Dotted lines depict ICF and ECF volumes at ideal state. Blue and green transparent boxes comparatively illustrate the ICF and ECF, respectively, for the initial, pre-interval, and post-interval states.
The calculator's model primarily uses the Rose equation, which assumes that effective plasma osmolarity = 2 x plasma [Na+].1 In accordance with the relationship described by Edelman et al. (1958),2 the calculator assumes that the serum sodium concentration is proportional to the ratio of total body exchangeable sodium and potassium to total body water: Plasma [Na+] ~= (TB Nae+ + TB Ke+).2 Only the effective solutes exchangeable total body sodium and potassium are included in this model at present. Potassium homeostasis has not yet been comprehensively integrated into version 1.0 of this calculator. Although potassium is overwhelmingly intracellular, any potassium lost in the urine in version 1.0 accounts for a loss of effective extracellular (rather than intracellular) solute that is equivalent to that of any equimolar amount of sodium lost in the urine.
Inclusion/Exclusion Criteria
In order to apply this calculator, the following must be assumed: no hyperglycemia and normal renal function. For version 1.0, the etiology of the hyponatremia is assumed to be SIADH. The chronicity of the initial state is assumed to be chronic hyponatremia (>48 hours).
Ideal State
In a baseline state with a normal tonicity balance and volume status, total body water (L) is assumed to be 60% or 55% of ideal body weight (kg) for cases in which the biological sex is classified as male or female, respectively. This relatively simple approach limits the need for additional case data, though other more complicated estimates of total body water incorporating age and height do exist.3 The ratio of ICF (intracellular fluid) to ECF (extracellular fluid) at baseline is assumed to be 60 : 40.1 Assuming a normal baseline serum sodium of 140 mEq/L, total body osmolarity can be calculated by way of the Rose and Edelman equations described above.
Initial State
Along with the time, an initial serum sodium must be logged by the user. While this allows for a calculation of total body osmolarity (2 x serum sodium), determining the total solute and water within the intra- and extra-cellular fluid compartments is less certain and requires multiple assumptions. Volume status and tonicity balance interact but are independent. In this version 1.0 of the calculator, we assume that the etiology of SIADH; therefore, with natiuresis presumably intact, the ECF is set to be at ideal baseline initially. The volume of the ICF cannot be certain, though in chronic hyponatremia, there is likely some degree of loss of intracellular fluid.4 Similar to what has been demonstrated in animal models,4 we assume that solute loss has occured along with increased TBW for the initial state of hyponatremia such that the increase is half of what it would be if gain in free water alone were the sole contributor. In future versions of this calculator, we hope to allow the user to manually adjust the initial weight (and therefore, modulate the expected initial TBW) and ECF volume status along with permitting additional etiologies of hyponatremia beyond SIADH.
Interval Changes
The net interval change in water and the net interval change in solute (defined as exchangeable total body sodium and potassium, as above) determine the post-interval total body water and total body solute, respectively, from which the new total body osmolarity and predicted post-interval sodium are calculated. Between each interval, the intracellular solute is assumed to remain constant (unlike above-described assumption regarding intracellular solute losses more chronically). Regardless of the precise timing of all effects within an interval period, the post-interval state is assumed to be at equilibrium; in reality, the kinetics of an evolving tonicity balance may be more complex.5
A.I. (Machine Learning)
As of this initial Version 1.0, the integrated machine learning prediction of sodium is still being trained and cannot yet be used to accurately predict post-interval sodium. The current maching learning technology is powered by the ml5.js API, which provides web browser access to TensorFlow.js machine learning models. Current predictive inputs include pre-interval total body water, pre-interval total body solute, interval change in water, and interval change in sodium. The neural network is being trained based on the single output of measured post-interval sodium. The predicted post-interval sodium output from the calculator is independent from the machine learning prediction model.
Future Features
Future versions of this calculator may permit a more complicated determination of the initial state such that the user may select alternative etiologies of hyponatremia and manually adjust the initial total body water (by inputting an updated initial weight) and the clinical volume status (by adjusting the ECF volume). Potassium lost or gained will currently impact total body osmolarity but is considered to be extracellular like sodium; in future versions, potassium homeostasis will be more accurately modeled, including its distribution within the intracellular compartment. Currently, only D5W, NS, and hypertonic (3%) saline are available as therapeutic options; additional options such as half-normal saline, LR, urea packets, potassium, and logging ddAVP administration may be integrated. As mentioned, the machine learning predictions are not yet accurate; further training will likely allow this feature to be better optimized.
References
1. Rose BD, Post TW. Clinical Physiology of Acid-Base and Electrolyte Disorders, 5th ed, McGraw-Hill, New York 2001
2. Edelman et al. Journal of Clinical Investigation. 37:1236-56, 1958
3. Watson PE, Watson ID, Batt RD. American Journal of Clinical Nutrition 1980, 33 (1): 27-39
4. Verbalis JG, Drutarosky MD. Adaptation to chronic hypoosmolality in rats. Kidney International, Vol. 34 (1988), pp. 351—360
5. Peronnet et al. Pharmacokinetic analysis of absorption, distribution and disappearance of ingested water labeled with D2O in humans. Eur J App Physiol. 2012. 112:2213-2222
Baseline Characteristics
Interval Data Table
HYPONATREMIA CALCULATOR
KIDNEYCALC.org
Welcome! This educational tool has been designed to aid in the clinician's understanding of hyponatremia and the associated physiology of water balance disorders.
After setting baseline characteristics and values for the initial state, adjust interval effects to view the predicted changes for each physiologic parameter as well as the predicted post-interval serum sodium based on the calculator's underlying models (see Models in the lower toolbar for details). Visualize the corresponding distribution of water between the intra- and extra-cellular fluid compartments by comparing the fluid compartments models for each state.
This initial version 1.0 of the hyponatremia calculator has not been clinically validated and should therefore not be used for patient care. Please also note that the A.I. feature, which uses machine learning to predict the post-interval sodium, has not yet been adequately trained and is not yet considered to be accurate.