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Purpose <p>Accurate modeling of nonlinear, time-dependent drug release from nanocarrier systems remains challenging, which limits rational formulation design. This study aims to establish a continuous-time predictive framework for Paclitaxel (PTX) release across diverse nanocarriers.</p> Methods <p>We applied a neural differential equation (NDE) model to a curated dataset of 115 PTX-loaded formulations, incorporating physicochemical descriptors, formulation parameters, and environmental triggers. The model learned the time derivative of cumulative release directly from data. Performance was benchmarked against classical kinetic equations and discrete-time machine learning models. Feature contributions were quantified using SHapley Additive exPlanations (SHAP).</p> Results <p>The NDE achieved high generalization, with validation and test R² exceeding 0.91 and RMSE of 4.23%. Continuous-time predictions accurately captured multiphasic and stimulus-responsive release profiles, outperforming diffusion-based and empirical models (R² ≤ 0.81; RMSE &gt; 7%). SHAP analysis identified pH sensitivity, loading efficiency, and particle size as primary determinants of release, with their influence varying temporally. Learned dynamics remained stable across early, intermediate, and late release phases.</p> Conclusions <p>Neural differential equations provide a robust framework for modeling drug release as a dynamical process, enabling continuous-time prediction and interpretable feature analysis. This approach supports in silico screening and optimization of nanocarrier formulations, reducing reliance on exhaustive experimental testing and enhancing temporal fidelity in controlled drug delivery design.</p>

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Dynamic Modeling of Paclitaxel Release Kinetics from Nanocarrier Systems Using Neural Differential Equations

  • 期刊论文

  • 发表日期：

    2026年6月22日

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  • Abbas Rahdar,
  • Sonia Fathi-karkan

摘要

Purpose

Accurate modeling of nonlinear, time-dependent drug release from nanocarrier systems remains challenging, which limits rational formulation design. This study aims to establish a continuous-time predictive framework for Paclitaxel (PTX) release across diverse nanocarriers.

Methods

We applied a neural differential equation (NDE) model to a curated dataset of 115 PTX-loaded formulations, incorporating physicochemical descriptors, formulation parameters, and environmental triggers. The model learned the time derivative of cumulative release directly from data. Performance was benchmarked against classical kinetic equations and discrete-time machine learning models. Feature contributions were quantified using SHapley Additive exPlanations (SHAP).

Results

The NDE achieved high generalization, with validation and test R² exceeding 0.91 and RMSE of 4.23%. Continuous-time predictions accurately captured multiphasic and stimulus-responsive release profiles, outperforming diffusion-based and empirical models (R² ≤ 0.81; RMSE > 7%). SHAP analysis identified pH sensitivity, loading efficiency, and particle size as primary determinants of release, with their influence varying temporally. Learned dynamics remained stable across early, intermediate, and late release phases.

Conclusions

Neural differential equations provide a robust framework for modeling drug release as a dynamical process, enabling continuous-time prediction and interpretable feature analysis. This approach supports in silico screening and optimization of nanocarrier formulations, reducing reliance on exhaustive experimental testing and enhancing temporal fidelity in controlled drug delivery design.