Mathematical modeling of drug delivery systems with diffusion and absorption equations

Kumar, Vipan; Bhardwaj, Uma; Sood, Yamini; Bhanuse, Vijaykumar; Musale, Vinayak; Kumar, M. Ramesh

doi:10.47974/JIM-2369

Open Access Research Article

Mathematical modeling of drug delivery systems with diffusion and absorption equations

Vipan Kumarer.vipingupta14@gmail.comDepartment of Electronics and Communication Engineering Sri Sai College of Engineering and TechnologyDepartment of Electronics and Communication Engineering Sri Sai College of Engineering and Technology BadhaniPathankot, Punjab, 145001, IndiaView full profile → , Uma Bhardwajvc@niu.edu.inDepartment of Biotechnology and Microbiology Noida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile → , Yamini Soodyaminisood1987@gmail.comDepartment of Computer Science and Engineering Sri Sai UniversityDepartment of computer science and Engineering Sri Sai UniversityPalampur, Himachal Pradesh, 176081, IndiaView full profile → , ^*Vijaykumar BhanuseCorresponding authorvijaykumar.bhanuse@vit.eduDepartment of Instrumentation and Control Engineering Vishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Vinayak Musalevinayak.musale@gmail.comDepartment of Computer Engineering and Technology Dr. Vishwanath Karad MIT World Peace UniversityPune, Maharashtra, 411038, IndiaView full profile → , M. Ramesh Kumarmrkpdy@gmail.comDepartment of Mathematics IFET Engineering CollegeDepartment of Mathematics IFET College of Engineering Villupuram, Tamil Nadu, 605108, IndiaView full profile →

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pp. 2273–2280Vol. 28Issue 6September 2025DOI: 10.47974/JIM-2369XML

Received:: 10 Dec 2024
Published Online:: 30 Sep 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-2369
Pages:: 2273–2280

Abstract

Mathematical modelling plays a fundamental role in designing drug delivery systems, where the goal is to release an active molecule at a controlled rate and in a specific target region. Diffusion and absorption processes govern how drugs migrate through polymers and tissues and how they are taken up by the body. Challenges arise from spatially varying material properties, nonlinear boundary conditions and the coupling between diffusion within the device and absorption by biological tissues. This paper formulates a one dimensional diffusion–absorption model for a controlled‐release reservoir coupled to a sink that mimics systemic uptake. Starting from Fick’s laws, we derive the governing partial differential equation with a first order absorption term and solve it using separation of variables and Laplace transforms. The model predicts concentration profiles inside the device and the fraction of drug released as functions of time. Results show that higher diffusion coefficients accelerate release, whereas stronger absorption reduces internal concentrations but increases the rate of systemic delivery. The proposed framework provides insights into the interplay between device parameters and pharmacokinetic outcomes and offers guidelines for optimizing controlled release formulations.

Keywords

Drug delivery Diffusion equation Absorption kinetics Fick’s law Controlled release Mathematical modelling

Subject Classifications

65L60

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