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Optimization of Initial Drug Distribution in Spherical Capsules for Personalized Release

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Abstract

Objective

Customization of the rate of drug delivered based on individual patient requirements is of paramount importance in the design of drug delivery devices. Advances in manufacturing may enable multilayer drug delivery devices with different initial drug distributions in each layer. However, a robust mathematical understanding of how to optimize such capabilities is critically needed. The objective of this work is to determine the initial drug distribution needed in a spherical drug delivery device such as a capsule in order to obtain a desired drug release profile.

Methods

This optimization problem is posed as an inverse mass transfer problem, and optimization is carried out using the solution of the forward problem. Both non-erodible and erodible multilayer spheres are analyzed. Cases with polynomial forms of initial drug distribution are also analyzed. Optimization is also carried out for a case where an initial burst in drug release rate is desired, followed by a constant drug release rate.

Results

More than 60% reduction in root-mean-square deviation of the actual drug release rate from the ideal constant drug release rate is reported. Typically, the optimized initial drug distribution in these cases prevents or minimizes large drug release rate at early times, leading to a much more uniform drug release overall.

Conclusions

Results demonstrate potential for obtaining a desired drug delivery profile over time by carefully engineering the drug distribution in the drug delivery device. These results may help engineer devices that offer customized drug delivery by combining advanced manufacturing with mathematical optimization.

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Data Availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Abbreviations

A :

Initial (erodible case) or fixed (non-erodible case) radius (m).

B :

Rate of erosion of the erodible sphere (m s−1).

c :

Concentration (mol m−3).

D :

Diffusion coefficient (m2 s−1).

J :

Order of the polynomial function.

M :

Number of layers.

M total :

Total drug amount (mol).

q a :

Actual drug release rate (mol s−1).

q d :

Desired drug release rate (mol s−1).

R :

Radius of erodible sphere as a function of time (m).

r :

Radial coordinate (m).

t :

Time (s).

λ :

Non-dimensional eigenvalue.

θ :

Non-dimensional concentration, θ = c/cref.

τ :

Non-dimensional time, τ = Dt/A2

ξ :

Non-dimensional radial coordinate, ξ = r/A

in :

Initial

ref :

Reference

m :

Layer number

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Funding

Funding from the European Research Council under the European Unions Horizon 2020 Framework Programme (No. FP/2014 \ 0552020)/ ERC Grant Agreement No. 739964 (COPMAT) is acknowledged. This work is also partially supported by Italian MIUR (PRIN 2017 project: Mathematics of active materials: from mechanobiology to smart devices, # 2017KL4EF3).

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Authors and Affiliations

  1. Mechanical and Aerospace Engineering Department, University of Texas at Arlington, 500 W First St, Rm 211, Arlington, TX, 76019, USA

    Ankur Jain & Kamesh Subbarao

  2. Division of Biomedical Engineering, University of Glasgow, Glasgow, UK

    Sean McGinty

  3. Glasgow Computational Engineering Centre, University of Glasgow, Glasgow, UK

    Sean McGinty

  4. Istituto per le Applicazioni del Calcolo – CNR, Via dei Taurini 19, 00185, Rome, Italy

    Giuseppe Pontrelli

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  1. Ankur Jain
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Contributions

A. Jain – Conceptualization, Methodology, Formal Analysis, Validation, Investigation, Data Curation, Project Administration; K. Subbarao – Formal Analysis, Validation, Investigation, Data Curation; S. McGinty – Methodology, Formal Analysis, Validation; G. Pontrelli – Methodology, Formal Analysis, Validation. All authors contributed towards Writing Original Draft, Review and Editing.

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Correspondence to Ankur Jain.

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Jain, A., Subbarao, K., McGinty, S. et al. Optimization of Initial Drug Distribution in Spherical Capsules for Personalized Release. Pharm Res 39, 2607–2620 (2022). https://doi.org/10.1007/s11095-022-03359-y

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