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<p>We develop a mathematical model to predict the most effective design of porous tissue-engineering scaffolds and analyze the choice of values for input parameters such as channel radius, shear stress, nutrient concentration, and nutrient flow pressure, while assuming a constant inlet flux of suspended nutrients. Our model utilizes a branching structure in which scaffold pores bifurcate at each layer junction, thereby allowing for investigation of the input parameters at a pore level. By assuming all branching structures to be equivalent, we assume homogeneity along two axes, meaning the biological scaffold’s geometry is effectively reduced to one dimension. We employ established fluid dynamics equations such as Darcy’s law, the continuity equation, and the advection–diffusion-reaction equation to model the evolution of parameters such as pore radius, shear stress, pressure, fluid velocity, and nutrient concentration. Further simplification of these equations is achieved via nondimensionalization and asymptotic analysis based on the small aspect ratio of the scaffold. Our results establish quantitative relationships among the input parameters to provide a foundation for effectual construction of engineered tissue in the shortest time possible. Further, we devise a trade-off analysis for differing scaffold geometries by comparing ratios of decreasing layer thickness and decreasing initial pore radius in successive downstream layers; these ratios guide predictions for candidates for ideal scaffold geometries according to priorities of time, cost, or total tissue volume. Particularly, we find that minimal values of both these ratios together yield larger volumes of new tissue, while jointly large ratios produce far less tissue but in much less time. Mixed values (e.g., small layer thickness ratio and large initial radius ratio) and intermediate values (in the middle range for both ratios) of these ratios produce moderate tissue growth, in a moderate amount of time, and yield less waste of material used to construct the scaffolds.</p>

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On mathematical modeling of cell proliferation in tissue-engineering scaffolds with branching channels

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • Amy María Sims,
  • Andrew Turvey,
  • Tianle Cao,
  • Yeeun Kim,
  • Devin Martin,
  • Pejman Sanaei

摘要

We develop a mathematical model to predict the most effective design of porous tissue-engineering scaffolds and analyze the choice of values for input parameters such as channel radius, shear stress, nutrient concentration, and nutrient flow pressure, while assuming a constant inlet flux of suspended nutrients. Our model utilizes a branching structure in which scaffold pores bifurcate at each layer junction, thereby allowing for investigation of the input parameters at a pore level. By assuming all branching structures to be equivalent, we assume homogeneity along two axes, meaning the biological scaffold’s geometry is effectively reduced to one dimension. We employ established fluid dynamics equations such as Darcy’s law, the continuity equation, and the advection–diffusion-reaction equation to model the evolution of parameters such as pore radius, shear stress, pressure, fluid velocity, and nutrient concentration. Further simplification of these equations is achieved via nondimensionalization and asymptotic analysis based on the small aspect ratio of the scaffold. Our results establish quantitative relationships among the input parameters to provide a foundation for effectual construction of engineered tissue in the shortest time possible. Further, we devise a trade-off analysis for differing scaffold geometries by comparing ratios of decreasing layer thickness and decreasing initial pore radius in successive downstream layers; these ratios guide predictions for candidates for ideal scaffold geometries according to priorities of time, cost, or total tissue volume. Particularly, we find that minimal values of both these ratios together yield larger volumes of new tissue, while jointly large ratios produce far less tissue but in much less time. Mixed values (e.g., small layer thickness ratio and large initial radius ratio) and intermediate values (in the middle range for both ratios) of these ratios produce moderate tissue growth, in a moderate amount of time, and yield less waste of material used to construct the scaffolds.