While the effects of external factors like fluid mechanical forces and scaffold geometry on tissue growth have been extensively studied, the influence of cell behavior-particularly nutrient consumption and depletion within the scaffold-has received less attention. Incorporating such factors into mathematical models allows for a more comprehensive understanding of tissue-engineering processes. This work presents a comprehensive continuum model for cell proliferation within two-dimensional tissue-engineering scaffolds. Through mathematical modeling and asymptotic analysis based on the small aspect ratio of the scaffolds, the study aims to reduce computational burdens and solve mathematical models for tissue growth within porous scaffolds. The model incorporates fluid dynamics of nutrient feed flow, nutrient transport, cell concentration, and tissue growth, considering the evolving scaffold porosity due to cell proliferation, with the crux of the work establishing the ideal pore shape for channels within the tissue-engineering scaffold to obtain the maximum tissue growth. We investigate scaffolds with specific two-dimensional initial porosity profiles, and our results show that scaffolds which are uniformly graded in porosity throughout their depth promote more tissue growth.

Amy María Sims

Mona James

Sai Kunnatha

Shreya Srinivasan

Haniyeh Fattahpour

Ashok Joseph

Paul Joseph

Pejman Sanaei

Bulletin of Mathematical Biology

BULLETIN OF MATHEMATICAL BIOLOGY 是数学生物学学会的官方期刊，传播原始研究成果和其他与生物学和数学科学接口相关的信息。贡献应该与这两个领域相关。为了适应广泛的新发展，该期刊接受各种投稿，包括：原创研究文章侧重于借助数学科学工具或新的数学工具和方法获得的新生物学见解，这些工具和方法已证明适用于生物学调查研究数学生物学教育评论评论观点，以及讨论对专业重要的问题的贡献所有贡献都经过同行评审。

The Bulletin of Mathematical Biology is the official journal of the Society for Mathematical Biology, dedicated to disseminating original research findings and information related to the interface between biology and mathematical sciences. Contributions should be relevant to both fields. The journal welcomes a variety of submissions, including original research articles that focus on new biological insights gained through mathematical tools or novel mathematical methods that have proven applicable to biological investigations; reviews on mathematical biology education; and discussions and viewpoints on issues of professional significance. All contributions undergo peer review.

《Bulletin of Mathematical Biology》是数学生物学学会的官方期刊，旨在传播原始研究成果及与生物学和数学科学交叉领域相关的信息。我们欢迎与这两个领域相关的各种投稿，包括：利用数学科学工具或新方法获得的新生物学见解的原创研究文章，这些工具和方法已被证明适用于生物学研究；数学生物学教育的评论；以及对专业重要问题的讨论和观点。所有投稿均经过同行评审。

Category	Quartile
数学	4
数学, 生物学	4
数学, 数学与计算生物学	4

A Simplified Mathematical Model for Cell Proliferation in a Tissue-Engineering Scaffold

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