Pharmaceutical Calculations (Dispensing)

Conversion Basics: As you convert between units, multiply or divide by 10^3 (or 1000).
- Mass Units:
- Milligrams (Mg)
- Kilograms (Kg)
- Grams (g)
- Milligrams (mg)
- Micrograms (mcg)
- Volume Units:
- Milliliters (mL)
- Kiloliters (kL)
- Liters (L)
- Milliliters (mL)
- Microliters (mcL)

Household Measurement Units:
- Teaspoon and tablespoon
Apothecary System:
- Originated in Europe, extensively used in the US.
- Usual measures include ounce, pound, scruples, drams, grain.
Common Household Conversions:
- 1 ounce = 30 mL = 30 g
- 2 tablespoons ≈ 4 drams = 15 mL = 15 g
- 1 tablespoon ≈ 2 drams = 7.5 mL = 7.5 g
- 1/2 tablespoon ≈ 1 dram = 60 grains = 5 mL = 5 g
- 1 teaspoon ≈ 1/2 dram = 30 grains = 2.5 mL = 2.5 g
- 1/2 teaspoon = (Specific quantities)

Definition: Expression of the ratio of the amount of an ingredient to the amount of product:
- Solid ingredient in a liquid vehicle: w/v (weight/volume)
- Liquid ingredient in a solid vehicle: v/w (volume/weight)
- Liquid ingredient in a liquid vehicle: v/v (volume/volume)
- Solid ingredient in a solid vehicle: w/w (weight/weight)

Four Types:
- Amount Strength (e.g. 50 mg/mL)
- Percentage Concentration (e.g. 0.2% w/v)
- Ratio Strength (e.g. 1 in 500)
- Parts per Million (ppm) (1 ppm weight in volume)

Amount strengths can appear in various forms:
- w/w: mg/g, g/g, mg/mg
- v/v: mL/L, L/L, mL/mL
- w/v: mg/mL, g/L, g/mL
- v/w: mL/g, mL/mg

Definition: A percentage is the amount of ingredients in 100 parts of the product.
Convention:
- w/v: g/100 mL
- v/w: mL/100 g
- w/w: g/100 g
- v/v: mL/100 mL
- Example for conversion:
  - Express 100 mg/dL in percentage strength:
  - 100 mg/dL ⇒ 100 mg/100 mL ⇒ 100% w/v?
  - Convert: 0.1 g/100 mL => 0.1% w/v

Definition: The quantity or amount of drug or drug formulation taken by or administered to a patient each time to achieve a therapeutic outcome.

Example 1: Calculate total tablets from a prescription requiring 2 tablets of drug X three times a day for 7 days:
- Total number of tablets = 2 x 3 x 7 = 42 tablets.
Example 2: Prescription requires 2 suppositories of drug Y for 3/day:
- Total number of suppositories = 2 x 3 = 6.
Example 3: Patient takes 30 mg of ISMN, two times a day for 20 weeks, available dosage is 60mg:
- Total tablets = 1/2 x 2 x 7 x 20 = 140 tablets.
- Cost = 140 tablets x $3 each = $420.
Example 4: Prescription for 15 mL of indigestion mixture, 4 times a day for 5 days:
- Each dose: 15 mL (three 5 mL spoonfuls).
- Total doses for 5 days: 4 x 5 = 20.
- Total volume = 20 x 15 mL = 300 mL.
Example 5: Patient taking 100 mL anti-histamine with dosing regimen two 5-mL four times a day:
- Dosing = 2 x 5 mL x 4 times = 40 mL/day.
- Lasts for 100 / 40 = 2.5 days.

Example 1: Domperidone prescription for 20 mg every 8 hours for 4 weeks, available in 10 mg tablets:
- Daily = 2 tablets x 3 times = 6.
- Total = 6 x 4 x 7 = 168 tablets.
Example 2: 8 mg of drug X once a week followed by 7 mg:
- 1st week: 8 mg by 2 x 4mg tabs = 14 tabs.
- 2nd week: 7 mg = one 4 mg and three 1 mg tabs = 7 four mg and 21 one mg tabs.
- Total = 21 four mg & 21 one mg.
Example 3: 360 mg of para. suspension 120 mg/5 mL, taken 4 times daily for 3 days:
- Volume = 360 mg / 120 mg x 5 mL = 15 mL.
- Total = 15 mL x 4 x 3 = 180 mL.
Example 4: Required dose of 200 mg of paracetamol suspension (250 mg/5 mL):
- Solve for X: X = 200 x 5 / 250 = 4 mL.
Example 5: Intramuscular injection of 0.5 mg of salbutamol (100 mcg/mL):
- 0.5 mg = 500 mcg.
- Let volume = x: x = 500 / 100 = 5 mL.

Principle: Dose often depends on the body weight of the individual receiving the drug, important for children.
- Doses are commonly expressed as mg of drug/kg of body weight.

*The figures refer to full-term infants, not pre-term, who may need adjusted dosages.

Exercise 1: Recommended dosage of fluconazole for 3-yr-old and 11-yr-old:
- 3-yr-old (15 kg) = 3 mg/kg daily → x = 45 mg → suspension of 50 mg/5 mL suggested. Requires => 45 * 5/50 = 4.5 mL daily.
- 11-yr-old (34 kg) = z = 102 mg → round to convenient 100 mg. Can take two 50 mg capsules or 10 mL of suspension.
Exercise 2: Co-trimoxazole intravenous dose of 36 mg/kg for children:
- For 5-year-old (18 kg): Total dose = 36 x 18 = 648 mg; per dose = 648/2 = 324 mg. Volume = 324/96 = 3.375 mL of sterile solution.

Amikacin: 5 mg/kg/dose, patient weight 80 kg.
Amoxicillin: 10 mg/kg/dose, patient weight 15 kg.
Ranitidine: 2.5 mg/kg/dose, patient weight 80 kg.
- Find ratio and percentage strength given 15 mg/mL concentration.
- How many mL should be given every 6 hours?
Clindamycin for 25 kg patient every 8 hours at 15 mg/kg/day.

Concept: Many physiological phenomena correlate with body surface area, thus some doses calculated using BSA.
- Dose is expressed as quantity of drug/m² BSA.
Common Drugs: Methotrexate, Zidovudine (for children), Lomustine.

Example: Calculate oral dose of methotrexate for a 5-year-old:
- Oral dose: 15 mg/m² weekly. BSA of 5-year-old = 0.73 m².
- Required mg = 15 x 0.73 = 10.95 mg → Suggest one 10-mg tablet.

Definition: Some drugs, usually large biological molecules, are expressed in units rather than weights due to purification challenges.
- Examples: Hormonal products, Insulin, Anti-infective products.

Example 1: Nystatin recommendation for candidiasis:
- Adult dose: 500,000 units every 6 hours → Total daily dose = 500,000 × 4 = 2,000,000 units.
- Total for 5 days: Total tablets = 20; Volume suspension = 100 mL.
Example 2: Comparing vitamins in different products:
- Product A: 8 mg vitamin A, 400 IU vitamin D.
- Product B: 2500 IU vitamin A, 10 mcg vitamin D.
Calculations for Comparison:
- Product A: Vitamin A = 8000 / 0.344 = 23256 IU; Vitamin D = 400 IU.
- Product B: Vitamin A = 2500 IU; Vitamin D = 10 mcg = 400 IU.
- Comparison result: Product A has more vitamins.