Dosage Calculations and Conversions chapter 6 pharmacology

Dosage Calculations and Conversions

• Label all terms in your proportions to ensure clarity and accuracy.
• Verify that all measures are in the same system of units before setting up the problem.
• Set up your problem as a proportion, labeling all terms, and complete the calculations.

Setting up Proportions

• The basic proportion setup is:
  • Dose on hand : Known quantity :: Dose desired : Unknown quantity (x)
  • Example: \frac{25 \text{ mg}}{1 \text{ tablet}} = \frac{\text{Dose Desired}}{x}
• Check that your answers are reasonable. If calculating tablets and the result is a decimal (e.g., 0.2 tablets), reconsider the calculation.

Example Problem: Phenobarbital Elixir for a Child

Problem Setup:

• A child weighing 44 pounds is prescribed phenobarbital elixir at 3 mg/kg at bedtime.
• The available elixir is labeled 15 mg per 5 ml.
• Question: How many milliliters will the child receive?

Conversion:

• Convert pounds to kilograms using the conversion factor: 2.2 pounds = 1 kilogram.
• \text{Weight in kilograms} = \frac{\text{Weight in pounds}}{2.2}
• \text{Child's weight in kilograms} = \frac{44 \text{ pounds}}{2.2} = 20 \text{ kilograms}

Dosage Calculation:

• The order is 3 mg/kg. Therefore, calculate the total required milligrams:
  • 3 \frac{\text{mg}}{\text{kg}} \times 20 \text{ kg} = 60 \text{ mg}

Setting up the Proportion:

• On hand: 15 mg per 5 ml.
• Desired dose: 60 mg.
• Proportion: \frac{15 \text{ mg}}{5 \text{ ml}} = \frac{60 \text{ mg}}{x \text{ ml}}

Solving the Proportion:

• Cross-multiply: 15x = 5 \times 60
• 15x = 300
• x = \frac{300}{15} = 20 \text{ ml}
• The child will receive 20 ml of phenobarbital elixir.

Alternative Method (Desired Dose over On Hand):

• Desired dose: 60 mg.
• On hand: 15 mg per 5 ml.
• \frac{60 \text{ mg}}{15 \text{ mg}} \times 5 \text{ ml}

Example Problem: Demerol Oral Solution

Problem Setup:

• Available: Demerol solution 50 mg per 5 ml.
• Order: Demerol 150 mg every 6 hours.

Verification:

• Verify that the measures are in the same units (milligrams).

Setting up the Proportion:

• On hand: 50 mg per 5 ml.
• Desired dose: 150 mg.
• Proportion: \frac{50 \text{ mg}}{5 \text{ ml}} = \frac{150 \text{ mg}}{x \text{ ml}}

Solving the Proportion:

• Cross-multiply: 50x = 5 \times 150
• 50x = 750
• x = \frac{750}{50} = 15 \text{ ml}

Alternative Method (Desired Dose over On Hand):

• Desired dose: 150 mg.
• On hand: 50 mg per 5 ml.
• \frac{150 \text{ mg}}{50 \text{ mg}} \times 5 \text{ ml} = 15 \text{ ml}

Example Problem: Morphine Liquid for a Child with Cancer

Problem Setup:

• An 88-pound child with cancer has an order for morphine liquid at 0.2 mg/kg.
• Available: 20 mg per 5 ml.

Conversion:

• Convert pounds to kilograms: \frac{88 \text{ pounds}}{2.2} = 40 \text{ kg}

Dosage Calculation:

• 0.2 \frac{\text{mg}}{\text{kg}} \times 40 \text{ kg} = 8 \text{ mg}

Setting up the Proportion:

• On hand: 20 mg per 5 ml.
• Desired dose: 8 mg.
• Proportion: \frac{20 \text{ mg}}{5 \text{ ml}} = \frac{8 \text{ mg}}{x \text{ ml}}

Solving the Proportion:

• Cross-multiply: 20x = 5 \times 8
• 20x = 40
• x = \frac{40}{20} = 2 \text{ ml}

Alternative Method (Desired Dose over On Hand):

• Desired dose: 8 mg.
• On hand: 20 mg per 5 ml.
• \frac{8 \text{ mg}}{20 \text{ mg}} \times 5 \text{ ml} = 2 \text{ ml}

Grams to Kilograms Conversion

Problem Setup:

• Convert 3400 grams to kilograms.

Known Equivalent:

• 1000 grams = 1 kilogram

Proportion Setup:

• \frac{1000 \text{ grams}}{1 \text{ kilogram}} = \frac{3400 \text{ grams}}{x \text{ kilograms}}

Solving the Proportion:

• 1000x = 3400
• x = \frac{3400}{1000} = 3.4 \text{ kilograms}

Conversion Rule:

• To convert grams to kilograms, move the decimal point three places to the left.

Cautions for Ratio and Proportion

• Label all parts of the equation.
• The ratio on the left should contain the known quantity, and the ratio on the right should contain the desired and unknown quantities.
• Terms of the second ratio must be in the same sequence as the first ratio (e.g., grams to kilograms on both sides).
• Multiply the extremes first (to keep x on the left).
• Take extra care with decimals.
• Convert fractions to decimals.
• Round off decimals to one decimal place.
• Label your answers.
• Verify the accuracy of calculations.
• Question any unusual dosages (e.g., less than half a tablet or more than two tablets/milliliters for an injection).

Pediatric Doses

• Children are not just small adults. Do not simply reduce the adult dose for a child.
• Consider body surface area, weight, and age.
• Neonates have immature renal function and enzyme systems for drug absorption and metabolism.
• Their blood-brain barrier is more permeable.
• Total body water affects absorption.
• Approximate dosage must consider age, weight, sex, metabolic, pathological, or psychological conditions.
• Refer to recommended dosages in drug packets or inserts.
• Drug samples often have package inserts with detailed dosing instructions, including weight-based recommendations.
• Example: Sometimes, bigger children, adults with high metabolism may require higher or duplicate doses.

Recommended Dosing

• Expressed as milligrams per unit of body weight (e.g., 6 mg/kg per 24 hours).
• Calculate the dose for the individual and check the appropriateness of the prescribed dose.

Example: Demerol Dosage for a Child

Problem Setup:

• Order: Demerol 6 mg/kg per 24 hours, divided into four to six-hour doses.
• Available: Demerol ampules labeled 50 mg/ml.
• Child's weight: 33 pounds.

Conversion:

• Pounds to kilograms: \frac{33 \text{ pounds}}{2.2} = 15 \text{ kg}

Dosage Calculation per 24 Hours:

• 6 \frac{\text{mg}}{\text{kg}} \times 15 \text{ kg} = 90 \text{ mg} \text{ per 24 hours}

Milliliters Needed in 24 Hours:

• On hand: 50 mg per 1 ml.
• Desired dose: 90 mg.
• Proportion: \frac{50 \text{ mg}}{1 \text{ ml}} = \frac{90 \text{ mg}}{x \text{ ml}}

Solving the Proportion:

• 50x = 90
• x = \frac{90}{50} = 1.8 \text{ ml} \text{ per 24 hours}

Milliliters Needed Every 6 Hours:

• Proportion: \frac{24 \text{ hours}}{1.8 \text{ ml}} = \frac{6 \text{ hours}}{x \text{ ml}}
  • 24x = 6 \times 1.8
  • 24x = 10.8
  • x = \frac{10.8}{24} = 0.45 \text{ ml} \text{ every 6 hours}

Clark's Rule

• Formula for estimating a child's dosage.
• \text{Child's Dose} = \frac{\text{Child's Weight in Pounds}}{150 \text{ (Average Adult Weight)}} \times \text{Adult Dose}

Example:

• Child weighs 33 pounds.
• Adult dose: 100 mg (available as 100 mg per 2 ml).
• \text{Child's Dose} = \frac{33 \text{ pounds}}{150} \times 100 \text{ mg}

Calculation:

• \text{Child's Dose} = \frac{3300}{150} = 22 \text{ mg}
  • Proportion: \frac{100 \text{ mg}}{2 \text{ ml}} = \frac{22 \text{ mg}}{x \text{ ml}}
  • 100x = 44
  • x = \frac{44}{100} = 0.44 \text{ ml}

Geriatric Dosing

• No specific formula.
• Start low and go slow.
• Elderly patients often have reduced kidney and liver function, which can lead to toxicity.
• Careful assessment on an individual basis is crucial.
• Constant monitoring is necessary.
• Reduce the dose whenever possible.
• Individual reactions vary significantly.

Prevention of Medication Errors

• Always put a zero before a decimal point (e.g., 0.2 instead of .2).
• Never place a decimal point and zero after a whole number (e.g., write 5, not 5.0).
• Avoid using decimals whenever possible; express doses in whole numbers of smaller units (e.g., 500 mg instead of 0.5 g).
• Have a qualified person double-check calculations.
• Question orders if there is difficulty interpreting the drug name or dosage, or if the dosage seems inappropriate.
• It is your ethical and legal responsibility to ensure the drugs you administer are safe, even if the order is written incorrectly. You are expected to recognize inappropriate dosages.