8.5 Advanced Calculations: Infusion Rates, Parenteral Nutrition, and Renal Estimation

8.5 Advanced Calculations: Infusion Rates, Parenteral Nutrition, and Renal Estimation

Exam Focus: Prescription calculations are a named subcategory of Pharmacy Practice. The examination is closed-book, but an on-screen scientific calculator and a PEBC reference sheet of formulas are provided, so the skill being tested is selecting and applying the right relationship, not recalling constants.

---

The Provided Reference Sheet

The PEBC Pharmacist Evaluating Examination reference sheet supplies the pharmacokinetic and clinical formulas below. Learn to recognise which one a question needs.

Two points about the creatinine clearance formula matter for the examination. First, it takes serum creatinine in micromoles per litre, the SI unit used in Canada, and the numeric factor of 1.2 goes with those units; formulas written for milligrams per decilitre use different constants and are not what the reference sheet supplies. Second, the sheet specifies actual body weight. In clinical practice, ideal body weight is commonly substituted in underweight patients and adjusted body weight in obesity to avoid overestimating clearance, and a good answer recognises both the supplied formula and that clinical caveat.

Worked example. A 72-year-old woman weighs 62 kg with a serum creatinine of 108 micromol/L.

• Male value: (140 − 72) × 62 × 1.2 ÷ 108 = 68 × 62 × 1.2 ÷ 108 = 5,059.2 ÷ 108 = 46.8 mL/min.
• Female value: 0.85 × 46.8 = 39.8 mL/min.

That result places her in the range where several direct oral anticoagulants, gabapentin, and many antimicrobials require dose reduction.

---

Intravenous Infusion Rates

The governing relationship is simple and must be applied consistently in one set of units:

Rate (mL/h) = dose required per hour ÷ concentration of the prepared solution (per mL)

Worked example. Heparin 25,000 units in 250 mL is ordered at 1,100 units/h.

Concentration = 25,000 ÷ 250 = 100 units/mL. Rate = 1,100 ÷ 100 = 11 mL/h.

Weight-based example. Dopamine 400 mg in 250 mL, ordered at 5 mcg/kg/min for an 80 kg patient.

1. Dose per minute = 5 × 80 = 400 mcg/min = 0.4 mg/min.
2. Dose per hour = 0.4 × 60 = 24 mg/h.
3. Concentration = 400 mg ÷ 250 mL = 1.6 mg/mL.
4. Rate = 24 ÷ 1.6 = 15 mL/h.

Gravity drip rate converts volume to drops:

Drops per minute = (volume in mL × drop factor in drops/mL) ÷ time in minutes

For 1,000 mL over 8 hours with a 15 drops/mL set: (1,000 × 15) ÷ 480 = 31 drops per minute.

---

Milliequivalents, Millimoles, and Osmolarity

• Milliequivalents: mEq = (mg × valence) ÷ molecular weight. For potassium chloride (molecular weight 74.5, valence 1), 1 g supplies 1,000 ÷ 74.5 = 13.4 mEq.
• Millimoles: mmol = mg ÷ molecular weight. Phosphate is ordered in millimoles rather than milliequivalents because its valence varies with pH.
• Osmolarity: mOsm/L = (grams per litre ÷ molecular weight) × number of dissociated species × 1,000. Sodium chloride 0.9% supplies 9 g/L; 9 ÷ 58.5 × 2 × 1,000 = 308 mOsm/L, which is why normal saline is very close to plasma osmolarity.

Peripheral infusions are generally limited to about 900 mOsm/L; more concentrated parenteral nutrition requires central access.

---

Parenteral Nutrition

Energy contributions differ from the familiar dietary values because dextrose in solution is monohydrated:

Worked example. A parenteral nutrition bag contains 500 mL of 50% dextrose, 500 mL of 8.5% amino acids, and 250 mL of 20% lipid.

• Dextrose: 500 mL × 0.50 = 250 g → 250 × 3.4 = 850 kcal.
• Amino acids: 500 mL × 0.085 = 42.5 g → 42.5 × 4 = 170 kcal.
• Lipid: 250 mL × 0.20 = 50 g fat → 50 × 9 = 450 kcal.
• Total ≈ 1,470 kcal in a total volume of 1,250 mL.

Protein energy is often reported separately as non-protein calories when calculating the non-protein calorie to nitrogen ratio, where nitrogen equals grams of protein divided by 6.25.

---

Isotonicity

Ophthalmic, nasal, and parenteral preparations should be approximately isotonic with body fluids, equivalent to 0.9% sodium chloride.

The sodium chloride equivalent (E value) is the mass of sodium chloride producing the same osmotic effect as 1 g of the drug.

Sodium chloride needed (g) = (0.009 × volume in mL) − (weight of drug in g × E value)

Worked example. Prepare 30 mL of a 1% solution of a drug with an E value of 0.20.

• Sodium chloride to make 30 mL isotonic alone: 0.009 × 30 = 0.27 g.
• Drug present: 0.3 g; its sodium chloride equivalent contribution = 0.3 × 0.20 = 0.06 g.
• Sodium chloride to add = 0.27 − 0.06 = 0.21 g.

---

Checking Your Work

Three habits prevent most calculation errors on this examination:

1. Carry the units through every step and confirm the final unit is the one asked for.
2. Estimate the order of magnitude first. A paediatric dose calculated as 4,000 mg, or an infusion rate of 900 mL/h, is wrong before the arithmetic is checked.
3. Re-read what was asked. Questions frequently ask for millilitres per hour when the calculation naturally produces milligrams per hour, or for the volume of the concentrate rather than the volume of the final preparation.

Remember the examination's numeric conventions: values are given in SI units, a period is the decimal separator in English, and a trailing zero may appear in a printed value even though the Institute for Safe Medication Practices discourages it in practice.