Letter pubs.acs.org/NanoLett
Physiologically Based Pharmacokinetic Model for Long-Circulating Inorganic Nanoparticles Xiaowen Liang,† Haolu Wang,† Jeffrey E. Grice,† Li Li,‡ Xin Liu,*,† Zhi Ping Xu,*,‡ and Michael S. Roberts*,# †
Therapeutics Research Centre, School of Medicine, The University of Queensland, Translational Research Institute, Woolloongabba, QLD 4102, Australia ‡ Australian Institute for Bioengineering and Nanotechnology, The University of Queensland, St Lucia, QLD 4067, Australia # School of Pharmacy and Medical Sciences, University of South Australia, Adelaide, SA 5001, Australia S Supporting Information *
ABSTRACT: A physiologically based pharmacokinetic model was developed for accurately characterizing and predicting the in vivo fate of long-circulating inorganic nanoparticles (NPs). This model is built based on direct visualization of NP disposition details at the organ and cellular level. It was validated with multiple data sets, indicating robust inter-route and interspecies predictive capability. We suggest that the biodistribution of long-circulating inorganic NPs is determined by the uptake and release of NPs by phagocytic cells in target organs.
KEYWORDS: Physiologically-based pharmacokinetic model, long-circulating, inorganic nanoparticles, biodistribution
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typical example of long-circulating NPs, quantum dots (QDs) are 2−10 nm semiconductor nanocrystals with significant advantages for biomedical imaging.10−14 The in vivo biodistribution of many types of QD has been intensively studied in animals15−20 either by quantifying their constituent elements in organs using various analytical techniques19 or by monitoring the QD fluorescence signal in vivo or ex vivo.16,20−24 Up to now, there have been only two research articles reporting PBPK models for QDs. Lee et al. found that a blood-flow-limited PBPK model with fixed partition coefficients could not adequately describe the complex biodistribution exhibited by different QD types.2 In contrast, Lin et al. developed a PBPK model using time-dependent organ distribution coefficient and applied it successfully to describe biodistribution of a commercial product QD705 in mice.25 However, this model was not based on observed physiological processes of administered QDs, and its applicability has not been validated by external data. Therefore, it is necessary to develop more precise and more reasonable PBPK models to better characterize and predict the in vivo distribution of long-circulating NPs, especially QDs. In this work, we used water-dispersible cadmium telluride/ cadmium sulfide (CdTe/CdS) QDs26 to represent long-
ith rapid growth in nanoparticle (NP) applications in various areas including cosmetics, medicine, energy, and electronics,1 there is an urgent need for understanding their behavior in the body to evaluate their toxicity and efficacy. Physiologically based pharmacokinetic (PBPK) modeling provides a powerful tool for integrating and comparing the diverse data and scaling up from animal to human. These models are based on the anatomical structure of the living system and provide a useful tool to predict biodistribution in the body over time and for dose and species extrapolation. Compared to small molecules, the in vivo behavior of NPs involves more complex and unique physiological processes such as opsonization in blood and cellular endocytosis. Although PBPK models for NPs have been developed recently,2−6 only a few of them attempt to simulate the endocytosis of NPs, which is a key process influencing their biodistribution.7,8 In addition, most PBPK models for NPs are developed using the published data set.7 It is necessary to develop more precise PBPK models based on the original experimental data and observed physiological processes of administered NPs. However, long-circulating inorganic NPs have great potential for application in long-term in vivo imaging and sustained drug release since they have long half-lives in the body.9 These NPs display unique patterns of concentration−time profiles in organs. In order to describe the biodistribution and assess the potential toxicity of long-circulating NPs, it is crucial to develop reasonable PBPK models to predict their in vivo behavior. As a © XXXX American Chemical Society
Received: September 23, 2015 Revised: January 12, 2016
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DOI: 10.1021/acs.nanolett.5b03854 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters
Figure 1. Characteristics of CdTe/CdS QDs. (A) Photoluminescence and absorption spectra of QDs; (B) TEM image (scale bar: 20 nm) showing morphology of QDs, inset demonstrating one QD crystal; (C) hydrodynamic particle size distribution; (D) zeta-potential of QDs.
Figure 2. QD disposition at the organ level and cellular level. (A) Representative fluorescence images of organs excised from mice injected with PBS (control) or QDs (5 min and 24 h after injection). The images were pseudocolored based on the fluorescence intensity (blue-green-red). (B) After intravenous injection, QDs were found distributed in the sinusoid of liver and in the peritubular capillaries during the observation periods by multiphoton microscopy. These particles were found to be taken up only by phagocytic cells using TEM. The arrows indicate the QD location in the Kupffer cells of liver and mesangial cells of kidney.
vivo biomedical imaging due to their high photoluminscence quantum yield, good dispersion, and stability in the physiological pH range.26 Our aim was to develop a
circulating inorganic NPs for investigation of their specific in vivo behavior. These QDs with a hydrodynamic particle diameter of 4.2 nm (Figure 1) are particularly suitable for in B
DOI: 10.1021/acs.nanolett.5b03854 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters
Figure 3. (A) Schematic diagram of the PBPK model for QDs. PCs represent phagocytic cells in organs, such as Kuppfer cells in the liver, mesangial cells in the kidney, and splenic macrophages in the spleen. Gray boxes indicate the QDs uptake by phagocytic cells isolated from blood circulation or tissues. It is noted that the tissue represents interstitial space of tissue when it is used to simulated our experimental data of QDs. (B) Observed and model-simulated QD concentration−time profile in mouse tissues after intravenous injection. Solid lines in each panel represent simulation results, and red circles represent mean value of measured data. Error bars represent standard deviation of measured data. The insets represent the observed and model-simulated QD concentration−time profile at the early phase (initial 24 h after intravenous injection).
published PBPK models focus on simulating the endocytosis and release of NPs by phagocytic cells, which are the most important processes affecting their biodistribution.3,7 Since “endocytosis” could be employed to represent different cellular uptake mechanisms including phagocytosis, micropinocytosis, and receptor-mediated endocytosis,7 we used “endocytosis” to represent the phagocytic cells uptake of NPs via multiple endocytic pathways in this study. After intravenous injection, QDs were quickly and evenly distributed to blood vessels of organs via the systemic circulation. These particles could be transported across the capillary wall and reach the interstitial space via a membrane-limited process since the QD size is far smaller than physiological upper limits of capillary pore size of many organs such as ∼15 and ∼150 nm in the kidney and liver, respectively.3 However, they could not be taken up by parenchymal cells as evidenced by above experimental results. After that, QDs were gradually taken up by phagocytic cells in organs from blood circulation or interstitial space, and a portion of them could be released back to blood circulation. In summary, the kinetics of QDs was assumed to be governed by two processes: (1) transport of QDs across the capillary wall; (2) interaction with phagocytic cells in organs. To build the PBPK model, the whole body was separated into five organ compartments (lung, liver, kidney, spleen, and the rest of the body), which were linked together via two blood (venous and arterial) compartments and connected in parallel by a constant and tissue specific blood flow (Figure 3A). In this PBPK model, each organ was separated into three subcompartments: vascular space, phagocytic cells, and tissue (interstitial space for QDs). Mass transfer between the three subcompartments was determined by the extent of cellular uptake of QDs from the blood (or interstitial space of tissue) and released back to the blood (or interstitial space of tissue). The mass balance equations are shown below: For vascular space:
mechanistic PBPK model using assumptions based on our own quantified experimental data and direct visualization of QD disposition in specific organs at the cellular level. The utility of this model was examined across different species and administration routes for describing and predicting the biodistribution of long-circulating inorganic NPs. Its applicability was also evaluated for the other types of long-circulating and biological compatible QDs. To investigate the in vivo fate of QDs, we performed whole body imaging (IVIS imaging system) on mice after intravenous injection of QDs. The liver and kidney were the two organs with the strongest fluorescence signals (Figure 2A), apart from the intestine due to the high autofluorescence.27 We then investigated the spatiotemporal disposition of QDs in the key organs at the cellular level by multiphoton microscopy. As shown in Figure 2B, QDs were quickly and evenly distributed in the blood vessels of liver and kidney, but not taken up by hepatocytes or tubular cells. Instead, these particles were found to be taken up only by phagocytic cells (Kupffer cells and endothelial cells in liver, and mesangial cells in kidney), as shown in TEM images (Figure 2B).28 Finally, inductively coupled plasma−mass spectrometry (ICP−MS) was used to determine cadmium level (as a representative of QDs level) in each organ. Consistent with the imaging observations, liver, kidney, and spleen were found to be the key organs for QD distribution, while only a low level of QDs were found in other organs (Figure S1). The proportion of QDs at 1 and 7 days after dosing were 14.68% and 4.68% in blood, 22.01% and 46.96% in liver, 2.03% and 8.13% in kidney, and 57.6% and 36.23% in the rest of body, which consisted of muscle, bone, and skin. The recovery rate was examined after intravenous injection at 1 and 7 days to calculate the proportion of QD distribution in blood, brain, heart, lung, spleen, intestine, liver, kidney, urine and feces, and the rest of body (Figure S2). The model structure for long-circulating inorganic NPs was based on all of the above experimental observations, while C
DOI: 10.1021/acs.nanolett.5b03854 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters Table 1. QD-Specific Parameters Used in the PBPK Model parameter (unit)
description
lung
liver
spleen
kidney
rest of body
P (unitless) PAC (unitless) Kmax (h−1) K50 (h) n (unitless) Krelease (h−1) Kbile or Kurine (L/h)a
tissue/plasma distribution coefficient permeability coefficient maximum uptake rate constant time for reaching half-maximum uptake rate Hill coefficient release rate constant biliary or urinary clearance
0.015 0.0001 0.0026 7.5 5 0.0061
0.15 0.001 0.15 2.78 7 0.011 0.000000001
0.15 0.001 0.09 1.5 2 0.0072
0.015 0.0001 0.07 6.82 3 0.002 0.000000001
0.15 0.001 0.2 7.5 5 0.0121
a
Kbile and Kurine were set to 0.000000001 in this model as only trace amounts of QDs were found in urine and feces up to 30 days after administration.
VV _t
PA t CT _t dC V = QT(CA − CVt ) − PA t CVt + dt Pt
ment.29 The curve fitting algorithm in Berkeley Madonna was used to minimize the root-mean-square (RMS) between predicted and experimental values. The parameter values obtained from the “open loop” model were then used as initial estimates in the whole-body PK model. Time profiles of QD concentration in tissues and plasma were fitted simultaneously to obtain QD and tissue-specific parameters. The goodness-of fit was assessed by system convergence, least RMS, and visual inspection. The developed PBPK model adequately described experimental tissue kinetics of intravenously injected QDs in blood, liver, kidney, and spleen during the 30-day experimental period (Figure 3B). As shown in Figure S3, an overall regression coefficient (R2) of 0.84 was achieved, indicating high goodnessof-fit of the model. The QD concentration in blood quickly dropped to a low level within 24 h (Figure 3B inset) and maintained at relative constant low levels up to 30 days, while QDs quickly accumulated in the liver and spleen and remained at high levels during the entire experimental period. The constant low level of QD concentration in blood probably corresponded to the slow release of QDs from organs into blood (krelease were 0.011 h−1 for liver, 0.002 h−1 for kidney, and 0.0072 h−1 for spleen). QD concentration in the kidney gradually increased after 24 h postinjection. Compared to liver and spleen, kidney showed the lowest QD level within 24 h, but highest level at 30 day postinjection, which might be explained by the lower Kmax (0.07 h−1) and Krelease (0.002 h−1) for kidney compared to those for liver and spleen (Table 1). The Kmax of QDs for the key organs is significantly lower than those reported for the other NPs,7,30 which could be attributed to their ultrasmall size and long half-life. Since individual types of phagocytic cells have different uptake capacities for the same type of NPs,30 the endocytosis related parameters could be different among organs. Liver was the most predominant organ for QD distribution and accumulation as evidenced by the highest Kmax of 0.15 h−1. To determine the effect of each parameter on the model simulation, sensitivity analysis was performed for all the organs at 1 and 30 days postinjection to capture the early and late kinetic phase, respectively. The relative sensitivity coefficients (RSC) of each parameter for QD concentration in the organs are shown in Table S2. Specifically, distribution coefficient (Pt) and permeability coefficient (PACt) in the liver, spleen, and kidney had negligible influence on all selected QDs concentration in the organs, indicating QDs distribution was not controlled by transcapillary transport. Among the endocytosis-related parameters for each organ t, Kmax_ t represents the maximum uptake rate and QDs concentration in liver, spleen, and kidney were highly sensitive to Kmax_l, Kmax_s, and Kmax_k, respectively (Table S2). K50 and n
(1)
For tissue (interstitial space): VT _t
dCT _t dt
= PA t CVt −
PA t CT _t Pt
− k up_tCVV t V _t
+ k release_tAPC _t
(2)
For phagocytic cells in organ: dAPC _t dt
= k up_tCVV t V _t − k release_t APC _t
(3)
where Pt is the tissue/plasma distribution coefficient for the organ t, PAt is the permeability area cross product between the blood and the tissue of the organ t (PAt = PACt × Qt; PACt, the product of permeability coefficient between capillary blood and tissue), CVt is the QD concentration in the venous blood of the organ t, APC_t is the amount of QDs in the phagocytic cell subcompartment of the organ t, Qt is the blood flow to the organ t, VV_t is the blood volume of the organ t, VT is tissue volume (interstitial space for QDs), CA is the QD concentration in the arterial blood, CT_t is the QD concentration in the tissue subcompartment of the organ t, kup_t is the uptake rate constant of the organ t, krelease_t is the release rate constant of the organ t. The processes of release and excretion of NPs in organs were assumed to follow first-order kinetics. The time-dependent uptake rate constant (kup) of QDs by phagocytic cells can be accurately described by the Hill function as previously reported:7 k up =
K maxT n K50 n + T n
(3)
where T is the time, Kmax is the maximum uptake rate constant, K50 is the time to reach half of Kmax, and n is the Hill coefficient. Key components included in this model were species-specific physiological parameters (body weight and organ volume, interstitial volume, blood volume, and blood flow, given in Table S1) and QD-specific parameters (Table 1). Coding of the PBPK model and simulations were conducted using Berkeley Modonna version 8.3.18 (University of California, Berkeley, CA, USA). The initial estimates of P and PAC were obtained from PBPK model for gold NPs7 and were further optimized by visually fitting to the measured data of QDs concentration after intravenous injection. The QD-specific parameters (Kmax, K50, Krelease, and n) for each organ were estimated in a tissue-by-tissue manner by fitting the time profiles of QD concentration in both tissue and plasma into a simplified “open loop” model with only one tissue compartD
DOI: 10.1021/acs.nanolett.5b03854 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 4. (A) Absorption of QDs from injection site after subcutaneous injection imaged by IVIS instrument. Whole body fluorescence images of one representative mouse at different time points after subcutaneous injection of QDs. (B) Time profile of QDs fluorescence intensity per pixel at injection site. (C) Model evaluation results with experimental data from QDs subcutaneously injected to mice. Solid lines represent simulation results and red circles represent mean value of measured data. Error bars represent standard deviation of measured data. The insets represent the observed and model-simulated QD concentration−time profile at the early phase, initial 24 h after subcutaneous injection.
Figure 5. Model evaluation results with independent data. (A) 3.5 nm QDs in liver, spleen, and kidney of mice after intravenous injection (1.1 μg/g) and data from Su et al.18 (B) 18.5 nm QDs in blood, liver, spleen, and kidney of mice after intravenous injection (0.921 μg/g) and data from Lin et al.19 (C) 21.2 nm PEG-QDs in liver, spleen, and kidney of rats after intravenous injection and data from Hauck et al.32 Solid lines represent simulation results using QD-specific parameters, and red circles represent mean value of measured data.
The validity of current PBPK model was first evaluated with our own data where the same type of QDs was injected subcutaneously to Balb/c mice (3.6 μg/g). An extra compart-
determine the time and the extent of activation of endocytosis,7 but have no significant effects on QD distribution. E
DOI: 10.1021/acs.nanolett.5b03854 Nano Lett. XXXX, XXX, XXX−XXX
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Although many isolated studies have been reported on NP biodistribution, only a few contain integrated models to characterize the in vivo fate of these particles. PBPK model is a useful tool to integrate available data for making explicit conclusions on the pharmacokinetics of NPs. To develop an appropriate PBPK model, it is important to understand the mechanisms of NP disposition at the organ level. In the present study, we developed such a model based on direct observation of kinetic processes of biocompatible QDs at both the organ and the cellular level. Compared to previously published PBPK models,2,25 our model showed better performance in predicting our experimental data and independent external data.18,25,32 Compared to simple traditional perfusion-limited models and membrane-limited models, our model shows a more explicit description of the complex in vivo behavior exhibited by longcirculating NPs. This model is especially useful for inorganic long-circulating NP in the body and provides a general framework for NP design. In the future, the predictive capacity of the model can be improved with the incorporation of new parameter values or advanced microscopic details when they become available. Although intravenous injection is the most common administration route for studies of NP biodistribution, other alternative routes such as subcutaneous injection and oral administration have also been reported.37 Our PBPK model has shown acceptable accuracy for inter-route extrapolation. More importantly, this model has revealed significantly different distribution patterns of QDs between intravenous and subcutaneous injection. The sensitivity analysis showed that the maximum uptake rate constant (kmax) is the most influential parameter determining the QD level in organs in the short and long terms, indicating cellular uptake is the key process for QD distribution. This result was confirmed by model simulation for several external data sets. There is substantial evidence that the physiochemical properties (e.g., size, surface charge, surface coating, and protein binding) of NPs play an important role in their in vivo biodistribution.20,38 It has been reported that 4 nm gold NPs showed a higher concentration in liver or spleen than that of 100 nm, indicating a size-dependent distribution.38 Bachler et al. included a size-specific parameter in PBPK model to predict the biodistribution of 15−150 nm silver NPs.3 Since most of long-circulating inorganic NPs are have small size (
