Parametric design is based on algorithms to generate 3D models with given parameters. It’s a conventional modeling method using computer-aided design (CAD), which has been widely used in CAD modeling, since lots of models can be rapidly constructed by this method. Although shapes of scaffolds can be achieved by additive manufacturing technology, it is difficult to accurately design microstructures closing to natural vascular scaffolds due to the inherent heterogeneity and complexity of blood vessels. Based on the above reasons, researches in vascular scaffold modeling are currently focused on construction of structures to functionally meet the anatomical and biological characteristics of vascular tissues. However, this method is time consuming and sometimes requires manual operations. To design scaffolds with specific external shapes and controllable internal structures, many modeling methods, such as the secondary development method of CAD software, have been proposed in current researches. Building models using available modeling software and programming languages are popular way of modeling. For example, a triply periodic minimal surface (TPMS) is defined as a surface with periodicity in X, Y, and Z directions of Cartesian coordinate systems. Main types of TPMS surfaces include P, G, and D surfaces. Each surface is described by a mathematical function. Kadkhodapour et al. [65] constructed models using a TPMS-based modeling method. The P and D surfaces of models with different volume fractions were designed, respectively (Fig. 4Ai). However, there is a disadvantage of function-based modeling methods like this. The obtained models are usually regular and simple, leading to inaccurate simulation of heterogeneous vascular scaffolds.

Modeling methods of vascular scaffolds: A Algorithms-based parametric modeling: Ai Modeling by a TPMS algorithm to build models with different volume fractions. Reproduced with permission [65]. Copyright 2014, Elsevier. Aii Modeling by an AI-based evolutionary algorithm to design reconfigurable structures. Reproduced with permission [66]. Copyright 2020, National Academy of Sciences. B Reverse engineering-based modeling to create models of blood vessels: Bi 3D reconstruction by micro-CT scanning. Reproduced with permission [67]. Copyright 2016, Springer Nature. Bii 3D reconstruction by MRI scanning. Reproduced with permission [47]. Copyright 2016, John Wiley and Sons. Biii Modeling by CT scanning and parametric modeling to build complex microstructures. Reproduced with permission [64]. Copyright 2020, Springer Nature

To overcome the shortcomings, Kriegman et al. [66] designed reconfigurable structures using artificial intelligence (AI). Based on multiple iterations, structural building blocks were created by an evolutionary algorithm. This algorithm automatically optimized structural design to achieve different functions for cells (Fig. 4Aii). Compared to the former method, the latter algorithm is evolvable and contributes to reasonable bionic designs of functional macro–micro structures. However, due to the limitations of computer memory and configuration, it is almost impossible to model sub-micron vascular structures by only machine learning methods because even simple calculations of modeling require millions of voxel units, and 10^9 to 10^10 or more voxel units are required for moderately complex calculations. The combination of traditional parametric design and machine learning may be an effective way. That is, macro-models are modeled using parametric modeling methods, and micro- and local models with high bionic requirements are modeled by AI-based evolutionary algorithms. Both approaches provide convenience, especially for engineering and technical personnel. The clinical need for vascular implants is urgent. In this context, the ability to quickly build same or similar models in batches is necessary. And standardized and generalized algorithms make it possible. Besides, in computer-aided manufacturing (CAM), expertise for modeling excluding algorithm designs and compilation of data files are rarely required. A common method in CAM systems is to input parameters in a data interaction system of software, and subsequently the model is obtained by running the algorithms. Although there are few standardized algorithms for blood vessel modeling, as one of the most promising approaches, parametric modeling is expected to be widely used.

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