6.1: Pharmaceutical Calculations: Doses & Unit Conversions

Pharmaceutical Calculations: Doses & Unit Conversions

Clinical calculations are a core component of the Overseas Pharmacist Readiness Assessment (OPRA) exam. In clinical pharmacy practice, mathematical errors can lead to serious patient harm. A solid grasp of units, conversions, and weight/BSA-based dosing methodologies is vital for patient safety.

1. Fundamental Unit Conversions

Before undertaking any clinical calculation, all values must be expressed in matching units. Metric conversions typically occur in factors of 1,000. In clinical practice, always double-check the placement of decimal points, as a single decimal error represents a 10-fold dose error.

Metric Mass Conversions

• 1 gram (g) = 1,000 milligrams (mg)
• 1 milligram (mg) = 1,000 micrograms (microg, mcg, or µg)
• 1 microgram (microg) = 1,000 nanograms (ng)

Safety Tip (ACSQHC & AMH Guidelines): To avoid medication errors, write the word 'microgram' in full on prescriptions rather than using 'mcg' or 'µg', which can easily be misread as 'mg' in handwritten documents.

Metric Volume Conversions

• 1 litre (L) = 1,000 millilitres (mL)
• 1 millilitre (mL) = 1,000 microlitres (µL)

Example: Microgram to Milligram Conversion

If a patient is prescribed a dose of 250 micrograms of digoxin, and the available tablets are 0.125 mg each: $\text{Dose in mg} = 250\text{ micrograms} \div 1,000 = 0.25\text{ mg}$ $\text{Number of tablets} = 0.25\text{ mg} \div 0.125\text{ mg/tablet} = 2\text{ tablets}$

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2. Weight-Based Dosing (mg/kg)

Many medications—especially low therapeutic index drugs (e.g., heparin, aminoglycosides, phenytoin) and paediatric therapies—are dosed based on body weight.

$\text{Total Dose (mg)} = \text{Patient Weight (kg)} \times \text{Dosed Amount (mg/kg)}$

Weight Adjustments in Clinical Practice

For patients within a normal body mass index (BMI) range, Actual Body Weight (ABW) is used for dosing. However, for patients who are overweight or obese, using actual body weight for hydrophilic drugs (which do not distribute well into adipose tissue) can lead to toxic serum concentrations. In such cases, pharmacists must calculate Ideal Body Weight (IBW) or Adjusted Body Weight (AdjBW).

Ideal Body Weight (IBW) Formula (Devine Formula - Metric Variant):

• Males: $\text{IBW (kg)} = 50 + 0.9 \times (\text{Height in cm} - 152)$
• Females: $\text{IBW (kg)} = 45.5 + 0.9 \times (\text{Height in cm} - 152)$

Adjusted Body Weight (AdjBW) Formula:

$\text{AdjBW (kg)} = \text{IBW} + 0.4 \times (\text{ABW} - \text{IBW})$

Clinical Dosing Rules of Thumb:

1. If ABW < IBW: Use ABW for all calculations.
2. If ABW is between 100% and 120% of IBW: Use ABW for most drugs.
3. If ABW > 120% of IBW (Obese): Use AdjBW for hydrophilic drugs (e.g., Gentamicin, Tobramycin, Acyclovir) to prevent overdose, and use IBW for drugs like Aminophylline/Theophylline.

Clinical Worked Example: Gentamicin Loading Dose

A 58-year-old female (height: 162 cm, weight: 92 kg) requires an intravenous loading dose of gentamicin (5 mg/kg) for suspected sepsis.

Step 1: Calculate Ideal Body Weight (IBW) $\text{IBW} = 45.5 + 0.9 \times (162 - 152) = 45.5 + 0.9 \times 10 = 54.5\text{ kg}$

Step 2: Check for Obesity (ABW > 120% of IBW) $\text{Obesity Threshold} = 54.5\text{ kg} \times 1.2 = 65.4\text{ kg}$ Since her actual weight (92 kg) is greater than 65.4 kg, she is considered obese. Thus, we must use Adjusted Body Weight (AdjBW) for gentamicin dosing.

Step 3: Calculate Adjusted Body Weight (AdjBW) $\text{AdjBW} = 54.5 + 0.4 \times (92 - 54.5) = 54.5 + 0.4 \times 37.5 = 54.5 + 15 = 69.5\text{ kg}$

Step 4: Calculate the Gentamicin Dose $\text{Gentamicin Loading Dose} = 69.5\text{ kg} \times 5\text{ mg/kg} = 347.5\text{ mg}$ (Clinically, this would be rounded to 340 mg or 350 mg depending on local institutional guidelines)

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3. Body Surface Area (BSA) Calculations

Body Surface Area (BSA) correlates better with metabolic activity, cardiac output, and renal function than body weight. It is the preferred parameter for dosing cytotoxic chemotherapy and some high-risk paediatric drugs.

The Mosteller Formula

The Mosteller formula is the standard method used in Australian clinical environments:

$\text{BSA } (m^2) = \sqrt{\frac{\text{Height (cm)} \times \text{Weight (kg)}}{3600}}$

Clinical Worked Example: Chemotherapy Dosing

A patient with a height of 175 cm and weight of 80 kg is prescribed a chemotherapy agent at a dose of $75\text{ mg}/m^2$.

Step 1: Calculate BSA using the Mosteller formula $\text{BSA} = \sqrt{\frac{175 \times 80}{3600}} = \sqrt{\frac{14000}{3600}} = \sqrt{3.889} \approx 1.97\text{ } m^2$

Step 2: Calculate the total dose $\text{Total Dose} = 1.97\text{ } m^2 \times 75\text{ mg}/m^2 = 147.75\text{ mg}$

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4. Paediatric Dosing Formulas and Practice

Paediatric drug clearance rates vary widely due to immature hepatic enzyme systems and developing renal function. Safe paediatric dosing relies on weight-based (mg/kg) or BSA-based (mg/m2) assessments. Traditional age-based formulas (such as Young's or Clark's rules) are obsolete and are not used in modern clinical settings; they are replaced by precise drug monograph databases (such as the Australian Medicines Handbook Children's Dosing Companion).

Paracetamol Paediatric Dosing Example

A 3-year-old child weighing 14 kg is prescribed paracetamol for fever. The standard paediatric dose is 15 mg/kg per dose (up to 4 times daily).

Step 1: Calculate the dose in milligrams $\text{Dose} = 14\text{ kg} \times 15\text{ mg/kg} = 210\text{ mg}$

Step 2: Determine the volume of liquid required The pharmacy stocks two strengths of paracetamol liquid: 120 mg/5 mL (infant suspension) and 250 mg/5 mL (children's suspension).

• Using the 120 mg/5 mL suspension: $\text{Volume} = \frac{210\text{ mg}}{120\text{ mg}} \times 5\text{ mL} = 8.75\text{ mL}$
• Using the 250 mg/5 mL suspension: $\text{Volume} = \frac{210\text{ mg}}{250\text{ mg}} \times 5\text{ mL} = 4.2\text{ mL}$

Clinical Pearl: Always choose the suspension concentration that allows for the most accurate and practical volume measurement for the parents or carers, avoiding very large volumes where possible.