Patent Publication Number: US-10309388-B2

Title: Continuous sample delivery peristaltic pump

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims benefit of priority under 35 U.S.C. § 119(e) to U.S. Provisional Application No. 62/208,465 filed on Aug. 21, 2015, and titled “CONTINUOUS SAMPLE DELIVERY PERISTALTIC PUMP,” which is hereby incorporated by reference herein in its entirety. 
    
    
     BACKGROUND 
     Various types of pumps exist for the purpose of pumping fluids, such as liquids. Pumps are used in numerous applications depending on the type of pump utilized. Many flow cytometers use peristaltic pumps, which have many advantages. Peristaltic pumps are positive displacement pumps. The fluid being pumped only contacts the flexible tubing and is not exposed to other pump components which could possibly cause cross-contamination. Both highly sterile fluids, as well as chemicals, can be pumped through the peristaltic pump, since the fluids only contact the flexible tubing. Peristaltic pumps are especially suited for pumping abrasives, viscous fluids and biological fluids. 
     SUMMARY 
     In one embodiment, a method of pumping a fluid through tubing that is positioned partially around the periphery of a first disk of a peristaltic pump and partially around the periphery of a second disk of the peristaltic pump may be provided. The method may include orbiting a plurality of first rollers at a constant angular speed around the periphery of the first disk such that the first rollers are constantly pressed into contact with the periphery of the first disk, the tubing, or the periphery of the first disk and the tubing. The first disk may include a first angular sector that is configured to cause the first rollers to move along a first section of the periphery of the first disk at a first tangential speed and a second angular sector that is configured to cause the first rollers to move along a second section of the periphery of the first disk at a second tangential speed less than the first tangential speed. The method may also include orbiting a plurality of second rollers at the constant angular speed around the periphery of a second disk such that the second rollers are constantly pressed into contact with the periphery of the second disk, the tubing, or the periphery of the second disk and the tubing. The second disk may be configured to cause each second roller to move at substantially the second tangential speed. The method may also include increasing the pressure of a portion of the fluid in the tubing between one first roller and one second roller by causing the one first roller to fully compress the tubing in the first angular sector and simultaneously causing the one second roller to fully compress the tubing in a first section of the periphery of the second disk and moving, after increasing the pressure of the portion of the fluid, the portion of the fluid through the tubing at a constant pressure towards an output of the tubing by causing the one first roller to fully compress the tubing in the second angular sector and simultaneously causing the one second roller to fully compress the tubing. 
     In some embodiments, the first disk may have a first nominal radius throughout at least part of the first angular sector and a second nominal radius throughout the second angular sector, the second disk may have the second nominal radius, and the first nominal radius may be larger than the second nominal radius. 
     In some such embodiments, the first disk may gradually transition in radius from the first radius to the second radius in between the first angular sector and the second angular sector. 
     In some embodiments, moving the portion of the fluid through the tubing at a constant pressure towards an output of the tube may further include causing, after the one first roller has moved along the second section of the periphery of the first disk, the one first roller to move along a third angular sector of the first disk that includes a third section of the periphery of the first disk, the one first roller to fully compress the tubing at at least the beginning of the third section, and the one first roller to not fully compress the tubing at at least the end of the third section of the periphery of the first disk. Moving the portion of the fluid through the tubing at the constant pressure towards an output of the tube may also include causing another second roller to fully compress the tubing against the second disk before causing the one first roller to not fully compress the tubing at at least the end of the third section of the periphery of the first disk. In such an embodiment, the first disk may be configured to cause the one first roller to move along the third section at the second tangential speed. 
     In some such embodiments, the method may further include causing another first roller to fully compress the tubing before causing the one first roller to not fully compress the tubing at at least the end of the third section of the periphery of the first disk. 
     In some other or additional such embodiments, the method may further include causing the one second roller to fully compress the tubing when the one first roller is at least at the beginning of the third section of the periphery of the first disk and not to compress the tube when the one first roller is at least at the end of the third section of the periphery of the first disk. 
     In some embodiments, there may be only two first rollers and only two second rollers. 
     In some embodiments, the method may further include drawing fluid into the tubing through an inlet by causing one of the first rollers to fully compress the tube and orbit around at least part of the periphery of the first disk. 
     In some embodiments, orbiting the plurality of first rollers at the constant angular speed around the periphery of the first disk and orbiting the plurality of second rollers at the constant angular speed around the periphery of the second disk may include fixing the first disk and the second disk in a position and causing the plurality of first rollers to orbit around the first disk and causing the plurality of second rollers to orbit around the second disk. 
     In some embodiments, the output may be configured to supply the fluid to one of a flow cell or a cuvette. 
     In some embodiments, the output of the tubing may have a pressure that substantially matches the constant pressure of the portion of the fluid. 
     In some embodiments, the output may be configured to supply the fluid to a nozzle of a flow cytometer. 
     In one embodiment, an apparatus may be provided. The apparatus may include a first disk that includes a first recess in the periphery of the first disk, the first recess configured to receive a first portion of tubing for conveying fluid; a first angular sector that has a nominal first radius and includes a first section of the periphery of the first disk; and a second angular sector that has a nominal second radius and includes a second section of the periphery of the first disk. In such an embodiment, the second radius may be smaller than the first radius, and the first section of the periphery of the first disk may be longer than the second section of the periphery of the first disk. The apparatus may also include a second disk that is substantially circular, has the nominal first radius, and includes a second recess in the periphery of the second disk, the second recess configured to receive a second portion of the tubing. The apparatus may also include a plurality of first rollers that are configured to orbit around the periphery of the first disk at a constant angular speed and that are also configured to, when the first portion of the tubing is in the first recess, constantly press into contact with the periphery of the first disk, the tubing, or the periphery of the first disk and the tubing. The apparatus may also include a plurality of second rollers that are configured to orbit around the periphery of the second disk at the constant angular speed and that are configured to, when the second portion of the tubing is in the second recess, constantly press into contact with the periphery of the second disk, the tubing, or the periphery of the second disk and the tubing. The first disk may be configured such that each first roller moves in the first angular sector at a first tangential speed while fully compressing the tubing and such that each first roller moves in the second angular sector at a second tangential speed while fully compressing the tubing, whereas the second disk may be configured such that each second roller moves around the periphery of the second disk at the second tangential speed. The first disk, second disk, first rollers, and second rollers may be configured to cause one first roller to fully compress the tubing while moving in the first angular sector and to simultaneously cause one second roller to fully compress the tubing while moving in a first section of the periphery of the second disk, and the first disk, second disk, first rollers, and second rollers may be further configured to cause, after the one first roller has moved past the first angular sector, the one first roller to fully compress the tubing in the second angular sector and to simultaneously cause the one second roller to fully compress the tubing. 
     In some embodiments, the first disk may gradually transition in radius from the first radius to the second radius in between the first angular sector and the second angular sector. 
     In some embodiments, the first disk may be further configured to cause, after the one first roller has moved along the second section of the periphery of the first disk, the one first roller to move along a third angular sector of the first disk that includes a third section of the periphery of the first disk. The first disk may be further configured to cause the one first roller to move along the third section at the second tangential speed, the one first roller to fully compress the tubing at at least the beginning of the third section, and the one first roller to not fully compress the tube at at least the end of the third section. The second disk may be further configured to cause another second roller to fully compress the tubing against the second disk before the one first roller is caused to not fully compress the tubing at at least the end of the third section of the periphery of the first disk. 
     In some embodiments, the apparatus may further include a first roller support on which the first rollers are mounted and a second roller support on which the second rollers are mounted. The first roller support and the second roller support may be configured to rotate about a common center axis at the constant angular speed. 
     In some embodiments, the apparatus may further include the tubing that is positioned partially around the periphery of the first disk in the first recess and that is positioned partially around the periphery of the second disk in the second recess. 
     In some embodiments, in the sections of the periphery of the first disk where the first rollers fully compress the tubing, the first recess may have a first depth that is less than the nominal outer diameter of the tubing, causing the tubing to extend past the periphery of the first disk such that the first rollers fully compress the tubing, and in the sections of the periphery of the second disk where the second rollers fully compress the tubing, the second recess may have a second depth that is less than the nominal outer diameter of the tubing and that causes the tubing to extend past the periphery of the second disk such that the second rollers fully compress the tubing. 
     In some embodiments, the first disk may include a first adjustment plate and the adjustment plate may be movable with respect to the remainder of the first disk such that locations along the periphery of the first disk where full compression of the tubing occurs between the first disk and a first roller are tunable. 
     In some embodiments, the second disk includes a second adjustment plate and the adjustment plate may be movable with respect to the remainder of the second disk such that locations along the periphery of the second disk where full compression of the tubing occurs between the second disk and a second roller are tunable. 
     In another embodiment, a method of reducing pressure variations of a fluid that is pumped through a peristaltic pump may be provided. The method may include creating a supply of pressurized fluid in a first stage of the peristaltic pump using a first disk to pressurize the fluid by causing first rollers to move at different speeds around a periphery of the first disk, pumping the pressurized fluid in a second stage of the peristaltic pump using a second disk to move the pressurized fluid to an output at a substantially constant pressure by causing second rollers to move at substantially equal speeds around a periphery of the second disk. 
     In some embodiments, the first rollers may pivot around the first disk at a substantially constant angular rotational speed. The first disk may have different radii at different angular locations on the first disk, which causes the first rollers to traverse longer and shorter paths around the periphery of the first disk, which causes the first rollers to traverse the periphery of the first disk at different speeds. 
     In some embodiments, the second rollers may pivot around the second disk at a substantially constant angular rotational speed, the second disk being substantially round so that the second rollers traverse around the periphery of the second disk at a substantially constant peripheral speed. 
     In one embodiment, a peristaltic pump that produces an output flow of fluid at a substantially constant output pressure may be provided. The peristaltic pump may include a first section of flexible tube and a first disk. The first section of flexible tube may be disposed in a recess in the first disk and wrapped around a peripheral portion of the first disk such that the first section of flexible tube protrudes from the recess at first predetermined locations around the periphery of the first disk and does not protrude from the recess at second locations around the peripheral portion of the first disk. The first disk may also have different radii that extend from a pivot point on the first disk to the peripheral portion at different angular locations on the first disk. The pump may also include first rollers that are biased against the peripheral portion of the first disk and that compress the first section of flexible tube wrapped around the peripheral portion of the first disk at the first predetermined angular locations, the first rollers being mounted to rotate around the pivot point at a substantially constant angular rotational speed so that the first rollers traverse shorter and longer paths around the periphery of the first disk, which causes the first rollers to traverse the periphery of the first disk at different speeds and thereby causes the fluid to be pressurized to create a pressurized fluid that flows from the first disk. The pump may also include a second section of flexible tube and a second disk having a round shape and a pivot point at a center of the round shape. The second section of flexible tube may be disposed in a recess in the second disk and wrapped around a peripheral portion of the second disk such that the second section of flexible tube protrudes from the recess at first predetermined locations around the peripheral portion of the second disk and does not protrude from the recess at second predetermined locations around the periphery of the second disk. The pump may also include second rollers that are biased against the peripheral portion of the second disk that compress the second section of flexible tube wrapped around the peripheral portion of the second disk at the first predetermined locations around the periphery of the second disk, and the second rollers may be mounted so as to rotate around the pivot point of the second disk at a substantially constant angular rotational speed so that the second rollers move at a substantially constant speed on the peripheral portion of the second disk and generate an output flow of the fluid that has a substantially constant output pressure. 
     In some embodiments, the peristaltic pump may include first adjustment plates disposed on the first disk adjacent to the peripheral portions of the first disk that provide an adjustment of the first predetermined locations where the first and second sections of flexible tube protrudes from the recess. 
     In some further embodiments, the peristaltic pump may further include second adjustment plates disposed on the second disk adjacent to the peripheral portion of the second disk that provide an adjustment of the first predetermined locations around the peripheral portion of the second disk. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of the first stage of an embodiment of a peristaltic pump. 
         FIG. 2  is a schematic top diagram of the second stage of an embodiment of a peristaltic pump. 
         FIGS. 3A and 3B  are schematic diagrams illustrating initial positions of rollers on a disk for both the first stage and the second stage of the peristaltic pump. 
         FIGS. 4A and 4B  are schematic illustrations of a second location of rollers on the disks of an embodiment of the first stage and the second stage. 
         FIGS. 5A and 5B  are schematic illustrations of the third location of rollers on the disks of an embodiment of the first stage and the second stage. 
         FIG. 6  is a schematic cross-sectional view of a roller and a disk with the opening in a flexible tubing being fully open. 
         FIG. 7  is a schematic illustration of a roller and a disk illustrating the flexible tubing having an opening that is only partially open. 
         FIG. 8  is a schematic illustration of a roller and a disk with the flexible tubing having an opening that is fully closed. 
         FIG. 9  is a schematic cross-sectional view of a roller and a disk and an adjustment plate to adjust the spacing between the roller and the disk. 
         FIG. 10  is a schematic perspective view of an embodiment of a peristaltic pump. 
         FIGS. 11A and 11B  are schematic illustrations of  FIGS. 3A and 3B . 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
       FIG. 1  is a schematic illustration of the first stage  100  of an embodiment of a peristaltic pump. As illustrated in  FIG. 1 , the first stage  100  of the peristaltic pump includes a first disk  102  having an irregular shape. As used herein, “disk” is used to refer to both a round disk and a non-round cam, and such items may have a circular or partially circular shape, as can be seen in  FIG. 1 . An intake tubing  101  is connected to an auto loader  134  that has an uptake probe  132 . The word “tubing,” as used herein, may refer to discrete sections of tubing that are joined together, e.g., via couplers, or a single length of unbroken tubing; it may also refer to different portions of such structures. The autoloader  134  moves the uptake probe  132  to the wells that are formed in the well plate  136  (or other media and containers) to obtain biological samples that are then pumped through the peristaltic pump.  FIG. 1  is but one example of the application of a peristaltic pump; it may be used in other contexts as well aside from a flow cytometer. 
     The peristaltic pump disclosed herein has two stages, the first stage  100  that is illustrated in  FIG. 1 , and a second stage  200  that is illustrated in  FIG. 2 . An advantage of peristaltic pumps is that the fluid that is being pumped through a peristaltic pump does not touch any of the pump parts except for the flexible tubing, such as intake tubing  101  and flexible tubing  104 . In a conventional peristaltic pump, the tubing is wrapped around a disk or cam and two or more spring-loaded rollers are orbited around the disk or cam so that the tubing is compressed against the disk or cam. The rollers, as they compress the tubing against the disk or cam during their orbit of the disk or cam, force or squeeze the fluid through the tubing. In this manner, the fluid that is being pumped through the peristaltic pump can avoid being contaminated. A disadvantage, however, of conventional peristaltic pumps is that the output pressure of the liquid varies substantially, such that the output is a pulsed output that pulses with the rotational speed of the peristaltic pump. In many applications, a pulsed output with varying output pressure of the fluid is unacceptable. For example, the present inventors have found that in a flow cytometry context, pulsations of fluid flow adversely affect flow cytometry data because such pressure fluctuations can cause the sample volume to fluctuate within the flow cell where flow cytometry measurements occur, thereby making it more difficult to properly quantify the number of particles or cells in the sample. Some peristaltic pumps attempt to reduce this pulsation by using three or more rollers to average out or smooth out the pulsations, but the additional rollers decrease the lifespan of the flexible tubing of the peristaltic pump thereby leading to increased maintenance costs and pump downtime. For example, the tubing will experience 50% more wear and tear with three rollers instead of two. 
     In view of the issue with pulsation in the flow cytometry context, a substantially constant output pressure is desirable in many flow cytometry applications. The pulsing of the output liquid from a conventional peristaltic pump may be acceptable in many instruments and other applications. However, it would be much more desirable to have a substantially constant pressure output that does not pulse in many other applications of a peristaltic pump, e.g., in flow cytometers. 
     Additionally, because samples in flow cytometry may be taken from small volume containers, such as a 5 milliliter tube or 96-well plate, it is more difficult and complex to use an air compression pump that utilizes a seal with such containers. Syringe pumps may also be used for flow cytometry, but such pumps are slow, have functional problems, are difficult to clean out or de-clog, and are unable to effectively draw samples of varying media and/or varying volumes. 
     The embodiments disclosed herein relate to a two-stage peristaltic pump that provides a substantially constant output pressure of the liquid being pumped through the peristaltic pump. The first stage  100  is used to increase the pressure of the liquid in the tubing above the inlet pressure and both the first stage  100  and the second stage  200  pump, e.g., move, the liquid through the tubing to an output of the tubing. When the two stage peristaltic pump disclosed herein is used in an application which provides back pressure, i.e., pressure that is higher than the inlet pressure, to the output of the tubing, the pump is configured to provide a substantially constant pressure which matches or exceeds the back pressure in order to prevent the fluid from flowing backward, into, and through the pump. 
     Referring back to  FIG. 1 , first stage  100  includes the first disk  102 , a plurality of first rollers  106 ,  108  (as discussed herein, the first disk and the second disk each have two rollers but additional rollers may be used; two rollers per disk results in the longest lifespan of the tubing by a significant margin, as discussed elsewhere herein), and flexible tubing  104  (a.k.a., “tubing” or “tubing  104 ”). As discussed in greater detail below, the first rollers  106 ,  108  orbit around the periphery of the first disk  102  at a constant angular speed and during the orbit, each roller is caused to contact the periphery of the first disk  102 , the tubing  104 , or the periphery of the first disk  102  and the tubing  104 , such that in various locations around the periphery of the first disk  102  one or more of the first rollers fully compresses the tubing  104 . It should be noted that such orbiting of rollers (i.e., the first and the second rollers) may also be referred to herein as the rollers rotating around or about the first disk; such orbiting also means the movement of rollers around, or encircling, the periphery of a disk. Such orbiting or movement around the periphery of a disk is not intended to mean the rotation of each roller around each roller&#39;s individual pivot point, as discussed below, although the rollers may typically rotate about their own centers as they orbit the disk and roll along the periphery of the disk. Therefore, as each roller orbits around the periphery of the disk, each roller is also simultaneously rotating about its own pivot point. 
     As seen in  FIG. 1 , the flexible tubing  104  is wrapped around the majority of the outside perimeter, i.e., the periphery, of the first disk  102 . As illustrated in more detail below with respect to  FIGS. 6-9 , the flexible tubing  104  is positioned in a recess, i.e., a trough, such that in certain positions around the periphery of the first disk  102 , the tubing  104  extends past the periphery of the first disk  102  to enable the first rollers  106 ,  108  that orbit, i.e., rotate, around the periphery of the first disk  102  to compress the flexible tubing  104  in such locations; such compression of the tubing by the first rollers  106 ,  108 , depends upon the depth of the trough or placement of the adjustment plate, as explained in more detail below. 
     As also seen in  FIG. 1 , roller support  128  is attached to roller brackets  112 ,  114  and causes the first rollers  106 ,  108  to rotate around the first disk  102  in a counterclockwise direction, as illustrated by arrow  111  in  FIG. 1 . The first rollers  106 ,  108  are forced against the periphery of the first disk  102  by springs  120 ,  122 , respectively, so that the flexible tubing  104  is compressed against the first disk  102  in locations where the flexible tubing  104  is exposed to rollers  106 ,  108 . Roller brackets  112 ,  114  pivot around pivots  118 ,  116 , respectively, that are mounted on the roller support  128 . First rollers  106 ,  108  rotate about points  140  and  142  as they roll along the outer periphery of the first disk  102  during their orbits of the first disk  102 . 
     As also illustrated in  FIG. 1 , the axis of the rotation  110  of the roller support  128  is located so that radii  124 ,  125 ,  126 ,  127 ,  129  exist between the axis  110  and the periphery of the first disk  102 . As such, the radii, e.g., radius  124 ,  125  and  129 , are greater than radii  126  and  127 . Because of this, the first rollers  106 ,  108  move at a higher tangential speed along the periphery of the first disk  102  at radii  124 ,  125 ,  129  than at radii  126 ,  127  for a given angular velocity of the roller support  128 . Accordingly, as discussed below, when fluid in the tubing is trapped between two rollers (e.g., two first rollers or a first roller and a second roller) and the rear roller, i.e., the roller closer to the intake tube, is moving at a greater tangential speed than the front roller, i.e., the roller further from the intake tube, the length of the tubing containing the fluid is decreased, but because the fluid is incompressible, the volume of the fluid remains constant and forces the tubing to expand to accommodate this fluid volume which in turn increases the pressure of the trapped fluid in the tubing between these two rollers. It is this process that is used by the peristaltic pump disclosed herein to increase the pressure of a fluid flowing through the pump. 
       FIG. 2  is a schematic top view of the second stage  200  of the peristaltic pump. As can be seen, the second stage  200  includes a second disk  202  and second rollers  206 ,  208  and roller support  228  on which the second rollers  206 ,  208  are mounted; roller support  228  is configured to rotate in a clockwise direction around the second disk  202 , as illustrated by arrow  211 . Roller support  228 , in the illustrated embodiment, rotates in the same direction and same angular speed as roller support  128 ; alternatively, the two roller supports may not be connected with one another, but may be driven at the same angular speed and in the same angular direction, e.g., by a common motor via two separate belt drives.  FIG. 2  illustrates the second stage  200  from a top perspective. Accordingly, the first stage  100 , when viewed from a bottom perspective, moves in a counterclockwise direction, while the second stage, which is rotating in the same direction, is rotating in a clockwise direction when viewed from the top. In order to coordinate the functions of the first stage  100  and the second stage  200 , the rotation of the roller support  228  and the rotation of the roller support  128 , of  FIG. 1 , are synchronized and, in this embodiment, rotate at the same rotational, i.e. angular, speed and in the same direction. 
     In  FIG. 2 , rollers  206 ,  208  are mounted on roller brackets  214 ,  212 , respectively, and are biased against the outer periphery of the second disk  202  by springs  222 ,  220 , respectively. As the roller support  228  rotates the second rollers  206 ,  208  in a clockwise direction, as shown by arrow  211 , rollers  206 ,  208  roll along the periphery of the second disk  202  and rotate around points  240  and  242 , respectively, thereby squeezing or compressing the flexible hose  204  at locations along the periphery of the second disk  202  where the flexible hose  204  is exposed to the surface of the second rollers  206 ,  208 . The fluid in tubing  204  that is in front of a second roller, i.e., located on the side of the roller further from the tubing inlet, is pumped by the second stage  200  by the rotation of the roller support  228  around the second disk  202  to move the second rollers  206 ,  208  such that the fluid moves through the flexible hose  204  around the periphery of the second disk  202  until the fluid exits the an output  230  of the tubing, which may be connected to a flow cell in a flow cytometer or a nozzle of a flow cytometer. Of course, the fluid can be pumped into any device for use and does not necessarily need to be pumped into a flow cytometer. The fluid in the second stage  200  that is in front of each of the second rollers  206 ,  208  (e.g., being pushed by each second roller) is not subjected to a pressure increase but is simply moved towards the output of the tubing at a constant pressure. Back pressure of the system to which the fluid is being applied assists in maintaining a substantially constant pressure of the fluid pumped from the second stage. 
     As indicated above, the second rollers  206 ,  208  are biased against (i.e., constantly pressed into contact with) the periphery of the second disk  202 , tubing  204 , or the periphery of the second disk  202  and tubing  204  by springs  222 ,  220 . The roller brackets  212 ,  214  pivot around pivots  216 ,  218 , respectively. Unlike the first disk  102  of  FIG. 1 , the second disk  202  has a substantially constant radius  232  so that the second rollers  206 ,  208  move at substantially the same tangential speed (there may be some minor variation in tangential speed of the rollers due, for example, to shifts in roller position due to the amount of tubing compression by the second rollers; generally speaking, the second rollers will be kept at the same nominal speed) around the periphery of the second disk  202 . As such, the pressure of the pumped fluid (e.g., the fluid that is pushed by each second roller  206 ,  208  towards the output of the tubing) remains substantially the same as the fluid is pushed around the second disk  202  by the second rollers. 
       FIGS. 3A, 3B, 4A, 4B, 5A and 5B  illustrate the operation of the first stage  100  and the second stage  200  of the peristaltic pump as the first and second rollers proceed around, i.e., orbit, the peripheries of the first and second disks, respectively. As shown in  FIG. 3A , first rollers  106 ,  108  are located in a first position  310  around the first disk  102 . First rollers  106 ,  108  rotate in a counterclockwise direction, as indicated by arrow  111 . The first stage  100  has a flexible tubing  104  that is wrapped around the majority of the outside periphery of the first disk  102 . The irregular shape of the first disk  102  results in radii  124  and  129  having different lengths than radii  125 ,  126 , and  127 . As mentioned above, first roller support  128  (not pictured) rotates around the axis  110  and supports roller bracket  112  and roller bracket  114 . Roller bracket  112  pivots around pivot  116 , while roller bracket  114  pivots around pivot  118 . Springs  120  and  122  bias rollers  106  and  108 , respectively, to contact the periphery of the first disk  102 , the tubing  104 , or the periphery of the first disk  102  and the tubing  104 . 
     In operation, the roller support  128  rotates the first rollers  106 ,  108  around the first disk  102  in the direction of rotation  111 , i.e., counterclockwise, as viewed from the bottom. Because of the irregular shape of the first disk  102 , the first rollers  106 ,  108  travel at different tangential speeds around the periphery of the first disk  108  because the roller support  128  moves at a constant angular rotational speed and the first rollers  106 ,  108  traverse the periphery of disk  102  at different radii  124 ,  125 ,  126 ,  127  and  129 . As used herein, the term “tangential speed” refers to the relative speed between a roller and the surface it is rolling along. For example, if a 1 inch diameter roller is rolling along a portion of the periphery of the first disk that has a radius of 4 inches and the support arm driving that roller is rotating at a speed of 30°/second, the tangential speed or velocity of the roller at the roller center would be 2π·(local disk radius+distance from disk periphery to roller center)·30°/second/360°=2π·4.5· 1/12 inches/second=2.35 inches/second. If that same roller is rolling along a portion of the periphery of the first disk that has a radius of 2 inches and the support arm is rotating at the same speed, however, the tangential speed or velocity of the roller at the roller center would be 2π·2.5· 1/12 inches/second=1.31 inches/second. Thus, when the first rollers  106 ,  108  traverse around the periphery of the first disk  102  where the radius is shown as radius  124  and radius  129 , the tangential speed of the first rollers  106 ,  108  on the periphery of the first disk  102  is greater than the tangential speed of the first rollers when they are traversing the periphery of the first disk  102  at radii  125 ,  126 , and  127 . Since the first rollers  106 ,  108  move faster in the areas where the radius is greater, the first rollers  106 ,  108  move along the flexible tubing  104  in these areas at a greater rate of speed. Conversely, when the first rollers  106 ,  108  are moving along the periphery of disk  102  on portions of the first disk  102  that have a shorter radius, such as radii  126 ,  127 , the first rollers  106 ,  108  move in these areas at a slower rate of speed along the flexible tubing  104 . When both first rollers  106 ,  108  are compressing the flexible tubing  104 , and one of the first rollers is moving faster on the periphery of first disk  102  than the other first roller, the fluid trapped in the tubing between first rollers  106  and  108  experiences a pressure increase. 
     As the first roller support  128  rotates around the first disk  102  at a constant angular rotational speed, the first rollers  106 ,  108  are biased against the periphery of the first disk  102 , the tubing  104 , or the periphery of the first disk  102  and the tubing  104 , and cause the flexible tubing  104  to experience various states of compression at various locations around the periphery of the first disk  102 . Fluid from the intake tubing  101  is drawn into the flexible tubing  104  as the first rollers  106 ,  108  move in a counterclockwise direction  111  and fully compress the flexible tubing  104 . Fluid is thus drawn from the intake tubing  101  and is forced out of the interconnecting tubing  130  and proceeds to the second stage that is illustrated in  FIG. 2 . 
     As seen in at least  FIGS. 3A and 3B , interconnecting tubing  130  extends from the first stage  100 , proceeds to the second disk  202 , and is wrapped around part of the periphery of the second disk  202  in a clockwise direction. Disk  102  and second disk  202  may be aligned with each other as discussed herein, although it is to be understood that there may be many other arrangements of the first and second disks that may still provide the same functionality as is discussed herein. For example, both disks may actually be arranged as depicted in  FIGS. 3A and 3B  (side-by-side), but with the second disk and rollers flipped over so that the direction of rotation of the roller support  228  rotates in the same direction as the roller support  128 —both roller supports  128  and  228  may be driven by the same drive system and the rollers and tubing may operate in effectively the same way as is described herein with regard to the depicted example. 
     First roller support  128  rotates around the first disk  102  (as shown in  FIG. 1 ) synchronously with second roller support  228 , which rotates round second disk  202 . Consequently, the rotational phase of the first rollers  106 ,  108  and the second rollers  206 ,  208  remains constant. As discussed above, the roller supports of the first stage  100  and the second stage  200  rotate in the same direction, even though arrow  111  indicates a counterclockwise rotation and arrow  211  indicates a clockwise rotation. Again, this is because  FIGS. 1 and 3A  are bottom views of the peristaltic pump and  FIGS. 2 and 3B  are top views of the peristaltic pump. 
     As illustrated in at least  FIGS. 2 and 3B , the second disk  202  has a substantially constant radius  232  (e.g., within ±1% or ±5% of round; 1% or less may result in the least amount of pressure variation in the fluid that gets trapped between the second rollers as they orbit the second disk). The flexible tubing  204  is wrapped around the majority of the periphery of the second disk  202  so that the second rollers  206 ,  208  can compress the flexible tubing  204  along portions of the periphery of the second disk  202  that are exposed to the second rollers  206 ,  208 , such as the portions including locations  314 ,  315 , and  316 . The fluid enters the flexible tubing  204  from interconnecting tubing  130  from the first stage  100 . As discussed below, the pressure of the fluid is increased while partially located in both the first and second stages between a first roller and a second roller that are both fully compressing the tubing. Second rollers  206 ,  208  are mounted on roller brackets  212 ,  214 , respectively. As stated above, roller brackets  212 ,  214  rotate on pivots  216 ,  218 , respectively, and springs  220 ,  222  constantly press the second rollers  206 ,  208  into contact with the periphery of the second disk  202 , the tubing  204 , or the periphery of the second disk  202  and the tubing  204 . 
     Referring back to  FIG. 3A , first roller  106  is located at position  310  on the outer periphery of the first disk  102  where there is no compression of the tubing  104  because at this location the first disk  102  is configured such that the flexible tubing  104  is not exposed to the pressure of the first roller  106 . In fact, the flexible tubing  104  is not even disposed along the periphery of the first disk  102  at location  310 . Uptake tubing  101 , as described above, provides intake fluid to the flexible tubing  104 . The flexible tubing  104  is wrapped around the periphery of the first disk  102  from the uptake tubing  101 , counterclockwise around the periphery of the first disk  102  to the interconnecting tubing  130 . At various locations along the periphery of the first disk  102 , the flexible tubing  104  will be exposed to, partially exposed to, or not exposed to the pressure of the first rollers  106 ,  108 , which results in the flexible tubing  104  being fully compressed, partially compressed or not compressed, as explained in more detail below. 
     As also shown in  FIG. 3A , roller  108  contacts the first disk  102  at location  305  and fully compresses the flexible tubing  104 . The labels of locations  303 ,  304 ,  305  and  306 , the flexible tubing  104  indicate that tubing  104  is fully compressed by the first rollers  106 ,  108  at these locations. At locations  308  and  310 , there is no compression of the flexible tubing  104  by the first rollers  106 ,  108 . At location  302 , the tubing  104  is partially compressed. 
     As further illustrated in  FIG. 3A , the first disk  102  has various length radii. For instance, the first disk  102  has longer radii  124  and  129  (e.g., longer radii in at least the regions between positions  310  and  304 , in a clockwise direction from position  310 ) which cause the first rollers  106 ,  108  to move at a faster tangential speed along the peripheral surface of the first disk  102  at and between these positions. Radii  125 ,  126 , and  127  are shorter than the radii  129 ,  124 , such that the first rollers  106 ,  108  do not move as quickly along the peripheral surface of the first disk  102  for these radii. For example, first roller  106  moves at a faster tangential speed as it moves in the clockwise direction (with the roller support maintaining a constant rotational speed) from position  310  (having radius  129 ) to position  303  (having radius  124 ) than its tangential speed as it moves from position  305  (having radius  125 ) to position  306  (having radius  126 , which in some embodiments may be the same length as radius  126 ) because the radii at positions  305  and  306  are shorter than the radii between positions  310  and  303 . 
     As additionally illustrated in  FIG. 3A , when the first rollers  106 ,  108  are at locations  310 ,  305 , respectively, first roller  106  is not compressing the flexible tubing  104 , while first roller  108  is fully compressing the flexible tubing  104 . As such, when first roller  108  moves into the position  305 , roller  108  is drawing fluid from the intake tubing  101 , since the flexible tubing  104  is not compressed by first roller  106 , i.e., at these positions the first roller  106  does not affect the fluid flow within the tubing. First roller  108  continues to draw fluid through the intake tubing  101 , as it rotates counterclockwise around the periphery of the first disk  102  through position  306  until first roller  106  starts fully compressing flexible tubing  104  between positions  302  and  303 . It should be noted that the first disk  102  and first rollers are configured such that as one first roller moves from position  306  to position  308 , that first roller does not stop fully compressing the tubing until after the other first roller is fully compressing the tubing. 
       FIG. 3B  illustrates the operation of the second stage  200 . When first rollers  106 ,  108  are in the locations illustrated in  FIG. 3A , second rollers  206 ,  208  are located in the corresponding positions illustrated in  FIG. 3B  on the periphery of the second disk  202 . For instance, second roller  208  is located at position  311  and is not compressing flexible tubing  204 . Second roller  206  is at position  315  and is fully compressing the flexible tubing  204 . As such, fluid trapped between first roller  108  at position  305  and the second roller  206  at position  315  is moved by first roller  108  and second roller  206  towards the output tubing  230  through the interconnecting tubing  130  and through the flexible tubing  204 . As the first roller  108  moves from position  305  to  306 , it is moving at the same tangential speed as the second rollers  206 ,  208  because the radius of disk  102  at positions  305  through  308  is substantially the same as the radius of the second disk  202 . Accordingly, the first roller  108  pushes (and the second roller  206  pulls at the same rate) and causes the fluid in the tubing  104  to move from position  305  towards the second disk  202  without increasing the pressure of the fluid trapped between first roller  108  and the second roller  206  as they move between these positions (i.e.,  305  to  306  and  315  to  316 , respectively). This constant-pressure movement of the fluid trapped between the first roller  108  and the second roller  206  continues until the first roller  108  no longer fully compresses the tubing, at which point the fluid is no longer trapped between the first roller  108  and the second roller  206 . However, before the first roller  108  stops fully compressing the tubing, the second roller  208  will start fully compressing the tubing, and the portion of the fluid in front of the second roller  208  will continue to be moved at constant pressure towards the outlet. At position  312  of disk  202 , there is partial compression of the flexible tubing  204  by a second roller and at position  314 , there is full compression of flexible tubing  204  by a second roller; the second roller transitions to full compression at some point between positions  312  and  314 . 
     As indicated above, at position  315 , there is full compression of the flexible tubing  204  against the second disk  202 . At position  316 , there is still full compression of the flexible tubing  204  and at position  318  there is no compression of the flexible tubing  204  by the second rollers  206 ,  208 . Flexible tubing  204  is fluidically connected to the output tubing  230 , which delivers fluid to a flow cell an embodiment in which the peristaltic pump is used in a flow cytometer. In some alternative embodiments, the output tubing  230  is fluidically connected to a nozzle of a flow cytometer and the output pressure of the output tubing  230  may be governed by the pressure of the fluid within the nozzle. In other implementations, output tubing  230  simply comprises the output of the second stage  200  of the peristaltic pump. As indicated in  FIG. 3B , the second rollers  206 ,  208  rotate, i.e., orbit, around the periphery of the second disk  202  in a clockwise direction, either compressing, partially compressing, or not compressing the flexible tubing  204  in at least the positions indicated in  FIG. 3B . 
       FIG. 4A  is a schematic illustration of the first stage  100  of the peristaltic pump with the first rollers  106 ,  108  in a second position. First roller  106  has moved from position  310  to position  303  where the first roller  106  is fully compressing the flexible tubing  104 . Similarly, first roller  108  has moved in a counterclockwise direction from position  305 , where the first roller  108  was fully compressing the flexible tubing  104 , to position  306 , where there is still full compression of the first roller  308  on the flexible tubing  104 . During the movement of first roller  106  from position  310  to position  303 , and the movement of first roller  108  from position  305  to position  306 , first roller  106  starts compressing and then fully compresses the flexible tubing  104  which causes a portion of fluid to be trapped between first rollers  106  and  108 ; this trapped portion of fluid will experience a pressure increase as the first rollers continue to advance while both first rollers fully compress the tubing. At the point depicted, the fluid that is trapped between the first roller  108  and the second roller  206 , which includes the fluid in the interconnecting tubing  130 , is already pressurized to the final output flow pressure. Subsequently, second roller  208  transitions to full compression of the tubing while second roller  206  is fully compressing the tubing. 
       FIG. 4B  is a schematic illustration of the second stage  200  of the peristaltic pump. Second roller  208  has moved from position  311 , where there was no compression of tubing  204 , in a clockwise direction, to position  312 , where there is partial compression of tubing  204 . Similarly, second roller  206  has moved from position  315 , where there is full compression of tubing  204 , to position  316 , where there is also full compression of tubing  204 . Here, first roller  108  is pushing, i.e., moving, the liquid in tubing  104  through tubing  104 , tubing  130 , and tubing  204  as it advances from position  305  to position  306  and going at the same tangential speed as second roller  206  because radii  125  and  126  are substantially the same as the radius of the second disk  202 . This prevents the pressure of this portion of fluid from increasing and instead causes the pressure to remain substantially constant during movement of this portion of the fluid. 
       FIG. 5A  is a schematic top view of the first stage  100  of the peristaltic pump illustrating first rollers  106 ,  108  in a third position. As illustrated in  FIG. 5A , first roller  106  has moved in a counterclockwise direction, as indicated by arrow  111 , from position  303 , where there was full compression of tubing  104 , to position  304 , where there is also full compression of the flexible tubing  104 . First roller  108  has moved from position  306 , where there was full compression of the flexible tubing  104 , to position  308 , where there is no compression of the flexible tubing  104 . As discussed below, the pressure of the fluid trapped between the first rollers  106 ,  108  as one of the first rollers moves from position  303  to  304  and the other first roller simultaneously moves from position  306  to  308  may increase because the roller moving from position  303  to  304  is moving at a faster tangential speed than the roller moving from position  306  to  308 . In some embodiments, this pressure increase may be negligible, e.g., if one first roller starts fully compressing the tubing just before the other first roller stops fully compressing the tubing. However, after a first roller stops fully compressing the tubing, e.g., between locations  306  and  308 , the fluid trapped between the other first roller and one of the second rollers may be further pressurized as those rollers continue to traverse the periphery of their respective disks—indeed, the bulk of the pressure increase that is experienced by the fluid may occur while the fluid is trapped between one of the first rollers and one of the second rollers. Accordingly, the fluid between the first rollers is moved by the first roller  106  to the interconnecting tubing  130  under pressure and transmitted to the second stage  200  that is illustrated in  FIG. 5B . 
     As the first rollers and second rollers move between the positions depicted in  FIGS. 4A, 4B, 5A, and 5B , respectively, a “handoff” may occur between the first rollers and the second rollers such that a portion of the fluid trapped between a first roller located in the region between locations  305  and  308  and a second roller located in the region between locations  315  and  318  is subdivided as another second roller fully compresses the tubing in which the trapped fluid is located. The portion of fluid that is trapped between the two second rollers is thus “handed off” from the first stage to the second stage, and the second stage rollers move this handed-off portion of the fluid to the outlet under constant pressure. The other portion of the fluid that is trapped between the first roller and the (recently compressing) second roller is also moved at constant pressure towards the outlet. However, when that first roller stops fully compressing the tubing, e.g., such as at location  308 , the portion of the fluid that was trapped between that first roller and a second roller will experience a pressure decrease as it equalizes with the lower-pressure fluid that was previously trapped between the two first rollers (which may be at or slightly above the intake pressure, depending on how much the pressure increases while such fluid is moved while trapped between the first rollers). The differential tangential speeds of the first roller and the second roller(s) as the first roller travels along the periphery of the first disk having the larger radii then raises the pressure of the fluid trapped between the first roller and the second roller up to the desired outlet pressure. 
       FIG. 5B  illustrates the second stage  200  of the peristaltic pump with second rollers  206 ,  208  in a third position. Second roller  208  has moved from position  312  to position  314 , and fully compressed tubing  204  at some location after position  312  and before reaching position  314 . Second roller  206  has moved from position  316 , where there is full compression, to position  318 , where there is no compression of tubing  204 . In this manner, second roller  208  has taken on the task of moving the fluid in tubing  204 , while second roller  206  has moved to a position (e.g., position  318 ) where there is no compression, so that the fluid being moved by second roller  208  can pass through to the output tubing  230 . As such, the second stage  200  simply moves the fluid by alternately using second rollers  206 ,  208  to advance the fluid in tubing  204 . In some embodiments, the second disk  202  is configured such that full compression of tubing  204  is caused by a second roller moving between positions  312  and  314  before another second roller simultaneously moving between positions  316  and  318  is not fully compressing tubing  204 . 
     As mentioned above, the peristaltic pump disclosed herein increases the pressure of a portion of fluid in the tubing between a first roller and a second roller by causing that first roller to move at a faster tangential speed around the first disk than that second roller. Again, this pressure increase is caused by the first roller pushing fluid against the second roller, thereby decreasing the length of tubing to contain the same volume of fluid, which causes the tubing to expand in order to accommodate the fluid, and thus increases the pressure of the fluid. The movement of the rollers and configuration of the disks to cause this pressure increase will now be discussed in further detail. 
       FIGS. 11A and 11B  depict the peristaltic pump of  FIGS. 3A and 3B , respectively, and as can be seen, most of the labels have been removed from  FIGS. 3A and 3B  and three shaded sectors in each disk have been added. As discussed above, the first rollers  106 ,  108  orbit around the periphery of the first disk at a constant angular speed and these first rollers  106 ,  108  are constantly pressed into contact to with the periphery of the first disk  102 , the tubing  104 , or the periphery of the first disk  102  and the tubing  104 . In  FIG. 11A , when first roller  106  orbits around disk  102  and reaches position  166  (which is between positions  303  and  304  on  FIG. 3A , and which are not labeled in  FIG. 11A ), first roller  106  is fully compressing the tubing  104  and first roller  108  is no longer compressing tubing  104 . At the same time, second roller  208  is at position  266  and is fully compressing tubing  204 . Accordingly, a portion of fluid exists between first roller  106  and second roller  208  in tubing  104 ,  130 , and  204 ; the bulk of the pressure increase in the fluid may occur in this trapped portion of the fluid. 
     First disk  102  in  FIG. 11A  includes a first angular sector  160  that spans between positions  166  and  168  (position  166  is between positions  303  and  304  and position  168  is between positions  304  and  305  of  FIG. 3A ), includes a first section of the periphery of the first disk  102  (not identified, but corresponding with the portion of the periphery between positions  166  and  168 ), and has a radius greater than the radius of the second disk  202  and greater than the radius in a second angular sector  162 . As a first roller, such as first roller  106 , moves along the first section of the periphery of first disk  102  between positions  166  and  168 , that first roller is moving at a first tangential speed and is fully compressing the tubing.  FIG. 11A  also shows the second angular sector  162  that spans between positions  170  and  172  of the first disk (position  170  corresponds to position  305  and position  172  corresponds to position  306  in  FIG. 3A ), includes a second section of the periphery of the first disk  102  (not identified but corresponding with the portion of the periphery of the first disk between positions  170  and  172 ), and has a radius substantially equal to the radius of the second disk  202  and smaller than the radius of the first angular sector  160  (this radius corresponds to radius  125  in  FIG. 3A ). A first roller moving along the second section of the periphery of the first disk fully compresses the tubing  104  and moves at a second tangential speed that is less than the first tangential speed. 
     Referring to  FIG. 11B , the second rollers  206 ,  208  orbit around the periphery of the second disk  202  at the same constant angular speed as the first rollers  106 ,  108 . As noted above, the second rollers are constantly pressed into contact with the periphery of the second disk  202 , the tubing  204 , or the periphery of the second disk  202  and the tubing  204 . Because the second disk has a substantially constant radius that also is substantially equal to the radius of the first disk in at least the second angular sector  162 , the second rollers  206 ,  208  also move at substantially the second tangential speed. The second disk  202  also includes an angular sector  260  that includes a portion of the periphery of the second disk  202  as well as another angular sector  262  that includes another portion of the periphery of the second disk  202 . 
     The first disk  102  of  FIG. 11A  and the second disk  202  of  FIG. 11B  and their respective rollers are aligned and configured as described herein in order to increase the pressure of the fluid trapped between a first roller and a second roller. For instance, when first roller  106  is at position  166  it is fully compressing the tubing  104 , first roller  108  is between positions  172  and  174  such that it is not compressing the tubing  104 , second roller  208  is at position  266  and fully compressing the tubing  204 , and second roller  206  is partially compressing the tubing  204 . As first roller  106  moves along the periphery of the first disk  102  within the first angular sector  160  at the first tangential speed, second roller  208  simultaneously moves along the angular sector  260  of the second disk at the second tangential speed. Because the first tangential speed is greater than the second tangential speed, first roller  106  pushes the fluid between the first roller  106  and the second roller  208  such that the pressure of this fluid is increased. The volume of the fluid remains the same but the length of tubing to contain the fluid is decreased, thus increasing the pressure in the tubing that expanded to accommodate the same fluid volume in the shorter length of tubing. In some embodiments, the pressure increase may cause the fluid to have a pressure increase of about 10 psi. This pressure increase occurs throughout the entire first angular sector  160 . 
     In between the first angular sector  160  and the second angular section  162 , there may be a transition sector, such as between positions  168  and  170 , that that transitions from the radius of the first angular sector  160  and the radius of the second angular sector  162 . This varying radius of the transition sector allows the radius of the first disk to reduce from the larger, first radius to the smaller, second radius. The pressure of the fluid may also be caused to increase as a first roller transits through the transition sector, although the rate at which the pressure increases increase will decrease as the first roller transits through the transition sector. 
     When the first roller  106  moves along the second angular sector  162 , it moves at substantially the second tangential speed while the second roller  208  is simultaneously moving along the periphery of the second disk  202  through the another angular section  262  at substantially the second tangential speed. Because the tangential speeds of the first roller  106  and the second roller  208  substantially match at this period, the pressure of the fluid is not increased, but rather is maintained at a substantially constant pressure. The term “substantially” is used, in this instance, because there may be slight variations in speed or pressure in this section due to manufacturing tolerances or other negligible contributing factors. This movement by roller  106  from position  166  to  170  not only increases the pressure of the fluid, but also moves the fluid towards the outflow tubing  230 ; the movement from position  170  to position  172  also moves the fluid towards the outflow tubing  230  but does not increase the pressure of the fluid. 
     Accordingly, first disk  102  functions to increase the pressure of the fluid that is being drawn from the intake tubing  101  by causing the first rollers  106 ,  108  to move faster than the second rollers on longer-radius portions of the first disk  102  during certain portions of the cycle. As such, the two stage peristaltic pump is capable of pumping fluids with minimal pressure variation at the outlet, which results in little or no pulsing of the fluid at the output tubing  230 . Additionally, referring back to  FIG. 3A , when second roller  206  moves from position  316 , where there is full compression, to position  318 , where there is no compression, a volume is created in the tubing. Second roller  208  moves from position  312 , where there is partial compression, to position  314 , where there is full compression. As such, second roller  208  compresses the tubing, which displaces the same volume as the volume that is created when second roller  206  moves from position  316  to position  318 . In this manner, a constant pressure is maintained. 
     As noted above, in some embodiments, the first disk  102  may have a first nominal radius throughout at least part of the first angular sector  160  and a second a second nominal radius throughout the second angular sector  162 , the second disk  202  may have the second nominal radius, and the first nominal radius may be larger than the second nominal radius. 
     Referring back to  FIG. 11A , after the first roller  106  has moved along the periphery of the first disk  102  of the second angular sector  162 , the first roller  106  may be caused to move along a third angular sector  164  of the first disk  102  that is adjacent to the second angular sector  162  and spans between points  172  and  174 . This third angular sector  164  may be configured to cause the first rollers to move along a third section of the periphery of the first disk at the second tangential speed (because the third angular sector  164  has substantially the same radius as the second angular sector  162  and the second disk  202 ). This third angular sector  164  may also be configured to cause the first roller to fully compress the tubing  104  at at least the beginning of the third angular sector  164  and to cause the one first roller  106  to not compress the tubing  104  at at least the end of the third angular section  164 . For instance, as seen in  FIG. 11A , the first roller  108  and  106  are fully compressing the tubing from positions  166  to at least  172 . As stated above, as a first roller moves through the third angular sector, that first roller transitions from fully compressing the tubing  104  to not compressing the tubing  104 . 
     Correspondingly, as a first roller is moving through the third angular sector  164 , the second roller is moving through a different angular sector  264  at the second tangential speed. This different angular sector  264  spans between positions  272  and  274  which correspond to positions  316  and  318 , respectively. As such, when a second roller traverses this angular section  264 , it is fully compressing the tubing  204  at position  272  and not compressing the tubing  204  at position  274 . 
     Additionally, as a first roller moves along the third angular sector  164 , the first disk  102  may be configured to cause another first roller to fully compress tubing  104  before the first roller in the third angular sector stops fully compressing the tubing in the third angular sector, such as fully compressing the tubing  104  at position  303  of  FIG. 3A , as described above. During this time, the second disk  202  may also be configured to cause another second roller to fully compress the tubing  204  against the second disk  202  before causing the one first roller to not fully compress the tubing  104  in the third angular sector  164 . For example, as first roller  108  moves along the third angular sector  164 , second roller  208  may fully compress tubing  204  at about position  266  on the second disk  202  before first roller  108  is not fully compressing tubing  104 . 
     Similarly, the second disk  202  may also be configured to cause a second roller, such as second roller  206 , to fully compress the tubing  204  when one first roller, such as first roller  108 , is at least at the beginning of the third section of the periphery of the first disk  102  (i.e., the beginning of the fourth angular sector  164 ) and not to compress the tubing  204  when first roller  108  is at the end of the third section of the periphery of the first disk  102 . For instance, when first roller  108  is at position  172  it is fully compressing tubing  104  and roller  206  is simultaneously at position  272  and fully compressing tubing  204 ; when first roller  108  is at position  174  and not compressing tubing  104 , second roller  206  is simultaneously at position  274  and is not compressing tubing  204 . As mentioned above, the second disk may be configured such that the other second roller is fully compressing tubing between positions  312  and  314  (as labeled in  FIG. 3A ) before the second roller is not compressing tubing  204  in third angular sector  264 . 
       FIG. 6  is a cross-sectional view of disk  102  and a first roller  602 . Although  FIGS. 6 through 9  are shown with the first disk  102 , such embodiments may be equally applicable to the second disk. As shown on  FIG. 6 , the outer periphery of the first disk  102  has a trough  606  (i.e., recess). Where the trough  606  has a first depth  610 , as shown in  FIG. 6 , the flexible tubing  104  is not compressed, since the first roller  602  rides along the outer, or peripheral portions of the first disk  102  and does not compress the flexible tubing  104 . The flexible tubing has an opening  608  in this state that is not compressed and is fully open, so that fluid can easily flow through the flexible tubing  104  as a result of the first depth  610  of the trough  606  at this location on the periphery of the first disk  102 . The tubing  104  has a nominal outer diameter in an undeformed state and trough  606  is configured such that the first depth  610  substantially matches this nominal outer diameter so that the first roller  602  does not compress the tubing  104 . The first roller  602  rolls along the outer peripheral surface of the first disk  102  at the edges of the trough  606  and rotates on the roller shaft  604 . 
       FIG. 7  is a cross-sectional view of the first disk  102 , first roller  602 , and flexible tubing  104  at a different location along the periphery of the first disk  102 . As illustrated in  FIG. 7 , the trough  606  is not as deep as the trough  606  in  FIG. 6 , i.e., the first depth  610  in  FIG. 7  is less than the first depth  610  depicted in  FIG. 6 . As such, the surface of the first roller  602  contacts the flexible tubing  104  and causes the flexible tubing  104  to be partially compressed in the trough  606 . Again, the first roller  602  is rolling along the outer peripheral surface of the first disk  102  and rotating about roller shaft  604 , as illustrated in  FIG. 7 . Since the flexible tubing  104  is compressed, the opening  608  is also partially compressed so that not as much fluid can flow through the opening  608  in the flexible tubing  104 . 
       FIG. 8  is a cross-sectional view of the first disk  102 , first roller  602 , and the flexible tubing  104  at another location along the periphery of the first disk  102 . As illustrated in  FIG. 8 , the trough  606  is not as deep as the trough  606  in  FIG. 7 . In other words, the trough, or first recess,  606  has a first depth  610  that is less than the nominal outer diameter of the tubing, thereby causing the tubing  104  to extend past the periphery of the first disk  102  such that the first roller  602  fully compresses the tubing  104  in the trough  606  when the surface of the first roller  602  contacts the flexible tubing  104 . Generally speaking, the first depth  610  would be less than or equal to twice the wall thickness of the tubing in order to cause such full compression. Tubing that is “fully compressed,” as the term is used herein, is tubing that has been squashed or compressed to the point where no fluid is able to pass the point of compression within the tubing at the operating pressures utilized. Opening  608  is fully closed. Again, the first roller  602  is rolling along the outer peripheral surface of the first disk  102  around roller shaft  604 , as illustrated in  FIG. 8 . Since the flexible tubing is fully compressed, the opening  608  is completely closed off so that no fluid can flow through the opening  608  in the flexible tubing  104 . 
       FIG. 9  illustrates another embodiment of the manner in which the first roller  602  can be used to compress the flexible tubing  104  using an adjustment plate  902 . As illustrated in  FIG. 9 , adjustment plate  902  is anchored to disk  102  by adjustment screws  906 ; the adjustment plate may be considered to be part of the first disk  102 . The adjustment screws  906  extend through the openings  904  in the adjustment plate  902  and are screwed into the first disk  102 . Other types of connectors could also be used that are well known in the art. The first roller  602 , which rotates on roller shaft  604 , rests on the outer surface of the adjustment plate  902 . In this manner, if the trough  606  is not the desired depth, the adjustment plate  902  can be used to provide adjustment as to the location and amount which the first roller  602  compresses the flexible tubing  604 . For instance, the adjustment plate may extend past a portion of the periphery of the first disk  102 , thereby effectively extending the periphery of the first disk  102 , and thereby cause the first roller  602  to be in contact with the first adjustment plate  902  and offset from the periphery of the first disk  102  such that the first roller  602  partially compresses the tubing  104 . In some embodiments, this adjustment plate may form part of the trough  606 , i.e., recess. Also, for example, at the location illustrated in  FIG. 9 , the opening  608  is partially open. Without the adjustment plate  902 , the opening  608  would be fully closed if the first roller  602  was sitting on the peripheral edge of the first disk  102 . In this manner, the pressure of the fluid can be adjusted, as well as the location where fluid can flow along the disk. By adjusting the radial location of the adjustment plate, the location where the roller fully compresses the flexible tubing can be adjusted, which allows both the pressure generated in the compression phase and the alignment of roller  206  and  208 &#39;s transition to be adjusted. 
       FIG. 10  is a schematic perspective view of the peristaltic pump  1000 . As illustrated in  FIG. 10 , second stage  200  is mounted directly over and aligned with the first stage  100 . Pulley  1002  drives pulley  1012 , with belt  1008 . Pulley  1012  is mounted in top plate  1016  and drives the rotation of the first stage  100 . Similarly, pulley  1004  drives belt  1010 , which, in turn, drives pulley  1014 ; pulley  1014  drives the rotation of the second stage  200 . Pulley  1002  and  1004  are connected to each other through a common shaft that proceeds through the center of both pulley  1002  and  1004  thus keeping the rotation of pulleys  1002  and  1004 , and therefore stages  100  and  200  synchronized. The common shaft between pulleys  1002  and  1004  is driven by motor  1006  and a motor pulley, belt, and shaft pulley (not shown). In this manner, the rotation of the support arms of stage one and stage two is synchronized. Bottom plate  1018  provides the structural support for pulley  1014 . Columns  1020 ,  1022  provide structural support for various portions of the peristaltic pump  1000 . Motor  1006  drives the shaft that connects the pulleys  1002 ,  1004 , which provides the rotational force to drive the peristaltic pump  1000 . Accordingly, the shafts connecting pulleys  1002 ,  1004  and  1012 ,  1014  provide synchronization between the first stage  100  and the second stage  200  of the peristaltic pump. Further, since the two stages are aligned and connected in the manner shown, a compact design is provided for the peristaltic pump  1000 . 
     The embodiments disclosed therefore provide a peristaltic pump  1000  with little or no pulsing of the output fluid at the desired output pressure. Disks are used that have varying radii that allow the fluid to be pre-pressurized in the first stage and subsequently pumped to an output by the second stage, resulting in little or no variations in output pressure of the output fluid. The fluid that is pumped by the peristaltic pump  1000  can be either a liquid or gas, or a mixture of liquid and gas. Although two rollers are illustrated in the various embodiments, three or more rollers can be used in either stage one and/or stage two. 
     It is to be understood that use of the term “substantially” in this application and the claims, unless otherwise indicated, refers to relationship that is within ±5% of the value specified. For example, “substantially the same tangential speed” would be within ±5% of the specified tangential speed. In a further example, a pressure that substantially matches another pressure would be within ±5% of that other pressure. A substantially circular shape would be a shape that has a boundary falling that falls within an annulus with an inner and outer diameter within ±5% of the diameter of a particular true circle. 
     The foregoing description of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and other modifications and variations may be possible in light of the above teachings. The embodiment was chosen and described in order to best explain the principles of the invention and its practical application to thereby enable others skilled in the art to best utilize the invention in various embodiments and various modifications as are suited to the particular use contemplated. It is intended that the appended claims be construed to include other alternative embodiments of the invention except insofar as limited by the prior art.