Problems occur regularly with intravenous therapy, especially with the flow behavior. A mechanical model can predict which components of intravenous therapy systems introduce non-ideal effects in the flow. This study concentrates on gaining quantitative information of each separate component for intravenous therapy, characterize its non-ideal effects and combine these quantities in one system-level model. The model will help in the development of a mass flow sensor which can be used in a control system for intravenous therapy

Alveringh, D.

Lötters, J.C.

Wiegerink, R.J.

Alveringh, Dennis

Wiegerink, Remco J.

Lötters, Joost Conrad

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Towards system-level modeling and characterization of components for intravenous therapy

University of Twente Research Information

4. Fluidic control systems PresentationTOWARDS SYSTEM-LEVEL MODELING AND CHARACTERIZATION OF COMPONENTSFOR INTRAVENOUS THERAPYD. Alveringh1, R.J. Wiegerink1, and J.C. Lötters1,21 MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands2 Bronkhorst High-Tech BV, Ruurlo, The NetherlandsABSTRACTProblems occur regularly with intravenous therapy,especially with the flow behavior. A mechanical modelcan predict which components of intravenous therapysystems introduce non-ideal effects in the flow. Thisstudy concentrates on gaining quantitative informationof each separate component for intravenous therapy,characterize its non-ideal effects and combine thesequantities in one system-level model. The model willhelp in the development of a mass flow sensor which canbe used in a control system for intravenous therapy.KEYWORDSintravenous therapy, flow sensor, infusion, CoriolisINTRODUCTIONAccording to reference [1], between 2005 and 2009,the FDA (US Food and Drug Administration) receivedmore than 56,000 reports of problems associated withinfusion pumps. To find the health risks for intravenoustherapy, measurements have been done in the past oninfusion pumps, tubes and other components. Reference[2], for example, summarizes the main problems based ona literature study. However, to understand all non-idealeffects and predict the behavior of intravenous therapy,the entire system must be described in one model.Our study concentrates on gaining quantitative infor-mation of each separate component, characterize its non-ideal effects and combine these quantities in one system-level model. This model is part of the development of anew micro Coriolis mass flow sensor based on reference[3], which can be used for real-time monitoring or as acalibration method for systems for intravenous therapy,leading to safer infusions.(a) Practical infusion setup.stepper motor belt worm syringetubesneedleinfusion pump(b) Schematic overview of the componentsTF TFmotor belt worm syringe tube needleM⋅sin(ωt) CtubeNwormMwormNsyringeRneedleRtubeωmotor v φTFNbelt ωbelt(c) System-level lumped elements model.Figure 1: Intravenous therapy.MODEL OVERVIEWSystems for intravenous therapy consist of infusionpumps, syringes, tubes and needles. Infusion pumps con-sist of stepper motors, belts and worm wheels (Figure1b). A stepper motor generates an angular velocityωmotor.This angular velocity is transmitted via a belt (ωbelt) to aworm, which transforms it into a velocity v of the plunger.The syringe transforms the velocity into a fluid flow φ.The mentioned components can be modeled withlumped elements (Figure 1c), where each component ismodeled as an equivalent electronic resistor (R), capac-itor (C) or transformer (N). This method for modelingdynamical systems is done in many applications; themodeling of micropumps [4], for example. For equivalentresistors (e.g. a small needle), the following equationshold:F (t) = Rt · v(t), (1)T (t) = Rr · ω(t), (2)P(t) = Rf · φ(t). (3)with t the time, F the force, T the torque and P thepressure. And for equivalent capacitors (e.g. a compianttube), the following equations hold:F (t) =1Ct∫v(t) dt, (4)T (t) =1Cr∫ω(t) dt, (5)P(t) =1Cf∫φ(t) dt . (6)Transformers (e.g. a syringe converts a velocity to aflow) are two-ports, and obey following equation:eout(t) =1Nein(t), with e = F ∨ T ∨ P, (7)fout(t) = N f in(t), with f = v ∨ ω ∨ φ. (8)In Figure 1c, the major parts of an intravenous therapysystem are represented using the described elements.The sine-block in Figure 1c models the shape ofa bent worm, modeled by a sine wave with amplitudeMworm and frequency dependent of the angular velocityof the worm.MODEL PARAMETERSAll parameters are estimated using calculations,finite element simulations and measurements oncommercially available components.Stepper motorStepper motors rotate by actuating the rotor insteps. This allows good control of the angular velocity,but may introduce non-smooth transitions betweensteps. Therefore, measurements where done using a10-bit contactless magnetic angular encoder (AvagoAEAT-6600-T16) on a stepper motor (17H130HM) froman infusion pump (NE-300), using the measurementsetup in Figure 2a. Oversampling of 30 times was usedto increase the resolution. As shown in Figure 3, therewhere no significant steps or other non-ideal effectsobserved, which means that the stepper motor can bemodeled as a straight-forward source of angular velocity.magneticangularencoderNZB(a)markcamera(b)Figure 2: Measurement setup for the characterization of theinfusion pump, with (a) contactless motor angle measurementand (b) displacement measurement.0501001502002503003500 500 1000 1500 2000Angle[degree]Time [s]152154830 840Figure 3: Characterization results of the stepper motor with anequivalent pumping speed of 0.49 mL h−1 at 100 Hz and 30×oversampling.WormNon-ideal transformation effects of the worm werefound using video measurements. By recording (640×480pixels, 15 FPS) the movement of the cart on the wormwheel, the displacement over time is measured. Figure 2bshows schematically the measurement setup. A movingaverage filter (31) is applied on the data, the result and itsderivative are shown in Figure 4.00.511.522.530 10 20 30 40 50 60-20246810Displacement[cm]Velocity[mm/s]Time [s]DisplacementVelocityFigure 4: Characterization results of the worm with an equiva-lent pumping speed of 49 mL h−1.It can be concluded that the the influence of thenon-ideal shape of the worm on the velocity is morethan 75 %. This value is expected to be much smaller formost infusion pumps, since this measurement was doneon a worn infusion pump. The measurement setup willbe used to characterize the worms of different infusionpumps in the future.Tubes and needlesCharacterization of two types of tubes and needles isdone using the setups in Figure 5.CRPφ(a)CRPφ(b)Figure 5: Measurement setup for the characterization of tubes,with (a) capacitive measurement and (b) resistance measure-ment.The capacitances have been measured by filling thetubes with water, clamping one end while expanding thetubes with constant flow of water. The equivalent capac-itance can be calculated from Equation 6. For constantflow, this is related to the flow, time and pressure as shownin following equations:Cf(t) = φtP(t). (9)The resistances have been measured by pumping aconstant flow and measuring the pressure. This can be cal-culated by deriving the following equation from Equation3:Rf(t) =P(t)φ. (10)The measurement results for two frequently usedtubes and needles are available in Table 1. The resultswere checked using finite element simulations for thecapacitive values and Hagen-Poiseuille calculations forthe resistive values. The values correspond in the sameorder of magnitude.Table 1: Resistance and capacitance measurements of infu-sion tubes and needles.Resistance CapacitanceTube 1a 1.3 · 1010 Pa s m−3 2.3 · 10−12 m3 Pa−1Tube 2b 4.8 · 1010 Pa s m−3 3.5 · 10−13 m3 Pa−1Needle 1c 3.3 · 1010 Pa s m−3Needle 2d 1.3 · 1012 Pa s m−3Flow sensore ≈1 · 1013 Pa s m−3a Clinico Medical Sp. z o.o PVC Infusion Line (2 m).b Biocath PE/PVC Extension Line (2 m).c BD Microlance 3 0.8 × 25 mm needle.d BD Microlance 3 0.3 × 13 mm needle.e Bronkhorst L01 flow sensor, derived from datasheet.Other parametersThe resistance of the plunger is connected in serieswith the source of velocity, hence, this will not influencethe flow. The compliance of the plunger is, according tofinite element simulations, also not significant comparedto the compliance of the tubes. The compliance of thebelt, the inertia of the worm and the compliance of theneedle are assumed not significant compared to the otherresistances and compliances in the system. For the rest,the used flow meter consists of a stainless steel tube thatis similar to a needle.SIMULATIONThe parameters used in the model of Figure 1care printed in Table 2. The simulation software 20-simwas used to simulate the model. The set point changesfrom 0 mL h−1 to 1 mL h−1 and back to 0 mL h−1, whichsimulates a practical medical situation. Results areshown in Figure 6. It is clear that the RC-effect and themodulation effect have a major influence on the flow.Table 2: Values used in the model of Figure 1c.Parameter Value DescriptionNbelt 0.5 Ratio of beltaNworm 1.3 · 10−4 m rad−1 Ratio of wormaMworm 5 % Worm modulationbNsyringe 6.2 · 10−4 m2 Ratio of syringecRtube 1.3 · 1010 Pa s m−3 Tube 1dCtube 2.3 · 10−12 m3 Pa−1 Tube 1dRneedle 1 · 1013 Pa s m−3 Flow sensorda Calculated from the results in Figure 3 and Figure 4.b Expected, to be specified in future work.c Calculated from the section area of a syringe.d From the results in table 1.-0.200.20.40.60.811.20 50 100 150 200 250 300Flow[ml/hr]Time [min]00.20.40.60.81265 270 275SetSim.Figure 6: Simulation results, with a clear RC-effect of tube andneedle combination and the modulation effect of a non-idealworm.MEASUREMENTSTo validate the model, measurements of the completesystem were done. The setup in Figure 1b was used,where the needle is replaced by a a flow sensor. Purifiedwater was used for the fluid flow. The results are shownin Figure 7.It can be concluded that there are differences betweenthe model and the measurements: the frequency of themodulation of the worm is higher in the simulation.Besides, the RC-time is lower. Latter may be becauseof the connection tubes between flow sensor and setup.Nevertheless, the model supports the major non-idealeffects.CONCLUSIONThe first system-level model for intravenous therapysystems is realized. A stepper motor and worm of aninfusion pump as well as two different tubes and needles-0.200.20.40.60.811.20 50 100 150 200 250 300Flow[ml/hr]Time [min]00.20.40.60.81265 270 275SetMeas.Figure 7: Measurement results, also with a clear RC-effect oftube and needle combination and the modulation effect of anon-ideal worm.are characterized and included in the simulation. The RC-time as a result of the compliance and resistance of thetube and needle and the modulation as a result of theshape of the worm have major influences on the flow.Measurements on a complete intravenous therapy systemagree with these observations.Future work will focus on further characterization ofdifferent systems for intravenous therapy, improving themodel and the development of a new mass flow sensorcan be used in a control system for intravenous therapy.ACKNOWLEDGEMENTSThe authors gratefully acknowledge support bythe Eurostars Programme through the TIPICAL project(E!8264), Roland Snijder and Jarno Groenesteijn.REFERENCES[1] T. Agres, “FDA seeking safer infusion pumps,” Phar-macy Practice News, may 4th 2010.[2] A. C. van der Eijk et al., “A literature review onflow-rate variability in neonatal iv therapy,” PediatricAnesthesia, vol. 23, no. 1, pp. 9–21, 2013.[3] J. Haneveld et al., “Modeling, design, fabricationand characterization of a micro coriolis mass flowsensor,” Journal of Micromechanics and Microengi-neering, vol. 20, no. 12, p. 125001, 2010.[4] T. Bourouina et al., “Modeling micropumps withelectrical equivalent networks,” Journal of Microme-chanics and Microengineering, vol. 6, no. 4, p. 398,1996.

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