Multi-infusion therapy, in which multiple pumps are connected to one access point, is frequently used in patient treatments. This practice is known to cause dosing errors following setpoint changes in the drug concentrations that actually enter the patients. Within the Metrology for Drug Delivery Project, we analyzed and quantified the two main physical phenomena leading to these errors: the “push-out” effect and the system mechanical compliance. We compared the dosing errors of a three-pump system with two infusion sets, both with and without anti-reflux valves, using in vitro spectrophotometric experiments. Additionally, computer simulations were used to study the compliance effect separately. We found a start-up time of more than 1 h, and a dosing error following a setpoint increase of another pump for the low flow rate pump, corresponding to 0.5 μg noradrenaline delivered in 8 min. We showed that the dead volume inside the tubes and syringe compliance produce opposite deviations from the setpoint values in the actual drug output concentrations, making the net result hard to predict and often counterintuitive. We conclude that metrology on compliance and push-out effects could be used by infusion device manufacturers to successfully improve drug delivery performance and relevant standards for high-risk multi-infusion applications.
Drug delivery is the process of administering a pharmaceutical compound to achieve a therapeutic effect. Almost all patients who are hospitalized, and many in home care, receive intravenous medication; in other words, drugs are delivered directly in their bloodstream. Infusion pumps, syringes, and infusion sets are therefore among the most widely used medical devices in hospitals.
On many occasions, several liquid therapeutic agents are administered to patients simultaneously, because vascular access sites are limited. Moreover, the procedure of inserting a catheter for high-risk medications is challenging for several reasons [8, 16]. Catheter insertion is also associated with a high risk of infection, which is potentially lethal. For these reasons, multiple pumps are often combined on one catheter. This administration method is called multi-infusion. In several papers [4, 11, 12], evidence is given that, in standard clinical practices, multi-infusion creates unintended variations in drug dosage. van der Eijk et al.  described flow rate variability at low infusion rates as a persistent problem in intravenous drug therapy for newborn infants. Ethgen et al.  showed that unintended drug delivery changes caused by multi-infusion effects could pose threats to the adult patient as well.
In standard infusion applications, the dosage is controlled by the flow rate setpoint and the drug solution of known concentration. Therefore, following the research mentioned above, this approach is not sufficient to achieve the required dosing accuracy. In particular, this is the case for potent drugs that have very short half-life and a narrow therapeutic range. In addition, if low flow rates are needed (e.g. for patients who can only tolerate a limited amount of fluid intake), the concentration of the drug to be infused will have to be increased. Consequently, deviations from intended flow rates can cause toxic concentrations in the blood more easily.
The chemical and pharmacological compatibility of drugs is customarily tested as a part of pharmacological and nursing protocols before combining two lines in a multi-infusion system. In contrast, up until now, barely any adequate description exists of customarily testing of the effect of the applied infusion system parameters on the infused drug dose. In a comprehensive review on intravenous drug delivery in neonates, Sherwin et al.  concluded that an evaluation of infusion protocols and practices in neonatal settings is needed to give insight into unexpected therapeutic outcomes in clinical practice.
The physical characteristics of the infusion system (e.g. of an infusion pump, a syringe, infusion tubing, and catheter) are known to contribute to dose variations.
The objective of this study is to create awareness that the actual dose that is administered to the patients’ blood vessels is influenced by these physical characteristics. In the next sections, we will investigate, by combining theoretical macroscopic analysis of a syringe pump multi-infusion system with exemplary in vitro spectrophotometric experiments and a computer model, how a “push-out effect” and the effect of mechanical compliance in the system cause clinically relevant dosing errors. Furthermore, we will discuss why the combination of the two effects yields a result that sometimes is hard to predict. Eventually, we will explore how we can more accurately predict the actual drug dosage delivered to patients where this is clinically relevant and how and when an accurate measurement of system mechanical compliance and actual flow rates can contribute to that goal.
Clinicians relate therapy effectiveness to the drug dose delivered to the patient, which can, for example, be expressed in microgram per kilogram per minute. In a multi-infusion setup, the intended drug doses delivered to the patients are set by adjusting the flow rates of the constituent pumps. In the case of syringe pumps, the parameter that is actually controlled is the displacement of the syringe plunger. The pump software makes an internal conversion to a flow rate from the syringes. For each patient, the drug dose that needs to be administered over a certain time, the dose rate, is specified in a medication scheme. The drug dose rate is converted to a setpoint for the flow rate by multiplying it with the concentration of the drug solution in the syringe. Today’s pumps typically indicate the set flow rate on a screen that is part of the pump front.
This indicated setpoint of pumps is based on a simple rule:
This equation, however, is based on two assumptions that have been shown not to hold in practice. These two assumptions are
where t is a point in time, N is the number of pumps, and i is an integer running from 1 to N.
First, in Equation (2), it is assumed that all elements in the total multi-infusion setup are infinitely stiff and mechanical compliance effects do not occur. This would imply that the sum of the flow rate setpoints of the pumps is always exactly equal to the flow rate entering the patient [Equation (2)].
Second, the concentration of the drug in the tip of the catheter, just before entering the bloodstream of the patient at time t, is assumed to be equal to the concentration entering the other end of the infusion set up, located outside the patient near the pumps [Equation (3)].
These two assumptions are not valid in many situations, and the improper use of multi-infusion setups may lead to dosing errors.
Instead of using Equations (2) and (3), a correct formulation of the situation would be
in which the mechanical compliance causes temporary effects following changes in flow rate (e.g. due to change in flow rate setpoints or the changes in the height of the pumps), and T is an unknown delay time that depends on the history of the actual flow rates inside the catheter.
The actual drug doses delivered to the patient are therefore not only determined by the flow rates from the pumps but also by the amount of drugs stored inside the infusion system as well.
To illustrate Equation (5), in Figure 1A, a simplified example of a multi-infusion setup schematic with two syringe pumps is given. The flows from the different syringes are combined via a one-piece infusion set and from thereon continue via the central line to the patient. Finally, the flow enters the patient via a catheter. When the flow rate setpoint of a pump is changed, the drug concentration entering the patient is affected by a “push-out” effect of the drug solution mixture after the mixing point. This effect is caused by the fact that the various concentrations of medications existing inside the catheter at a given moment in time t reflect the history of the setpoint values of the pumps before time t. However, the flow rate with which this content is pushed out of the infusion line is determined by the setpoint values of the moment in time t itself. Figure 1B shows that, if the setpoint value of the pump of one of the medications is increased, then the other medication, which is still present inside the infusion line, is pushed out of the infusion line into the bloodstream with increased speed, potentially causing a relevant temporary overdose.
As setpoint increases, part of the drug solution can temporarily be stored in the infusion system because of system mechanical compliance. This compliance refers to the compressibility of certain elements in the infusion setup, primarily the plungers in the syringes. In a steady-state situation, when the setpoint values of the pumps have not been altered for a long time, equilibrium exists between the line pressure and mechanical stress in the various components. When the setpoint value of one of the pumps is increased, however, the pressure is increased inside the entire multi-infusion system, causing an increased compression of the plungers. Thus, an additional amount of space is created near the plunger that is now being filled with fluid. As a result, the system mechanical compliance effect causes a delay in reaching the actual flow rate increase with respect to the setpoint increase of the pump. If, in a multi-infusion system, the flow rates of two pumps differ greatly, the drug solution originating from the pump with the highest flow rate could even flow into the infusion line connected to another pump with a substantially lower flow rate. This phenomenon is called backflow and is known to cause dose fluctuations starting with a temporary delivery stop followed by an overdose [4, 27]. Backflow can be countered by adding anti-reflux valves. However, at the same time, anti-reflux valves add to the delay of reaching the setpoint .
The purpose of this paper is threefold. It is shown by theory and experiments that
both the “push-out” effect and the effect of mechanical compliance can lead to substantial dosing errors,
these dosing errors are clinically relevant, and
the “push-out” effect and the effect of mechanical compliance may be of the same order of magnitude but will be “opposite” in direction, which adds strongly to the unpredictability of the total net effect.
Furthermore, it will be corroborated that the present clinical practices, in which the push-out effect and the effects due to mechanical compliance are not satisfactorily dealt with by the protocols that determine the flow rate setpoints of the pumps, possess serious risks for patients and that action and innovation are needed.
In the following sections, we present both the results of in vitro experiments as well as predictive computer calculations for a multi-infusion setup using three pumps.
To illustrate the push-out effect and the effect of system mechanical compliance, preliminary in vitro experiments were carried out. In the section “Start-up time measurement using in vitro flowmetry”, the start-up characteristics of the flow rate from a single pump were investigated. In the section “Dosing deviations in a clinical medication scheme”, an analysis was made of dosing deviations resulting from compliance and push-out effects in a medication scheme used in a clinical situation. The experiment was carried out both for an infusion set with and without anti-reflux valves.
In this experiment, a Coriflow M12P Coriolis mass flowmeter (Bronkhorst, Ruurlo, The Netherlands) was used. The sample time was 1 s. A single-pump syringe pump (B.Braun perfusor, Melsungen, Germany) setup was used. The syringe used was a 50 ml (B.Braun Omnifix syringe, Melsungen, Germany), which was filled with distilled water. The pump was connected to a 1-m infusion (d=1 mm) line (Cair LGL, Tunisie), which was subsequently connected to the flowmeter. The nominal flow rate was 0.5 ml/h. The flowmeter measured a mass flow rate, and the measured values were corrected for the density of water at the laboratory temperature of 20°C (i.e. 998.2071 kg/m3). The mean plot, resulting from the three measurements, was fitted using an exponential fit. From this fit, the 95% of the start-up time, which was defined as the onset time of steady-state drug delivery, as well as the RC time, was acquired. This time period equals the resistance (pressure per volume/time) multiplied by the compliance (volume/pressure) of the entire infusion setup.
Two parameters were calculated to investigate whether clinically relevant dose deviations were found.
The start-up time in all three pumps was investigated for the standard line as well as for the octopus line with valves. The time required from T=0 h to reach 95% as well as 50% of the steady-state flow rate was assessed (see Figure 2A).
The dosing error was assessed using the procedure illustrated in Figure 2B: the deviation from steady state in outflow of one drug was recorded, resulting from the increase in the flow rate setpoint value of “another” drug in another pump. The results are presented as the area under the curve (AUC) in percentages as well as in milliliters and milligrams.
The exact analytical methodology is explained in the section “Data analysis”.
Experimental setup: In these in vitro experiments, we used an absorption spectrophotometric method that was developed in our group, in which multiple spectral photometric measurements were performed simultaneously on fluids consisting of laser dyes solved in water. The purpose of the laser dyes, which mimicked the various pharmaceuticals of a medication scheme used in clinical practice, was to distinguish output concentrations. Absorption spectrophotometry allows for an accurate measurement of the concentration of the various dyes in the water when it exits inside the infusion line (at the point where it theoretically would enter the bloodstream of the patient).
The setup consists of the following elements. A light source (DT-100, Ocean Optics, Dunedin, FL, USA) emits light in the visible spectrum. Subsequently, this light is guided through 200 μm optical fibers into a flow cell (FIA-Z-SMA, Ocean Optics, Dunedin, FL, USA). The flow cell was also connected to a 200-cm-long central line (2.5 mm in diameter), where the solvents from each syringe pump are joined. Consequently, the light emitted from the source passes through the solution, allowing the solvent to absorb a part of the light spectrum. The spectrum is finally analyzed by a spectrometer (QE65000, Ocean Optics, Dunedin, FL, USA). After the measurement, the solvent was guided through a line of 50 cm (1.0 mm in diameter) and released into an Erlenmeyer flask. A precision (±0.0001 g) balance (PGW 450, Adam Equipment, Danbury, CT, USA) was used to verify the total mass measurements, additionally allowing to obtain a (mass) flow rate. The sample time was 10 s.
A calibration method was needed to relate the measured absorbances to concentration values to be assessed. This calibration was performed as follows:
where A is an N-dimensional vector containing the absorbances at various wavelengths and n is an index running from 1 to N enumerating the various wavelengths at which the absorbances were measured. Because the number of dyes equals the number of measured wavelengths, n is the enumeration of the dyes as well. Because this was a calibration procedure, both the measured absorbances in vector A and the concentration Cn of the dye n at the point of measurement were known. From these data, the vectors a and b were retrieved (using the linear regression function in MATLAB 7.5.0 [The Mathworks, Natick, MA, USA]), which completed the calibration procedure. Subsequently, the vectors a and b were available for normal (i.e. noncalibration) measurements to solve the unknown C values from the measured A values.
Clinical situation: This experiment was based on a clinical situation that could occur in the intensive care unit, where patients received among others a combined noradrenaline and midazolam infusion therapy with an isotonic saline carrier flow. After 1 h, indicated as T=1, the intensive care specialist decides that additional medication is needed. This drug is added to the carrier flow, setting the total flow rate from the carrier flow to 16 ml/h. An hour later (T=2), the dose of this drug needs to be adjusted and the flow rate of this drug is raised from 8 to 17 ml/h. Finally, half an hour later, the noradrenaline is doubled after the patients’ blood pressure decreases. The experiment was ended after 3 h.
The nominal flow rates of the medication schedule are listed in Table 1.
|Pump 1 (carrier flow, NaCl, and additional medication)||8||16||25||25||25|
|Pump 2 (midazolam 1 mg/ml)||5||5||5||5||5|
|Pomp 3 (noradrenaline 0.1 mg/ml)||2||2||2||4||4|
The flow rate profiles were compared between a “standard infusion set,” which consisted of a manifold (Variostop Multiple Stopcock System, Clinco Medical/Fresenius Kabi, Bad Homburg, Germany), and an “octopus infusion set” (Smartsite extension set, three-needle-free valve ports, Medica Europe, Oss, The Netherlands) with anti-reflux valves (valve-operated three-way, IMF, Dortmund/Hagen, Germany).
Data analysis was performed using MATLAB 7.5.0 (The Mathworks, Natick, MA, USA) for the absorption spectrometric method in Section “Dosing deviations in a clinical medication scheme”. The results from the experiment using the flowmeter in the section “Start-up time measurement using in vitro flowmetry” were analyzed with Origin 9.0 (OriginLab, Northampton, MA, USA).
In the section “Dosing deviations in a clinical medication scheme”, the steady-state flow rate, measured using absorption spectrophotometry, was defined as a period over which the flow rate did not change significantly. The steady-state flow rates were estimated from means over 1000 s. The artifacts in the order of one sample were ignored in any measurement. The accuracy of the mass flow measurement conducted by our precision balance was ±1 mg, which is equal to approximately ±1 μl. The results were therefore presented as three decimals at most.
In case the steady-state flow rate was different before and after a dosing error, linear interpolation was used to estimate the differences between the steady state before the dosing error and the steady state after the dosing error. The AUC of this linear interpolation was subtracted from the AUC of the dosing error.
All experiments were repeated three times (n=3). A two-sample, two-tailed, t-test for unequal variances was used to investigate the statistical significance for the differences in start-up times between the standard infusion set and the octopus infusion set with valves. All results are presented as mean±SD.
A basic framework for predictive computer modeling of multi-infusion output flow rate was set up by Murphy and Wilcox .
We extended this model to acquire expressions for any number of pumps. In our multi-infusion network model, capacitances, resistances, and flow sources are used to simulate the outflow of a realistic multi-infusion setup (see Figure 3 for an example of such a network model). To derive analytical expressions for the various flows in the model depicted in Figure 3, we combined Kirchhoff’s laws with a Laplace transform.
A realistic infusion pump can be described as a (mathematically pure) current source Q, in combination with a capacitor C that represents the compliance (compressibility) of the plunger of the syringe in the pump. Each segment of an infusion line in the total setup has a resistance R.
The model predicts the flow rates of the individual medications (q1, q2, q3, etc.).
A great advantage of these computer simulations is that the impact of the “push-out” effect and “compliance” effect can be studied individually. In the computer simulations presented here, the effect of compliance was studied independently from other effects, because the flow rates were calculated for every point in the system, including individual flow rates from the syringes before the mixing point. Each pump is represented by the combination of a (mathematically pure) current source Q1 (or Q2 or Q3 for pumps 2 and 3, respectively) in combination with a capacitor C that represents the compliance (compressibility) of the plunger of the syringe in the pump. Each of the three pumps is connected to a mixing point by a segment of tube having a resistance R, through which the fluid flows toward the mixing point with a flow rate q1 (or q2 or q3). Finally, a tube segment with resistance R0 connects the mixing point to the outflow point (representing the point at which the infusion system releases the fluid into the bloodstream of the patient).
We calculated the case for three infusion pumps. Three drug solutions were simulated in these calculations to illustrate the effect of system mechanical compliance in steady-state flows if one of the pumps alters speed suddenly. At t=0.5 h, the flow rate setpoint of pump 1 (blue) was doubled. Furthermore, at t=2 h, the flow rate setpoint of pump 1 was suddenly decreased to its original level.
The effect of the system mechanical compliance on start-up behavior of a single-pump setup is shown in Figure 4. It shows the start-up curve, which results purely from system mechanical compliance, for a substantial part from the syringe compliance. The effect of the system mechanical compliance therefore causes a delay of 232±28.6 s (3.9±0.5 min) in reaching 95% of the flow rate setpoint and 102±5.20 s (1.7±0.1 min) before reaching 50%. The RC time, estimated from the exponential fit, was 45.9 (0.8 min).
This result confirms that the compliance effect takes place in the opposite direction with respect to the direction of the flow rate setpoint change.
In Figure 4, it can be seen that, after t=70 s, the curve can be approximated using an exponential fit. Before t=70, the phenomena with other time constants play a part. After that, the start-up period can be approximated by a single exponential function with sufficient statistical accuracy.
A typical measurement result in the section “Dosing deviations in a clinical medication scheme” is rendered in Figure 5. The deviation from the flow rate setpoint is clearly visible in the green line, which shows the reaction of the midazolam solution to a change in flow rate setpoint of the carrier flow only. From Figure 5, it is clear that the deviation in the green line after approximately t=2.0 h (the “push-out effect”) takes place in the same direction as the direction of the change in flow rate setpoint in carrier flow at t=2.0 h. The flow rate from the noradrenaline pump increases during approximately 10 min with more than 25%.
Start-up delays of more than 1 h were found. Table 2 lists the start-up times of the standard infusion set and the octopus infusion set with valves for all three pumps. Figure 6 shows the start-up of the standard infusion set and the octopus infusion set with valve times graphically.
|Standard infusion set, mean±SD||Octopus infusion set with valves, mean±SD||p-Value|
|Start-up (95%) pump 1 (s)||1980±111||1587±220||0.070|
|Start-up (50%) pump 1 (s)||1440±274||1440±113||1.00|
|Start-up (95%) pump 2 (s)||2277±307||2247±32||0.88|
|Start-up (50%) pump 2 (s)||1943±221||1877±155||0.69|
|Start-up (95%) pump 3 (s)||3797±329||4430±327||0.077|
|Start-up (50%) pump 3 (s)||3623±230||4113±81||0.074|
The start-up times found in this experiment (amounting to more than 1 h) were substantially larger than those found in the first experiment (adding to a few minutes). The largest difference found between the sets was the 50% start-up time in the noradrenaline, which was slower with the infusion set with valves. However, none of the results were statistically significant (p<0.05).
Figure 7 shows the dosing errors found in pump 2 representing midazolam (a) and pump 3 representing noradrenaline (b) of the standard infusion set at T=2.0 h following an initiated, nominal flow rate change in pump 1, representing the carrier flow.
The mean AUC of the dosing errors found for midazolam was 0.16±0.03 ml, 27.5±10.4%, which lasted 483±172 s. For a 1 mg/ml midazolam solution and a standard 80 kg patient, this volume corresponds to a total additional dose of 0.16 mg midazolam in 8 min. The mean maximum dosing error of pump 2 representing midazolam was approximately 30%.
The mean AUC of the dosing errors found in pump 3, representing noradrenaline, was 0.05±0.01 ml, 23.5±8.7%, which lasted 490±156 s. This volume corresponds to a total additional dose of 0.5±0.1 μg noradrenaline in 8 min. For an 0.01 mg/ml noradrenaline solution and a standard 80 kg patient, this amounts to a total overdose of approximately 0.5 µg noradrenaline that is delivered in 8 min, which is comparable to an additional 5% of the maintenance dose (2–4 μg/min). Noradrenaline, a drug with an instantaneous effect on the heart action, is known to cause blood pressure variations upon infusion setpoint changes that can be dangerous [5, 7], considering its small therapeutic width and low plasmatic half-life of approximately 2 min after intravenous administration .
The results of the calculations are rendered in Figure 8. The initial values of the setpoint values of pumps 1–3 were 7, 2, and 5 ml/h, respectively.
In Figure 8, the deviations in the green and red lines are caused by the “mechanical compliance” of the “red” and “green” syringes; if these compliances would have been zero, the deviations in the red and green lines would disappear.
From Figure 8, two important phenomena can be seen.
In all cases, the deviations from the constant setpoint values of the red and green lines take place in a direction “opposite” to the direction of the change (in setpoint value) of the blue line.
The depth of the dip in the red line at t=0.5 h, with respect to the red steady-state line of 2 ml/h, is approximately 1.3 ml/h. This is equal to the depth of the dip in the green line, at the same point in time, with respect to the green steady-state line of 5 ml/h, because all syringes have the same compliance. As a result, when expressed as a percentage of the intended (setpoint) flow rate, the relative deviation caused by the dip in the red line at t=0.5 h is much larger than the relative deviation caused by the dip in the green line at the same point in time.
It is found, from the in vitro experiments, that the dosing errors caused by the physical effects studied can be substantial. We found in the section “Dosing deviations in a clinical medication scheme” that a standard intervention of coupling an additional medication on the carrier flow causes an overdose in both other pumps, representing midazolam and noradrenaline. The dosing error in midazolam was 30% in more than 8 min. This could cause an adverse effect on the respiration. Although for at least some patients a relevant effect, the saturation of intensive care patients is intensively monitored, which would ensure that timely interventions could take place. Therefore, the most disturbing dosing error is the one found in the noradrenaline solution. This dosing error with a mean of 25% would cause the patient to experience a direct and higher increase in blood pressure than intended by the noradrenaline medication itself. Because of the small therapeutic range and short biological half-life of noradrenaline, such an overdose could cause serious effects. Furthermore, in emergency situations in the operating room, for example, if a patient’s blood pressure is falling rapidly, physicians need to act quickly. In such cases, higher flow rates, typically up to 50 ml/h, tend to be applied. When using carrier flows or multi-infusion combining high and low flow rates, the central line can become filled with a high concentration of noradrenaline or other potent drugs. If the physician is not aware of the “push-out” effect and only adjusts the noradrenaline and not the carrier flow in reaction to a blood pressure overshoot, this action can quickly lead to a dangerous and even fatal situation. Such a case was previously described by Ethgen et al. . Therefore, the push-out effect is more pronounced when using high carrier flow rates or a combination of medications running with flows that greatly differ in rate. Moreover, in critical situations, the start-up times of more than 1 h for noradrenaline, as seen in the section “Dosing deviations in a clinical medication scheme” (see Table 2), are of major clinical concern. Often in such cases, if the needed reaction in the patient fails to occur for too long due to the “push-out” effect, this can even prompt the physician to set the dose too high. From the part of the physician, however, this would be quite an intuitive action.
In the section “Start-up time measurement using in vitro flowmetry”, the start-up time could be approximated using a single exponential fit from 70 s onwards. The phenomenon before t=70 s is often observed and may have several causes. A small gap between the pump and the plunger has been described [10, 18] to prolong the start-up time. Moreover, the friction between the plunger and the syringe wall may cause an extra resistance. The experiments show that the start-up time is a result of the combination of the mechanical compliance effects and the time delay due to the internal volume inside the infusion system. This explains the large difference in start-up times between the two experiments. The start-up time assessed in the section “Start-up time measurement using in vitro flowmetry” shows the effect of compliance only, typically a few minutes. Unfortunately, it is only this curve that is mandatorily measured to assess the quality of the infusion system. The start-up measurements in the section “Dosing deviations in a clinical medication scheme” show that the time delay due to the internal volume is often clinically far more relevant.
The theoretical considerations, the in vitro experiments, and the computer simulations show that compliance is an important factor, contributing to the origin of relevant dose deviations. This is consistent with earlier studies [17, 19, 26]. The computer simulations show that, when the deviations are viewed as a percentage of the intended flow rate, the syringe compliance effects are particularly important at low flow rates. This underlines that, especially if low flow rates are applied, such as used in neonatology, the mechanical compliance of the syringes can significantly contribute to dosing errors, which was mentioned previously by several authors [14, 24, 28]. Unfortunately, the lowest flow rates are often used for the most potent drugs, such as inotropes. It is instructive to compare the magnitude of the dosing errors found from our experiments to the maximum volume displaced because of compliance effects (the compliance volume) set in standards of infusion devices, such as the NEN-ISO-7886-2 describing syringes for use in power-driven syringe pumps. In this particular standard and for a syringe of 20 ml and a typical maximum pressure of 40 kPa, the maximum compliance volume is 0.2 ml. This volume represents a 20 μg dose of our noradrenaline solution, which is clinically relevant. In many hospitals, 50 ml syringes are used as the default, even in the neonatology ward, because this practice is more efficient and reduces errors and the risk of infection that accompany syringe changes. Following the norm mentioned above, the maximum compliance volume for a 50 ml syringe is 1.2 ml. Therefore, conformation to this norm will not prevent dosing errors as large as 1.2 ml.
The mechanical compliance of the syringes used is known to be dependent on several variables. In a related research , it is shown that especially the 50 ml syringes have the largest contribution to the compliance of the complete infusion set. The authors measured the compliance of different infusion system components. Lucas et al.  found that only at low flow rates temperature influences the system’s compliance.
Many authors have stressed the necessity of placing anti-reflux valves  or minimizing internal volume [11, 12, 15]. Both 10 years ago  and recently [6, 20], innovative connection mechanisms were invented but have not extensively or successfully become a best practice yet. The exact reason is not known, but the fact that the difference in performance lies in the infusion system, which is not routinely measured in the standard quality measurements, might play a part. However, we think that the actual application of these innovations of infusion technology, both of the pumps and of the disposable infusion sets and syringes, is badly needed to really solve the problems found during multi-infusion.
No significant differences in the onset of drug delivery were found between the standard infusion set and the octopus infusion set with valves. A limitation of our experiment was that the octopus infusion set and the standard infusion line setups differed in internal volume: 1.8 ml for the standard infusion set and 1.6 ml for the octopus infusion set with valves, respectively. The measured quantities of both the start-up time and the dead volume were in agreement with the theoretical implications of the dead volume. However, the results from the infusion line with valves confirm that, in spite of the anti-reflux valves, dosing errors are still found.
van der Eijk et al.  found longer start-up times with check valves (up to 43.7±2.7 min) than without check valves (up to 27.6±3.8 min) for a flow rate setpoint of 0.1 ml/h. McCarroll et al.  evaluated anti-syphon at nominal flow rates of 2, 10, and 50 ml/h using syringe pumps. The start-up times were longer when an anti-siphon valve was used at the lower setpoint of 2 ml/h.
However, literature shows that, at the higher flow rate setpoints of 10 and 50 ml/h, the start-up time differences between using a valve and not using a valve were less pronounced . In fact, virtually none of the differences, using a valve and not using a valve, were statistically significant at higher flow rates [14, 24]. These results are consistent with the differences found with our flow rate setpoints between 15 and 34 ml/h.
The outcome of this theoretical analysis is in agreement with the conclusion from a review on multi-infusion measurements by Snijder et al. . They found that particularly system mechanical compliance and dead space volume (“push-out” effect) are often mentioned to play an important role in creating dose variations. Up until now, the typical way of dealing with these dose variations in clinical practice is to use practical solutions such as piggyback techniques  or quick change . However, even when using these practicalities or rules of thumb, the errors unfortunately do not seem to be satisfactorily diminished.
In summary, our in vitro experiments and computer simulations of a three-pump multi-infusion setup show the following observations.
First, the “push-out” effect produces dosing deviations (e.g. in midazolam or noradrenaline; see Figure 5) in the “same direction” as the direction of the change in flow rate setpoint (of another pump; e.g. the carrier flow).
Second, the “syringe compliance effect” produces a deviation in the “opposite direction” with respect to the direction of the flow rate setpoint change.
Finally, if the temporary deviations are viewed as “percentual” deviations with respect to the intended setpoint values, the (syringe) compliance effects are particularly important at “low flow rates”.
As a result, the direction as well as the strength of the net total effect is highly unpredictable and often counterintuitive. This causes variations in drug delivery that are undesirable and can at times be dangerous. For example, a temporary deviation from the intended flow rate of a potent drug such as noradrenaline might cause dangerous blood pressure variations. For drugs that are intended to act quickly, be titrated to a customary dose, and intended be life-saving, this is a very unwanted situation.
Therefore, to remedy this undesirable unpredictability, the amount of compressibility of notably the plungers in syringes should be reduced, especially for high-risk applications. Alternatively, the compliance can be measured to enable better predictions of the net outflow during setpoint changes, which might, in the future, be used to adapt and control the pump driver inline.
Unfortunately, there are no written standards yet that give specific guidelines on the methods of ensuring a safe and sound drug delivery for (multi)infusion at high-risk applications.
At this time in Europe, the main directive concerning medical devices is the “Council Directive 93/42/EEC” (1993), including various amendments (e.g. 2000 and 2001). This directive is rather general and does not specify requirements on (the use of) drug delivery devices other than the statement that the manufacturer is responsible for an adequate flow rate accuracy and stability. The manufacturer should state the accuracy ranges.
There are various written standards concerning the dosing accuracy and calibration of drug delivery devices (e.g. IEC/EN 60601-2-24). Manufacturers typically follow this written standard during the development and maintenance of their devices. However, no general standard exists on how the infusion devices should be used. Furthermore, there are no particular instructions on specific applications where accuracy counts most.
Adopting specific standards for high-risk applications would improve the reliability of the performance of the infusion system. We therefore advise to include specific requirements, into relevant standards, on the subject of syringe plunger mechanical compliance and system internal volume, for low flow rate and high-risk pharmaceutical multi-infusion applications.
In this paper, we showed that dosing errors can be studied using in vitro experiments based on spectroscopy and numerical modeling. The important mechanisms in multi-infusion are the “push-out” effect and system mechanical compliance. The two effects produce deviations in opposite directions with respect to each other. The in vitro experiments as well as computer simulations show that the direction as well as the strength of the deviations from the intended flow rates in multi-infusion are hard to predict in clinical practice and often counterintuitive.
The measurements show that substantial dose deviations can occur long enough to have undesirable clinical effects, particularly when using inotropics or other potent drugs with a small therapeutic range. Where the “push-out” effect can have its most pronounced and dangerous effects when using high (carrier) flow rates, the compliance effect is most influential at low flow rates. This is confirmed in clinical case reports.
From the results, we conclude that there is a need for a quantification of the impact of the compliance and “push-out” effect because these effects can cause clinically relevant dosing errors. Potentially, this quantification is required (once) for each specific (multi)infusion setup. To quantify the performance of the complete setup, there is a need for an accurate measurement of essential parameters in the multi-infusion setup, such as the mechanical compliance of the syringes. A next step would be to control the pump setpoints to deliver the required dosage to the patient. Infusion device manufacturers could thus use this metrological data to successfully improve drug delivery performance. We therefore advise to include specific requirements on compliance and system push-out effect of infusion medical devices for high-risk applications in relevant standards. In this process, the flow rate dependency of these effects for low and high flow rates should be taken into account.
Thus, an increased focus and effort directed to the metrology of compressibility at low flow rates, combined with the preferential use of innovative techniques minimalizing “push-out” effects, will lead to enhanced controllability of drug delivery and consequently to better patient care.
EURAMET EMRP Researcher Grant Contract No. HLT07-REG1.
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