LayeredSpheres_DDSdesign

Code for performing parameter estimation on core-shell or core microspheres using available data and simulating various bi-layered microsphere configurations.

Overview

This repository contains the MATLAB and COMSOL files from the manuscript cited below that simulates drug delivery from a single- or bi-layered microsphere and estimates the parameters (drug diffusion coefficient in chitosan, drug diffusion coefficient in PCL, burst release, and partition coefficient) that best fit a given input dataset of cumulative release vs. time. Latin hypercube sampling is used to determine the initial guesses in the multi-start approach. The model accounts for key transport process parameters, including burst release, drug partitioning, and diffusion coefficients across bi-layered polymeric spheres. Sensitivity analyses revealed different parameter dominance depending on the specific parameter regimes driving drug release. In the chitosan-PCL case study, we identified drug diffusivity in the core and burst release as the primary drivers of the long-term release behavior. The estimated transport parameters were fitted to experimental release data for BSA and bevacizumab using both finite difference (MATLAB) and finite element (COMSOL) methods. Using clinically relevant thresholds for therapeutic delivery, we simulated drug release from chitosan-PCL microspheres and showed that core radius has a greater impact on therapeutic performance than shell thickness in the data-driven parameter regime. We further developed a customizable MATLAB tool to explore the trade-off of using different layer sizes through automated simulations, providing visual outputs of the profiles of cumulative drug release and drug release rate across a range of core and shell sizes. This tool supports rapid hypothesis testing and formulation design, and the generalizable modeling framework enables easy adaptation to other bi-layered spherical DDSs. To run the MATLAB tool, download this repository as a zip file, unzip the folder, navigate to MATLAB/DesignCharacteristics/MultipleDesigns_Output.mlx, and run the file in that location so it can access the other dependent files.

Code Authors

Eduardo A. Chacin Ruiz, Samantha L. Carpenter, Katelyn E. Swindle-Reilly, Ashlee N. Ford Versypt

Contact: ashleefv@buffalo.edu

Manuscript

E.A. Chacin Ruiz, S. L. Carpenter, K. E. Swindle-Reilly, and A. N. Ford Versypt, Modeling and Design of Chitosan-PCL Bi-Layered Microspheres for Intravitreal Controlled Release, bioRxiv preprint, DOI: 10.1101/2024.01.11.575289 Preprint

MATLAB Folder Scripts and Data

• bilayernumericaldiffn_paramest.m This file initializes the parameter estimation problem and calls the following code scripts to perform necessary functions.
• FDspheresvariablediffusivitytwo_spheres.m This file contains the finite difference discretization scheme for spheres.
• simps_license.txt This file contains the license for simps.m.
• simps.m This file performs Simpson's numerical integration. Source
• solvecumuldrug_rel.m This file runs the forward problem for the average and best results for the parameter estimation.
• solveFDspheresvariablediffusivity.m This file solves the PDE for Fickian diffusion within a radially symmetric sphere.
• CreateNodeFigure.m creates Figure S1
• ScriptForExportingImages.m Converts and saves MATLAB plots to .pdf and .tiff, for the specified width and height size in inches.
• twospheresdataform1PCLandChitosan.mat This data file contains the data for the experiments involving drug release from chitosan microparticles. A mat file must be loaded to perform the parameter estimation.
• twospheresdataform2PCLandChitosan.mat This data file contains the data for the experiments involving drug release from PCL-chitosan microparticles. A mat file must be loaded to perform the parameter estimation.

Concentration_Comparisons Folder Scripts and Data

• Plotconcentrationprofiles.m This script reads the information from the datasheet and makes a figure composed of four concentration subplots. Creates Figure S2.
• Concentration_comparison.xlsx This datasheet contains the concentration vs time data at four different microparticle position. At the center, at the middle of the core, at the interface, and at the middle of the shell.

CumulativeReleaseVerification Folder Scripts and Data

• Analytical_Sln.m This script contains the implementation of the analytical solution for a loaded-core and empty shell microsphere based on the derivation by Lu and Chen J. Control. Rel. (1993).
• Cumulrelcomparison.xlsx This datasheet contains the cumulative release vs time data for two different set of parameters. The solutions stored are for the analytical solution, MATLAB, and COMSOL results.
• Plotcumulrel.m This script reads the information from the datasheet and makes a figure composed of two subplots. Creates Figure S3.

Design_Characteristics Folder Scripts and Data

• 3DSurfacedata.mat This .mat file contains the data obtained from SurfacePlot3D.m for a release rate threshold of 2 micrograms/day.
• 3DSurfacedataSupplementary.mat This .mat file contains the data obtained from SurfacePlot_3D.m for a release rate threshold of 1 microgram/day.
• BilayeredMPsPrediction.xlsx This datasheet contains the cumulative drug release and drug release rate vs time data for the different core-shell designs for 180 days.
• BilayeredMPsPrediction_Supplementary.xlsx This datasheet contains the cumulative drug release and drug release rate vs time data for the different core-shell designs for 360 days.
• Cumulrelandrelrate.m This script reads the information from BilayeredMPsPrediction.xlsx and makes two 6x4 figures with microparticles of different sizes. One figure shows the cumulative drug release and the other the drug release rate. Creates Figure 5 and Figure 6.
• CumulrelandrelrateSupplementary.m This script reads the information from BilayeredMPsPredictionSupplementary.xlsx and makes two 6x4 figures with microparticles of different sizes. One figure shows the cumulative drug release and the other the drug release rate. Creates Figure S9 and Figure S10.
• MPsrelease6_months.xlsx This datasheet contains the experimental data for cumulative drug release with time, and its standard deviation.
• MultipleDesignsOutput.mlx This script allows to define a set of chitosan and PCL radii to test and the output is two figures with microparticles of the different sizes chosen. One figure shows the cumulative drug release, and the other the drug release rate.
• plotfill.m This scripts serves as a function to color the area that is within a predefined threshold.
• Plot3DSurface_Results.m This script creates Figure 7.
• Plot3DSurface_Results.m This script creates Figure S11.
• SurfacePlot3D.m The output from this script are 3 3D surface plots where one of the axis represents chitosan radii, another one PCL radii, and the last one depends on the plot. One plot is for days it takes to release a certain drug threshold, one plot is for days releasing a determined amount of drug, and the final plot is the intersection between the previous two plots.
• SurfacePlot3DSupplementary.m Similar to SurfacePlot_3D.m but it extents up to 360 days.

Diffusion_Boundaries Folder Scripts

• LowerAndUpperLimitsForDiffusion.m This script plots a figure showing the experimental data for BSA and Bevacizumab from Jiang et al. (2020), and the cumulative release curves assuming the same diffusion coefficients in both layers. Creates Figure S4.

Diffusion_Regimes Folder Scripts and Data

• balanced_diffusion.mat Contains the concentration matrix (at different times and positions) for the case of DChi = DPCL.
• corelimiteddiffusion.mat Contains the concentration matrix (at different times and positions) for the case of DChi << DPCL.
• PlotDiffusionRegimes.m This script plots the concentration profile with respect to position, at different time points, for the three regimes. Creates Figure S7.
• shelllimiteddiffusion.mat Contains the concentration matrix (at different times and positions) for the case of DChi >> DPCL.

ParameterEstimationResults Folder Scripts and Data

• InitialGuesses100Simulations.xlsx This datasheet contains the information used and results for the preliminary parameter estimation for both BSA and bevacizumab in MATLAB and COMSOL.
• InitialGuesses50Simulations.xlsx This datasheet contains the information used and results for the final parameter estimation for both BSA and bevacizumab in MATLAB and COMSOL.
• PlotsBev100IC.m This script reads the preliminary parameter estimation results for bevacizumab from InitialGuesses100_Simulations.xlsx and the output is a 2x2 plot comparing average and best results for COMSOL and MATLAB, and the error values obtained. Creates Figure S6.
• PlotsBev50IC.m This script reads the final parameter estimation results for bevacizumab from InitialGuesses50_Simulations.xlsx and the output is a 2x2 plot comparing average and best results for COMSOL and MATLAB, and the error values obtained. Creates Figure 4.
• PlotsBSA100IC.m This script reads the preliminary parameter estimation results for bevacizumab from InitialGuesses100_Simulations.xlsx and the output is a 2x2 plot comparing average and best results for COMSOL and MATLAB, and the error values obtained. Creates Figure S5.
• PlotsBSA50IC.m This script reads the final parameter estimation results for BSA from InitialGuesses50_Simulations.xlsx and the output is a 2x2 plot comparing average and best results for COMSOL and MATLAB, and the error values obtained. Creates Figure 3.

SensitivityandConfidence_Interval Folder Scripts and Data

• Combinedlocaland_SOBOL.m This file plots a 3x2 figure where the top row is composed of local sensitivity analysis obtained from MATLAB and the bottom row is composed of SOBOL indices obtained from COMSOL. Creates Figure 2.
• Confidence_Intervals.m This scripts calculates the sensitivity matrix S and uses it for the calculation of the confidence interval of the specified paramters.
• InitialGuesses50_Simulations.xlsx This datasheet contains the information used and results for the final parameter estimation for both BSA and bevacizumab in MATLAB and COMSOL.
• MOAT.m This script is used to plot the Morris one-at-a-time results obtained from COMSOL. Creates Figure S8.
• MOATInfoCOMSOL.xlsx This datasheet contains the COMSOL results of the MOAT mean and MOAT standard deviation for the parameters under different drug release regimens.
• MPsrelease6_months.xlsx This datasheet contains the experimental data for cumulative drug release with time, and its standard deviation.
• Sensitivity_Analysis.m This scripts solves the local sensitivity analysis for a given perturbance percentage and plots the normalized change in cumulative drug release for the specified parameters.
• solveFDspheressensitivity.m This file solves the PDE for Fickian diffusion within a radially symmetric sphere. It is an optimized version of "solveFDspheresvariable_diffusivity.m" reporposed for the type of input and output required for the sensitivity analysis.

COMSOL Folder Scripts and Data

• BSAExperimentaldataMPsChitosan-PCL.csv This datasheet contains the experimental data for the cumulative release of BSA with time (in seconds).
• BevacizumabExperimentaldataMPsChitosan-PCL.csv This datasheet contains the experimental data for the cumulative release of bevacizumab with time (in seconds).
• OptimizationMPChitosan_PCL.mph This file can be used to perform the parameter estimation for a given dataset.
• UncertaintyMPChitosan_PCL.mph This file can be used to perform sensitivity analysis (MOAT and SOBOL) for the model parameters.

Acknowledgements

This work was supported by National Institutes of Health grant R35GM133763 to ANFV, R01EB032870 to KESR and ANFV, and the Owen Locke Foundation to KESR. The content is solely the responsibility of the authors and does not necessarily represent the official views of the funding agencies.