In the management of hyper- and hyponatremia a quantitatively sound approach is of utmost importance to ensure adequate speed and magnitude of tonicity correction.
The Edelman Equation
Thanks to Edelman and coworkers (Ref. 1) we have an empirical validation of the theoretically plausible relationship between the plasma sodium concentration (P-[Na]) as a surrogate of tonicity on one hand, and the exchangeable amount of sodium and potassium in the body in addition to the total body water (TBW) on the other.
Over the years the original equation has been used in different, often simplified formulations. For clinical practice the differences are probably of negligible magnitude. Here I use the formula published by Nguyen and Kurtz (Ref. 2).
By using the Edelman equation the effects of changes in sodium-, potassium- and water balance on the P-[Na] can be calculated accurately.
Myths and Reality
Unfortunately many clinicians use the equation only to estimate the impact on the P-[Na] of a certain amount of infusion. Even worse the misconception that this simple calculation will predict the future P-[Na] is widespread. No wonder that clinicians are often less than impressed with the formulas perfomance.
In reality the equation can of course only estimate the expected difference in P-[Na] solely due to the addition or excretion of the stated solution in the stated amount. All other changes that influence the P-[Na] are obviously not accounted for by one simple calculation. To predict the P-[Na] during the course of treatment the complete balance of water, sodium and potassium has to be considered.
To use these rather laborious calculations in a clinically reasonable time frame, I'm using an excel sheet, the swissnephrokalk Dysnatremia Tables.
With the only input being the current P-[Na] and an estimate of the TBW, the Dysnatremia Tables allow rapid and easy
- Assessment of the impact of complex infusion and supplementation regimens on the P-[Na].
- Provision of corrective steps with hypertonic solutions or free water.
- Development of safe follow-up strategies using output/urine flow monitoring.
The Importance of Urine Volume and Potassium
Two important points, that become very obvious when using the Dysnatremia Tables regularly, merit special emphasis, as they are often neglected in the care of patients with dysnatremia:
- It is virtually impossible to overcorrect hyponatremia by the infusion of isotonic fluids alone. Excessive loss of free water, usually by a water diuresis, is by far the most common reason of to fast an increase in the P-[Na]. Urine output monitoring is therefore an essential part of the management of hyponatremic patients.
- Do not forget the impact of potassium supplementation or loss on the P-[Na]. It might not have the same clinical consequences, as the potassium will preferentially end up intracellularly, but the P-[Na] depends as much on the potassium balance as on that of sodium.
- Minor deviations in the estimation of the TBW usually do not have a significant impact on the results of the formula.
- The calculations are based on equilibrated conditions, which obviously might not be present in every patient.
- The volumes and infusion types used in the Dysnatremia Tables can easily be adjusted to your personal needs.
- The calculations should not supersede regular measurement of the P-[Na]. They are a helpful tool to design the right therapy from the start and keep on track during the course of treatment.
- Edelman IS, Leibman J, O’Meara MP, Birkenfeld LW. Interrelations between serum sodium concentration, serum osmolarity and total exchangeable sodium, total exchangeable potassium and total body water. Journal of Clinical Investigation. 1958;37(9):1236–1256. doi:10.1172/jci103712.
- Kurtz I, Nguyen MK. Evolving concepts in the quantitative analysis of the determinants of the plasma water sodium concentration and the pathophysiology and treatment of the dysnatremias. Kidney International. 2005;68(5):1982–1993. doi:10.1111/j.1523-1755.2005.00652h.x
Appendix - Examples
Consider a 67yo woman with a P-[Na]=116mmol/l. She weighs 74kg and you estimate her TBW at 37l.
- Because she is hypovolemic you want to give her 2000ml of NaCl 0.9% over the next 24h. What impact on the P-[Na] will this have? (Answer: +1mmol/l, (A)).
- She is also profoundly hypokalemic. How would supplementing 80mmol of KCl affect the P-[Na]? (Answer: +2.2mmol/l, (B)).
- You want the P-[Na] to increase no more than 8 mmol/l in the first 24h. So how much maximally dilute urine ([Na+K]=20mmol/l) can this patient pass without risking overcorrection? (Answer: 1500ml, (C), (8-1-2.2=4.8)).
- Let's assume she develops a seizure due to cerebral edema. Now you want to increase her P-[Na] on the spot by 2mmol/l. How much NaCl 3% or NaBic 8.4% do you have to give? (Answer: 200ml NaCl 3%, 100ml NaBic 8.4%, (D))
- Now a different scenario: 8 hours ago her P-[Na] was at 105mmol/l. You want to lower her P-[Na] by 4mmol/l. How much additional free water do you have to give? (Answer: ~1100ml, (E)).
Cautionary Note: Adding up the values from different columns is strictly speaking incorrect, as changes in the TBW that might be taking place are not correctly accounted for. The magnitude of the error is usually well below 1mmol/l. If that is not good enough for you, you can add up all sodium and potassium, calculate an average concentration of Na and K, and manually plot it against the water balance. (In the above example 2000ml of normal saline plus 80mmol of potassium gives an average [Na+K] of 194mmol/l, which translates into an increase in P-[Na] of 3.1mmol/l (F) versus 3.2mmol/l calculated above (A+B).)