Phosphate replacement: K-Phos addition with concurrent KCl
A 55 lb DKA dog has serum phosphorus of 1.2 mg/dL (severe). You want to give K-Phos at 0.03 mmol/kg/hr. K-Phos stock is 3 mmol/mL phosphate, with 4.4 mEq of potassium per mL (the same vial supplies both). The patient is already on a fluid line containing 20 mEq/L KCl at 50 mL/hr. Is the combined potassium delivery safe (cap 0.5 mEq/kg/hr)?
Hint
Convert lb to kg first. Both the phosphate dose and the K cap depend on kg. Then three sub-problems: pump rate of K-Phos, K from the K-Phos, K from the maintenance line. Sum the K and compare to the cap.
Another hint
(1) lb → kg via 2.2 lb/kg. (2) K-Phos rate (mL/hr): phosphate dose × weight ÷ K-Phos phosphate concentration. (3) K from K-Phos: that rate × 4.4 mEq/mL. (4) K from maintenance line: 20 mEq/L × 50 mL/hr (watch your L/mL conversion). Sum, divide by weight, compare to 0.5 mEq/kg/hr.
Show worked answer
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Convert the patient's weight from lb to kg.
$$\frac{55 \,\cancel{lb}}{2.2 \,\cancel{lb}/kg} = 25 \,kg$$ -
Compute the K-Phos rate in mL/hr from the phosphate dose.
$$0.03 \,\tfrac{mmol}{\cancel{kg}\cdot hr} \times 25\,\cancel{kg} = 0.75 \,\tfrac{mmol}{hr}$$ -
Convert mmol/hr to mL/hr using the K-Phos phosphate concentration. mmol cancels.
$$\frac{0.75 \,\cancel{mmol}/hr}{3 \,\cancel{mmol}/mL} = 0.25 \,\tfrac{mL}{hr}$$ -
Potassium delivered by the K-Phos: each mL has 4.4 mEq K. So 0.25 mL/hr × 4.4 mEq/mL gives the K from K-Phos.
$$0.25 \,\tfrac{\cancel{mL}}{hr} \times 4.4 \,\tfrac{mEq}{\cancel{mL}} = 1.1 \,\tfrac{mEq}{hr}$$ -
Potassium from the maintenance line: 20 mEq/L × 50 mL/hr. Convert L to mL (× 1000) so the mL cancel.
$$\frac{20 \,mEq}{1{,}000 \,\cancel{mL}} \times 50 \,\tfrac{\cancel{mL}}{hr} = 1.0 \,\tfrac{mEq}{hr}$$ -
Sum the two sources and divide by weight to check against the 0.5 mEq/kg/hr cap.
$$\frac{1.1 + 1.0 \,mEq/hr}{25\,kg} = 0.084 \,\tfrac{mEq}{kg\cdot hr}$$ -
0.084 mEq/kg/hr is well below the 0.5 mEq/kg/hr cap, so combined delivery is safe.
Run K-Phos at 0.25 mL/hr. Combined K delivery is ≈ 2.1 mEq/hr (0.08 mEq/kg/hr), comfortably below the 0.5 mEq/kg/hr cap.