Liposome Particle Size Prediction by In‐Line Process Analytical Technology (PAT)‐Integrated Machine Learning

ABSTRACT

Precise control of liposome size is critical for drug delivery. We developed an in‐line PAT‐integrated machine learning model that predicts particle size with high accuracy (root mean square error 7.18 nm) using limited experimental data. By integrating physicochemical membrane characteristics, the model demonstrates generalization (root mean square error 7.53 nm) and interpretability, establishing a practical framework for advanced liposome particle size control.

An in‐line PAT‐integrated ML strategy for microfluidic liposome synthesis accurately predicted particle size from formulation parameters and fluoresence sensing data. The model captured both seen and unseen conditions, demonstrating robust generalization and process control with low error.

1. Introduction

Liposomal drug delivery systems–which serve as carriers for a wide range of therapeutics including small molecules, proteins, and nucleic acids–particle size is a critical quality attribute (CQA) [1, 2, 3]. Liposome particle size attribute directly dictates the formulation's in vivo behavior, influencing its circulation half‐life, biodistribution, cellular uptake, and its efficacy and safety profile [4, 5, 6, 7, 8, 9, 10]. Consequently, pharmaceutical guidelines such as the U.S. Food and Drug Administration (FDA)[11] and the International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use (ICH) Q6B [12], mandate that the mean particle size and its distribution be rigorously established and controlled throughout the liposomal drug as its specification.

Microfluidic systems have emerged as enabling highly controlled, rapid mixing of a lipid‐in‐solvent stream with an aqueous phase, facilitate a reproducible self‐assembly process [13, 14], yielding liposomes with a narrow size distribution consistency compared to conventional bulk methods [15, 16, 17]. In this system, the final particle size is the result of a complex interplay between numerous critical process parameters [18, 19, 20, 21], such as initial lipid concentration, total flow rate (TFR), and the flow rate ratio (FRR) of the aqueous and organic phases (Figure 1a).

Figure 1.

(a) Schematic illustration of critical process parameters (Total flow rate (TFR), flow rate ratio (FRR), initial lipid concentration) and process variables (membrane hydrophobicity, membrane rigidity) of liposome particle size in microfluidic mixing. (b) Integration of the in‐line fluorescence spectroscopy process analytical technology (PAT)‐integrated control loop.

Previous studies have highlighted that the physicochemical characteristics of lipid membranes are process variables to liposome size [17, 22] (Figure 1a). Experimental data obtained by fluorescence spectroscopy has proposed that rigid membranes delay the closure of bilayer phospholipid fragment intermediates, while increased membrane hydrophobicity enhances hydrophobic interactions and accelerates growth. Statistical analysis confirmed that both rigidity and hydrophobicity, obtained by fluorescent probe, exhibit strong correlations with liposome size. This result underscore that membrane physicochemical characteristics must be balanced with synthesis conditions to achieve precise size control in a previous study [22]. However, determining the optimal variables through conventional one‐factor‐at‐a‐time experimentation remains inefficient and resource‐intensive, posing a bottleneck for liposome size optimization.

The integration of machine learning (ML) has become a promising strategy to navigate the complex parameter relationships of microfluidic liposome synthesis [23, 24]. ML models learn the complex relationships between input parameters and output particle sizes [25, 26]. Despite this potential, liposomal particle size prediction has relied on a data amount approach, where the predictive power of a model is assumed to scale with the volume of training data.

This study introduces a strategic approach towards membrane characteristic based ML prediction in microfluidic liposome synthesis. We proposes a framework integrating in‐line fluorescence spectroscopy process analytical technology (PAT) within a closed‐loop control ML‐driven prediction (Figure 1b). The central hypothesis is that the key to improving ML performance in liposome formation may rely more strongly on the physicochemical relevance of input features than on increasing dataset size or algorithmic complexity, particularly under small‐sample experimental conditions. This approach bridges the gap between uncertain particle size and ML‐driven prediction, providing a practical blueprint for the rapid and precise size controlling of liposomes.

2. Results

2.1. In‐line Process Analytical Technology Data and Particle Size Correlation

Stability and spectral reproducibility of in‐line process analytical technology (PAT) system were summarized in Supporting Information. The particle size exhibited a wide dynamic range from 29.87 nm (Min) to 152.97 nm (Max) with a median of 94.89 nm (Figure 2a), while the polydispersity index (PDI) was consistently maintained at a low level (Mean: 0.20, Range: 0.10–0.26) demonstrating the high reproducibility and monodispersity of the microfluidic process (Figure 2b). This indicates that the dataset contains sufficient variance in particle size to train the regression model, while the consistently low PDI confirms that the observed variation in particle size is a direct result of process modulation, rather than experimental inconsistency.

Figure 2.

(a,b) Distribution of target variables for the collected dataset ($N$ = 48). (a) Particle size ranges from 29.87 nm to 152.97 nm with a mean of 94.89 nm. (b) polydispersity index (PDI) distribution shows a mean of 0.19 with a maximum value of 0.26. (c) Framework and data splitting strategy for machine learning‐based predictive modeling. Input parameters integrate microfluidic critical process parameters with physicochemical membrane characteristics (process variables), targeting particle size and polydispersity index as output parameters. The dataset was divided into an internal set (training/validation by leave‐one‐out cross‐validation) for hyperparameter tuning and a distinct external set. Five algorithms were implemented, ranging from linear regression models (linear regression, lasso regression) to support vector machines (linear support vector machine, polynomial support vector machine) and XGBoost. (d) Schematic illustration of the in‐line PAT‐integrated ML model for liposome particle size prediction.

To evaluate whether the parameters obtained from in‐line PAT system are valid features for machine learning (ML)‐based prediction, the Spearman's rank correlations were investigated between each parameter and outputs–particle size and polydispersity index (PDI) (Figure S10). Across tested conditions, hydrophobicity, and rigidity be strongly related with particle size, as characterized by in‐line PAT system.

2.2. Development of In‐Line PAT‐Integrated Machine Learning Prediction

ML models were constructed to predicting liposome particle size and PDI. In the development of ML for predicting liposome size, these physicochemical parameters were employed as input features with five ML algorithms (Figure 2c,d). Each algorithm was optimized via a grid search over the hyperparameters listed in Tables S3–S7.

Prediction accuracy was compared across models using root mean square error (RMSE), summarized in heatmaps for visual comparison (Figures 3a and 4a). Among the algorithms tested, linear regression (LR) and polynomial support vector machine (P‐SVM) achieved the highest accuracy for particle‐size prediction. On the other hand, PDI was best predicted by LR and XGBoost (XG). The normalized RMSE heatmaps are also provided in Figure S15 to offer a view of the performance differences with normalization.

Figure 3.

(a) Normalized root mean square error (RMSE) of machine learning algorithms for liposome particle size prediction. The RMSE values were standardized using Min‐Max normalization (scaled between 0 and 1) across all models to enable direct visual comparison. LR: linear regression. LASSO: LASSO regression. XG: XGBoost. L‐SVM: linear support vector machine. P‐SVM: polynomial support vector machine. (b) SHAP (SHapley Additive exPlanations) summary plot illustrating the impact of process parameters and material attributes on liposome particle size at optimized model(P‐SVM). Features are ranked by their global importance (y‐axis). (c)(d) Learning curve of linear regression for predicting liposome particle size (c) input parameters: TFR, FRR, lipid concentration (d) input parameters: TFR, FRR, lipid concentration, membrane rigidity $r_{DPH}$. (e) Experimental versus predicted value plots of particle size with optimized linear regression. (f)(g) Learning curve of polynomial support vector machine for predicting liposome particle size (f) input parameters: TFR, FRR, lipid concentration (g) input parameters: TFR, FRR, lipid concentration, membrane hydrophobicity $G{P}_{340}$. (h) Experimental versus predicted value plots with optimized polynomial support vector machine. Predicted values were evaluated using Leave‐One‐Out Cross‐Validation.

Figure 4.

(a) Normalized root mean square error (RMSE) of machine learning algorithms for liposome polydispersity index prediction. The RMSE values were standardized using Min‐Max normalization (scaled between 0 and 1) across all models to enable direct visual comparison. LR: linear regression. LASSO: LASSO regression. XG: XGBoost. L‐SVM: linear support vector machine. P‐SVM: polynomial support vector machine. (b) SHAP (SHapley Additive exPlanations) summary plot illustrating the impact of process parameters and material attributes on liposome polydispersity index at optimized model(XG). Features are ranked by their global importance (y‐axis). (c)(d) Learning curve of XGBoost for predict liposome polydispersity index (c) input parameters: TFR, FRR, lipid concentration (d) input parameters: TFR, FRR, lipid concentration, membrane rigidity $r_{DPH}$. (e) Experimental versus predicted value plots with optimized XG. (f)(g) Learning curve of Lasso regression for predict polydispersity index (f) input parameters: TFR, FRR, lipid concentration (g) input parameters: TFR, FRR, lipid concentration, membrane rigidity $r_{DPH}$. (h) Experimental versus predicted value plots with optimized LR. Predicted values were evaluated using Leave‐One‐Out Cross‐Validation.

2.3. Elucidating the Role of In‐Line PAT‐ML via SHAP Analysis

SHAP (SHapley Additive exPlanations) analysis quantifies the contribution of each input feature to the model's output, enabling the visualization of both the magnitude and direction of their impact on output parameters.

Figure 3b illustrates the SHAP summary plot derived from the polynomial P‐SVM particle size prediction. Total flow rate (TFR) appears as the most dominant factor, showing a negative correlation (red dots on the left) consistent with kinetic size control. A key finding is the role of in‐line PAT data, which serves as a critical indicator for the membrane's physicochemical characteristics. This result is in agreement with the mechanism we proposed in a previous study [22].

Figure 4b SHAP summary plot for PDI prediction using the XG. Unlike the particle size prediction (which relied on membrane properties), the magnitude of SHAP values is considerably small (mostly within $\pm$0.02), indicating that the polydispersity of the liposomes is less sensitive to parameter variations compared to particle size.

2.4. Evaluation of Predictive Performance and Model Selection

To verify the validity of the selected model training for size prediction, learning curves were plotted. To isolate the contribution of the in‐line PAT descriptors, we performed an ablation analysis comparing models trained with and without the membrane physicochemical features. Models trained without in‐line PAT data (i.e., using only process parameters) exhibited poor convergence and significantly higher RMSE values (Figure 3c,f), indicating that process parameters alone are insufficient to capture the full variance of particle formation. In contrast, the learning curves confirmed that the models were not exhibiting underfitting or overfitting in the PAT‐ML framework(Figure 3d,g). This underscores the importance of in‐line physicochemical data for achieving high predictive accuracy model training. Particle size prediction performance were evaluated using actual versus predicted value plots (Figure 3e,h), demonstrating strong generalization capability in ML prediction. PDI learning curve and prediction performance were also evaluated using actual versus predicted value plots (Figure 4). Among the algorithms tested, P‐SVM achieved the best particle size prediction (lowest leave‐one‐out cross‐validation (LOOCV) RMSE, highest ${\mathrm{R}}^2$), whereas XG performed best for PDI. Optimized input parameters and hyperparameters for each algorithm are listed in Tables S8–S13.

Consequently, the P‐SVM demonstrated superior performance of particle size prediction in in‐line PAT‐ML; it achieved the highest predictive accuracy (RMSE = 7.18 nm, approximately 7.6% relative to the mean particle size) without overfitting, demonstrating generalization with the small sample size. The learning curves of non‐selected algorithms are presented in the Figures S11 and S12 to illustrate their respective training characteristics and to support the model selection.

Required time and optimized prediction performance of in‐line PAT system was summarized in Table 1. Required time per sample of conventional batch workflow was estimated by the formulation, dialysis/solvent exchange, off‐line measurement process.

Table 1.

Comparison of required time and prediction performance for Particle Size and PDI.

Methods	Required time per sample	Particle size prediction		PDI prediction
		Average RMSE (nm)	$R^2$	Average RMSE [−]	$R^2$
In‐line PAT‐ML	10 – 60 min	7.18	0.94	0.030	0.40
Conventional batch workflow	$>$ 1 day	n.d.	n.d.	n.d.	n.d.

2.5. External Validation of Generalization Capability on Unseen Conditions

To evaluate the predictive capability beyond the training dataset, an external validation was conducted using eight independent experimental conditions (Table 2) that were completely excluded from the model training phase. These conditions specifically targeted intermediate process parameters and novel lipid compositions. As shown in Figure 5, the in‐line PAT‐ML model successfully predicted the particle sizes of these unseen samples, achieving an RMSE of 7.53 nm and an ${\mathrm{R}}^2$ of 0.87. The predicted values are plotted against the experimental data, demonstrating a linear correlation along the diagonal line, demonstrating generalization.

Table 2.

Experimental conditions of the external validation dataset.

Parameter	TFR (${\mathrm{mLh}}^{-1}$)	FRR [−]	Total lipid conc. (mM)	Lipid Ratio [−]
				DOPC	Chol	ESM
Interpolation (TFR)	3.5	3	5	5	3	2
	15	3	5	5	3	2
Interpolation (FRR)	5	7	5	5	3	2
	5	15	5	5	3	2
Interpolation (Conc)	5	10	7.5	5	3	2
	5	10	17.5	5	3	2
Extrapolation 1 (Ratio)	10	3	5	7	1.5	1.5
Extrapolation 2 (All)	3.5	7	7.5	7	1.5	1.5

Figure 5.

(a) Schematic illustration of the external validation strategy used to assess the generalization capability of the in‐line PAT‐integrated ML model. The model was trained exclusively on a predefined set of experimental conditions (training domain) using in‐line PAT signals and process parameters. External validation was performed using an independent dataset completely excluded from training, consisting of (i) interpolation conditions with intermediate process parameters and (ii) extrapolation conditions involving novel lipid compositions. Model predictions for these unseen conditions were compared against experimental particle sizes to evaluate generalization beyond the training domain. (b) (c) External validation of the polynomial support vector machine using an independent dataset of unseen experimental conditions (completely excluded from the model training phase). (b) Residual analysis of the internal and external validation dataset. Dashed line: 0 $\pm$ 20 nm. (c) The comparison between the experimentally measured particle size and the model‐predicted value. Dashed line: y =x (perfect prediction). (d) Comparison of prediction accuracy for particle size estimation using machine learning models with and without in‐line PAT. Bars represent RMSE, and open circles denote ${\mathrm{R}}^2$.

2.6. Analysis of the Applicability Domain

To define the applicability domain (AD) of the model, we quantitatively analyzed the relationship between the distance of the external validation points from the training set and their corresponding prediction errors. We defined the distance from training set centroid as the Euclidean distance from the mean center of the training data to each external validation point within the normalized multidimensional feature space. As illustrated in Figure S14, the absolute prediction error exhibits lower than 13 nm both interpolation and extrapolation conditions span a normalized distance range of approximately 1.3 to 2.6 from the centroid.

3. Discussion

3.1. Particle Size Prediction by In‐Line PAT‐ML

3.1.1. In‐Line Spectral Analysis Yields Size Process Variables of Particle Size

The Spearman's correlation analysis [27] revealed that the membrane characteristics data exhibited a stronger positive correlation with the final liposome particle size compared to total flow rate (TFR), flow rate ratio (FRR), lipid concentration (Figure S10). This nonparametric rank‐based approach is appropriate for assessing monotonic relationships in potentially non‐normally distributed process data. This result validated the strategy of leveraging in‐line process analytical technology (PAT) with spectroscopic measurements to generate information‐rich data that provide relevant features for the ML model, consistent with previous reports on spectroscopic PAT for pharmaceutical processes and liposomal or particulate systems [28, 29, 30].

3.1.2. Algorithm Selection

To develop a predictive model for liposome particle size, five machine learning algorithms were selected (Figure 2c).

Linear regression (LR) was employed as an interpretable baseline to test for linear relationships between process parameters and the target variables. To address multicollinearity and perform embedded feature selection, LASSO regression was implemented, which shrinks coefficients and drives some to zero via an L1 penalty [31].

Support vector machines (SVMs) were chosen to capture low‐order nonlinearities with strong regularization [32]. A linear SVM (L‐SVM) was used to establish a maximum‐margin linear decision boundary, while a polynomial SVM (P‐SVM) was selected to model modest interaction effects and data curvature without the high parameterization burden of fully nonparametric models, which is advantageous in small‐sample regimes.

To account for higher‐order interactions and non‐additive effects, tree‐based ensembles were evaluated. XGBoost employs a stage‐wise boosting approach with built‐in regularization mechanisms, enabling it to effectively model heterogeneous effects and complex interaction structures in tabular data [33].

In this study, the P‐SVM successfully captured the non‐linear physical interactions between mixing kinetics and membrane characteristics that govern particle size. Since P‐SVM achieved the highest accuracy without overfitting, it was adopted as the final model.

3.1.3. Particle Size Prediction With Physical Interpretation

In‐line PAT‐ML model demonstrated high predictive accuracy using a small dataset ($N$ = 48). The learning curve analysis showed that the RMSE for both the training and validation sets converged to a low value as the dataset grew to 48 datasets. This convergence indicates that the model learned the relationships effectively without underfitting or overfitting, a common challenge with small datasets [34, 35, 36]. The final model's performance is visually represented in the plot of predicted versus experimental particle size (Figure 3h), the model achieved a quantitatively predictive accuracy.

The prediction of the in‐line PAT‐ML model is from its ability to learn the governing physicochemical characteristics of liposome. The SHAP (SHapley Additive exPlanations) summary plot (Figure 3b) visualizes this “physicochemical insight,” leveraging Shapley‐value based feature attributions to decompose model predictions into contributions from individual process and descriptors [37, 38]. The model identified TFR as the dominant factor with a strong negative correlation, reflecting the kinetic control driven by rapid mixing. Crucially, in‐line PAT data emerged as the second most significant feature with a distinct positive correlation in SHAP analysis. This pattern confirms that the ML model independently reproduced the competition between kinetic forces (TFR) and membrane characteristics described in mechanistic studies of liposome self‐assembly [17, 21, 22, 39, 40], thereby supporting the in‐line PAT strategy.

To further assess the contribution of in‐line spectroscopy data, alternative models were trained excluding physicochemical information obtained from in‐line PAT. Despite performing hyperparameter optimization in the same manner as for the in‐line PAT‐ML, these models exhibited poor performance as reflected by significantly over 10 nm RMSE. As shown in the corresponding learning curves (Figure 3c,f), the models trained without in‐line PAT parameters displayed persistently higher validation error and limited learning curve patterns of underfitting or information‐poor feature sets [41]. These observations support that in‐line PAT spectroscopy contributes essential physicochemical descriptors that materially enhance predictive accuracy.

3.1.4. Generalization Capability With External Validation

The external validation results confirm the generalization of the proposed model, as assessing performance on an independent dataset is a key requirement for evaluating clinical and pharmaceutical prediction models [42, 43]. In this study external validation set was strategically designed to assess the model across two distinct regimes (i) Interpolation, targeting intermediate process parameters (e.g., TFR 3.5, 15 mL ${\mathrm{h}}^{-1}$) that fill the gaps within the training grid; and (ii) Extrapolation, challenging the model with novel lipid compositions not encountered during training (Table 3).

Table 3.

Summary of training and validation datasets.

Parameter	Training dataset (LOOCV)	External validation set
	(Training conditions)	(Unseen Conditions)
Total flow rate (${\mathrm{mLh}}^{-1}$)	1, 2, 5, 10, 20, 30	3.5, 15
Flow rate ratio (−)	3, 6, 10, 20	7, 15
Lipid Conc. (mM)	5, 10, 15, 20	7.5, 17.5
Lipid Composition (DOPC: Chol: ESM)	(1: 2: 7), (5: 3: 2), (4: 2: 4), (10: 0: 0)	(7: 1.5: 1.5)

The residual analysis shown in Figure 5b reveals clear differences between the Non‐PAT‐ML and PAT‐ML models. The Non‐PAT‐ML model exhibits large and widely scattered residuals across the entire particle size range, with deviations exceeding $\pm$40 nm in some cases, indicating poor predictive stability when relying solely on process parameters. In contrast, the PAT‐ML model demonstrates substantially reduced residuals, with most predictions confined within $\pm$10 nm of the experimental values. Importantly, residuals from the external validation dataset (red symbols), which were completely excluded from training, show a distribution comparable to those obtained from internal validation, without apparent size‐dependent bias. This suggests that the incorporation of in‐line PAT signals enables the model to capture features of liposome formation.

Consistent trends are observed in the parity plot (Figure 5c). Predictions from the Non‐PAT‐ML model deviate from the ideal y = x line, particularly in the intermediate and larger particle size regimes, reflecting limited prediction. In contrast, the PAT‐ML model exhibits a strong linear correlation between predicted and experimental particle sizes for both internal and external validation datasets. Notably, external validation data points closely follow the diagonal trend established by the internal validation results, indicating that the model retains predictive accuracy even under unseen manufacturing conditions, including both interpolation and extrapolation regimes.

These observations are quantitatively summarized in Figure 5d, which compares the RMSE and coefficient of determination ($R^2$). The Non‐PAT‐ML model shows a higher RMSE and lower $R^2$, whereas the PAT‐ML model achieves a marked reduction in prediction error. The RMSE obtained from external validation remains comparable to that from internal cross‐validation, with only a minimal performance gap.

Across the investigated applicability domain, the absolute prediction errors remained consistently below 13 nm. Notably, the prediction errors were maintained within a moderate range (approximately 6–8 nm), without evidence of systematic error amplification (Figure S14). Taken together, this distance–error analysis provides a quantitative characterization of the applicability domain of the in‐line PAT‐ML framework, demonstrating that predictive performance remains stable even in sparsely populated regions of the training space.

3.1.5. Conclusion on Particle Size Prediction

Overall, these results confirm that in‐line PAT integration is strategy for achieving both accurate and generalizable particle size prediction. By providing descriptors of the liposome formation, PAT signals enhance the model's ability to extrapolate to new process conditions and lipid compositions, supporting the applicability of this approach for predictive control and optimization in liposomal manufacturing.

Although predicting unseen conditions is inherently challenging, the model maintained high precision with an RMSE comparable to that of the internal validation (7.53 nm for unseen conditions vs. 7.18 nm for in‐line PAT‐ML LOOCV), and such small discrepancies between internal cross‐validation and external test errors are generally interpreted as evidence of good generalization rather than overfitting (Figure 5d) [44]. This minimal performance gap is a critical indicator that the model has successfully captured the underlying structure in the data rather than memorizing the training dataset, since overfit models typically show substantially worse performance on external data compared with internal estimates [36, 45]. Consequently, this demonstrates that the in‐line PAT‐ML strategy enables reliable size prediction even for novel manufacturing conditions, aligning with recommendations to confirm model utility on out‐of‐sample data in applied ML for pharmaceutical and process modeling tasks [46, 47].

3.2. PDI Prediction and Comparative Analysis

The PDI prediction model exhibited a lower coefficient of determination $R^2$ (Figure 4e, h and Table 1), suggesting limited explanatory power in terms of variance captured. However, the RMSE remained low at 0.030(Table 1), indicating that the absolute prediction errors were small. This can be reasonably explained by the nature of microfluidic liposome formation: Due to the controlled mixing environment and the bottom‐up self‐assembly mechanism, microfluidic systems yield liposomes with low polydispersity [48, 49]. In this study, all PDI values were observed to fall below 0.3(Figure 2b), which is generally considered an acceptable or even desirable threshold for liposomal drug products and reflects a narrow and constrained outcome range [50]. Under such restricted variance, even small absolute deviations can disproportionately depress $R^2$ despite low RMSE, because the statistic is sensitive to the spread of the dependent variable [51]. Alternatively, given the target range of PDI, a classification model (e.g., pass/fail based on a specific threshold) could also be a practically applicable alternative for quality control.

The difference in predictive performance between size and PDI stems from the underlying liposome formulation mechanisms. Mean particle size is governed by thermodynamic self‐assembly, which correlates strongly with the membrane physichochemical characteristics. In contrast, minor variations in PDI within this highly uniform microfluidic range (0.1–0.26) may be driven by stochastic fluid dynamic factors (e.g., micro‐mixing variations) rather than membrane thermodynamics. Indeed, our previous study demonstrated that there is no significant correlation between PDI and these specific membrane physichochemical characteristics [22]. Consequently, because the fundamental correlation is absent from the input features, further mathematical data transformations (e.g., log transformation) could not resolve this limitation (Figure S16), making PDI intrinsically more challenging to predict than size using membrane‐specific PAT.

It underscores that while PAT descriptors can enhance model performance with limited data, this strategy is inherently dependent on the existence of a fundamental physical correlation between the features and the output. In the absence of such a correlation–as seen with PDI–the limitations of a small dataset become more apparent, suggesting that increasing data quantity or incorporating mechanical fluid‐dynamic descriptors would be needed to achieve higher predictive power for such stochastic variables.

3.3. Data Efficiency

In‐line PAT strategy demonstrates that precise particle size prediction from a small dataset was accomplished not by designing a complex “black‐box” algorithm, but by fundamentally improving the quality of the input data via in‐line PAT. Compared with the conventional batch workflow (vesicle formulation, dialysis/solvent exchange, off‐line measurement), this system reduced the per‐sample from 24 h to 10–60 min (Table 1). Therefore, this system enabled real‐time monitoring and control, in line with reported benefits of PAT for shortening development timelines and enabling real‐time release testing [52]. The immediate readout also allowed on‐the‐fly adjustment of TFR/FRR, shortening the number of iterations needed. Also, precise particle size prediction from a small data was accomplished not by designing a more complex algorithm to handle sparse data, but by fundamentally improving the quality of the data fed into the model.

3.4. Aligning Nanofabrication With Regulatory and Clinical Expectations

Regulatory guidelines such as FDA [11] and ICH [12] emphasize particle size as a critical quality attribute (CQA) that necessitates rigorous monitoring and control. While specific acceptance criteria are determined on a case‐by‐case basis, minimizing size variation—often targeting a deviation range within 10–20 nm—is comparable to stringent quality standards to ensure consistent pharmacokinetics and biodistribution because shifts in liposome or nanoparticle diameter are known to alter clearance, tissue distribution, and tumor accumulation profiles [53, 54]. By enabling precise control from the earliest stages of development, this technology could help to de‐risk the formulation process, reducing the likelihood of failure in later preclinical or clinical stages due to inconsistent liposome particle size. This proactive quality assurance is the central goal of the PAT framework.

For practical implementation, the developed in‐line PAT‐ML framework offers workflow for liposome manufacturing. When formulating a novel liposome, researchers can initially acquire a small‐scale dataset by systematically varying critical process parameters such as TFR and FRR. During this phase, the integrated PAT sensor continuously captures the fluorescence spectral signals reflecting membrane physicochemical characteristics. An initial predictive machine learning model can be trained using standard open‐source computational libraries. The dataset can train an initial predictive model, transferring the time‐consuming offline quality control burden to real‐time predictive monitoring.

3.5. Methodological Comparison With Previous Studies

Previous studies have demonstrated the prediction of liposome size and/or PDI using various ML algorithms, often leveraging conventional process parameters such as TFR, FRR, and lipid composition [55, 56, 57, 58, 59]. Several studies further explored PDI classification‐based approaches (e.g., distinguishing monodisperse vs. polydisperse systems) [55, 56], Design of Experiments (DoE) [57], or drug encapsulation efficiency prediction [58, 59]. These contributions have significantly advanced the empirical modeling of microfluidic liposome systems.

Thomas et al. (2025) explored 13 different ML models using open‐source libraries, to predict the characteristics of drug‐loaded liposomes on a fixed lipid composition [59]. Jia et al. (2025) introduced environmental variables such as buffer type, pH, and ionic strength as input features, achieving size predictions across a broad range of 100–600 nm [56]. While their work provides valuable insights into external environmental effects, they treated PDI as a binary classification (qualified vs. unqualified). Similarly, Remo et al. (2023) focused on stability analysis and employed classification for PDI (monodisperse vs. polydisperse) [58]. Regarding data scale and lipid diversity, Remo et al. (2024) utilized an extensive set of lipids and data set ($N$ = 1382)–including DMPC, DOPC, DPPC, HSCP, DSPE‐PEG2000, and POPC–supported by robust wet‐lab validation and explainable AI (XAI) analysis. Rebollo et al. (2022) utilized DoE sampling to optimize process parameters through artificial neural networks [59].

This study incorporates in‐line fluorescence‐derived membrane state parameters (hydrophobicity $G{P}_{340}$ and rigidity $r_{DPH}$) as mechanistically features. This state‐informed modeling strategy enables stable size prediction ($RMSE=7.18$ nm for validation, $RMSE=7.53$ nm for unseen conditions) using a comparatively small dataset ($N=48$), supported by learning‐curve analysis and internal, external validation.

Another distinguishing feature is interpretability analysis using SHAP links model predictions to physically meaningful process mechanisms (e.g., the dominant negative contribution of TFR and the positive contribution of membrane descriptors), thereby bridging machine learning outputs with mechanistic understanding.

3.6. Limitations and Future Research

While this study demonstrates an in‐line PAT proof‐of‐concept, further research is necessary to expand its capabilities to address the multifaceted nature of nanomedicine formulation. The current model focuses exclusively on particle size; critical next step is to expand the model to predict and control other essential CQAs, such as zeta potential [60]. Also, future studies with a larger number of unseen formulations are needed to fully validate its broader generalization.

The balance between model usability and prediction accuracy requires careful consideration. Introducing experimental parameters (such as in‐line fluorescence PAT metrics) inherently increases the prediction cost and experimental effort for new samples compared to models relying solely on basic machine settings. However, as demonstrated in this study, the inclusion of these parameters enhances the model's predictive accuracy and, more importantly, its capability to generalize to unseen lipid formulations. Therefore, this PAT‐ML framework is positioned as a tool for early formulation development and process optimization phases.

While future applications will involve complex drug‐loaded systems, establishing a baseline correlation using drug‐free liposomes is a prerequisite to decouple process‐induced variations from drug‐membrane interactions [61]. Therefore, this study focuses on validating the precision and explainability of the in‐line PAT‐ML framework as a foundational platform. Finally, the modular nature of the platform allows for the integration of additional automated unit operations [62]. Future development could include the incorporation of automated downstream processing steps, such as tangential flow filtration or continuous composition gradient‐based screening.

4. Conclusion

This study developed a framework integrating in‐line process analytical technology (PAT) with machine learning (ML) for the precise prediction and control of liposome particle size. The model's root mean square error (RMSE) was 7.18 nm, approximately 7.6% relative to the mean particle size.

SHAP (Shapley additive exPlanations) analysis revealed that the model successfully captured the governing competition between process parameters and in‐line PAT data. Furthermore, external validation on unseen experimental conditions—including novel process parameters and lipid composition—confirmed generalization (RMSE 7.53 nm), proving the model generalization capability.

This achievement represents a significant reduction in the data, time, and resources required for high predictive accuracy ML model development. The in‐line PAT‐integrated ML platform was inspired by quality by design (QbD) and PAT principles. Ultimately, this in‐line PAT‐ML platform provides a practical blueprint for the rapid and precise development of liposomal nanomedicines, directly aligning nanofabrication with critical regulatory and quality control.

5. Experimental Section

5.1. Materials

SU‐8 2100 negative photoresist (PR) was purchased from MicroChemicals GmbH (Ulm, Germany) and a silicon wafer (525‐µm thick) was used to fabricate a silicon master mold. Polydimethylsiloxane (PDMS, Sylgard184) was purchased from Dow Corning (Midland, MI, USA), mixed with curing agent (10:1 ratio) for soft molding. 1,2‐dioleoyl‐sn‐glycero‐3‐phosphocholine (DOPC) was purchased from FUJIFILM Wako Pure Chemical Corporation (Osaka, Japan). Cholesterol, sphingomyelin from egg yolk (Egg sphingomyelin) and 1,6‐diphenyl‐1,3,5‐hexatriene (DPH) were purchased from Sigma‐Aldrich (St. Louis, MO, USA). Ethanol was purchased from FUJIFILM Wako Pure Chemical Corporation (Osaka, Japan). 6‐dodecanoyl‐N,N‐dimethyl‐2‐naphthylamine (Laurdan) was purchased from Cayman Chemical (Ann Arbor, Michigan, USA).

5.2. Fabrication of a Microfluidic Chip

A silicon master mold was prepared following general photolithographic techniques for negative photoresist (SU‐8 2075). The photoresist was spin‐coated to achieve a thickness of 80 µm, followed by a two‐step baking process at 60 for 3 min and 95 for 9 min. Subsequently, the photoresist was exposed to ultraviolet light at an intensity of 10 mJ ${\mathrm{s}}^{-1}$ using a mask aligner. After exposure, a post‐baking step was conducted at 60 for 2 min and 95 for 9 min. To eliminate any residual photoresist, the silicon wafer was developed for 5 minutes.

For the fabrication of the microfluidic chip, the base polymer and curing agent were mixed in a 10:1 ratio, poured onto the silicon master mold, and degassed under vacuum. The polymer mixture was then cured in an oven at 70 for 2 h and carefully separated from the mold. The patterned PDMS layer was bonded to a flat PDMS sheet after undergoing plasma treatment, and the assembled chip was cured further at 80 in a convection oven for 8 h.

The dimensions of the PDMS microfluidic chip were 38 mm $\times$ 12 mm $\times$ 8 mm. The channel was composed of a Y‐junction with two inlets and an outlet. The asymmetry of the herringbones was 2/3 for the staggered herringbone channel. The geometric parameters of the herringbone structures were channel width and depth: 80 µm, groove depth: 30 µm, groove angle: 45 relative to the channel axis.

5.3. Development of Process Analytical Technology System

The process analytical technology (PAT) system was constructed to directly couple a microfluidic device with an optical detection module capable of acquiring continuous fluorescence spectra during liposome synthesis as shown in Figure 1b. The fluorescence detection zone was positioned downstream of the microfluidic chip, allowing for spectral acquisition after vesicle formation was complete. The outlet of the microfluidic device was connected to the detection unit using disposable silicone tubing, ensuring smooth transfer of the liposome‐containing solution without introducing contamination.

Four different compositions were chosen (Table 4) for synthesize different characteristic of liposomes. Liposomes were synthesized by mixing ultra‐pure water (aqueous phase) and ethanol solution of lipids in a microfluidics. Each phase was adjusted using two syringe pumps MSP‐1D (ASONE, Osaka, Japan). Total flow rate (TFR), flow rate ratio (FRR), and lipid concentration were adjusted as shown in Table 5. Particle size and polydispersity index data were obtained from our previous study [22]. For fluorescence measurement, the flowing liposome solution was directed into a T‐59FL‐ES‐10 quartz flow cell with an optical path length of 10 mm and a cell volume of 440 $\mu \mathrm{L}$ (Tosoh Quartz Corporation, Japan) installed in front of a fluorescence spectrometer. Fluorescence spectra were acquired continuously throughout the process. The measurement interval was synchronized with the residence time of the flow cell (ranging from 55 s to 1600 s depending on TFR). The specific number of averaged scans for each experimental condition are detailed in Tables S1 and S2.

Table 4.

Lipid compositions and molar ratio used in liposome formulations.

Composition No.	Lipid ratio [−]
	DOPC	Chol	Egg sphingomyelin
1	0.1	0.2	0.7
2	0.5	0.3	0.2
3	0.4	0.2	0.4
4	1.0	—	—

Table 5.

Experimental condition (TFR, FRR, total lipid concentration).

TFR (${\mathrm{mLh}}^{-1}$)	FRR [−]	Total lipid concentration (mM)
1, 2, 5, 10, 20, 30	3	5
5	10	5, 10, 15, 20
5	3, 6, 10, 20	5

5.4. Physicochemical Evaluation of Lipid Membrane Characteristics

To evaluate the physicochemical characteristics of lipid membranes, liposomes were synthesized by mixing lipids with a fluorescent probe at a specific molar ratio. Specifically, lipid‐to‐probe molar ratios of 100:1 and 250:1 were employed for Laurdan and DPH, respectively. The lipid–probe mixture in ethanol and ultra‐pure water was introduced into the microfluidic system. The resulting fluorescently labeled liposomes were then transported through silicone tubing into a quartz flow cell connected to a fluorescence spectrophotometer, enabling real‐time fluorescence monitoring.

To estimate the membrane hydrophobicity using Laurdan, liposomes were excited at 340 nm, and emission intensities were recorded using a fluorescence spectrophotometer (FP‐8500, JASCO, Tokyo, Japan). The steady‐state generalized polarization ($G{P}_{340}$) was calculated using Equation (1):

$$G{P}_{340}=\frac{I_{440}-I_{490}}{I_{440}+I_{490}}$$ (1)

where $I_{440}$ and $I_{490}$ represent the emission intensities at 440 and 490 nm, respectively.

To evaluate the lipid membrane rigidity using DPH, liposomes were excited at 360 nm, and the emission intensity was recorded at 430 nm using a fluorescence spectrophotometer (FP‐8350, JASCO, Tokyo, Japan). The fluorescence anisotropy ($r_{DPH}$) was calculated using Equations (2) and (3):

$$r_{DPH}=\frac{I_{\parallel }-G{I}_{\perp }}{I_{\parallel }+2G{I}_{\perp }}$$ (2)

$$G=\frac{i_{\perp }}{i_{\parallel }}$$ (3)

where $I_{\perp }$ and $I_{\parallel }$ represent the vertical and horizontal emission intensities obtained from vertically polarized excitation light, respectively, and $G$ is the correction factor.

The standard error ($SE$) was calculated using Equation (4):

$$SE=\frac{\sigma }{\sqrt{n}}$$ (4)

where $\sigma$ is the standard deviation and $n$ is the number of samples.

Both $G{P}_{340}$ and $r_{DPH}$ were calculated for each individual spectrum, and the final reported values represent the arithmetic mean of consecutive measurements.

5.5. Development of Machine Learning Prediction Models

Machine learning (ML) models were trained and validated using in‐line Process Analytical Technology (PAT) measurement data. The dataset incorporated TFR, FRR, lipid concentration, $G{P}_{340}$, and $r_{DPH}$ as input features, with the corresponding experimentally determined liposome characteristics (particle size and PDI) as output variables. Particle size and PDI data were obtained from our previous study [22]. To construct the ML dataset, each input–output data pair was systematically aligned from existing experimental records.

Five distinct ML algorithms were selected to evaluate the predictive performance: (i) linear regression (LR), (ii) LASSO regression (LASSO), (iii) XGBoost (XG), (iv) linear support vector machine (L‐SVM), and (v) polynomial SVM (P‐SVM). L‐SVM and P‐SVM were implemented as support vector regression for continuous variable prediction. All algorithms were implemented in Python (v3.8) using libraries such as scikit‐learn (v1.1.3) for regression models and XGBoost (v1.6.2) for gradient‐boosted decision trees.

Hyperparameter optimization was performed (Tables S2–S6) using a grid search strategy combined with Leave‐One‐Out Cross‐Validation (LOOCV) to minimize the root mean square error (RMSE).

The predictive ML models can be reconstructed using standard open‐source libraries. Details necessary for reproduction, including the hyperparameter grid search spaces and the final optimized parameters for all evaluated algorithms, are documented in Tables S3–S13.

5.6. SHAP Analysis for Model Interpretation

SHAP (SHapley Additive exPlanations) analysis [37] was employed to decompose the model's predictions into the marginal contributions of each input feature, based on cooperative game theory. In this study, the Kernel SHAP explainer (implemented via the shap Python library) was utilized to compute the Shapley values for the trained polynomial SVM model. This approach allowed for a quantitative assessment of how each input feature, such as $G{P}_{340}$ and $r_{DPH}$, influenced the predicted liposome characteristics.

5.7. External Validation on Unseen Conditions

To assess the generalization capability and robustness of the optimized model, an external validation was performed using an independent dataset that was excluded from the training phase. The external validation set was strategically designed to evaluate the model under three distinct scenarios: (i) novel process parameters (e.g., TFR of 3.5 and 15 mL ${\mathrm{h}}^{-1}$) that lie within the gaps of the training grid (interpolation); (ii) novel lipid compositions (e.g., DOPC:Chol:ESM = 7:1.5:1.5) that were not introduced during training (extrapolation 1); and (iii) combined novel process parameters and lipid compositions (extrapolation 2) as shown in Table 2

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting File: smtd70663‐sup‐0001‐SuppMat.pdf.

Lee J., Morishita Watanabe N., Yoshimoto N., et al. “Liposome Particle Size Prediction by In‐Line Process Analytical Technology (PAT)‐Integrated Machine Learning.” Small Methods 10, no. 12 (2026): e70663. 10.1002/smtd.70663

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.