A physiological model of the effect of hypoglycemia on plasma potassium

Abstract

Background: Adrenaline release and excess insulin during hypoglycemia stimulate the uptake of potassium from the bloodstream, causing low plasma potassium (hypokalemia). Hypokalemia has a profound effect on the heart and is associated with an increased risk of malignant cardiac arrhythmias. It is the aim of this study to develop a physiological model of potassium changes during hypoglycemia to better understand the effect of hypoglycemia on plasma potassium.

Method: Potassium counterregulation to hypokalemia was modeled as a linear function dependent on the absolute potassium level. An insulin-induced uptake of potassium was modeled using a negative exponential function, and an adrenaline-induced uptake of potassium was modeled as a linear function. Functional expressions for the three components were found using published data.

Results: The performance of the model was evaluated by simulating plasma potassium from three published studies. Simulations were done using measured levels of adrenaline and insulin. The mean root mean squared error (RMSE) of simulating plasma potassium from the three studies was 0.09 mmol/liter, and the mean normalized RMSE was 14%. The mean difference between nadirs in simulated and measured potassium was 0.12 mmol/liter.

Conclusions: The presented model simulated plasma potassium with good accuracy in a wide range of clinical settings. The limited number of hypoglycemic episodes in the test set necessitates further tests to substantiate the ability of the model to simulate potassium during hypoglycemia. In conclusion, the model is a good first step toward better understanding of changes in plasma potassium during hypoglycemia.

Figure 1.

Overview of plasma potassium regulation during hypoglycemia. Increased levels of insulin and adrenaline stimulate the influx of potassium. Low plasma potassium triggers the potassium counterregulation to hypoglycemia, causing an increased efflux of potassium.

Figure 2.

Magnitude of hypokalemia counterregulation, f₁, as a function of potassium concentration. R = 0.65 for the fit of f₁.

Figure 3.

Rate of insulin-induced uptake of potassium, f₂, as a function of insulin concentration. R² = 0.81 for the fit of f₂.

Figure 4.

Rate of adrenaline-induced uptake of potassium, f₃, as a function of adrenaline concentration. R² = 0.78 for the fit of f₃.

Figure 5.

Measured serum potassium and simulated plasma potassium following an intravenous injection of insulin (0.1 U/kg) resulting in hypoglycemia (blood glucose <32 mg/dl) 30 minutes after injection. Subjects were given an oral dose of propranolol (160 mg) or placebo before the insulin injection. Data adapted from Petersen and colleagues.¹⁰

Figure 6.

Measured and simulated potassium concentrations from three euglycemic clamps. Data adapted from Robinson and colleagues.⁴

Figure 7.

Measured and simulated potassium concentrations from two hypoglycemic clamps. Data adapted from Robinson and colleagues.⁴

Figure 8.

Measured and simulated potassium levels following an OGTT. Data adapted from Beretta-Piccoli and colleagues.¹⁹