Design and Fabrication of 3D Printed Tissue Scaffolds

Proceedings of the ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC/CIE 2017 August 6-9, 2017, Cleveland, Ohio, USA

DETC2017-67602

DESIGN AND FABRICATION OF 3D PRINTED TISSUE SCAFFOLDS INFORMED BY MECHANICS AND FLUIDS SIMULATIONS Paul F Egan Health Sciences and Technology Swiss Federal Institute of Technology Zurich, Switzerland

Veronica C Gonella Mechanical and Process Engineering Swiss Federal Institute of Technology Zurich, Switzerland

Max Engensperger Mechanical and Process Engineering Swiss Federal Institute of Technology Zurich, Switzerland

Stephen J Ferguson Health Sci and Tech/Institute for Biomechanics Swiss Federal Institute of Technology Zurich, Switzerland

Kristina Shea Mechanical and Process Engineering Swiss Federal Institute of Technology Zurich, Switzerland ABSTRACT

1.0 INTRODUCTION AND BACKGROUND

Advances in additive manufacturing are enabling the fabrication of lattices with complex geometries that are potentially advantageous as tissue scaffolds. Scaffold design for optimized mechanics and tissue growth is challenging, due to complicated trade-offs among scaffold structural properties including porosity, pore size, surface-volume ratio, elastic modulus, shear modulus, and permeability. Here, a design for additive manufacturing approach is developed for tuning unit cell libraries as tissue scaffolds through (1) simulation, (2) design automation, and (3) fabrication. Finite element simulations are used to determine elastic and shear moduli of lattices as a function of porosity. Fluids simulations suggest that lattice permeability scales with porosity cubed over surface-volume ratio squared. The design automation approach uses simulation results to configure lattices with specified porosity and pore size. A cubic and octet lattice are fabricated with pore sizes of 1,000µm and porosities of 60%; these lattice types represent unit cells with high unidirectional elastic modulus/permeability and high shear modulus/surface-volume ratio, respectively. Imaging suggests the 3D printing process recreates the form accurately, but distorts microscale features. Future iterations are required to determine how lattices perform in comparison to computational predictions. The developed approach provides the foundations of a design automation approach for optimized 3D printed tissue scaffolds informed by simulation and experiments.

Complex 3D printed structures enabled by rising additive manufacturing technologies are potentially advantageous as tissue scaffolds for regenerative medicine [1, 2]. Tissue scaffolds provide in vivo mechanical support while facilitating biological tissue growth. An emerging strategy is the use of beam-based lattices to construct scaffolds with favorable mechanical properties [3-5]. Controlled material placement in lattices can produce structures with higher mechanical efficiency than stochastic porous scaffolds of similar density, such as foams [69]. We aim to build upon our past work in biologically informed mechanical design and 3D printing [10-13] to develop a design for manufacturing approach informed by simulations and experiments to automate tissue scaffold design (Fig. 1), with spinal fusion as an exemplary application.

Figure 1: Design for additive manufacturing approach with lattice-based tissue scaffolds

1

Copyright © 2017 ASME

Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 06/12/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use

The Figure 1 proposed design approach begins with a library of lattices that are evaluated through modeling and simulation. Results enable design automation for configuring structures with preferred properties. The configured structures are suitable for fabrication via 3D printing and empirical validation through experiments can provide a basis for improving designs in future iterations. The approach is potentially advantageous because it enables an automated and efficient way for configuring complex lattice structures that are customizable at print time and could potentially outperform traditional tissue scaffolds. The evaluated tissue scaffold performance is primarily centered on tissue growth and providing sustainable mechanical support for in vivo tissue generation. Empirical studies have demonstrated tissue growth on lattices and the feasibility of using computational approaches for generating and evaluating scaffolds [14-16]. Common properties linked to scaffold performance include tissue growth related morphological properties of porosity, pore size, surface area [17], mechanically related properties of elastic modulus and shear modulus [18-20], and properties related to nutrient transport such as permeability [21, 22]. To determine suitable property values for tissue scaffold designs, it is necessary to understand its interactions with the body and, in the case of spinal cage devices, other support aspects of the cage system. Spinal cages are porous structures placed between adjacent vertebrae after surgical removal of an intervertebral disc and are designed to bear mechanical load while providing a biological niche for vertebral fusion [23, 24]. One feasible approach for spinal cage systems uses a solid shell containing a lattice with pedicle screw hardware in adjacent vertebrae (Figure 2).

of the primary compressive load in the spine, unit cells with elements aligned with the loading direction tend to achieve a high elastic modulus, while unit cells with diagonally oriented elements tend to perform better for shearing loads [28-30]. Functionality related to biological growth and nutrient transport, such as surface-volume ratio (i.e. surface area divided by volume) and permeability, is also dependent on a unit cell’s topology. A higher surface-volume ratio provides more area for initial cell attachment and is facilitated by including small pores throughout a scaffold. Permeability is a measure of fluid flow through a porous material and a higher permeability ensures nutrients are provided to tissue and waste is removed [31-33]; higher permeability is facilitated by including larger pores and minimizing surface area [34]. Permeability has been empirically demonstrated for bone [35] and stochastic foam scaffolds [9] to scale with porosity cubed over surface-volume ratio squared, referred to as the Kozeny-Carmen relation [36-38]. Since surface area and permeability are dependent on the topology of a scaffold, they also have trade-offs with mechanical properties, which creates a complex design space for optimizing scaffold lattices [39-41]. There is a need for developing effective design approaches for configuring lattices with favorable property trade-offs [4244]. However, lattice design is challenging even from a purely mechanical perspective—lattices can have hundreds of thousands of elements and varied unit cells [12, 45]. The design space is often simplified by patterning identical beam-based unit cells to fill the lattice volume. These unit cells form libraries for scaffold design and provide a starting point for tuning scaffold properties by altering parameters of unit cell size and beam element diameter [46]. Past studies for spinal cages have used unit cells with spherical pores to investigate an initial desirable form to facilitate nutrient transport and tissue growth [47]. These studies were followed by tuning the structure for desirable mechanics with spherical pores based on 3D printing approaches [48]. 3D printing is particularly advantageous because it provides a high degree of control over structural features of a design, and enables personalized medical fabrication. Our approach expands upon these past approaches by considering beam-based lattice designs and additionally including pore size as a key lattice property trade-off, which influences surface area and nutrient transport throughout a scaffold. The goal of this paper is to develop a design for additive manufacturing approach for generating and evaluating lattices for bone tissue engineering applied to spinal cage systems. Lattice generation is conducted by proposing unit cell topologies while using mechanics and fluids simulations to evaluate lattice properties. Simulation findings provide a foundation for design automation of scaffold structures with specified properties, such as a desired elastic modulus and pore size for bone tissue engineering. These outcomes enable the fabrication of scaffold prototypes that may be used for experiments while also informing future design iterations.

Figure 2: Structural components of spinal fusion system

Mechanical loads in the cage system are distributed among the lattice, shell, and hardware during spinal extension, flexion, bending, and rotation [23, 24]. The lattice only bears a portion of the 0.1MPa to 2MPa compressive load previously experienced by the removed intervertebral disc [25]. Cage designs include single and dual cage systems with common dimensions of 10mm to 20mm in length/width and 10mm in height [26]. Spinal cage porosity ranges from fifty to ninety percent, with a higher porosity being desirable for greater tissue growth volume and nutrient transport. Although higher porosities are desirable biologically, higher porosity reduces mechanical properties since it decreases the lattice’s relative material density [27]. For a given density, mechanical properties vary based on the topological organization of material, such as the topology of a base unit cell repeated to form a lattice. For unidirectional loads, which is representative

2.0 METHODS 2.1 Unit cell library A library of eight unit cells is used to generate lattices for

scaffolds. Each unit cells consists of beam elements within a cubic volume with edges of length 𝐿𝑐 . Beam elements have octagonal cross sections and an element diameter ø that is centered on element connections. The material portion that

2



extends beyond the cubic volume, due to elements being centered on nodes, is removed to ensure unit cells are patterned with no overlaps [49]. The unit cell library has three families (Fig. 3): a Cubic family that has elements along each cubic volume edge, an Octahedron family has a large proportion of diagonal elements [29], and a Truncated family with features of both the Cubic and Octahedron families.

Porosity 𝑃 is determined by dividing a lattice’s void volume by the total nominal volume occupied by the lattice. Surfacevolume ratio 𝑆/𝑉 is found by dividing a lattice’s inner surface area by the total nominal volume of the lattice. The inner surface area is the total exposed lattice surface area minus the surface area of each lattice face, and is found using Abaqus once unit cells are generated. Porosity and surface-volume ratio remain constant for a unit cell of a given element diameter and length regardless of how many unit cells a lattice contains. Pore size 𝑝 is defined as the largest circular shape that remains parallel to a lattice face, has a majority of its perimeter surrounded by in-plane beam elements, and does not intersect with any beam elements [28]. Planar interconnectivity pores are chosen for pore size calculations since they typically fill prior to larger three dimensional spaces in open-porous scaffolds [15]. Pores lie either on the face of a single unit cell (Cube, FD-cube, BC-cube, and T-cube), at the intersection of two adjacent unit cells (Octet and V-octet), or the intersection of four connecting unit cells (Octa and T-Octa) as shown in Figure 4.

Figure 3: (A) Cubic, (B) Octahedron, and (C) Truncated unit cell families

The Cube unit cell consists of 12 elements that span each edge of the cubic volume. The face diagonal cube (FD-Cube) retains the elements of the Cube unit cell and adds a diagonal element across each face to form an 18 element unit cell. The Body-Centered Cube (BC-Cube) has the same 12 elements as the Cube unit cell and adds 8 elements that begin from the corner of the cubic volume and connect at the center to produce a structure with 20 total elements [49]. The Octahedron (Octa) unit cell consists of 12 elements that begin and end at the center of each face of the cubic volume, thus it has a similar geometry to the Cube unit cell but elements are aligned diagonally and shorter relative to the cubic volume. The Octet (Octet) unit cell has 36 total elements that consists of the same elements as the Octa unit cell and 24 additional elements to form a tetrahedron in each corner of the cubic volume [27]. The Void Octet (V-Octet) unit cell consists of the 24 elements of the Octet unit cell that are not present in the Octa unit cell. The Truncated Cube (T-Cube) introduces triangular faces at each corner of the Cube unit cell to form a structure of 48 total elements with 6 octahedron faces and 8 triangular faces [46]. Each triangular face has an element that begins and ends at a point on the edge of the cube that is a distance 0.42 ∙ 𝐿𝑐 from the corner of the cubic volume; this distance is chosen to ensure that access to smaller pores remains for relevant tissue engineering porosities. The Truncated Octahedron (T-Octa), also known as a Kelvin cell [8], is formed by introducing a square face for each connection point in the Octa unit cell to form a 36 element unit cell with 8 hexagonal and 6 square faces.

Figure 4: Lattice cross-sections with red squares indicating unit cells and blue circles indicating pores.

Pore sizes are the diameter of each circle in Figure 4 and expressed with unit cell length 𝐿𝑐 and element diameter ø design parameters. The Cube, BC-Cube, and T-Octa unit cells have pore size 𝑝 = 𝐿𝑐 − ø, the Octa, Octet, and V-Octa unit cells have pore size 𝑝 =

√2 2

(𝐿𝑐 − ø), and the T-Cube unit cell has pore size

𝑝 = 0.84 ∙ 𝐿𝑐 − ø. The FD-Cube unit cell pore size is 𝑝 = √2ℓ ∙ √

2ℓ−√2ℓ

,

2ℓ+√2ℓ

where

ℓ = (𝐿𝑐 − ø) −

√2ø 2

,

which

is

a

more

complicated geometrical relationship since the pore resides within a triangular shape [28]. These defined pore sizes are representative of interconnectivity pores where nutrients flow throughout the scaffold and are the initial points of tissue growth [15]. 2.3 Elastic simulation

The elastic modulus is found using a beam analysis with each beam composed of three finite elements in Abaqus software. Each member’s linear elastic behavior is approximated using the Euler-Bernoulli beam theory. 125 unit cells are patterned to fill a cubic volume (Fig. 5), which was justified as an acceptable number of unit cells and analysis approach via related work on lattice sensitivity analyses [29]. Elements that

2.2 Pore size

Lattices are patterned with repeating unit cells and have the same number of unit cells in all directions. Adjacent FD-Cube unit cells are mirrored to ensure shared unit cells faces have the same directionality of diagonal elements.

3



lie entirely on a lattice face have their cross-sectional area divided by half, while elements that lie entirely on a corner have their area divided by four, which corrects for the area of beam elements that extends outside of a cubic volume. A generic material with a modulus of 100MPa is used for all beams, which facilitates relative comparisons of the lattice to a solid structure of the same material, which should remain constant regardless of the base material [27]. The relative elastic modulus 𝐸𝑟 is found by applying a unidirectional displacement 𝛿 = 0.1 ∙ 𝐿 to all nodes on one face of the scaffold, where 𝐿 is the length of the scaffold. Nodes on the opposite face are fixed in the displacement direction. Additional displacement constraints are applied to two corner nodes to ensure the lattice does not rotate and includes one pin and one unidirectional displacement constraint. The reaction force 𝐹 on the face opposite of displacement is found and the elastic modulus is 𝐸𝑟 =

𝐹∙𝐿 𝐴∙𝛿

The loading for the shear case causes two sides of the lattice to move towards a common corner, with reaction forces being on all face nodes in-plane to the displacement constraints. Reaction forces differ for each node based on beam connections at the node.

(1)

where 𝐴 is the area of one lattice face and forces are found from simulation results (Fig. 5).

Figure 6: Reaction forces for shear modulus simulation. 2.5 Fluids simulation

Permeability 𝑘 is determined using computational fluid dynamics to simulate unidirectional fluid flow through a lattice as a means for gaining data to determine the validity of the Kozeny-Carmen relation for estimating lattice permeability. Walls are placed around four sides of a cubic lattice consisting of 27 unit cells to emulate the conditions of a flow channel or bioreactor chamber [9, 21, 50]. Navier-Stokes equations of continuity and momentum are solved using the finite volume method with ANSYS Fluent software. The fluid is modeled as incompressible water with a viscosity of 𝜈 = 0.001𝑃𝑎 ∙ 𝑠 and density of 1000𝑘𝑔/𝑚3 [22]. Boundary conditions include an inlet flow velocity of 0.001𝑚/𝑠, a null outlet pressure, and noslip conditions on all surfaces. The boundary conditions ensure that fluid flow is laminar with a Reynolds number less than ten for each simulation (Fig. 7).

Figure 5: Reaction forces for elastic modulus simulation.

The reaction forces occur only on the top and bottom face of the structure. Due to the asymmetry of the FD-Cube unit cells used to form the lattice, the magnitude of the reaction force differs based on the connections of beams at each node. 2.4 Shear simulation

The shear modulus of lattices is found using the same finite element environment in Abaqus software as the elastic modulus, but different boundary conditions and displacements are used. The relative shear modulus is found by applying on adjacent faces a unidirectional displacement of 𝛿 = 0.1 ∙ 𝐿 towards their common edge. Opposite faces are fixed to not displace along the same direction as their opposing face’s displacement. Additional constraints are applied to ensure the lattice does not rotate out of plane and a pin is applied to one corner. The relative shear modulus is then calculated as 𝐺𝑟 =

𝐹∙𝐿 𝐴∙𝛿

(2) Figure 7: Flow velocity for fluid dynamics simulation; highest velocity indicated in red as 4.77e-3 m/s.

where forces are found from simulation results (Fig. 6).

4



modulus than those of the Octahedron family (𝐺𝑟 ≈ 0.16 at 𝑃 = 0.6). The remaining topologies have similar relative shear moduli (𝐺𝑟 ≈ 0.10-0.12 at 𝑃 = 0.6).

Permeability is found with Darcy’s equation 𝑘=

𝑄𝜈𝐿 ∆𝑝𝐴

(3)

where 𝑄 is the volumetric flow rate per unit time, 𝐿 is the lattice length, 𝐴 is the lattice cross-sectional area, and 𝛥𝑝 is the pressure gradient through the fluid domain [9]. Samplings of velocity at the outlet and pressure in the central unit cell are used to determine the velocity of fluid flow representative of an intrinsic permeability [51]. The lattice size and sampling choice minimize the computational effort of fluid flow simulations while ensuring minimal influence of boundary conditions from walls surrounding outside unit cells so permeability remains constant regardless of the number of unit cells. 3.0 RESULTS 3.1 Elastic Modulus

Figure 9: Shear modulus 𝑮𝒓 for porosity 𝑷.

Elastic modulus is simulated by fixing element diameter to ø = 200𝜇𝑚 and increasing unit cell length to generate lattices with fixed porosity. Porosity is equal to a lattice’s relative density subtracted from unity, therefore mechanical properties remain constant for a given porosity [6]. The relative elastic modulus 𝐸𝑟 is plotted for porosity 𝑃 = 0.6 to 𝑃 = 0.9 in Figure 8.

3.3 Permeability

Permeability 𝑘 is assumed to adhere to the Kozeny-Carmen relation such that permeability scales with porosity 𝑃 and surface-volume ratio 𝑆/𝑉 for 𝑘 = 𝐾 ∙ 𝑃3 /(𝑆/𝑉)2 , where 𝐾 is an empirically informed Kozeny-Carmen coefficient [36-38]. The assumption is checked by fitting the Kozeny-Carmen relation to data from computational fluid dynamics models. Lattices are generated with porosity 𝑃 = 0.6 and 𝑃 = 0.8 while increasing element diameter from ø = 200𝜇𝑚 to ø = 1,000𝜇𝑚. Permeability is calculated with Darcy’s equation (Equation 3) and plotted for 𝑃3 /(𝑆/𝑉)2 up to 𝑘 = 1 × 10−7 𝑚2 (Fig. 10), and is a range suitable for matching bone’s permeability [35].

Figure 8: Elastic modulus 𝑬𝒓 for porosity 𝑷.

As porosity increases, relative elastic modulus decreases for all topologies. Cube lattices have the highest relative elastic modulus (𝐸𝑟 ≈ 0.16 at 𝑃 = 0.6) due to their having the highest proportion of elements aligned with the loading direction, followed by FD-Cubes (𝐸𝑟 ≈ 0.12 at 𝑃 = 0.6). All other topologies have similar relative elastic moduli (𝐸𝑟 ≈ 0.065-0.08 at 𝑃 = 0.6), but the T-Octa has the lowest (𝐸𝑟 ≈ 0.055 at 𝑃 = 0.6), due to it being a bending dominated topology [8].

Figure 10: Kozeny-Carmen fitting for mapping permeability to porosity and surface-volume ratio.

When the Kozeny-Carmen relation is linearly fit to all simulated data points and forced through the origin, the best fit line is 𝑘 = 3.4×10−7 ∙ 𝑃3 /(𝑆/𝑉)2 , with a coefficient of determination 𝑅2 = 0.957. The high coefficient of determination suggests that the permeability of lattices for all topology types may be found using the Kozeny-Carmen relation as an estimation comparable to computational fluid dynamics simulations, but significantly less computationally expensive.

3.2 Shear Modulus

Shear modulus is simulated for the same lattice designs as Fig. 8, with relative shear modulus 𝐺𝑟 plotted for porosity 𝑃 = 0.6 to 𝑃 = 0.9 in Fig. 9. Cube lattices have the lowest relative shearing modulus (𝐺𝑟 ≈ 0.04 at 𝑃 = 0.6) while all topologies of the Octahedron family attain a high relative shear modulus, with the Octa unit cell having a slightly higher relative shear modulus (𝐺𝑟 ≈ 0.2 at 60% porosity) than the Octet and V-Octet lattices (𝐺𝑟 ≈ 0.17 at 𝑃 = 0.6). The BC-Cube lattice has a slightly lower relative shear

5



3.4 Design automation

The foundations of a design automation approach are developed for configuring lattices tuned for bone tissue engineering [1] by using simulation results. Due to dependencies of variables on one another, there is one lattice structure for each topology type that fulfills the criteria of having a porosity of 𝑃 = 0.6 and pore size 𝑝 = 1,000𝜇𝑚, as solved in Figure 11.

The designs generated have element diameters ranging from about 350µm to 1050µm, and is a range that is reproducible for a broad range of additive manufacturing technologies [13, 28]. The unit cell lengths range from 1.35mm to 3.48mm. The difference in unit cell length suggests that different unit cells are suitable for different application specifications depending on overall number of pores desired and dimensions of the scaffold. Properties of elastic modulus, shear modulus, surfacevolume ratio, and permeability solved from Figure 11 for each Table 1 scaffold are normalized on a scale of 0 to 1 in comparison to the highest value among all topologies and plotted in Figure 12. An Average line is included in the plot that is the mean of normalized properties for each lattice.

Figure 11: Design automation for scaffolds with porosity and pore size inputs

When porosity is chosen as a design input variable (Fig. 111) the relative elastic and shear modulus of the structure are defined as a function of porosity (Fig. 11-2) as demonstrated by simulation results in Figures 8 and 9. The ratio of material to void area of the scaffold (i.e. density/porosity) remains constant according to the cell ratio 𝑟 of element diameter ø to unit cell length 𝐿𝑐 such that 𝑟 = 𝐿𝑐 /ø. The cell ratio is found for a structure by generating lattices with varied element diameters until the input porosity is reached, and then dividing the unit cell length by element diameter to find the cell ratio at that porosity. The pore size input (Fig. 11-3) enables the solving of element diameter and unit cell length (Fig. 11-4) by solving one of the design parameters in terms of cell ratio 𝑟, which is known, and then solving the pore size equations for each lattice topology with equations provided in Section 2.2. The solved values define the structure of the scaffold, and enable the finding of surfacevolume ratio from a generated solid model (Section 2.2). The surface-volume ratio is used with the Kozeny-Carmen constant (Section 2.5) and porosity to determine permeability (Fig. 11-5). Scaffold designs automatically configured using the method of Figure 11 are presented in Table 1.

Figure 12: Relative comparison of designed scaffolds normalized to 𝑬𝒓 = 𝟏𝟔. 𝟓𝑴𝑷𝒂, 𝑮𝒓 = 𝟐𝟎. 𝟒𝑴𝑷𝒂, 𝒌 = 𝟒. 𝟒×

𝟏𝟎−𝟕 𝒎𝟐 , and 𝑺/𝑽 = 𝟑. 𝟓𝟏𝒎−𝟏 .

Results suggest that the Cube lattice has the highest elastic modulus, the Octa lattice has the highest Shear modulus, the BCCube has the highest surface-volume ratio, and the FD-Cube has the highest permeability. The only other normalized properties above 0.75 are the shear modulus for the BC-Cube, Octet, and V-Octet, and the surface-volume ratio for the Octet, and T-Octa topologies. These findings suggest that certain unit cells tend to have highly specialized properties with only two unit cells, the BC-Cube and Octet, having two relative properties above 0.8. Although the Cube unit cell achieves a high elastic modulus that is desirable for spinal cage applications, it has a shear modulus that is below 0.2 relative to all other scaffolds. The FDCube, which has the second highest normalized elastic modulus of 0.69, has a normalized shear modulus of 0.55 that is a potentially more favorable trade-off. The FD-Cube also has the highest averaged normalized properties of 0.64, further supporting its potential use as a scaffold. All other Cubic and Octahedron family topologies have average normalized values of about 0.6 while the T-Cube and T-Octa perform the lowest, with about 0.55 and 0.48 average normalized properties, respectively. The average of normalized values highlights aggregate property values for selecting a well-rounded design when all properties are weighted equally. Depending on the design application, relative weightings may change to skew selection towards designs with favorable properties according to alternate criteria. For instance, a high shear modulus may not be important for scaffolds when shear loading is handled by another component of a spinal fusion system.

Table 1: Automated configuration of scaffold designs.

6



to measurements since it is difficult to distinguish when a beam surface begins and ends. The roughness generally fluctuates within 100µm. The intended pore size for each design was 1,000µm, and measured for the Cube as about 960µm and for the Octet as about 1,020µm. The intended Cube element diameter is 901µm and measured as 960µm while the intended Octet element diameter is 403µm and measured as 412µm. These results suggest the printer qualitatively recreates the form of the scaffolds, but there are inaccuracies in micro features that may cause deviations in scaffold performance compared to computational predictions.

3.5 Scaffold 3D printing

The Cube and Octet designs from Table 1 were chosen as representative fabrication samples. The Cube has a simple geometry (i.e. low number of elements per unit cell), and the highest elastic modulus at a given porosity among all topology types. The Cube is potentially a high performing design when compressive strength and high porosity are needed, as is relevant for spinal tissue engineering. The Octet has a complex geometry (i.e. large number of elements per unit cell) and a high relative combination of shear and surface-volume properties among all topology types. The Octet is a potentially high performing design when material choice may compensate for low elastic modulus and nutrient transport does not limit tissue growth, therefore the design would benefit from a higher shear to reduce failure risks and a higher surface-volume ratio to promote higher initial tissue volume and growth. Designs were fabricated (Fig. 13) with a Stratysys Objet 500 Connex3 polyjet 3D printer using the manufacturer’s MED610 material and SUP706 support material [12]. The printer works by jetting liquid material onto a surface and immediately curing it with a UV light positioned at the print head. The MED610 material is biocompatible and approved for temporary in-mouth placement. The MED610 material is acrylic based and reported by the manufacturer as non-cytotoxic and to have an elasticity of 2,000 to 3,000 MPa. The material is potentially suitable for tissue culture experiments and is representative of polymer materials that could eventually be approved for tissue engineering with human patients. The SUP706 support material is removed through dissolution with basic solution that enables the cleaning of small pores chemically rather than mechanically to avoid destroying the structure.

4.0 DISCUSSION

The developed design for additive manufacturing approach provides a basis for configuring lattices with favorable trade-offs for bone tissue engineering. The approach is well-suited for validating computational predictions with empirical testing as a basis for optimizing scaffolds with rapid prototyping. The automated aspects facilitate efficient iterations between configuration and fabrication, and are essential for improving design configurations as experiments are conducted. Although each designed scaffold has a homogenous unit cell configuration, the diversity in properties across unit cell families in Figure 12 suggests the design space was sufficiently explored for providing a diversity of potentially favorable scaffold designs. Computationally predicted porosity, surface-volume ratio, and pore size properties may be corroborated with experiments by imaging manufactured lattices and comparing results to the intended lattice design. Mechanical properties are measurable with standard compression and shear loading tests [5, 19, 20] while permeability properties are measurable with unidirectional flow chambers [21, 33]. The current set of trade-offs considered is particularly important, because it builds on common engineering knowledge of lattice structures but includes considerations for pore size that is essential for tissue scaffold applications. Computational predictions may also be compared with existing empirical data. The results in Figure 12 show Cube unit cells having a relatively high elastic modulus and low shear modulus in comparison to unit cells with many diagonal elements, and agrees with previous computational approaches using beam element simulations [29]. The predicted relative modulus of the Octet in Figure 9 agrees well with studies that have found its relative elastic modulus as about 0.01 for a relative density of 10% [27, 52]. Permeability predictions agree well with studies that have found permeability on the order of 1×10−8 𝑚2 for scaffolds with similar porosities and pore sizes in experiments [21, 33] and fluid simulations [38, 47]. These comparisons suggest that although experiments are required to validate computational predictions, the approaches utilized in this paper are a suitable approximation for scaffold properties and performance. Beyond properties considered in this paper, the tissue growth of scaffolds is essential to measure and evaluate during design. Tissue growth may be measured in vitro or in vivo to provide insights for favorable trade-offs among pore size, surface-volume ratio, and permeability since tissue growth rates are influenced by nutrition availability and both are influenced by these properties [15, 16]. Insights concerning trade-offs based on the tissue growth rate can inform design decisions. For instance, increasing the permeability of a scaffold is only

Figure 13: 3D printed scaffold prototypes with pores and element diameters indicated; scale bar length is 500µm.

Fabricated samples were imaged using light microscopy to determine fabrication accuracy and surface details (Fig. 13). The surface was found to have a roughness that provides uncertainty

7



necessary if it provides further nutrients essential for tissue growth. The design approach could utilize these considerations to evaluate designs with altered weightings of normalized properties to promote design configurations with favorable balances in tissue growth and nutrient transport. A key contribution to the developed design approach is the reduction in evaluation time that enables design automation for complex lattice structures. For instance, the expensive simulations conducted for mechanics and fluids were used to find trends to configure and evaluate design properties analytically (Fig. 11). The use of scaling relationships across levels is essential in biomechanical design [11], particularly when considering pore size is a micro property and porosity is a bulk property of scaffolds. Configured designs are suitable for fabrication with no further design tuning necessary. Findings learned from the fabrication stage can inform future iterations for automatically configuring manufacturable designs, such as the suitable minimum dimensions for printing. The design automation and fabrication approach is suitable for personalizing scaffolds with complex geometries at print time, which is advantageous for personalized medical treatments. Further work using the developed approach could begin integrating design generation and search approaches for more complex geometries that could potentially aid in discovering complex scaffold geometries with favorable property trade-offs.

[3]

[4]

[5]

[6]

[7]

5.0 CONCLUSION

The foundation of a design for additive manufacturing approach was developed for 3D printed tissue scaffolds using lattice design libraries; steps consisted of (1) simulation, (2) design automation, and (3) fabrication. A library of eight unit cells was used for configuring lattices suitable as bone tissue scaffolds. Simulations demonstrated that elastic modulus and shear modulus scale for lattices with porosity, and permeability scales with porosity cubed over surface-volume ratio squared. Lattices for each unit cell type were configured with a porosity of 60% and pore size of 1,000µm. A cubic based scaffold with the highest relative elastic modulus and an octet based scaffold with favorable shear and surface area properties were fabricated with polyjet 3D printing approaches. The process accurately produced the overall form of the structures, but had high surface roughness that influences accuracy at the microscale. Future work is necessary to compare computational predictions with experimental measurements. Findings demonstrate the merits of design automation for 3D printed lattices tuned as tissue scaffolds, and provide a basis for exploration and optimization of complex designs for regenerative medicine. ACKNOWLEDGMENTS

Funding support was provided by postdoctoral research fellowship program.

ETH

[8]

[9]

[10]

[11]

[12]

Zurich’s [13]

REFERENCES

[1]

[2]

X. Wang, S. Xu, S. Zhou, W. Xu, M. Leary, P. Choong, M. Qian, M. Brandt, and Y. M. Xie, "Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: A review," Biomaterials, vol. 83, pp. 127-141, 2016. M. K. Thompson, G. Moroni, T. Vaneker, G. Fadel, R. I. Campbell, I. Gibson, A. Bernard, J. Schulz, P. Graf, and B. Ahuja, "Design for Additive Manufacturing:

[14]

8

Trends, opportunities, considerations, and constraints," CIRP Annals-Manufacturing Technology, vol. 65, pp. 737-760, 2016. M. de Wild, S. Zimmermann, J. Rüegg, R. Schumacher, T. Fleischmann, C. Ghayor, and F. E. Weber, "Influence of Microarchitecture on Osteoconduction and Mechanics of Porous Titanium Scaffolds Generated by Selective Laser Melting," 3D Printing and Additive Manufacturing, vol. 3, pp. 142-151, 2016. Y. Li, Z.-g. Wu, X.-k. Li, Z. Guo, S.-h. Wu, Y.-q. Zhang, L. Shi, S.-h. Teoh, Y.-c. Liu, and Z.-y. Zhang, "A polycaprolactone-tricalcium phosphate composite scaffold as an autograft-free spinal fusion cage in a sheep model," Biomaterials, vol. 35, pp. 5647-5659, 2014. F. N. Habib, M. Nikzad, S. H. Masood, and A. B. M. Saifullah, "Design and Development of Scaffolds for Tissue Engineering Using Three-Dimensional Printing for Bio-Based Applications," 3D Printing and Additive Manufacturing, vol. 3, 2016. M. Ashby, "The properties of foams and lattices," Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 364, pp. 15-30, 2006. W.-Y. Jang, S. Kyriakides, and A. M. Kraynik, "On the compressive strength of open-cell metal foams with Kelvin and random cell structures," International Journal of Solids and Structures, vol. 47, pp. 28722883, 2010. X. Zheng, H. Lee, T. H. Weisgraber, M. Shusteff, J. DeOtte, E. B. Duoss, J. D. Kuntz, M. M. Biener, Q. Ge, and J. A. Jackson, "Ultralight, ultrastiff mechanical metamaterials," Science, vol. 344, pp. 1373-1377, 2014. R. Singh, P. Lee, T. C. Lindley, R. Dashwood, E. Ferrie, and T. Imwinkelried, "Characterization of the structure and permeability of titanium foams for spinal fusion devices," Acta biomaterialia, vol. 5, pp. 477-487, 2009. P. Egan, J. Cagan, C. Schunn, F. Chiu, J. Moore, and P. LeDuc, "The D3 Methodology: Bridging Science and Design for Bio-Based Product Development," Journal of Mechanical Design, vol. 138, 2016. P. Egan, J. Moore, C. Schunn, J. Cagan, and P. LeDuc, "Emergent systems energy laws for predicting myosin ensemble processivity," PLoS Computational Biology, vol. 11, 2015. T. Stanković, J. Mueller, P. Egan, and K. Shea, "A Generalized Optimality Criteria Method for Optimization of Additively Manufactured Multimaterial Lattice Structures," Journal of Mechanical Design, vol. 137, p. 111705, 2015. P. Egan, S. Ferguson, and K. Shea, "Design of hierarchical 3D printed scaffolds considering mechanical and biological factors for bone tissue engineering," Journal of Mechanical Design, vol. 139, 2017. L. Geris, Y. Guyot, J. Schrooten, and I. Papantoniou, "In silico regenerative medicine: how computational tools allow regulatory and financial challenges to be addressed in a volatile market," Interface Focus, vol. 6, p. 20150105, 2016.



[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

Y. Guyot, I. Papantoniou, Y. C. Chai, S. Van Bael, J. Schrooten, and L. Geris, "A computational model for cell/ECM growth on 3D surfaces using the level set method: a bone tissue engineering case study," Biomechanics and modeling in mechanobiology, vol. 13, pp. 1361-1371, 2014. S. Checa and P. J. Prendergast, "Effect of cell seeding and mechanical loading on vascularization and tissue formation inside a scaffold: a mechano-biological model using a lattice approach to simulate cell activity," Journal of biomechanics, vol. 43, pp. 961-968, 2010. A. C. Jones, C. H. Arns, D. W. Hutmacher, B. K. Milthorpe, A. P. Sheppard, and M. A. Knackstedt, "The correlation of pore morphology, interconnectivity and physical properties of 3D ceramic scaffolds with bone ingrowth," Biomaterials, vol. 30, pp. 1440-1451, 2009. S. Sturm, S. Zhou, Y.-W. Mai, and Q. Li, "On stiffness of scaffolds for bone tissue engineering—a numerical study," Journal of biomechanics, vol. 43, pp. 17381744, 2010. P. Moongkhamklang, V. Deshpande, and H. Wadley, "The compressive and shear response of titanium matrix composite lattice structures," Acta Materialia, vol. 58, pp. 2822-2835, 2010. J. Wieding, A. Fritsche, P. Heinl, C. Körner, M. Cornelsen, H. Seitz, W. Mittelmeier, and R. Bader, "Biomechanical behavior of bone scaffolds made of additive manufactured tricalciumphosphate and titanium alloy under different loading conditions," Journal of applied biomaterials & functional materials, vol. 11, 2013. M. Lipowiecki, M. Ryvolova, Á. Töttösi, N. Kolmer, S. Naher, S. A. Brennan, M. Vazquez, and D. Brabazon, "Permeability of rapid prototyped artificial bone scaffold structures," Journal of Biomedical Materials Research Part A, vol. 102, pp. 4127-4135, 2014. S. Truscello, G. Kerckhofs, S. Van Bael, G. Pyka, J. Schrooten, and H. Van Oosterwyck, "Prediction of permeability of regular scaffolds for skeletal tissue engineering: a combined computational and experimental study," Acta biomaterialia, vol. 8, pp. 1648-1658, 2012. Y.-H. Lee, C.-J. Chung, C.-W. Wang, Y.-T. Peng, C.-H. Chang, C.-H. Chen, Y.-N. Chen, and C.-T. Li, "Computational comparison of three posterior lumbar interbody fusion techniques by using porous titanium interbody cages with 50% porosity," Computers in biology and medicine, vol. 71, pp. 35-45, 2016. P.-I. Tsai, C.-C. Hsu, S.-Y. Chen, T.-H. Wu, and C.-C. Huang, "Biomechanical investigation into the structural design of porous additive manufactured cages using numerical and experimental approaches," Computers in Biology and Medicine, vol. 76, pp. 14-23, 2016. H. J. Wilke, P. Neef, M. Caimi, T. Hoogland, and L. E. Claes, "New in vivo measurements of pressures in the intervertebral disc in daily life," Spine, vol. 24, pp. 755762, 1999. M. Zhang, F. Pu, L. Xu, L. Zhang, J. Yao, D. Li, Y. Wang, and Y. Fan, "Long-term effects of placing one or two cages in instrumented posterior lumbar interbody fusion," International orthopaedics, pp. 1-8, 2016.

[27]

[28]

[29]

[30]

[31]

[32]

[33]

[34]

[35]

[36] [37]

[38]

9

L. Dong, V. Deshpande, and H. Wadley, "Mechanical response of Ti–6Al–4V octet-truss lattice structures," International Journal of Solids and Structures, vol. 60, pp. 107-124, 2015. S. Arabnejad, R. B. Johnston, J. A. Pura, B. Singh, M. Tanzer, and D. Pasini, "High-strength porous biomaterials for bone replacement: A strategy to assess the interplay between cell morphology, mechanical properties, bone ingrowth and manufacturing constraints," Acta biomaterialia, vol. 30, pp. 345-356, 2016. J. Wieding, A. Wolf, and R. Bader, "Numerical optimization of open-porous bone scaffold structures to match the elastic properties of human cortical bone," Journal of the mechanical behavior of biomedical materials, vol. 37, pp. 56-68, 2014. X. Huang, A. Radman, and Y. Xie, "Topological design of microstructures of cellular materials for maximum bulk or shear modulus," Computational Materials Science, vol. 50, pp. 1861-1870, 2011. A. Jonitz-Heincke, J. Wieding, C. Schulze, D. Hansmann, and R. Bader, "Comparative analysis of the oxygen supply and viability of human osteoblasts in three-dimensional titanium scaffolds produced by laserbeam or electron-beam melting," Materials, vol. 6, pp. 5398-5409, 2013. C. Bergemann, P. Elter, R. Lange, V. Weißmann, H. Hansmann, E.-D. Klinkenberg, and B. Nebe, "Cellular nutrition in complex three-dimensional scaffolds: a comparison between experiments and computer simulations," International journal of biomaterials, vol. 2015, 2015. I. Ochoa, J. A. Sanz-Herrera, J. M. García-Aznar, M. Doblaré, D. M. Yunos, and A. R. Boccaccini, "Permeability evaluation of 45S5 Bioglass®-based scaffolds for bone tissue engineering," Journal of biomechanics, vol. 42, pp. 257-260, 2009. J. K. Guest and J. H. Prévost, "Design of maximum permeability material structures," Computer Methods in Applied Mechanics and Engineering, vol. 196, pp. 1006-1017, 2007. G. Baroud, R. Falk, M. Crookshank, S. Sponagel, and T. Steffen, "Experimental and theoretical investigation of directional permeability of human vertebral cancellous bone for cement infiltration," Journal of biomechanics, vol. 37, pp. 189-196, 2004. N. S. Martys, S. Torquato, and D. Bentz, "Universal scaling of fluid permeability for sphere packings," Physical Review E, vol. 50, p. 403, 1994. P. Xu and B. Yu, "Developing a new form of permeability and Kozeny–Carman constant for homogeneous porous media by means of fractal geometry," Advances in water resources, vol. 31, pp. 74-81, 2008. S. Van Bael, Y. C. Chai, S. Truscello, M. Moesen, G. Kerckhofs, H. Van Oosterwyck, J.-P. Kruth, and J. Schrooten, "The effect of pore geometry on the in vitro biological behavior of human periosteum-derived cells seeded on selective laser-melted Ti6Al4V bone scaffolds," Acta biomaterialia, vol. 8, pp. 2824-2834, 2012.



[39]

[40]

[41]

[42]

[43]

[44]

[45]

[46]

Y. Chen, S. Zhou, and Q. Li, "Microstructure design of biodegradable scaffold and its effect on tissue regeneration," Biomaterials, vol. 32, pp. 5003-5014, 2011. H. Kang, C.-Y. Lin, and S. J. Hollister, "Topology optimization of three dimensional tissue engineering scaffold architectures for prescribed bulk modulus and diffusivity," Structural and Multidisciplinary Optimization, vol. 42, pp. 633-644, 2010. L. Zhao, S. Ha, K. W. Sharp, A. B. Geltmacher, R. W. Fonda, A. H. Kinsey, Y. Zhang, S. M. Ryan, D. Erdeniz, and D. C. Dunand, "Permeability measurements and modeling of topology-optimized metallic 3-D woven lattices," Acta Materialia, vol. 81, pp. 326-336, 2014. T. Adachi, Y. Osako, M. Tanaka, M. Hojo, and S. J. Hollister, "Framework for optimal design of porous scaffold microstructure by computational simulation of bone regeneration," Biomaterials, vol. 27, pp. 39643972, 2006. A. Boccaccio, A. E. Uva, M. Fiorentino, L. Lamberti, and G. Monno, "A Mechanobiology-based Algorithm to Optimize the Microstructure Geometry of Bone Tissue Scaffolds," International journal of biological sciences, vol. 12, p. 1, 2016. S.-I. Roohani-Esfahani, P. Newman, and H. Zreiqat, "Design and Fabrication of 3D printed Scaffolds with a Mechanical Strength Comparable to Cortical Bone to Repair Large Bone Defects," Scientific reports, vol. 6, 2016. P. S. Chang and D. W. Rosen, "The size matching and scaling method: a synthesis method for the design of mesoscale cellular structures," International Journal of Computer Integrated Manufacturing, vol. 26, pp. 907927, 2013. N. Chantarapanich, P. Puttawibul, S. Sucharitpwatskul, P. Jeamwatthanachai, S. Inglam, and K. Sitthiseripratip,

[47]

[48]

[49]

[50]

[51]

[52]

10

"Scaffold library for tissue engineering: a geometric evaluation," Computational and mathematical methods in medicine, vol. 2012, 2012. M. Dias, P. Fernandes, J. Guedes, and S. Hollister, "Permeability analysis of scaffolds for bone tissue engineering," Journal of biomechanics, vol. 45, pp. 938-944, 2012. H. Kang, S. J. Hollister, F. La Marca, P. Park, and C.-Y. Lin, "Porous biodegradable lumbar interbody fusion cage design and fabrication using integrated globallocal topology optimization with laser sintering," Journal of biomechanical engineering, vol. 135, p. 101013, 2013. S. Xu, J. Shen, S. Zhou, X. Huang, and Y. M. Xie, "Design of lattice structures with controlled anisotropy," Materials & Design, vol. 93, pp. 443-447, 2016. Y. Guyot, F. Luyten, J. Schrooten, I. Papantoniou, and L. Geris, "A three‐dimensional computational fluid dynamics model of shear stress distribution during neotissue growth in a perfusion bioreactor," Biotechnology and bioengineering, vol. 112, pp. 25912600, 2015. R. P. Widmer and S. J. Ferguson, "On the interrelationship of permeability and structural parameters of vertebral trabecular bone: a parametric computational study," Computer methods in biomechanics and biomedical engineering, vol. 16, pp. 908-922, 2013. V. S. Deshpande, N. A. Fleck, and M. F. Ashby, "Effective properties of the octet-truss lattice material," Journal of the Mechanics and Physics of Solids, vol. 49, pp. 1747-1769, 2001.

