15.2 Loading & Maintenance Dosing

The Maintenance Dose Rate

At steady state, the rate of drug administration equals the rate of elimination. The rate of elimination is CL × Css, so the required input rate is:

Maintenance dose rate = CL × target Css / F

where F is bioavailability (F = 1 for intravenous dosing). Worked example (theophylline): a 70 kg non-smoking adult has a theophylline clearance of about 0.04 L/h/kg, i.e. CL = 2.8 L/h. Target steady-state concentration = 15 mg/L and an oral sustained-release product has F ≈ 1. The required rate is 2.8 × 15 / 1 = 42 mg/h, which is 42 × 24 = 1008 mg/day, rounded to a practical regimen such as 400–600 mg twice daily of a suitable product. Notice what did not enter the calculation: the volume of distribution. Maintenance dosing replaces what the organs remove, so it is governed by clearance alone.

The Loading Dose

When the target concentration is needed now rather than in 4–5 half-lives, a loading dose fills the volume of distribution up front:

Loading dose = Vd × target Cp / F

Worked example (digoxin): digoxin's Vd is roughly 7 L/kg, so in a 70 kg patient Vd ≈ 490 L, rounded to 500 L. For a target plasma concentration of 1.5 µg/L (1.5 ng/mL) with oral tablets of F ≈ 0.7: loading dose = 500 × 1.5 / 0.7 ≈ 1071 µg, practically about 1000 µg (1 mg), traditionally given in divided portions — for example 500 µg, then 250 µg after 6 hours, then a further 250 µg — so response and tolerability can be assessed between aliquots. Clearance does not appear in this formula: the loading dose answers only 'how much drug is needed to occupy the volume at the target concentration?'.

Loading vs Maintenance — the Key Contrast

A patient with renal failure generally needs the same loading dose (Vd is unchanged) but a smaller maintenance dose (clearance is reduced) — a favourite exam distinction.

Dosing Interval, Accumulation and Peak–Trough Behaviour

With intermittent dosing, concentrations oscillate between a peak (Css,max, shortly after each dose) and a trough (Css,min, just before the next). For a first-order drug given every τ hours:

• Css,max = (F × Dose / Vd) / (1 − e^(−kτ))
• Css,min = Css,max × e^(−kτ)

The term 1 / (1 − e^(−kτ)) is the accumulation ratio — how much higher steady-state peaks sit above the concentration produced by the first dose. Worked example: a drug with Vd = 20 L and k = 0.08 h⁻¹ (t½ ≈ 8.7 h) is given as 300 mg intravenously every 12 hours. First, e^(−kτ) = e^(−0.96) ≈ 0.383. Then Css,max = (300/20) / (1 − 0.383) = 15 / 0.617 ≈ 24.3 mg/L, and Css,min = 24.3 × 0.383 ≈ 9.3 mg/L. The accumulation ratio is 1 / 0.617 ≈ 1.62. Choosing τ about equal to the half-life gives roughly a two-fold peak-to-trough swing, which suits most drugs; drugs needing flat concentrations are dosed at intervals shorter than the half-life (or by infusion), while once-daily aminoglycoside dosing deliberately exploits a long interval relative to the half-life to gain a high peak and a low, low-toxicity trough.

Intravenous Infusion Kinetics

For a constant intravenous infusion at rate R0:

Css = R0 / CL

The concentration rises along a curve that is the mirror image of elimination: 50% of steady state after one half-life, 75% after two, about 94% after four and 97% after five. Two exam points follow. First, the infusion rate sets the height of Css but not the time to reach it — doubling R0 doubles Css yet steady state still takes 4–5 half-lives. Second, the only way to reach the target immediately is a loading bolus (Vd × Cp) given alongside the infusion. Worked example: R0 = 40 mg/h with CL = 4 L/h gives Css = 40 / 4 = 10 mg/L; if t½ is 7 hours, that level is not approached until roughly 28–35 hours without a bolus.

Dose Adjustment in Renal Impairment

For a predominantly renally cleared drug, clearance falls roughly in proportion to creatinine clearance, so the maintenance regimen is scaled the same way. Two equivalent strategies exist:

1. Proportional dose reduction — keep the interval, shrink each dose (e.g. 500 mg q12h becomes 250 mg q12h when clearance halves). This keeps the peak–trough pattern similar.
2. Interval extension — keep the dose, stretch the interval (500 mg q12h becomes 500 mg q24h). This preserves full peaks and is preferred for concentration-dependent killers such as aminoglycosides, where efficacy tracks the peak.

Loading doses are usually unchanged. Finally, once a patient is on therapy, a measured level lets you re-compute empirically. For a linear drug at steady state, dose and concentration are proportional: if 500 mg/day produced a measured Css of 8 mg/L and the target is 12 mg/L, the new rate is 500 × 12/8 = 750 mg/day, with a repeat level after a further 4–5 half-lives to confirm. Never apply this proportional trick to phenytoin or other nonlinear drugs — there, small increments and patience are the rule.