Pharmacology & Dosage

Drug dosing, pharmacokinetics, clearance and IV-drip calculations for clinical practice

t_{1/2} = \frac{0.693}{k_e}

Time for the plasma concentration of a drug to fall to half its initial value.

C_{ss} = \frac{F \times D}{CL \times \tau}

Average plasma drug concentration when intake and elimination are balanced.

LD = \frac{C_{target} \times V_d}{F}

Initial higher dose to rapidly achieve the desired plasma concentration.

MD = C_{ss} \times CL \times \tau

Recurring dose needed to sustain the steady-state concentration.

V_d = \frac{D}{C_0}

Apparent volume into which a drug distributes — a larger Vd means the drug leaves the bloodstream and enters tissues.

CL = k_e \times V_d

Volume of plasma completely cleared of a drug per unit time.

F = \frac{AUC_{oral}}{AUC_{IV}} \times 100

Fraction of an oral dose that reaches systemic circulation compared with an IV dose.

\text{Rate} = \frac{V \times gtt}{T}

Drops per minute to deliver a given volume over a set time via IV drip.

CrCl = \frac{(140 - \text{age}) \times \text{weight}}{72 \times S_{cr}} \times (0.85 \text{ if female})

Estimates kidney function to guide drug dosing adjustments.

TI = \frac{TD_{50}}{ED_{50}}

Ratio of the dose causing toxicity to the effective dose — a safety measure for drugs.

C(t) = C_0 \times e^{-k_e t}

Drug concentration decreases exponentially — a constant fraction is eliminated per unit time.

D = d \times W

Calculate the total dose from a per-kilogram dosing rate — common in paediatrics.