Applications of Partial Differential Equations in Bioengineering

Dear Colleagues,

Partial Differential Equations (PDEs) are fundamental mathematical tools for modeling complex processes in bioengineering, capturing the dynamic, multi-scale, and often non-linear phenomena seen in biological systems. The use of PDEs allows for the analysis and prediction of behavior in areas ranging from tissue engineering and cellular interactions to drug delivery systems and biomechanical structures. This special edition aims to highlight the innovative applications of PDEs in bioengineering, showcasing the diverse ways these equations are used to address challenges in healthcare, regenerative medicine, and biological research.

This Special Issue will bring together cutting-edge research that utilizes PDEs to model, simulate, and solve bioengineering problems. By focusing on PDE applications in bioengineering, this Special Issue seeks to encourage collaboration between applied mathematicians, bioengineers, and clinicians. This interdisciplinary Special Issue will enhance our understanding of biological processes and support the development of new therapeutic and diagnostic tools. Key areas of interest include, but are not limited to:

• Modeling Tissue Growth and Morphogenesis: Articles examining how PDEs can represent tissue growth dynamics, morphogenesis, and cellular patterns, especially for applications in tissue engineering and regenerative medicine.
• Drug Delivery and Pharmacokinetics: Studies focusing on PDE-based models for controlled drug release, diffusion through biological membranes, and pharmacokinetics to predict drug behavior in the human body.
• Biomechanics and Cardiovascular Modeling: Research that applies PDEs to study the mechanics of soft tissues, bones, and vascular systems, including applications for personalized medicine in cardiovascular health.
• Neuroscience and Brain Modeling: PDE models of neuronal activity, brain wave propagation, and neurovascular coupling to support brain–computer interfaces, neurological disorder research, and neural tissue engineering.
• Biochemical Reaction-Diffusion Systems: Studies using reaction-diffusion PDEs to simulate biochemical processes within cells and tissues, including models of enzyme activity, gene expression, and signal transduction.
• Biomedical Imaging and Inverse Problems: Research on the application of PDEs in imaging techniques, such as Computed Tomography, Magnetic Resonance Imaging, and ultrasound, with a focus on inverse problems and image reconstruction.
• Integrative PDE’s for multi-OMIC ((epi)-genomics, transcriptomics, and metabolomics) analysis towards the development of diagnosis and follow-up tools in different contexts of disease.

Dr. José Alberto Rodrigues
Dr. Jacinta Serpa
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Bioengineering is an international peer-reviewed open access monthly journal published by MDPI.

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