Wojciech Krzyzanski (1), Robert Bauer (2)
(1) University at Buffalo, USA, (2) ICON Gaithersburg, USA
Introduction: Cell trafficking encompasses movement of the immune system cells (e.g., granulocytes, lymphocytes) between the blood and the extravascular tissues (e.g., lymph nodes). Basophils are effector cells responsible for inflammatory reactions during the immune challenge. Basophils are used as biomarkers of inflammatory responses. Corticosteroids are known to suppress cell trafficking [1]. Existing models of cell trafficking employ the methodology of compartmental systems where the cells transfer between two compartments at first-order rates. Such an approach limits the model ability to account for prolonged times most of the immune cells spend outside the vasculature before recirculating to the blood. The age-structured population models introduce the transit time as a structure that allows to quantify the distribution of times the immune cells spend in the blood and the extravascular tissues. The key tools are the hazards of transfer between the tissues and hazards of cell death. The hazard can depend on the cell age (e.g., the time it spends in the tissue) and the time (e.g., through the time-dependent drug effect). The numerical challenge is that the age-structured population models are first-order partial differential equations with two independent variables (time and age) that require integration over the age domain to obtain the observable cell counts.
Objectives:
- To develop an age-structured population model capable of describing drug effects on cell trafficking
- To implement the model in pharmacometric software to enable parameter estimation and simulations
- To validate our model using published data on corticosteroid inhibition of the basophil counts in healthy volunteers
Methods:
We adopted the well-known McKendrick age-structured population model [2] to describe the age distributions nB(t,aB) and nE(t,aE) in two cell populations: blood cells and cells in the extravascular space. We neglected cell death since our focus was on the cell trafficking rather than cell elimination. The hazard of cell extravasation mBE was assumed to be constant. The hazard of cell recirculation from the extravascular tissues was age dependent and described by the Weibull function parameters shape n and scale b. The drug effect on the cell trafficking was modeled as the product of the Emax function of the drug plasma concentration and the Weibull hazard. The blood cell count CB(t) was obtained by the integration of nB(t,aB) with respect to aB. The integration reduced our model to a distributed delay differential equation (DDDE) with a constant past [3]. The model was implemented in NONMEM 7.5.1 (ICON LLC) where the DDDE was solved by a new approximation of the convolution integral based on the transit compartment models. The model was applied to the basophil data in 34 healthy subjects who received a single intramuscular (IM) of oral (PO) dose of 6 mg dexamethasone (DEX) [4]. A recently published pharmacokinetic model was applied to describe DEX plasma concentration [5]. Typical values of parameter estimates were further used to simulate the DEX effect of the basophil mean transit time in the extravascular tissues (MTTE).
Results: Simulations of CB(t) time courses for varying n demonstrated that the rebound in the blood count data following drug administration is only possible for n >1. For this range of values, the response exhibits an oscillatory pattern whereas for n ≤ 1, the response monotonically returns to the baseline after reaching a nadir. Population analysis by importance sampling was successfully applied and completed in 5.7 hours. The estimates of typical values of model parameters were CB0 =29.1 cells/uL, mBE = 0.131 1/h, n = 6.76, b =0.00489 1/h, and IC50 = 6.35 ng/mL. The calculated baseline mean transit times of basophils in the blood MTTB = 7.6 h and MTTE = 190.9 h agree with the values reported in the literature. A single dose of DEX increases MTTE up to 271.7 h (IM) and 281.3 h (PO).
Conclusions: We introduced an age-structured population model to describe cell trafficking between the blood and extravascular tissues. The model was adopted to account for the inhibitory drug effect on the cell recirculation. We showed that the age structure is essential to explain the rebound observed in the blood count response to a single dose drug administration. The model was validated using the basophil responses to DEX treatment in healthy subjects.
References:
[1] Wald JA, Salazar DE, Cheng H, Jusko WJ (1991) Two-compartment basophil cell trafficking model for methylprednisolone pharmacodynamics. J Pharmacokinet Biopharm 19:521-236
[2] McKendrick AG (1926) Applications of mathematics to medical problems. Proc Edinburgh Math Soc 40:98-130
[3] Hu S, Dunlavey M, Guzy S, Teuscher N (2018) A distributed delay approach for modeling delayed outcomes in pharmacokinetics and pharmacodynamics studies. J Pharmacokinet Pharmacodyn, 45:285–308
[4] Jobe AH, Milad MA, Peppard T, Jusko WJ (2020) Pharmacokinetics and pharmacodynamics of intramuscular and oral betamethasone and dexamethasone in reproductive age women in India. Clin Transl Sci 13:391-399
[5] Krzyzanski W, Milad MA, Jobe AH, Peppard T, Bies RR, Jusko WJ (2021) Population pharmacokinetic modeling of intramuscular and oral dexamethasone and betamethasone in Indian women. J Pharmacokinet Pharmacodyn 48:261-272
Reference: PAGE 30 (2022) Abstr 9995 [www.page-meeting.org/?abstract=9995]
Poster: Methodology - New Modelling Approaches