Steady-State Concentration and the Therapeutic Window
The foundation of rational pharmacotherapy is achieving a steady-state concentration ($C_{ss}$). This is a state of physiological equilibrium where the rate of drug input into the systemic circulation exactly equals the rate of its elimination. The simplest and most controllable way to achieve this equilibrium is continuous intravenous infusion.
Any drug must function strictly within the therapeutic window (therapeutic range). This is the concentration interval that guarantees a therapeutic effect while remaining safe for the patient.
- Lower limit ($C_{ss}^{min}$): minimum effective concentration. If levels drop below this, pharmacological action is lost.
- Upper limit ($C_{ss}^{max}$): maximum safe concentration. Exceeding this threshold leads to toxic effects.
The physician's goal is to select an administration rate such that the average therapeutic concentration remains strictly within this corridor.
Drug Accumulation Dynamics
How quickly will a drug accumulate in the body and reach a plateau? This process depends exclusively on a single pharmacokinetic parameter: the half-life ($t_{1/2}$).$.
There is a clear rule for drug accumulation in blood plasma (as a percentage of the target $C_{ss}$):
- After 1 $t_{1/2}$, the blood contains 50% of the desired level.
- After 2 $t_{1/2}$, 75% is reached.
- After 3.3 $t_{1/2}$, the level reaches 90% (a clinically significant concentration).
- Full stabilization and 100% equilibrium occur after 4–5 half-lives.
Two-Stage Dosing Strategy
If a drug has a long half-life, waiting 4–5 cycles to achieve a therapeutic effect is too slow. In situations requiring an immediate result, a two-stage regimen is used:
- Loading dose ($D_H$): administered first in a large amount. Its purpose is to instantly fill the volume of distribution (volume of distribution, $V_d$) and immediately bring the concentration to the $C_{ss}$ level, bypassing the slow accumulation phase. It is calculated using the formula: $D_H = V_d \cdot C_{ss}$.
- Maintenance dose ($D_{pod}$): administered subsequently (via infusion or intermittent doses) to compensate for the natural elimination of the drug.
Intermittent Administration and Maintenance Dose Calculation
In clinical practice, medications are often prescribed not as continuous infusions, but as discrete doses at regular intervals (e.g., oral tablets). With this intermittent administration, the drug level in the blood is not constant, but fluctuates (oscillates) around the average $C_{ss}$.
On a pharmacokinetic graph, this looks like a "sawtooth" curve:
- Ascent: drug absorption occurs after taking a dose.
- Descent: elimination occurs in the interval between doses (denoted by the parameter $\tau$).
The golden rule is that these fluctuations must not breach the upper and lower limits of the therapeutic range.
The basic formula for calculating the maintenance dose is: $D_{pod} = \frac{Cl_t \cdot C_{ss} \cdot T}{F}$
If the drug is administered orally (per os), bioavailability (bioavailability, $F$) must be included in the formula—this is the fraction of the drug that reaches systemic circulation unchanged, as a portion is lost during first-pass hepatic metabolism.
An alternative calculation method uses the half-life: $D_{pod} = \frac{C_{ss} \cdot V_d \cdot T}{1.44 \cdot F \cdot t_{1/2}}$, where $1.44$ is a coefficient equal to $1 / \ln 2$.