Drug Strength Calculations: Dilution & Reconstitution

This cheat sheet covers essential calculations for altering drug product strength through dilution and reconstitution, focusing on simple dilutions, alligation medial, and alligation alternate methods.

Core Principles

Dilution reduces concentration by adding a diluent.
Reconstitution involves adding a diluent to a powdered drug to achieve a specific concentration.
Alligation Medial finds the final concentration when mixing multiple products of the same drug.
Alligation Alternate determines the quantities of stock products needed to achieve a desired concentration.
Units must be consistent throughout calculations.
Powder volume in reconstitution contributes to the final volume unless otherwise specified.
Reconstituted concentrations are based on the final reconstituted volume, not just the diluent volume.

Action Steps

For simple dilutions, use $C_1V_1 = C_2V_2$ or $C_1W_1 = C_2W_2$ to relate initial and final concentrations and volumes/weights.
For Alligation Medial, calculate the weighted average concentration: sum of (concentration * volume/weight) divided by the sum of volumes/weights.
For Alligation Alternate, use the chart method: subtract diagonally to find parts, then use ratios to determine actual quantities.
For reconstitution, determine the default reconstituted volume and powder volume.
Calculate the new concentration by dividing the total amount of drug by the new total volume.
When mixing three or more stock items, perform alligation twice, ensuring the desired concentration is between the chosen stock strengths.

Formulas

$C_1V_1 = C_2V_2$
$C_1W_1 = C_2W_2$
$C_{FINAL} = \frac{\sum (c \cdot v)}{\sum v}$
$C_{FINAL} = \frac{\sum (c \cdot w)}{\sum w}$
$|b - x| \text{ parts of } a + |a - x| \text{ parts of } b = \text{ parts } x$

Key Terms

Dilution: The process of reducing the concentration of a solute in a solution, usually by adding more solvent.
Stock Product: A concentrated solution or preparation that is used to make a more dilute solution.
Diluent: A substance (usually a solvent) that does not contain the item of interest, used to dilute a stock product.
Reconstitution: The process of adding a liquid diluent to a powdered drug to create a liquid medication.
Alligation Medial: A method used to find the final concentration when mixing multiple solutions of the same drug.
Alligation Alternate: A method used to determine the quantities of stock solutions needed to prepare a solution of a desired concentration.
Powder Volume: The volume occupied by the dry powder in a vial before reconstitution.