Multiple Dose Trough Concentration

\[C_{min,ss}=\frac{D\,e^{-k\tau}}{V_d\left(1-e^{-k\tau}\right)}\]

Variables

Cminsssteady-state trough 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 Trough Concentration estimates the minimum plasma concentration present immediately before the next scheduled dose at steady state.

When to use it

Use this formula when evaluating whether drug concentrations remain above therapeutic thresholds and when designing dosing intervals.

Example

Data:

D = 500 mg

Vd = 40 L

k = 0.1 1/h

tau = 12 h

Formula:

Cminss = ((D/Vd) × ℮^(-k×tau))/(1 − ℮^(-k×tau))

Substitution:

Cminss = ((500/40) × ℮^(-0.1×12))/(1 − ℮^(-0.1×12))

Result:

Cminss = 5.41 mg/L

Applications

- Therapeutic drug monitoring

- Antibiotic therapy

- Antiepileptic medications

- Pharmacokinetic studies

- Dose interval optimization

Note

This formula is derived from a one-compartment pharmacokinetic model with first-order elimination and instantaneous distribution. Real-world drug concentrations may differ due to absorption kinetics, multicompartment distribution, nonlinear elimination, and patient-specific factors. The result should be interpreted as an approximation.