6. Dimensional Analysis

Dimensional Analysis Overview

Conversion factors are essential tools in dimensional analysis, serving as equivalent values stacked together, allowing for unit cancellation during calculations.
Example: The relationship between minutes and hours can be represented mathematically as:
- (1 hour) / (60 minutes)
- (60 minutes) / (1 hour)
This flexibility enables practitioners to convert measurements by flipping the factors to cancel out units as necessary.
Major units involved in veterinary medicine include:
- Weight: Common units are kilogram (kg), gram (g), milligram (mg), and microgram (µg).
- Volume: The primary units used are liter (L) and milliliter (mL).

Dosage Form pertains to the physical shape or manifestation of the medication being administered. This includes forms such as tablets, capsules, suspensions, solutions, and elixirs.
The concentration or strength of these dosage forms is crucial for determining the appropriate dosage for a patient.
Example of Concentration:
- 500 mg amoxicillin capsules (each capsule contains 500 mg),
- 50 mg/mL amoxicillin suspension (where 1 mL contains 50 mg of the drug).

Dosage: This is the prescribed amount of a drug required per unit of body weight or body surface area of an animal. Units can vary widely and may include weight (mg, kg), volume (mL, L), and insulin units, among others.
Examples:
- For carprofen: 2.2 mg/kg administered every 12 hours (q 12 hr) orally (PO).
- For ProZinc insulin: 1 unit per cat every 12 hours subcutaneously (q 12 hr SQ).
Dose: Refers to the specific amount of medication given to a patient upon administration.
Examples of Doses:
- 75 mg carprofen,
- 1 unit of ProZinc.

An antibiotic requires a DOSAGE of 5 mg/kg for a 10 kg dog leading to a resultant DOSE of 50 mg:
- Calculation: 5 mg/kg × 10 kg = 50 mg.
- Possible Dosage Forms:
  - One 50 mg tablet
  - 1 mL of a 50 mg/mL solution.

General Rounding Principles
- It’s essential to determine the required accuracy level for the calculations typically using one additional decimal place during rounding.
- Rounding Rules:
  - If the number is 5 or greater, round up.
  - If the number is less than 5, round down.
- Examples:
  - 1.85 rounds to 1.9; 5.69 rounds to 6.0
  - 1.84 rounds to 1.8; 5.49 rounds to 5.0.
Volume Rounding Rules:
- For volumes greater than 1 mL: round to the nearest 0.1 mL.
- For volumes less than 1 mL: round to the nearest 0.01 mL.
- Example syringe accuracy:
  - 1 mL syringe: precision to 0.01 mL
  - 3 mL syringe: precision to 0.1 mL
  - 6 mL syringe: precision to 0.2 mL.
Tablet Rounding Guidelines:
- Rounding of tablets is also based on whether the tablet is scored or whole:
  - For whole tablets: 1.1 - 1.4 gives 1 tablet; 1.5 - 1.9 gives 2 tablets.
  - For half tablets: 2.0 - 2.25 gives 2 tablets; 2.26 - 2.5 gives 2.5 tablets.
  - For quarter tablets: Rounding varies further based on the decimal values displayed.

Example 1: Calculating Dose
- Begin calculations from left to right focusing on weight:
- Dose calculation method: (4.5 mL)(100 mg) × (1 mL) = 450 mg.
Example 2: Lactulose Solution Dose Calculation
- Dosage prescribed: 0.5 mL/kg every 8 hours (q 8 hr) PO.
- For a cat weighing 12 lbs:Perform necessary conversion (1 kg = 2.2 lb). The calculation then illustrates the final dosage accurately.
Example 3: Phenobarbital Dose Calculation
- Dosage prescribed: 1 mg/lb every 12 hours (q 12 hr) PO for a dog weighing 90 lbs.
- The systematic calculation confirms final dosing requirements and subsequent applications of the medication.