Devices, systems and methods for fluid delivery

(56)

References cited:

EP-A1- 0 319 275 US-A- 5 840 026 US-A1-2004 074 453

US-A- 4 854 324 US-A1-2003 216 683 US-B1- 6 691 047

EP 2 902 053 Β1

Note: Within nine months ofthe publication ofthe mention ofthe grant ofthe European patent in the European Patent Bulletin, any person may give notice to the European Patent Office of opposition to that patent, in accordance with the Implementing Regulations. Notice of opposition shall nőt be deemed to have been filed until the opposition fee has been paid. (Art. 99(1) European Patent Convention).

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EP 2 902 053 Β1

Description

BACKGROUND OF THE INVENTION [0001] The present invention is relates to devices, systems and methods forfluid delivery, and, particularly, to devices, systems and methods for delivery ofa pharmaceutical fluid to a patient, and, especially for delivery ofa contrast médium to a patient during a medical injection procedure.

[0002] In many procedures, the administration of contrast médium (with an electronic power injector) for radiological exams starts with the clinician filling an empty, disposable syringe with a certain volume of contrast agent pharmaceutical. For other procedures, a syringe pre-filled with contrast agent is used. The clinician then determines a volumetric flowrate and a volume of contrast to be administered to the patient to enable a diagnostic image. An injection of saline solution, having a volume and flow rate determined by the operator, often follows the administration of contrast agent intő the veins or arteries. A number ofcurrently available injectors allow for the operator to program a plurality ofdiscrete phases of volumetric flow rates and volumes to deliver. For example, the SPECTIRS SOLARIS and STELLANT injectors available from Medrad, Inc. of Indianola, provides for entry of up to and including six discrete pairs or phases of volumetric flow rate and volume for delivery to a patient (for example, for contrast and/or saline). Such injectors and injector control protocols for use therewith are disclosed, for example, in U.S. Patent No. 6,643,537 and Published U.S. Patent Application Publication No. 2004-0064041, assigned to the assignee ofthe present invention. The values or parameters within the fields for such phases are generally entered manually by the operator for each type of procedure and for each patient undergoing an injection/imaging procedure. Alternatively, earlier manually entered values of volume and flow rate can be stored and later recalled from the computer memory. However, the manner in which such parameters are to be determined for a specific procedure for a specific patient are nőt well developed.

[0003] In that regard, differences in contrast dosing requirements for different patients during imaging and other procedures have been recognized. For example, U.S. Patent No. 5,840,026, assigned to the assignee of the present invention discloses devices and methods to customize the injection to the patient using patient specific data derived before or during an injection. Although differences in dosing requirements for medical imaging procedures based upon patient differences have been recognized, conventional medical imaging procedures continue to use pre-set doses or standard delivery protocols for injecting contrast média during medical imaging procedures. Given the increased scan speed of recently available CT scanners including MDCT scanners, single phase injections are dominant over biphasic or other multiphasic injections in regions ofthe world where such fást scanners are used. Although using standard, fixed or predetermined protocols (whether uniphasic, biphasic or multiphasic) for delivery simplifies the procedure, providing the same amount of contrast média to different patients under the same protocol can produce very different results in image contrast and quality. Furthermore, with the introduction ofthe newest MDCT scanners, an open question in clinical practice and in the CT literature is whether the standard contrast protocols used with single-slice, helical scanners will translate well to procedures using the MDCT rnachines. See, for example, Cademartiri, F. and Luccichenti, G., et al., (2004). Sixteen-row multislice computed tomography: basic concepts, protocols, and enhanced clinical applications. Sémin Ultrasound CT MR 25(1): 2-16.

[0004] Afew studies have attempted quantitative analyses ofthe injection process during CT angiography (CTA) to improve and predict artéria! enhancement. For example, Bae and coworkers developed pharmacokinetic (PK) models ofthe contrast behavior and solved the coupled differential equation system with the aim of finding a driving function that causes the most uniform artéria! enhancement. K.. T. Bae, J. P. Heiken, and J. A. Brink, Aortic and hepatic contrast médium enhancement at CT. Part I. Prediction with a computer model, Radiology, vol. 207, pp. 647-55, 1998; K. T. Bae, Peak contrast enhancement in CT and MR angiography: when does it occur and why? Pharmacokinetic study in a porcine model, Radiology. vol. 227, pp. 809-16, 2003, K. T. Bae et al., Multiphasic Injection Method for Uniform Prolonged Vascular Enhancement at CT Angiography: Pharmacokinetic Analysis and Experimental Porcine Method, Radiology, vol. 216, pp. 872-880, 2000, U.S. Patent Nos. 5,583,902, 5,687,208, 6,055,985, 6,470,889 and 6.635,030. An inverse solution to a set of differential equations ofa simplified compartmental model setforth by Bae et al. indicates that an exponentially decreasing flow rate of contrast médium may result in optimal/constant enhancement in a CT imaging procedure. However, the injection profiles computed by inverse solution ofthe PK model are profiles nőt readily realizable by most CT power injectors without major modification.

[0005] In another approach, Fleischmann and coworkers treated the cardiovascular physiology and contrast kinetics as a black box and determined its impulse response by forcing the system with a short bolus of contrast (approximating an unit impulse). In that method, one performs a Fouriertransform on the impulse response and manipulates this transfer function estimate to determine an estimate ofa more optimál injection trajectory than practiced previously. D. Fleischmann and K. Hittmair, Mathematical analysis of artéria! enhancement and optimization of bolus geometry for CT angiography using the discrete Fourier transform, J Comput Assist Tomogr. vol. 23, pp. 474-84. 1999.

[0006] Uniphasic administration of contrast agent (typically, 100 to 150 ml of contrast at one flow rate) results in a non-uniform enhancement curve. See, for example, D. Fleischmann and K. Hittmair, supra; and K. T. Bae, Peak contrast

EP 2 902 053 Β1 enhancement in CT and MR angiography: when does it occur and why? Pharmacokinetic study in a porcine model, Radiology, vol. 227, pp. 809-16, 2003. Fleischmann and Hittmairthus presented a scheme that attempted to adapt the administration of contrast agent intő a biphasic injection tailored to the individual patient with the intent of optimizing imaging ofthe aorta. Afundamental difficulty with controlling the presentation of CT contrast agent is that hyperosmolar drug diffuses quickly from the Central blood compartment. Additionally, the contrast is mixed with and diluted by blood that does nőt contain contrast.

[0007] Fleischmann proscribed that a small bolus injection, a test injection, of contrast agent (16 ml of contrast at 4 ml/s) be injected prior to the diagnostic scan. A dynamic enhancement scan was made across a véssél of interest. The resulting processed scan data (test scan) was interpreted as the impulse response of the patient/contrast médium system. Fleischmann derived the Fourier transform ofthe patient transfer function by dividing the Fourier transform of the test scan by the Fourier transform ofthe test injection. Assuming the system was a linear time invariant (LTI) system and that the desired output time domain signal was known (a fiat diagnostic scan at a predefined enhancement level) Fleischmann derived an input time signal by dividing the frequency domain representations ofthe desired output by that ofthe patient transfer function. Because the method of Fleischmann et. al. computes input signals that are nőt realizable in reality as a result ofinjection system limitations (fór example, flow rate limitations), one must truncate and approximate the computed continuous time signal.

[0008] In addition to control of a powered injector to provide a desired time enhancement curve, the operation of a powered injector should be carefully controlled to ensure the safety of the patient,. Fór example, it is desirable nőt to exceed a certain fluid pressure during an injection procedure. In addition to potential hazards to the patient (fór example, véssél damage) and potential degradation of the diagnostic and/or therapeutic utility of the injection fluid, excessive pressure can lead to equipment failure. Fór example, because ofthe potential of cross-contamination between patients, the syringe and tubing used to carry fluid to a patient are typically changed on a per-patient basis. Such disposable syringes and otherfluid path components (sometimes referred to collectively as a disposable set) are typically fabricated from plastics of various burst strengths. If the injector causes pressure in the fluid path to rise above the burst strength of a disposable fluid path element, the fluid path element will fail.

[0009] In controlling system or injection pressure, many currently available injectors use motor current as an indirect indication of system pressure. This technique has inherent accuracy problems, as there are many variables between the paraméter being measured (motor current) and the paraméter of interest (fluid pressure). These include, fór example, measurement inaccuracies, motor torque constant variation, motor variation with temperature, frictional effects in the drive train, and frictional effects in the syringe. In generál, any control algorithm must aliow fór such errors and must make a conservative estimate of fluid pressure to prevent actual fluid pressure from reaching a hazardous value. [0010] Many current systems typically predefine a conservative pressure control value. As the prését pressure control level (as, fór example, determined by monitoring motor current) is reached, such injectors begin to slow down the flow rate of injection in an effort to stop the build up pressure. At that point, an injector system that was originally intended to servo control the volume and flow rate ofthe injection fluid begins to servo control pressure. The inaccuracies inherent in using motor current to dérivé pressure result in a compliant system, and the operation of the servo in that state is oscillatory. Pressures in excess of desirable limits can occur, resulting in potentially hazardous operation ofthe injector. [0011] In addition to problems of control with current injector systems, many such systems lack convenience and flexibility in the manner in which the injector systems must be operated. In that regard, the complexityof medical injection procedures and the hectic pace in all facets ofthe health care industry piacé a prémium on the time and skills ofan operator. [0012] Pressure measurement in injection systems and pressure control and/or limitation are discussed, fór example, in U.S. Patent Nos. 5,808,203, 6,520,930 and 6,673,033, assigned to the assignee ofthe present invention. U.S. Patent No. 6,520,930 discloses an injector control methodology which treats pressure as a hazard, rather than as a variable to be controlled. Fór example, a pressure hazard limit can be set as a trip point. When pressure in the system (as measured directly or indirectly) reaches the pressure hazard level, the injection may be terminated. The performance ofthe injector can be further limited in a manner to ensure that the user is nőt inconvenienced by continual shutdowns during normál operations. Fór example, the power delivered to the drive mechanism can be limited in a manner so that the pressure hazard limit or upper hazard level is nőt reached. In that regard, a pressure limit below the pressure hazard limit can be set such that power delivered to the drive mechanism is limited when the lower pressure limit isreached.

[0013] Although advances have been made in the control of fluid delivery systems to, fór example, provide a desirable time enhancement curve and to provide fór patient safety, it remains desirable to develop improved devices, systems, and method fór delivery of fluids to a patient.

[0014] Patent documents US 5,840,126, US 2004/0074453 A1, US 2003/0216683 A1, US 4,854,324, EP 0 319275 A1 and US 6,691,147 B1 disclose several methods and apparátus fór injection of a contrast agent intő the humán body.

SUMMARY OF THE INVENTION [0015] The invention is solely defined in independent claims 1 and 4 and their dependent claims 2, 3 and 5-7. All

EP 2 902 053 Β1 non-claimed embodiments and examples disclosed in the description and figures do nőt form part thereof.

[0016] As used herein with respect to an injection procedure, the term protocol refers to a group of parameters such asflow rate, volume injected, duration etc. that define the amountof fluid(s) to be delivered to a patient during an injection procedure. Such parameters can change over the course ofthe injection procedure. As use herein, the term phase refers generally to a group of parameters that define the amount of fluid(s) to be delivered to a patient during a period of time (or phase duration) that can be less than the totál duration ofthe injection procedure. Thus, the parameters of a phase provide a description ofthe injection over a time instance corresponding to the time duration ofthe phase. An injection protocol for a particular injection procedure can, for example, be described as uniphasic (a single phase), biphasic (two phases) or multiphasic (two or more phases, bút typically more than two phases). Multiphasic injections alsó include injections in which the parameters can change continuously over at least a pofion ofthe injection procedure.

BRIEF DESCRIPTION OF THE DRAWINGS [0017]

Figure 1 illustrates an embodiment ofa multi-phasic Graphical User Interface (GUI) for use in the present invention to set forth parameters for a plurality of phases for a two-syringe injector alsó illustrated in Figure 1.

Figure 2 illustrates an embodiment of a graphical interface from which an operator can choose a vascular region of interest for imaging.

Figure 3 illustrates an embodiment of a graphical interface of a proposed work flow environment for use in the present invention.

Figure 4 illustrates an embodiment ofan iodine flux algorithm for use in the present invention.

Figure 5 illustrates an embodiment ofa weight based algorithm for use in the present invention.

Figure 6 illustrates an embodiment ofa breath hold duration algorithm for use in the present invention.

Figure 7 illustrates an embodiment of a reduce -order compartmental model and the first-order coupled differential equation system describing this model.

Figure 8A illustrates a simulated enhancement curve in the heart/aortic compartment of a 65 cm, 120kg male. Figure 8B illustrates an enhancement curve to a test/timing injection from the simulated patient in Figure 8A. Figure 9 illustrates a simulated enhancement curve for the simulated patient of Figure 8A using the proposed methodology described within.

Figure 10 illustrates a time enhancement curve resulting from a 120 ml unpihasic injection.

Figure 11 illustrates a time enhancement curve resulting from a 75 ml contrast bolus followed with a 50 ml saline push or flush.

Figures 12 illustrate simulated time enhancement curves resulting from of injections performed with a 75 ml main bolus followed by a diluted phase of contrast of the same flow rate having a contrast/saline ratios of 50/50.

Figures 13 illustrate simulated time enhancement curves resulting from of injections performed with a 75 ml main bolus followed by a diluted phase of contrast of the same flow rate having a contrast/saline ratios of 30/70.

Figures 14 illustrate simulated time enhancement curves resulting from of injections performed with a 75 ml main bolus followed by a diluted phase of contrast of the same flow rate having a contrast/saline ratios of 70/30.

Figure 15 illustrates an injection process of contrast matéria! with a fixed, time axis wherein the bottom axis presents the contrast injection profile, the middle axis sets forth the enhancement profiles for left and right heart compartments, and the top axis sets forth the scanning duration.

Figure 16 illustrates a heuristic for determining contrast/saline ratio ofan admixture ordual flow phase on the basis of peak enhancement of a test bolus.

Figure 17 sets forth preliminary clinical data for uniphasic injections, biphasic injection and multiphasic, admixture injections ofthe present invention.

Figure 18 illustrates a several scan images of the left and right heart for a uniphasic injection, a biphasic injection and a multiphsic injection includíng a phase in which a contrast/saline admixture is injected.

Figure 19 illustrates an embodiment ofa graphical user interface for use with an embodiment ofa paraméter generátor ofthe present invention.

Figure 20 illustrates another portion ofa graphical user interface for use with an embodiment ofa paraméter generátor ofthe present invention.

Figure 21 illustrates another portion ofa graphical user interface for use with an embodiment ofa paraméter generátor ofthe present invention.

Figure 22 illustrates another portion ofa graphical user interface for use with an embodiment ofa paraméter generátor ofthe present invention.

Figure 23 illustrates another portion ofa graphical user interface for use with an embodiment ofa paraméter generátor ofthe present invention.

EP 2 902 053 Β1

Figure 24 illustrates a graphical representation ofan embodiment ofa user interface for interacting with a contrast injection system.

Figure 25A illustrates a graphical user interface for use with an embodiment ofa paraméter generátor ofthe present invention for use with MRI.

Figure 25B is another portion or window ofthe graphical user interface of Figure 25A.

Figure 26 illustrates an embodiment of a pressure modeling or pressure prediction system ofthe present invention. Figure 27 illustrates pressure modeling is several section of a fluid path.

Figure 28 illustrates a graphically a pressure prediction curve determined by an embodiment ofa pressure model ofthe present invention for flow ofthe contrast MAGNEVIST through the system.

Figure 29 illustrates a graphically a pressure prediction curve determined by an embodiment ofa pressure model ofthe present invention for flow of saline through the system.

Figure 30 illustrates a graphically a pressure prediction curve determined by an embodiment ofa pressure model ofthe present invention for flow ofthe contrast MAGNEVIST through the system.

DETAILED DESCRIPTION OF THE INVENTION [0018] In several embodiments ofthe present invention, an injection system (such as a dual syringe injector system 100 as illustrated in Figure 1 and as, for example, disclosed in U.S. Patent No. 6,643,537 and Published U.S. Patent Application Publication No. 2004-0064041) for use with the present invention includes two fluid delivery sources (sometimes referred to as source A and source B herein; such as syringes) that are operable to introduce a first fluid and/or a second fluid (for example, contrast médium, saline etc.) to the patient independently (for example, simultaneously, simultaneously in different volumetric flow proportion to each other, or sequentially or subsequent to each other (that is, Athén B, or B then A)). In the embodiment of Figure 1, source A is in operatíve connection with a pressurizing mechanism such as a drive member 110A, and source B is in operatíve connection with a pressurizing mechanism such as a drive member 110B. The injection system includes a controller 200 is in operatíve connection with injector system 100 and is operable to control the operation of drive members 110A and 110B to control injection of fluid A (for example, contrast médium) from source A and injection of fluid B (for example, saline) from source B, respectively. Controller 200 can, for example, include a user interface comprising a display 210. Controller 200 can alsó a processor 220 (for example, a digital microprocessor as known in the art) in operatíve connection with a memory 230. An imaging system 300 (for example, a CT system, a Magnetic Resonance Imager (MRI) system, an ultrasound imaging system, or a Positron Emission Tomography (PET) system). The injection system can be in communicative connection with imaging system 300 and one, a plurality or all the components of the injection system and imaging system 300 can be integrated. [0019] In one embodiment ofthe present invention phase variables or parameters as described above are populated within a phase programming mechanism (see Figure 1 for an embodiment of a user interface therefor that can, for example, be used with injector system 100) based on one or more parameters of interest, including, for example, bút nőt limited to, contrast agent concentration (for example, iodine concentration in the case of a CT procedure), body weight, height, gender, age, the type of scan being performed, and the type of catheter inserted intő the patient for intravascular access. As discussed above, differences in dosing requirements for different patients during imaging and other procedures have been recognized. For example, U.S. Patent Nos. 5,840,026 and 6,385,483, assigned to the assignee ofthe present invention disclose devices and methods to customize the injection to the patient using patient specific data derived before or during an injection. Likewise, PCT International Patent Application entitled MODELING OF PHARMACEUTICAL PROPAGATION, filed November 16,2005 under U.S. Express Mail Label No. EV724425366US and Attorney Docket No. IN/04-005.PCT (for which a PCT International Patent Application No. is nőt yet available), claiming the benefit of U.S. Provisional Patent Application Serial No. 60/628,201, assigned to the assignee ofthe present invention alsó discloses customization of injections to a patient using patient specific data and sets forth a number of models to describe a time enhancement output for a given input or protocol.

[0020] Because optimál sets offlow rates and volumes are nőt readily known to the operator ofthe injector, the present invention eases the task of an operator in, for example, scanning patients in an imaging procedure by providing a set of injection protocols that are predetermined as being effective for the type of procedure being performed. For example, such protocols can be established in the clinical literature, established by collection of patient data over time (by, for example, employing artificial intelligence techniques, statistical means, adaptive learning methodologies etc.), established through mathematical modeling or otherwise established for a type of procedure being performed.

[0021] In one embodiment ofthe present invention, the operator first chooses the concentration of contrast agent (for example, concentration of iodine in a CT procedure) to be delivered intő a patient. This choice is made, for example, by a selection mechanism, or by direct input of numerical values on the graphical user interface. The clinical operator can alsó select the gauge ofthe catheter inserted intő that specific patient. Catheter size can be entered so that in subsequent steps, when the volumetric flow rate is determined, the pressure head to be developed in a disposable fluid path set can be calculated as described below (for example, via a computer program). Alternatively, one or more sensors can be

EP 2 902 053 Β1 provided to sense catheter size and provide this information to the injector.

[0022] The clinical operator can, for example, control the injection system by either entering volumes and fiow rates manually intő the fields provided on the User Interface (see Figure 1) or by entering a protocol wizard mode, helper mode or operator assist mode as described above wherein such fields are automatically populated. Ifthe operator chooses to enter the operator assist mode, the operator can be presented with a mechanism or mode (see, for example, Figure 2) of selecting an organ or vascular system to be scanned.

[0023] The present invention provides systems, devices and methodologies or algorithms that predict the fiow rate profile (which can be constant during a phase or varying) and volume of contrast agent to deliver depending upon the procedure and the region of interest chosen. For example, an operator can choose the heart, descending aorta or ascending aorta (referred to as cardiac imaging, aform of Computed Tomography Angiography (CTA)). One embodiment of a graphical interface from which the operator chooses the vascular region of interest, and which follows the work fiow described herein, is depicted in Figure 2. The operator can, for example, choose a region of interest by highlighting (for example, using a touch sereen or a mouse controlled cursor) a region of interest on an illustration ofthe body set forth on the user interface or can choose a region of interest from a menü such as a pool down menü. Hierarchical groupings of regions of interest can be provided.

[0024] Upon choosing the region to be imaged, the operator can, for example, be prompted to enter values for other variables (for example, patient physiological variables such as the patient’s weight, height, gender etc.). An example of an embodiment or implementation of this is to provide a keypad on the user interface intő which the operator enters the patient’s weight in pounds or kilograms. In another embodiment, the operator chooses a weight rangé from among low, mid and high ranges. Such variables can alsó be measured by one or more sensing devices associated with the system and/or read electronically or digitally from patient records as may be kept in a hospital database. The steps necessary to conduct a contrast injection can be presented to the operator as depicted in Figure 3. In the embodiment of Figure 3, the operator can, for example, be prompted in an order (for example, a suggested or required sequential order) natural to the type of imaging procedure to be performed. The operator can, for example, be given the ability to choose a vascular region or organ of the body to image, the type of algorithm to conduct the injection, and an ability to change the type contrast, catheter gauge, and physical attributes ofthe patient.

[0025] As discussed above, the operator can be presented with a choice of the type of algorithm the operator would like the system to use to produce a set of fiow rates and volumes (that is, phase parameters) for that patient. In the case of cardiac imaging, algorithm choices can, for example, include: (i) an Iodine Flux Algorithm, (see Figure 4) (ii) a Weight Based Algorithm (see Figure 5), or (iii) a Breath Hold Duration Algorithm (see Figure 6). Each of these algorithms can, for example, be based upon empirical data (for example, as published in the radiological medical literature). Additiönai algorithms can be included for other types or classes of imaging procedures. The methodology and/or logic for an embodimentof the three algorithms described above is setforth in Figures 4 through 6, respectively. Upon entering the data required for a particuíar algorithm, the operator can be queried ifthe operator wishes to perform a test injection (or timing injection). Ifthe operator chooses yes, the software can provide that, for example, two additiönai phases (corresponding to the test injection) must be inserted in the start ofthe injection protocol (for example, one phase for contrast delivery and a subsequent phase for a saline flush injection).

[0026] Based upon the selections made, the software implementing the present invention computes an injection protocol for the user’s review. Ifthe operator chooses to perform a test-injection, then the first two phase ofthe protocol can, for example, include injection of 15 or 20 ml of contrast agent (for example, 15 ml if the patient weight < 90 kg, 20 ml > 90 kg) delivered at 4 ml/s. The second phase of the protocol can include injection of 20 ml of saline injected at 4 ml/s. The next phase or phases can, for example, include volumes and fiow rates computed by one ofthe three algorithms discussed above in connection with Figures 4 through 6.

[0027] In one embodiment ofthe present invention, injection parameters for an injection procedure including a phase in which an admixture of contrast média and a diluent/flushing fluid (for example, saline) are calculated. In that regard, to address a number of problems associated with, for example, heart imaging procedures have been developed which include the injection of saline following the contrast agent bolus, and, more recently, the admixture of contrast média with saline via simultaneous injection of contrast média and saline (sometimes referred to herein as dual fiow).

[0028] As discussed above, Bae et al. have proposed a solution to the non-uniform enhancement problems by suggesting that one injects contrast with an exponentially decaying fiow rate over time. While this technique can indeed produce more uniform contrast enhancement in a large véssél, it alsó reduces the maximum enhancement, which is nőt necessarily desirable. See, for example, (Bae, Tran et al. 2004). Bae, Κ. T., H. Q. Tran, et al. (2004). Uniform vascular contrast enhancement and reduced contrast médium volume aehieved by using exponentially decelerated contrast matéria! injection method. Radiology 231(3): 732-6. While, theoretically, it seems logical to believe that the exponentially decaying fiow rates can help with right-heart artifacts (for example, by introducing less contrast later in the injection and mixing less with the earlier injected contrast), it has nőt been demonstrated or investigated. Furthermore, because the latter portion ofthe decayed injection is at a lower fiow rate, there is a Ioss of momentum for that section ofthe bolus, slowing its entry to the right heart. While a saline push after the decayed exponential injection may help in ensuring the

EP 2 902 053 Β1 contrast is all pushed intő the right heart, turbulence resulting from the mixing of contrast and blood at different flow rates may cause flow artifact within the right heart.

[0029] An alternative for reducing right heart artifact is to inject a volume of contrast at a diserete flow rate followed by an admixture of contrast and saline (with a final push of saline). The admixture can be injected as the same flow rate as the initial bolus of contrast. The admixture can be produced by the simultaneous injection of contrast and saline with, for example, a dual-syringe power injector; wherein the flow rates of contrast and saline are proportional to each other. This technique has been recently adopted in the clinical setting and initial resuits are suggesting that it reduces right heart artifact. See Sablayrolles, J. (2004). Cardiac CT:Experience from Daily Practice. Advanced CT Aug: 4-10. However, in implementing such admixture protocols, there are currently no established systems or methods for determining appropriate or ideál injection parameters for a given patient (for example, initial flow rate and volume, percentage of admixture, duration ofthe phases, and scan delay).

[0030] In one embodiment, the present invention provides systems and methods for interfacing with the injection system to reduce clinician guesses at appropriate or optimál flow rate and volume parameters for a given patient. The systems and methods ofthe present invention provide for the consideration ofa number of variable including, bút nőt limited to, patient specific parameters such as patient weight (and other habitus indicators), time of contrast arrival from a timing injection, contrast concentration, and totál desired contrast agent (for example, iodine) load. The systems and methods ofthe present invention can, for example, include a per-patient saline admixture protocol generátor.

[0031] The predicted contrast enhancement in the aortic/heart compartment of a humán male can be used in this section to elaborate the principle ofthe proposed algorithm. Simulations were performed in a SIMULINK® (available from MathWorks, Inc. of Natick Massachusetts) implementation of a reduced-order PK model as described in Bae et al. See Bae, K. T., J. P. Heiken, et al. (1998). Aortic and hepatic contrast médium enhancement at CT. Part I. Prediction with a computer model. Radiology 207(3): 647-55 and Bae, K. Τ., H. Q. Tran, et al. (2000). Multiphasic injection method for uniform prolonged vascular enhancement at CT angiography: pharmacokinetic analysis and experimental porcine model. Radiology 216(3): 872-80, U.S. Patent Nos. 5,583,902, 5,687,208, 6,055,985, 6,470,889 and 6,635,030. The modeling approach in that work recognized that the full body physiologic pharmacokinetic model taught in Bae, Heiken et al, 1998 supra, was too large and included too may unknowns to feasibly compute on a per patient basis. Bae and colleagues, therefore, approximated large parts of the anatomy with single compartments and, because first-pass enhancement dynamics are of interest, removed the capillary transfer compartments. The resulting, reduced-order model is illustrated in Figure 7. In Figure 7, V are the fluid volumes of the respective compartments, C are the predicted concentrations in each compartment, and Q are the volumetric flow rates of blood throughout the body. Q and V are estimated from anatomical data. The first-order, coupled differential equation system deseribing this model is formulated assuming a continuous time proeess are alsó set forth in Figure 7.

[0032] In several studies of the present invention, an assumption was made that the aortic/heart compartment was well mixed. Although the x-axes in the Figures 8A through 9 are labeled in time units, another assumption was that the time axis maps to spatial dimensions in the compartment of interest. Figure 8A demonstrates the phenomenon of nonuniform contrast enhancement (caused by recirculation of contrast intő the compartment). Figure 8B presents the resuits of performing a small volume test or timing injection on the same patient scanned in connection with Figure 8A (the cardiac output and Central blood volume for the model were derived from anthropometric data tables). The time to peak contrast enhancement was measured as 12 seconds in Figure 8B. The time of peak represents the transit time for a small bolus of contrast to migrate from the injection site, to the right heart, through the pulmonary circulation, and to the left heart compartment. The simulated time to peak enhancement may be less than that from a reál patient. In that regard, the Bae model set forth in Figure 7 was nőt directly validated with humán data, bút was allometrically sealed from porcine data. In any event, the absolute values in these simulations are nőt critical. Rather, we are interested in the dynamics of the system. Noticeable in Figure 8B is the recirculation of contrast after the peak (or first moment) of the bolus arrived in the compartment (> 15 sec). The reduced-order model set forth in Figure 7 does nőt reproduce with high fidelity the recirculation dynamics (for example secondary peaks).

[0033] Bae et al. concluded that if an injection duration is longer than the time for contrast arrival as computed from a timing injection, that the time to peak contrast enhancement increases linearly as the duration of injection increases. As the duration of the injection exceeds the duration of the time to peak of the test injection, the asymmetry of the enhancement curve beeomes pronounced because the new contrast is mixing with the contrast already present in the compartment. This phenomenon serves as a basis of one embodiment of one algorithm of the present invention for computing admixture protocol (for example, saline plus contrast média).

[0034] Figure 9 sets forth a time enhancement curve that was simulated with a biphasic protocol. The first phase’s duration was computed to equal the time to peak enhancement ofthe timing bolus, plus three seconds (an arbitrary offset term). The second phase was a diluted phase (90%contrast, 10%saline) that resulted in an effective contrast concentration of 288 mgl/ml (concentration in the dilution phase = desired or programmed ratio (90/100 in this instance) * concentration of drug (320 mgl/ml)). The volume was set so that a totál volume of 120 ml was injected intő the patient. The flow rate was the same in both phases to maintain the momentum of the contrast intő the right heart. Figure 9

EP 2 902 053 Β1 demonstrates a reduction in the asymmetric peak in the second half of the injection, while maintaining a contrast enhancement about 350 HU. In comparison, the exponentially decreasing flow rate technique recommended by Bae et al. results in a lower peak enhancement. An advantage ofthe injection protocol ofthe present invention (as compared to a decelerating injection flow rate protocol) arises in that, because the volumetric flow rate of the injected fluid is nőt decreasing, there is less likelihood fór flow artifacts within the peripheral venous system before the heart. In that regard, injectate moving with a flow rate less than the endogenous flow rate ofthe venous system can result in dispersion of the contrast média because somé parts of the bolus arrive to the right heart with different velocities. In the present invention, a multiphasic injection protocol can be provided in which one or more ofthe parameters are changed periodically or continuously over at least a period ofthe injection duration, wherein totál flow rate is maintained constant. In this manner, fór example, a concentration of contrast active agent (fór example, iodine, gadolinium etc.) delivered to a patient can be decreased over time while maintaining flow rate constant (fór example, by increasing the portion of saline injected during that time). A broader, more uniform peak of enhancement can thereby be maintained (see, fór example, Figure 9). Moreover, that uniformity can be changed between different phase of the injection procedure. Fór example, liver enhancement can be changed during different phases ofthe imaging procedure to, fór example, correspond to different portions ofthe liver in which peak enhancement time can vary because ofvariations in blood supply.

[0035] Another embodiment of the present invention fór protocol determination in the case of a dual flow injection or simultaneous injection of an admixture of diluent/flushing fluid and contrast is discussed in connection with Figures 10 through 18. Once again, a primary goal of rational CT contrast protocol design is to develop injection protocols tailored to each patient considering, fór example, the individual’s hemodynamic state, the imaging region of interest, and the injection system constraints. The injection strategy can, fór example, make use ofthe ability ofthe Stellant D injection system, available from Medrad, Inc. of Indianola, Pennsylvania, to provide simultaneous delivery (and thus dilution) of contrast média and saline. As described below, an additional phase of diluted contrast média allows fór additional left heart enhancement, bút with a reduced contrast agent (iodine) load to reduce or eliminate right heart artifacts.

[0036] Figures 10 thorough 14 illustrated enhancement profiles (simulated as described above) fór a 35 yr old, healthy male (200 Ibs, 6 ft tail) injected with 370 mgl/ml contrast médium. Enhancement curves are presented fór the right heart and the left heart compartments as predicted with the compartmental, pharmacokinetic model setforth in Figure 7. Figure 10 depicts enhancement with a 120 ml unpihasic injection, whereas Figure 11 presents the enhancement resulting from a 75 ml bolus followed with a 50 ml saline push orflush. Whereas the enhancement ofthe left heart in Figure 10 is above 300 Hounsfield Units (HU) throughout the scan duration, the right heart is enhanced brightly throughout the scan window, and is more likely to produce image artifacts.

[0037] Figures 12-14 illustrate simulated time enhancement curves resulting from of injections performed with a 75 ml main bolus followed by a diluted phase of contrast ofthe same flow rate in the following contrast/saline ratios: 50/50, 30/70, and 70/30, respectively. The enhancements ofthe left and right hearts were clearly modified by the additional phase of diluted contrast. The 70/30 phase (Figure 14) provided good left heart enhancement, bút the right heart enhancement may have been too great. The 30/70 ratio (Figure 13) provided good right heart enhancement, bút nőt enough left heart enhancement throughout the scan window. The 50/50 ratio (Figure 12) provides the best trade-off, fór this simulated patient, of right heart and left heart enhancement.

[0038] Figure 15 illustrates an injection process of contrast matéria! with a fixed, time axis. The bottom axis presents the contrast injection profile (in this instance, a uniphasic injection at 5ml/s), the middle axis sets forth the enhancement profiles fór left and right heart compartments, and the top, axis presents the scanning duration. The two vertical lines representthe start and completion times ofthe scan. In one embodiment, an algorithm ofthe present invention assumes that the clinician performs a small, test bolus injection of contrast (fór example, a test injection of 20-25 ml of contrast at the same flow rate as the flow rate to be used during the diagnostic scan) followed by a saline push. A dynamic CT scan generates an enhancement curve from which the time to peak of the test bolus and the enhancement peak of the test bolus can be measured/recorded. It is alsó assumed that the scan duration is known before the test bolus and diagnostic injections begin.

[0039] The first bolus of contrast is made equal in duration to the scan duration. The flow rate is given by the operator (assumed to be 5 ml/s in this study). The volume ofthe first phase, therefore, is the product of scan duration and flow rate. The determination ofthe volume ofthe second phase is made by considering the time to peak ofthe test injection, the duration ofthe first phase, and the end ofthe scan. The contrast injection shouid nőt last longer than the end ofthe scan. Because ofthe propagation delayof contrast from the injection site to the right átrium (about 5-8 seconds typically), contrast injection is stopped 5-8 seconds before the end ofthe scan so that the follow on contrast can fill the right heart. The approach taken in connection with the embodiment of Figure 15 proscribed a saline flush of 40 ml at 5 ml/s, so we ended the contrast injection ofthe dilution phase 8 seconds before the end ofthe scan.

[0040] The volume of the second, diluted phase is then determined by:

EP 2 902 053 Β1

The value T, scan_end . ,, 40/«/

Vol = ((t -ζ _5mJ/s ) - duration^ )·5 ml! s is computed by consideration ofthe time to peak ofthe test bolus and the scan duration:

Iscm^end ~ $ test _bolus_ peak + duration_sam

The ratio ofthe second phase is determined by a heuristic that maps peak enhancement ofthe test bolus to contrast/saline ratio as set forth in Figure 16.

[0041] To limit the totál amount of contrast delivered to each patient (in the event of an extremely long time to peak of the test enhancement), a maximum of 40 ml is made available for the dilution phase. If the computations above suggest a contrast volume greater than 40 ml., the system can limit the totál contrast volume to 40 ml, compute the totál volume in that phase (with the saline) considering the dilution ratio so as nőt to exceed 40 ml of contrast. The totál contrast volume allowable in the dilution phase can alsó be set as a function of weight, estimated cardiac output, Body Mass Index, or other physiometric indicator.

[0042] The threshold values in Figure 16 were determined by analyzing clinical data from a sample of 50 test bolus injections and subsequent numerical modeling. Heuristically, the rule is designed to provide more contrast in patients with smaller peak enhancements (assuming that more contrast is needed for sufficient left and right heart enhancement) and less contrast to patients with strong test enhancements. Because the volume of agent is being tailored to patient’s with longer or shorter times to peak, and the totál iodine load is adjusted based on test bolus enhancement, variability among patient enhancement should be reduced with this approach. Figure 17 sets forth preliminary clinical data indicating this outcome. In Figure 17, the first 2 bars are data generated with the algorithm just described forthe left and right heart (SF_L and SF_R, respectively). The error bars indicate +/-1 standard deviation. The remaining data points are enhancement values generated with a uniphasic protocol of 120 ml of contrast (350 mgl/ml, no saline push; UNI_R and UNI_L), a biphasic protocol (75 ml of 350 mgl/ml with 40 ml of saline; BI_R and BI_L), and finally a dilution protocol with a fixed dilution ratio of 30/70 for all subjects (initial phase volume of 350 mg l/ml = scan duration*5ml/s; DF_R and DF_L). The volume of the second phase was a fixed 50 ml of fluid. A saline flush of 40 ml followed).

[0043] Figure 18 sets froth scan images for the left and right heart in the case of a uniphasic or monophasic injection protocol (contrast only, no saline flush), a biphasic protocol (contrast followed by a saline flush) and a dual flow injection protocol as described above (contrast, followed by a contrast/saline admixture, followed by a saline flush). As illustrated in Figure 18, a dual flow injection procedure in which the injection protocols can be determined as described above can provide improved imaging procedures for the left and right heart.

[0044] Figures 19 through 23 illustrate several screen captures of a graphical user interface suitable to effect the dual flow injection protocol determination described above. In Figure 19 and 20 the algorithm set forth above in connection with Figures 10 through 18 is selected via the designation Cardiac CT1. A patient weight of 65 kg and a test scan duration of 30 seconds are input. An iodine fluxof 1.0 g/s is established forthe imaging procedure injection. As the concentration of contrast fluid is 250 mgl/ml, a flow rate of 4 ml/s will be used in the imaging procedure injection.

[0045] As set forth in Figure 21, the flow rate during the test injection is 1.0 ml/s. During the 30 second test injection a bolus of saline (from source B) is first injected at a flow rate of 4.0 ml/s for 5 seconds. A bolus of contrast (from source A) is then injected at a flow rate of 4.0 ml/s for 5 seconds. Finally, a flushing bolus of saline is injected at a flow rate of 4.0 ml/s for 20 seconds. After the completion of the test bolus injection, the time to peak and the peak enhancment are determined as illustrated in Figure 22. Using the values set forth above, the diagnostic injection protocol is determined using the system/method described in connection with Figures 10 through 18. Figure 23 sets forth the determined diagnostic injection protocol including the following three phases: (1) injection of a 70 ml volume of contrast (source A) at 4 ml/s (duration of 18 seconds); (2) injection of volume of 35 ml of a 50/50 contrast/saline admixture (dual flow from sources A and B) at 4 ml/s (duration of 9 seconds); and (3) injection of an 80 ml volume of saline (source A) at 4 ml/s (duration 20 seconds). Thus, a totál of 185 ml of fluid is injected over a time period (totál duration) of 47 seconds. As alsó set forth in Figure 23, a pressure limit of 300 psi for the fluid path used in the injection procedure was set. Alsó, a scan delay of 5 seconds was established.

[0046] Figure 24 illustrates a graphical representation of an embodiment of an interface for interacting with a contrast injection system that can, for example, be in operatíve connection with an imaging system. The bottom axis (Desired enhancement axis) provides an area for an operator to input (for example, draw) a desired enhancement curve, commencing at a particular time and reaching a certain enhancement value. The operator, for example, can chose multiple imaging sequences and alsó injections throughout a time interval based on the type of diagnostic procedure to be performed. The top axis presents the timing for an imaging sequence (for example, CT, MRI, PÉT etc.) in which the

EP 2 902 053 Β1 duration ofthe scan sequence is known. Once the operator draws the desired enhancement profile, the injection system computes an injection protocol that will achieve the desired enhancement. Computations neeessary to achieve the injection protocol may rely upon a model of the patient, drug and imagíng system or can be derived from statistical analysis of explicit feedback from the scanner as, for example, described in PCT International Patent Application entitled MODELING OF PHARMACEUTICAL PROPAGATION, filed November 16, 2005 under U.S. Express Mail Label No. EV724425366US and Attorney Docket No. IN/04-005.PCT. Once again, using such a model, an operator can enter or draw a contrast injection profile on the injection system axis, and the resulting enhancement curve from the entered protocol would be presented on the bottom, enhancement axis. The operator can then examine the predicted enhancement and decide ifit issatisfactory. lf nőt, the operator can redraw an input function (injection profile/protocol). A computer to iteratively arrive at a predetermined enhancement level can, for example, be used perform the operation.

[0047] The representative embodiments setforth above are discussed primarily in the context of CT imagíng. However, the devices, systems and methods ofthe present invention have wide applicability to the injection of pharmaceuticals. For example, the systems devices and methods ofthe present invention can be used in connection with the injection of contrast médiai for imagíng procedures other than CT (for example, MRI, ultrasound, PÉT etc.). In that regard, Figures 25A and 25B illustrate one embodiment ofthe present invention for use with MRI.

[0048] Figure 25A illustrates one embodiment of a system to compute an injection profile for an MRI procedure using a Gadolinium agent. The operator chooses the type of drug being injected (for example, from a menü in which the drug/contrast is listed by brand name and/or concentration). The operator then enters the patient’s weight and the desired scan duration.

[0049] A number of currently available injectors will inject fluid at a programmed flow rate until the pressure generated in the syringe exceeds a set threshold. When this occurs, the computer controlling the fluid injection reduces the volumetric flow rate until the pressure is nőt exceeded and the injection continues, albeit at a lowerflow rate than initially programmed. Pressure limited operation of an injector is discussed, for example, in U.S. Patent No. 6,520,930, assigned to the assignee ofthe present invention. In a number of pressure limiting control schemes, the control computer ofthe injector endeavors to deliver the programmed volume of fluid by reducing the volumetric flow rate from that programmed to avoid exceeding the pressure limit or threshold. Injection can alsó be halted ifa pressure hazard limit is exceeded.

[0050] This mode or operation is nőt optimál for CT scans performed with, for example, Multi-Detector CT (MDCT). In that regard, a primary factor influencing image enhancement in MDCT procedures is the volumetric flow rate of contrast delivered intő the circulatory system. The pressure modeling system ofthe present invention addresses this problem by alerting the operator before the injection commences that the choice of injection parameters will result in an overpressure situation. The operator can thus altér the injection parameters to avoid the over-pressure situation and the associated variation from the programmed volumetric flow rate.

[0051] After resolving any potential over-pressure situations, the system can inserts numerical values in the remaining phases of the protocol. The last phase can, for example, be a saline phase (from the 2^nd or B fluid path) at a volume of, for example, 40 ml at the flow rate ofthe preceding phase.

[0052] The operator can be given the choice to override any or all ofthe parameters presented in the protocol interface. Ifthe values are acceptable to the operator, then the system is armed and the injection continues.

[0053] lf a test injection is chosen, the system performs the test injection of contrast médium followed by an injection saline and then a hold or pause. The operator may then enter a scanning delay. The present invention can provide the operator with a set of options to choose a scan delay (the time from the commencement ofthe contrast injection to when the diagnostic scan should begin). As depicted, for example, in Figures 4 through 6, the operator may choose from an option of several delays. Moreover, a scan delay can be automatically generated from, for example, an analysis of a test injection.

PRESSURE MODELING [0054] To adequately and efficiently control injector pressure in an injector system, it is desirable to be able to predict the pressure at various points in the flow path ofthe injector system during an injection. To predict such pressures, one can mathematically model the flow through the injector flow path using equations of state.

[0055] In one embodimentof a mathematical or numerical model for calculating pressure at various points in an injector system flow path ofthe present invention, the following assumptions were made: the flow is steady; the flow is uniform; a Newtownian fluid is present in the system; the continuity equation is valid throughout the flow geometry (that is, the mass flux of liquid exiting the tip ofthe syringe is the same as that exiting the catheter - O_in = O_out in Figure 26); and the pressure within the entire syringe is the same as at the tip of the syringe.

[0056] By assuming that the spatial domain of interest is enclosed within a fixed control volume (inertial reference frame), the generál energy equation can be used to deseribe the behavior of fluids throughout the volume. See, for example, Potter and Swiggert, Fluid Mechanics. Englewood Hills, NJ: Prentice Hill, 1992. Using vector notation, the most generál form of the energy equation for steady fluid flow through a stationary, closed control volume is:

EP 2 902 053 Β1

<img file="HUE034171T2_D0001.tif" />

77Zg

Equation l with the constraint (continuity equation) for steady fiow through stationary control volume:

o=cf pV-ndA •c.v.

Equation 2 [0057] The losses term in Equation 1 represents losses arising from thermal exchange, boundary layer interaction, wall shear, viscous heating, and geometry losses (resulting from tubing constriction, valves, coiling, etc.). If one imposes the condition that fiow throughout the spatial domain is uniform (the fiow rate (dV/dt) is constant throughout), Equation 1 can be simplified to the familiar Bernoulli equation (with the addition of th loss terms specified before - HLoss). See, for example, Baker A, Sanders J., Fluid Mechanics Analysis of a Spring-Loaded Jet Injector, IEEE Transactions on Biomedical Engineering, vol. 46, No 2., Feb 1999.

<img file="HUE034171T2_D0002.tif" />

Equation 3 [0058] In Equation 3, y=pg (specific mass of the fluid), wherein p is the density of the fluid and g is gravitational acceleration. Equations 1 through 3 are expressed in dimensional units of length. To express the result in pressure units, one must multiply both sides by the specific mass ofthe fluid γ. HLoss in Equation 3 is the sum ofthe geometry losses and the losses resulting from the viscous properties ofthe fluid as setforth in Equation 4:

<img file="HUE034171T2_D0003.tif" />

Equation 4 [0059] The velocities presented in Equations 1 through 3 are averaged quantities. Because we are primarily interested in volume per unit time, average linear velocities (the velocity of a cell of liquid along a streamline) may be changed to fiow rates by the following relation:

<img file="HUE034171T2_D0004.tif" />

Equation 5 [0060] It is common in many engineering calculations to ignore the kinetic energy component of Equation 1 (the V²/2

EP 2 902 053 Β1 term) when the average fluid velocities are low. However, because ofthe small opening of intravenous catheters through which the injection fluid (for example, contrast agent) must exit, the linear velocity components ofthe fluid may become non-trivial, thus contributing to the overall pressure head developed in the syringe.

[0061] The first term in Equation 4 is the loss factor for the minor losses in the system. The K terms in Equation 4 are numerical values determined by empirical analysis and found in most fluid dynamics text books. See, for example, Potter and Swiggert, Fluid Mechanics. Englewood Hills, NJ: Prentice Hill, 1992. The three terms considered in the model ofthe present invention are:

K_va|_ve - losses attributable to a stop-cock in line with the fluid path. When the valve is open, this coefficient goes to 0. K_coi| - loss attributable to the coiled effect of the low pressure connector (LPCT) tubing. The model and subsequent simulation uses a value of 80, which was determined by multiplying the loss coefficient for a single 90 degree bend (K=45) by 4 (forone loop ofthe LPCT) and then again by 30 (roughly the numberof loops in a 96 LPCT). This operation results in a product of 54. A value of 26 was added to the product after comparing simulation outputs with experimental data. Simulation resulting from use of a coil loss of 80 fit the experimental data fairly well. However, it is possible to further optimize this coefficient with respect to experimental data sets.

KcontractiorT '^oss attributable to the pressure generated when the fluid is forced from the larger diameter LPCT intő the smaller diameter catheter. The value of this coefficient may again be found in fluid textbooks. The actual value of the constant is dependent on the ratio ofthe LPCT’s area to the catheter’s area. The following relationship exists between the two areas and the coefficient (as presented by Potter and Swiggert):

Table 1

<td> Area Ratio</td><td> Value of K_cont_ractj_on</td>

<td> 2:1</td><td> .25</td>

<td> 5:1</td><td> .41</td>

<td> 10:1</td><td> .46</td>

The relationship in Table 1 may be interpolated for values nőt directly specified.

[0062] The second and third terms in Equation 4 describe the energy lost (or pressure needed to maintain flow) in the fluid path resulting from the viscous properties of the contrast média. For laminar, viscous flow in a tűbe, the f term correlating to a friction factor can be expressed as:

<img file="HUE034171T2_D0005.tif" />

Equation 6 [0063] The Reynolds Number Re is a ratio of the inertial forces to internál viscous forces for an infinitesimal volume of fluid along a streamline. With relation to flow rate (Q), the Reynolds Number can be expressed as:

πΰ μ

Equation 7 where p is, once again, the fluid’s density, D is the tube’s diameter, and μ is thefluid’s viscosity. As evidenced by Equation 7, if the fluid’s viscosity increases Re will decrease (for a fixed D and p). If the tube’s diameter decreases, the Reynolds Number will alsó increase (for a fixed p and μ). Substituting Equation 6 and Equation 7 intő Equation 4, one derives a function for pressure dependent on flow rate, viscosity, length and diameter when the flow is laminar:

EP 2 902 053 Β1

1280/ζΔ

<img file="HUE034171T2_D0006.tif" />

Equation 8 wherein Δρ = p_syr - p_exit, assuming that p_exit = p_gauge = p₀ = 0.

[0064] In addition to the assumptions set forth above, neglecting the impact of gravity, and including the minor losses (resulting from geometry and coiling) and losses resulting from fluid viscosity, Equation 1 can be restated and solved for the pressure at the tip of the syringe (laminar flow - Re less than 2500) as follows:

<img file="HUE034171T2_D0007.tif" />

^ÍLLPCT

Equation 9 [0065] Because offluid viscosity, complex interactions occur among boundary layers in pipes/tubes. When flow exceeds a critical threshold, the boundary layers may begin to interact (termed boundary layer shedding), and the flow may become turbulent. When flow is turbulent (or near turbulent), the standard assumption of Poiseuille flow (a parabolic flow profile) is nőt sufficient to predict pressure vs. flow dependencies. The friction term in Equation 6 is applicable only when the flow is in the laminar region.

[0066] To fully describe turbulent flow, one must solve a time averaged Navier-Stokes along the boundary of interest. This solution is extremely difficult as the Navier-Stokes equations are highly non-linear and extremely sensitive to initial condition perturbations. Several empirical methods have been developed to approximate the fluid performance in a turbulent régimé. Moody published a series of curves correlating the friction factor to Reynolds Number. Theses charts are based on experiments performed in the laté 1940s. Colebrookfit equations to these curves and derived an analytic expression relating the friction factor to the Reynolds Number, pipe diameter, and wall roughness. Swamee and Jain developed a more exact relationship between a tube’s physical parameters and the pressure head generated across it. They developed an empirically derived equation for flow turbulence, and this relationship is used in one embodiment of the fluid model ofthe present invention. In the Swammee-Jain approximation for turbulent flow, the pressure drop across a length of tubing L, having diameter D, and wall roughness e is expressed by:

1.07β²Ζ/7

<img file="HUE034171T2_D0008.tif" />

In

3.77) + 4.62

<img file="HUE034171T2_D0009.tif" />

Equation 10 [0067] The value of the Reynolds Number dictates whether the model of the present invention uses Equation 8 or Equation 10 to predict pressures. There is never a clean transition from laminar flow into turbulent flow. In engineering fluid modelling, typically flows having Reynolds Numbers greater than 2500 are considered turbulent (thus Equation 10 is applicable), although the true change to turbulent flow can happen at much greater Reynold’s numbers dependent on the stability of the flow and other properties of the flow field. A region known as the transition zone lies between laminar flow and turbulent flow. lt is very difficult to accurately describe the fluid dynamics in the transition zone, especially for fást flow through narrow tubes, which can account for somé of the error observed when comparing theoretical descriptions of injectorfluid paths to empirical results. The model used in the present invention transitioned from laminar flow to turbulent flow (that is, transitioned from Equation 8 to Equation 10) when the Reynolds Number exceeds 2500. The above discussion above is summarized schematically in Figure 27.

[0068] With the addition ofthe turbulent flow description, the model predicts the pressure across the fluid path as:

EP 2 902 053 Β1

<img file="HUE034171T2_D0010.tif" />

ln

72) ^J LLPCT

<img file="HUE034171T2_D0011.tif" />

<img file="HUE034171T2_D0012.tif" />

1.O7Ö²XP

<img file="HUE034171T2_D0013.tif" />

In e

<img file="HUE034171T2_D0014.tif" />

+ 4.62

<img file="HUE034171T2_D0015.tif" />

&lt; PQ y ~ Equation 11

Pressure generation equation fór fluid model assuming turbulent flow (Reynolds No. &gt; 2500, e=lxl0'⁵ fór plastic tubing) [0069] Figures 28 through 30 illustrate graphs of pressured predicted by the analytical model described above. The experimental data are taken from a study testing the pressure performance of MR disposable components (.075 ID LLPCT, 20-24 ga Angiocath catheters) with various MR contrast agents (Gadovist, Magnevist, and Saline were tested). The pressure data generated from the model are outputs ofthe model assuming the flow has achieved steady state. As one can see in the figures, there is good agreement between the theoretical predictions and the experimentally determined pressures. The error bars about each experimental point are +/-1 standard deviation ofthe sample taken fór each flow rate. There were 5 pressure samples taken at each flow rate in that study. The above computations can be made more precise if measurements of pressure were available to the system via sensors located within the fluid path, fór example MEMS transducers manufactured by Verimetra Inc. of Pittsburgh PA.

[0070] Although the present invention has been described in detail in connection with the above embodiments and/or examples, it should be understood that such detail is illustrative and nőt restrictive, and that those skilled in the art can make variations without departing from the invention. The scope of the invention is indicated by the following claims rather than by the foregoing description. All changes and variations thatcome within the meaning and rangé ofequivalency of the claims are to be embraced within their scope.