US20060272384A1 - Flow sensor methods and apparatus - Google Patents
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- G—PHYSICS
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- G01N30/00—Investigating or analysing materials by separation into components using adsorption, absorption or similar phenomena or using ion-exchange, e.g. chromatography or field flow fractionation
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- G01F25/10—Testing or calibration of apparatus for measuring volume, volume flow or liquid level or for metering by volume of flowmeters
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Abstract
Apparatus and methods of calibrating a microfluidic flow sensor, in which the flow of a fluid through a flow sensor is stopped and a first value is read from the flow sensor, then the fluid is pumped through the flow sensor sequentially at first and second selected rates, and readings from the flow sensor of the flow rate are taken for each of the rates. The readings are used in a polynomial equation to determine the actual flow rate, which is used to calibrate the sensor. The flow sensor can be connected to a computer programmed to perform the calibration method, determine the actual flow rate of the sensor, and make appropriate adjustments to the flow rate of a pump.
Description
- The application is a continuation-in-part of and claims priority to U.S. patent application Ser. No. 10/851,728, filed May 21, 2004, published as US 2005/0257595 A1 on November 24, 2005, titled “Flow Sensor Calibration Methods and Apparatus,” which is hereby fully incorporated by reference herein.
- The invention relates to methods and apparatus for calibrating and using flow rate sensors useful in liquid chromatography, mass spectrometry, and other analytical methodologies. More particularly, the invention relates to methods and apparatus useful for the calibration and operation of ultra-low flow rate liquid sensors used in micro/nano flow chromatography, mass spectrometry and other analytical applications.
- Much of the analytical drive in biological research areas results from the desire to understand biological systems and to develop therapeutic agents for treating disease. Increasingly, worldwide research is focused on obtaining an understanding of protein pathways in organisms, and on the correlation between protein modification and disease. Current thinking in biology avers that manifestation of disease states ultimately involves the interaction of proteins in a manner that differs from non-disease tissue. The interest in understanding protein function is therefore becoming prevalent in all biologically relevant fields, including proteomics, biotechnology, drug discovery, and molecular diagnostics.
- The study of protein samples obtained directly from tissue or cell media or cell media is extremely difficult work. Many biologically significant proteins are present in minute quantities in living organisms, and can be produced using in vitro methods only in limited and minute quantities.
- One conventional technique for protein identification is mass spectrometry (MS) as a detection and quantification tool. Mass spectrometry is often used because it is more or less universally amenable to diverse analytes, and provides large amounts of useful analytical information from relatively small amounts of biological sample.
- Mass spectrometry is conventionally used in biological research and development activities to identify unknown compounds, or to examine the structure or abundance of certain compounds. Simply put, a mass spectrometer is a detector that is capable of identifying the molecular mass of constituents within a mixture. The mass spectrometer produces a mass spectrum that can be used to identify unknowns or to determine the basic building blocks that constitute a molecule's structure.
- Conventional MS identification techniques typically rely on four steps:
- 1) The analyte (e.g. protein or peptide) is separated from its complex biological matrix and converted to an analyzable species. Typical methods used in this step may involve any combination of such techniques as gel electrophoresis, adsorption chromatography, size exclusion chromatography, immunoprecipitation, blotting, osmosis, and chemical labeling, amongst many others. The methodology chosen for a given application typically depends on the nature of the analyte, its matrix, and the type of information required from the investigation.
- 2) The sample is ionized to produce gas-phase molecular ions. The ionization method may be electrospray, nanospray, atmospheric pressure chemical ionization (APCI), or matrix assisted laser desorption/ionization (MALDI), amongst others. In conventional methods, electrospray, nanospray, and MALDI are utilized for the analysis of proteins and peptides.
- 3) The analyte's molecular ion is introduced into a high vacuum and fragmented to produce ions. The number and size of the “daughter” ions produced are determined by the structure of the analyte and the fragmentation method. Typically, molecular ions are fragmented inside the mass spectrometer by colliding with them with a low-pressure gas.
- 4) The molecular fragments are sorted according to molecular mass and detected, producing a fingerprint of the original protein. This fingerprint can be used to determine characteristics (e.g., identity, quantity, or structure) of the unknown protein.
- The methods used in
step 1 are also conventional in most other fields of biological and chemical analysis and are not limited in scope to MS detection methods. - For complex and more difficult protein separation and analysis, the ionization procedure in
step 2 often employs nanospray techniques. The reasons for this method choice may include: 1) very small sample volumes typically require low flow rate analytical methods for efficient analysis, 2) the nanospray procedure is typically amenable to established chromatographic methods (albeit at lower flow rates), and 3) the efficiency of sample ionization increases with reduction in flow rate (thus increasing the sensitivity of analysis for low-abundance proteins/peptides). - In conventional nanospray applications, an analyte flow stream is ionized and introduced into a mass spectrometer by passing a solution of the analyte through a very small (e.g., about 20 μm inner diameter) high voltage electrified needle. The fluid passing through the needle accepts electrical charge imparted by the applied voltage, and emerges from the open end of the capillary as a finely dispersed aerosol. This charged aerosol travels at atmospheric pressure toward a counter electrode at the mass spectrometer entrance. Once the aerosol enters the mass spectrometer, it largely consists of gas-phase ions that may be analyzed using
steps - In addition to mass spectrometric elucidation methods, diagnostic research has been increasingly concerned with investigating biological systems using microelectromechanical systems (MEMS). When applied to biological investigation, these methods are sometimes referred to as Lab-on-a-chip (LOC) analyses. Systemically, many LOC instruments can be viewed as incorporating nano flow, microarray, and biosensor technologies into an integrated device. In a typical approach, macroscopic analytical devices (e.g., valves, columns, detection chambers, and flow channels) are miniaturized and micro-fabricated onto glass, silicon, or polymeric material.
- To date, such systems and methods utilize non-feedback based pumping solutions, including syringe and positive displacement pumps. Because of the relatively small flow rates required in such applications, many conventional systems utilize electroosmotic flow (EOF) pumping in lieu of mechanical pumps. Although the EOF pumping method is convenient to use and can operate at low average flow rates, it presents significant disadvantages when required for precise control, or when used on fluids that have high ionic strength.
- In addition to the foregoing applications, worldwide experience over the past several years have heightened interest in the detection and elucidation of chemical or biological threat agents introduced into the environment through terrorist or military action.
- In a conventional implementation, a point detector for such threat agents operates as a self-contained analytical module that is capable of analyzing environmental samples and initiating an alarm if hazards are found to be present above a prescribed threshold concentration. Current developmental point detection technologies rely on such conventional techniques as enzyme linked immunosorbent assay (ELISA), polymerase chain reaction (PCR), surface plasmon resonance (SPR), cell cytometry, cell staining, immunoprecipitation, mass spectrometry, and native fluorescence, to name a few.
- In order to adapt higher flow methods to nanospray, lab-on-a-chip, or other ultra-low flow methodology, two different approaches have been utilized. In the “split flow” method, a fraction of the analytical fluid is split from a conventional high-flow stream into a low-flow stream and the reduced flow stream is applied to the analytical method. Equipment designed to do this are known as splitflow instruments. In the typical conventional split flow configuration, the flow stream is passed into a tee connector with different backpressures generated on each outlet arm of the tee. One arm becomes the high-flow arm and the other becomes the low-flow arm. The ratio of high to low flow is determined by the pressure ratio between the two arms. Flow split ratio can be adjusted by changing tubing lengths or diameters (thus adjusting the pressure generated at a given flow rate) on each arm.
- The two largest disadvantages of the split flow technique are that most of the analytical solvents is discarded in the process, and that high precision is very difficult (or impossible) to obtain at low flow rates. Imprecision in flow rates can easily result from changes in temperature, particulates in the fluid, or gradual changes in backpressure created from downstream devices.
- In “splitless” methods, the chromatographic and upstream fluid systems are converted to low flow technologies. This method requires pumping and fluid transfer systems that are capable of operating at rates from 10-1,000 nl/min. Such methods are deemed splitless flow. The main disadvantages of this method are the requirements for precise control of ultra-low flow rates and the requirement for very low dead volume flow paths in the instrumentation. The splitless configuration has the advantage of very low solvent consumption, and is directly amenable to injection and handling of very small samples.
- Analytical methods and systems have been developed that demand sensitive high-throughput analyses of biological materials in small quantities. Often, such analyses require precise control of the fluid flow rates in the range of about one (1) nano-liter (nL) per minute to about five (5) microliters (μL) per minute, with pressures varying over a range of several orders of magnitude. Such analytical applications include, among others, nano-scale liquid chromatography (nano-LC), mass spectrometry (MS), or capillary electrophoresis (CE). These microfluidic applications typically utilize fluid flow rates as low as tens of nanoliters per minute up to several microlitres per minute. Designing systems to precisely achieve and maintain ultra-low flow rates is a difficult task, fraught with several potential problems.
- One problem affecting such microfluidic techniques comes from the susceptibility of various components of systems used for conventional ultra-low flow applications to compress or decompress in response to a change in system pressure. This component adjustment to pressure change often creates a significant delay time before achieving a desired flow rate in conventional microfluidic systems and applications, and can also hinder accurate flow rate adjustment in such systems and applications.
- Another persistent problem with such conventional microfluidic systems and applications occurs when air or other gases are inadvertently entrained into the flow path of such a system. If these compressible gases are present in the flow path of conventional systems for such applications, the compression and expansion of gas bubbles creates difficulties in achieving a desired flow rate.
- In many conventional microfluidic systems, the flow rate of a fluid is established in a pump by displacing liquid at a controlled rate using, for example, a piston or syringe plunger. To obtain desired flow rates in such conventional systems, the displacing element of the pump is moved at a fixed velocity using a preprogrammed control system. Such conventional systems often show undesirable flow rate fluctuations created from imprecision in the mechanical construction of the drive system used to displace the liquid. In conventional lead screw-driven systems, for example, inaccuracies often arise from periodic changes in screw characteristics as the screw turns through a complete revolution, and from inaccuracies in thread pitch along the screw, among other types of mechanical errors.
- In order to overcome these difficulties in achieving and maintaining desired flow rates, conventional flow sensors may be employed to allow the system to compensate for inaccuracies through use of a feedback loop to a preprogrammed control system. Many conventional flow sensors used in microfluidic analysis, such as the SLG1430 sensor that is commercially available from Sensirion Inc. (of Zurich, Switzerland), have a non-linear response to fluid flow. For such flow sensors, the sensor response to increasing flow rate approximates a polynomial equation, with the equation order and constants dependent on variables such as flow sensor design, the liquid that is being monitored, and the operating flow rate range.
- In order to use such conventional flow sensors to measure and maintain accurate ultra-low flow rates in conventional systems via a feedback loop, the sensor must be calibrated for the solvent that is to be passed through the sensor. Conventional calibration methods usually involve preparation of a list of the sensor responses at different flow rates for a given solvent. When a particular solvent is used, the actual flow rate is obtained by comparing the sensor response to tabulated calibration values gathered from repeated observations made for that particular sensor and solvent combination. Calibration curves for a given sensor and solvent can be obtained by fitting the calibration data to a best-fit curve from the empirical data in such conventional calibration methods.
- A major problem with this conventional calibration tabular methodology is that data values must be collected for any solution mixture that is to be passed through the system. Doing so for numerous solvents can require a significant amount of time and effort. Moreover, for reliable operation, this data must be collected using a precise flow rate reference. Often, a conventional microfluidic system will be used to deliver different solutions that possess diverse characteristics, and calibrating a conventional system for these various solutions is often time consuming and laborious.
- In conventional chromatograph applications, analytical columns consist of narrow-bore tubes made of fused silica, polymeric material, stainless steel, or other material that should be compatible with the analyte mixture and mobile phase. The columns may be one centimeter to several meters long, and they are typically packed with small beads ranging in size from a few microns to several millimeters in diameter. The tubes may have fritted on the downstream end to prevent loss of beads when liquid is flowed through. Long-chain carbon polymers are coated on the beads to comprise the stationary phase in conventional reverse-phase separations. A sample is introduced into the head of the column using an injection valve. Detection is performed using UV absorbance, fluorescence, mass spectrometry, emission spectroscopy, nuclear magnetic resonance (NMR), or some other method that is sensitive to the analyte in question.
- When the analyte compounds are similar in nature, then the mobile phase mixture can remain constant throughout the entire separation. This type of separation is known as isocratic. For more complex mixtures that contain diverse compounds covering a range of hydrophobicity, increasing the organic content of the mobile phase during the separation may be desired. This later method is known as gradient chromatography.
- In a conventional reverse-phase gradient chromatography analysis, the amount of organic modifier in the mobile phase may be increased from the beginning of the analysis until elution of the most hydrophobic compounds. This increase in hydrophobic nature of the mobile phase serves to enhance elution of very highly retained compounds, but allows the weakly-retained compounds to separate under low organic modifier concentrations.
- The present invention, among other things, provides a method for calibrating a liquid flow sensor by pumping a volume of a fluid through the sensor for a series of fixed rates. In one embodiment, the flow rate is first determined by moving a displacing element at a controlled velocity and, by use of a valve, allowing the system output to dispense through a low-pressure orifice or piece of tubing. Because the system is pumping at low pressure during the calibration procedure, system response is rapid, regardless of component compressibility or entrapped gas pockets. In fluidic systems that utilize lead screw drives, flow sensor response is determined by averaging the measured flow rate for a complete revolution of the pump lead screw, thereby minimizing periodic lead screw derived flow rate noise.
- The flow sensor response can be determined for several different flow rates, depending on the order of polynomial fit. In one embodiment, the sensor response is approximated using the general equation:
y=ax 2 +bx+c
where y is the sensor response, x is the actual flow rate, a is the first quadratic constant, b is the second quadratic constant, and c is the equation intercept, which is the sensor response measured with no fluid flow. In this embodiment, the constants can be determined by measuring the sensor response and actual flow rate at three individual pump infusion rates. - In another embodiment, during which a flow sensor can be calibrated during operation of an analytical system, the actual flow rate is determined by evaluating the quadratic equation using:
using the real root. In this embodiment, x is determined from the measured flow sensor response. - In yet another embodiment, the sensor may be calibrated in the same general way over a larger flow rate range by extending the order of the polynomial and using more calibration data points to determine the constants.
- In another embodiment, a gradient flow system with two or more pumps with corresponding drivers, fluid sources, selection valves, and flow sensors may be used to mix fluids from the two or more sources. In such a system, one or more of the pumps may be calibrated as summarized above and described below. In addition, and in another embodiment, controllers may be used in such a gradient system so that one or more pumps is automatically calibrated. In addition, the flow rate of one or more of the fluids in a gradient system may be controlled automatically in response to signals from one or more flow sensors in the gradient system.
- It is an object of the invention to provide methods and apparatus which allow precise calibration of a flow sensor in a system which has periodic flow rate fluctuations.
- It is another object of the invention to provide methods and apparatus which allow precise calibration of a flow sensor by minimizing the potential effects of trapped gases or compression of system components.
- It is yet another object of the invention to provide methods and apparatus which allows precise calibration of a flow sensor for use with a given fluid over a wide range of flow rates.
- It is yet another object of the invention to provide methods and apparatus to allow precise calibration of a flow sensor during operation of an analytical system to thereby allow an operator to obtain a desired flow rate.
- It is an object of the invention to provide a method that accurately and precisely allows an operator to calibrate a flow sensor for a particular fluid more quickly and easily than conventional methods.
- It is an object of the invention to provide a method which allows an operator to calibrate a flow sensor for a fluid without having to generate or use a table of empirical data.
- It is an object of the invention to provide a method that allows precise flow control using inexpensive, mechanically-driven pump systems.
- It is an object of the invention to provide a method that allows rapid in-situ calibration of a flow sensor while consuming small amounts of fluid.
- These and other objects and advantages of the invention will be apparent from the following detailed description.
-
FIG. 1 is a schematic diagram of the components of a fluidic system in accordance with the present invention. -
FIG. 2 is a flow diagram showing the steps of a method in accordance with the present invention. -
FIG. 3 is a schematic diagram of a system used to provide an example test of the methods of the present invention. -
FIG. 4 is a graph showing the data collected in one example of the present invention. -
FIG. 5 is a flow diagram showing an alternative embodiment of the present invention. -
FIG. 6 is a graph showing data collected in another example of the present invention. -
FIGS. 7A-7S are examples of source code in accordance with the present invention. -
FIG. 8 is a schematic diagram of the components of a system in accordance with an embodiment of the present invention. -
FIG. 9 is a graphic user interface provided to a user of a system in accordance with an embodiment of the present invention. -
FIG. 10 is a portion of a computer program used in a system in accordance with an embodiment of the present invention. -
FIG. 11 is a diagram illustrating results obtained with a system in accordance with the present invention. -
FIG. 12 is a diagram illustration flow rates obtained with a system in accordance with the present invention. -
FIG. 13 is a diagram illustrating flow responses obtained with a system in accordance with the present invention. -
FIG. 14 is a diagram illustrating a designed step change in flow rate obtained with a system in accordance with the present invention. - Referring to
FIG. 1 , the components of a fluid control system are depicted. It will be appreciated by those skilled in the art that the methods and apparatus of the invention may be used with chromatography, mass spectrometry, capillary electrophoresis, or other analytical applications and systems. As shown inFIG. 1 , this particular embodiment of the fluid control system includes aselection valve 4 with a plurality of ports. Oneport 4 a ofvalve 4 has a fluid connection to a first side offlow sensor 2. The second side offlow sensor 2 has a fluid connection to the input and output port of apump 1. Those skilled in the art will appreciate that any one of a number of conventional selection valves, flow sensors, and pumps may be used forvalve 4,sensor 2, andpump 1. For best results, I prefer to use the 100 μl, positive displacement pump which is commercially available from Sapphire Engineering Inc. (Pocasset, Mass., USA), the flow sensor SLG 1430 which is commercially available from Sensirion Inc. (Zurich, Switzerland), and the V-485 selection valve that is commercially available from Upchurch Scientific, Inc. (Oak Harbor, Wash., USA). - As shown in
FIG. 1 , thepump 1 is electronically connected to acontroller 3 which, in turn, is electronically connected to adriver 5. Thecontroller 3 is also electronically connected to thesensor 2. Thecontroller 3 can be preprogrammed with computer software to perform the steps of the method of the invention. For best results, I prefer to use as thedriver 5, a driver MICROLYNX® which is commercially available from Intelligent Motion Systems Inc. (of Marlborough, Conn., USA). Thecontroller 3 preferably consists of a preprogrammed PIC 18F452 microcontroller, which is commercially available from Microchip Technologies Inc. (of Chandler, Ariz., USA) with serial communications and digital input/output connections. Thecontroller 3 is essentially an application specific integrated circuit, with the computer program incorporated therein. The computer program preferably is written to allow thecontroller 3 and the system to perform the steps detailed below. - Still referring to
FIG. 1 , it can be seen that at least one of the output ports ofvalve 4 is in fluid communication with a waste receptacle 7. Another port of thevalve 4 is in fluid communication with areservoir 8, which holds the subject fluid to be considered for purposes of calibration (often referred to as the solvent). Theport 4d of thevalve 4 is in fluid connection with the input of a downstreamanalytical system 6. Those skilled in the art will appreciate that any of a number of analytical systems may represent the downstream analytical system, including chromatography or mass spectrometry systems. - The
controller 3 is electronically connected to thevalve 4, and controls the position of thevalve 4. Those skilled in the art will appreciate that any of a number of analytical systems or devices may be attached to other unused ports on the chosen selection valve. - Referring now to
FIG. 2 , the steps of the method of the invention will be described with respect to the flow diagram. (For ease of reference, the same numbers are used to refer to the components shown inFIG. 1 .) Before beginning the calibration cycle, it is useful to first purge and prime the system to remove excess trapped air or other gases. Accordingly,step 100 is filling the pump 1 (inFIG. 1 ) from thereservoir 8 via theselection valve 4. Next, thepump 1 is rinsed 110 by expelling the fluid in thepump 1 to a waste-receptacle viavalve 4. Thepump 1 is then refilled 120 with the fluid of interest. Together, steps 100, 110, and 120 can be considered the purging/priming cycle. - Still referring to
FIG. 2 , the calibration cycle is described next. Instep 130, an operator pumps a volume of the fluid through thesensor 2 to a waste receptacle via thevalve 4. There will be negligible pressure present in the system during thisstep 130. The operator then stops thepump 1 and the flow of the fluid through thesensor 2 atstep 140. Once the rate of change of flow sensed by thesensor 2 has minimized, the flow sensor will output this value and transmit it to thecontroller 3 asstep 145. This value transmitted to thecontroller 3 atstep 145 will be considered the constant c in the equation y=ax2+bx+c in the quadratic equation (or, if the controller is programmed to solve a cubic or other equation, the value shall be deemed the constant in such equation corresponding to the y-intercept in the equation). - During the
next step 150, the operator then starts thepump 1 to pump the fluid so that it flows at a preselected rate, such as 2 microliters per minute through thesensor 2 and to a waste receptacle. The rate of flow can be determined by knowing the linear distance that the piston of thepump 1 travels based on the pitch of the lead screw thread that drives the piston of thepump 1. The cross-sectional area of the piston inpump 1 is also known. Thus, the volume of the fluid moved per unit time per rotation of the lead screw (or the lead screw nut, as the case may be) is known or readily determined. For best results, thecalibration step 150 should be performed only with the output of the fluid flowing to waste so that there is negligible back pressure within the microfluidic system and therefore any elasticity of any components within the system will not be of significance in the calibration. Once the preselected first flow rate is reached, thesensor 2 will transmit a second averaged value to thecontroller 3 atstep 155. This averaged value is determined by averaging the flow sensor response for the entire cycle of periodic noise in the pump mechanism. In the case of a lead screw driven pump, the flow rate is averaged for a complete turn of the lead screw. - Still referring to
FIG. 2 , the operator then sets thepump 1 to pump the fluid so that it flows at a second preselected rate atstep 160, such as 4 microliters per minute, through thesensor 2 and to a waste receptacle. As noted above, the rate of flow can be determined precisely by knowing the dimensions of the distance traveled by the lead screw of the piston ofpump 1 and the area of the piston inpump 1. Instep 165, once the second preselected flow rate is reached, thesensor 2 will transmit a third value to thecontroller 3. This averaged value is determined by averaging the flow sensor response for the entire cycle of periodic noise in the pump mechanism. In the case of a lead screw driven pump, the flow rate is averaged for a complete turn of the lead screw. - For the highest order n in the equation to be solved, we prefer to measure and determine the
sensor 2 responses for n+1 different flow rates. By using the measuredflow sensor 2 responses and the known pumping rate of the fluid for thecorresponding sensor 2 output responses, the operator can determine atstep 170 the constants a, b, and c for the quadratic equation (and other constants where the equation to be used has higher orders than the second). Alternatively, thecontroller 3 can be preprogrammed to determine 170 the values of the constants. - Once the
sensor 2 has been calibrated in accordance with the invention, the system can be used by the operator as follows: The operator can for example read the output of theflow sensor 2 during operation of the system atstep 180. The flow rate value output by thesensor 2 can also be determined automatically by the preprogrammedcontroller 3. Thecontroller 3 can be preprogrammed so that it transmits appropriate signals todriver 5 atstep 190 depending on the incremental values of flow rate of change measured by thesensor 2 and transmitted to thecontroller 3. Thedriver 5 then adjusts the output of thepump 1 based on the signals received bysensor 2 to maintain the flow rate set by the operator of the system atstep 195. - Although not shown (apart from controller 3), those skilled in the art will appreciate that a preprogrammed computer can be used as the
controller 3. Those skilled in the art will appreciate that such a computer can be easily programmed to receive and store the values it receives from thesensor 2, together with the information for determining the flow rate based on the dimensions of the pump. The programmed computer can be set so that it automatically calculates the constants a, b, and c (or others depending on the particular equation to be solved) and then outputs those values for use by the operator. Similarly, the computer (not shown apart from controller 3) can be preprogrammed with such constants so that the computer receives updated signals corresponding to the flow rate as determined by thesensor 2 during operation, the computer (not shown apart from controller 3) and, as appropriate according to its programmed instructions, sends signals to thedriver 5 to adjust thepump 1 to obtain the flow rate selected by the operator for operation of thesystem 1. Those skilled in the art will appreciate that such computer programs can be stored on the hard drive of the computer (not shown apart from controller 3), or on a disk, CDROM, DVD, EEPROM, ASIC, per drive, or other electronic storage device with non-volatile memory. - Referring now to
FIG. 3 , anexperimental system 301 used to evaluate one embodiment of the invention is shown. InFIG. 3 , thesystem 301 includes a high-pressurepositive displacement pump 310, an inlinenon-invasive flow sensor 315, and a four-way selection valve 320 (for filling and dispensing solvent mixtures in the system 301). Thesystem 301 maintains a precise flow rate to a desired value regardless of back pressure insystem 301. Thesystem 301 is able to use the output signal from theflow sensor 315 to adjust the piston velocity of thepump 310 to clamp the output flow rate from thepump 310 to the selected value. As shown inFIG. 3 , theexperimental system 301 also includes a source of a solvent 322, which is in fluid communication with theflow sensor 315. Theflow sensor 315, in turn, is connected to allow fluid communication with both a waste receptacle 324 and aninjection valve 330. The injection valve is also in fluid communication with asample syringe 332 and asecond waste receptacle 334. In addition, theinjection valve 330 is in fluid communication with a first end of acolumn 340, which is housed within acolumn oven 345. Thecolumn oven 345 is used to maintain the temperature of thecolumn 340 at 35.0° C.±0.05° C. The second end of thecolumn 340 is in fluid communication with adetector 350. For this experiment, I used a V-485 NANOPEAK injection valve (commercially available from Upchurch Scientific of Oak Harbor, Wash.) for theinjection valve 330, a 15 cm by 75 μm inner diameter nano column (the PEPMAP C18 column commercially available from LC Packings of Amsterdam, The Netherlands) for thecolumn 340, and an ULTIMATE UV detector (also commercially available from LC Packings of Amsterdam, The Netherlands) for thedetector 350. - Using a timed injection routine, numerous 5 nL plugs of a mixture consisting of naphthalene, fluorine, biphenyl, and uracil dissolved in 75% acetronitrile/water were repeatedly injected into the
column 340. Analytes were detected via absorbance at 250 nm using thedetector 350. All experimental data were collected at 1.6 Hz using analog/digital circuitry and preprogrammed computer software performing the methods described above. The data collected are shown graphically inFIG. 4 . As shown inFIG. 4 , the system flow sensor output for a variety of increasing flow rates applied to the column 340 (over a range of 50 nL/minute to 700 nL/minute) shows that the system flow sensor possesses a 90% risetime of 12 seconds at 700 nL/minute (a pressure of 3,000 psi) and exhibits a RMS flow rate noise of approximately 1 nL/minute at an output flow rate of 50 nL/minute. - Referring now to
FIG. 5 , a flow chart of an another alternative embodiment of the present invention is shown. Instep 500, the system begins the methods of the invention. Instep 501, the system checks to see if the flow sensor has already been calibrated. This can be done by checking a flag or the status of a value stored in computer memory. If the flow sensor has been determined to have been calibrated atstep 501, then the next step is reading the data value from the flow sensor atstep 505. Thisstep 505 is repeated as many times as is necessary to obtain the data values needed to calculate the constants for the polynomial equation to be solved. If the equation is of the order n, then at least n+l data values should be measured. For example, if the flow sensor is known to have a non-linear response that is quadratic, then the program will need to measure at least three data values in order to solve the equation y=ax2+bx+c. Similarly, if the equation used to model the response of the flow sensor is cubic, then at least four data values should be read from the flow sensor. - Still referring to
FIG. 5 , the data values read instep 505 are provided to the preprogrammed computer (not shown inFIG. 5 ) so that it can use the data values measured by the flow sensor to calculate the constants and solve the polynomial equation. By solving the equation, the computer has calculated a value for the real flow rate of the system at step 510. Next, at step 515, the computer reads the required flow rate from memory. This value can be input by the operator when setting up the system. Atstep 520, the computer then calculates the required pump velocity needed to achieve the preselected flow rate based on the value of the real flow rate and the stored value for the desired flow rate. Atstep 525, the computer then sends a signal to the pump driver in order to have the pump operate at the required velocity determined instep 520. Atstep 530, the system checks to see if the user or operator has input a new flow rate. If not, the next step is to determine if a new calibration is required. Of course, an operator may choose to calibrate based on the passage of time or after some other selected interval or event has occurred. If not, the next step is to repeatstep 505 and continue the foregoing cycle. If a user has input a new flow rate, the system first stores the new value in computer memory atstep 550, as shown inFIG. 5 . The system then checks to see whether a new calibration is required atstep 540. - Still referring to
FIG. 5 , if the computer determines that a new calibration is needed atstep 540, the computer then performs the following steps. First, the computer sends a signal to the valve (not shown inFIG. 5 ) to switch the fluid communication with at least one valve port to a waste receptacle atstep 560. Next, atstep 561, the computer sends a signal to stop the pump. Atstep 562, the data value is read from the flow sensor. Although this can be a single data reading, I prefer to have a number of readings taken of the flow sensor's reading, each of which can be stored in the computer memory and then averaged. Once the average has been obtained instep 562, the computer sends a signal to have the pump operate at a preselected first speed atstep 563. Instep 564, a number of values are read from the flow sensor, stored in computer memory and an average of those values is determined. Next, instep 565, the computer sends a signal to the pump to have it operated at a second preselected speed. Instep 566, a number of readings are taken of the flow sensor, stored in computer memory, and an average is determined. Instep 567, the computer stores the values for the averages determined in thesteps step 568, the computer then sends a signal to stop the pump. The computer then calculates the constants for the polynomial equation corresponding to the flow sensor using a least-squares algorithm (sometimes referred to as a “best square fit”), or a similar algorithm. Once the constants have been calculated and the equation solved, the computer can use those values in the equation based on the new required flow rate input and the new calibration is completed atstep 569. Once the new calibration is completed atstep 569, the computer can then repeat the performance of the steps by returning to step 505 and reading the values of the flow rate from the flow sensor. - Referring now to
FIG. 6 , data from another example of the present invention is provided in graphical form. InFIG. 6 , the flow rate FR is shown, as is the measured pressure P.FIG. 6 shows that the pressure P rapidly adjusts to changes made to the flow rate in a system using the methods of the present invention. - Now referring to
FIGS. 7A-7S , source code of a computer program is provided, in accordance with one embodiment of the present invention. The source code shown inFIGS. 7A-7S may be used to implement some or all of the steps of the methods of the present invention as described above. - Those skilled in the art will appreciate that the methods of the invention can be used to attenuate noise from mechanical sources, such as the leadscrew of the pump. This can be done by averaging the values obtained from the flow sensor over one entire rotation of the leadscrew. For example, when a stepping motor (not shown) is used to actuate the pump, the number of steps corresponding to a complete rotation of the leadscrew can be determined. For example, in the system used in the above example, the stepping motor (not shown) has 200 steps per complete revolution, and a complete revolution of the leadscrew pumps 5 μL of the fluid. At a rate of 1.56 Hz, the computer is able to obtain 94 data points per minute, all of which can be stored in memory of the computer and then averaged. This averaging eliminates the variations which can result from the mechanical variations in the leadscrew due to thread size and the like. Those skilled in the art will appreciate that this method can also be used to calibrate any mechanical pump that provides periodic noise (i.e., fluctuations in the data due to various mechanical features) by averaging the data values obtained over the entire period of the noise source, thus allowing a user to calibrate for noise from such pumps with drive mechanisms other than leadscrews.
- Attached hereto as Appendix A, and incorporated fully by reference herein, is a copy of the User Guide—100 μL version for the Scivex Confluent Nano Fluidic Module. This Appendix A provides further details and information regarding the use of calibration methods and apparatus of the present invention, such as in the operation of a pump controlled by a preprogrammed computer which uses values measured by a flow sensor to calculate a solution to a polynomial equation, such as is described above, then uses the calculated values to determine what, if any, adjustments to the pump's actions need to be made to obtain a preselected flow rate.
- Those skilled in the art will appreciate that the data points obtained using the methods of the invention can be used to perform other interpolation algorithms, such as a cubic spline. Such techniques include those described in the book “numerical Recipes in C: The Art of Scientific Computing” by William H. Press, published by the Cambridge University Press in 1988, which is hereby incorporated by reference herein. Those of skill in the art will also appreciate that the methods of the invention can be used with other equipment and solution combinations. For example, a system using two pumps (not shown) and two solutions (not shown) that are mixed together using a T-junction (also not shown) can be used for a binary gradient system.
- A new gradient system has been developed and an embodiment of the same is now described as follows. A new gradient
nanoflow pump system 800 is designed to deliver splitless nano-gradients in the 50-4500 nanoliter per minute (n/min) range, yet is able to operate at pressures as high as 5000 pounds per square inch or so. Moreover, it may be made of materials that are biocompatible and are otherwise compatible with most commonly used chromatography solvents. Referring now toFIG. 8 , a schematic diagram of one embodiment of thegradient system 800 is shown. As shown inFIG. 8 ,gradient system 800 includes several components, including two high pressurepositive displacement pumps stepper motor drivers nano flow sensors 820, 822, threemicrocontrollers selection valves mixing chamber 850, and acomputer 860. In addition,FIG. 8 also shows the use of twofluid sources FIG. 8 , thefluid sources valves valves pumps valves flow sensors 820, 822, respectively, which are in turn in fluid communication withmixer 850. Afluid outlet tube 880 is provided from themixer 850; theoutlet tube 880 provides the mixed fluid from thegradient system 800. As also shown inFIG. 8 , the computer 360 is in electrical communication, such as via the RS-232 electronic signal protocol, with amain controller 834. Themain controller 834, in turn, is in electrical communication with each ofcontrollers controllers drivers flow sensors 820, 822 andvalves system 800 can be considered as comprising twoindependent units 885, 887, which can be operated and function in the manner described below. - Still referring to
FIG. 8 , the operation of thegradient system 800 is now described. In normal operation, eachpump position selection valve valves valves - The
gradient system 800 can be operated as twoindependent pump units 885, 887 whose outputs are combined via amixing chamber 850. Eachpump unit 885, 887 is managed by amicrocontroller valve driver common host controller 834 is responsible for timing and gradient formation; this controller synchronizes the activities of bothpumps 885, 887. Those skilled in the art will understand thatcontrollers computer 860 can be used in place ofcontrollers controllers gradient system 800 can be a physically and/or operationally stand-alone unit. Examples of computer software for various functions are described both above and below. - When operating in normal feedback mode, the velocity of each
pump flow sensor 820, 822 that is inline with the outlet of thepump valves controller pump respective flow sensor 820, 822 output signal and performs proportional-integral-derivative (PID) control on thepump micro-stepping motor driver pump pump - During operation, the
selection valve pump pump pumps selection valve - During pump filling operation, the
pump valve solvent reservoir rear pump front pump valve - For regular dispensing operation, the
valve front pump valve rear pump valve pump - Solvent may also be delivered to a waste receptacle (not shown) by rotating the
valve rear pump pumps pump flow sensor 820, 822. This attachment has been omitted from the diagram to simplify the description. - Because the
gradient system 800 contains twopumps 802, 804 (one for each solvent), pumping may be performed by filling eachpump pump gradient system 800 supports operation at 250 nl/min and can provide 1000 minutes of analysis time before thepump pumps - Continuous flow pumping schemes can be developed for the
gradient system 800, such as by incorporating additional pumps and controllers (not shown). Those skilled in the art will readily understand that thegradient system 800 may be used with such additional components. - The
gradient system 800 usesnon-invasive flow sensors 820, 822 for measurement and feedback of flow rate data. Thesesensors 820, 822 operate by measuring the flow-induced modulation of heat transfer through the wall of fused silica capillary. Different solution mixtures may possess disparate thermal characteristics, requiring re-calibration of theflow sensor 820, 822 if it is to be used for alternative solutions. The calibration techniques and apparatus discussed above may be used to precisely calibrate and adjust flow rates through thepumps gradient system 800. The flow sensors may be of a type and configuration as is shown in Dykas, et al., U.S. Pat. No. 7,021,134 B2, issued Apr. 4, 2006, which is hereby incorporated by reference herein. Those skilled in the art will appreciate that other flow sensing apparatus may be used if desired. - For example, the
gradient system 800 calibration procedure can automatically collect integrated flow information at several different flow rates. In this procedure, thepump pump - The raw sensor data collected during the calibration procedure may be used to produce a best-fit equation defining sensor response over the feedback operating range of the
pump individual pump controllers - One specific embodiment of the automated calibration routine is described in the following table:
TABLE 1 Step Description 1 Switch valve to the Dispense position. 2 Dispense fluid for ½ minute at 2000 nl/ min 3 Stop pump 4 Switch valve to the Waste position 5 Average the zero flow response for ½ minute 6 Switch valve to the Dispense position 7 Increase the pump speed to 4 microliters per minute. 8 Integrate the flow sensor response for 1 turn of the pump lead screw. 9 Increase the pump speed to 6 microliters per minute. 10 Integrate the flow sensor response for 1 turn of the pump lead screw. 11 Increase the pump speed to 8 microliters per minute. 12 Integrate the flow sensor response for 1 turn of the pump lead screw. 13 Stop the pump 14 Calculate cubic equation - Using this method, each fluid may be uniquely defined using four numbers: these numbers are the equation coefficients a, b, c, and d in the generic cubic equation y=ax3+bx2+cx+d. Users can upload and download the calibration equation for any solvent on each
pump computer 860 or non-volatile memory of any or all ofcontrollers - In one embodiment, the
gradient system 800 can be operated in three different modes: 1) direct control from ahost computer 860, 2) stand-alone programmed operation, and 3) operation from digital signals presented to the system 800 (so-called contact closure control). All three of these control modes may be utilized in a given experiment. For example, a user may begin by homing and filling thepumps host PC 860, and then the user downloads an automated gradient software program (not shown) to thesystem 800. After the gradient program has begun running on thesystem 800, it is usually timed and coordinated with data collection using contact closure control. - The
gradient system 800 can be operated from ahost computer 860 using a pre-defined command set communicated through RS-232 protocol. In one embodiment, a graphical user interface (GUI) may be used by an operator for operation and programming of thegradient system 800. TheGUI 900 of one embodiment is shown inFIG. 9 . As shown inFIG. 9 ,GUI 900 has a blue-tintedportion 910, with theblue portion 910 corresponding to the unit 885 (pump A) shown inFIG. 8 , andred portion 920 corresponding to unit 887 (pump B) shown inFIG. 8 . The data illustrated in red inFIG. 12 below corresponds to data from pump A 885, while the data illustrated in blue inFIG. 12 below corresponds to data frompump B 887. Those skilled in the art will appreciate thatcomputer 860 may be of any desired type of conventional personal computer (PC), such as are commercially available from Dell Computer Corp. of Austin, Tex. - In one embodiment, the commands used for operating the
gradient system 800 directly from ahost PC 860 are given in Table 2. As evidenced by examining the table, thegradient system 800 module provides diverse functionality, allowing thesystem 800 to be operated in a variety of modes (isocratic, gradient, load and wash, etc.). Each of the command strings may be sent to thesystem 800 using RS-232 protocol and is terminated with a carriage return for simplicity of communication.TABLE 2 Command Action @axxxxxx Set position of pump A to xxxxxx @bxxxxxx Set position of pump B to xxxxxx oaxxx Set pressure sensor offset of pump A (for pressure calibration) obxxx Set pressure sensor offset of pump B (for pressure calibration) !a (b) Cancel calibration on pump A (B) rxxxxx Set total flow rate (A + B) =xx Set percent B cala Calibrate pump A calb Calibrate pump B daxxxxx Dispense pump A at rate xxxxxx (nl/min-valve switches automatically to dispense line) dbxxxxx Dispense pump B at rate xxxxxx (nl/min-valve switches automatically to dispense line) faxxxxx Fill pump A (nl/min-valve switches automatically to fill line) fbxxxxx Fill pump B (nl/min-valve switches automatically to fill line) go Start gradient (needs to be programmed first-see next section) homea Home pump A homeb Home pump B list List gradient program m1 Set output marker (1 is TTL low from rear port) paxxxxx Purge A pump with xxxxxnl per stroke pbxxxxx Purge B pump with xxxxxnl per stroke <a (b) Cancel purge on pump A (B) qa1(0) Enable (disable) PID on pump A qb1(0) Enable (disable) PID on pump B sas Stop pump A saxxxx Set pump A rate to xxxxnl/min (valve does not switch) sbs Stop pump B sbxxxx Set pump B rate to xxxxnl/min (valve does not switch) tx.xx Set time constant for flow rate buffer (0.1-5) vaf Set valve A to Fill vac Set valve A to Column va1 Set valve A to Waste vbf Set valve B to fill vbc Set valve B to column vb1 Set valve B to Waste xaxxxxx Set first calibration constant for pump A yaxxxxx Set second calibration constant for pump A zaxxxxx Set third calibration constant for pump A xbxxxxx Set first calibration constant for pump B ybxxxxx Set second calibration constant for pump B zbxxxxx Set third calibration constant for pump B Begin download of gradient program End download of gradient program Stop gradient % xx Set percent B - As noted, the
gradient system 800 can be pre-programmed with computer software to operate autonomously after a series of time-based commands have been downloaded to thesystem 800. This methodology is termed gradient programming. There are several commands that may be used in a gradient program in addition to the ones listed in the previous section; illustrative examples of such commands are provided in Table 3.TABLE 3 Command Action % xx Set percent B ra1 Output high marker from rear of unit a1 Wast for trigger input on rear of unit O1(0) Set the output line to high (low) wait Wait loop Loop to beginning rxxxx Set total output rate to xxxx - Each of the commands in Table 3 can be programmed with the addition of time for the respective action. An example of a
gradient program 300 of one embodiment of the invention is shown inFIG. 10 . As shown inFIG. 10 , inprogram 1000, theprogram 1000 sets the total output rate to 300 nl/min, and then waits for an input trigger. After the trigger, thesystem 800 linearly increases the percentage of B delivered from 0% to 50% over a period of 1798 seconds. After arriving at 50% B, thesystem 800 steps its rate to 90% B and delivers for a period of 600 seconds, then ramps down to 0% B over a period of 400 seconds. Once the ramp down is complete, theprogram 1000 is repeated. These commands may be sent to thesystem 800 via the RS-232 communication protocol, and theprogram 1000 is stored in thesystem 800 until the power is cycled or theprogram 1000 is overwritten. - The
gradient system 800 may have two digital input/output (I/O) lines that can be used to synchronize thesystem 800 with external devices. One example is a TTL-compatible (0-5V) digital input (not shown) that is used to trigger an event in the system's 800 internal program (using the wait trigger command above). Another example of a digital I/O line is a TTL-compatible digital output (not shown) that can be sent at any time during operation of thesystem 800 to signal an external device. Additional I/O lines can be added to thesystem 800 if required for a specific implementation. - Preferably, the
gradient system 800 meets the following specifications:Specification Details Quantity Units Size L × W × H 8 × 8 × 5 Inches Weight Dependent on design 7 Lbs Power Peak power 24VDC, 3 A Pump capacity Per pump head 250 microliters Delay volume Dependent on external tubing <300 nanoliters length only Proportioning steps Relative change @ 300 nl/min 0.2 percent Gradient % RSD on elution time for <0.1 percent reproducibility sequential 1-hour runs Flow rate range 0.05-4 microliters per minute Flow rate accuracy >98 percent Pressure range 346 bar Solvent compatibility All solvents compatible with PEEK, Acetonitrile, water, stainless steel, zirconia, fused-silica, methanol, ethanol, Perlast ®, and UHMW propanol Chemical resistance All chemicals compatible with PEEK, TFA, acetic acid, stainless steel, zirconia, fused-silica, formic acid, etc. Perlast ®, and UHMW Automated control yes Pressure reading 0-344 bar - The
gradient system 800 provides extremely precise flow outputs from both the A and B pumps 885, 887, respectively, providing the excellent chromatographic separations shown inFIG. 11 . These data represent five overlaid 1-hour chromatographic runs performed at 300 nl/min. The percent relative standard deviation (% RSD) for elution time between runs is shown inFIG. 11 for many of the peaks in a peptide mixture. RSD values inFIG. 11 were calculated by taking the absolute standard deviation in elution time of a given peak for all runs, then dividing by the average elution time for that peak. These % RSD numbers indicate absolute variability in retention time of only 0.6-1.2 seconds over the entire run. - This peptide sample consisted of a tryptic digest of cytochrome c dissolved in water with 0.05% TFA as additive. These experiments were conducted at a total flow rate of 300 nl/min with an injection volume of 1 nl. For these experiments, the pump A 885 solvent consisted of 5% ACN/water with 0.05% TFA, and the
pump B 887 solvent consisted of 80% ACN/water with 0.04% TFA. The gradient profile was linearly ramped from 0-50% B over thirty minutes, followed by a wash at 80% B for 10 minutes. Prior to new injections, the column was re-equilibrated at 0% B for the balance of an hour. - The column used was a 75 μm ID×15 cm long PepMap™ nano-column packed with 3 μm C18 stationary phase, and detection was performed at 220 nm using the LC Packings' UltiMate UV detector module. This high level of run-to-run precision in
FIG. 11 represents a significant improvement (5-10 fold) over conventional instruments. The data shown inFIG. 11 indicate that overall relative precision increases with time during the run. The type of sample separation shown inFIG. 11 is typical for Proteomics analyses, and indicates that thesystem 800 is amenable to real world applications. -
FIG. 12 shows the output flow rates for both pumpunits 885, 887 over four sequential chromatographic runs performed on the nano-column used above withsystem 800. InFIG. 12 , the flow rate obtained from pump A (885) is shown in blue and the flow rate from pump B (887) is shown in red. The total output rate was 300 nl/min. The gradient ramp portions of these experiments show excellent flow rate linearity with a residual error (r2) of 0.9999. -
FIG. 12 shows variability in flow rate output for this series of experiments of less than 0.01% RSD run-to-run. This estimate of precision is calculated by taking the standard deviation in the average flow rate for the 0% B region over sequential runs, and then dividing by the average flow rate. -
FIG. 13 shows thesystem 800 responses to step changes in the desired flow rate on thegradient system 800. This experiment (the result of which are shown inFIG. 13 ) was conducted with a short length of narrow-bore capillary tubing inline with thegradient system 800outlet 880, providing the flow-dependent backpressures indicated inFIG. 13 . The achieved rates represent the mathematical average of the actual flow sensor output for the period of the step change. It should be noted that the desired and achieved rates are precise to within 0.01%. - For each of the rate levels shown in
FIG. 13 , the achieved (measured) output rate remains constant even though thesystem 800 backpressure is changing. This flow rate performance is a product of flow feedback and is not achievable with conventional split flow systems. Insystem 800, flow rate change requires approximately 10 seconds. -
FIG. 14 depicts a step change in flow rate of 1 nl/min performed at 300 nl/min withsystem 800. These data are indicative of the resolution achievable withsystem 800. InFIG. 14 , the desired rate is the average flow rate as measured by theflow sensors 820, 822 of thesystem 800. The desired step change (1 nl/min) and the achieved (measured) step change are within 0.009 nl/min. - The foregoing description of the invention is of the preferred embodiments and should not be considered a limitation on the scope of the invention claimed. Those skilled in the art will appreciate that changes may be made in the use of specific components, solutions, sample sizes, flow rates, and the like without departing from the spirit of the invention and the scope of the claims.
Claims (16)
1. A method of calibrating a microfluidic flow sensor comprising the steps of:
pumping a fluid through a microfluidic flow sensor;
stopping the flow of the fluid and determining a first value from the flow sensor for the rate of flow;
pumping the fluid through the sensor at a first preselected rate of flow and determining a second value output by the sensor corresponding to the first preselected rate of flow;
pumping the fluid through the sensor at a second preselected rate of flow and determining a third value output by the sensor corresponding to the second preselected rate of flow;
calculating the constants c, b, and a, respectively, in a quadratic equation y=ax2+bx+c based on the corresponding first, second, and third values; and
calibrating the sensor based on the calculated values for c, b, and a.
2. The method according to claim 1 wherein the flow sensor comprises a thermal anemomity sensor.
3. The method according to claim 1 wherein the fluid comprises one selected from a group consisting of the following: tetrahydrofuran, methanol, water, ethanol, dimethylsulfoxide, and acetonitrile.
4. The method according to claim 1 further comprising the steps of first rinsing a pump used for pumping the fluid.
5. The method according to claim 1 wherein the steps of pumping the fluid through the flow sensor further comprises pumping the fluid through a valve to a waste receptacle.
6. The method according to claim 1 further comprising the step of providing a pump with a known flow rate.
7. The method according to claim 1 further comprising the steps of transmitting the first, second, and third values from the sensor to a computer.
8. The method according to claim 7 wherein the calculating step is performed by the computer in accordance with a computer program.
9. A method of calibrating a microfluidic flow sensor comprising the steps of:
rinsing a pump with a selected fluid;
pumping the fluid through a flow sensor with the pump;
stopping the pump;
transmitting to a computer a first value for fluid flow as determined by the sensor;
pumping the fluid through the flow sensor at a first selected flow rate;
transmitting to the computer a second value for fluid flow as determined by the sensor at the first flow rate;
pumping the fluid through the flow sensor at a second selected flow rate;
transmitting to the computer a third value for fluid flow as determined by the sensor at the second flow rate;
pumping the fluid through the flow sensor at a third selected flow rate;
transmitting to the computer a fourth value for fluid flow as determined by the sensor at the third flow rate;
calculating values for constants a, b, c, and d in an equation y=ax3+bx2+cx+d based on the first, second, third, and fourth values; and
determining the flow rate x according to the equation.
10. The method according to claim 9 wherein the first flow rate is between approximately −1000 microliters per minute or so and approximately +1000 microliters per minute or so.
11. The method according to claim 9 wherein the second flow rate is between about −5000 microliters per minute or so and about +5000 microliters per minute or so.
12. An article of manufacture comprising: an electronic storage device comprising computer software having program instructions directing a computer running said instructions to receive and store in memory a first value for a first flow rate transmitted from a microfluidic flow sensor, receive and store in memory a second value for a second flow rate transmitted from said flow sensor, receive and store in memory a third value for a third flow rate transmitted from said flow sensor, and calculating values for constants a, b, and c corresponding to said first, second and third values for calibration of said flow sensor.
13. The article according to claim 12 wherein said article comprises a hard disk.
14. The article according to claim 12 wherein said article comprises a CDROM.
15. The article according to claim 12 wherein said article comprises a non-volatile computer memory device.
16. The article according to claim 12 wherein said program instructions further direct the computer to adjust the flow rate of a pump responsive to the flow rate calculated using the values calculated for constants a, b, and c.
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US11/403,650 US20060272384A1 (en) | 2004-05-21 | 2006-04-13 | Flow sensor methods and apparatus |
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US10/851,728 US7055366B2 (en) | 2004-05-21 | 2004-05-21 | Flow sensor calibration methods and apparatus |
US11/403,650 US20060272384A1 (en) | 2004-05-21 | 2006-04-13 | Flow sensor methods and apparatus |
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Also Published As
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WO2005114227A1 (en) | 2005-12-01 |
JP2008500553A (en) | 2008-01-10 |
EP1747473A1 (en) | 2007-01-31 |
US20060272385A1 (en) | 2006-12-07 |
US20050257595A1 (en) | 2005-11-24 |
US7516641B2 (en) | 2009-04-14 |
EP1747473A4 (en) | 2012-11-14 |
WO2005114227B1 (en) | 2006-01-05 |
US7055366B2 (en) | 2006-06-06 |
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