One of the greatest challenges in fabricating artificial tissues and organs is the incorporation of vascular networks to support the biological requirements of the embedded cells, encouraging tissue formation and maturation. With the advent of 3D printing technology, significant progress has been made with respect to generating vascularized artificial tissues. Current algorithms to generate arterial/venous trees are computationally expensive and offer limited freedom to optimize the resulting structures. Furthermore, there is no method for algorithmic generation of vascular networks that can recapitulate the complexity of the native vasculature for more than two trees, and export directly to a 3D printing format. Here, we report such a method, using an accelerated constructive constrained optimization approach, by decomposing the process into construction, optimization, and collision resolution stages. The new approach reduces computation time to minutes at problem sizes where previous implementations have reported days. With the optimality criterion of maximizing the volume of useful tissue which could be grown around such a network, an approach of alternating stages of construction and batch optimization of all node positions is introduced and shown to yield consistently more optimal networks. The approach does not place a limit on the number of interpenetrating networks that can be constructed in a given space; indeed we demonstrate a biomimetic, liver-like tissue model. Methods to account for the limitations of 3D printing are provided, notably the minimum feature size and infill at sharp angles, through padding and angle reduction, respectively.

中文翻译：

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用于组织工程的加速约束构造优化生成的 3D 可打印血管网络

制造人造组织和器官的最大挑战之一是纳入血管网络以支持嵌入细胞的生物学要求，促进组织形成和成熟。随着 3D 打印技术的出现，在生成血管化人造组织方面取得了重大进展。当前生成动脉/静脉树的算法在计算上是昂贵的，并且提供有限的自由来优化结果结构。此外，没有算法生成血管网络的方法可以概括两棵树以上的原生血管系统的复杂性，并直接导出为 3D 打印格式。在这里，我们报告了这样一种方法，使用加速的建设性约束优化方法，通过将过程分解为构建、优化和冲突解决阶段。新方法将问题规模的计算时间减少到几分钟，而以前的实现报告了数天。通过最大化可以围绕这种网络生长的有用组织的体积的最优性标准，引入了一种交替构建阶段和所有节点位置的批量优化的方法，并显示出始终如一地产生更优化的网络。该方法不限制在给定空间中可以构建的互穿网络的数量；事实上，我们展示了一个仿生的、类似肝脏的组织模型。提供了解决 3D 打印局限性的方法，特别是分别通过填充和角度减小来实现锐角处的最小特征尺寸和填充。