Four-Compartment Diffusion Model of Cortisol Disposition: Comparison With 3 Alternative Models in Current Clinical Use

Abstract

Context: Estimated rates of cortisol elimination and appearance vary according to the model used to obtain them. Generalizability of current models of cortisol disposition in healthy humans is limited.

Objective: Development and validation of a realistic, mechanistic model of cortisol disposition that accounts for the major factors influencing plasma cortisol concentrations in vivo (Model 4), and comparison to previously described models of cortisol disposition in current clinical use (Models 1-3).

Methods: The 4 models were independently applied to cortisol concentration data obtained for the hydrocortisone bolus experiment (20 mg) in 2 clinical groups: healthy volunteers (HVs, n = 6) and corticosteroid binding globulin (CBG)-deficient (n = 2). Model 4 used Fick's first law of diffusion to model free cortisol flux between vascular and extravascular compartments. Pharmacokinetic parameter solutions for Models 1-4 were optimized by numerical methods, and model-specific parameter solutions were compared by repeated measures analysis of variance. Models and respective parameter solutions were compared by mathematical and simulation analyses, and an assessment tool was used to compare performance characteristics of the four models evaluated herein.

Results: Cortisol half-lives differed significantly between models (all P < .001) with significant model-group interaction (P = .02). In comparative analysis, Model 4 solutions yielded significantly reduced free cortisol half-life, improved fit to experimental data (both P < .01), and superior model performance.

Conclusion: The proposed 4-compartment diffusion model (Model 4) is consistent with relevant experimental observations and met the greatest number of empiric validation criteria. Cortisol half-life solutions obtained using Model 4 were generalizable between HV and CBG-deficient groups and bolus and continuous modes of hydrocortisone infusion.

Keywords: albumin; compartmental modeling; computer-assisted; corticosteroid binding globulin (CBG); cortisol; hydrocortisone; metabolic clearance rate; numerical analysis; septic shock.

Figure 1.

Model 4 simulation showing time-varying cortisol concentrations for 20 mg hydrocortisone bolus. (A) Cortisol concentrations as a function of time (0-15 minutes) following IV hydrocortisone bolus (20 mg infused over 20 seconds) in all 4 compartments, including vascular (plasma) free cortisol (X_F, circle symbol, blue), vascular (plasma) albumin-bound cortisol (X_FA, square symbol, orange), vascular (plasma) CBG-bound cortisol (X_FC, diamond symbol, green), and extravascular (free) cortisol (X_Fe, red curve, triangle symbol, red). In this example a unique intersection point, where extravascular and plasma free cortisol concentrations are momentarily equal (X_F = X_Fe) occurred at T* = 8.9 minutes, indicated by dashed vertical line, and at free cortisol concentration of 223 nmol/L (X_F = X_Fe = 223 nmol/L). (B) The same data with axes expanded in cortisol concentration and time (0-120 minutes), symbols as in Panel A. (C) Model 4 predicted concentrations for 2 more commonly measured analytes: plasma free cortisol (X_F, solid line, blue) and plasma total cortisol (X_TotF, dotted line, black), which is the sum of free, albumin-bound, and CBG-bound cortisol concentrations in the vascular (plasma) compartment.

Figure 2.

Model 4 simulation showing time-varying cortisol mass for 20 mg hydrocortisone bolus. (A) Cortisol mass in all 4 compartments as a function of time, symbols and colors are as in Fig. 1. (A) Cortisol mass by compartment for 0 to 15 minutes. (B) The same data with axes expanded to 120 minutes.

Figure 3.

Model 4 simulation for continuous hydrocortisone infusion (8 mg/hour). (A) Model 4 predicted cortisol concentrations as a function of time for continuous infusion of hydrocortisone (8 mg/h) for all 4 compartments, symbols and line format as in Fig. 1. (B) Predicted concentration of vascular (plasma) total (X_TotF, black line) and free (X_F, blue line) cortisol. Steady-state cortisol concentrations (95% of asymptote) are shown by dashed lines. (C) Comparison of predicted plasma free (X_F, blue line) and extravascular (X_Fe, red line) cortisol concentrations as a function of time. The dashed horizontal line indicates the free cortisol concentration at 50% of the asymptotic, steady-state value.

Figure 4.

Simulation of computer-generated cortisol concentrations for 20 mg hydrocortisone bolus obtained using Model 4 for CBG-deficient vs HV groups. (A) Model-predicted plasma free (X_F) and extravascular (X_Fe) cortisol concentrations for HV and CBG-deficient groups. For the CBG-deficient simulation, X_F and X_Fe are indicated as dotted (purple) and dashed (green) lines, respectively. For HV, X_F and X_Fe are indicated by circles (blue line) and triangles (orange line), respectively. Vertical lines indicate times to intersection point postbolus (T*) for HV (intersection (Fe* at 224 nmol/L, black) and CBG-deficient (intersection Fe* at 390 nmol/L, purple). (B) Model-predicted, log-transformed total cortisol concentrations (X_TotF) for HV and CBG-deficient groups and Model 1 half-life solutions (τ₁) for the log-transformed cortisol concentrations (terminal half-life shown in bold).