Predicting Nanoparticle Delivery to Tumors Using Machine Learning and Artificial Intelligence Approaches

Figures & data

Table 1 Summary of Modeling Algorithms Used in This Study

Model	Synonym	Model Category	Tuning Parameters
Machine Learning Algorithms
Linear regression	Linear	Simple model	Alpha, Lambda
k-nearest neighbors	KNN	Simple model	K
Random Forest	RF	Ensemble model	mtry
Bagged Model	Bag	Ensemble model	None^a
Stochastic Gradient Boosting	Gbm	Ensemble model	n.trees; shrinkage, n.minobsinnode
Support vector machine	SVM	Support vector machine	C
Least-squares SVM	LS-SVM	Support vector machine	Cost, loss
L2-Regularized SVM	L2-SVM	Support vector machine	Cost, loss
Deep Learning Algorithm
Deep neural networks	DNN	Neural networks	Rate, L1, L2

Notes: Alpha, Lambda: the penalty parameters in the elastic regression model. C: A regularization parameter that controls the trade-off between the misclassification and width of the margin. Cost: The cost function in Least-squares or L2-Regularized SVM model. Loss: The Loss function in Least-squares or L2-Regularized SVM model. K: A parameter in KNN model that refers to the number of nearest neighbors. mtry: Number of variables randomly sampled as candidates at each decision tree. n.trees: Number of decision trees in the stochastic gradient boosting model. n.minobsinnode: Minimum number of samples in tree terminal nodes. L1: a loss function to minimize the error which is the sum of all the absolute differences between the measured values and predicted values. L2: a loss function to minimize the error which is the sum of all the squared differences between the measured values and predicted values. Rate: The learning rate in deep learning model that controls how much to change the model in response to the estimated error when model weights are updated for each of the iterations. shrinkage: The learning rate in the stochastic gradient boosting model. ^aNone of the parameters were tuned in this model.

Table 2 List of Variables and Its Levels/Values in the Tumor-Nano Database

Variables	Unit	Symbol	Levels or Ranges
Type of nanoparticles	-	Type	Inorganic; Organic
Core materials of nanoparticles	-	MAT	Gold, Dendrimers, Liposomes, Polymeric, Hydrogels, Other Organic Material, Other Inorganic Material
Targeting strategy	-	TS	Passive, Active
Hydrodynamic diameter	nm	HD	[3, 399]
Log10-transformed HD	nm	Size	[0.43, 2.66]
Zeta potential	mV	ZP	[−59.4, 71.3]
Shape of nanoparticles	-	Shape	Spherical, Rod, Plate, Others
Tumor Model	-	TM	Allograft Heterotopic (AH), Allograft Orthotopic (AO), Xenograft Heterotopic (XH), Xenograft Orthotopic (XO)
Cancer Type	-	CT	Brain, Breast, Cervix, Colon, Liver, Lung, Ovary, Pancreas, Prostate, Skin
DE at 24 hours	%ID	DE24	[0.008, 50.3]
DE at 168 hours	%ID	DE168	[0.008, 23.8]
DE at the last sampling time point	%ID	DETlast	[0.008, 56.9]
Maximum DE	%ID	DEmax	[0.008, 29.8]

Note: DE_Tlast, DE₂₄, DE₁₆₈ represent tumor delivery efficiency estimated at the last sampling time point, 24 h and 168 h after intravenous injection. DE_max is the maximum tumor delivery efficiency.

Abbreviations: DE, tumor delivery efficiency of nanoparticles; %ID, percentage of initial dose or injected dose.

Figure 1 Overview of the study framework to develop machine learning and deep learning models to predict delivery efficiency of nanoparticles to the tumor site in tumor-bearing mice. X represents the initial input variables and W represents the variables after feature selections.

Abbreviations: R², adjusted coefficient of determination; RMSE, root mean square error; MAE, mean absolute error.

Figure 2 Overview of the Nano-Tumor Database. (A–C) Percentages of data related to cancer therapy scenarios based on the Targeting Strategy (TS), Cancer Type (CT), and Tumor Model (TM). (D–H) Percentages of data that were categorized based on the physicochemical properties of the studied nanoparticles, including the type (D), the shape (E), the core (F), the log-transformed hydrodynamic diameter (G), and Zeta potential (H). In Panel H, Zeta potential values are presented using box whisker plots across 2.5th, 25th, 50th, 75th, and 97.5th percentiles. Data in the Nano-Tumor Database are from Cheng et al.⁵

Table 3 Five-Fold Cross-Validation and Testing Results for Tumor Delivery Efficiency Using Different Machine Learning and Deep Learning Models

	DEmax		DE24		DE168		DETlast
Model	5-Fold CV	Test	5-Fold CV	Test	5-Fold CV	Test	5-Fold CV	Test
LR
R^2	0.06 ± 0.05	0.08	0.10 ± 0.10	0.08	0.07 ± 0.03	0.06	0.07 ± 0.07	0.13
RMSE	3.98 ± 1.03	7.56	3.89 ± 0.61	6.56	2.18 ± 0.60	3.20	3.98 ± 0.88	4.73
MAE	2.42 ± 0.48	3.31	2.37 ± 0.24	2.70	1.29 ± 0.20	1.44	2.42 ± 0.44	2.46
KNN
R^2	0.03 ± 0.04	0.06	0.04 ± 0.04	0.08	0.03 ± 0.04	0.04	0.01 ± 0.04	0.08
RMSE	4.05 ± 1.12	7.55	3.95 ± 0.71	6.51	2.31 ± 0.56	3.22	4.05 ± 1.01	4.77
MAE	2.36 ± 0.47	3.51	2.31 ± 0.30	2.82	1.33 ± 0.21	1.50	2.36 ± 0.43	2.59
RF
R^2	0.19 ± 0.12	0.16	0.19 ± 0.16	0.17	0.19 ± 0.10	0.11	0.15 ± 0.16	0.29
RMSE	3.71 ± 1.03	7.15	3.64 ± 0.62	6.18	2.06 ± 0.61	3.17	3.72 ± 0.82	4.24
MAE	2.21 ± 0.48	2.92	2.17 ± 0.27	2.37	1.20 ± 0.21	1.30	2.22 ± 0.45	2.15
Bag
R^2	0.09 ± 0.07	0.08	0.13 ± 0.12	0.08	0.10 ± 0.06	0.04	0.09 ± 0.09	0.15
RMSE	3.91 ± 1.06	7.49	3.86 ± 0.64	6.50	2.16 ± 0.58	3.22	3.91 ± 0.91	4.63
MAE	2.38 ± 0.47	3.34	2.34 ± 0.25	2.66	1.27 ± 0.19	1.35	2.38 ± 0.46	2.44
Gbm
R^2	0.08 ± 0.08	0.09	0.12 ± 0.11	0.17	0.11 ± 0.06	0.05	0.08 ± 0.07	0.24
RMSE	3.91 ± 1.03	7.48	3.81 ± 0.62	6.30	2.16 ± 0.57	3.22	3.92 ± 0.85	4.46
MAE	2.42 ± 0.47	3.27	2.34 ± 0.26	2.60	1.30 ± 0.20	1.32	2.42 ± 0.42	2.38
R-SVM
R^2	0.02 ± 0.03	0.23	0.04 ± 0.03	0.19	0.04 ± 0.03	0.14	0.02 ± 0.02	0.25
RMSE	4.12 ± 1.29	7.80	4.02 ± 0.87	6.76	2.28 ± 0.67	3.31	4.12 ± 1.12	4.97
MAE	1.93 ± 0.54	2.82	1.87 ± 0.35	2.32	1.06 ± 0.24	1.22	1.93 ± 0.47	2.08
LS-SVM
R^2	0.02 ± 0.03	0.23	0.05 ± 0.03	0.18	0.05 ± 0.03	0.13	0.03 ± 0.03	0.24
RMSE	4.12 ± 1.29	7.81	4.02 ± 0.87	6.77	2.27 ± 0.66	3.31	4.12 ± 1.12	4.98
MAE	1.92 ± 0.54	2.83	1.86 ± 0.26	2.32	1.05 ± 0.24	1.22	1.93 ± 0.47	2.09
L2-SVM
R^2	0.07 ± 0.06	0.14	0.11 ± 0.10	0.14	0.08 ± 0.04	0.18	0.08 ± 0.07	0.19
RMSE	4.01 ± 0.97	7.32	3.91 ± 0.59	6.37	2.23 ± 0.56	3.03	4.02 ± 0.78	4.54
MAE	2.52 ± 0.46	3.20	2.45 ± 0.26	2.61	1.38 ± 0.19	1.37	2.52 ± 0.42	2.39
DNN
R^2	0.47 ± 0.20	0.70	0.40 ± 0.34	0.46	0.45 ± 0.24	0.33	0.35 ± 0.23	0.63
RMSE	3.58 ± 1.35	2.38	2.75 ± 0.92	3.10	1.96 ± 1.09	1.78	3.24 ± 1.04	3.01
MAE	2.20 ± 0.65	1.64	1.72 ± 0.50	1.84	1.10 ± 0.42	0.94	1.92 ± 0.54	1.81

Note: DE_max, DE₂₄, DE₁₆₈ and DE_Tlast represent the maximum tumor delivery efficiency (DE), DE at 24 h, 168 h, and the last sampling time, respectively.

Abbreviations: LR, linear regression; KNN, k-nearest neighbors; RF, random forest; Bag, bagged model; Gbm, stochastic gradient boosting; R-SVM, regular support vector machine; LS-SVM, least-squared support vector machine; L2-SVM, L2-regulated support vector machine; DNN, deep learning neural network; CV, cross-validation.

Figure 3 Correlation between values from the Nano-Tumor Database and the deep neural network model-predicted values for (A) DE_max, (B) DE₂₄, (C) DE₁₆₈ and (D) DE_Tlast. Root mean square error (RMSE) and coefficient of determination (R²) in the training set and test set are shown. RMSE_train and R²_train represent the best performance of RMSE and R² values in the training set, while RMSE_test and R²_test represent the values for external validation. DE_max, DE₂₄, DE₁₆₈ and DE_Tlast represent the maximum tumor delivery efficiency (DE), DE at 24 h, 168 h, and the last sampling time, respectively.

Figure 4 Correlation between values from the Nano-Tumor Database and the predicted values based on the simple linear regression model for (A) DE_max, (B) DE₂₄, (C) DE₁₆₈ and (D) DE_Tlast. Root mean square error (RMSE) and coefficient of determination (R²) in the training set and test set are shown. RMSE_train and R2_train represent the best performance of RMSE and R² values in the training set, while RMSE_test and R²_test represent the values for external validation. DE_max, DE₂₄, DE₁₆₈ and DE_Tlast represent the maximum tumor delivery efficiency (DE), DE at 24 h, 168 h, and the last sampling time, respectively.

Figure 5 Correlation between values from the Nano-Tumor Database and the predicted values based on the random forest model for (A) DE_max, (B) DE₂₄, (C) DE₁₆₈ and (D) DE_Tlast. Root mean square error (RMSE) and coefficient of determination (R²) in the training set and test set are also shown. RMSE_train and R²_train represent the best performance of RMSE and R² values in the training set, while RMSE_test and R²_test represent the values for external validation. DE_max, DE₂₄, DE₁₆₈ and DE_Tlast represent the maximum tumor delivery efficiency (DE), DE at 24 h, 168 h, and the last sampling time, respectively.

Figure 6 Importance percentage in the deep learning model for each feature variable. (A–D) represent results for the feature variable of DE_max, DE₂₄, DE₁₆₈ and DE_Tlast, respectively. Individual importance is represented by colors in the stacked bars.

Abbreviations: ZP, zeta potential; Type, type of nanoparticles; TS, targeting strategy; TM, tumor model; Size, log-transformed value of the hydrodynamic size; Shape, shape of nanoparticles; MAT, core material of nanoparticles; CT, cancer type; AH, allograft heterotopic; AO, allograft orthotopic; XH, xenograft heterotopic; XO, xenograft orthotopic.

Cheng YH, He CL, Riviere JE, Monteiro-Riviere NA, Lin ZM. Meta-analysis of nanoparticle delivery to tumors using a physiologically based pharmacokinetic modeling and simulation approach. ACS Nano. 2020;14(3):3075–3095. doi:10.1021/acsnano.9b08142

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