Multiple Dose Peak Concentration

\[C_{max,ss}=\frac{\frac{D}{V_d}}{1-e^{-k\tau}}\]

Variables

Cmaxsssteady-state peak concentration (mg/L)

Ddose administered (mg)

Vdvolume of distribution (L)

kelimination rate constant (1/h)

taudosing interval (h)

Description

What is this formula?

The Multiple Dose Peak Concentration estimates the maximum plasma concentration reached at steady state after repeated dosing. It accounts for drug accumulation caused by incomplete elimination between doses.

When to use it

Use this formula when designing repeated-dose regimens, evaluating drug accumulation, and estimating peak concentrations during chronic therapy.

Example

Data:

D = 500 mg

Vd = 40 L

k = 0.1 1/h

tau = 12 h

Formula:

Cmaxss = (D/Vd)/(1 − ℮^(-k×tau))

Substitution:

Cmaxss = (500/40)/(1 − ℮^(-0.1×12))

Result:

Cmaxss = 17.97 mg/L

Applications

- Therapeutic drug monitoring

- Antibiotic dosing

- Antiepileptic therapy

- Clinical pharmacokinetics

- Dose regimen design

Note

This formula is derived from a one-compartment pharmacokinetic model with first-order elimination and instantaneous distribution. Real drugs may exhibit multicompartment behavior, delayed absorption, nonlinear kinetics, or variable bioavailability. The result should be interpreted as a model-based estimate.