3D-printed ceramic triply periodic minimal surface structures for design of functionally graded bone implants

Journal Pre-proof 3D-printed ceramic triply periodic minimal surface structures for design of functionally graded bone implants

Sanjairaj Vijayavenkataraman, Lai Yee Kuan, Wen Feng Lu PII:

S0264-1275(20)30136-2

DOI:

https://doi.org/10.1016/j.matdes.2020.108602

Reference:

JMADE 108602

To appear in:

Materials & Design

Received date:

10 December 2019

Revised date:

23 February 2020

Accepted date:

24 February 2020

Please cite this article as: S. Vijayavenkataraman, L.Y. Kuan and W.F. Lu, 3D-printed ceramic triply periodic minimal surface structures for design of functionally graded bone implants, Materials & Design(2020), https://doi.org/10.1016/j.matdes.2020.108602

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© 2020 Published by Elsevier.

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3D-Printed Ceramic Triply Periodic Minimal Surface structures for design of functionally graded bone implants Sanjairaj Vijayavenkataraman1,2*, Lai Yee Kuan3, Wen Feng Lu3 1

Division of Engineering, New York University Abu Dhabi, Abu Dhabi, UAE

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Department of Mechanical and Aerospace Engineering, Tandon School of Engineering, New York University, NY, USA 3

Department of Mechanical Engineering, National University of Singapore (NUS), Singapore

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(*Corresponding author: [email protected])

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Abstract

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Stress shielding is one of the main problems that lead to bone resorption and revision surgery after implantation. Most of the commercially available metallic non-porous bone

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implants are have a much greater stiffness than the native human bones and are prone to cause stress-shielding. With an open cell structure and intricate architecture, hyperbolic

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minimal surfaces offer several advantages such as less stress concentration, high permeability and high surface area to volume ratio, thus providing an ideal environment for

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cell adhesion, migration, and proliferation. This paper explores the use of porous bone implant design based on Triply Periodic Minimal Surfaces (TPMS) which is additively manufactured with ceramic material (Alumina)

using

Lithography-based Ceramics

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Manufacturing (LCM) technology. A total of 12 different primitive surface structure unit cells with pore size in the range of 500 – 1000 µm and porosity above 50% were considered. This is one of the earliest studies reporting the 3D printing of TPMS-based structures using ceramic material. Our results suggest that the choice of material and a porous TPMS-based design led to fabrication of structures with a much lesser compressive modulus comparable with the native bone and hence could potentially be adopted for bone implant design to mitigate the stress-shielding effect. Keywords: bone implants; triply periodic minimal surfaces; ceramics; stress-shielding; vat polymerization, 3D printing.

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1. Introduction A bone implant is one of the most commonly used medical devices in the healthcare industry. Many government regulators had classified bone implants to be one of the riskiest medical devices in use [1], with over 11,000 revision surgeries performed on failed implants in the UK in one year (2016) [2]. The common cause of revision surgery is loosening of implants [3, 4] and the most common reason for implant loosening is bone resorption due to stress shielding [5]. The bone implant shares the load carrying capacity with the bone after being implanted into the body. Since most of the implants have a higher stiffness than the native

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bone, the load will be transferred predominantly through the implant; the bone thereby experiencing reduced stress and becomes stress shielded. Based on Wolff’s law, a bone will

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remodel in response to the loads acting upon it [6]. The decrease in bone mass leads to weaker bones and reduction in support for implants, increasing the risk of implant loosening

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and a second surgery to replace the implant. The risks associated with revision surgery is exceptionally high including complications such as cardiac problem and mortality [7].

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Therefore, the need for revision surgery should be minimized.

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For instance, consider the example of a Total Hip Replacement (THR). Approximately 2.5 million people are living in the USA with a hip replacement [8]. THR is not exempt from the

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problem of revision surgery. To reduce the modulus, provide better functionality and prevent revision surgeries, there are several designs and combinations of the femoral head and acetabular bearing surface materials that were introduced [9]. A systematic review of these

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different implants [9] revealed that the newer implant combinations did not reduce the risk of revision surgery. Revision surgery is more expensive than the primary surgery with longer operating time, lengthier hospital stays, and more postoperative investigations [10, 11]. The high cost of implants and the discomfort caused by surgeries warrants the need for new implant design that would mitigate the stress-shielding effects, thereby preventing the need for revision surgery. Most of the commercially available bone implants are metallic implants and non-porous, thus possessing mechanical properties much greater than the native human bones [12]. This challenge could be overcome by two different approaches, the first being alternative materials with lesser stiffness compared to metals and incorporating porous structures in the design of implants is the second approach. In the first approach, ceramics are a potential class of materials that are less stiff than metals, possess mechanical properties similar to the native bone and could be considered in place of metals. Although there had been many works reported on fabrication of ceramic structures such as calcium phosphate-PLA [13],

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Journal Pre-proof calcium silicate [14], and hydroxyapatite [15], the studies were more focused on the material aspects and not on the design aspects. In the second approach, the porous structure helps to reduce stiffness of implants and provide more open volume for bone ingrowth, thereby aiding bone healing and high osseointegration [16, 17]. Larger pores lead to better flow transportation of metabolic wastes and nutrients while smaller pores provide adequate surface area for cell attachment and proliferation, as well as better mechanical properties [18]. Though many lattice-based structures were reported previously, porous scaffolds with hyperbolic minimal surfaces (mean curvature of zero) have received much attention in the area of tissue engineering due to their biomimetic structure. With an open cell structure and intricate architecture, these structures provide an ideal environment for cell and tissue

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ingrowth, needed structural integrity, transport, and strength [19].

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In our previous work [19], we reported a parametric optimization approach for TPMS sheet scaffolds and demonstrated the versatility of the approach by different applications, one of

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which is functionally graded scaffolds [20-22] with biomimetic functional gradients. Inspired by the biomimetic architecture of the design and the ability to tune the mechanical properties

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of the TPMS structures [23-25] by varying the porosity, wall thickness, and cell size, we attempted to address the problem of stress-shielding of bone implants using TPMS-based

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implant design in this work. While attempts to mimic the native bones in terms of mechanical, material and biological properties were reported previously as described above, works on

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biomimetic design are just gaining traction [26]. This paper aims to incorporate the biomimetic design into the field of bone implants to mimic the native bone structure which is

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functionally-graded. We report an integrated approach of combining the right method of design (TPMS-based functionally-graded), and the right choice of material (ceramic) and process (3D Printing) that could lead to novel customized bone implant designs to mitigate the stress-shielding effects caused by the conventional implants. From our previous work [19], of the three different TPMS sheet structures studied, namely, the primitive (P), gyroid (G), and diamond (D) surfaces, the P-surface offered the lowest modulus value. Since this study aims to mitigate the stress-shielding by reducing the modulus of the conventional bone implant design, P-surface based TPMS sheet structures were chosen. A total of 12 different unit cells and 12 different Primitive surface structures were studied to understand the influence of the unit cell structure on the mechanical properties and to evaluate the deviations of the 3D-printed structure from the original design. The structures were made of ceramic, Alumina Al2O3 (also known as Aluminium Oxide), and fabricated in millimeter (mm) scale using Lithography-based Ceramics Manufacturing (LCM) technology. Using experimental compressive testing, the mechanical properties of the structures were determined. Based on the mechanical properties determined experimentally,

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Journal Pre-proof a functionally graded implant was designed to represent the trochanter region in the femur of hip implants with three different unit cell types.

2. Experimental Section 2.1 Design and modelling Primitive surfaces can be approximated using implicit methods [27], which will generate 3D surfaces. Primitive periodic surfaces with cubic unit cells are mathematically approximated by the following trigonometric function [19]: 2𝜋

2𝜋

2𝜋

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𝜙𝑃 (𝑥, 𝑦, 𝑧) = cos( 𝑎 𝑥) + cos( 𝑎 𝑦) + cos⁡( 𝑎 𝑧) = 𝑐

(1)

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where 𝑥, 𝑦, 𝑧 are spatial coordinates and 𝑎 is the size of a unit cell.

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𝜙 is the level-set function and 𝜙 = 𝑐 is known as the c-level set. The constant c in Eq. (1)

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controls the geometry and surface area of the Primitive surfaces. If constant c is substituted with different values, a family of surfaces possessing the topology and symmetry of Primitive

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TPMS with different volume fractions could be obtained. The solid model of Primitive surfaces were created by extracting the zero-level set surface (when 𝑐 = 0) from Eq. (1). Then, the surface is uniformly offset into all directions. In this paper, Matlab was used to

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generate the unit cells and Materialise 3-Matic was used to create and repair the structures. Materialise Magics was used to import the resultant 3D stereolithography (STL) models for

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slicing prior to 3D printing.

A total of 12 different Primitive surface structure unit cells were studied. The selection of the 12 different unit cells was based on our previous work [19]. Initially, ten thickness values (0.1 – 1 mm in increments of 0.1) and nine cell sizes (1 – 5 mm in increments of 0.5 mm) was selected. The permutation of the ten thickness values and nine cell sizes yielded a total of 90 different unit cells. From the 90 unit cells, the unit cells that satisfied the criteria of pore size in the range of 500 – 1000 µm and porosity above 50% are selected. The selection criteria were based on the desired pore size and porosity range of native bone structure. A total of 14 unit cells resulted of which 2 unit cells with thickness 0.1 mm are eliminated due to the structural resolution of the printing process, resulting in the 12 unit cells that are listed in Table 1. The unit cells were cubic with a length of 1.5, 2, 2.5, 3 and 3.5 mm. There were 6 thickness values – 0.2, 0.3, 0.4, 0.5, 0.6 and 0.7 mm. The details of all 12 specimens are listed in Table 1 and the 3D STL models of all 12 specimens are shown in Figure 1 (A-L).

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Journal Pre-proof Table 1. Specifications of Primitive surface structures Unit cell size [mm]

Overall dimension [mm3]

Lattice configuration

Number of cells

0.2

1.5 2 2.5 2 2.5 2 2.5 3 2.5 3 3 3.5

10.5 x 10.5 x 10.5 10 x 10 x 10 10 x 10 x 10 10 x 10 x 10 10 x 10 x 10 10 x 10 x 10 10 x 10 x 10 12 x 12 x 12 10 x 10 x 10 12 x 12 x 12 12 x 12 x 12 10.5 x 10.5 x 10.5

7x7x7 5x5x5 4x4x4 5x5x5 4x4x4 5x5x5 4x4x4 4x4x4 4x4x4 4x4x4 4x4x4 3x3x3

343 125 64 125 64 125 64 64 64 64 64 27

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0.6 0.7

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0.5

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0.4

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0.3

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Thickness [mm]

Figure 1. (A-L) 3D STL Models of the twelve P-surface TPMS-based lattices

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Journal Pre-proof 2.2 Fabrication of TPMS-based structures All the 12 specimens were fabricated using the Lithoz CeraFab 8500 ceramic printer with Alumina (Al2O3). The ceramic printer uses Lithography-based Ceramics Manufacturing (LCM) technology. The slurry consisting of the ceramic powder dispersion in a photo-sensitive matrix will be selectively cured (solidify) through mask exposure. The build plate will be raised after curing. The vat will rotate and apply another layer of slurry, repeating the printing process. The layer thickness was set at 25 μm. The technical properties of the printer are shown in Table 2.

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Lithoz CeraFab 8500 ceramic printer 60 μm (423 dpi) 10 – 100 μm 1920 x 1080 115 mm x 64 mm x 200 mm .stl (binary) LED Up to 100 slices per hour

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Technical properties Lateral resolution Layer thickness Number of pixels (X, Y) Building envelope (X, Y, Z) Data format Light source Building speed

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Table 2. Technical specifications of the ceramic printer

2.3 Post-processing

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The printed structures underwent post-processing including debinding and sintering processes. The debinding process removes any residual binder by thermal treatment. In the

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debinding furnace, the specimens undergo heat treatment for 156 h at a temperature ranging from 25°C to 900°C. After debinding, the specimens were sent to the sintering furnace. In the sintering furnace, the specimens undergo heat treatment for 48 h at a temperature ranging from 50°C to 1600°C. After post-processing, the fabricated bulk material has a fracture strength of 464 MPa and a mass density of 3.888 g/cm3, which deviates from the theoretical density of 3.95 g/cm3 by 1.58%. These values were based on a bending test conducted according to EN 843-1:2006 standards. The printed specimens are shown in Figure 2 (A-L). 2.4 Material Characterization The surface morphology of the printed TPMS structures was investigated using a scanning electron microscope (JEOL JSM-5500). Surface defects and surface roughness were examined. Additionally, the shell thicknesses were measured from the SEM images using an image analysis software (ImageJ, National Institute of Health, Bethesda, MD). Five measurements were taken for each sample (n=3) and the values are averaged. The Keyence VHX-1000 Digital Microscope (VH-Z20R Zoom Lens) was used to capture

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Journal Pre-proof microscopic images of the top, side, and bottom faces of the structures at x20 magnification. All the printed TPMS structures were weighed using the Ohaus Pioneer electronic balance (precision of 0.0001 mm) and their dimensions were measured using the Mitutoyo digital micrometre (precision of 0.001 mm) to calculate the total volume of each structure. The

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surface areas of the structures were obtained from the 3D STL models.

Figure 2. (A-L) 3D-printed structures of the twelve P-surface TPMS-based lattices 2.5 Mechanical Testing

All 12 specimens were tested under uniaxial compression loading to determine their mechanical properties such as Young’s modulus and fracture strength. The compression tests were carried out using a Shimadzu AG-25TB testing machine with a 250 kN load cell. TRAPEZIUM X, a material testing operation software specifically for Shimadzu testing machines, was used to control the machine and record measurements such as force and displacement. The tests were performed under displacement control with a strain rate of 0.001/s. When the TPMS structures experience a fracture, the tests were terminated. The TPMS structures were placed between two high carbon steel flat plates to protect the surfaces of the machine’s platens during the compression tests.

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2.6 Statistical Analysis Experiments were run in triplicates and all measurements were expressed as mean±SD. One way ANOVA test was used to determine the differences between the mean values of the experimental groups. Differences were considered statistically significant at p < 0.05.

3. Results and Discussion

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3.1 Dimensional variations between the design and 3D-printed structures A few representative SEM images of the 3D-printed structures are shown in Figure 3. Most

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specimens have relatively smooth surfaces. The top surface is found slightly rougher than the side surface as seen between Figures 3(A) and 3(B) and between 3(C) and 3(D), which

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might be attributed to the printing direction. There are certain defects observed in the structures when their SEM images were examined. For example, residual particles were

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found attached to the fabricated structures as shown in Figure 3(E). After the ceramic structures were printed, compressed air was used to remove most of the slurry. The

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structures were then washed with a solution to remove the remaining slurry. These two steps were done before the structures were placed inside the furnace for debinding and sintering.

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The residual particles are probably caused by the trapped slurry inside the structure which was not completely removed during the slurry removal process. This contributes to the

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thickness and weight variations and also results in increased local surface roughness. Most structures do not have any macro defects, such as pores and significant distortions. However, cracks can be seen in several structures as shown in Figure 3(F). The formation of cracks might be due to the stresses arising in the material during thermal treatment. The presence of cracks is unavoidable in ceramic structures and these cracks are difficult to be closely controlled during fabrication. The thickness of each structure was measured using ImageJ software with the SEM images. Table 3 shows the measured average top and side surfaces’ thickness of all the structures, the measured average overall thickness and the error. It is found that the thickness measured from the top surface of the structures are slightly larger than that of the structures’ side surface. A possible reason is that the top surfaces are slightly rougher than the side surfaces. Comparing the measured average overall thickness with nominal shell thickness, the error represented in Figure 4(A) shows that structures with smaller shell thickness tend to have a higher percentage error than those with larger shell thickness. The error is calculated using Eq. (2),

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Journal Pre-proof 𝑒𝑟𝑟𝑜𝑟 =

𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑⁡𝑣𝑎𝑙𝑢𝑒⁡−⁡𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙⁡𝑣𝑎𝑙𝑢𝑒

(2)

𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙⁡𝑣𝑎𝑙𝑢𝑒

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where theoretical value = the nominal value.

Figure 3. Representative SEM images of the 3D-printed TPMS structures (A) Top surface of a structure with t = 0.2 mm and a = 2 mm, (B) Side surface of a structure with t = 0.2 mm and a = 2 mm, (C) Top surface of a structure with t = 0.7 mm and a = 3.5 mm, (D) Side surface of

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Journal Pre-proof a structure with t = 0.7 mm and a = 3.5 mm, (E) Side surface of a structure with t = 0.2 mm and a = 1.5 mm, and (F) Side surface of a structure with t = 0.3 mm and a = 2 mm. Table 3. Thickness variation in 3D-printed structures measured from SEM images Unit cell size [mm]

Measured average top thickness [mm]

Measured average side thickness [mm]

Measured average overall thickness [mm]

Thickness error [%]

0.2

1.5 2 2.5 2 2.5 2 2.5 3 2.5 3 3 3.5

0.259 0.264 0.239 0.353 0.344 0.477 0.467 0.471 0.548 0.574 0.667 0.759

0.233 0.246 0.231 0.320 0.321 0.439 0.445 0.430 0.507 0.516 0.609 0.731

0.246 0.255 0.236 0.337 0.333 0.458 0.454 0.451 0.528 0.545 0.638 0.745

23.092 27.401 17.922 12.218 10.897 14.478 13.413 12.669 5.507 9.045 6.385 6.454

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0.6 0.7

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0.5

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0.4

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0.3

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Nominal shell thickness [mm]

The surface area, total volume VT and solid volume VS of the structures were obtained from

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their 3D STL models on Materialise Magics (Supplementary Table S1). The void volume VV and porosity were calculated from Eqs. (3) and (4). It can be observed that as the unit cell

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size increases (with different thickness values), the porosity increases too. The mass, apparent density ρa and relative density ρr were calculated using Eqs. (5) – (8). As the unit cell size increases at each thickness, apparent and relative densities decrease. The values taken from 3D STL models were used to compare with the measurements obtained from the printed structures in Table 3.

𝑉𝑉 = 𝑉𝑇 − 𝑉𝑆 𝑃𝑜𝑟𝑜𝑠𝑖𝑡𝑦 = ⁡

𝑉𝑉 𝑉𝑇

𝑚𝑎𝑠𝑠 = 𝑉𝑆 ⨯ 𝜌𝐴𝑙𝑢𝑚𝑖𝑛𝑎 𝜌𝑎 = 𝜌𝑟 =

(3) (4)

(5)

𝑚𝑎𝑠𝑠 𝑉𝑇

(6)

𝜌𝑎

(7)

𝜌𝐴𝑙𝑢𝑚𝑖𝑛𝑎

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Eq. (7) can be further simplified to: 𝑉

(8)

𝜌𝑟 = 𝑉𝑆

𝑇

The mass and total volume error of the structures were calculated using Eq. (3) and tabulated in Supplementary Table S2. The solid volume VS was calculated using Eq. (6), void volume VV was calculated using Eq. (4) and porosity was found using Eq. (5). The mass

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error is shown graphically in Figure 4(B). From Table S2, it is observed that all the structures

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have mass values higher than nominal mass values. Additionally, as seen in Figure 4(B), structures with smaller unit cell size (e.g. 1.5 and 2 mm) experience a higher deviation from

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nominal mass values. During fabrication, a layer of slurry is deposited on the build plate before the structures are being printed onto the build plate. After the structures were printed,

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a sharp and flat object (e.g. knife or spatula) is used to remove the structures from the build plate. As seen in Figure 4(F), the bottom surfaces of the structures have a layer of slurry. In

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Figure 4(G), the structure had most of the slurry successfully removed manually, while in Figure 4(F) the slurry is not removed completely. This is because the structure has a cell size

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of 2 mm which is smaller and much more intricate. Thus, it is difficult to remove the slurry without the risk of breaking the structure. Therefore, the layer of slurry on all the structures contribute to an increase in mass and the increase is greater for structures with smaller cell

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size as the slurry removed is much lesser. Also, the residual particles mentioned before (Figure 3(E)) contribute to the additional mass. The total volume error is shown in Figure 4(C) and it is small for all structures, indicating that the printed structures have almost the same total volume as the 3D STL models. Negative volume error means that the volume of the structure is smaller than that of the 3D STL model. Referring to Table S2, there were only a very few cases of negative volume error, which might be due to the damage in structures caused during slurry removal and shrinkage during the post-processing processes. Using Eq. (3), the porosity error was determined and is shown in Figure 4(D). The porosity values measured from the structures were smaller than the nominal porosity values, indicated by the negative error. The deviation might have been caused by the layer of slurry attached to the bottom surface of structures (as described above for mass error), which explains why structures with smaller cell size experience greater porosity deviations as compared to structures with a larger cell size. 11

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Figure 4. Dimensional variations between the design and 3D-printed structures (A) Mean error in thickness, (B) Mass error, (C) Volume error, (D) Porosity error, (D) Relative density error, and (F, G) Microscopic images of the bottom surface of the structures.

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Journal Pre-proof The apparent density ρa was calculated using Eq. (7), relative density ρr was calculated using Eq. (8) and the relative density percentage error was determined using Eq. (3) and is shown in Figure 4(E). The relative density is proportional to the mass of the structure. From Figure 4(B), the mass percentage error is higher for smaller cell size, which attributes to the higher relative density percentage error for smaller cell size such as 1.5 and 2 mm.

3.2 TPMS-based design reduces the Young’s modulus (compression) of the structures Force and displacement output were obtained from TRAPEZIUM X software. Stress σ and

𝜀=

𝐷 ℎ

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𝐹 𝐴𝑐

(9)

(10)

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𝜎=

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strain ε were calculated using the equations below.

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where F is the applied load, Ac is the cross-sectional area of the structure, D is the total displacement and h is the original height of the structure.

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The representative stress-strain curves are shown in Figures 5(A) and 5(B), and it follows the pattern of a typical brittle material under loading. The curve only has an elastic region with a

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linear behavior up to the fracture point. Unlike ductile materials (e.g. 316L Stainless Steel), brittle materials like Alumina have higher yield strength than fracture strength. In other words, the structures will first fracture before yielding. Thus, it can be observed that the stress-strain

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curves only have elastic region and do not have plastic region. The significant drop in stress towards the end indicates a sudden catastrophic failure exhibited by the structures, which is expected for brittle materials. Some of the structures exhibited stress-strain curves as shown in Figure 5(B). There is a decrease in stress followed by an increase again. This is caused by cracks and other deformities present in the structures as discussed in the previous section.

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Figure 5. Mechanical properties of 3D-printed TPMS structures (A) Stress-strain curve of the structure with t = 0.3 mm and a = 2.5 mm, (B) Stress-strain curve of the structure with t = 0.2 mm and a = 2.5 mm, (C) Experimental Young’s modulus (compression), (D) Experimental Fracture strength (compression), (D) Experimental Young’s modulus (compression) trend line, and (F) Apparent density trend line obtained by Eq. (15).

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Journal Pre-proof From the stress-strain curves, different mechanical properties were deduced. Young’s modulus (compression) is determined by the slope of the curve at the elastic region [28-30]. Young’s modulus may be characterized as the stiffness or the ability of the structure to resist deformation within the linear portion. Fracture strength is the highest stress in the stressstrain curve and it is defined as the stress at which a specimen fails via fracture. The Young’s modulus (compression) and fracture strength of all the structures are shown in Figures 5(C) and 5(D) respectively. The Young’s modulus (compression) ranges from 2 to 5.5 GPa and the fracture strength ranges from 11 to 133.5 MPa. From Figure 5(E), it can be observed that the Young’s modulus decreases with increasing unit cell size. This is generally

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true except for structure with thickness 0.3 mm, where Young’s modulus increases instead. There is no definite trend concerning the effects of shell thickness on Young’s modulus. At

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unit cell size 2 mm, as thickness increases from 0.2 to 0.4 mm, Young’s modulus increases. At unit cell size 2.5 mm, structure with thickness 0.2 mm has the lowest Young’s modulus

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and as thickness increases from 0.3 to 0.5 mm, Young’s modulus decreases. At unit cell size 3 mm, structure with thickness 0.5 mm has the highest Young’s modulus, followed by

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thickness 0.4 mm and 0.6 mm. This might be due to the presence of microscopic flaws such as micro-cracks and internal pores. In the future, fatigue strength of these structures would

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be evaluated as these structures are intended for use as long-term permanent implants.

3.3 Theoretical and actual Young’s modulus (compression) of the structures

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When investigating TPMS sheet structures, their theoretical Young’s modulus can be determined by the following equation: 𝐸 = 𝐶𝐸𝑠 𝜌𝑟 𝑛

(12)

where coefficient C and exponent n depend on the unit cell geometries, Es is the base material’s Young’s modulus and ρr is the relative density. Although the analytical model developed to predict Eq. (12) is based on lattice structures, it is also suitable for TPMS-based cellular structures. For Primitive TPMS sheet structures, the coefficient C is found to be 0.29 and the exponent n is 1.28 from our previous work [19]. Eq. (12) will then become: 𝐸 = 0.29𝐸𝑠 𝜌𝑟 1.28

(13)

In this study, Eq. (13) cannot be used to find the theoretical Young’s modulus of Primitive surface structures as Young’s modulus of Alumina is not available (proprietary material). Therefore, in this work, an equation to approximate the actual Young’s modulus of the

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Journal Pre-proof printed structures was derived instead. By modifying Eq. (12), the following equation was obtained: 𝐸 = 𝐶1 𝜌𝑎 𝑛

(14)

where coefficient C1 =CEs and ρa is the apparent density. The coefficient C1 and exponent n were computed by the least square method (Supplementary Figure 1) using the experimental results obtained from the compression tests. By substituting coefficient C1 into the equation, the actual Young’s modulus of the printed structures can be calculated without using the base material’s Young’s modulus. Exponent n is taken as the slope of the least square curve and coefficient C1 is taken as 10

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where E is in GPa and ρa is in g/cm3.

(15)

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𝐸 = 2.001𝜌𝑎 0.588

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Hence, the following equation was derived:

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to the power of the offset of the least square curve.

Eq. (15) gives the approximated Young’s modulus of the printed structures. Since apparent

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density and relative density is correlated to Young’s modulus, by controlling the apparent density or relative density of the structures, the desired Young’s modulus can be obtained. From Figure 5(F), it can be observed that the apparent density decreases with increasing

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unit cell size. The trend is similar to that of the Young’s modulus of the structures shown in Figure 5(E). Therefore, equation (15) can be used to calculate the theoretical Young’s

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modulus of the printed structures when the properties of the (proprietary) materials are unknown. The equation is very useful since most of the commercially available raw materials for 3D printing are proprietary materials and the accurate mechanical properties cannot be determined.

3.4 Design of functionally graded TPMS structure With the TPMS unit cells and their mechanical properties determined, an example of constituting a functionally gradient structure for the femur region in the hip implant was explored. The femur contains structural and mechanical gradients across a spatial volume. Hence, it is important that the hip implant designed also exhibit similar gradients to mimic the femur and minimize the effect of stress shielding. The hip implant consists of several different regions, of which the trochanter region and its Young’s modulus was considered in this study. The trochanter has four distinct quadrants namely medioanterior (MA), lateroanterior (LA), lateroposterior (LP) and medioposterior (MP) (Supplementary Figure 2). 16

Journal Pre-proof There is Young’s modulus gradient across the quadrants and Young’s modulus of trabecular and cortical bone at each region, derived from the literature [31-33], and are stated in Supplementary Table S3. Since the range of Young’s modulus throughout the trochanter region is large, the design of a functionally graded structure for the trochanter region of a hip implant was simplified. Three different unit cells were used, one for the MA and MP quadrants, one for the LA and LP quadrants, and one for the trabecular bone for all the quadrants. Hence, the functionally graded structure is cylindrical with three distinct regions as shown in Figure 6(A) and three different Young’s modulus values. Region 1 consists of the cortical bone of quadrants MA

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and MP, region 2 consists of the trabecular bone and region 3 consists of the cortical bone of quadrants LA and LP. The overall diameter of the structure is 20 mm, height is 10 mm and

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the radius of region 2 is 7.5 mm. The characteristic dimensions (thickness and unit cell size) of the three different unit cells along with their Young’s modulus (compression) values used

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for the three regions are indicated in Figure 6(A). By optimizing the unit cell structures with the required properties as discussed in our previous work [19], it is possible to match the

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exact properties of the native bone and construct a biomimetic functionally gradient structure.

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One of the key steps in designing a functionally graded TPMS structure is to combine different substructures with smooth shape transitions. Numerous design and modeling methods were developed for generating functionally graded architectures. In this work, a

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method based on sigmoid function for generating functionally graded TPMS structures [29] was adopted, with which the transitions and boundaries of the two zones can be controlled

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with ease. Using the following equation, two substructures can be combined: 1

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𝜙(𝑥, 𝑦, 𝑧) = 1+𝑒 𝑘.𝑏(𝑥,𝑦,𝑧) 𝜙1 (𝑥, 𝑦, 𝑧) + 1+𝑒 −𝑘.𝑏(𝑥,𝑦,𝑧) 𝜙2 (𝑥, 𝑦, 𝑧)

(16)

where 𝜙1 (𝑥, 𝑦, 𝑧) and 𝜙2 (𝑥, 𝑦, 𝑧) represent the two substructures, 𝜙(𝑥, 𝑦, 𝑧) represent the resultant structure, function 𝑏(𝑥, 𝑦, 𝑧) describes the boundary and factor k controls the transition zone near the boundary.

The higher the k value, the smaller the transition zone and vice versa. Eq. (16) can also be used to combine any number of substructures. Therefore, using this equation, multiple substructures with different cell size can be combined with controllable boundaries and smooth shape transitions. A functionally graded TPMS structure for the trochanter region of a hip implant designed using this method is shown in Figures 6(B) and 6(C). The functionally graded structure consists of three substructures with variations in cell size and shell thickness.

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Figure 6. Design of a functionally gradient TPMS based trochanter region (in the femur) of a hip implant (A) Schematic drawing (top view) of the functionally graded structure, (B) Top structure.

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4. Conclusion

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view of the functionally graded structure, and (C) Isometric view of the functionally graded

This paper reports one of the earliest attempts of incorporating the biomimetic design into the field of bone implants along with the right choice of materials and fabrication method to mimic the native bone structure which is functionally-graded. A TPMS-based design of bone implants with 3D-printed ceramic material is investigated in this study. No macro defects were seen in the printed specimens but cracks were present on the surfaces of some structures, which are unavoidable with ceramics. The printed structures have similar total volume as the STL models and the total volume percentage error for all structures were less than 2.5%. However, the mass of the printed structures deviates greatly from the STL models, with the highest mass percentage error being 100%. The mass percentage error is greater especially for structures with smaller unit cell size (1.5 and 2 mm). The unremoved residual slurry at the bottom layer is the main cause for this large deviation. The deviation in mass directly affects the relative density, which explains the high relative density percentage error. The printed structures have lower porosity values than STL models as indicated by the negative porosity percentage error values. The Young’s modulus of the printed structures

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Journal Pre-proof decreases with increasing cell size. Apparent density and relative density of the structures are correlated to Young’s modulus, thus by controlling these density values, structures with desired Young’s modulus can be obtained. An equation is derived to calculate the theoretical Young’s modulus of the printed structures when the properties of the (proprietary) materials are unknown. Using the experimental results, a functionally graded TPMS structure for the trochanter region of a hip implant is designed, with three different unit cell structures. An integrated approach of combining the right method of design (TPMS-based, functionallygraded), right choice of material (ceramic) and process (3D Printing) is reported in this work that could lead to novel customized bone implant designs to mitigate the stress-shielding effects caused by the conventional implants. Future biological validation with in vitro and in

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vivo cell culture studies would further the clinical translation of this approach.

Data Availability

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The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

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References

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[1] D.B. Kramer, S. Xu, A.S. Kesselheim, Regulation of medical devices in the United States and European Union, Mass Medical Soc, 2012. [2] M. Green, N. Wishart, E. Young, V. Mccormack, M. Swanson, NJR 14th annual report, Natl Jt Regist 14th Annu Rep 1821 (2017). [3] H. Malchau, P. Herberts, L. Ahnfelt, Prognosis of total hip replacement in Sweden: follow-up of 92,675 operations performed 1978–1990, Acta Orthopaedica Scandinavica 64(5) (1993) 497-506. [4] L.I. Havelin, B. Espehaug, S.E. Vollset, L.B. Engesæter, N. Langeland, The Norwegian arthroplasty register: a survey of 17,444 hip replacements 1987–1990, Acta Orthopaedica Scandinavica 64(3) (1993) 245-251. [5] R. Huiskes, H. Weinans, B. Van Rietbergen, The relationship between stress shielding and bone resorption around total hip stems and the effects of flexible materials, Clinical orthopaedics and related research (1992) 124-134. [6] M. Ridzwan, S. Shuib, A. Hassan, A. Shokri, M.M. Ibrahim, Problem of stress shielding and improvement to the hip implant designs: a review, J. Med. Sci 7(3) (2007) 460-467. [7] M.W. Pagnano, L.A. McLamb, R.T. Trousdale, Primary and revision total hip arthroplasty for patients 90 years of age and older, Mayo Clinic Proceedings, Elsevier, 2003, pp. 285-288. [8] H.M. Kremers, D.R. Larson, C.S. Crowson, W.K. Kremers, R.E. Washington, C.A. Steiner, W.A. Jiranek, D.J. Berry, Prevalence of total hip and knee replacement in the United States, The Journal of bone and joint surgery. American volume 97(17) (2015) 1386. [9] E.M. Marques, R. Humphriss, N.J. Welton, J.P. Higgins, W. Hollingworth, J.A. Lopez-Lopez, H. Thom, L.P. Hunt, A.W. Blom, A.D. Beswick, The choice between hip prosthetic bearing surfaces in total hip replacement: a protocol for a systematic review and network meta-analysis, Systematic reviews 5(1) (2016) 19. [10] R. Kallala, I. Vanhegan, M. Ibrahim, S. Sarmah, F. Haddad, Financial analysis of revision knee surgery based on NHS tariffs and hospital costs: does it pay to provide a revision service?, The bone & joint journal 97(2) (2015) 197-201. [11] F. Henshaw, E. Karasouli, R. King, U. Rahman, D. Langton, J. Madete, F. Otsyeno, V. Mutiso, J. Atinga, M. Underwood, Engineering standards for trauma and orthopaedic implants worldwide: a systematic review protocol, BMJ open 8(10) (2018) e021650. [12] M. Jäger, H. Jennissen, F. Dittrich, A. Fischer, H. Köhling, Antimicrobial and osseointegration properties of nanostructured titanium orthopaedic implants, Materials 10(11) (2017) 1302. [13] S. Sahmani, A. Khandan, S. Esmaeili, S. Saber-Samandari, M.G. Nejad, M. Aghdam, Calcium phosphate-PLA scaffolds fabricated by fused deposition modeling technique for bone tissue applications: Fabrication, characterization and simulation, Ceramics International 46(2) (2020) 24472456. [14] A. Kordjamshidi, S. Saber-Samandari, M.G. Nejad, A. Khandan, Preparation of novel porous calcium silicate scaffold loaded by celecoxib drug using freeze drying technique: Fabrication, characterization and simulation, Ceramics International 45(11) (2019) 14126-14135. [15] S. Esmaeili, H.A. Aghdam, M. Motififard, S. Saber-Samandari, A.H. Montazeran, M. Bigonah, E. Sheikhbahaei, A. Khandan, A porous polymeric–hydroxyapatite scaffold used for femur fractures treatment: fabrication, analysis, and simulation, European Journal of Orthopaedic Surgery & Traumatology 30(1) (2020) 123-131. [16] X. Wang, S. Xu, S. Zhou, W. Xu, M. Leary, P. Choong, M. Qian, M. Brandt, Y.M. Xie, Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: A review, Biomaterials 83 (2016) 127-141. [17] F. Matassi, A. Botti, L. Sirleo, C. Carulli, M. Innocenti, Porous metal for orthopedics implants, Clinical Cases in Mineral and Bone Metabolism 10(2) (2013) 111.

20

Journal Pre-proof

Jo ur

na

lP

re

-p

ro

of

[18] S. Zhang, S. Vijayavenkataraman, W.F. Lu, J.Y. Fuh, A review on the use of computational methods to characterize, design, and optimize tissue engineering scaffolds, with a potential in 3D printing fabrication, Journal of Biomedical Materials Research Part B: Applied Biomaterials 107(5) (2019) 1329-1351. [19] S. Vijayavenkataraman, L. Zhang, S. Zhang, J.Y. Hsi Fuh, W.F. Lu, Triply Periodic Minimal Surfaces Sheet Scaffolds for Tissue Engineering Applications: An Optimization Approach toward Biomimetic Scaffold Design, ACS Applied Bio Materials 1(2) (2018) 259-269. [20] S. Vijayavenkataraman, S. Zhang, W.F. Lu, J.Y.H. Fuh, Electrohydrodynamic-jetting (EHD-jet) 3Dprinted functionally graded scaffolds for tissue engineering applications, J Mater Res 33(14) (2018) 1999-2011. [21] S. Yu, J. Sun, J. Bai, Investigation of functionally graded TPMS structures fabricated by additive manufacturing, Mater Design 182 (2019) 108021. [22] F. Liu, Z. Mao, P. Zhang, D.Z. Zhang, J. Jiang, Z. Ma, Functionally graded porous scaffolds in multiple patterns: New design method, physical and mechanical properties, Mater Design 160 (2018) 849-860. [23] D.W. Abueidda, M. Elhebeary, C.-S.A. Shiang, S. Pang, R.K.A. Al-Rub, I.M. Jasiuk, Mechanical properties of 3D printed polymeric Gyroid cellular structures: Experimental and finite element study, Mater Design 165 (2019) 107597. [24] E. Yang, M. Leary, B. Lozanovski, D. Downing, M. Mazur, A. Sarker, A. Khorasani, A. Jones, T. Maconachie, S. Bateman, Effect of geometry on the mechanical properties of Ti-6Al-4V Gyroid structures fabricated via SLM: A numerical study, Mater Design 184 (2019) 108165. [25] Z. Chen, Y.M. Xie, X. Wu, Z. Wang, Q. Li, S. Zhou, On hybrid cellular materials based on triply periodic minimal surfaces with extreme mechanical properties, Mater Design 183 (2019) 108109. [26] S. Zhang, S. Vijayavenkataraman, G.L. Chong, J.Y.H. Fuh, W.F. Lu, Computational Design and Optimization of Nerve Guidance Conduits for Improved Mechanical Properties and Permeability, J Biomech Eng-T Asme 141(5) (2019). [27] S. Rajagopalan, R.A. Robb, Schwarz meets Schwann: design and fabrication of biomorphic and durataxic tissue engineering scaffolds, Medical image analysis 10(5) (2006) 693-712. [28] V. Sanjairaj, S. Kannan, T. Cao, J.Y.H. Fuh, G. Sriram, W.F. Lu, 3D-Printed PCL/PPy Conductive Scaffolds as Three-dimensional Porous Nerve Guide Conduits (NGCs) for Peripheral Nerve Injury Repair, Frontiers in Bioengineering and Biotechnology 7 (2019) 266. [29] S. Vijayavenkataraman, S. Thaharah, S. Zhang, W.F. Lu, J.Y.H. Fuh, 3D-Printed PCL/rGO Conductive Scaffolds for Peripheral Nerve Injury Repair, Artif Organs 43(5) (2019) 515-523. [30] S. Vijayavenkataraman, S. Zhang, S. Thaharah, G. Sriram, W. Lu, J. Fuh, Electrohydrodynamic jet 3D printed nerve guide conduits (NGCs) for peripheral nerve injury repair, Polymers-Basel 10(7) (2018) 753. [31] L. Yang, A.C. Burton, M. Bradburn, C.M. Nielson, E.S. Orwoll, R. Eastell, Distribution of bone density in the proximal femur and its association with hip fracture risk in older men: the osteoporotic fractures in men (MrOS) study, Journal of Bone and Mineral Research 27(11) (2012) 2314-2324. [32] E.F. Morgan, H.H. Bayraktar, T.M. Keaveny, Trabecular bone modulus–density relationships depend on anatomic site, Journal of biomechanics 36(7) (2003) 897-904. [33] V. Bousson, F. Peyrin, C. Bergot, M. Hausard, A. Sautet, J.D. Laredo, Cortical bone in the human femoral neck: three‐dimensional appearance and porosity using synchrotron radiation, Journal of Bone and Mineral Research 19(5) (2004) 794-801.

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Journal Pre-proof Author Statement

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Sanjairaj Vijayavenkataraman: Conceptualization, Methodology, Validation, Formal analysis, Writing – Original Draft, Writing – Review & Editing, Visualization, Supervision, Project administration Lai Yee Kuan: Methodology, Software, Validation, Formal Analysis, Investigation, Writing – Original Draft Wen Feng Lu: Conceptualization, Writing – Review & Editing, Supervision, Project administration

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Journal Pre-proof Declaration of competing interest

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Graphical abstract

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Journal Pre-proof Highlights

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3D-printed Ceramic Triply Periodic Minimal Surfaces-based structures exhibit Young’s modulus values between 2 – 5.5 GPa comparable to the native bone The open cell structure and intricate architecture offer conducive cell-microenvironment (less stress concentration, high permeability and surface area to volume ratio) Difficulty in slurry removal with smaller unit cell sizes (<2 mm) resulted in greater mass deviations (up to 100%) An equation is derived to calculate the theoretical Young’s modulus of the printed structures when the properties of the (proprietary) materials are unknown A functionally-graded structure for the trochanter region of hip implant is designed to mitigate stress-shielding effects caused by conventional implants

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