Letter to the Editor: “Prevention of Adrenal Crisis: Cortisol Responses to Major Stress Compared to Stress Dose Hydrocortisone Delivery” Free

The modeling component of the multifaceted study by Prete et al raises several questions regarding the use of pharmacokinetic parameters to predict time-dependent variation of cortisol concentrations during cortisol replacement therapy (CRT) (1). Because endogenous cortisol secretion complicates the relationship between rates of hydrocortisone administration and serum cortisol concentrations, including individuals with primary adrenal insufficiency is a welcome innovation. However, clinical applications should proceed cautiously because the authors’ use of the single compartment pharmacokinetic model (2) to predict cortisol concentrations during CRT results in important inaccuracies (3).

To illustrate the concern, they report a total cortisol half-life of 2.57 hours (total cortisol half-life (t_1/2) = ln(2)/k ~0.693/0.27 h^–1 ~2.57 hours), and cortisol concentrations predicted by their model for continuous intravenous infusion (CIV) (as in Fig. 5E and 5F but without superposition of intravenous bolus) indicate that steady state is achieved, as expected, in 5 half-lives (13 hours). Using the reported pharmacokinetic parameters of total cortisol elimination rate constant k = 0.27 h^–1 and total cortisol appearance rate = 224.5 nmol/L/h, the single compartment model predicts a steady-state total cortisol concentration of 831 nM, and 97% of steady-state concentration is attained in 5 half-lives (~13 hours). Yet experimental measurements of cortisol concentrations during CIV tell a different story, reaching steady state within 2 hours (Fig. 3D, Table 2).

The statement “a model should be made as simple as possible, but not simpler” has been attributed to Albert Einstein. We believe that the discordance between measured and predicted cortisol concentrations in the analysis by Prete and colleagues is related to application of a single-compartment model that is “too simple” insofar as it relies only on total cortisol concentrations without acknowledging the existence of corticosteroid-binding globulin (CBG) or distinguishing free and protein-bound cortisol (2). One consequence of using the “too simple” model is that the pharmacokinetic parameters obtained are subject to the confounding influence of CBG, resulting both in error and bias (3-5). By contrast, the 3-compartment model is consistent with known physiology and yields half-life estimates that are shorter than those they report (by greater than an order of magnitude) (3, 6, 7). Applying normative values (6), the 3-compartment model achieves the same steady-state concentration in 1.9 hours, which is consonant with their experimental results during CIV. We suggest that the 3-compartment model is “as simple as possible” and in this case certainly provides a more realistic prediction of dynamic cortisol concentrations during CRT.

Their report also highlights the relevance of steady-state conditions to contemporary CRT (1, 8). The 3-compartment model is expressed as 3 simultaneous, nonlinear differential equations (6), for which steady-state conditions are obtained by setting the derivatives (change in concentrations by time) to zero (7). This steady-state solution yields a simple, linear equation that relates serum free cortisol concentration to rates of free cortisol appearance and elimination (F = Z_C/α, where F is the concentration of free cortisol, Z_C is the [free] cortisol appearance rate [nmol/L/h], and α is the [free] cortisol elimination rate constant [h^–1]). Because these relationships are independent of variation in serum concentrations of CBG and albumin, this equation may provide a more accurate prediction of steady-state (free) cortisol concentrations during continuous cortisol infusion (7).

The most useful models for CRT would accurately predict total and free cortisol concentrations both for dynamic and steady-state conditions. That the current modeling approach by Prete and colleagues overestimates by greater than 6-fold the time to steady-state during CIV underscores its limitations and suggests the potential utility of higher-order models that, at a minimum, account for saturable binding of cortisol to CBG and distinguish the metabolic fate of free vs protein-bound cortisol.

Abbreviations

Abbreviations
 
• CBG

  corticosteroid-binding globulin

 
• CIV

  continuous intravenous infusion

 
• CRT

  cortisol replacement therapy

Acknowledgments

Financial Support: This work was supported by the use of resources and facilities at the New Mexico VA Healthcare System.

Additional Information

Disclosure Statement: The authors have nothing to disclose.

References