Quantitative assessment of the abnormalities of hyperosmolar coma when glucose excess is larger than Na deficit

Computing Na and water deficits of hyperosmolar coma (HC) is important in correcting the derangement, to avoid unwanted iatrogenic electrolyte derangements and brain oedema. This paper derives and applies formulas valid when GA (glucose accumulation) >2·ΔNa (sodium loss), with or without AV (water depletion). We built a model system and wrote the equations describing the relationships between volume and concentration of solutes within the body water compartments. HC was simulated on computer experiments by adding GA in different amounts combined with a large variety of ANa and AV. The ensuing concentrations in Na (PNa₁) and glucose ( PG₁ ) were used to identify the condition GA > 2· ΔNa, ΔV=0 ≠ 0, and then, with original formulas, to back calculate GA, ANa and AV. These same calculations were applied to 31 patients with HC. The procedure to recognize the conditions under investigation unerringly discarded all simulations except those characterized by GA >2 · ΔNa, with or without AV. When AV=O, the computations yielded values identical to the true ones for GA and ANa (R² = 1.00, p < 0.0001 ). When AV was present, the correlation coefficients between calculated and true values were 0.92 (p<0.001) for GA, 0.73 (p<0.001) for ANa, 0.74 (p<0.001) for AV in computer experiments, while they were R² >0.47 < 0.95 (p< 0.001) in patient studies. The accuracy in computing solute and water changes demonstrates the validity of our model system of HC, and of the calculation formulas, which can be used to quantitatively evaluate the deficits in Na and volume, as well as the addition of glucose, improving the effectiveness of treatment.