DESIGNING DOSING REGIMENS

Bolus Dose Calculations

The definition of concentration is amount divided by volume. We can rearrange the definition of concentration to find the amount of drug required to produce any desired concentration for a known volume:

Amount = C_T × Volume (10)

where C_T is the desired or "target" concentration. Many introductory pharmacokinetic texts suggest using this formula to calculate the loading bolus required to achieve a given concentration. The problem with applying this concept to anesthetic drugs is that there are several volumes: V₁ (central compartment), V₂ and V₃ (the peripheral compartments), and Vd_SS , the sum of the individual volumes. V₁ is usually much smaller than Vd_SS , and thus it is tempting to say that the loading dose should be something between C_T × V₁ and C_T × Vd_SS .

Figure 12-13 Interaction at a 50% drug effect between propofol, midazolam, and alfentanil. Downward deflection of the surface represents synergy, in units of fractional reduction in C₅₀ . The three edges represent relative amounts of propofol to midazolam (theta_Mid-Prop ), alfentanil to midazolam (theta_Mid-Alf ), and alfentanil to propofol (theta_Alf-Prop ). The surface between the edges represents the relative synergy of all three drugs taken together. (From Minto CF, Schnider TW, Short TG, et al: Response surface model for anesthetic drug interactions. Anesthesiology 92:1603–1616, 2000.)

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Consider the dose of fentanyl required to attenuate the hemodynamic response to intubation when combined with thiopental. The C₅₀ for fentanyl, when combined with thiopental for intubation, is approximately 3 ng/mL. The V₁ and Vd_SS for fentanyl are 13 and 360 L, respectively. The aforementioned equations can thus be interpreted as suggesting that an appropriate dose of fentanyl to attenuate the hemodynamic response is between 39 µg (3 ng/mL × 13 L) and 1080 µg (3 ng/mL × 360 L). A fentanyl bolus of 39 µg achieves the desired concentration in plasma for an initial instant, but plasma levels almost instantly decrease below the desired target. Levels at the effect site will never be close to the desired target concentration of 3 ng/mL. A fentanyl bolus of 1080 µg, not surprisingly, produces an enormous overshoot in plasma levels that persists for hours ( Fig. 12-14 ). Additionally, it is absurd to use equations to calculate the fentanyl dose if the resulting recommendation is "pick a dose between 39 and 1080 µg."

The usual dosing guidelines for a bolus dose, presented earlier, are designed to produce a specific plasma concentration. Because plasma is not the site of drug effect, it is illogical to base calculation of the initial bolus on a desired plasma concentration. As pointed out previously, by knowing the k_e0 of an intravenous anesthetic, we can design a dosing regimen that yields the desired concentration at the site of drug effect. If we do not want to overdose the patient, we should select the bolus that produces the desired peak concentration at the effect site.

The decline in plasma concentration between the initial concentration after the bolus (amount/V₁ ) and the concentration at the time of peak effect can be thought of as a dilution of the bolus into a larger volume than the volume of the central compartment. This approach introduces the concept of Vd_pe , the apparent volume of distribution at the time of peak effect,^{[29] [78]} or pseudoequilibration between plasma and the site of drug effect.^[79] The size of this volume can be readily calculated from the observation that the plasma and effect-site concentrations are the same at the time of peak effect:





where C_pe is the plasma concentration at the time of peak effect.

Let us assume that our clinical goal is to select the dose required to produce a certain drug effect without producing an overdose. We can rearrange Equation 11 by substituting C_T , the target concentration (which is the same in plasma and the effect site at the moment of peak effect), for C_pe to calculate the size of the initial bolus:

Loading dose = C_T × Vd_pe (12)

The Vd_pe for fentanyl is 75 L. Producing a peak fentanyl effect-site concentration of 3.0 ng/mL requires 225 µg, which achieves a peak effect in 3.6 minutes. This dosing guideline is much more reasonable than the previous recommendation of picking a dose between 39 and 1080 µg. Table 12-4 lists V₁ and Vd_pe for fentanyl, alfentanil, sufentanil, remifentanil, propofol, thiopental, and midazolam. Table 12-1 lists the k_e0 , t½ k_e0 , and time to peak effect of the commonly used intravenous anesthetics.