Phenylephrine is frequently used in the OR or the ICU and is chosen as a representative infused vasoactive drug. The principals should apply, however, to any drug delivered by continuous IV infusion, including vasopressors such as epinephrine or norepinephrine, vasodilators such as nitroglycerine or sodium nitroprusside, analgesics such as remifentanil or fentanyl, or sedative-hypnotic drugs including propofol.
The concentration of a drug in the dead volume of an infusion system at steady-state depends on the flow rate of the carrier fluid diluting the infused drug. For a given planned drug infusion rate, the dead volume drug concentration decreases as the carrier rate increases (Equation 2). At slow carrier rates (I/Cd > Qc), the stock concentration of drug is only slightly diluted. At steady-state there is a predictable mass of drug in the dead volume (Fig. 1A). For example, at a planned phenylephrine infusion dose of 100 μg/min, a dead volume of 2 mL, a stock concentration of 1.2 mg/mL, and a carrier rate of 10 mL/h, there are 800 μg of phenylephrine contained in the dead volume reservoir at steady-state. Alternatively, if the carrier flow rate was 100 or 500 mL/h, the drug stored in the dead volume would be 114 or 24 μg, respectively. Conversely, if the infusion ran without a carrier, as is the practice in some ICUs, the dead volume would store 2.4 mg of phenylephrine regardless of the infusion rate (Qc = 0). These drug masses would be potentially available as boluses should the carrier flow rate abruptly and dramatically increase or if a flush of crystalloid or other drug is given upstream through the infusion tubing. In general, the mass of drug stored in the dead volume increases with drug infusion dose rate, the stock concentration of drug (Fig. 1B), and the size of the dead volume (Fig. 1C).
The impact of an alternative possibility, the abrupt cessation of a carrier flow, on drug delivery was also investigated. The total flow of fluid reaching the patient's vasculature is the sum of the carrier and infused drug flows. As carrier flow abruptly ceases, fluid enters the patient only at the rate of the flow of infused drug. However, the concentration of drug will initially be small, reflecting the earlier dilution of drug by the carrier fluid. Consequently, the patient will initially receive a reduced drug dose for some time. For example, as predicted for phenylephrine (Cd = 1.2 mg/mL; I = 100 μg/min; Qc = 10 mL/h) the steady-state concentration of drug at the most downstream end of the infusion set will be 0.4 mg/mL. When the carrier abruptly ceases the total flow rate decreases from 15 to 5 mL/h, resulting in an initial drug infusion rate of 33 μg/min (Fig. 2). The slower the carrier flow before cessation, the closer the initial resulting infusion remains to the desired dose. At rapid planned drug infusion rates, the impact of suddenly stopping the carrier is diminished. In both of these instances, the drug infusion rate (Qd) is rapid relative to the carrier rate (Qc), and therefore, the initial dilution from the carrier is minimized. However, with rapid carrier flow before cessation, there is an initial large reduction in drug delivery. Note that these effects are independent of the dead volume (Equation 4) but depend on the relative rates of drug and initial carrier flow.
In the event that the carrier flow is not restored and drug infusion continues, both the plug-flow and the well-mixed models predict that the planned dose of drug will eventually be delivered, albeit with different kinetics (Fig. 3). The plug-flow model predicts an abrupt restoration to steady-state in one time constant, whereas the well-mixed model predicts a gradual return in approximately three time constants. The delay until the planned delivery is restored depends on the rate of drug infusion, the stock-drug concentration, and the size of the dead volume (Equation 5 with Qc = 0; Fig. 4). In the case of phenylephrine with a planned delivery of 150 μg/min and a dead volume of 2 mL (Cd = 1.2 mg/mL), the plug-flow model predicts a delay of 16 min from cessation of the carrier until restoration of steady-state. Drug delivery remains under-dosed until the ‘plug‘ of infused medication traverses the dead volume in one time constant. The well-mixed model predicts a gradual return to steady-state in approximately three time constants or 48 min. Should the absence of carrier flow be recognized and then become abruptly restored, the dead volume will contain stock drug, which may enter the patient as an undesired and potentially delayed bolus (15). The magnitude of the bolus will depend on the rate of infused drug flow, the size of the dead volume, the stock drug concentration, and the time elapsed without carrier flow.
The plug-flow model predicts the minimum time (one time constant) for achieving steady-state after changing either the drug infusion dose or the carrier rate (Equation 5; Fig. 5). This transition period is the time for a change in drug dilution by the carrier to propagate through the infusion system dead volume. The minimum delay will increase along with the size of the dead volume (Fig. 5A) and with the concentration of the drug in the stock solution (Fig. 5B). The delay decreases with carrier flow rate. The well-mixed model predicts a threefold longer time to achieve steady-state. The actual time to return to steady-state is between the boundaries defined by the plug-flow and well-mixed models (15).
The use of continuous medication infusions is common in the clinical environments of the OR and the ICU. This is because many medications used in these environments, such as epinephrine or nitroglycerin, have short half-lives in the circulation. Sustained therapeutic effects can only be achieved with continuous infusion. In settings where the clinical condition of a patient may fluctuate rapidly, as during surgery or even in an ICU environment, there is a significant advantage to using medications whose effects are readily titratable.
Under- or over-dosing of powerful medications can have significant consequences. A bolus dose of phenylephrine or norepinephrine, if untreated, would probably result in significant vasoconstriction and hypertension lasting for at least a few minutes. Whereas some patients may tolerate this fluctuation in hemodynamics, those with failing ventricles, aneurysms, or tenuous tissue blood flow would be at risk for catastrophic complications. Conversely, a bolus dose of nitroglycerin or nitroprusside would, if untreated, probably result in significant hypotension lasting for at least a few minutes. Some patients with certain clinical conditions, such as aortic stenosis or vasoocclusive disease of the cerebral or coronary circulations, might suffer sustained morbidity. The modeling demonstrated in this study, and validated in our previous study (15), predicts that such boluses of vasodilators and vasoconstrictors can occur under clinical conditions.
The potential for unplanned bolus delivery may be unrecognized because the magnitude of dead-volume reservoirs is unappreciated. IV infusion systems and various intravascular catheters may have significant dead volumes, ranging up to several milliliters (Table 1). As a rule of thumb, the maximum drug mass stored in the dead volume equals the dead volume multiplied by the stock-drug concentration (Equation 3 with Qc set to zero). If, for example, an infusion of phenylephrine or any other drug is mainlined into the side port of a pulmonary artery catheter introducer sheath, with a dead-space volume of 2.75 mL, a potential drug reservoir of hundreds to thousands of micrograms is established. This may be a safe and effective practice in the circumstance where one caregiver, such as an anesthesiologist or ICU nurse, is the sole provider. However, in situations where multiple caregivers are involved, or when there is hand over of a patient from one team to another (for example, OR anesthesia team to ICU team or vice versa), the potential for error and harm is significant.
The predictions illustrated in this study concerning the time course of the return to steady-state after a perturbation in carrier or infusion dose rate are based on previously derived and validated computational models of IV delivery (15). An essential variable of the plug-flow model is the time constant, τ, defined as the ratio of dead volume over total flow (Equation 5). This model fails to account for diffusion or dispersion of drugs within the infusion line, which may be significant at extremes of carrier flow. The well-mixed model better accounts for drug dispersion (15), and after any perturbation, predicts a gradual return to steady-state over three time constants. In reality, drug infusions likely behave between the extremes defined by these two models. This would effect only the absolute magnitudes of under- or over-dosing and the absolute duration of delays in drug delivery.
All of the predictions have been illustrated with phenylephrine; however, the equations are generic and can be applied to any drug given by IV infusion. The results of this study assume a fixed carrier flow rate. In reality, carriers are often gravity-driven so that flow will vary according to the height of the carrier fluid reservoir above the patient's central venous pressure and with outflow resistance produced by a poorly running IV line. This adds a level of complexity to estimating the absolute concentrations of drugs in infusion tubing and the potential size of boluses. Also, with gravity-driven carriers, there may not be a true steady-state. With placement of a BP cuff proximal to the cannulation site, the flow rates become even more unpredictable.
To minimize safety problems, clinical personnel must first recognize the complexities of drug delivery by IV infusion. When transitions of care occur between providers, explicit descriptions of the architecture of infusion systems must be thoroughly communicated. However, practical steps to reduce the likelihood of drug errors would include (a) minimizing dead volume when constructing infusion setups, (b) ensuring a fixed rate of carrier flow, (c) using pumps with minimal fluctuations in output, and (d) mechanically preventing the possibility of upstream pushes of fluid, as by removing or blocking upstream side ports or stopcocks. Reducing the stock concentrations of infused drugs would build in safety, but this comes at the price of obligate additional fluid delivery to the patient.
Medication error accounts for a significant portion of preventable patient morbidity (16). Our findings are consistent with a role for infusion errors in patient morbidity attributable to methods of medication administration. The concepts presented in this study, whereas perhaps intuitive, may not receive full appreciation by novice caregivers, when multiple caregivers are involved, or when the clinical situation becomes particularly dynamic, such as during a resuscitation event. The models allow quantitative estimates of the magnitudes of dose alterations and delays in drug delivery. Recognition may ultimately have a patient safety benefit.
We thank Ward R. Maier, MD, and Lisa Warren, MD, for their helpful reviews and comments on this manuscript. We also thank Catherine Brush, RN, for providing the dead volumes of several catheters used in our institution, shown in Table 1.
The drug delivery to the patient after the carrier flow ceases is predicted by the well-mixed model to be:
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© 2006 International Anesthesia Research Society
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