6.2 Dosage Calculations, Unit Conversions & Pediatric/Geriatric Adjustments

6.2 Dosage Calculations, Unit Conversions & Pediatric/Geriatric Adjustments

Accurate clinical calculation is an absolute prerequisite for medication safety. A single decimal point error can result in a 10-fold ($1000\%$) overdose or underdose, leading to severe toxicity or therapeutic failure. Registered nurses in Singapore must master unit conversions, oral and parenteral dose formulas, intravenous flow rates, powder reconstitutions, and specialized pediatric and geriatric adjustments.

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Core Metric Conversions & Safe Writing Practices

Clinical calculations in Singapore public health institutions strictly adhere to the International System of Units (SI). Nurses must seamlessly convert between metric mass and volume units:

• Mass: $1\text{ gram (g)} = 1,000\text{ milligrams (mg)} = 1,000,000\text{ micrograms (mcg)}$
• Volume: $1\text{ liter (L)} = 1,000\text{ milliliters (mL)}$

Safe Writing Rules (ISMP & MOH Directives):

• NEVER use trailing zeros: Write $5\text{ mg}$, NEVER $5.0\text{ mg}$ (misreading $5.0$ as $50\text{ mg}$ is a major error source).
• ALWAYS use leading zeros: Write $0.25\text{ mg}$, NEVER $.25\text{ mg}$ (misreading $.25$ as $25\text{ mg}$ causes a 100-fold overdose).
• Use standardized microgram abbreviations: Write $\text{mcg}$, NEVER $\mu\text{g}$ (which can be confused with $\text{mg}$ in handwritten notes).

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Fundamental Dosage Formulas

1. Desired over Have Formula:

$$\text{Amount to Administer } (X) = \frac{\text{Desired Dose } (D)}{\text{Hand/Available Dose } (H)} \times \text{Vehicle Volume } (V)$$

Example: Order: Digoxin $125\text{ mcg}$ PO daily. Available: Digoxin oral solution $0.05\text{ mg/mL}$.

1. Convert units to match: $125\text{ mcg} = 0.125\text{ mg}$.
2. Calculate: $X = (0.125\text{ mg} / 0.05\text{ mg}) \times 1\text{ mL} = 2.5\text{ mL}$.

2. Intravenous Flow Rate Calculations:

• Volumetric Pump Rate (mL/hr):

$$\text{Pump Rate (mL/hr)} = \frac{\text{Total Volume to Infuse (mL)}}{\text{Total Time (hours)}}$$

• Gravity Manual Drip Rate (gtt/min):

$$\text{Drip Rate (gtt/min)} = \frac{\text{Total Volume (mL)} \times \text{Drop Factor (gtt/mL)}}{\text{Time (minutes)}}$$

Common Drop Factors in SG Hospitals:

• Macrodrip Sets: $10\text{ gtt/mL}, 15\text{ gtt/mL}, 20\text{ gtt/mL}$ (standard adult blood/fluid tubing).
• Microdrip Sets: $60\text{ gtt/mL}$ (pediatric, neonatal, and ICU precision tubing).

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Powder Reconstitution & Volume Displacement

When reconstituting powdered medications (e.g., IV Ampicillin, Ceftriaxone, Hydrocortisone), nurses must calculate the final drug concentration by accounting for powder displacement volume:

$$\text{Final Volume} = \text{Volume of Diluent Added} + \text{Powder Displacement Volume}$$ $$\text{Final Concentration} = \frac{\text{Total Solute Mass}}{\text{Final Volume}}$$

Clinical Example: A vial contains $1\text{ g} (1,000\text{ mg})$ of powdered Ceftriaxone. The package insert states that adding $9.6\text{ mL}$ of Sterile Water for Injection yields a final volume of $10.0\text{ mL}$ (powder displaces $0.4\text{ mL}$). The final concentration is $1,000\text{ mg} / 10\text{ mL} = 100\text{ mg/mL}$. To administer a prescribed dose of $750\text{ mg}$, the nurse draws up: $(750\text{ mg} / 100\text{ mg/mL}) = 7.5\text{ mL}$.

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Pediatric Dosing Adjustments & Body Surface Area (BSA)

Children possess immature hepatic enzyme systems, underdeveloped renal clearance, and variable fluid balance, making weight-based and BSA-based dosing essential.

1. Weight-Based Dosing (mg/kg):

Always calculate the daily or per-dose allowance in $\text{mg/kg}$ and cross-reference with maximum adult single doses.

Example: A pediatric patient weighing $14\text{ kg}$ is prescribed Paracetamol $15\text{ mg/kg/dose}$ PO. Syrup concentration is $120\text{ mg} / 5\text{ mL}$.

1. Calculate target dose: $14\text{ kg} \times 15\text{ mg/kg} = 210\text{ mg}$.
2. Calculate volume: $(210\text{ mg} / 120\text{ mg}) \times 5\text{ mL} = 8.75\text{ mL}$.

2. Body Surface Area (BSA) Formula (Most Accurate for Cytotoxic / Chemotherapy Agents):

$$\text{BSA (m}^2) = \sqrt{\frac{\text{Height (cm)} \times \text{Weight (kg)}}{3600}}$$ $$\text{Pediatric Dose} = \text{Child's BSA (m}^2) \times \text{Standard Adult Dose per m}^2$$

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Geriatric Pharmacokinetics & Renal Clearance Adjustments

Age-related physiological changes alter drug handling significantly in elderly patients ($> 65$ years):

Cockcroft-Gault Equation for Creatinine Clearance (CrCl):

$$\text{CrCl (mL/min)} = \frac{(140 - \text{Age}) \times \text{Weight (kg)}}{72 \times \text{Serum Creatinine (mg/dL)}} \times (0.85 \text{ if female})$$