arterial pressure in the extracorporeal circulation. From the table it can be seen that in addition to the slipping out of the venous cannula and a blood leak in the venous branch and slipping out of the arterial cannula and a blood leak in the arterial branch of the extracorporeal circuit can be detected.

0027Slippage of the arterial cannula or a blood leak in the arterial branch of the extracorporeal circuit can then be inferred if the following conditions are met:<ol id="ol0002" compact="compact"><li>a) Σ N d (P_s) is positive and greater than a threshold M₃ (Equation 7)</li><li>b) Σ N d (ΔP) is positive and greater than a threshold value M₄ (Equation 8)</li></ol>

0028<figref idref="f0002">FIG. 2</figref> shows a simplified schematic representation of a dialysis machine with a device for monitoring the vascular access.

0029As a blood treatment device, the dialysis apparatus has a dialyzer 1, which is subdivided by a semipermeable membrane 2 into a blood chamber 3 and a dialysis fluid chamber 4. At the inlet of the blood chamber, an arterial blood line 5 is connected, in which a peristaltic blood pump 6 is connected. Downstream of the blood chamber 3, a venous blood line 7 leads from the outlet of the blood chamber to the patient. Into the venous blood line 7, a drip chamber 8 is connected. At the ends of the arterial and venous blood lines 5, 7 cannulas 5a, 7a are connected, which are pricked into the patient. The arterial and venous blood lines are part of a designed as Disposible hose line system.

0030In a dialysis fluid source 9, fresh dialysis fluid is provided. From the dialysis fluid source 9, a dialysis fluid supply line 10 leads to the inlet of the dialysis fluid chamber 4 of the dialyzer 1, while a dialysis fluid discharge line 11 leads from the outlet of the dialysis fluid chamber to a drain 12.

0031The dialysis machine can still have other components, eg. As a balancing device and an ultrafiltration device, etc., have, which are not shown for the sake of clarity.

0032To interrupt the blood flow, a shut-off terminal 13 is provided on the venous blood line 7 downstream of the drip chamber 8, which is actuated electromagnetically. The arterial blood pump 6 and the venous shut-off 13 are controlled by control unit 16 via control lines 14, 15.

0033The device 17 for monitoring the vascular access has an arterial pressure sensor 18 monitoring the pressure in the arterial blood line 5 and a venous pressure sensor 19 monitoring the pressure in the venous blood line 7. The measured values ​​of the pressure sensors 18; 19 are transmitted via data lines 20, 21 to a computing unit 22 which calculates characteristic values ​​from the measured values ​​for the state of the vascular access. In a memory unit 23, which is connected via a data line 24 to the arithmetic unit 22, the intermediate results obtained during the calculation are stored. To evaluate the characteristic values ​​for the vascular access, the monitoring unit has an evaluation unit 25, which is connected to the arithmetic unit via a data line 26. The evaluation unit 25 is connected via a control line 27 to an alarm unit 28, which is connected via a control line 29 to the control unit 16.

0034Hereinafter, the operation of the monitoring device 17 will be described with reference to FIG <figref idref="f0003">FIG. 3</figref> described in detail.

0035First, the number N of successive measured values ​​to be used for the evaluation, the measuring frequency f and the threshold values ​​M₁ and M₂ established. These values ​​can be stored in the memory unit 23 or also specified by the user (step 1).

0036By evaluating N successive measured values, the susceptibility of the protection system, eg. B. reduced in short-term artificial pressure fluctuations. The value for N is an integer and depends on the frequency f at which the pressure values ​​are determined. It can be adapted to the respective damping D of the pressure sensors. For N, the following boundary condition applies:<maths id="math0005" num="(Gleichung 9)"><math display="block"><mi mathvariant="normal">N</mi><mo>></mo><mi>f</mi><mo>⋅</mo><mi mathvariant="normal">D</mi></math><img file="EP1584339B1_D0005.tif" /></maths>

0037At a typical measurement frequency f of z. B. 1/3 Hz and an attenuation of about 18 s, N should therefore be> 6. This ensures that the pressure drop is completely detected.

0038The negative thresholds M₁ and M₂ indicate the sensitivity of the protection system. Generally, the smaller M₁ and M₂The higher the threshold at which a machine alarm is triggered. To ensure that the protection system responds, the values ​​for M₁ and M₂ however, be greater than the negative value of venous pressure in the vascular access.

0039The arterial fistula pressure drops slightly after slipping out of the venous cannula from the vascular access through the bleeding at the venous puncture site. This effect can be achieved by the appropriate choice of M₂ be taken into account, the condition M₁&lt;M₂ must apply. Suitable values ​​are z. B. M₁= -15 Torr and M₂= -10 Torr.

0040The response time of the protection system <i>T</i> is given by:<maths id="math0006" num="(Gleichung 10)"><math display="block"><mi>τ</mi><mo>=</mo><mfrac><mi mathvariant="normal">N</mi><mi mathvariant="normal">f</mi></mfrac></math><img file="EP1584339B1_D0006.tif" /></maths>

0041During the dialysis treatment, the arterial and venous pressures P are detected by means of the pressure measuring sensors 18, 19_art., P_ven. at the measuring frequency f in N consecutive measurements (step 2).

0042The computing unit 22 calculates the sum P after each measurement according to equation 1_s of venous and arterial pressure and according to equation 2 the difference .DELTA.P of the venous and arterial pressure. These values ​​are stored in the storage unit 23. According to Equation 3, the arithmetic unit 22 calculates the difference d (P_s) between the sum P_SN the venous and arterial pressure of a subsequent measurement and the sum P_SN-1 the venous and arterial pressure of a previous measurement. The difference d (ΔP) between the difference d (ΔP) of the arterial and venous pressure of a previous measurement ΔP_N and the difference ΔP_N-1 The arithmetic unit 22 calculates the arterial and venous pressure of a subsequent measurement according to equation 4. These measured values ​​are also stored in the memory unit 23. The sum changes d (p_S) of the N consecutive measurements are then used to calculate a first value W characteristic of the vascular access condition₁ in the arithmetic unit 22 according to equation 5 added. To calculate a second value W characteristic of the vessel condition₂ In the arithmetic unit 22, the difference changes d (ΔP) are added according to equation 6 (step 3).

0043The evaluation unit 25 checks the sign of the two characteristic values ​​W₁ and W₂, Are the first or the second characteristic value W₁, W₂ negative, no alarm occurs (step 4). However, if both the first and second characteristic values ​​W₁, W₂ are negative, the characteristic values ​​in the evaluation unit 25 are compared with the first and second threshold values ​​M1, M2 (step 5).

0044In the event that both W₁ less than M₁ as well as W₂ small M₂, the evaluation unit 25 outputs an alarm signal to the alarm unit 28. The alarm unit 28 generates an audible and / or visual alarm and controls the control unit 16, which in turn stops the blood pump 6 and closes the obturator 13. This ensures that in the event that the venous cannula 7a has slid out or there is a leak in the venous blood line 7, the patient is not endangered.

0045In an analogous manner, however, according to equations 7 and 8, a faulty vessel state can also be concluded when both the first characteristic value W₁ as well as the second characteristic value W₂ are positive and the first characteristic value W₁ greater than a predetermined threshold value M₃ and the second characteristic value W₂ greater than a predetermined threshold value M₄ is. In this case, the arterial cannula has slipped out or there is a blood leak in the arterial branch of the extracorporeal circuit.

0046The arithmetic unit 22 with the memory unit 23 and the evaluation unit 25 may be part of the microcomputer, which is already present in the known dialysis devices.

0047If the dialysis device has an ultrafiltration device, the monitoring device is deactivated within the first one to two minutes after the ultrafiltration device has been switched on or off in order to avoid a false alarm.

0048The characteristic principles on which the method according to the invention for monitoring the vascular access is based are explained below.

0049The pressures P measured in the extracorporeal circuit_art. and P_ven. are composed of the dynamic pressure in the extracorporeal system, which is generated by the flow of the blood pump, and the dynamic pressure in the vascular access of the patient.

0050Here, the dynamic pressure in the extracorporeal system is a function of the extracorporeal blood flow as well as the sum of the flow resistances in the extracorporeal circuit. Since arterial and venous flow resistance differ due to the different geometry of the perfused components, the pressure sum P_s also a function of blood flow.

0051In general, in the known blood purification method, the delivery rate of the blood pump Q_B set to a fixed value. Thus, the sum of the flow resistances in the extracorporeal circulation with constant viscosity of the blood is also constant. An increase in viscosity, z. As by ultrafiltration, long-term leads to the lowering of the arterial negative pressure and to increase the venous overpressure. Consequently, the pressure behavior with constant increase in viscosity is identical to a small increase in blood flow.

0052<figref idref="f0004">FIG. 4</figref> shows the extracorporeal pressures as a function of blood flow Q_B at constant viscosity (fistula flow Q_F = 1255 ml / min, arterial fistula pressure P_{F art.} = 27 Torr, venous fistula pressure P_Fven. = 17 torr).

0053The above and all subsequent measurements were made during a simulated dialysis treatment. As a vascular access a hose segment with an inner diameter of 8 mm was used, which was connected to a gear pump. To measure the flow within the vascular access, a Doppler flowmeter was used. The arterial and venous pressures within the vascular access (P_fistula) were controlled with two pressure gauges and could be adjusted via hose clamps. All measurements used water (T = 37 ° C). For vascular puncture cannulas were used, which were connected via two conventional tube systems with the dialysis machine.

0054The dynamic pressure in the patient's vascular access, referred to below as fistula pressure, is also a function of blood viscosity, systemic blood pressure, and systemic vascular flow resistance. The fistula pressure is thus a patient-specific parameter and additionally depends on the type of vascular access, the viscosity of the blood and the vascular system that supplies the vascular access with blood. Similar to the dynamic pressure in the extracorporeal system, a change in the fistula pressure, z. B. by blood pressure fluctuation, viscosity increase or change in position of the patient to change both the arterial and the venous pressure value.

0055<figref idref="f0004">FIG. 5</figref> shows the behavior of extracorporeal pressures at constant effective blood flow Q_Bif the position of the patient changes by Ah = -33.5 cm relative to the extracorporeal pressure sensors (Q._B= 300 ml / min, Q_F= 1252 ml / min; Pressure in the vascular access: P_{F art.} = 27 Torr, P_{F ven.} = 17 torr). This is z. As is the case when the patient lies down or drives down his couch. Here, the arterial and venous pressure values ​​are reduced by the amount of the hydrostatic pressure difference (about 0.78 Torr per cm height difference between pressure sensor and fistula). Since changes in the position of the patient, the arterial and venous pressure in the extracorporeal circuit by the same value, the pressure difference .DELTA.P remains constant. On the other hand, the sum of the pressures P decreases_s by twice the amount of hydrostatic pressure difference.

0056This behavior manifests itself (though in an abraded form) even with a fall in blood pressure during treatment. In this case, the arterial and venous pressure in the extracorporeal circulation also decreases.

0057<figref idref="f0005">FIG. 6</figref> shows the pressure conditions when slipping out of the venous dialysis cannula from the patient's fistula (Q_B= 300 ml / min, Q_F= 1254 ml / min, P_{F art.}= 27 Torr, P_{F ven.} = 17 torr). The pressure on the venous sensor of the extracorporeal circuit (P_ven.) decreases within about 15-20 seconds by the amount of venous fistula pressure. The delay time is due to the electronic damping of the extracorporeal pressure signals. The arterial pressure value (P_art.) is reduced only slightly within the first few minutes, as explained below.

0058The loss of blood, which is due to the open venous puncture site and leads to a decrease in fistula pressure, can be roughly estimated by the energy conservation law:<maths id="math0007" num="(Gleichung 11)"><math display="block"><mi>P</mi><mo>⋅</mo><mi>V</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>M</mi><mo>⁢</mo><msup><mi>v</mi><mn>2</mn></msup></math><img file="EP1584339B1_D0007.tif" /></maths> with the following abbreviations:<dl id="dl0005" compact="compact"><dt>P:</dt><dd>pressure</dd><dt>V:</dt><dd>volume</dd><dt>M:</dt><dd>Dimensions</dd><dt>v:</dt><dd>speed</dd></dl>

0059With V = M / ρ follows for the velocity of the blood jet from the open puncture site: <maths id="math0008" num="(Gleichung 12)"><math display="block"><mi>v</mi><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mo>⁢</mo><mi>P</mi></mrow><mi mathvariant="normal">ρ</mi></mfrac></msqrt></math><img file="EP1584339B1_D0008.tif" /></maths><dl id="dl0006" compact="compact"><dt>ρ:</dt><dd>density</dd></dl>

0060At a venous fistula pressure of 17 Torr (= 22.6 mbar) and a blood density of 1.0506 g / cm³ (37 ° C), the jet velocity is about 2.1 m / s. Assuming a constant opening of the puncture site, the volume flow in the case of a cylindrical jet profile is given by:<maths id="math0009" num="(Gleichung 13)"><math display="block"><mi>Q</mi><mo>=</mo><mi mathvariant="normal">π</mi><mo>⋅</mo><msup><mi>r</mi><mn>2</mn></msup><mo>⋅</mo><mi>v</mi></math><img file="EP1584339B1_D0009.tif" /></maths>

0061With a typical cannula diameter of 1.6, this results in a value of about 250 ml / min. (= 1/5 of the fistula flow). In vivo, the open puncture site swells, making the effective hole diameter smaller than the cannula diameter. Thus, the specified value is to be regarded as the upper limit.

0062As the pressure and flow are proportional, the venous fistula pressure is consequently reduced by 17/5 = 3.4 Torr (Hagen-Pbiseuille law). Due to the reduced venous fistula pressure, the arterial extracorporeal pressure drops by the same amount. However, since the arterial pressure change is always smaller than the venous pressure change, both P decreases_s as well as ΔP.

0063<figref idref="f0005">FIG. 7</figref> shows the pressure conditions in case of a blood leak in the venous tubing system. For this purpose, the venous tube was punctured below the drip chamber with an injection cannula (Q_B= 300 ml / min, Q_F= 1250ml / min, P _{F art.} = 27 Torr, P_{F ven.} = 17 Torr, leak rate 50 ml / min). The pressure on the venous sensor decreases at a leak rate of 50 ml / min within about 15-20 s by about 33 Torr. The arterial pressure, however, does not change appreciably. Analogous to<figref idref="f0005">FIG. 6</figref> both ΔP and P decrease_SThus, the sum changes according to Equations 6 and 7 are negative in both cases.