Pharmacokinetic/Pharmacodynamic Modeling of Dexamethasone Anti-Inflammatory and Immunomodulatory Effects in LPS-Challenged Rats: A Model for Cytokine Release Syndrome

Abstract

Dexamethasone (DEX) is a potent synthetic glucocorticoid used for the treatment of variety of inflammatory and immune-mediated disorders. The RECOVERY clinical trial revealed benefits of DEX therapy in COVID-19 patients. Severe SARS-CoV-2 infection leads to an excessive inflammatory reaction commonly known as a cytokine release syndrome that is associated with activation of the toll like receptor 4 (TLR4) signaling pathway. The possible mechanism of action of DEX in the treatment of COVID-19 is related to its anti-inflammatory activity arising from inhibition of cytokine production but may be also attributed to its influence on immune cell trafficking and turnover. This study, by means of pharmacokinetic/pharmacodynamic modeling, aimed at the comprehensive quantitative assessment of DEX effects in lipopolysaccharide-challenged rats and to describe interrelations among relevant signaling molecules in this animal model of cytokine release syndrome induced by activation of TLR4 pathway. DEX was administered in a range of doses from 0.005 to 2.25 mg·kg⁻¹ in LPS-challenged rats. Serum DEX, corticosterone (CST), tumor necrosis factor α, interleukin-6, and nitric oxide as well as lymphocyte and granulocyte counts in peripheral blood were quantified at different time points. A minimal physiologically based pharmacokinetic/pharmacodynamic (mPBPK/PD) model was proposed characterizing the time courses of plasma DEX and the investigated biomarkers. A high but not complete inhibition of production of inflammatory mediators and CST was produced in vivo by DEX. The mPBPK/PD model, upon translation to humans, may help to optimize DEX therapy in patients with diseases associated with excessive production of inflammatory mediators, such as COVID-19.

SIGNIFICANCE STATEMENT

A mPBPK/PD model was developed to describe concentration-time profiles of plasma DEX, mediators of inflammation, and immune cell trafficking and turnover in LPS-challenged rats. Interrelations among DEX and relevant biomarkers were reflected in the mechanistic model structure. The mPBPK/PD model enabled quantitative assessment of in vivo potency of DEX and, upon translation to humans, may help optimize dosing regimens of DEX for the treatment of immune-related conditions associated with exaggerated immune response.

Introduction

Dexamethasone (DEX) is a synthetic corticosteroid (CS) used in the treatment of many immune-related disorders, such as rheumatoid arthritis, lupus erythematosus, and allergic reactions. It has been shown to be effective in reducing mortality of severely ill COVID-19 patients requiring mechanical ventilation or oxygen therapy (Horby et al., 2021). Severe SARS-CoV-2 infection causes an excessive inflammatory reaction called cytokine release syndrome or cytokine storm that often produces an acute respiratory distress syndrome resulting in a high mortality. It was shown that the toll like receptor 4 (TLR4) signaling pathway is closely associated with pathogenesis of COVID-19 (Sohn et al., 2020; Aboudounya and Heads, 2021; Kaushik et al., 2021; Shirato and Kizaki, 2021; Ma et al., 2022). The signaling cascade triggered upon ligand binding to TLR4 results in the activation of a transcription factor nuclear factor kappa-light-chain-enhancer of activated B cells (NF-κB), which leads to the expression of proinflammatory cytokines and chemokines including tumor necrosis factor α (TNFα) and interleukin-6 (IL-6) (Aboudounya and Heads, 2021). In patients with COVID-19, elevated TNFα and IL-6 serum concentrations were correlated with severity of the disorder and their excessive production was associated with worse prognosis and higher mortality (del Valle et al., 2020).

It is postulated that the mechanism of action of DEX in the treatment of COVID-19 may be attributed to its potent anti-inflammatory effect arising from inhibition of transcription of genes coding proinflammatory signaling molecules, such as TNFα and IL-6 (Andreakos et al., 2021). The anti-inflammatory effects of DEX are related to the genomic mechanism including binding of DEX to glucocorticoid receptors (GR) resulting in their conformation changes, subsequent dissociation from hetero complex, and translocation into the nucleus, where the GR-CS complex regulates expression of genes coding inflammatory mediators by negative regulation of transcription factors, including NF-κB and activator protein 1 (Vandewalle et al., 2018). DEX, compared to other synthetic CS, displays a very high affinity for the GR that is reflected in the single-digit nanomolar IC₅₀ and EC₅₀ values of this drug (Perrin-Wolff et al., 1996; Mager et al., 2003). Beside anti-inflammatory effects, DEX causes changes in immune cell trafficking and turnover by influencing the expression of genes coding adhesion molecules and by impacting proliferation and degradation of immune cells (Shacham and Ishay, 2022). In addition, synthetic glucocorticoids suppress the production of endogenous CS, both in humans and in animals, by inhibiting the hypothalamic-pituitary-adrenal (HPA) axis responsible for regulation of production of cortisol in humans and corticosterone (CST) in rats (Mager et al., 2003; Yao et al., 2008).

The lipopolysaccharide (LPS)-induced model in rats appears useful to investigate the pharmacokinetics (PK) and pharmacodynamics (PD) of DEX in acute inflammation related to excessive production of cytokines and other signaling molecules. LPS-induced systemic inflammation in rats triggered by intraperitoneal (IP) administration of this toxin is a commonly used model of acute respiratory distress syndrome arising from hyperinflammatory reactions (Chen et al., 2010). In this animal model, an excessive production and release of several mediators of inflammation, such as cytokines, interferons, and biomarkers of oxidative stress, are observed. LPS-induced production of inflammatory mediators is triggered upon LPS binding to TLR4 leading to activation of the NF-κB pathway and subsequent expression of genes coding inflammatory mediators including TNFα and IL-6. Therefore, this model may closely mimic some pathophysiological features of severe SARS-CoV-2 infection that is also related to an exaggerated innate immune response via activation of TLR4 signaling cascade (Sohn et al., 2020; Aboudounya and Heads, 2021; Shirato and Kizaki, 2021).

Our study monitored the time courses of plasma DEX, CST, TNFα, IL-6, and nitric oxide (NO) in LPS-challenged rats treated with an array of DEX doses ranging from 0.005 to 2.25 mg·kg⁻¹. A complex but minimal physiologically based pharmacokinetic/pharmacodynamic (mPBPK/PD) model was sought that describes the interrelations among DEX, CST, and the signaling molecules (i.e., TNFα, IL-6, and NO). In addition, simpler PK/PD models were enacted to describe the concentration-effect relationship between DEX and each of the inflammatory mediators. Further, a mPBPK/PD model was proposed that explains changes in the numbers of lymphocytes and granulocytes in blood in LPS-challenged rats and the influence of LPS and DEX on plasma CST concentrations.

Materials and Methods

Chemicals and Reagents

The DEX sodium phosphate solution for injection was obtained from VetOne (Boise, ID). The LPS lyophilized powder from E. coli (serotype O111:B4, LOT #12181202), DEX (≥99% purity), and CST (≥98.5% purity) standards were purchased from Sigma-Aldrich (St. Louis, MO). Deuterated DEX (D5-DEX) and CST (D8-CST) were from Toronto Research Chemicals Inc. (Toronto, Canada). Liquid chromatography tandem-mass spectrometry (LC-MS/MS)–grade methanol, acetonitrile, formic acid, and phosphoric acid were purchased from Fisher Scientific (Pittsburgh, PA). Water obtained from a Milli-Q IQ Water Purification System was used (Millipore Corporation, Bedford, MA). All other reagents and solvents were of analytical or LC-MS/MS grade and were obtained from standard commercial providers.

Animals

Male Wistar rats weighing 300 ±20 g were obtained from Envigo (Indianapolis, IN). The animals were acclimatized in a room at constant temperature and light-dark cycle (12/12 hours) for 7 days prior to the study and were given free access to water and food. All experiments were performed in accordance with the Principles of Laboratory Animal Care (National Institutes of Health publication 85-23, revised 1985) and were approved by the University at Buffalo Institutional Animal Care and Use Committee (protocol number PROTO202100008).

Pharmacokinetic Study

The LPS as a lyophilized powder was mixed with saline for injection to yield a concentration of 2.5 mg·mL⁻¹. The mixture was sonicated for a total of 20 minutes to ensure dissolution and then administered within 30 minutes. The LPS solution was injected intraperitoneally to give a dose of 5 mg·kg⁻¹. The DEX for injection was diluted with saline and the solution with appropriate concentration was injected subcutaneously within 30 minutes after preparation at a volume of 1 mL·kg⁻¹ to give the desired doses.

The rats were randomly divided into three groups (n = 6–8). The experiments started at 8 am (time 0) that was the onset of the light cycle. All rats received DEX subcutaneous (SC) injection at the base of the neck at one of three doses (0.005, 0.225, or 2.25 mg·kg⁻¹), and, 0.5 hour later, they were challenged with LPS at an IP dose of 5 mg·kg⁻¹. Blood samples were collected from the tail artery at several time points post-DEX dosing (0.25, 0.5, 1, 2, 4, 6, 8, 12, 24, and 34 hours) into EDTA-coated tubes. Rats were terminated at 48 hours by exsanguination via the abdominal aorta under isoflurane anesthesia. Up to five blood samples were taken from each rat to limit the maximum blood volume collection to 1.5 mL and a final blood sample was taken at the time of termination. All samples were centrifuged for 10 minutes at 2000 g and 4°C. Plasma samples were kept frozen at –20°C until analysis.

Pharmacodynamic Study

The experiments started at 8 am (time 0) that was the onset of the light cycle. Rats divided into eight groups (n = 6–8) were given DEX at doses of 0.005, 0.008, 0.025, 0.075, 0.225, 0.675, or 2.25 mg·kg⁻¹, or saline in the case of the control group. After 30 minutes, animals were given LPS at an IP dose of 5 mg·kg⁻¹. Two additional groups were given DEX at doses of 0.225 or 2.25 mg·kg⁻¹ and saline for injections IP instead of LPS. Blood samples were collected at 0.25, 0.5, 1, 2, 4, 6, 8, 12, 24, and 34 hours post-LPS dosing via the tail artery. The final blood sample was collected at the time of termination. Rats were terminated at 24 or 48 hours. Up to five blood samples were taken from each rat to limit the maximum blood volume collection to 1.5 ml. Twenty µL of the blood samples were used for hematology analysis, and the remaining blood was handled as described previously.

Analytical Methods

Concentrations of TNFα and IL-6 in plasma were quantified using a Rat TNFα Quantikine ELISA Kit and a Rat IL-6 Quantikine ELISA Kit (R&D Systems, Minneapolis, MN) according to the protocols provided by the manufacturer. Plasma nitrite concentrations were measured using a Non-Enzymatic Nitric Oxide Assay Kit obtained from Oxford Biomedical Research (Rochester Hills, MI). In aqueous solutions, NO converts to nitrate and nitrite. The Non-Enzymatic Nitric Oxide Assay Kit utilizes cadmium for quantitative reduction of nitrate to nitrite and subsequently uses the Griess reagent to quantify nitrite. It is assumed that 1 µM nitrite is equivalent to 1 µM NO in an analyzed plasma sample. Plate readings for ELISA analyses and NO assay were performed using a SpectraMax i3 Multi-Mode Microplate Reader (Molecular Devices, LLC, San Jose, CA).

Lymphocyte and granulocyte counts in blood were quantified using a BC-2800Vet Auto Hematology Analyzer (Mindray, Shenzhen, Guangdong, China).

Plasma concentrations of DEX and CST were quantified simultaneously by an LC-MS/MS method developed, described, and validated earlier with some modifications (Li et al., 2017). Stock solutions of all compounds were prepared in methanol at a concentration of 1 mg·mL⁻¹. Working solutions were prepared by dilution of the standard solutions in acetonitrile/water 1:1 (v/v). Charcoal-stripped plasma was used for preparation of standard curves and quality control (QC) samples. In brief, 100 µl of 4% phosphoric acid aqueous solution was added to 100 µl of analyzed plasma spiked with 10 µl of IS solution containing D5-DEX and D8-CST. The samples were vortexed for 1 minute at room temperature and centrifuged at 13,000 g for 10 minutes at 10°C. Then 190 µl of supernatants was subjected to solid-phase extraction using Oasis HLB 30 mg 1 cm³ cartridges (Waters Corp., Milford, MA) and a Vac Elut SPS24 solid-phase extraction manifold (Varian, Palo Alto, CA). After loading the sample, the cartridges were washed with water containing 5% (v/v) methanol and subsequently eluted with pure methanol. The methanol fraction was transferred to glass tubes and dried under a gentle nitrogen flow. The dried residue was reconstituted with 200 µl of acetonitrile/water 1:1 (v/v). Ten μL of a sample was subjected to LC-MS/MS analysis using an Exion LC AC HPLC system (Danaher Corporation, Framingham, MA) coupled with a SciEx QTRAP 6500 triple-quadrupole MS (Danaher Corporation). The mobile phase consisted of eluent A composed of acetonitrile/water 5:95 (v/v) containing 0.1% formic acid and the eluent B composed of acetonitrile/water 95:5 (v/v) containing 0.1% formic acid. The oven temperature was set at 35°C. Chromatographic separation was performed using an XTerra MS C18 (2.1 × 100 mm, 5 μm) column (Waters, Ireland). The mobile phase was pumped at a flow rate of 0.2 mL·min⁻¹ in a gradient elution mode. After injection, the percentage of eluent B was increased linearly for 2 minutes from 25% to 35%, then maintained at 35% during 3.5 minutes, increased rapidly to 95% during 0.1 minute, maintained at 95% for 2.4 minutes, decreased linearly to 25% for 0.1 minute, and maintained at 25% until the end of analysis resulting in the total run time of 12 minutes. All detections were performed in a positive ion mode using a multiple reaction monitoring (MRM) scan mode. MRM is a highly specific and sensitive technique for quantifying compounds. Transitions from precursor ions to product ions (precursor (m/z)) →product (m/z)) were selected and the mass spectrometer parameters for each compound were optimized. The MRM transition for DEX was 393.3→373.3, for D5-DEX it was 398.5→378.6, for CST it was 347.4→329.3, and for D8-CST it was 355.4→337.4. The declustering potential was set at 5 V, the entrance potential at 10 V, and the cell exit potential at 10 V for all analytes. The collision energy was set at 15 V for DEX and D5-DEX and 22 V for CST and D8-CST. Data acquisition and processing were carried out using the Analyst 1.4 software. The calibration curves were constructed by plotting the ratio of the peak area of the studied compounds to the peak area of the corresponding IS versus the concentration of the compound and generated by weighted (1/y) nonlinear regression analysis using a quadratic formula. The validated quantitation ranges were from 0.2 to 3000 ng·mL⁻¹ for DEX and from 1 to 1000 ng·mL⁻¹ for CST. The QC samples had concentrations of 1000, 100, and 5 ng·mL⁻¹ for DEX and 500, 50, and 5 ng·mL⁻¹ for CST. The accuracy of samples was within 15% deviation from the nominal values, and precision was within 15% relative standard deviation.

Pharmacokinetics

Plasma concentration-time profiles of DEX in LPS-treated rats were described using a mPBPK model developed previously (Song and Jusko, 2021). The model schematic is presented in Fig. 1.

Fig. 1.

Schematic representation of the mPBPK of DEX in LPS-challenged rats. The model was described previously, and part of the figure was reprinted from Song and Jusko (2021) with permission from Wiley. The symbols are defined in Table 1 and in the text.

The differential equations for the model are:

where D is the SC dose of DEX, A_SC is the amount at the absorption site, k_a is the first-order absorption rate constant, F is the bioavailability after SC injection, C_p is the DEX plasma concentration, C_t1 is the concentration in the first tissue compartment (V_t1), C_t2 is the concentration in the second tissue compartment (V_t2), Q_CO is cardiac blood flow, f_d1 and f_d2 are the fractions of Q_CO accessing V_t1 and V_t2, K_p is the tissue to plasma partition coefficient, R_b is the blood to plasma ratio, V_blood is blood volume, and CL is the systemic plasma clearance. The tissue volume fractions for the compartments (F_t) were related to body weight (BW) assuming 1 g·mL⁻¹ tissue density.

The Q_CO in rats was calculated based on the allometric equation (Brown et al., 1997):

mPBPK/PD Modeling

A complex mPBPK/PD model of anti-inflammatory effects of DEX in LPS-challenged rats was developed that describes TNFα, IL-6, and NO dynamics and interplay among these biomarkers. The model is composed of several simple components accounting for turnover of separate biomarkers that were described in previous publications. The model schematic is presented in Fig. 2. The proposed model is composed of the mPBPK model of DEX (Song and Jusko, 2021). The next part of the mPBPK/PD model is a submodel of TNFα dynamics accounting for LPS-induced production of this cytokine that is composed of central and peripheral compartments for TNFα. A similar model of TNFα dynamics upon LPS challenge was enacted previously (Held et al., 2019). The next submodel accounts for NO disposition and dynamics (Sukumaran et al., 2012). The last part accounts for IL-6 dynamics as a simple indirect response model (Dayneka et al., 1993). The original submodels were modified to account for interrelations between TNFα and NO or IL-6 and influence of DEX on TNFα production.

Fig. 2.

Schematic of the proposed mPBPK/PD model of DEX anti-inflammatory effects in LPS-challenged rats. It consists of a mPBPK model of DEX and extended indirect response models describing TNFα, IL-6, and NO turnover. The symbols are defined in the text and in Tables 2, 3, and 4.

TNFα Dynamics

The LPS-triggered signaling cascade leading to the production and release of TNFα was reflected in a series of transit steps:

where LPS₁ is the signal representing relative quantity of LPS at the administration site. The LPS₁ is transduced through a cascade of transit compartments (LPS₁ – LPS₁₁) where k_tLPS represents the first-order transit rate constant of LPS between the transit steps and the removal rate constant of LPS₁₁ from the last transit compartment. Eventually, LPS₁₁ serves as a driving force for the stimulation of TNFα production. The initial condition of all differential equations in the series was set at 0, and, in the case of the starting equation, it was set at 10 at 0.5 hour that accounts for the IP LPS injection 30 minutes after DEX administration. The number of transit steps (11) was chosen based on trial-and-error method. The trial-and-error optimization was performed during model building by testing various numbers of transit compartments and comparing goodness-of-fit criteria of the tested models. The model with the lowest Akaike information criterion (AIC) value was selected. Concentration-time profiles of plasma TNFα in rats given DEX or saline and subsequently challenged with LPS were described using a modified indirect response model:

where TNF_c and TNF_p represent the concentration of this cytokine in the central (plasma) and peripheral compartments. A bi-exponential post-peak decline in plasma TNFα, which was also observed previously (Pang et al., 1991; Held et al., 2019) and is evident in this study when plotting the concentration-time data of plasma TNFα on a semi-log scale, was captured by implementing k_tTNF as the first-order transfer rate constant between central and peripheral compartments. Baseline concentrations of TNFα in rat plasma were undetectable using the ELISA kit (lower limit of quantification = 12.5 pg·mL⁻¹). Therefore, it was assumed that TNFα production in healthy rats is negligible and TNFα is produced and released into blood in response to LPS dosing. Thus, the initial conditions of the differential equations representing TNFα concentrations in the central and peripheral compartments (Eq. 12 and 13) were set at 0. Proinflammatory substances, such as LPS, can induce TNFα expression and stimulate the release of soluble TNFα from immune cells. On the other hand, it is well known that DEX inhibits expression and production of proinflammatory cytokines, such as TNFα (Rowland et al., 1998). Therefore, the model assumes LPS-triggered formation of TNFα with the linear stimulatory coefficient S_LPSonTNF and inhibition of the production of TNFα by DEX with the maximum inhibitory potency I_maxDEX and IC_50DEX being the DEX plasma concentration producing 50% of I_maxDEX. TNFα is eliminated from the plasma with the first-order rate constant k_outTNF.

IL-6 Dynamics

Plasma concentration-time profiles of IL-6 in rats challenged with LPS and treated with DEX at various dose levels were described using an indirect response model as follows:

where IL6 is the plasma IL-6 concentration and k_outIL6 is the first-order degradation rate constant. It is assumed that the production of IL-6 is stimulated by TNFα (TNF_c) and S_TNFonIL6 is the linear stimulatory coefficient of TNFα-mediated IL-6 production. As the baseline plasma IL-6 concentrations in normal rats were undetectable using the ELISA kit (lower limit of quantification = 62.5 pg·mL⁻¹), it was assumed that IL-6 production in healthy rats is negligible. Therefore, the initial condition of Eq. 14 was set at 0. TNFα-mediated production of IL-6 is a commonly known phenomenon (Ghezzi et al., 2000). This mechanism of IL-6 production was successfully applied in a PD model of baicalein effects in LPS-stimulated RAW264.7 macrophages (Xiang et al., 2018).

NO Dynamics

The NO disposition and dynamics in rats was described using a model composed of central and peripheral compartments as described previously (Sukumaran et al., 2012) and was implemented in this study with some modifications. The equations describing the PD model of NO dynamics in LPS-challenged rats are:

where NO_c and NO_p are the amounts of NO in the central and peripheral compartments. CL_NO and CL_dNO are the systemic and distribution clearances, V_cNO and V_pNO are the central and peripheral volumes of distribution, and S_TNFonNO is the stimulatory coefficient of TNFα-mediated NO production. An assumption of TNFα-induced production of NO in LPS-treated rodents was successfully applied previously (Chakraborty et al., 2005; Hu et al., 2019). In our model, the production of NO is stimulated by TNF₃ that is the signal from the third step in the transit cascade accounting for a multistep process of NO production triggered by TNFα:

where k_TNF serves as the first-order transit rate constant of TNFα between the transit compartments (TNF₁ – TNF₃) and elimination rate constant of TNF₃ from the third compartment. This signaling cascade may be related to a multistep process of TNFα-induced expression of inducible nitric oxide synthase (iNOS) being the main NO-producing enzyme during inflammation. The number of transit steps was selected based on the trial-and-error optimization as described previously. The model with the lowest AIC value was chosen. The baseline concentration of NO (C_0NO) in the central compartment was set at 22 µM (measured mean value of plasma NO in healthy rats) and R_0cNO and R_0pNO as the baseline amounts of NO in the central and peripheral compartments, were calculated as: R_0cNO = C_0NO · V_cNO and R_0pNO = C_0NO · V_pNO assuming that the steady-state NO concentrations are equal in these compartments.

Corticosterone Dynamics

The endogenous glucocorticoid produced in rats by the adrenal cortex is CST. Its production is regulated by the HPA axis that is activated by light. Therefore, endogenous glucocorticoids undergo a circadian rhythm resulting in different CST plasma concentrations depending on the time of day (Fonken and Nelson, 2014). CST is the main CS stress hormone in rodents. It was shown that, under stress conditions, such as LPS administration, trauma, or severe infection, the HPA axis is activated, leading to increased production of cortisol in humans or CST in rodents (Givalois et al., 1994). Fig. 3 shows a schematic of the proposed mPBPK/PD model of DEX influence on CST dynamics and immune cell trafficking and turnover in LPS-challenged rats. In the proposed mPBPK/PD model, LPS is one of the factors influencing CST dynamics as well as immune cell trafficking and turnover. The function accounting for the LPS-triggered immunomodulatory activity is:

Fig. 3.

Proposed mPBPK/PD model of DEX effects on CST dynamics and immune cell trafficking and turnover in LPS-challenged rats. The mPBPK model of DEX controls an extended indirect response model for CST turnover, a modified indirect response model describing lymphocyte trafficking, and a transit model combined with an indirect response model for granulocyte turnover. The symbols are defined in the text and in Tables 5, 6, and 7.

where A_LPS is the relative quantity of signal representing LPS-triggered activity with elimination as the first-order rate constant k_eLPS. The initial condition of Eq. 20 was set at 0, and it was set at an arbitrary value of 10 at 0.5 hour post-DEX injection. The A_LPS serves as a driving force for the stimulation of CST production and stimulation of lymphocyte degradation in the subsequent parts of the model.

The CST input function (R_CST (t)) in normal rats was described by a two-harmonic function:

where A₁, A₂, B₁, and B₂ are the Fourier coefficients representing the frequency of the harmonic functions. The circadian rhythm period T is 24 hours. Parameters reported previously were used for simulations of CST dynamics in normal (healthy) rats (Yao et al., 2008). In normal rats, CST turnover was described as:

where C_CST is the plasma CST concentration and k_inH (t) represents stress-induced CST production as described by:

where S_H is the maximum stress-induced CST production and k_H is its disappearance rate constant, IC_50DEX1 is the DEX concentration in plasma causing 50% of maximum inhibition (I_maxDEX1) of CST production in normal rats, and k_outCST is the first-order degradation rate constant of CST.

In contrast, it was assumed that, upon LPS stimulation, the physiologic circadian rhythm governing the CST production in rats is disturbed, and CST turnover was described:

where IC_50DEX2 is the DEX plasma concentration causing 50% of maximum inhibition (I_maxDEX2) of CST production in LPS-challenged rats. The initial conditions of Eq. 22 and 24 were set at the baseline plasma CST concentration (C_CSTb) of 33.59 ng·mL⁻¹ measured at 8 am (start of the light cycle) according to (Yao et al., 2008). It is assumed that, in normal rats, CST production is governed by a circadian rhythm described by the R_CST (t) variable. On the other hand, in LPS-treated rats, the circadian rhythm is disturbed and the production of CST is governed by the zero-order rate constant k_inCST, the stimulatory coefficient, S_LPS,CST, and the relative quantity of LPS, A_LPS, serving as a driving force for CST production. As a consequence, in diseased animals, a new steady-state with a higher baseline CST concentration is achieved. The k_inH (t) variable was implemented in both models, and it reflects stress-induced production of CST resulting from handling of the rats, SC DEX dosing, or SC saline injection.

Lymphocyte Dynamics

Glucocorticoids influence trafficking of lymphocytes in normal rats, and, in addition, LPS challenge causes a drop in the number of lymphocytes in blood (Lowell and Berton, 1998; Fasanmade and Jusko, 1999). In the present mPBPK/PD model, similarly as in previous work (Yao et al., 2008), it is assumed that lymphocyte trafficking between blood and lymphatic tissues is regulated by CS, including both exogenous DEX and endogenously produced CST. The proposed model of lymphocyte dynamics in LPS-challenged rats is described by:

Movement of lymphocytes between blood (LYM_B) and tissues (LYM_T) is governed by the first-order rate constants k_inL (from tissues to blood) and k_outL (from blood to tissues). The second-order rate constant, k_degL, represents the loss of lymphocytes from blood due to the inflammatory state induced by LPS that may be related to apoptotic cell death of lymphocytes (Norimatsu et al., 1995). The C_TE represents the total effective steroid concentration, and IC_50L,DEX and IC_50L,CST are the plasma concentrations of DEX and CST causing 50% of maximum inhibition of lymphocyte trafficking from tissues to blood (I_maxL,DEX). It was assumed that k_inL is 50 times lower than k_outL and the volumes of blood and lymphatic tissue compartments are the same. In consequence, at steady-state (without influence of CS and LPS), the quantity of lymphocytes in the blood equals approximately 2% of the total lymphocyte number in the rat in line with the literature (Caldwell and Lacombe, 2000). The initial condition of lymphocytes in blood, LYM_Bb, was set at the measured value of 9.7·10³ cells·µL⁻¹ and, for lymphocytes in tissues, LYM_Tb was set at the calculated (50 times higher) value of 485.0·10³ cells·µL⁻¹. It was assumed that, throughout the experimental period of 48.5 hours, the lymphocyte counts in the blood are not substantially affected by the production of these cells. The first-order rate constant k_eLPS representing the dissipation of the LPS stimulating signal (A_LPS) was estimated separately for this part of the model, and, therefore, it is different from the value estimated for stimulation of CST production.

Granulocyte Dynamics

The simultaneous influence of DEX and LPS on the time courses of the granulocyte counts in rat blood was modeled by an indirect response model combined with a transit model reflecting extended time for release and movement of granulocytes from the extravascular pool into blood. Neutrophils are the dominant fraction of granulocytes in rat blood (90%) while basophils and eosinophils constitute the remaining 10%. Therefore, while designing the model of granulocyte dynamics, we assumed that the changes in the numbers of peripheral granulocytes mainly result from the changes in the numbers of neutrophils. Despite the fact that eosinophils and basophils also contribute to the changes in numbers of granulocytes, we were not able to account for their contributions as the analytical method did not allow for differentiation of subpopulations of granulocytes. It was shown that, in response to an infection, the bone marrow releases an increased number of neutrophils (Ma et al., 2021). A significant increase in peripheral neutrophils in response to LPS challenge was observed in previous studies (Kitajima et al., 1995), and it could be due to either mobilization of mature neutrophils from lymphoid tissues (Territo and Golde, 1976) or increased proliferation of neutrophil precursor cells in bone marrow (Quesenberry et al., 1975). Given the uncertainty, we assumed that LPS stimulates the production of granulocyte precursor cells. In addition, it has been shown that CS promote maturation and release of neutrophils from bone marrow (Cavalcanti et al., 2007); therefore, in the mPBPK/PD model, it was assumed that the exogenous CS DEX stimulates the production of granulocytes. The model is composed as follows:

where GRA₀, GRA₁, and GRA₂ are the quantities of granulocyte precursors in the subsequent transit compartments and GRA₃ is the absolute granulocyte count in the rat blood. k_inG is the zero-order rate constant of granulocyte precursor production that may be attributed to maturation of granulocyte precursor cells and their release from bone marrow, 1/k_outG is the transit time of granulocyte precursors between transit compartments, and, in addition, k_outG serves as the first-order rate constant of granulocyte loss from blood. Initial conditions of the model equations were set at value of 2.0·10³ cells·µL⁻¹, which is the baseline granulocyte count in the blood of healthy rats (GRA_b) measured in this study. It was assumed that LPS induces production of granulocyte precursor cells with the stimulatory coefficient S_G,LPS and DEX stimulates production of granulocyte precursors with the maximum stimulation of S_maxG,DEX and SC_50G,DEX being the DEX plasma concentration resulting in 50% of S_maxG,DEX. The LPS is a square wave input function accounting for IP administration of LPS at 0.5 hour post-DEX dosing that takes a value of 0 for t <0.5 hour and 1 at t ≥ 0.5 hour.

Separate Modeling of TNFα, IL-6, and NO Dynamics

In addition to the more complex mPBPK/PD model presented in Fig. 2, simple mPBPK/PD models were tested assuming direct inhibition of production of inflammatory mediators (plasma TNFα, IL-6, and NO) by DEX. This approach assumes that DEX displays direct inhibitory activity on production of the inflammatory mediators and there are no interrelationships among TNFα, IL-6, and NO. The model schematics, equations, and assumptions are presented in the Supplemental Materials.

Data Analysis

Parameter Estimation and Calculations

Minimal PBPK and mPBPK/PD model fittings were performed by nonlinear regression using the maximum likelihood algorithm and a naïve-pooled approach in ADAPT 5 (University of Southern California, Los Angeles, CA). The mPBPK model parameters of DEX were obtained by simultaneous fitting of the model to the DEX concentration-time data for all dose levels, and a one set of mPBPK model parameters was obtained. The mPBPK model parameters were fixed during the fitting procedure of mPBPK/PD models. The complex mPBPK/PD model (Fig. 2) was simultaneously fitted to all concentration-time profiles of plasma TNFα, IL-6, and NO at all dose levels of DEX. As a result, one set of PD parameters was obtained in one run of the model. In addition, the simple models of TNFα, IL-6, and NO dynamics (Supplemental Fig. 1) were fitted to the concentration-time profiles for each biomarker separately but utilizing all DEX dose levels. Therefore, using this approach, one set of PD parameters was obtained for each of these biomarkers (Supplemental Table 1). The ADAPT model code is provided in the Supplemental Materials. In the mPBPK/PD modeling of plasma CST, granulocyte, and lymphocyte dynamics, plasma concentration-time profiles for CST were fitted and the estimated PD parameters for CST were fixed while fitting the quantity-time profiles of lymphocytes and granulocytes. As a result, one set of PD parameters was obtained for each biomarker (CST, granulocytes, and lymphocytes). The residual variance model used was the additive and proportional error model:

where V_i is the variance of DEX plasma concentration or biomarker quantity at the i^th time point (t_i), Y_i(t_i) is the model prediction at the i^th time point, and Intercept and Sigma are additive and proportional errors. The goodness-of-fit of the tested models was assessed taking into consideration visual inspection of model fitting, the AIC values, the CV% of the estimated parameters, and parsimony. All area under the concentration-time curve (AUC) and area under the effect-time curve (AUEC) values were calculated using the trapezoidal rule. The maximum concentration (C_max) and the time of C_max (t_max) values were obtained directly from the model predictions.

Regression Analysis

To assess the relationship between IL-6 or NO and TNFα, an orthogonal regression analysis of relative AUEC of the measured biomarkers was performed using STATGRAPHICS Centurion v. 18. (Statgraphics Technologies, Inc., Plains, VA) software. The AUEC_DEX(NO), AUEC_DEX(IL6), and AUEC_DEX(TNF) are the AUECs for NO, IL-6, and TNFα calculated from time 0 to the last quantifiable concentration based on the mean plasma concentrations of NO, IL-6, and TNFα at each time point in rats given LPS and treated with DEX at different dose levels (0.005, 0.008, 0.025, 0.225, and 0.675 mg·kg⁻¹). The AUEC_Control(NO), AUEC_Control(IL6), and AUEC_Control(TNF) are the plasma AUECs of each biomarker after LPS without DEX treatment (saline control group) calculated similarly. Relative exposures of the biomarkers were calculated as a ratio of the AUEC after DEX treatment (AUEC_DEX) to the AUEC after saline (AUEC_Control) in LPS-challenged rats. Therefore, the control-normalized values of exposure (AUEC_DEX/AUEC_Control) can range from 0 to 1. Relative exposures of 1 were included in the analysis to relate to maximum exposures of NO, IL-6, and TNFα.

Results

Pharmacokinetics

A minimal PBPK model was used to describe concentration-time profiles of plasma DEX after its SC dosing in LPS-challenged rats. The fitting of the mPBPK model to the experimental data are shown in Fig. 4. As it can be seen, the mPBPK model accurately captured the plasma concentration-time profiles of DEX given the three SC doses in LPS-challenged rats. The mPBPK model parameter estimates of DEX and the corresponding CV% values are listed in Table 1. The K_P value estimated here is similar to our previous value (Song and Jusko, 2021) based on the mPBPK model of DEX integrated with allometric scaling. There it was 1.07 across 11 species. In this study, the k_a value was around 1.5 hour⁻¹ indicating relatively rapid absorption of the drug from the SC space, close to the value reported of 1.87 hour⁻¹ (Song et al., 2020). This value was lower than a reported k_a of 2.9 hour⁻¹ after intramuscular injection of DEX in rats (Samtani and Jusko, 2005). The systemic plasma clearance of DEX was 0.195 L·h⁻¹·kg⁻¹, similar to values reported in healthy rats ranging from 0.18 to 0.23 L·h⁻¹·kg⁻¹ (Song and Jusko, 2021). This parameter in healthy Wistar rats was 0.198 L·h⁻¹·kg⁻¹ (Song et al., 2020). These observations indicate that there is no substantial influence of the inflammatory state triggered by LPS on the metabolism and elimination of DEX.

Fig. 4.

Time courses of plasma DEX concentrations in LPS-challenged rats given DEX at three indicated dose levels. Symbols are measured concentrations and lines represent mPBPK model fittings.

TABLE 1.

Minimal PBPK model parameter estimates, corresponding CV% values, and the values of fixed parameters for the pharmacokinetics of DEX.

Parameter	Definition	Estimate (CV% or reference source)
Kp	Tissue to plasma partition coefficient	0.925	(5.2)
ka (h−1)	Absorption rate constant	1.462	(17.3)
fd1	Fraction of QCO for tissue 1	0.85a	(Song and Jusko, 2021)
fd2	Fraction of QCO for tissue 2	0.15a	(Song and Jusko, 2021)
Ft	Fraction of total tissue volume for tissue 1	0.26a	(Song and Jusko, 2021)
F	Bioavailability after IM dosing	0.86a	(Samtani and Jusko, 2005)
Rb	Blood to plasma ratio	0.725a	(Song et al., 2020)
CL (L·h−1·kg−1)	Systemic plasma clearance	0.195	(4.0)
Residual variability
Sigma	Proportional error	0.28	(10.2)
Intercept (ng·mL−1)	Additive error	0.2b	(fixed)

^a Fixed based on literature data.

^b Fixed at lower limit of quantification.

Regression Analysis

To evaluate the relationships between TNFα exposures and IL-6 or NO exposures at different dose levels of DEX in LPS-challenged rats, a regression analysis was performed. The results of the regression analysis are shown in Fig. 5. Significant (P < 0.05) linear correlations were found between the natural logarithms of AUEC_DEX/AUEC_Control and AUEC_DEX(TNF)/AUEC_Control(TNF) for both IL-6 and NO. Coefficient of determination (R²) values indicate that around 74% and 89% of variance in the relative exposures of NO and IL-6 can be explained by the relative exposure of TNFα.

Fig. 5.

Correlations between relative exposures of NO or IL-6 (AUEC_DEX(NO)/AUEC_Control(NO) or AUEC_DEX(IL6)/AUEC_Control(IL6)) and TNFα (AUEC_DEX(TNF)/AUEC_Control(TNF)). Graphs demonstrate positive correlations between log-transformed relative exposures of NO or IL-6 and TNFα. Symbols are calculated values of relative exposures for each biomarker and lines depict orthogonal regression fittings.

PK/PD Modeling

TNFα Dynamics

TNFα is a key proinflammatory cytokine and a potent mediator of inflammation engaged in the pathogenesis of a variety of immune-related disorders including sepsis, autoimmune diseases, as well as COVID-19 (Baugh and Bucala, 2001; Vieira et al., 2021). In LPS-induced inflammation, TNFα is the first cytokine that is released into blood within the first 2 hours post-LPS challenge. Plasma concentration-time profiles of TNFα at various doses of DEX in LPS-challenged rats as well as mPBPK/PD model fittings are presented in Fig. 6. As it can be seen, the model captured the experimental data quite well. According to model fittings, the t_max of plasma TNFα was around 1.4 hours post-LPS dosing, which is in line with previous reports involving LPS-induced inflammation in rats (Held et al., 2019; Somann et al., 2019). The mPBPK/PD model parameter estimates for TNFα dynamics along with corresponding CVs% are presented in Table 2. The half-life of TNFα calculated as ln2/k_outTNF is 26 minutes. This is somewhat higher than an 8-minute value reported for intravenous (IV) LPS-challenged rats (Larsson et al., 2021). The intercompartmental transit rate constant of TNFα was lower compared to a previous value of 0.419 hour⁻¹ found after IV LPS dosing in Sprague–Dawley rats (Held et al., 2019). The I_max value of TNFα inhibition was around 80%, close to a reported value for DEX (Waage, 1987).

Fig. 6.

Time courses of TNFα plasma concentrations in LPS-treated rats given DEX or saline as indicated. Symbols are observed values and lines are mPBPK/PD model fittings.

TABLE 2.

Final mPBPK/PD model estimates for DEX effects on TNFα dynamics and their CVs%

Parameter (Units)	Definition	Estimate (CV%)
ktLPS (h−1)	Transit and removal rate constant of LPS	9.375 (2.6)
koutTNF (h−1)	Elimination rate constant of TNFα from plasma	1.621 (6.9)
IC50DEX (ng·mL−1)	DEX plasma concentration producing 50% of ImaxDEX	3.521 (19.0)
ImaxDEX	Maximum inhibition of TNFα production by DEX	0.8051 (2.2)
SLPSonTNF (pg·mL−1·h−1)	Stimulatory coefficient of TNFα production by LPS	17040 (13.5)
ktTNF (h−1)	Transfer rate constant of TNFα between compartments	0.1153 (11.6)
Residual variability
Sigma	Proportional error	0.8636 (11.3)
Intercept (pg·mL−1)	Additive error	12.5a (fixed)

^a Fixed at the lower limit of quantification.

IL-6 Dynamics

IL-6 plays an important role in the pathogenesis of immune-mediated diseases by the stimulation of acute phase responses and regulation of immune reactions. Therefore, anti-IL-6 receptor therapy was developed and used in the treatment of immune-related diseases, such as rheumatoid arthritis or cytokine release syndrome (Tanaka et al., 2014). Results of a clinical trial showed that serum IL-6 concentrations were higher in nonsurvivors compared with survivors from COVID-19 (del Valle et al., 2020). In addition, tocilizumab, an IL-6 receptor blocker, is recommended in treatment of COVID-19 (Liu et al., 2020). As it can be seen in Fig. 7, the proposed mPBPK/PD model assuming exclusive production of IL-6 in response to TNFα reasonably captured the plasma IL-6 concentration-time profiles in rats challenged with LPS and treated with ascending doses of DEX. The model-predicted time of maximum concentration of IL-6 was around 2.5 hours post-LPS challenge and is in line with a previous report (Huang et al., 1998). The parameter estimates of the mPBPK/PD model of IL-6 dynamics and their precision (CV%) are shown in Table 3. The half-life of IL-6 calculated as ln2/k_outIL6 is 117 minutes, while it was 55 minutes for human recombinant IL-6 given to rats (Castell et al., 1988) and 103 minutes in humans with meningococcal disease (Waage et al., 1989).

Fig. 7.

Time courses of plasma IL-6 concentrations in LPS-treated rats given DEX or saline as indicated. Symbols are observed values and lines are mPBPK/PD model fittings.

TABLE 3.

Final pharmacodynamic model estimates of IL-6 dynamics and their CV%

Parameter (Units)	Definition	Estimate (CV%)
koutIL6 (h−1)	Elimination rate constant of IL-6	0.3566 (5.9)
STNFonIL6 (h−1)	Stimulatory coefficient of TNFα-induced IL-6 production	2.621 (14.7)
Residual variability
Sigma	Proportional error	0.7343 (11.5)
Intercept (pg·mL−1)	Additive error	51.0 (61.2)

NO Dynamics

NO is engaged in a vast array of physiologic processes and also serves as a mediator of inflammation. The enzyme iNOS produces NO that is primarily involved in host defense and inflammation. At high concentrations, NO may exert cytotoxic effects and induce vasodilation and hypotension. In addition, the increased vascular permeability caused by NO results in greater immune-cells infiltration into tissues (Coleman, 2001). As it can be seen in Fig. 8, the model assuming stimulation of NO production in response to increased plasma TNFα concentrations stemming from LPS reasonably captured the concentration-time profiles of plasma NO. The t_max of NO in plasma estimated by the model is around 16.5 hours post-LPS dosing. The model-estimated C_max of plasma NO was 430 µM in the control group, which was reduced to 124 µM for the highest dose of DEX, a 3.5-fold reduction. The parameter values for NO disposition and turnover obtained from Sukumaran et al. (2012) allowed satisfactory fitting of the model to the plasma NO concentration-time profiles. Their study featured direct assessment of NO PK after IV dosing of nitrate. The model involving three transit steps and linear stimulatory coefficient for TNFα-mediated stimulation of NO production reasonably captured the experimental data, and, as can be seen in Table 4, the S_TNFonNO and k_TNF parameters were estimated with good precision (CVs% <15%).

Fig. 8.

Time courses of NO plasma concentrations in LPS-treated rats given DEX or saline as indicated. Symbols are observed values and lines are mPBPK/PD model fittings.

TABLE 4.

Final PD model parameter estimates with corresponding CVs% and fixed values for NO dynamics

Parameter (Units)	Definition	Estimate (CV%)
kinNO (µmole·h−1)	Production rate constant	3.60a (fixed)
CLNO (L·h−1·kg−1)	Systemic clearance	0.1610a (fixed)
CLdNO (L·h−1·kg−1)	Distribution clearance	0.1150a (fixed)
VcNO (L·kg−1)	Central volume of distribution	0.4690a (fixed)
VpNO (L·kg−1)	Peripheral volume of distribution	0.2760a (fixed)
STNFonNO (pg−1·mL)	Stimulation coefficient of TNFα-triggered NO formation	0.0452 (11.4)
kTNF (h−1)	Transit rate constant of TNFα	0.1760 (4.0)
Residual variability
Sigma	Proportional error	0.2025 (22.8)
Intercept (µM)	Additive error	34.70 (13.8)

^a Fixed based on Sukumaran et al. (2012).

Corticosterone Dynamics

The dynamics of CST was described differently for healthy and LPS-challenged rats. It is well known that, under physiologic conditions in rats, CST displays circadian rhythms with maximum CST concentration occurring in the evening and the nadir occurring in the morning (Yao et al., 2008; Ayyar et al., 2019). In addition, in acute inflammatory conditions, such as LPS-induced inflammation, CST increases. Therefore, it was assumed that concentration-time profiles of CST in rats given saline instead of LPS are governed by the natural circadian rhythm while the circadian rhythm is disturbed and acute inflammation leads to increased CST in blood in the LPS-challenged rats. As can be seen in Table 5, DEX inhibits LPS-induced CST production with I_max of around 45% and IC₅₀ value of 2.1 ng·mL⁻¹. It was not feasible to precisely estimate the value of IC_50,DEX1 in normal rats based on our study data. Therefore, based on the literature, we assumed that the IC₅₀ value of DEX inhibiting CST production in normal male rats is 0.2 ng·mL⁻¹, which is around 18 times lower than the IC₅₀ value of methylprednisolone (Mager et al., 2003; Ayyar et al., 2019). Fig. 9 presents fittings of the mPBPK/PD model to the concentration-time profiles of plasma CST in normal and LPS-challenged rats treated with DEX at different dose levels. The model predictions reasonably captured the experimental data. As it can be seen from this figure, DEX at a dose of 2.25 mg·kg⁻¹ almost completely inhibited the production of CST in healthy animals for 48 hours post-LPS injection. In turn, in LPS-challenged rats, DEX at the highest tested dose (2.25 mg·kg⁻¹) did not cause complete inhibition of CST production. In LPS-challenged rats, CST plasma concentrations were highly variable, and it may be concluded that, upon LPS administration, the circadian rhythm of CST was disturbed and other factors affecting CST production overlap.

TABLE 5.

Final PD model parameter estimates of CST turnover in normal and LPS-challenged rats treated with DEX

Parameter (Units)	Definition	Estimate (CV%)
A0	Fourier coefficients	116b
A1		−121b
A2		38.8b
B0		—
B1		−41.1b
B2		1.58b
SH (ng·mL−1·h−1)	Maximum stress-induced CST production	3230a
kH (h−1)	Rate constant of decay of stress-induced CST production	2.19a
IC50DEX1 (ng·mL−1)	DEX plasma concentration causing 50% of Imax,DEX1	0.2c
ImaxDEX1	Maximum inhibition of CST production by DEX in normal rats	1c
IC50DEX2 (ng·mL−1)	DEX plasma concentration causing 50% of Imax,DEX2	2.055 (81.48)
ImaxDEX2	Maximum inhibition of CST production by DEX in LPS-treated rats	0.447 (14.78)
SLPS,CST	Stimulatory coefficient of LPS-induced CST production	0.086 (30.2)
kinCST (ng·mL−1·h−1)	CST production rate constant in LPS-treated rats	1030.56 (10.75)
koutCST (h−1)	CST elimination rate constant	4.56a
keLPS (h−1)	Degradation rate constant of the signal representing LPS-triggered activity	0.1172 (58.2)
Residual variability
Sigma	Proportional error	0.49 (8.4)
Intercept (ng·mL−1)	Additive error	2.5 (16.4)

^aFixed based on Yao et al. (2008).

^bFixed based on Yao et al. (2006).

^cFixed based on model assumptions.

Fig. 9.

Time courses of CST plasma concentrations in normal and LPS-treated rats given DEX or saline as indicated. Symbols are observed values and lines are mPBPK/PD model fittings. The data in the upper-left plot were reprinted from Yao et al. (2006) with permission from Elsevier, using a WebPlotDigitizer Version 4.3 (https://automeris.io/WebPlotDigitizer/).

Lymphocyte Dynamics

Lymphocyte trafficking is governed by the endogenous CS and may be altered by dosing with synthetic CS such as DEX (Fasanmade and Jusko, 1999; Mager et al., 2003). The presented model accounts for the influence of both endogenous as well as exogenous glucocorticoids on the movement of lymphocytes between blood and the extravascular space. In addition, the proposed model incorporates the influence of LPS administration on the degradation of lymphocytes that may arise from their apoptotic cell death (Norimatsu et al., 1995). To this end, the second-order degradation rate constant of lymphocytes loss mediated by LPS, k_degL, was incorporated in the model. This part of the mPBPK/PD model is a modification of a previous model of CST suppression and lymphocytopenia by methylprednisolone in rats (Yao et al., 2008). Our model is an extension accounting for LPS-induced effects on lymphocyte trafficking and turnover. As it can be seen in Fig. 10, the model captured very well the blood lymphocyte versus time profiles in normal and LPS-challenged rats. The circadian rhythm governing CST dynamics and its influence on the number of blood lymphocytes is reflected in lymphocyte number versus time profile in healthy, saline-treated animals. Dosing LPS produced a rapid and strong decrease in the number of peripheral lymphocytes, which was probably caused by the movement of immune cells to the site of inflammation and subsequent apoptotic cell death. Based on the literature data and results of our preliminary experiments, it was assumed that DEX inhibits lymphocyte movement from lymphatic tissue to blood. Indeed, the observed drop in the number of peripheral lymphocytes in the LPS-challenged rats is more prominent at higher doses of DEX. The model estimated PD parameters with corresponding CV% values are listed in Table 6. DEX administration caused a strong inhibition of lymphocyte movement from lymphatic tissues to blood with the IC_50L,DEX value that was around 47 times lower than the IC₅₀ value of 29.5 ng·mL⁻¹ found for methylprednisolone (Yao et al., 2008).

Fig. 10.

Time courses of absolute blood lymphocyte counts in normal and LPS-treated rats given DEX or saline as indicated. Symbols are observed values and lines are mPBPK/PD model fittings.

TABLE 6.

Final PD model parameter estimates with corresponding CVs% and fixed values of lymphocyte trafficking and turnover in normal and LPS-challenged rats treated with DEX or saline

Parameter (Units)	Definition	Estimate (CV%)
kinL (h−1)	Rate constant of lymphocyte movement from tissue to blood	0.0012 (19.8)
koutL (h−1)	Rate constant of lymphocyte movement from blood to tissue	0.06b
IC50L,DEX (ng·mL−1)	DEX plasma concentration causing 50% of ImaxL	0.634 (41.7)
ImaxL,DEX	Maximum inhibition of lymphocyte movement from tissue to blood	1a
IC50L,CST (ng·mL−1)	CST plasma concentration causing 50% of ImaxL	590.0a
kdegL (h−1)	Degradation rate constant of lymphocytes from the blood	0.150 (25.9)
keLPS (h−1)	Degradation rate constant of the signal representing LPS-triggered activity	0.862 (31.8)
Residual variability
Sigma	Proportional error	0.2 (22.4)
Intercept (cells·103·µL−1)	Additive error	1.3 (11.1)

^a Fixed based on Yao et al. (2008).

^b Secondary parameter.

Granulocyte Dynamics

The proposed mPBPK/PD model describing granulocyte dynamics in LPS-challenged rats treated with DEX accounts for the stimulation of granulocyte precursor production. Since baseline granulocyte numbers in normal rats appeared to be relatively constant throughout the experimental period, it was assumed that CST concentrations have no effect on granulocyte versus time profiles. As can be seen from Fig. 11, the mPBPK/PD model predictions reasonably captured the experimental data. The parameter estimates with corresponding CVs% are presented in Table 7. DEX exhibits stimulation of granulocyte precursor production with the SC₅₀ value that is higher compared with the SC₅₀ values for DEX found in previous studies in humans (7.9 and 4.8 ng·mL⁻¹) for stimulation of neutrophil trafficking and stimulation of neutrophil release from bone marrow into blood (Mager et al., 2003; Krzyzanski et al., 2021).

Fig. 11.

Time courses of absolute granulocyte counts in normal and LPS-treated rats given DEX or saline as indicated. Symbols are observed values and lines are mPBPK/PD model fittings.

TABLE 7.

Final PD model parameter estimates of granulocyte dynamics in normal and LPS-challenged rats treated with DEX or saline

Parameter (Units)	Definition	Estimate (CV%)
kinG   (cells·103·µL−1·h−1)	Rate constant of granulocyte precursor production	0.7308a
koutG (h−1)	Rate constant of granulocyte loss from the blood	0.3654 (7.6)
SC50G,DEX (ng·mL−1)	DEX plasma concentration causing 50% of SmaxG,DEX	18.63 (60.3)
SmaxG,DEX	Maximum stimulation of granulocyte precursor production by DEX	1.985 (20.3)
SG,LPS	Stimulation coefficient of granulocyte precursor production by LPS	1.446 (13.1)
Residual variability
Sigma	Proportional error	0.12 (39.0)
Intercept (cells·103·µL−1)	Additive error	1.36 (15.4)

^a Secondary parameter.

Separate Modeling of TNFα, IL-6, and NO Dynamics

The results of separate fittings of mPBPK/PD models and the model parameter estimates are presented in the Supplemental Fig. 2–4 and Supplemental Table 1. All three models for the separate biomarkers yielded very similar I_max values ranging from 0.81 to 0.83 and IC_50DEX values ranging from 1.8 to 3.4 ng·mL⁻¹. Considering the fact that the CVs% for the IC_50DEX parameters are in the range from 29% to 39%, it may be concluded that the IC_50DEX values for each biomarker are similar. In addition, the I_max and IC_50DEX values estimated using the presented models are close to the values obtained using a complex mPBPK/PD model assuming stimulation of production of NO and IL-6 by TNFα and a direct inhibition of TNFα by DEX (Table 2).

Discussion

Synthetic CS, including DEX, reduce inflammation caused by infectious diseases, but, on the other hand, they may put the patients at risk of secondary bacterial, viral, and opportunistic infections. Therefore, an appropriate dose and dosing schedule may be critical for improvement of therapeutic effects and reduction of undesired effects of CS in infectious diseases, such as COVID-19 (Chen et al., 2021). Our modeling results are important considering the fact that DEX was shown to reduce mortality in critically ill COVID-19 patients requiring oxygen supplementation or mechanical ventilation, but some later reports indicate that CS therapy may not be beneficial to all COVID-19 patients (Chen et al., 2021; Patel et al., 2022).

To the best of our knowledge, this is the first study that assessed the PK of DEX in LPS-challenged rats. The estimates of CL and k_a were close to the values found in healthy rats (Song et al., 2020; Song and Jusko, 2021). However, previous reports indicate an influence of increased concentrations of TNFα and IL-6 on the expression of CYP enzymes including CYP3A4 (Dunvald et al., 2022). The elimination pathway for DEX in rats is predominantly hepatic metabolism through CYP3A (Tomlinson et al., 1997). The anti-inflammatory activity of DEX as dosed 30 minutes prior to LPS could have alleviated changes in the expression of CYP enzymes resulting from increased plasma TNFα and IL-6. In a previous study in collagen-induced arthritic rats, the CL of DEX was only slightly increased compared with healthy animals (Earp et al., 2008).

In COVID-19 patients, hyperinflammatory responses were observed that were characterized by overproduction of proinflammatory cytokines, including TNFα and IL-6 (Liu et al., 2020). DEX once a day at an oral dose of 6 mg for up to 10 days is a recommended dosing regimen for treatment of COVID-19 patients requiring mechanical ventilation. A clinical trial found that mean concentrations achieved in the blood of COVID-19 patients upon single oral administration of DEX at a dose of 6 mg were far above IC₅₀ values of inhibition of TNFα, IL-6, and NO production estimated in this study (Abouir et al., 2022). In that clinical trial, the mean blood concentration of DEX at 8 hours was around 74 ng·mL⁻¹ in normal-weight patients. Considering the blood:plasma R_b of around 1 in humans, this result may imply the possibility of dose reduction of DEX in the treatment of severe SARS-CoV-2 infection assuming that its efficacy is mainly due to its anti-inflammatory activity. However, further studies are needed aiming at translation of the results of preclinical studies on DEX with the proposed mPBPK/PD model into the clinical settings.

DEX mechanism of action involving binding to GC receptor leads to inhibition of the production of proinflammatory cytokines. However, DEX does not act against inflammatory mediators that have already been produced and released such as might a monoclonal antibody. Therefore, to accurately estimate the in vivo I_max values of DEX against relevant biomarkers, it is crucial to assure that DEX reaches the site of action before TNFα starts to increase. Thus, predosing of DEX before LPS administration was chosen as a preferable dosing regimen to assure that DEX is present at the site of action before TLR4-triggered pathways are activated by LPS. The 30-minute time interval between DEX and LPS administration was selected based on the facts that the t_max of DEX after SC dosing is around 1 hour and TNFα starts to increase around 30 minutes post-LPS IP administration. In addition, it needs to be noted that predosing of test drugs in LPS-induced inflammation is an established and frequently used approach (Chakraborty et al., 2005; Held et al., 2019; Larsson et al., 2021).

Several PK/PD models describing changes in concentrations of cytokines and other inflammatory mediators in LPS-challenged animals and humans have been published. There is a model of susalimod inhibition of TNFα production in LPS-challenged mice (Gozzi et al., 1999) and a much more complex model assessing interactions between recombinant mouse IL-10 and prednisolone in mice given LPS (Chakraborty et al., 2005). The more recent models described in the literature involve more biomarkers of inflammation, are more mechanistic, include more complexities, and, therefore, provide more comprehensive description of changes in these biomarkers and the interrelations among them and therapeutic agents. One study describes coptisine effects in LPS-induced endotoxemia in rats (Hu et al., 2019). The authors assumed TNFα-mediated stimulation of iNOS production and subsequent NO production and release. The PK/PD model presented in this study is a combination of a mPBPK model of DEX and PD models describing time courses of inflammatory mediators, CST, and immune cells and interrelations among them in LPS-challenged rats. The utilization of a mPBPK model allows for incorporation of physiologic elements into the PK part of the model and separation of drug- and system-specific parameters in a situation when only plasma drug concentrations are available. This approach may facilitate further translation of the results into the clinical settings since mPBPK models are easily scalable among species (Song and Jusko, 2021). The structures of the proposed PD submodels result from a compromise between sophisticated mechanistic models that require extensive experimental data and are at risk of overparameterization and parsimonious models that appropriately and sufficiently characterize the available data.

Values obtained for DEX inhibitory activity on lymphocyte proliferation in in vitro assays were 1.1 ng·mL⁻¹ in human lymphocytes (Sakuma et al., 2000) and 2.3 ng·mL⁻¹ in rat lymphocytes (Yu et al., 2020). TNFα was shown to stimulate lymphocyte proliferation, so the observed in vitro effect of DEX is ascribed to its inhibitory activity on TNFα production (Gaur and Aggarwal, 2003). The IC₅₀ value for inhibition of TNFα production by prednisolone in LPS-challenged mice was 171 ng·mL⁻¹ and is considerably weaker than the more potent DEX. Assuming that values of sensitivity parameters of a given GC are similar across different species, the low IC₅₀ value of DEX against TNFα in this study (3.5 ng·mL⁻¹) compared to prednisolone in LPS-challenged mice confirms a higher activity of DEX that was also demonstrated previously in some in vitro tests (Luchak et al., 2020) and probably results from a higher affinity of this drug to GC receptors (Daley-Yates, 2015). The half-life value for plasma TNFα in our study was 26 minutes. In previous PK/PD modeling studies, half-life values of TNFα in LPS-challenged mice were typically around 24 minutes (Larsson et al., 2021), and for humans it was around 116 minutes (Liu et al., 2022) indicating possible species differences. A multiphasic post-peak decline in plasma TNFα concentrations was reported recently in rats and humans (Held et al., 2019; Larsson et al., 2021; Liu et al., 2022) that is in accordance with our findings. A complex mPBPK model of human recombinant TNFα in healthy rats and monkeys integrated with allometric scaling was developed (Chen et al., 2017). In that model, nonlinear elimination of hrTNFα was noted that may be attributed to its saturable binding to the TNFα receptor that influences the disposition of this signaling molecule. In our mPBPK/PD model, linear elimination of TNFα was successfully applied due to the fact that the concentrations of TNFα in LPS-challenged rats were relatively low compared to the concentrations of this cytokine achieved after SC or IV dosing of hrTNFα.

In this study, IL-6 dynamics was described by an indirect response model with the input function assuming exclusive production of IL-6 induced by TNFα. This assumption is in line with Ghezzi et al. (2000) and is supported by the result of our regression analysis indicating a positive linear correlation between relative exposures of TNFα and IL-6 and by the results of separate modeling of biomarker dynamics yielding very similar IC₅₀ values for inhibition of TNFα and IL-6 production by DEX (Supplemental Table 1). In our mPBPK/PD model, we assumed stimulation of NO production by TNFα. This assumption was made previously (Chakraborty et al., 2005) and later adapted by others (Hu et al., 2019) and is supported by the regression analysis (Fig. 5) and our separate modeling approach (Supplemental Table 1). The IC₅₀ value of inhibition of NO production by DEX estimated in this study using a separate modeling approach was 1.8 ng·mL⁻¹, and it was close to the IC₅₀ value of 3.6 ng·mL⁻¹ obtained previously in an in vitro assay (Walker et al., 1997). Interestingly, the I_max of NO generation in murine macrophages was around 80% for DEX, which is close to our I_max value (Supplemental Table 1). The IC₅₀ and I_max values for inhibition of iNOS by methylprednisolone in a previous investigation were 285.3 ng·mL⁻¹ and 73%, indicating that DEX is much more potent inhibitor of NO production (Sukumaran et al., 2012).

The typical IC₅₀ value of inhibition of cortisol release for DEX was around 0.05 ng·mL⁻¹ based on the population PK/PD model in healthy women (Krzyzanski et al., 2021) and 0.17 ng·mL⁻¹ in healthy men (Mager et al., 2003). In our mPBPK/PD model, the IC₅₀ value of CST production was fixed at 0.2 ng·mL⁻¹ based on relatable studies with methylprednisolone (Mager et al., 2003; Ayyar et al., 2019).

The IC₅₀ value of DEX inhibiting movement of lymphocytes from the extravascular space to the blood pool estimated based on a clinical trial in healthy man for T-helper cell trafficking was 3.36 ng·mL⁻¹ and for T-suppressor cell trafficking was 18.7 ng·mL⁻¹ (Mager et al., 2003). Based on a population PK/PD model in healthy Indian woman, the IC₅₀ value of inhibition of T-helper cells trafficking was 4.13 ng·mL⁻¹ and for T-cytotoxic cells was 14.7 ng·mL⁻¹ (Krzyzanski et al., 2021). The SC₅₀ estimates for stimulation of neutrophil movement by DEX obtained previously were 7.9 ng·mL⁻¹ and 4.8 ng·mL⁻¹ (Mager et al., 2003; Krzyzanski et al., 2021). The considerably different values of sensitivity parameters estimated in this study might have been due to species-related differences, changes in the expression of adhesion molecules related to LPS-induced inflammation, lack of distinction between different subpopulations of lymphocytes and granulocytes in the present study, or different assumptions between the models. Possibly, the inhibition of lymphocytes migration from lymphatic tissue to the blood pool by DEX may lead to decreased death and exhaustion of lymphocytes during inflammation due to their lower availability in the blood. This may constitute an additional beneficial mechanism for DEX action in the treatment of COVID-19, given that lymphopenia is a predictor of poor outcomes in severe SARS-CoV-2 infection (Simon et al., 2022). According to the results of our preliminary experiments (data not shown), the diverse values of sensitivity parameters of DEX ranging from 0.6 to 18 ng·mL⁻¹ may be used to isolate individual effects of this drug. It is possible to adjust the dose of DEX to inhibit lymphocyte movement from the extravascular space to the blood without influencing cytokine production or to inhibit production of inflammatory mediators without substantial influence of DEX on granulocyte movement. This observation is especially interesting from the clinical point of view since it may help in optimizing DEX dosing regimens to achieve specified treatment endpoints.

In conclusion, this study provides a comprehensive mathematical description of time courses of DEX effects in LPS-challenged rats. DEX PK appears to be not influenced by the LPS-induced inflammation. DEX displayed high but incomplete inhibition of production of TNFα, IL-6, and NO with single digit nanogram per milliliter IC₅₀ values and an I_max of around 80%. Production of CST in healthy rats was strongly inhibited by DEX. In turn, in LPS-challenged rats, DEX displayed only partial inhibition of CST production. The mPBPK/PD model proposed herein may be useful to assess potential beneficial interactions between CS and other immunomodulatory compounds for treatment of cytokine release syndrome. The model, upon translation to humans, may serve for optimizing of DEX dosing regimens in the treatment of immune-mediated conditions involving excessive production of inflammatory mediators.

Abbreviations

AIC

Akaike information criterion

CS

corticosteroids

CST

corticosterone

CV%

coefficient of variation %

DEX

dexamethasone

HPA

hypothalamic-pituitary-adrenal

IC₅₀

concentration resulting in 50% of the maximum inhibition

IL-6

interleukin 6

I_max

maximum inhibition

iNOS

inducible nitric oxide synthase

IP

intraperitoneal

IV

intravenous

LC-MS/MS

liquid chromatography tandem-mass spectrometry

LPS

lipopolysaccharide

mPBPK/PD

minimal physiologically based pharmacokinetic/pharmacodynamic

MRM

multiple reaction monitoring

NF-κB

nuclear factor kappa-light-chain-enhancer of activated B cells

NO

nitric oxide

PD

pharmacodynamic

PK

pharmacokinetic

PK/PD

pharmacokinetic/pharmacodynamic

QC

quality control

SC

subcutaneous

SC₅₀

concentration resulting in 50% of the maximum stimulation

TLR4

toll-like receptor 4

TNFα

tumor necrosis factor α

Authorship Contributions

Participated in research design: Świerczek, Jusko.

Conducted experiments: Świerczek.

Performed data analysis: Świerczek.

Wrote or contributed to the writing of the manuscript: Świerczek, Jusko.