Table 2.

Pharmacokinetic–Pharmacodynamic (PK–PD) modeling systems in liposomal drug delivery.

Model Approach	Mathematical Model	Mathematical Model of the Rest of the Body	Drugs	Notes	Ref
Simplified physiologically-based pharmacokinetic (PBPK) model Simplified PBPK model Simplified PBPK model	Tumor was divided into capillary, interstitial and tumor cell sub-compartments.	1-compartment PK model for liposome and 2-compartment PK model for drug.	Doxorubicin	Liposomal retention in tumors and the local release rate were identified to play pivotal roles in antitumor efficacy.	[118,119]
	Tumor was divided into capillary, interstitial, tumor cell and nucleus sub-compartments.	1-compartment PK model for liposome and2-compartment PK model for drug.	Doxorubicin	The detailed drug transport into and out of the cell, drug-target association and dissociation, and liposome uptake and release in tumor cells were described.	[120]
	Liver hepatocyte compartment with endosomal and cytoplastic compartments.	Plasma compartment.	hUGT1A1-modRNA	Endocytosis, release and transcription processes were described. After translated to humans, this model was used to estimate the first-in-human dose.	[121]
Whole-body PBPK model	/	Plasma and tissue (liver, spleen, kidneys, gut, lungs, heart and others) compartments.	Amphotericin B	The first whole-body PBPK model described the disposition of both liposome and drug simultaneously.	[122]
Model with spatiotemporal characterization Model with spatiotemporal characterization	The combination of tumor growth, angiogenesis, oxygen transport, nanoparticle transport and antitumor effect models.	/	/	The physiological properties of the tumor were considered. The model described the interactions between tumor progression and liposome disposition.	[125,127,128]
	Tumor vascular network and nanoparticle transport model.	/	/	Tumor blood vessel properties were simulated in this model. The interactions between the liposome and blood vessel were simulated to optimize the particle properties.	[129,130,131]
Model with in vitro—in vivo correlation (IVIVC)	Using in vitro studies to determine the model parameters and replace in vivo study in liposome optimization study.	Plasma and tissues compartments.	Doxorubicin	Liposome property–disposition relationships were established to facilitate liposome optimization.	[137]