An artificial intelligence-assisted physiologically-based pharmacokinetic model to predict nanoparticle delivery to tumors in mice

Abstract

The critical barrier for clinical translation of cancer nanomedicine stems from the inefficient delivery of nanoparticles (NPs) to target solid tumors. Rapid growth of computational power, new machine learning and artificial intelligence (AI) approaches provide new tools to address this challenge. In this study, we established an AI-assisted physiologically based pharmacokinetic (PBPK) model by integrating an AI-based quantitative structure-activity relationship (QSAR) model with a PBPK model to simulate tumor-targeted delivery efficiency (DE) and biodistribution of various NPs. The AI-based QSAR model was developed using machine learning and deep neural network algorithms that were trained with datasets from a published "Nano-Tumor Database" to predict critical input parameters of the PBPK model. The PBPK model with optimized NP cellular uptake kinetic parameters was used to predict the maximum delivery efficiency (DEmax) and DE at 24 (DE24) and 168 h (DE168) of different NPs in the tumor after intravenous injection and achieved a determination coefficient of R² = 0.83 [root mean squared error (RMSE) = 3.01] for DE24, R² = 0.56 (RMSE = 2.27) for DE168, and R² = 0.82 (RMSE = 3.51) for DEmax. The AI-PBPK model predictions correlated well with available experimentally-measured pharmacokinetic profiles of different NPs in tumors after intravenous injection (R² ≥ 0.70 for 133 out of 288 datasets). This AI-based PBPK model provides an efficient screening tool to rapidly predict delivery efficiency of a NP based on its physicochemical properties without relying on an animal training dataset.

Keywords: Artificial intelligence; Drug delivery; Machine learning; Nanomedicine; Nanotechnology; Physiologically based pharmacokinetic modeling.

Fig. 1.

Overview of the computational workflow to integrate machine learning and deep learning models with physiologically based pharmacokinetic (PBPK) modeling to predict delivery efficiency of nanoparticles (NPs) to the tumor site in tumor-bearing mice. (A) Step 1: Nano-Tumor Database, (B) Step 2: Development of AI-QSAR model, (C) Step 3: AI-assisted PBPK model. Abbreviations: DNN, deep neural network; RF, random forest; Adj-R², adjusted coefficient of determination; RMSE, Root mean square error; KTRES_max, maximum uptake rate constant of tumor cells; KTRES_50, time reaching half maximum uptake rate of tumor cells; KTRES_n, Hill coefficient for the uptake of tumor cells; KTRES_rel, release rate constant of tumor cells.

Fig. 2.

Schematic diagram of physiologically based pharmacokinetic (PBPK) model for NPs in (A) tumor-bearing mice intravenously (IV) administrated with AuNPs and various inorganic and organic nanomaterials. (B) This PBPK model consists of eight compartments including plasma, lungs, liver, kidneys, spleen, brain, muscle, remaining tissues (i.e., pooled other tissues) and tumors. (C) Except plasma and brain, each compartment was divided into three major parts: capillary blood, interstitium, and endocytic or phagocytic cells (PCs), or tumor cells (TCs).

Fig. 3.

Densities of predicted (yellow bar) and data-driven parameters (purple bar) distributions for (A) KTRES_50, (B) KTRES_max, (C) KTRES,_n and KTRES_rel. The range of predicted and data-drive values were expressed as median (95% CI) in the plots. The adjusted-R2 (Adj-R²) was estimated by linear regression model.

Fig. 4.

Evaluation results of AI-PBPK model-predicted tumor delivery efficiency. A global evaluation of goodness of model fit between the data-driven (x-axis) and AI-PBPK model-predicted delivery efficiency (DE) (y-axis) at (A) 24 hours, (B) 168 hours and (C) the maximum DE. Abbreviations: %2e and %3e, represent the percentage of data points within 2-fold and 3-fold errors, respectively; Adj-R² and RMSE represent the adjusted determination coefficients and root mean square, respectively.

Fig. 5.

Evaluation results of AI-PBPK model-predicted time-dependent distribution of nanoparticles (NPs) to tumors. (A) Comparisons between observed and predicted NPs in tumors (%ID/g) for all datasets (i.e., all types of NPs and different tumors) and (B) predicted-to-observed ratio versus model prediction plot. Abbreviations: %2e and %3e, represent the percentage of data points within the 2-fold and 3-fold errors, respectively; Adj-R² represent the adjusted determination coefficients.

Fig. 6.

Representative evaluation results of comparisons between the AI-PBPK model predictions versus experimentally measured pharmacokinetic profiles of NPs in tumors. NP concentration in tumor (%ID/g) predicted from the PBPK model with optimized parameters (dashed line) compared to the observed NPs amount in tumor from experimental data (black closed circles) for 15 randomly selected NPs from the study of (A-B) Cabral et al. (2011) [65], (C-E) Guo et al. (2013) [66], (F-G) Sumitani et al. (2013) [67], (G-M) Bae et al. (2007) [68], (N) Bibby et al. (2005) [69] and (O) Bae et al. (2005) [70]. Tumor tissue concentrations as presented in the y-axis are expressed in the units of percent of the injected dose (%ID/g) according to units used in the original articles.