Abstract:

Objective The braiding process for braided vascular stent preforms is relatively straightforward and fixed, with drawbacks including weak mechanical qualities and singular applications that cannot satisfy the genuine market needs. Complex correspondence between fabrics and processes, as well as long development cycles, are issues of developing a process by hexagonal three-dimensional (3-D) braider with a variety of braiding processes. Therefore, it is suggested that a simulation technique considers the connection between the hexagonal braiding process and the fabric structure, so as to create a 3-D virtual model of the stents under particular hexagonal braiding processes and to speed up the development of braiding processes.

Method Firstly, the units were mathematically coordinated by building the geometric relationships of the hexagonal braider chassis, so that the yarn movements could be transformed from the braiding process and recorded in matrices. By using matrix operations, the spatial coordinate sets of the yarns were produced, and the related formulas for the yarn trajectory and the fundamental 3-D shape of the stent were then created. The 3-D form of the stent was expanded, and by analyzing the characteristics of the unidirectional fabric, a system of linear equations was applied to solve for the yarns' interweaving points and identify the type of interweaving in conjunction with the yarn movement. Finally, the yarn fluctuation equation was modified to generate formulas for the trajectory with interweaving properties, and the solid model of the holder was constructed and tested against the actual object to verify the correctness of the model.

Results In detail, matrixes were applied to record the information transformed by the hexagonal braiding process, and in combination with the mathematical model of the carrier-suspender-mandrel established, the tangent points of the yarn wound on the mandrel, i.e., the set of coordinates of the spatial trajectory of the yarn, were calculated by matrix operations. The discrete points in the coordinate sets were connected and fitted to create a model of the spatial trajectory of the yarn, which was compared with the trajectory obtained by the numerical calculation, suggesting that the spatial spiral curve could be used to simplify and more accurately show the spatial trajectory of the yarn, and the model obtained by this method was used as the 3-D basic form of the stent. In order to further demonstrate the interwoven form of the stent, the 3-D basic form of the stent was expanded along the z-axis direction, enabling the interweave points to be solved in reduced dimensions. On this basis, calculation of yarn winding tangent point was created to calculate the 2-D coordinates of the yarn interweaving points and to find the 3-D coordinates by means of the z-values. In addition, the z-values enabled information relating to the interweaving of the yarns in the braiding process to be found, which was used to determine the carrier interaction of the inter-weaving yarns, and in turn to apply interweaving principle to determine the change in position of the yarns in the fabric to obtain the fabric in-terweaving type (U∶V) defined. Based on the above, the modified yarn fluctuation equations were applied to obtain the mathematical formulas for left- and right-handed yarns reflecting the type of interweaving of the hexagonal braiding, thus creating a solid numerical model of a virtual fabric with 3-D interweaving characteristics. In order to validate the method above, 3-D virtual braiding experiments were carried out on stents with different hexagonal braiding processes, comparing the type of interweaving and related dimensions of the virtual fabric and the real one, and it was discovered that both were almost identical in terms of morphology and values. By inputting the hexagonal braiding process and dimensional parameters, the method was able to produce a corresponding 3-D model of the virtual vascular stent.

Conclusion The viability and accuracy of the virtual braiding approach for the hexagonal 3-D braiding process of the stent preforms were confirmed through modelling of forms, interwoven manipulation, and solidification of the hexagonal braided stent preforms. This would offer technical assistance for the quick advancement of the hexagonal braiding process and the evaluation of the stent's mechanical characteristics. It was important to note that many companies had concentrated on the structure of stents with variable yarn rotation and superimposed inter-weaving layers and their braiding process in addition to the widely used unidirectional structure of hexagonal 3-D braided stents. As a result, the virtual modelling needs of braided stents had been further broadened and the 3-D virtual braiding algorithm of the stent would also become more complex.

Key words: hexagonal three-dimensional braiding, vascular stent, virtual braiding, unidirectional tubular fabric, interwoven judgment