Kinetic Sodium Equation with Built-In Rate of Correction: Aid to Prescribing Therapy for Hyponatremia or Hypernatremia

Abstract

Purpose Both hyponatremia and hypernatremia occur frequently in patients with cancer. To understand these disorders, investigators have mathematically modeled the serum sodium concentration in humans. Methods We expanded the model to incorporate time, in a “kinetic sodium” equation, and then a term explicitly appears for the rate of sodium correction, a key consideration to avoid treatment complications. The equation is solved for the fluid administration rate to assist the clinician with the hospital order in the management of dysnatremia. Results With baseline data on the input and output rates of Na/K/water along with the patient's body weight, a clinician can use the kinetic equation to aim for a desired [sodium] over a safe timeframe. The formula returns the infusion rate for any treatment fluid, such as normal saline, hypertonic saline, or 5% dextrose in water. The formula can also calculate treatment in terms of the dosage of salt tablets. If an abrupt water diuresis is anticipated, the equation should be entered with the predicted urine [Na+K] and flow rate to avoid overcorrection of hyponatremia. To demonstrate efficacy, we applied the kinetic equation to real-life cases of hypo- and hypernatremia. Conclusions The kinetic equation improves upon existing sodium equations by potentially accounting for all inputs and outputs, if known, and incorporating a rate of correction. The quantitative approach provides a basis for prescribing intravenous fluids and salt tablets.