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Physiologically-based kinetics modelling for nanomaterials

Biokinetics offer a methodology for predicting the internal distribution and exposure of a substance in an organism.

Compartmental modelling is a concept broadly used in pharmacokinetics for describing the biodistribution of a substance inside an organism. Physiologically-based pharmacokinetic (PBPK) models represent one of the two major approaches used in compartmental modelling, with empirical models being the second one. PBPK models are mechanistic; they consist of compartments representing real organs and tissues, whose number varies based on the target substance, species, administration route and available information. A common approach is to incorporate in the model the main body tissues, i.e. brain, heart, kidney, skin, spleen, liver, lung, gut, bone, adipose and muscle. In most cases, PBPK models are utilised for describing the kinetics of a substance in the whole body of a species, thus such models are more formally called “whole body physiologically-based pharmacokinetic models” (WBPBPK).

WBPBPK can be grouped into two classes: perfusion-limited and permeability-limited models. The first group applies for small lipophilic molecules, where the limiting step of substance absorption is the transportation to the tissue via the blood flow. On the other hand, permeability-limited models assume that the limiting process is the membrane permeability which acts as a diffusion barrier, so it applies for larger and hydrophilic molecules, which is the case for NMs. The compartments of a WBPBPK model are interconnected through the arterial and venous blood pools; all organs receive blood from the arterial blood compartment and the outflow ends up in the venous blood compartment. The blood loop is closed by the lungs compartment, in which the blood flow is reversed in comparison to the rest of the organs. Apart from the regional blood flows, the underlying physiology also defines the second set of substance-independent parameters, the organ volumes. Besides these physiological parameters, PBPK models incorporate information about the target substance as well, through the substance-dependent parameters, which can be obtained using data generated by in vivo, in vitro or in silico experiments.

PBPK models have inherent advantages due to their mechanistic nature. Firstly, they enable predictions of concentration/mass profiles of individual organs and not just of plasma. In addition, their relation with physiology and modularity facilitate the integration of literature information, making predictions prior to in vivo experiments possible. Lastly, their biggest advantage is the ability to perform inter-species (e.g. from rat to human) or intra-species (e.g. from adults to children) extrapolation through scaling methods.

Nano-PBPK models

Several PBPK models that describe the biodistribution of NMs can be found in literature and an extensive review of the modifications of traditional PBPK models that need to be considered in the case of NMs can be found in (Li et al., 2010, Yuan et al., 2019).

Figure 1. generic PBPK model (A) and two types of tissue model structure (B). Qi: blood or plasma flow; kp: tissue partitioning coefficient, namely concentration ratio between tissue and blood at steady-state; PS: membrane permeability coefficient; CLhep: hepatic clearance; CLrenal: renal clearance (extracted from DOI: 10.1016/j.xphs.2018.10.037

A list containing nano-PBPK models is presented in the table below:

Nanoparticle Species Administration route Reference
Quantum Dot 705 (QD705) Mouse Intravenous http://doi.org/10.1021/es800254a
99mTechnetium - labelled carbon nanoparticles (Technegas) Male human Pulmonary http://doi.org/10.3109/08958370902748542
Silver nanoparticles Rat Intravenous http://doi.org/10.1016/j.biomaterials.2010.07.045
poly(lactic - co - glycolic) acid (PLGA) nanoparticles Mouse Intravenous http://doi.org/10.2147/IJN.S23758
gold/dendrimer composite nanodevices (CNDs) Mouse Intravenous http://doi.org/10.1007/s11095-012-0784-7
Silver, silver alloy and ionic silver Rat Intravenous http://doi.org/10.2147/IJN.S46624
192Ir radio-labeled iridium particles and ultrafine carbon particles Rat Pulmonary http://doi.org/10.1115/1.4025333
Polyacrylamide (PAA) Rat Intravenous http://doi.org/10.3109/17435390.2013.863406
Gold nanoparticles Mouse Intravenous https://doi.org/10.3109/17435390.2015.1027314
Silver nanoparticles Rat Intragastric http://doi.org/10.1134/S1995078015020081
Titanium dioxide (TiO2) nanoparticles Mouse, Rat Intravenous http://doi.org/10.3109/17435390.2014.940404
Zinc oxide (ZnO) and Zinc Nitrate (Zn(NO3)2) nanoparticles Mouse Intravenous http://doi.org/10.2147/IJN.S86785
Cadmium telluride/cadmium sulphide quantum dots (CdTe/CDS Qds) Mouse Intravenous http://doi.org/10.1021/acs.nanolett.5b03854
Silver and Carbon black (CB) nanoparticles Mouse Pulmonary http://doi.org/10.1371/journal.pone.0080917
PAA, Gold, TiO2 Rat Intravenous http://doi.org/10.2147/IJN.S94370
QD705 Mouse Intravenous http://doi.org/10.1021/nl803481q
TiO2 Rat Intravenous http://doi.org/10.1371/journal.pone.0124490
Amphiphilic block copolymers poly (ethylene glycol) (PEG) - caprolactone) (PCL) bearing pendant cyclic ketals Mouse Intravenous http://doi.org/10.1002/psp4.13
Nanocrystals of SNX-2112 Rat Intravenous http://doi.org/10.2147/IJN.S79734
192Ir radio - labelled iridium and silver nanoparticles Rat Pulmonary, Intravenous https://doi.org/10.1016/j.yrtph.2015.06.019
Gold Mouse, rat, pig Intravenous http://doi.org/10.2217/nnm.15.177
PAA Rat Intravenous https://doi.org/10.1016/j.taap.2010.11.017
192Ir radio-labelled iridium and silver nanoparticles Rat Pulmonary https://doi.org/10.1088/1742-6596/151/1/012028
Gold Rat Pulmonary https://doi.org/10.1088/1742-6596/151/1/012029
Molecular imaging nanoparticles (MINs) Mouse Injection https://doi.org/10.1089/oli.2009.0216
Cerium dioxide (CeO2) Rat Pulmonary http://doi.org/10.1186/s12989-016-0156-2
CeO2 Rat Pulmonary, Intravenous, oral or its instillation http://doi.org/10.2147/IJN.S157210
Superparamagnetic iron oxide nanoparticles (SPIONs) Mouse Intravenous http://doi.org/10.1515/ejnm-2017-0001

Nano-PBPK web services

NTUA has developed all the necessary infrastructure to develop, host and share PBPK models through the Jaqpot computational platform, thus, a series of models have been integrated with the NanoCommons KnowledgeBase through the Jaqpot Cloud Platform and can be readily integrated in risk assessment computational pipelines. Potential users can learn how to acquire predictions from these models by visiting the detailed documentation files that have been uploaded in zenodo:

To acquire access to the models, a user should be part of the NanoCommons organisation in Jaqpot. For this purpose, email Prof. Harry Sarimveis requesting access (hsarimv@central.ntua.gr)

PBPK model on polyethylene glycol-coated polyacrylamide (PAA-peg) nanoparticles on rat

This PBPK model has been developed on a rat population to describe the biodistribution of polyethylene glycol-coated (PAA-peg) nanoparticles. It consists of 7 compartments describing the mass distribution of the nanoparticles in various organs, namely liver (LI), kidney (KI), brain (BR), bone marrow (BM), , heart (HT), spleen (SPL) and lungs (LU), one compartment to model the rest of the body (ROB) as well as two blood pools; venous (VEN) and arterial (ART). All compartments include a sub-compartment describing the uptake of nanoparticles by phagocytizing cells (PCs), while all but the blood compartments have a third component describing the distribution of nanoparticles in the capillary blood.The detailed description of the PBPK model used can be found in Li et al., 2014.

PBPK model on Titanium dioxide (TiO2) nanoparticles on mice

This PBPK model was initially developed on rat data Kreyling et al., 2019 to describe the biodistribution of TiO2 nanoparticles after inhalation. After adaptation to the biodistribution data, the model was extrapolated to mice using scaling of physiological parameters and MPPD for extrapolating parameters related to inhalation. Its schematic representation can be seen in the following figure. It consists of 10 compartments describing the mass distribution of the nanoparticles in various organs, namely liver, kidney, brain, gonads, heart, spleen, lungs, skin, skeleton, one compartment to model the soft tissues, which acts as a rest of the body compartment, as well as two blood pools; venous and arterial. Because the model refers to inhalation, a more detailed description of the respiratory tract was implemented, with analytical equations for the upper airways, tracheobronchial and alveolar regions. Most compartments include a sub-compartment describing the uptake of nanoparticles by phagocytizing cells (PCs), while all compartments connected to the systemic circulation have a third component describing the distribution of nanoparticles in the capillary blood.The structural model was built upon the PBPK of Li et al., 2016. This model was developed using financial support by NanoCommons (Grant Agreement 731032), a project funded by the European Commission under the Horizon 2020 Programme.

Naive Human PAA-PEG PBPK Model

This PBPK model is a human extrapolation of the Li et al., 2014 PBPK model and describes the biodistribution of polyethylene glycol-coated polyacrylamide (PAA-peg) nanoparticles. The set of physiological parameters which were changed from the original values of Li et al., 2014 are the weights, the volume of capillary blood and the blood flow of each tissue/organ. The values of these parameters are provided by Brown et al., 1997.

The PBPK model consists of 7 compartments describing the mass distribution of the nanoparticles in various organs, namely liver (LI), kidney (KI), brain (BR), bone marrow (BM), heart (HT), spleen (SPL) and lungs (LU), one compartment to model the rest of the body (ROB) as well as two blood pools; venous (VEN) and arterial (ART). All compartments include a sub-compartment describing the uptake of nanoparticles by phagocytizing cells (PCs), while all but the blood compartments have a third component describing the distribution of nanoparticles in the capillary blood.

PBK model for 99m-Technetium-labelled carbon nanoparticles inhaled by humans

This Physiologically Based Kinetic (PBK) model has been developed using radioactivity data resulting from inhalation of technetium- labelled carbon nanoparticles (5-10 nm) from healthy male volunteers (24 to 47 years old). The detailed description of the PBK model can be found in Pery et al., 2009.

The model considers a concentration for technetium bound to small particles, in other words labelled nanoparticles, and free technetium. Hence the web service reports both the concentration of free and bound technetium in each compartment, as well as the total technetium concentration which is calculated as the summation of the two technetium forms. The concentration that is related to technetium bound to large particles cannot translocate the air:blood barrier and, thus, only the bound and total amounts of the lungs and stomach lumen ( through translocation from the lungs) contain radiation intensity from technetium bound to large particles, which is considered constant over time.

References

  • Brown et al., 1997: Brown, R.P.; Delp, M.D.; Lindstedt, S.L.; Rhomberg, L.R.; Beliles, R.P. Physiological parameter values for physiologically based pharmacokinetic models. Toxicol Ind Health 1997, 13(4), 407–84. https://doi.org/10.1177/074823379701300401
  • Carlander et al., 2016: Carlander, U.; Li, D.; Jolliet, O.; Emond, C.; Johanson, G.; Toward a general physiologically-based pharmacokinetic model for intravenously injected nanoparticles. Int J Nanomed 2016, 11, 625–640. https://doi.org/10.2147/IJN.S94370
  • Kreyling et al., 2019: Kreyling, W.G.; Holzwarth, U.; Schleh, C. et al. Quantitative biokinetics over a 28 day period of freshly generated, pristine, 20 nm titanium dioxide nanoparticle aerosols in healthy adult rats after a single two-hour inhalation exposure. Part Fibre Toxicol. 2019, 16, 29. https://www.doi.org/10.1186/s12989-019-0303-7
  • Li et al., 2014: Li, D.; Johanson, G.; Emond, C.; Carlander, U.; Philbert, M.; Jolliet, O.; Physiologically based pharmacokinetic modeling of polyethylene glycol-coated polyacrylamide nanoparticles in rats. Nanotoxicology 2014, 8, 128–137. https://doi.org/10.3109/17435390.2013.863406
  • Li et al., 2016: Li, D.; Morishita, M.; Wagner, J.G.; et al. In vivo biodistribution and physiologically based pharmacokinetic modeling of inhaled fresh and aged cerium oxide nanoparticles in rats. Part Fibre Toxicol. 2016, 13(1), 45. https://www.doi.org/10.1186/s12989-016-0156-2
  • Li et al., 2010: Li, M.; Al-Jamal, K.T.; Kostarelos, K.; Reineke, J. Physiologically Based Pharmacokinetic Modeling of Nanoparticles. ACS Nano 2010, 4(11), 6303–6317. https://doi.org/10.1021/nn1018818
  • Pery et al., 2009: Pery, A.R.R.; Brochot, C.; Hoet, P.H.M.; Nemmar, A.; Bois, F.Y. Development of a physiologically based kinetic model for 99m-Technetium-labelled carbon nanoparticles inhaled by humans. Inhalation Toxicology 2009, 21(13), 1099-1107. https://doi.org/10.3109/08958370902748542
  • Yuan et al., 2019: Yuan, D.; He, H.; Wu, Y.; Fan, J.; Cao, Y. Physiologically Based Pharmacokinetic Modeling of Nanoparticles. J Pharm Sci 2019, 108(1), 58–72. https://doi.org/10.1016/j.xphs.2018.10.037