Maintenance Infusion Rate

By definition, the rate at which drug exits the body is systemic clearance, Cl_S , times the plasma concentration. To maintain a given target concentration, C_T , drug must be delivered at the same rate that drug is exiting the body. Thus,

Maintenance infusion rate = C_T × Cl_S (13)

For drugs with multicompartmental pharmacokinetics, which includes all the intravenous drugs used in anesthetic practice, drug is distributed into peripheral tissues as well as cleared from the body. The rate of distribution into tissues changes over time as tissue levels equilibrate with plasma levels. Equation 13 is correct only after the peripheral tissues have fully equilibrated with plasma, which requires many hours. At all other times, this maintenance infusion rate underestimates the infusion rate to maintain a target concentration.

In some situations, this simple maintenance rate calculation may be acceptable. For example, if an infusion at this rate is used along with a bolus dose based on Vd_pe and the drug has a long delay between the bolus and peak effect, much of the distribution of drug into tissues may have occurred by the time that the effect-site concentration reaches the target concentration. In this case, the maintenance infusion rate calculated as clearance times target concentration may be fairly accurate because Vd_pe is sufficiently higher than V₁ to account for the distribution of drug into peripheral tissues. Unfortunately, most drugs used in anesthesia have sufficiently rapid equilibration between plasma and the effect site that Vd_pe does not adequately encompass the distribution process, thus making this approach unsuitable.

Another example of calculating infusion rates for drugs with multicompartmental pharmacokinetics is the two-step approach proposed by Wagner.^[80] In this method, two infusions, Q₁ and Q₂ , are administered in sequence. The loading infusion, Q₁ , is selected on the basis of convenience and the degree of overshoot in plasma concentration that will be clinically acceptable. The second infusion, Q₂ , is calculated as C_T × Cl_S , exactly as noted earlier. The Wagner two-step approach does not consider the time course of drug effect and thus is probably not appropriate for most anesthetic drugs.

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Having offered to the reader two approaches that do not work very well, we now turn to approaches that are mathematically and clinically sound. Because the net flow of drug into peripheral tissues decreases over time, the infusion rate required to maintain any desired concentration must also decrease over time. If the initial bolus has been based on Vd_pe , no infusion need be administered until the effect-site concentrations peak. After the peak in effect-site concentration, the (nearly) correct equation to maintain the desired concentration is

Maintenance infusion rate = C_T × V₁ × (k₁₀ + k₁₂ e^{−k₂₁ t} + k₁₃ e^{−k₃₁ t} ) (14)

This equation indicates that a high infusion rate is initially required to maintain C_T . Over time, the infusion rate gradually decreases (see Fig. 12-4 ). At equilibrium (t = ∞), the infusion rate decreases to C_T V₁ k₁₀ , which is the same as C_T Cl_S . Few anesthesiologists would choose to mentally solve such an equation during administration of an

TABLE 12-3 -- Plasma drug concentration ranges

		Stimulus
Drug *	Skin Incision	Minor Surgery	Major Surgery	Spontaneous Ventilation	Awakening	Analgesia or Sedation
Alfentanil (ng/mL)	200–300	250–450	100–300	<200–250	—	50–100
Fentanyl (ng/mL)	3–6	4–8	2–5	<1–2	—	1–2
Sufentanil (ng/mL)	1–3	2–5	1–3	<0.2	—	0.02–0.2
Remifentanil (ng/mL)	4–8	4–8	2–4	<1–3	—	1–2
Propofol (µg/mL)	2–6	2.5–7.5	2–6	—	0.8–1.8	1.0–3.0
Methohexital (µg/mL)	5–10	5–15	5–10	—	1–3	2–5
Thiopental (µg/mL)	7.5–12.5 (with N2 O) 35–45 (without N2 O)	10–20	10–20	—	4–8	7.5–15.0
Etomidate (ng/mL)	400–600	500–1000	300–600	—	200–350	100–300
Midazolam (ng/mL)	—	50–250 (combined with an opioid)	50–250 (combined with an opioid)	—	150–200 (reduced to 20–70 in the presence of an opioid)	40–100
Ketamine (µg/mL)	—	—	1–2	—	—	0.1–1

*Drug levels are when combined with 65% to 70% nitrous oxide (N₂ O) unless otherwise stated. Effective plasma concentrations may differ markedly, depending on premedication and intraoperative drug combinations.

Figure 12-15 is a nomogram in which Equation 14 has been solved, and it shows the infusion rates over time necessary to maintain any desired concentration of fentanyl, alfentanil, sufentanil, and propofol. This nomogram is complex, so we will review it in detail. The y axis represents the target concentration C_T . The x axis is the time since the beginning of the anesthetic (i.e., since the initial bolus). The suggested target initial concentrations (shown in red) are based on the work of Vuyk and colleagues^[40] with propofol and alfentanil (see Fig. 12-8 ) and are scaled to fentanyl and sufentanil based on their relative potencies.^[78] The intersections of the target concentration line and the diagonal lines indicate the infusion rate appropriate at each point in time. For example, to maintain a fentanyl concentration of 1.5 ng/mL, the appropriate rates are 4.5 µg/kg/hr at 15 minutes, 3.6 µg/kg/hr at 30 minutes, 2.7 µg/kg/hr at 60 minutes, 2.1 µg/kg/hr at 120 minutes, and 1.5 µg/kg/hr at 180 minutes. Of course, you can select target concentrations and different times of rate adjustment, depending on clinical circumstances

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Figure 12-14 Pharmacokinetic simulation demonstrating the limitations of infusion regimens based on simple pharmacokinetic parameters, with fentanyl used as an example. These infusion schemes were designed to achieve a plasma fentanyl concentration of 3 ng/mL. The upper curve shows that a regimen using a loading dose based on the volume of distribution followed by a constant infusion based on clearance results in a transient period of extremely high plasma concentrations. If the same maintenance infusion is given but the loading dose is based on the volume of the central compartment, distribution of drug to the peripheral compartments causes the plasma concentration to fall below the desired level until the compartments reach steady-state concentrations, as shown in the lower curve. Cp, plasma drug concentration.

Another recent approach to manually determining infusion rates for maintenance of anesthesia to a desired target concentration is through the use of concepts used with a slide rule.^[81] Figure 12-16 illustrates such a slide rule for propofol. As described by Bruhn and coauthors, "The bolus dose required to reach a given target plasma concentration is the product of the (weight-related) distribution volume

TABLE 12-4 -- Volume of distribution at the time of peak effect

Drug	V1 (L)	Vdpe (L)
Fentanyl	12.7	75
Alfentanil	2.19	5.9
Sufentanil	17.8	89
Remifentanil	5.0	17
Propofol	6.7	37
Thiopental	5.6	14.6
Midazolam	3.4	31
V1 , volume of the central compartment; Vdpe , apparent volume of distribution at the time of peak effect.

Figure 12-15 Nomogram for calculating maintenance infusion rates to maintain a stable concentration of fentanyl, alfentanil, sufentanil, or propofol. The y axis is the desired concentration. The x axis is the time relative to the initial bolus. The diagonal lines show the infusion rates at different times required to maintain the desired concentration selected on the y axis.

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Figure 12-16 Slide rule for calculating the maintenance propofol infusion rate from the patient's weight, the desired target concentration, and the elapsed time. (Adapted from Bruhn J, Bouillon TW, Ropcke H, Hoeft A: A manual slide rule for target-controlled infusion of propofol: Development and evaluation. Anesth Analg 96:142–147, 2003.)