A Two-Scale Multi-Resolution Topologically Optimized Multi-Material Design of 3D Printed Craniofacial Bone Implants

Abstract

Bone replacement implants for craniofacial reconstruction require to provide an adequate structural foundation to withstand the physiological loading. With recent advances in 3D printing technology in place of bone grafts using autologous tissues, patient-specific additively manufactured implants are being established as suitable alternates. Since the stress distribution of these structures is complicated, efficient design techniques, such as topology optimization, can deliver optimized designs with enhanced functionality. In this work, a two-scale topology optimization approach is proposed that provides multi-material designs for both macrostructures and microstructures. In the first stage, a multi-resolution topology optimization approach is used to produce multi-material designs with maximum stiffness. Then, a microstructure with a desired property supplants the solid domain. This is beneficial for bone implant design since, in addition to imparting the desired functional property to the design, it also introduces porosity. To show the efficacy of the technique, four different large craniofacial defects due to maxillectomy are considered, and their respective implant designs with multi-materials are shown. These designs show good potential in developing patient-specific optimized designs suitable for additive manufacturing.

Keywords: bone implants; bone replacements; craniofacial surgery; multi-material; topology optimization.

Figure 1

The workflow of using structural topology optimization for craniofacial bone replacement.

Figure 2

Design of microstructure using topology optimization. Maximization of (a) uniaxial (x) stiffness, and (b) bulk modulus.

Figure 3

Basic facial skeleton anatomy.

Figure 4

The segmented Digital Imaging and Communications in Medicine (DICOM) data with an isotropic spatial resolution of the four clinical cases used in this study are shown. The DICOM data have a total of 512 images on the frontal and sagittal planes. The number of images on the horizontal plane varies depending on each case. (a) Case 1: Bilateral subtotal maxillectomy. (b) Case 2: Bilateral subtotal maxillectomy II. (c) Case 3: Right limited maxillectomy. (d) Case 4: Left limited maxillectomy and mandibular defect in left lateral segment.

Figure 5

Case 1. (a) Design domain extraction from patient CT scan, (b) boundary condition used in the analysis, (c) bone replacement shape using single material topology optimization, (d) bone replacement shape using multi-material (2 materials) topology optimization.

Figure 6

Effect of the ratio of traumatic force (top) and the masticatory force on the design for Case 1. (a) top/bottom = 10, (b) top/bottom = 1.

Figure 7

Case 2—Scenario 1: mastication loading is purely vertical. (a) Design domain extraction from patient CT scan, (b) boundary condition used in the analysis, (c) bone replacement shape using single material topology optimization, (d) bone replacement shape with 2 material topology optimization.

Figure 8

Case 2—Scenario 2: mastication loading has 2 components vertical and horizontal towards center. (a) Boundary condition used in the analysis, (b) bone replacement shape using single material topology optimization, (c) bone replacement shape using multi-material (2 materials) topology optimization.

Figure 9

Case 3. (a) Extraction of design domain from patient CT scan, (b) boundary condition used in the analysis, (c) bone replacement shape using single material topology optimization, (d) bone replacement shape using multi-material (2 materials) topology optimization.

Figure 10

Case 4. (a) Design domain extraction from patient CT scan, (b) boundary condition used in the analysis, (c) bone replacement shapes using single material topology optimization, (d) bone replacement shapes using two material topology optimization.

Figure 11

Bone replacements embedded in the defect.

Figure 12

Geometric complexity control using perimeter control constraint [43]. (a) Cross-section of midface across first molar teeth, (b) initial configuration generated by randomly locating circles in the design domain (P = 46,187), (c) topology optimized internal geometry ($P_{min}$ = 30,000). A 60% increase in the compliance is observed while achieving 80% volume (weight) reduction.

Figure 13

The effect of microscopic property variation for trabecular architecture using perimeter control. (a) Microstructure library for different macroscopic properties $E_{11}$ and $E_{12}$ represents axial and shear properties, respectively, (b) reference design using homogeneous material, and (c) a sample design using local functional materials with different macroscopic properties.

Figure 14

(a) Stage 1 multi-material topology optimization of the macrostructure for Case 1, (b) Stage 2 multi-material topology optimization with microstructure presenting two different materials for Case 1.