System and Method For Measuring Pressure of Fluid Flow

Abstract

An apparatus for measuring pressure within a fluid path includes a housing defining the structure of the apparatus. The housing includes a fluid path that extends through the housing and allows a fluid to pass through the housing. The apparatus also includes a first volume chamber that is in fluid communication with the fluid path and has a first volume chamber opening, and a second volume chamber with a second volume chamber opening that is less than the first volume chamber opening. A diaphragm separates the first volume chamber from the second volume chamber and fluidly disconnects the second volume chamber from the fluid path. The diaphragm deforms based upon the pressure within the fluid path. The apparatus also includes an interface that is connectable to a pressure sensor, and the second volume chamber is in fluid communication with the interface.

Claims

1. An apparatus for measuring pressure within a fluid path, the apparatus comprising: a housing defining the structure of the apparatus and having a fluid path at least partially extending through the housing, the fluid path configured to allow a fluid to pass through the housing; a first volume chamber in fluid communication with the fluid path and having a first volume chamber opening; a second volume chamber having a second volume chamber opening, the second volume chamber opening being smaller than the first volume chamber opening; a diaphragm separating the first volume chamber from the second volume chamber and fluidly disconnecting the second volume chamber from the fluid path, the diaphragm configured to deform based upon the pressure within the fluid path; and an interface connectable to a pressure sensor, the second volume chamber in fluid communication with the interface.

2. An apparatus according to claim 1, wherein the housing includes a first portion and a second portion, the first volume chamber located within the first portion, the second volume chamber located in the second portion, the diaphragm located between the first and second portion.

3. An apparatus according to claim 2, wherein the second portion is an air manifold.

4. An apparatus according to claim 2, wherein the first portion is disposable and configured to be disconnected from the second portion.

5. An apparatus according to claim 2, further comprising a gasket extending between the first and second portion, the gasket configured to prevent air leakage when the first and second portions are coupled.

6. An apparatus according to claim 5, wherein the gasket includes an opening therethrough, the opening defining at least a portion of the second volume chamber.

7. An apparatus according to claim 2, wherein the fluid path at least partially extends through the first portion of the housing

8. An apparatus according to claim 2, wherein the diaphragm is ultrasonically welded to the first portion, thereby sealing the first volume chamber.

9. An apparatus according to claim 1, wherein the housing includes a vent port in fluid communication with the second volume chamber via a vent channel, the vent port and vent channel configured to allow the second volume chamber to vent as the diaphragm deforms.

10. An apparatus according to claim 9, further comprising a vent valve located on the vent port.

11. An apparatus according to claim 1, wherein the diaphragm is configured to deform into the second volume chamber if the pressure within the fluid path is positive.

12. An apparatus according to claim 1, wherein the diaphragm is configured to deform into the first volume chamber if the pressure within the fluid path is negative.

13. An apparatus according to claim 1, wherein a wall of the second volume chamber has a curved surface, the diaphragm configured to deform to the curved surface at a maximum pressure within the fluid path.

14. An apparatus according to claim 1, wherein the housing includes an air path between the second volume chamber and the interface.

15. An apparatus according to claim 14, wherein the second volume chamber includes a recess located within a wall of the second volume chamber, the recess configured to prevent the diaphragm from occluding the air path.

16. An apparatus according to claim 1, wherein the housing includes a wall between the first volume chamber and the fluid path, the wall including one or more holes extending through the wall to fluidly connect the first volume chamber and the fluid path.

17. An apparatus according to claim 1, further comprising a pressure sensor connectable to the interface and configured to measure the pressure within the fluid path.

18. An apparatus according to claim 1, wherein the first volume chamber includes a first volume and the second volume chamber includes a second volume, the second volume being less than the first volume.

19. An apparatus according to claim 1 wherein a ratio of the size of the second volume chamber opening to the first volume chamber opening is between 4:1 and 9:1.

20. An apparatus according to claim 1, wherein the first volume chamber is a liquid chamber, the first volume configured to fill with at least a portion of the fluid passing through the fluid path.

21. An apparatus according to claim 1, wherein the second volume chamber is an air chamber.

22. A method for monitoring pressure within a fluid path, the method comprising: fluidly connecting a pressure monitoring device to a fluid flow system, the pressure monitoring device comprising: a housing defining the structure of the apparatus and having a fluid path at least partially extending through the housing, the fluid path configured to allow a fluid to pass through the housing, a first volume chamber in fluid communication with the fluid path and having a first volume chamber opening, a second volume chamber having a second volume chamber opening, the second volume chamber opening being smaller than the first volume chamber opening, a diaphragm separating the first volume chamber from the second volume chamber and fluidly disconnecting the second volume chamber from the fluid path, and an interface connectable to a pressure sensor, the second volume chamber in fluid communication with the interface; flowing a fluid through the pressure monitoring device via the fluid path, thereby creating a pressure within the fluid path, a negative pressure within the fluid path causing the diaphragm to deform into the first volume chamber, a positive pressure within the fluid path causing the diaphragm to deform into the second volume chamber and compress the second volume; and measuring the pressure within the fluid path using a pressure monitoring device, the pressure within the fluid path being a function of an amount of compression or expansion of the second volume.

23. A method according to claim 22, wherein the housing includes a first portion and a second portion, the first volume chamber located within the first portion, the second volume chamber located in the second portion, the diaphragm located between the first and second portion.

24. A method according to claim 23, wherein the second portion is an air manifold.

25. A method according to claim 23, wherein the first portion is disposable and configured to be disconnected from the second portion.

26. A method according to claim 23, further comprising a gasket extending between the first and second portion, the gasket configured to prevent air leakage when the first and second portions are coupled.

27. A method according to claim 26, wherein the gasket includes an opening therethrough, the opening defining at least a portion of the second volume chamber.

28. A method according to claim 23, wherein the fluid path at least partially extends through the first portion of the housing.

29. A method according to claim 23, wherein the diaphragm is ultrasonically welded to the first portion.

30. A method according to claim 22, wherein the housing includes a vent port in fluid communication with the second volume chamber via a vent channel, the vent port and vent channel configured to allow the second volume chamber to vent as the diaphragm deforms.

31. A method according to claim 30, further comprising a vent valve located on the vent port.

32. A method according to claim 22, wherein a wall of the second volume chamber has a curved surface, the diaphragm configured to deform to the curved surface at a maximum pressure within the fluid path.

33. A method according to claim 22, wherein the housing includes an air path between the second volume chamber and the interface.

34. A method according to claim 33, wherein the second volume chamber includes a recess located within a wall of the second volume chamber, the recess configured to prevent the diaphragm from occluding the air path.

35. A method according to claim 22, wherein the housing includes a wall located between the first volume chamber and the fluid path, the wall including one or more holes extending therethrough to fluid connect the first volume chamber and the fluid path.

36. A method according to claim 35, wherein the wall is configured to prevent liquid from the fluid path from entering the first volume chamber.

37. A method according to claim 22 wherein the first volume chamber has a first volume and the second volume chamber has a second volume, the second volume being less than the first volume.

38. A method according to claim 22, wherein the first volume chamber is a liquid chamber, the first volume configured to fill with liquid passing through the fluid path.

39. A method according to claim 22, wherein the second volume chamber is an air chamber.

40. A method according to claim 22, further comprising connecting the pressure monitoring device to the interface.

41. A method according to claim 22, wherein the fluid flow system is a blood processing device.

42. An apparatus for measuring pressure within a fluid path, the apparatus comprising: a housing defining the structure of the apparatus and having a fluid path at least partially extending through the housing, the fluid path configured to allow a fluid to pass through the housing; a first volume chamber in fluid communication with the fluid path and having a first volume; a second volume chamber having a second volume, the second volume being less than the first volume; a diaphragm separating the first volume chamber from the second volume chamber and fluidly disconnecting the second volume chamber from the fluid path, the diaphragm configured to deform based upon the pressure within the fluid path; and an interface connectable to a pressure sensor, the second volume chamber in fluid communication with the interface.

43. An apparatus according to claim 42, wherein the housing include a first portion and a second portion, the first volume chamber located within the first portion, the second volume chamber located in the second portion.

44. An apparatus according to claim 43, further comprising a gasket extending between the first and second portion, the gasket configured to prevent air leakage when the first and second portions are coupled.

45. An apparatus according to claim 44, wherein the gasket includes a hole therethrough, the hold defining the second volume chamber opening.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The foregoing features of the invention will be more readily understood by reference to the following detailed description, taken with reference to the accompanying drawings, in which:

[0023] FIG. 1 schematically shows a pressure measurement device for measuring the pressure within a fluid path, in accordance with embodiments of the present invention.

[0024] FIG. 2 schematically shows a cross-sectional view of the pressure measurement device shown in FIG. 1, in accordance with some embodiments of the present invention.

[0025] FIG. 3 schematically shows a bottom view of an air manifold section of the pressure measurement device shown in FIG. 1, in accordance with some embodiments of the present invention.

[0026] FIG. 4 schematically shows a fluid flow section of the pressure measurement device shown in FIG. 1, in accordance with some embodiments of the present invention.

[0027] FIG. 5 schematically shows a cross-sectional view of an alternative pressure measurement device, in accordance with additional embodiments of the present invention.

[0028] FIG. 6 schematically shows a bottom view of an air manifold section of the alternative pressure measurement device shown in FIG. 5, in accordance with some embodiments of the present invention.

[0029] FIG. 7A schematically shows a gasket for use with the additional alternative pressure measurement device shown in FIG. 5, in accordance with further embodiments of the present invention

[0030] FIG. 7B schematically shows a cross-sectional view of a pressure measurement device with an alternative gasket, in accordance with further embodiments of the present invention.

[0031] FIG. 8 schematically shows a cross-sectional view of an additional alternative pressure measurement device, in accordance with further embodiments of the present invention.

[0032] FIG. 9 schematically shows a fluid flow section of the additional alternative pressure measurement device shown in FIG. 8, in accordance with some embodiments of the present invention.

[0033] FIG. 10 schematically shows a further alternative pressure measurement device for measuring the pressure within a fluid path, in accordance with various embodiments of the present invention.

[0034] FIG. 11A schematically shows a top view of a fluid flow section of the pressure measurement device shown in FIG. 10, in accordance with some embodiments of the present invention.

[0035] FIG. 11B schematically shows a bottom view of the fluid flow section of the pressure measurement device shown in FIG. 10, in accordance with some embodiments of the present invention.

[0036] FIG. 11C schematically shows a top view of a fluid flow section of the pressure measurement device shown in FIG. 10 with the diaphragm secured, in accordance with some embodiments of the present invention.

[0037] FIG. 12 schematically shows an additional alternative embodiment of a pressure measurement device in accordance with various embodiments of the present invention.

[0038] FIGS. 13 and 14 show an exemplary device's pressure response, in accordance with various embodiments of the present invention.

[0039] FIGS. 15 and 16 show a single exemplary device's pressure response repeatability, in accordance with some embodiments of the present invention.

[0040] FIGS. 17 and 18 show pressure measurements at a pump's outlet and inlet, in accordance with various embodiments of the present invention.

[0041] FIGS. 19A-19C schematically show a cross-section of an exemplary pressure monitoring device during use, in accordance with various embodiments of the present invention.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

[0042] FIG. 1 schematically shows a pressure measurement device 100 in accordance with various embodiments of the present invention. The device 100 includes a housing 110 that defines the structure of the device 100. The housing 110 may be a single piece or a multi-piece structure. For example, the housing 110 may have a first/bottom housing 120 and a second/top housing 130. The housing components may be assembled in a variety of ways including, but not limited to, clamping, adhesives, solvent bonding, thermal bonding, snap-fit, ultrasonic welding, and laser welding. Alternatively, the bottom and top housing 120/130 may be connected together (and, as discussed in greater detail below, subsequently disconnected) via a snap/clamp mechanism that allows a user to connect and disconnect the portions of the housing 110 as needed.

[0043] To facilitate fluid flow through the device 100, as shown in FIG. 2, the device 100 (e.g., the bottom housing 120, also referred to as the fluid housing below) may include an inlet port 140, an outlet port 150, and a fluid path 160 extending between the inlet 140 and outlet 150. When connected to a fluid flow/processing device (e.g., a blood processing device), fluid (e.g., blood or a blood component) may enter the pressure measurement device 100 via the inlet 140, flow through the fluid path 160, and exit the device 100 via the outlet 150. It should be noted that, although much of the discussion herein refers to port 140 as an inlet, and port 150 as an outlet, the ports 140/150 also may be respectively used as outlet and inlet ports. In other words, fluid may enter the device 100 via port 150, flow through the fluid path 160, and exit the device 100 via port 140.

[0044] As mentioned above, the device 100 may measure the pressure within the fluid path 160 as fluid (e.g., blood or blood components) is passing through the device 100. To that end, the fluid housing 120 may include a volume chamber (e.g., a fluid chamber 170) that is in fluid communication with the fluid path 160 such that fluid passing through the device 100 may enter the fluid chamber 170. In a similar manner, the top housing 130 (e.g., an air manifold/housing as discussed in greater detail below) may also include a volume chamber (e.g., an air chamber 180). To separate the fluid chamber 170 from the air chamber 180 and fluidly disconnect the air chamber 180 from the fluid path 160, the device 100 has a diaphragm 190 that extends between the housings 120/130. In some embodiments, the diaphragm 190 may be secured to and part of the fluid housing 120 and, as discussed in greater detail below, deform (e.g., into the fluid chamber 170 or air chamber 180 depending on whether the pressure is positive or negative) in response to the changes in pressure within the fluid path 160. The diaphragm 190 may be PVC film or other plastic material compatible with the fluid being sent through the device 100 and the fluid path 160.

[0045] As best shown in FIG. 2, the top housing 130 may include an interface 220 to which a pressure sensor/transducer 200 may be connected, and an air pathway 182 extending from the air chamber 180 to the interface 220. As discussed in greater detail below, the air pathway 182 allows pressure changes within the device 100/fluid path 160 to be translated to the pressure sensor/transducer 200. To prevent the air pathway 182 from becoming blocked by the diaphragm 190 as the diaphragm 190 deforms (e.g., in a max pressure scenario), the top housing 130 may include a recess 184 at the entrance to the air pathway 182. Furthermore to allow the air chamber 180 to vent in the presence of increased pressure and/or draw in air in the presence of a decreased pressure, the top housing 130 may also include a vent channel 212 and a vent port 214. To selectively control the flow in and out of the vent channel 212 via the vent port 214, the device 100 may include a vent valve 210 connected to the vent port 214.

[0046] It should be noted that, because the fluid passes through the fluid housing 120 and is separated from the top housing 130 via the diaphragm 190 (e.g., so that the fluid cannot enter the top housing 130 and the fluid chamber 170 is sealed), the bottom housing 120 essentially acts as a fluid housing (or blood flow unit in blood processing applications). Conversely, because the fluid never enters the top housing 130, the top housing 130 essentially acts as an air housing/manifold. Additionally, because the top housing 130 includes many of the more expensive components of the device 100 (e.g., the pressure sensor 200, the vent valve 210, etc.) and because the fluid never contacts any of the components of the top housing 130, the top housing 130 may be reusable and/or may be part of a larger device/machine (e.g., a blood processing device/system), whereas the fluid housing 120 may be disposable. Alternatively, in some applications and embodiments (e.g., in applications in which the fluid is corrosive, erosive, hazardous, or a biohazard), if a sufficiently inexpensive pressure sensor/transducer is used, the entire device 100 may be disposable.

[0047] As shown in FIGS. 2-4, the fluid chamber 170 and the opening 172 to the chamber 170 (e.g., approximately 2188 μL and 30×15 mm elliptic, 32×15 mm elliptic or 30×22 mm elliptic) may be considerably larger than the air chamber 180 and the opening 186 to the air chamber 180 (e.g., approximately 191 μL and 12 mm in diameter). In this manner, a larger membrane/diaphragm area can deflect toward the fluid/liquid chamber 170 than toward the air chamber 180. The ratio of fluid chamber opening 172 to the air chamber opening 186 may between 1.4:1 and 100:1. For example, the ratio of the fluid chamber opening 172 to the air chamber opening 186 may between 2.5:1 and 25:1 or between 4:1 and 9:1. Additionally, the openings 172/186 to the fluid and air chambers 170/180 may be any number of shapes (e.g., circular, elliptical, oval, square, rectangular etc.,) as long as the flow through the fluid path 160 and fluid chamber 170 is smooth and bubble free. Furthermore, the shape of the fluid chamber opening 172 need not be the same as the shape of the air chamber opening 186 (e.g., as shown in FIGS. 3 and 4, the air chamber opening 186 may be circular and the fluid chamber opening 172 may be elliptical).

[0048] By providing this unequal deformable membrane area, various embodiments of the present invention are able to accurately measure very large positive pressures and very large negative pressures (e.g., high vacuum), making the device 100 more robust than systems having equal chambers 170/180 and openings 172/186. For example, if the fluid chamber opening 172 is approximately 25.4 mm, and the air chamber opening 186 is 18 mm, the system/device 100 is able to measure positive pressures up to 700 mmHg with full scale (“FS”) error less than 0.5% and negative pressures up to 400 mmHg with FS error less than 1%.

[0049] Furthermore, by utilizing the unequal chambers 170/180 and openings 172/186, some embodiments can tolerate certain non-perfect membrane conditions, temperature variation, and, possibly, some membrane property changes. For example, various embodiments of the system/device 100 can tolerate an initial membrane deflection equivalent to a deflection caused by a 0.5 mmHg cross-membrane pressure differential as well as a 15° C. temperature variation without sacrificing the device performance and with only a small reduction of full scale accuracy (e.g., for 700 mmHg positive pressure, FS error goes up to 1.5% and for 400 mmHg negative pressure, FS error increases to 1.8%). In contrast, prior art systems that utilize equal chambers 170/180 and openings 172/186 (e.g., 25.4 mm) can only measure 240 mmHg negative pressure with an estimated FS error 2.75%.

[0050] It should be noted that the each of the chambers 170/180, like their respective openings 172/186) can have any number of shapes (e.g., rectangular, circular, oval, square, etc.). Additionally or alternatively, in some embodiments, the wall 188 of the air chamber 180 (FIG. 2) may rounded/curved. In this manner, when the diaphragm 190 deforms into the air chamber 180, the diaphragm 190 may conform to the shape of the wall 188 (e.g., when under maximum pressure). However, in some embodiments, the depth of the curved surface 188 may be slightly larger than the expected maximum diaphragm deflection. Additionally, as discussed above, the recess 184 will prevent the diaphragm 190 from blocking the air path 182 when exposed to maximum pressure and when the diaphragm 190 has reached maximum deflection into the air chamber 180.

[0051] During use, the user/technician may connect the fluid pressure monitoring device 100 to a fluid flow system (e.g., a blood processing system). For example, the user/technician may connect the inlet 140 to a fluid source (e.g., a whole blood bag, a patient, a source of anticoagulant, a blood component bag, etc.) and the outlet 150 to fluid flow/processing equipment (e.g., blood processing equipment such as centrifuges, pumps, blood cleaning devices or other equipment that can be used to separate whole blood or otherwise process blood) or a patient/donor (if returning blood components to the donor). Once the inlet 140 and outlet 150 are connected, the user may begin to flow the fluid/liquid through the device (e.g., the user may begin the blood processing procedure).

[0052] As the fluid/liquid passes through the device 100, the fluid/liquid will enter the fluid chamber 170 and the pressure within the fluid path 160 will cause the diaphragm 190 to deform. In particular, if the fluid path 160 is under a positive pressure, the diaphragm will deform into the air chamber 180, translating the positive pressure within the fluid path 160 to the air chamber 180 and air path 182, and ultimately to the pressure sensor/transducer 200 connected to the interface 220 (e.g., by compressing the air within the air chamber 180). Conversely, when the fluid path 160 is under a negative pressure (e.g., a vacuum), the diaphragm 190 will deform into the fluid chamber 170, causing the air chamber 180 to expand and, thus, translate the negative pressure to the pressure sensor/transducer 200.

[0053] In some embodiments, as the pressure sensor/transducer 200 measures the pressure within the fluid path 160, the device 100 may transmit/send/communicate the pressure information to the fluid flow/processing system (e.g., the blood processing device). If the fluid flow/processing system is so equipped (e.g., with a microprocessor or other controller), the blood processing system may then increase, decrease, or maintain the fluid flow within the fluid path 160 based upon the pressure measured by the pressure monitoring device 100.

[0054] Although the device described above and shown in FIGS. 2-4 only has the diaphragm 190 located between the air and fluid housings 130/120 of the device 100, as shown in FIGS. 5 and 6, other embodiments may include additional components. For example, in some embodiments, the device 100 may include a gasket 230 between the air and fluid housing 130/120. When the housings 120/130 are secured together, the gasket 230 may create a seal between the housings 120/130 to prevent air from leaking into or out of the chambers 170/180 from between the housings 120/130 (e.g., between the air manifold 130 and the diaphragm 190).

[0055] It should be noted that, in some embodiments, the gasket 230 may form at least part of the air chamber 180. For example, as best shown in FIG. 5, the air chamber 180 (e.g., with or without the recess 184) may be formed directly into the gasket 230 (e.g., as opposed to the body of the first housing 130) (FIG. 7A). Alternatively, in other embodiments, the air chamber 180 may still be formed within the first housing 130, and the gasket 230 can merely include a through-hole 232 that is sized similar to the air chamber 180. In such embodiments, the through-hole 232 in the gasket 230 may act as the opening 186 to the air chamber 180 to allow the diaphragm 190 to deform into the air chamber 180.

[0056] Alternatively, as shown in FIG. 7B, the gasket 230 may be a solid film with no through-hole. In such embodiments, the gasket 230 will deform into the air chamber 180 and the fluid chamber 170 with the diaphragm 190 (e.g., acting as part of the diaphragm 190 as the pressure within the fluid path 160 increases and decreased). In such embodiments, the plain/solid gasket 230 may be a thin flexible silicone rubber film that fully covers the air chamber opening 186 and applies no or minimal resistance to the diaphragm deformation.

[0057] The gasket 230 may be made from any number of materials including, but not limited to silicone rubber or a removable double adhesive film. For example, in embodiments in which the air chamber 180 is formed in the gasket 230, the gasket 230 may be a relatively thick silicone rubber. Alternatively, if the air chamber 180 is not formed in the gasket 230, the gasket 230 may a thin silicon rubber film. Regardless of the material and thickness chosen, the gasket material should have a non-sticky surface at the air chamber opening 186 on the air chamber 180 side (to prevent the diaphragm 190 from sticking the air chamber walls) and at the fluid chamber opening 172 on the fluid chamber 170 side where the gasket contacts the moving diaphragm 190 (to prevent the diaphragm 190 from sticking to the gasket).

[0058] In some applications, it may be beneficial to at least partially isolate the fluid chamber 190 from the fluid path 160. To that end, as shown in FIGS. 8 and 9, some embodiments of the fluid housing 120 may include a wall 132 that separates the fluid chamber 170 from the fluid path 160. The wall 132 may include one or more holes 134A/B that fluidly connect the fluid chamber 170 and the fluid path 160 and allow the pressure within the fluid path 160 to be communicated to the fluid chamber 170. It should be noted that, in some embodiments, the wall 132 and the holes 134A/B may allow the liquid flowing through the device 100 to enter the fluid chamber 170. However, in other embodiments, the holes 134A/B may be sized such that the liquid flowing through the device does not enter the fluid chamber 170.

[0059] Although the embodiments discussed above have a fluid path 160 that extends straight through the device 100 (e.g., such that the inlet 140 and outlet 150 are aligned and on opposite sides of the housing 110), other embodiments may have different fluid path configurations. For example, as shown in FIGS. 10 and 11A-11C, the fluid path 240 may my U-shaped (FIG. 11B) and the inlet 140 and outlet 150 may be located on the same side of the housing 110. In such embodiments, the fluid/liquid may enter the inlet 140, flow through the U-shaped fluid path 240 and exit the device 100 through the outlet 150 on the same side of the device 100 as the inlet 140.

[0060] Like the embodiments discussed above, the fluid path 240 may be in fluid communication with the fluid chamber 170. For example, as best shown in FIG. 11A, the fluid housing 120 may include a wall 132 that separates the fluid chamber 170 from the fluid path 240, and one or more holes 134A/B that allow the pressure changes within the fluid path 240 to be translated to the fluid chamber 170 (e.g., to cause the diaphragm 190 to deform as discussed above). Alternatively, the fluid chamber 170 may be in direct fluid communication with the fluid path 240 (e.g., the fluid housing 120 may not include the wall 132 in a manner similar to that shown in FIGS. 2 and 4). Also like the embodiments discussed above, the diaphragm 190 may secured to/sealed to the fluid housing 120 (FIG. 11C).

[0061] Although the figures show and the embodiments discussed above have a rectangular housing 100, other embodiments can have different housing configurations. For example, as shown in FIG. 12, the housing 100 can be oval in shape (e.g., a shape similar to the shape of the fluid chamber 170) to reduce the overall size of the device 100. Alternatively, the housing 100 may circular, square, triangular, to name but a few. In some embodiments, the shape of the fluid chamber housing 120 can differ from the shape of the air chamber housing 130. For example, the air chamber housing 130 can be rectangular, while the fluid chamber housing 120 can be elliptical. Alternatively, the air chamber housing may be elliptical and the fluid chamber housing can be rectangular.

[0062] It is important to note that, although the embodiments described above are essentially standalone devices/systems that measure the pressure within the fluid path 160, other embodiments may be incorporated into the fluid processing device. For example, if the fluid processing device is a blood processing device, the pressure sensor 200 and the air manifold 130 may be incorporated into and part of the blood processing device. In such embodiments, the user may insert the fluid housing 120 into the blood processing device to connect the air manifold 130 and the fluid housing 120, and connect tubing within the blood processing system to the inlet 140 and outlet 150 of the fluid housing 120. The user/technician may then flow the liquid (e.g., blood or blood components) through the fluid housing 120, and the pressure sensor 200 can measure the pressure within the fluid path 160 (or fluid path 240) as described above.

Exemplary Study

[0063] Different fluid chamber and air chamber sizes, membrane materials and construction methods were tested, and a 32 mm×15 mm elliptic (equivalent to 21 mm circular) fluid chamber was designed and injection molded using PVC plastics. A 0.015″ (nominal 0.016″) PVC membrane was ultrasonically welded to the PVC substrate, and a 12 mm circular hole was punched through a 1/16″ thick silicone gasket as the main air chamber. The air manifold had a boss protruding into the circular air chamber to reduce the air volume. The total air volume was about 190 ul, including air channels in the air manifold and part of the plastic vent tubing. The parts were clamped together to form a sealed air chamber and the fluid chamber was connected to external sources, liquid and/or air.

[0064] Results are shown in FIGS. 13-16. For the results shown in FIGS. 13 and 14, four individual pressure interface devices were tested together on four different clamps with the same pressure source (connected). For the results shown in FIGS. 15 and 16, a single device was repeatedly tested ten times (positive and negative tests alternatively including switch of clamps and change of fluids—water and air). Each device was tested on two clamps and the results were averaged. FIG. 13 shows the positive pressure responses of four devices and FIG. 14 shows the negative pressure responses of the same four devices. FIGS. 15 and 16 show the single device repeatability for both positive and negative responses. There was no temperature variation. The full scale errors for the results shown are about 6% for the positive pressures at 600 mmHg and 12% for the negative pressures at −400 mmHg. Since the air volume was much larger than an optimal value, the full scale errors were quite large, so a fluid pressure-air chamber pressure correlation was needed for the measurement. The response curves were very repeatable from device to device and for the single device, and also the hysteresis (pressure increases to maximum and then decreases to 0) was very small with the largest less than 1%. FIGS. 17 and 18 are the results of dynamic pump tests in comparison with prior art pigtail pressure tubing. The pressure interface device (with correlation) has very good dynamic response and accuracy, and can measure up to positive 900 mmHg and negative 400 mmHg without significant errors.

Calculating Air and Fluid Chamber Openings and Volumes

[0065] FIGS. 19A-19C illustrate an unequal diaphragm pressure sensing interface configuration, which consists of an air chamber cavity on the left and a fluid (liquid) chamber cavity on the right with a diaphragm in between. The air chamber is smaller than the fluid chamber not by the depth or cross-sectional area shown in the sketch but by the diaphragm area it covers (e.g., the interface length shown in FIGS. 19A-19C), assuming the diaphragm areas covered by both chambers are circular (shown as a line in the cross-sectional sketch) with diameters d.sub.a and d.sub.f. The diaphragm is a one piece membrane covering the air chamber opening on the left and the fluid chamber opening on the right and has the same diameter as the fluid chamber opening, d.sub.f, with the edge ultrasonically welded to the fluid chamber substrate or fixed using other methods. Described below is how to determine, with a given membrane material (material properties and thickness), the minimum air chamber and fluid chamber depths, maximum initial air chamber volume, and maximum initial membrane deflection or air volume variation that can be tolerated, as well as the optimal air chamber opening and fluid chamber opening sizes.

[0066] Let V.sub.0 be the initial air chamber volume (including all channels and with perfectly flat diaphragm), P.sub.0 be the initial air pressure and T.sub.0 the initial air temperature, and assume the initial fluid (liquid) chamber pressure P.sub.f0=P.sub.0, which can be realized by venting both chambers to atmosphere before the fluid chamber is filled or flowing with liquid. Since a flexible plastic membrane will be used as the diaphragm, perfect diaphragm flatness is difficult to achieve even if the cross membrane pressure difference is zero. There will be always some initial membrane deformation, causing the true initial air chamber volume to deviate from its design volume V.sub.0. We use δV.sub.0 to represent this deviation, so the initial air volume is actually V.sub.0+δV.sub.0. Here, δV.sub.0 can be positive and negative. After the liquid chamber is filled or flowing with liquid, the fluid chamber pressure will be P.sub.f, and the air chamber pressure changes to P.sub.a, volume becomes V.sub.a and temperature T.sub.a. The diaphragm will be deflected toward either the air chamber or the fluid chamber depending on whether the fluid pressure P.sub.f is positive or negative. The magnitude of the deflection f.sub.m depends on the cross membrane pressure difference ΔP=P.sub.a−P.sub.f. Based on the Ideal Gas Law, PV=nRT, where R is the gas constant and n is the air molar mass (a fixed value for a sealed volume), we have:

P.sub.aV.sub.a/T.sub.a=nR=P.sub.0(V.sub.0+δV.sub.0)/T.sub.0  (1)

[0067] Let ΔT=T.sub.a−T.sub.0, ΔV=V.sub.a−(V.sub.0+δV.sub.0), and β=ΔT/T.sub.0, from Eq. (1), we have:

[00001]$\begin{array}{cc}{P}_a=\left(1+\beta \right)P_0\frac{V_0+{\mathrm{\delta V}}_0}{\left(V_0+\delta V_0+\Delta V\right)}& \left(2\right)\end{array}$

[0068] Here, the change of air chamber volume ΔV is caused by the diaphragm deformation under the cross membrane pressure difference ΔP, i.e., ΔV is a function of ΔP,

ΔV=f(ΔP)  (3)

[0069] With given β, P.sub.0, V.sub.0 and δV.sub.0, we still cannot solve Eq. (2) unless we know the function in Eq. (3). Since ΔV is caused by the membrane deformation, we can find f.sub.m under ΔP and then calculate ΔV from the deformed membrane geometry.

[0070] We assume the diaphragm is a circular isotropic elastic membrane with uniform thickness and diameter d, clamped at the edge, and under uniform pressure with initially flat membrane (δV.sub.0=0). Based on Fichter's analysis (NASA Technical Paper 3658, 1997), we have the theoretical solution as follows:

[0071] The deflection of membrane at any point with radius r from the center is

[00002]$\begin{array}{cc}\begin{array}{cc}w=\frac{d}{2}.Math.w_{2n}\left[1-{\left(\frac{2r}{d}\right)}^{2n+2}\right],& n=0,1,2,3,...\end{array}& \left(4\right)\end{array}$

[0072] The maximum deflection is at the center with r=0, so

[00003]$\begin{array}{cc}\begin{array}{cc}{f}_m=\frac{d}{2}\Sigma w_{2n},& n=0,1,2,3,...\end{array}& \left(5\right)\end{array}$

[0073] where the coefficients w0, w2, w4, . . . can be calculated with the following expressions,

[00004]$\begin{array}{cc}\begin{array}{c}{w}_0=\frac{n_0}{4}\\ w_2=\frac{1+8{\mathrm{an}}_{0}q}{512n_0^{4}q}\\ w_4=\frac{\left(1+8{\mathrm{an}}_{0}q\right)\left(5+8n_{0}q+32{\mathrm{an}}_{0}q\right)}{147456n_0^7{q}^2}\\ w_6=\frac{\left(1+8{\mathrm{an}}_{0}q\right)\left(55+192n_{0}q+704{\mathrm{an}}_{0}q+128n_0^2{q}^2+1344{\mathrm{an}}_0^2{q}^2+2176a^2{n}_0^2{q}^2\right)}{75497472n_0^{10}{q}^3}\\ w_8=\begin{array}{c}\begin{array}{c}\begin{array}{c}\left(1+8{\mathrm{an}}_{0}q\right)[259+\left(1366+5030a+288n_0^2\right)n_{0}q+\\ \left(1920+19008a+31744a^2+4608n_0^2\right)n_0^2{q}^2+\end{array}\\ (768+1395a+65408a^2+64512a^3+36864{\mathrm{an}}_0^2-\end{array}\\ 18432a^2{n}_0^2)n_0^3{q}^3]/15099494400n_0^{13}{q}^4\end{array}\\ \mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\\ \mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\\ \mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\end{array}\}& \left(6\right)\end{array}$

[0074] where

[00005]$a=\frac{3+\mu }{2},q=\frac{\Delta \mathrm{Pd}}{2Eh},$

with μ is Poisson ratio, E the elastic modulus and h the thickness of the membrane; and n.sub.0 is the solution of the following equation,

[00006]$\begin{array}{cc}\left(\frac{3-\mu }{2}\right)n_0+\left(\frac{3-\mu }{2}\right)n_2+\left(\frac{5-\mu }{2}\right)n_4+\left(\frac{5-\mu }{2}\right)n_6+\left(\frac{9-\mu }{2}\right)n_8+...+w_0+2w_2+3w_4+4w_6+5w_8+...=0& \left(7\right)\end{array}$

[0075] where n.sub.2, n.sub.4, n.sub.6, n.sub.8, . . . are related to n.sub.0 by the following equations,

[00007]$\begin{array}{cc}\begin{array}{c}2n_0{w}_2+n_2{w}_0=0\\ 3n_0{w}_4+2n_2{w}_2+n_4{w}_0=0\\ 4n_0{w}_6+3n_2{w}_4+2n_4{w}_2+n_6{w}_0=0\\ 5n_0{w}_8+4n_2{w}_6+3n_4{w}_4+2n_6{w}_2+n_8{w}_0=0\\ \mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\\ \mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\\ \mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\mathrm{.Math.}\end{array}\}& \left(8\right)\end{array}$

[0076] Or by direct expression as:

[00008]$\begin{array}{cc}\begin{array}{c}{n}_2=-\frac{\left(1+8{\mathrm{an}}_{0}q\right)}{64n_0^{2}q}\\ n_4=-\frac{\left(1+8{\mathrm{an}}_{0}q\right)\left[1+4n_{0}q\left(1+a\right)\right]}{6144n_0^5{q}^2}\\ n_6=-\frac{\begin{array}{c}\left(1+8{\mathrm{an}}_{0}q\right)[13+n_{0}q\left(96+128a\right)+\\ 576{\mathrm{an}}_0^2+n_0^2{q}^2\left(128+256a\right)]\end{array}}{4718592n_0^8{q}_3}\\ \begin{array}{c}{n}_8=-\left(1+8{\mathrm{an}}_{0}q\right)[39+n_{0}q\left(366+670a+288n_0^2\right)+\\ \begin{array}{c}\begin{array}{c}{n}_0^2{q}^2\left(960+4608a+3584a^2+4608n_0^2\right)+\\ n_0^3{q}^3(768+6272a+14208a^2+5632a^3+36864{\mathrm{an}}^2-\end{array}\\ 18432a^2{n}_0^2)/754974720n_0^{11}{q}^4\end{array}\end{array}\end{array}\}& \left(9\right)\end{array}$

[0077] Substituting Eq. (6) and Eq. (9) into Eq. (7), we can solve n.sub.0, so we can get the ws from Eq. (6). The membrane deflection is the summation of all ws, theoretically infinite terms. Fortunately, in general, the summation of the first five terms, w.sub.0, w.sub.2, w.sub.4, w.sub.6, w.sub.8, in Eq. (5) is sufficient to represent the true deflection f.sub.m. The higher number terms are very small in value and negligible. An iterative method can be used to solve the above equations.

[0078] The deformed membrane will have stress proportional to the deflection. The maximum stress occurs at the edge of the membrane, which can be estimated by the following formula,

[00009]$\begin{array}{cc}N=\Delta P\frac{d}{2}.Math.n_{2m},m=0,1,2,3,......& \left(10\right)\end{array}$

[0079] where n.sub.0, n.sub.2, n.sub.4, . . . are calculated from Eq. (9). By assuming a spherical shape of the deformed membrane (actually parabolic), which is a quite accurate estimation for small membrane deflection, the air chamber volume change ΔV can be related to the membrane deflection f.sub.m through the following formula,

[00010]$\begin{array}{cc}\Delta V=-\frac{\pi f_m}{24}\left(3d^2+4f_m^2\right)& \left(11\right)\end{array}$

[0080] Under positive fluid pressure, the membrane deflects toward the air chamber, use d.sub.a in place of the membrane diameter d, and the f.sub.m is negative because ΔP is negative. Under negative fluid pressure, the membrane deflects toward the fluid chamber, use d.sub.f in place of d and f.sub.m is positive.

[0081] Once ΔV is known, from the maximum expected fluid pressure P.sub.f to be measured, we can calculate the maximum air chamber volume that matches the deformed membrane shape (plus a safety volume or depth δf.sub.m). The total air volume V.sub.0 can be estimated as:

[00011]$\begin{array}{cc}{V}_0=\frac{\Delta V}{\left(1+\beta \right)P_0/\left(\Delta P+P_f+P_0\right)-1}+V_{ch}& \left(12\right)\end{array}$

[0082] where V.sub.ch is the air volume attributed from air channels, vent ports and other structures (the smaller the better), and the ΔV is calculated based on the maximum expected membrane deflection f.sub.m+safety depth δf.sub.m or maximum estimated pre-deflection f.sub.m0, whichever is larger. P.sub.f is gauge pressure and P.sub.0 equals local atmospheric pressure. The ΔP required to deform the membrane to satisfy the air chamber pressure-volume relationship defines the measurement error, i.e.,

Error (%)=ΔP/P.sub.f*100  (13)

Examples of Pressure Interface Design

[0083] As an example, a 0.016″ (0.406 mm) thick PVC membrane was chosen as the diaphragm, circular shape, with elastic modulus E=13.79 MPa, Poisson ratio 0.382, density 1.21 g/cm3. Let initial air pressure P.sub.0=760 mmHg (atmospheric pressure), T.sub.0=22° C.=295.15K and assume air chamber bottom is curved, matching the deformed membrane shape (smallest air volume), with a depth of 1.2 times the expected maximum air chamber membrane deflection. The target pressure measurement range is −300 mmHg to +600 mmHg (for high Hct red blood cell removal from the rotating centrifuge and returning to the donor on a centrifuge based blood apheresis instrument). To allow for fluctuations and tolerances, 100 mmHg may be added to both ends, i.e., from −400 mmHg to +700 mmHg, as the pressure sensing interface design requirement. The full scale measurement error is required to be less than 2%. Assume the portion of air volume contributed from the air channels, sensor & vent ports and other structures is fixed at V.sub.ch=24 ul, which cannot be changed (e.g., in this example). The diameters of the air chamber opening and the fluid chamber opening, d.sub.a and d.sub.f, may be determined and then based on the maximum expected membrane deflection to determine the minimum depths required for the air and fluid chambers. The total initial air volume V.sub.0 is equal to the sum of the air chamber volume and the air channel volume (24 ul in this example).

[0084] In the following, the expected performance of three equal diaphragm designs (d.sub.f=d.sub.a=12.7, 25.4 and 50.8 mm) and two unequal diaphragm designs (d.sub.f/d.sub.a=25.4/12.7 and 25.4/18.0) is compared. Below demonstrates how the unequal diaphragm design is better than the equal diaphragm design in terms of performance and robustness in some applications.

[0085] With Initially Perfect Flat Diaphragm (f.sub.m0=0),

[0086] In this example, the assumption is that everything is perfect, no initial membrane deflection, no temperature variation. When the design is capable of measuring maximum pressures (+700 mmHg or −400 mmHg), the goal is to see the accuracy the device can achieve. When the design is not able to reach maximum performance, the goal is to see how large a pressure the device can measure with a 2% full scale error. The air chamber volume is determined by the maximum membrane deflection f.sub.m under the highest positive pressure it can measure. The air chamber depth is equal to 1.2 times of f.sub.m (δf.sub.m=20% f.sub.m) to accommodate unexpected conditions.

[0087] Table I shows the predicted results. The results show that with the small air chamber opening (d.sub.a=12.7 mm), the pressure interface device can measure pressures up to 550 mmHg. In order to measure 700 mmHg, the air chamber opening may be increased to at least 18 mm. The fluid chamber opening size has no effect on positive pressure measurement. However, the air chamber size has effect on the negative pressure measurement. With equal diaphragm design, the pressure interface cannot measure negative 400 mmHg when d.sub.a is 25.4 mm and less. Even when the membrane size is doubled to 50.8 mm, it can barely measure negative 400 mmHg with a full scale error 2%. While, with the unequal diaphragm design, it can easily measure negative pressure up to 400 mmHg with the smallest air chamber size 12.7 mm and with a doubled accuracy (FS error <1%). Therefore, the unequal diaphragm design described herein has significant advantages over prior art systems with equal diaphragm configurations.

TABLE-US-00001 TABLE I Different pressure interface designs and their expected performance. Input Target Pressure Mem Defl Air Chamber T0 ΔT d.sub.a d.sub.f f.sub.m0 δV.sub.0 P.sub.f FS Error f.sub.m depth Vol 22° C. ° C. mm mm mm ul mmHg % mm mm ul Equal diaphragm 0 12.7 12.7 0 0 550 2 0.314 0.377 47.89 0 0 −150 2 0.183 25.4 25.4 0 0 700 0.5 0.520 0.625 182.37 0 0 −380 2 0.718 50.8 50.8 0 0 700 0.5 1.387 1.665 1713.6 0 0 −400 2 1.946 Unequal 0 12.7 25.4 0 0 550 2 0.314 0.377 47.89 Diaphragm 0 0 −400 1 0.550 18   25.4 0 0 700 0.5 0.319 0.383 72.81 0 0 −400 1 0.550

Effect of Initial Membrane Deflection and Temperature Variations:

[0088] In the above example, a perfectly flat initial membrane condition was assumed (e.g., δV.sub.0=0 was assumed—which may be hard to achieve in practice). When δV.sub.0≠0, (e.g., the membrane is pre-deflected by an amount f.sub.m0) the pressure measurement accuracy will be affected. If the membrane pre-deflects toward the air chamber (δV.sub.0<0), intuitively, one may expect a better performance because the air volume is smaller so that a higher pressure can be measured based on the Ideal Gas Law, however, on the contrary, the positive pressure measurement accuracy will drop because higher cross-membrane pressure difference is required for the increased membrane deformation, meaning a lower air pressure reading P.sub.a for the same input fluid pressure P.sub.f. However, it is beneficial for the negative pressure measurement because less final membrane deformation is required for the same P.sub.f. On the other hand, if the membrane pre-deflects toward the fluid chamber (δV.sub.0>0), it will benefit positive pressure measurement but not negative pressure measurement.

[0089] For robust device design, the pressure interface should be able to tolerate a non-flat initial membrane condition. For worst case scenarios, a negative δV.sub.0 for positive pressure measurement and positive δV.sub.0 for negative pressure measurement should be considered. For fair comparison, the initial deflection value is set, for all cases, equivalent to that caused by a 0.5 mmHg cross-membrane pressure difference in the following calculations.

[0090] At the same time, the pressure interface performance will be affected by temperature variations based on the Ideal Gas Law. In some practical applications, the fluid temperature may vary. For example, blood drawn from the donor has a temperature close to the body temperature (˜37° C.) initially and cools down during processing at room temperature (about 22° C.). Also, some reagents or stored blood may have a temperature below room temperature when they are taken from the refrigerator (˜8° C.). When the system is calibrated and started at room temperature, the fluid temperature changes will affect the air pressure measurement. In general, a decreased temperature will decrease the accuracy of positive pressure measurement but benefit the negative pressure measurement; while an increased temperature will decrease the accuracy of negative pressure measurement but benefit the positive pressure measurement. In order to design a device able to tolerate temperature variations, a temperature drop of 14° C. (22° C.-8° C.) for the positive pressure measurement and a temperature increase of 15° C. (37° C.-22° C.) for negative pressure measurement may be considered as worst case scenarios to test the tolerance of different interface designs.

[0091] The non-flat membrane condition and temperature variation may be combined together in the analyses. The results are shown in Table II. The results show that the initial membrane deflection and temperature variation have dramatic effects on the negative pressure measurement of all equal diaphragm designs, making them unworkable, but only slight effects on the negative pressure measurement of both unequal diaphragm designs, only suffering a little reduction on the measurement accuracy (still less than 2%). For the positive pressure measurement, the effects are the same for equal and unequal diaphragm designs. From these results, it can be seen that the equal diaphragm designs are not able to tolerate any membrane or temperature variations while the unequal diaphragm designs can. This is a significant advantage of the unequal diaphragm designs. With the unequal diaphragm design, it is possible to develop a robust pressure sensing interface device that can tolerate certain membrane condition changes including material property changes and operation environmental condition variations such as temperature and operation errors as long as the deviations are not too large.

TABLE-US-00002 TABLE II Expected performance of different pressure interface designs under the effects of initial membrane deflection and temperature change. Input Target Pressure Mem Defl Air Chamber T0 ΔT d.sub.a d.sub.f f.sub.m0 δV.sub.0 P.sub.f FS Error f.sub.m depth Vol 22° C. ° C. mm mm mm ul mmHg % mm mm ul Equal diaphragm −14 12.7 12.7 −0.086 −5.45 200 2.90 0.154 0.240 39.20 15 0.086 5.45 −70 4.43 0.099 −14 25.4 25.4 −0.23 −58.28 700 1.20 0.520 0.750 214.36 15 0.23 58.28 −240 2.75 0.445 −14 50.8 50.8 −0.616 −624.39 700 1.23 1.387 2.003 2058.5 15 0.616 624.39 −260 2.69 1.227 Unequal −14 12.7 25.4 −0.086 −5.45 200 2.90 0.154 0.240 39.20 Diaphragm 15 0.23 58.28 −400 1.45 0.412 −14 18   25.4 −0.141 −17.94 700 1.50 0.368 0.509 88.78 15 0.23 58.28 −400 1.80 0.474

[0092] The embodiments of the invention described above are intended to be merely exemplary; numerous variations and modifications will be apparent to those skilled in the art. All such variations and modifications are intended to be within the scope of the present invention as defined in any appended claims.