The physiological system-specific parameters represent physiological values such as blood flow, life-span of cells, expression of enzymes, and transporters ( Danhof et al., 2005 Danhof et al., 2007 Sager et al., 2015). The drug delivery system-specific parameters represent the properties of carriers, such as the clearance, release rate, and the internalization rate of the carrier. Drug-specific parameters (e.g., drug clearance and receptor binding affinity) illustrate the interaction between the drug and the biological system. The PK and PD modeling can quantify the relationship of drug exposure and response, and further characterize the influences of drug-specific, delivery system-specific, physiological and pathological system-specific parameters on this relationship ( Agoram et al., 2007 Danhof et al., 2007). PD modeling evaluates the time course of the pharmacological effects of drugs, with the consideration of the mechanism of drug action and major rate-limiting steps in the biology of the system ( Mager et al., 2003). Explicitly, PK modeling quantitatively describes the process of absorption and disposition of drug in the body. As Figure 1 shows, the mechanism-based PK-PD model can be incorporated into multiple stages in drug development. PK-PD modeling, an indispensable component of drug discovery and development, is a mathematical approach to study pharmacokinetics (PK), pharmacodynamics (PD), and their relationship ( Peck et al., 1992 Danhof et al., 2005). Mechanism-based pharmacokinetic-pharmacodynamic (PK-PD) modeling could be used to untangle these complexities and improve the understanding of the in vivo behavior of these drug delivery systems, consequently informing their preclinical-to-clinical translation and clinical development. The lack of understanding of the in vivo behavior of these delivery systems may limit their successful translation into clinics. As a result, the drug absorption and disposition processes after administration of these drug delivery systems become exceedingly complex. With the advancement of technology, drug delivery systems with more complex architectures are developed. The research field of drug delivery focuses on the development of new techniques to manipulate drug absorption and disposition to achieve a desirable effect ( Anselmo and Mitragotri, 2014 Asiri and Mohammad, 2018). The limitations and challenges of the mechanism-based PK-PD model were also discussed. Furthermore, the model-based simulation using primary PD models for direct and indirect PD responses was conducted to explain the assertion of hypothetical minimal effective concentration or threshold in the exposure-response relationship of many drugs and its misconception. In particular, we exemplified the application of PK-PD modeling in the development of extended-release formulations, liposomal drugs, modified proteins, and antibody-drug conjugates. The linkage between PK and PD was highlighted. In this review, we summarized the basic PK-PD modeling theory in drug delivery and demonstrated how it had been applied to help the development of new delivery systems and modified large molecules. As the pharmacokinetic and pharmacodynamic (PK-PD) modeling allows for the separation of the drug-, carrier- and pharmacological system-specific parameters, it has been widely used to improve understanding of the in vivo behavior of these complex delivery systems and help their development. As a result, the drug absorption and disposition processes after administration of these drug delivery systems and engineered molecules become exceedingly complex. With the advancement of technology, drug delivery systems and molecules with more complex architecture are developed.
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