Skip to main content
ENDO 2026 Main banner

Adrenal (Excluding Mineralocorticoids)

MON-500 - Physiologic prediction model for time-varying salivary corticosteroid concentrations using plasma free cortisol and cortisone as input (and back again)

Monday, June 15, 2026
9:00 AM - 2:00 PM CT


Introduction: Prior studies support the measurement of salivary concentrations of cortisone (E_S ) and cortisol (F_S) as a surrogate for plasma free cortisol 〖(F〗_P) and in the clinical diagnosis of adrenal disorders (e.g., adrenal insufficiency and hypercortisolism). Obtaining time-varying concentrations of salivary cortisone (E_S (t)) and cortisol (F_S (t)) as functions (convolution integrals) of input signal (time-varying concentrations of plasma free cortisol (F_P (t)) and cortisone (E_P (t)) predicts that salivary corticosteroid levels are a modified (by an ordered system of gains and delays) version of plasma free corticosteroid levels. We evaluate a physiologic model relating plasma free corticosteroid concentration time series to salivary steroid concentrations (forward solution) and prediction of F_P and E_P from corresponding values of F_S and E_S (inverse solution).

Methods: Differential equations for F_S (t) and E_S (t) in 4x2 salivary compartment model use Fick’s law for flux rates, conservation of mass for 11-HSD2 mediated F->E conversion, and a Michaelis Menten-like function for saturable F->E conversion rate (β^'). Algebraic solutions are obtained using convolution and Volterra integral equations and cubic spline approximation with integration by parts.

Results: Model predictions and parameter solutions are validated by comparison to experimental time series, including simultaneous measurements of E_S,F_S,E_P, and F_P at intervals
(0-480 min) after iv hydrocortisone bolus (20 mg) in healthy humans (n=8). The augmented response of E_S (compared to input E_P) and reduced response of F_S (compared to input F_P) depends in part on Vmax of 11-HSD2 in the salivary intracellular compartment.

Conclusions: Novel convolution integral solution strategies using linear combinations of hypoexponential kernel probability density functions (pdfs) give algebraic solutions to the forward dynamic problem. Inverse prediction of F_P (t) and E_P (t) from measured F_S (t) and E_S (t) is also feasible by algebraic reversal and deconvolution. Numerical procedures, including Volterra integral equation solutions and model-trained AI for parameter estimation (1), are amenable to implementation in a pipeline computational platform. The proposed algebraic solution strategy is (i) complementary and potentially advantageous relative to alternative methods (e.g., numerical integration of differential equations), (ii) adaptable to saturable functions, and (iii) generalizable to many other models of dynamical endocrine systems. The model and corresponding convolution integral solutions constitute mathematical affirmation and reconstruction of the free hormone hypothesis.

Urban FK et al. Computers in Biology & Medicine 2026 doi: 10.1016/j.compbiomed.2025.111379

*Unless otherwise noted, all abstracts presented at ENDO must not be released to the press or the public until the date and time of presentation. For oral presentations, the abstracts are embargoed until the session begins. The Endocrine Society reserves the right to lift the embargo on specific abstracts that are selected for promotion prior to or during ENDO.*