What is the formula to calculate urine volume when urine osmolality (uOsm) is 600 mmol/kg and a person is given hypertonic saline with an osmolality of 1000 mOsm/L?

Formula for Calculating Urine Volume with Hypertonic Saline Administration

The formula to calculate urine volume when urine osmolality is 600 mmol/kg and hypertonic saline with osmolality of 1000 mOsm/L is administered is: Urine Volume = (Amount of Solute Administered) ÷ Urine Osmolality.

Understanding the Physiological Principles

When hypertonic saline is administered, the body must excrete the excess solute to maintain osmotic balance. The volume of urine produced depends on:

1. The total osmolar load administered (amount of solute)
2. The concentration at which the kidneys can excrete this solute (urine osmolality)

Step-by-Step Calculation

1. Calculate total osmolar load:

   • Multiply the volume of hypertonic saline (in L) by its osmolality (1000 mOsm/L)
   • Example: If 1 L of hypertonic saline is given, osmolar load = 1 L × 1000 mOsm/L = 1000 mOsm

2. Calculate urine volume required:

   • Divide the total osmolar load by the urine osmolality
   • Urine Volume = 1000 mOsm ÷ 600 mmol/kg = 1.67 L

Important Clinical Considerations

• This formula assumes that all administered solute must be excreted and that urine osmolality remains constant at 600 mmol/kg 1.

• The actual urine volume may vary based on:

  • Changes in urine concentrating ability
  • Concurrent fluid intake or losses
  • Underlying renal function
  • Hormonal responses (particularly ADH)

• In clinical settings, hypertonic saline (3% saline) has an osmolality of approximately 1026 mOsm/L 1, which is close to the 1000 mOsm/L in this scenario.

• Patients with SIADH who have urine osmolality below 530 mOsm/kg may actually improve their sodium levels with isotonic saline, while those with higher urine osmolality (like our example of 600 mmol/kg) may worsen with isotonic saline 2.

Clinical Applications

This calculation is particularly important in:

• Managing fluid balance in patients with diabetes insipidus
• Treating SIADH (Syndrome of Inappropriate ADH secretion) 1
• Calculating fluid requirements in patients receiving hypertonic solutions
• Predicting fluid shifts when administering osmotically active solutions

Potential Pitfalls

• Failure to account for ongoing fluid losses or intake
• Not considering changes in urine osmolality over time
• Overlooking the impact of medications on renal concentrating ability
• Not monitoring serum osmolality, which should be kept below 320-330 mOsm/kg to avoid complications 3

Remember that rapid changes in serum osmolality can lead to serious neurological complications, so the rate of hypertonic saline administration should be carefully controlled.