Integrated cellular bone homeostasis model for denosumab pharmacodynamics in multiple myeloma patients

Abstract

The purpose of this study is to couple a cellular bone homeostasis model with the pharmacokinetics (PK) and mechanism of action of denosumab, an inhibitor of receptor activator of nuclear factor-kappaB ligand, to characterize the time course of serum N-telopeptide (NTX), a bone resorption biomarker, following single escalating doses in multiple myeloma (MM) patients. Mean PK and median serum NTX temporal profiles were extracted from a previously conducted randomized, double-blind, double-dummy, active-controlled, multicenter study including 25 MM patients receiving escalating denosumab doses. Nonlinear denosumab PK profiles were well described by a target-mediated disposition model that includes rapid binding of drug to its pharmacological target. Fixed PK profiles were integrated into a previously reported theoretical cellular model of osteoblast-osteoclast interactions, and the NTX concentrations were linked to a resorbing active osteoclast (AOC) pool by a nonlinear transfer function. Reasonable fits were obtained for the NTX profiles from maximal likelihood estimation using the final model. Transfer function parameters, including the basal NTX level and the AOC concentration producing 50% of maximal NTX production, were estimated with good precision as 5.55 nM and 1.88 x 10(-5) pM. An indirect response model for inhibition of NTX production by denosumab was also used to characterize the data. Although this model adequately characterized the pharmacodynamic data, simulations conducted with the full model reveal that a cellular model coupled with clinical data has the distinct advantage of not only quantitatively describing data but also providing new testable hypotheses on the role of cellular system variables on drug response.

Figure 1

Target-mediated disposition model for denosumab pharmacokinetics. Drug administered subcutaneously gets absorbed (k_a) into the plasma compartment (C_p, V_c). Drug can be eliminated (k_el) or rapidly bind to the pharmacological target to form a drug-ligand complex (RC). The model also includes the internalization of the drug-ligand complex (k_int).

Figure 2

Schematic diagram of the integrated cellular bone homeostasis model. Adapted from Lemaire et. al. (2004). Details of the model are provided in the Methods.

Figure 3

Pharmacokinetic profiles of denosumab after simultaneously fitting the rapid binding target-mediated disposition model to the mean data of four single SC doses of 0.1 (●, thin solid), 0.3 (▲, dashed), 1.0 (■, dash-dotted), and 3.0 mg/kg (▼, thick solid). Symbols represent mean data from the literature (Body et al., 2006) and lines represent the predicted profiles from the model.

Figure 4

Serum NTX concentration-time profiles after simultaneously fitting the basic indirect response model to the median data for four single SC doses of 0.1 (●, thin solid), 0.3 (▲, dashed), 1.0 (■, dash-dotted), and 3.0 mg/kg (▼, thick solid). Symbols represent data from the literature (Body et al., 2006) and lines represent the predicted profiles from the model.

Figure 5

Serum NTX concentration-time profiles after simultaneously fitting the integrated cellular bone homeostasis model to the median data for four single SC doses. Symbols and lines are as defined in Figure 4.

Figure 6

Simulated predictions of the cellular bone homeostasis model under varying conditions. A) Concentration-time profiles of the bone cells with continuous administration of 1000 pMday⁻¹ of PTH for 60 days. B) Concentration-time profiles of the bone cells with continuous administration of 0.0001 pMday⁻¹ of active osteoclasts for 60 days. Symbols (●, ▲, ■) represent digitized data from simulations conducted by Lemaire et al. (2004) with the value of D_A, 0.7 day⁻¹ and lines (dash-dotted, dashed, solid) represent the predicted profiles of the responding osteoblasts, active osteoblasts and the active osteoclasts respectively from this study using a value of D_A, 29.8 day⁻¹. C) Serum NTX concentration-time profiles following multiple SC dosing of denosumab every 90 days. D) Serum NTX concentration-time profiles following multiple SC dosing of denosumab with a linear increase in RANKL in the system. The thin solid, dashed, dash-dotted and thick solid lines represent escalating SC doses of 0.1, 0.3, 1.0, and 3.0 mg/kg.

Scheme 1