Steady-state concentration and therapeutic window
The basis of sound pharmacotherapy is achieving a steady-state concentration (steady-state concentration, $C_{ss}$). This is a state of physiological equilibrium where the rate of drug entry 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 of the drug.
Any drug must work strictly within the therapeutic window (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 the level drops below this, pharmacological action is absent.
- Upper limit ($C_{ss}^{max}$): maximum safe concentration. Exceeding this threshold leads to toxic effects.
The physician's goal is to select an infusion rate such that the mean therapeutic concentration always remains strictly within this corridor.
Dynamics of drug accumulation
How quickly will the drug accumulate in the body and reach a plateau? This process depends entirely 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.
- In 3.3 $t_{1/2}$, the level reaches 90% (this is already a clinically significant concentration).
- Full stabilization and reaching 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 volume. Its task 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 long phase of slow accumulation. Calculated by the formula: $D_H = V_d \cdot C_{ss}$.
- Maintenance dose ($D_{pod}$): prescribed subsequently (via infusion or fractionally) to compensate for the natural elimination of the drug.
Intermittent administration and maintenance dose calculation
In practice, drugs are often prescribed not as a continuous infusion, but in separate doses at regular intervals (e.g., oral tablets). With such intermittent (discrete) administration, the drug level in the blood is not constant, but fluctuates (oscillates) around the mean $C_{ss}$.
On a pharmacokinetic graph, this looks like a "sawtooth" curve:
- Rise: drug absorption occurs after taking the next dose.
- Fall: elimination takes place in the interval between doses (denoted by the parameter $\tau$).
The main rule is that these fluctuations must not breach the upper and lower limits of the therapeutic range.
To calculate the maintenance dose, the basic formula is used: $D_{pod} = \frac{Cl_t \cdot C_{ss} \cdot T}{F}$
If the drug is taken orally (per os), the formula must include bioavailability (bioavailability, $F$) — the fraction of the substance that reaches the systemic circulation unchanged, since part of it is lost during first-pass hepatic metabolism.
There is also an alternative calculation method via 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 $1 / \ln 2$.
Briefly: answers to topical questions
What factors reduce the bioavailability of a drug when administered orally?
The reduction in bioavailability of drugs when administered orally is due to a number of barriers and processes in the gastrointestinal tract and liver. The main factors include:
- Physicochemical and enzymatic factors of the GI tract — destruction of the substance by gastric hydrochloric acid, inactivation by digestive enzymes, and incomplete absorption of hydrophilic compounds.
- Metabolism in the intestinal wall — conversion of the substance inside enterocytes before entering the bloodstream.
- Active transport (efflux) — pumping of substrates out of enterocytes back into the intestinal lumen by P-glycoprotein.
- First-pass hepatic effect — presystemic elimination (metabolism by liver enzymes and excretion in bile).
- Effect of food — mechanical barrier to mucosal contact and acceleration of motility.
What formula is used to calculate total drug clearance?
Total (systemic) drug clearance is calculated using several mathematical formulas depending on the known parameters.
- Additivity formula — the sum of metabolic and excretory clearances: $Cl_{met} + Cl_{excr} = Cl_t$.
- Relationship with volume of distribution — the product of the volume of distribution and the elimination rate constant: $Cl_t = V_d \times k_{el}$.
- Relationship with concentration — the ratio of the elimination rate to the substance concentration in biofluid: $Cl_t = \frac{\text{Elimination rate}}{C}$.
Clearance can also be expressed from the intravenous infusion rate formula: $Cl_t = \frac{D}{T \cdot C_{ss}}$, where $D$ is the dose, $T$ is the infusion time, and $C_{ss}$ is the steady-state concentration.
Which routes of administration avoid the first-pass hepatic effect?
Routes of administration that allow bypassing the first-pass hepatic effect (presystemic elimination) are those where the drug enters the systemic circulation while avoiding the portal vein. These include:
- Sublingual route (sublinguim) — absorption occurs under the tongue directly into the systemic circulation.
- Parenteral routes (parenteralis) — injection, inhalation, transdermal, and topical methods that completely bypass the gastrointestinal tract.
- Rectal route (partially) — absorption from the lower and middle parts of the rectum occurs into the middle and inferior rectal veins (vv. rectales mediae et inferiores), from where the drug enters the inferior vena cava, bypassing the liver. Absorption from the upper part of the rectum undergoes presystemic elimination.
To remember the drug accumulation rule, use the count: 1-2-3-4. In 1 half-life, 50% accumulates; in 2, 75%; in 3 (more precisely 3.3), 90%; and in 4 (up to 5), all 100% of the steady-state concentration.
Class and exam questions
What happens if the concentration drops below the minimum effective concentration?
The pharmacological action of the drug will completely cease, as its level in the blood will fall below the lower limit of the therapeutic range.
Why is a loading dose necessary?
It allows for instantly filling the volume of distribution and creating the required steady-state concentration in the blood without waiting 4–5 half-lives. This is critically important for drugs with a long $t_{1/2}$.
Why does blood concentration fluctuate when taking pills?
During intermittent (discrete) administration, the drug level fluctuates: it rises during absorption after dosing and falls during elimination, forming a "sawtooth" curve on the graph.
What else to study on this topic
- Mathematical justification of the relationship between total clearance and infusion rate
- Influence of bioavailability on oral dose calculations
- Calculation of the maintenance dose via half-life
- Analysis of the sawtooth pharmacokinetic curve and the tau parameter
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