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Department of Anesthesia and Critical Care, Massachusetts General Hospital, Harvard Medical School, Boston
Address correspondence and reprint requests to Robert Peterfreund, MD, PhD, Department of Anesthesia and Critical Care, Clinics 3, 55 Fruit St., Massachusetts General Hospital, Boston, MA 02114. Address e-mail to rpeterfreund{at}partners.org.
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Abstract |
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Introduction |
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There are potential dangers when infusing concentrated drugs at slow flow rates (1). Concentrated drugs fill the infusion tubing and intravascular catheter. Clinical experience confirms the real risk of unintended, large drug boluses if fluid is inadvertently given upstream of the concentrated infusion. Recognizing this danger, some clinical settings require dedicated IV lines for each drug infusion. Alternatively, concentrated drugs can be "piggybacked" to a carrier flow (1,2), thus diluting the reservoir of the concentrated drug contained within the infusion set and catheter, and minimizing the impact of an accidental fluid bolus at the expense of increased delivered volume and complexity.
IV drug infusion systems configured with a crystalloid carrier have a finite dead-volume (V), serving as reservoirs for the drug. V is defined as the total volume of the intravascular catheter, IV tubing, stopcock, and connectors from the point where drug and carrier flow streams meet up to the patient’s blood (Fig. 1A). While the individual components have a fixed volume, the total V of the infusion system depends on how the carrier and drug infusions are connected. Each connector, IV extension tube, stopcock, and side-port on tubing potentially adds additional dead volume, which will impact the dynamics of drug administration (2–4). Whereas the use of carrier flows is perceived to minimize the impact of infusion set V as a drug reservoir (1), patients continue to receive inadvertent, substantial, doses of potent drugs when clinicians fail to understand the significance of the drug reservoir residing in the infusion set V. Many ICUs use slow carrier flow rates comparable to the rate of drug administration and therefore do not appreciably dilute the concentration of a potent drug in the V reservoir.
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Previous studies have elucidated the dynamics of drug delivery and subsequent pharmacodynamics imparted by idiosyncrasies in pump mechanics (5–8), syringe and tubing compliance (9–11), and syringe pump vertical displacement (11–13). While the dynamics of drug delivery after a bolus injection into an existing IV catheter have been rigorously evaluated (2–4), the interplay between the V, carrier, and drug flow rates have not been formally studied. We derived simple mathematical models for the flow of drug within the V and tested their predictions with data obtained from a laboratory model. We then predicted the dynamic response of drug infusion to changing carrier or drug flow rates. The data and models demonstrate the clinical utility of minimizing V.
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Methods |
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In the Well-Mixed model, the concentration of a drug within V is always uniform (Fig. 1D). Changes in drug or carrier flow are instantly reflected in the concentration of the exiting flow but take some time to reach steady state. The rate of change of a drug in V is described through a mass balance:
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where c is the concentration of the drug exiting the V, and cd is the stock concentration. This differential equation was solved through standard techniques (14). If drug infusion is initiated with a steady carrier, and V contains no drug, (c(0) = 0):
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Any change in carrier or drug flow from steady state can be described by:
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where Q’c and Q’d are the carrier and drug flow rates after making any changes, respectively.
Experimental Methods
Drug delivery was experimentally simulated using methylene blue as a model drug (catalog MB-1; Sigma, St Louis, MO). One syringe pump (Harvard 2 Clinical Pump, South Natick, MA) controlled a normal saline carrier flow through a standard IV extension tubing (Lifeshield 32"Extension, catalog #11316; Abbot Laboratories, Chicago, IL). This extension set has two needleless access ports for infusions. Another pump controlled a syringe with methylene blue (1 mg/mL) connected to a side-port of the extension set via microbore tubing (Partners Healthcare Systems T-ext, Boston, MA) using either a locking blunt connector (LBC; RF-150; ICU Medical, Inc, San Clemente, CA) or a blunt needle (Lifeshield, #11302–01) passed through the cap of the side-port. The V of the main fluid pathway within the extension set was measured to be 1.0 mL and 3.9 mL using the downstream and upstream side-ports, respectively. An 18-gauge angiocatheter was connected to the patient end of the extension tubing. Samples were collected from the angiocatheter outflow every 60 s using a fraction collector.
The mass flow rate of methylene blue egress from the angiocatheter was spectrophotometrically quantified (15). On each day of experimentation, a fresh set of calibration standards was made from serial dilutions of the original methylene blue stock. Samples less than 1 mL were diluted to 1 mL using saline. Samples exceeding the spectrophotometer’s linear range were diluted in saline. Data represent at least two similar or identical separate trials.
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Results |
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Transiently Stopping the Carrier
In clinical settings, carrier flows may become transiently interrupted. The models predict transient under- and overdosing resulting from carrier cessation and resumption. These predictions were tested experimentally using the extension set’s downstream (V = 1 mL; Fig. 3A) and upstream (V = 3.9 mL; Fig. 3B) side-ports. Starting at steady-state (Qd = 3 and Qc = 10 mL/h), carrier flow was simulated to stop for 15 min. Both models predict an immediate, abrupt decrease in drug delivery when carrier flow stops. Whereas the Plug-Flow model predicts that drug delivery remains low until carrier flow resumes (or V turns over to the stock concentration [see below]), the Well-Mixed model predicts a slow increase in drug delivery. On resumption of the carrier, the Plug-Flow model predicts a delayed drug bolus, which appears later for larger Vs. In contrast, the Well-Mixed model predicts an immediate overdose on carrier resumption. The experimental data show features of both models; drug delivery decreases after carrier cessation, and the V fills with the concentrated drug, eventually causing drug delivery to slowly increase. Carrier resumption generates a bolus, which is less than predicted by the Plug-Flow model but more than predicted by the Well-Mixed model. With a larger V, the drug delivery profile’s experimental peak is lower and more distributed, likely reflecting increased time for dispersion and the delay before carrier resumption (Fig. 3B).
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When the carrier transiently ceases, the stock drug may partially or totally fill the V. Plug-flow simulations compare conditions where the stock drug rapidly replaces the entire V during the period with no carrier flow (V = 1 mL, Qd = 30 mL/h, and Qc = 10 mL/h) to conditions where the V is only partially replaced when the carrier is off (V = 10 mL, Qd = 30 mL/h, and Qc = 10 mL/h). With small V/Qd, the entire V is replaced by the stock drug, and quasi–steady state is established before the carrier resumes. Resuming the carrier results in an immediate bolus of drug (Fig. 3C). With large V/Qd, carrier resumption initially returns drug delivery to the previous level (Fig. 3D). Minutes later, concentrated drug arrives at the patient resulting in a delayed bolus. Thus, a delayed bolus can occur with resumption of carrier flow with large Vs or slow drug flow rates.
Impact of Dead Volume and Carrier Flow Rate
Drug infusions may be connected to carrier flows at points close to, or far from, the patient. The drug delivery profiles for drug infusion initiation into a steady carrier flow, using two different Vs, were both simulated and tested (V = 1 and 3.9 mL; Fig. 4A). Both model predictions and experimental data show that the delay in drug delivery increases with V. Modeling also suggests that the delay in drug delivery decreases with faster carrier flow rates (Qc = 10 and 100 mL/h; Fig. 4).
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Changes in Carrier Rate Transiently After Drug Delivery
Simulations predict that simple step changes in carrier flow rates, with constant drug infusion rates (Qd = 3 mL/h) produce transient drug delivery changes. Drug delivery temporarily increases as carrier flow jumps from 10 to 40, 10 to 160, or 10 to 640 mL/h (Fig. 5A). The resulting increase is largest, but of shortest duration, for the most rapid final carrier rate. Steady state resumes when V has completely turned over to the more dilute concentration. Conversely, reducing the carrier flow rate transiently from 500 to 10, 500 to 40, or 500 to 160 mL/h decreases drug delivery (Fig. 5B). The slower the final carrier flow rate, the lower the transient drug delivery rate and the slower the restoration of steady state.
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Architecture of Connectors Impacts Drug Delivery
Commercially available IV infusion sets use a variety of designs for access ports and connectors. To begin to test the potential impact of alternative means of connecting drug infusions to carriers, drug delivery profiles were compared experimentally using two different connection methods (Fig. 6). A blunt needle passed through a side-port and extended into the carrier stream was compared to a locking blunt connector (LBC), which deposits drugs near the side-port’s blind end (V = 1 mL, Qd = 3 mL/h, and Qc = 10 mL/h). Onset of drug delivery is faster after initiation with the needle through side-port connection. Inspection of the LBC connection reveals that the side-port’s blind end must fill with the drug before it enters the carrier stream. Prepriming the side-port by previous drug infusion, and then stopping drug flow for 45 min while carrier flow continues, clears V of drug, but residual drug amounts remain in the side-port. The data show reduced response times to drug resumption with a primed LBC connection so that the delivery profile resembles that of the needle-through-side-port configuration.
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Discussion |
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Modeling
Inspection of small boluses of visible drugs, such as propofol or indigo carmine, within IV tubing suggested that a drug travels as a plug, with dispersion caused by diffusive and shear forces (16). Longer transit times through V presumably increase drug dispersion via diffusion and layering (2,16). Because the physical forces that govern dispersion are complex, we modeled drug movement under two extreme conditions. The Plug-Flow model assumes no dispersion at all within the V. Any step change in concentration at the point where the carrier and drug flows meet propagates according to the total flow rate, and therefore, the V turns over to a new steady state in one time constant (V/[Qc + Qd]). At the other extreme, the Well-Mixed model assumes complete dispersion and homogenous concentration within V. In this model, drug concentration changes exponentially (Equation 3), and the V turns over to a new steady-state concentration in approximately three time constants.
In reality, there is always some dispersion of drug about the moving interface, and therefore, our empiric data are bounded by, and show features of, both models. When drug infusion is initiated, there is a delay before the patient receives any drug, as predicted by the Plug-Flow model (Fig. 2). The data show a smooth transition to steady state, as predicted by the Well-Mixed model. Both models predict that temporary carrier interruption reduces drug delivery (Fig. 3). Whereas the Plug-Flow model predicts sustained decreased delivery until the carrier resumes, the Well-Mixed model predicts slow exponential increases in drug delivery. Our empiric data show initially reduced delivery that slowly increases over time. The peak delivery rate that the patient receives after carrier resumption is over-predicted by the Plug-Flow model and under-predicted by the Well-Mixed model. Whereas the Plug-Flow model describes the delayed bolus seen with resuming a stalled carrier, the Well-Mixed model, by definition, cannot. Any entry into the V by stock drug will be evenly distributed and sensed immediately at the patient end. Thus, each model captures different unique features of the empiric data. The most important prediction of both models is the delay to steady state after any change in infusion settings; however, there is only a threefold difference in predicted delay between these extreme models.
Carrier Cessation and Resumption
Carrier flows inadvertently cease, sometimes because fluid bags empty unnoticed, as might happen in transport or during an acute intraoperative event. This initially decreases drug delivery as the dilute drug in the V enters the patient at a much slower rate while the carrier is off (Fig. 3). The V eventually fills with the concentrated stock drug, resulting in an overdose upon carrier resumption. Practical constraints may dictate larger dead volumes (e.g., connecting an infusion at an upstream side-port when a downstream side-port is inaccessible). Therefore, simulations were performed for an infusion attached to the extension tubing side-port closest to the patient and farthest from the patient. With the larger V, both the Plug-Flow model and the experimental data suggest a significant delay in the bolus of drug after the carrier resumes (Fig. 3B). While the carrier is off, the concentrated drug fills the upstream end of the V only. When carrier flow resumes, the dilute drug near the patient is delivered forming a quasi–steady-state, with the concentrated bolus to follow. With large Vs, the concentrated drug occupies a relatively small upstream fraction of the volume, and the delivered bolus on resumption of the carrier is significantly delayed.
Should the V be sufficiently small or the drug flow rate sufficiently large to completely convert the V to concentrated drug while the carrier is off, the dynamics of drug delivery will be very different (Fig. 3C). With complete turnover of the V to concentrated drug after one time constant, quasi–steady-state drug infusion is restored. When the carrier ultimately resumes, there will be an immediate bolus of concentrated stock drug. If the V was much larger, only the upstream end of the V would contain the concentrated stock drug, and resumption of the carrier would transiently return drug delivery to steady state, as the dilute drug downstream entered first (Fig. 3D). Moments later, the concentrated stock drug enters the patient, resulting in an overdose. These findings demonstrate that drug delivery after cessation and resumption of the carrier can be complex.
Impact of Dead Volume and Carrier Flow Rate
These analyses demonstrate the importance of the infusion system configuration in determining drug delivery delays after initiating an infusion. By extrapolation, the time to achieve planned changes in drug dosing depends on the interplay of flow rates and V. Connecting an infusion as close to the patient as possible optimizes the response time of drug delivery to planned changes in drug dosing (Fig. 4). Minimizing V limits the temptation and need to run carriers at faster flow rates. Indeed, the response time is reduced for higher carrier flow rates (Fig. 4A and B). However, the need for faster carrier flow to reduce response time to planned dose changes can result in deleterious volume overload for some patients.
Changing Carrier Rate Transiently Alters Drug Delivery
To hasten response to vasoactive drugs in the OR, it is tempting to alter carrier flow rates in anticipation of surgical events, such as bleeding or placement of an aortic cross-clamp. When transporting patients between the ICU and the OR, carriers are often adjusted to meet the needs of the new environment. Strikingly, simple changes in carrier flows transiently alter drug delivery, even with a stable drug infusion rate (Fig. 5A). Our models predict a transient increase in drug delivery simply by increasing the carrier rate. Steady state at the faster carrier flow resumes when more of the dilute drug fills the V. In contrast, slowing a rapid carrier flow reduces drug delivery because the V drug flushes out less rapidly. Differences in the duration of these perturbations are expected as the total final flow determines the time until the V has turned over. Thus, large changes to carrier rates can result in deleterious overdoses, or near complete withdrawal, of the infused drug.
As an example of potential dangers in changing stable carrier flow rates, a nitroglycerin infusion (100 µg/min, 1-mg/mL stock, carrier flow 10 mL/h, and V of 5 mL) would have 1.9 mg of nitroglycerin in the V at any time. If the carrier rate suddenly jumped to 500 mL/h, as might happen when an ICU patient is brought to the OR, this large amount of nitroglycerin would be delivered over 36–108 seconds (1 to 3 time constants). After returning from the OR, reducing the carrier flow in the ICU to 10 mL/h would result in delivery of 3.2 µg/min of nitroglycerin for 18.75 minutes and steady-state may not be fully reestablished for 56 minutes.
Architecture of Connectors Impacts Drug Delivery
Because each component of an infusion system can contribute to V (2–4), we compared the onset of drug delivery after drug infusion initiation with two common methods of connecting an infusion to a carrier (Fig. 6). Note that the side-ports of extension sets have small dead volumes of their own (approximately 0.1 mL). Drugs must fill this volume before they can enter the carrier stream if the LBC or a similar device is used. Observations with visible drugs suggested that when an infusion using an LBC is stopped, the side-port remains filled with drug. Thus, the next time the drug infusion is activated, the port will already have been primed, thereby reducing the delay time for entry of the drug into the carrier flow and hastening drug delivery. Although many clinicians prime the infusion pump tubing, it is impractical to prime the side-port of the main carrier catheter without delivering the drug. These studies illustrate that the delay in drug initiation is longer the first time a drug infusion is used. In contrast, a needle passed through the diaphragm of the side-port deposits the drug directly into the carrier stream, bypassing the additional volume of the side-port. The data show that the response to drug infusion initiation in this arrangement is virtually identical to a preprimed infusion with a LBC. These findings suggest that subtleties in the design and use history of the connections can impact the dynamics of drug infusion and warrant further investigation.
Implications and Applications
Both mathematical and experimental simulations have been used to illustrate the complexity, yet predictibility, of drug delivery by infusion and lead to the following recommendations:
Although the concepts delineated in this study may be intuitive, precise understanding of the specifics of each patient’s infusion system and the dynamics of drug delivery that result from any changes is critical for safe patient care in ICUs, ORs, and transport between these complex environments.
The authors wish to thank Matthew Peterfreund for help in the laboratory and Dr. Nathaniel Sims, Dr. Harry Demonaco, Katherine Brush RN, and Ellen Kinnealey RN for their insights into drug infusion practices and policies at our institution.
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Footnotes |
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This article has been cited by other articles:
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  M. A. Lovich, M. E. Kinnealley, N. M. Sims, and R. A. Peterfreund The delivery of drugs to patients by continuous intravenous infusion: modeling predicts potential dose fluctuations depending on flow rates and infusion system dead volume. Anesth. Analg., April 1, 2006; 102(4): 1147 - 1153. [Abstract] [Full Text] [PDF]
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