In silico study of the influence of different microstructures on the mechanical properties of a bioceramics' bone graft

Abstract

Craniomaxillofacial surgery is the field of medical sciences that reconstructs the faces of patients who have had, for example, a car accident or bone cancer. This type of surgery mainly consists of the implantation of a graft to allow the rehabilitation and restoration of the shape and the function of the injured bone region. The current treatments, such as autografts, allografts or alloplastic grafts, present some disadvantages that can have severe consequences for the patient. Cerhum, a company focused on ceramic 3D printing, proposes an implant that overcomes some of these disadvantages: a 3D printed bioceramic bone graft. The ceramic used, which is mainly composed of hydroxyapatite, allows excellent biocompatibility. In addition to its supporting role, the microstructure must have a geometry that guides and stimulates bone regeneration in the implant.

The main aim of this research work is to study in silico the influence of different microstructures on the mechanical support performance of the implant. In order to fulfil their role as a guide and stimulus for the bone regeneration process, the microstructures must exhibit several geometrical characteristics, such as a pronounced tortuosity. The different architectures selected are Orthogonal unit cells, TPMS (Triply Periodic Minimal Surface) unit cells (Primitive, Gyroid and Diamond) and Isometric TPMS unit cells (Isometric Gyroid and Isometric Diamond). These microstructures are numerically modelled in scaffolds with four cell repetitions in all three directions. For a given architecture, several scaffolds are built with different porosity percentages. Finite Element (FE) analysis in compression, under the assumption of a quasi-static state, are performed on these models. From this FE analysis, Young's moduli in compression of the different structures are compared.

The two main characteristics affecting the elastic mechanical performance of a structure are its architecture and its porosity rate. Young's modulus decreases when the porosity rate increases. The results of this research work suggest that, in the 35-85\% porosity range, Diamond cells present a higher elastic modulus than Orthogonal and other TPMS structures. However, Gyroid scaffolds have Young's moduli in the same order as the bone, unlike Primitive and Diamond. Regarding structures made of Isometric TPMS cells, Diamond and Isometric Diamond have similar Young's moduli in compression. While Isometric Gyroid cells offer higher elastic strength than Gyroid cells.

The second part of this research work focuses on scaffolds made of Primitive, Gyroid and Diamond cells including a porosity gradient within the structure. Indeed, as in natural bone, the implant shell is made of a compact structure, i.e. with low porosity, while the interior is spongy, i.e. with higher porosity. The region linking them present a porosity gradient. This study suggests that inserting a porosity gradient weakens the structures. Moreover, regarding the Young's modulus, the sensitivity to porosity gradient is less significant for Gyroid cells than Diamond and Primitive cells.

In conclusion, microstructures made of Gyroid cells are the more interesting. Their Young's moduli are matching the native bone one which leads to better implant osseointegration. Their high mechanical resistance remains when explored to porosity gradients.