Topology optimised metallic bone plates produced by electron beam melting: a mechanical and biological study

Bone is a highly vascular and specialised tissue responsible for maintaining the shape of the skeleton, protecting soft tissues, transmitting the force of muscular contraction during movement, serving as a reservoir for ions and contributes to the regulation of the extracellular matrix, blood cell production and blood pH regulation [1].

Bone is prone to traumatic injuries as well as diseases. In the case of minor fractures, bone heals and remodels with little detectable scarring. However, in the case of pathological and traumatic fractures, traumatic bone loss or primary tumour resection, bone is not able to heal itself [2‐4]. Bone fractures that are displaced or unstable are frequently surgically treated with bone fixation implants such as internal fixation devices, external fixators and intramedullary pins. In the case of internal fixation devices, the locking compression plate (LCP) is widely used to treat various types of fractures due to its hybrid screw system containing two means of fixation techniques. This allows the application of absolute stability or relative stability leading to both primary healing and secondary healing [5]. Similar to other internal fixation plates (e.g. dynamic compression plate and periarticular locking plate system), LCP is made from an inert and biocompatible metal. The most commonly used metallic materials are titanium and its alloys, stainless steel, or cobalt chrome and its alloys [6, 7].

The role of the internal fixation plates is to stabilise the fractured bone during the union/healing process. After the fracture is healed, the implant is no longer required to stay in the body. Currently, around 30% of the metallic implants have to be surgically removed after the healing process [8]. However, this procedure presents significant risks of bone refracture and nerve damage. Bone refracture is due to the lack of density of the bone in the close vicinity of the implant due to the significant mechanical differences between bone and fixation plates. For example, the Young’s modulus of Ti6Al4V is around 120 GPa whilst the Young’s modulus of trabecular bone ranges between 50 and 100 MPa and between 15 and 25 GPa in the case of cortical bone [7, 9, 10]. This Young’s modulus mismatch results in a phenomenon named stress shielding which is usually associated with implant loosening and bone loss. Alternatively, the implant can be left in the body, but this option also presents problems such as risks of periprosthetic fracture due the stress risers at the cortical bone and implant junctions, corrosion, release of metal ions and the risk of allergic and potentially carcinogenic reactions [11, 12].

Several researchers also explored the use of novel additive manufacturing technologies to produce fully personalised metallic implants. A notable example was the fabrication of a metallic complex jaw implant coated with bioceramic and implanted in an 83-year-old lady. Partners in Belgium and the Netherlands (universities of Leuven and Hasselt, AM bureau LayerWise) designed the implant to guarantee good attachment of muscles and space for nerves and used a powder-bed fusion system to produce it [13]. Other research groups also explored powder-bed fusion techniques (selective laser melting and electron beam melting) to produce personalised metallic bone plates without any concerns regarding the stress shielding effect [14]. Very few studies addressed this problem by changing the plate design (e.g. plate thickness) to improve its performance through a trial and error approach [15]. A systematic approach is still required. This paper presents an integrated approach linking computer modelling, simulation and optimisation together with additive manufacturing to address this problem. The following research questions are addressed:

There are no standard dimensions (i.e. length, width and thickness) or number of screw holes for commercially available bone fixation plates. Different commercial companies are also commercialising plates of the same type (e.g. locking compression plates) with different dimensions. Commercial bone plates from the same company present the same width and thickness but different lengths. Therefore, the number of distinct topologies (geometry and number of holes) is high.

In this research, the DePuy Synthes narrow locking compression plate (DePuy Synthes, Synthes GmbH, Switzerland) was considered as the reference design. Plates containing four, six and eight holes, with 180 mm in length, 14 mm in width and 5 mm in thickness, were defined (see Table 1) and considered for redesigning.

Plates were initially designed using Solidworks (Dassault Systèmes, France). Optimisation was conducted using the Abaqus Topology Optimization Module (ATOM) software (Dassault Systèmes, France), and the Solid Isotropic Microstructure with Penalization (SIMP) method proposed by Bendsøe [16]. Mathematically topology optimization is described as follows [17]:subject towhere C is the compliance, f is the force vector, K_e is the element stiffness matrix, u is the displacement vector, V^* is the user-defined fraction volume, p is the penalisation factor, ρ_e is the element density, ρ_o is the initial density and v_e is the volume of each element.

The iterative process to achieve the optimal design starts with the definition of a design domain, Ω, discretised into a set of elements with specific density (ρ) and Young’s modulus (E) values. Loading and boundary conditions are imposed, generating stresses and strains at each element, determining the corresponding sensitivity, i.e. the element that will have their density updated. Filtering techniques are implemented to restrict the optimisation from common disadvantages such as checkerboarding. The density is distributed along the design domain and updated after each iteration toward optimality according to the derivative of Eq. (1), considering for each element the value of ρ = 1 for full element stiffness and ρ = 0 for a void. The density update process is repeated until reaching the optimal solution.

Even though topology optimization is a load magnitude independent process, a post-operative case of a 70-kg patient was considered. Post-operation, patients suffering from a fractured tibia walk with crutches and their gait induces an overall load on the legs equivalent to 10% of the bodyweight [18]. Therefore, we assume a static compression force of 70 N applied on both far-end sides of the bone plate. Screw holes were considered a frozen design region. Ti6Al4V (Young’s modulus of 120 GPa and 0.3 Poisson’s ratio) was considered as the bone plates’ material. Different volume reductions (25, 45 and 75%) were considered and a mesh of approximately 50,000 8-node linear hexahedral elements was used for all considered geometries.

The redesigned plates were computationally assessed considering a static mechanical tensile test to determine their equivalent stiffness. In this case, a longitudinal force (F_xx) in the x-axis direction is applied to one side of the plate constraining the movement of the opposite side. Following a previously reported procedure [19], the equivalent stiffness of the designed plates can be determined as follows:where K is the structural stiffness, RF_xx is the reaction force on the constraint face and U_xx is the displacement.

Bone fixation plates were prepared (e.g. part orientation, design of support structures and position in the building platform) using the software Magics (Materialise, Belgium) and exported as STL files to the Build Assembler software where the models were sliced and uploaded to the machine. Support structures were designed considering part stability and to reduce both thermal stresses and warping. The EBM Arcam A2 model (Arcam, Sweden) was used for producing the plates. Its schematic configuration is shown in Fig. 1a. The machine consists on an electron beam emitted from a hot tungsten filament, operates at 60 kV under vacuum pressure of 2.0 × 10–3 mBa, scanning speed of 4530 mm/s, beam focus offset of 3 mA, line offset of 0.1 mm and layer thickness of 50 μm. The substrate plate temperature was kept at ~ 600 °C and the build temperature was defined to be ~ 750 °C. Parts were produced using standard Ti6Al4V powder supplied by the machine manufacturer. The powder material consists of spherical gas atomised particles with a size raging between 45 and 100 μm (see Fig. 1b), composed of 6.04% of aluminium, 4.05% of vanadium, 0.013% of carbon, 0.0107% of iron, 0.13% of oxygen and balanced titanium.

The EBM fabrication process initiates with the entire titanium powder being scanned and preheated to 750 °C (80% of its melting temperature) with a low beam current of approximately 0.2 mA and high scanning speed up to 8000 m/s to minimise residual stresses. After fabrication, the powder recovery system was used to remove all trapped powder through blasting a stream of high-pressure air and the support structures were removed using pliers. Parts were not submitted to any post-processing operation or thermal treatment.

The topology optimization method is based on the material redistribution, eventually leading to a material reduction whilst optimising stiffness. As also previously reported, topology optimization can be used to create lightweight structures capable of keeping satisfactory mechanical performance [21, 22]. By imposing high volume reduction, the effect of material removal becomes the significant contributing factor to an overall reduction in the stiffness of the plates. This was previously reported by the authors with 2D designed plates [23]. Different volume reductions were considered (25%, 45% and 75%) but the obtained volume reduction was not always exactly the same as the imposed value. In the case of eight-hole bone plates and imposed volume reductions of 25% and 45%, no significant differences were observed on the optimised shapes in terms of equivalent stiffness as the optimisation procedure stopped at relatively similar volume reductions. This is due to the fact that the optimisation procedure stops once it reaches a local optimal value, which is not necessarily the global one. It can also be explained by Eq. 1a, which shows that the optimisation process approximates to the user-defined volume, and to the fact that the optimisation process is mesh-dependent. However, the effect of the mesh on the topology optimization is not considered here. An automatic mesh generation procedure was considered.

The function of a bone plate is to resist the stresses occurring in the physiological environment whilst stabilising the fractured bone. Therefore, avoiding mechanical failure as well as plastic deformation is critical. In this research, both the elastic and plastic deformations were considered. The elastic linear region was analysed to measure both the equivalent stiffness and equivalent Young’s modulus. Equivalent stiffness values were used to characterise each family of bone plates (four, six and eight holes). Results show, for all cases, a reduction on the equivalent stiffness by increasing the volume reduction. A good approximation between numerical and experimental results was also obtained, showing that the computational tools considered in this research represent a viable approach to design and simulate their behaviour before expensive fabrication and experimental steps. Results also show that topology optimization is a viable tool to redesign bone plates, reducing their equivalent stiffness and consequently the stress shielding effect. The equivalent Young’s modulus was used to position the mechanical properties of produced plates and commercial ones against cortical bone. Initial designed plates present higher equivalent Young’s modulus values than commercial plates. These differences are reduced through topology optimization. Although as mentioned earlier, taking into consideration that the dimensions of the bone plates defer from one another, the EBM plates containing six holes (45% of volume reduction) and four holes (75% of volume reduction) show equivalent Young’s modulus similar to commercial plates. However, produced plates containing six and eight holes (75% of volume reduction) show a significant reduction in the equivalent Young’s modulus, presenting values in the cortical bone region, which is not possible to achieve with the commercially available plates. This confirms that topology optimization can be used to create lightweight plates (less material volume) with reduced equivalent stiffness and sufficiently strong without impairing the plate’s mechanical performance, thus minimising the stress-shielding phenomena.

This study is limited in terms of considering the mechanical stability of the topology optimised bone plates, assuming that a significant decrease in the material volume could result in stress concentration and plate failure, leading to a delay of bone healing. However, the authors are addressing this limitation by analysing the plastic region of the mechanical tests, considering the commercial plate (i.e. DePuy Synthes LCP, the gold standard for bone fracture healing) as a reference to base the stability of the bone plates in terms of the yield stress results. Most of the bone plates presented a higher yield stress with two plates (four-hole 75% volume reduction and six-hole 25% volume reduction plates) showing similarity with the commercial ones in terms of yield behaviour. The resulting yield stresses for the two bone plates that have similar equivalent Young’s modulus to the cortical bone showed approximately half of the commercial bone plate yield. However, if we consider that the maximum force required to yield the two bone plates are 4191 N (six holes and 75% of volume reduction) and 5481 N (eight hole and 75% of volume reduction), this is still clinically acceptable as it corresponds to 6 to 8 times the bodyweight of a 70-kg patient.

EBM-produced plates were not submitted to any post-processing treatment (e.g. elimination of residual stresses, surface finishing and polishing). This was decided to avoid the use of any additional time, consumables and costly steps and to avoid any additional effects of the post-processing on the topography, microstructure and properties of the plates, partially answering the question: is it necessary to perform any post-processing to produce plates with adequate physical and biological characteristics? Due to the nature of the EBM process (powder-bed fusion technique), rough parts were produced. As observed by Karlsson et al. [24] and Tong et al. [25], the surface characteristics of EBM parts are influenced by the raw powder characteristics (e.g. particle size) and processing conditions (e.g. scan speed) that result in the presence of both partially melted particles and fully melted ones (flattest zones aligned with the build direction). Despite presenting high surface roughness compared to commercial plates, produced plates were not polished to understand if the rough values were within an acceptable range to allow cell attachment and cell-cell communication. This was investigated by accessing the in vitro response of osteosarcoma cells seeded on both EBM and the commercial plates.

Contradictory results were previously reported regarding the biological influence of smooth and rough surfaces. According to De Wild et al. [26], EBM implants should be surface treated as their study showed improved biological response on acid-etched and sand-blasted implants. Pattanayak et al. [27] showed that heat treated smoother implants improve the osteo-integration of the implants. However, Thomson et al. [28] and Bertollo et al. [29] did not observe significant differences between no post-processed implants and conventionally wrought machined and plasma-sprayed implants. Ponader et al. [30] observed high cell attachment and proliferation in EBM parts with Ra values lower than 24.9 μm and reduced cell proliferation values in rough parts (Ra higher than 56.9 μm), surprisingly showing that the highest proliferation rate and cell viability were obtained with highly smooth surfaces (R_a of 0.07 μm). In contrast, the results presented in this paper showed that surface roughness of the produced plates (19.15 ± 1.56 μm) allowed a high level of cell attachment and proliferation suggesting that no polishing post-processing step is required after the plate printing phase. Results also show high cell attachment on the EBM rough plates than in the commercial plates with a smooth surface (0.37 ± 0.01 μm). Cell viability studies also show a significant number of dead cells in the commercial plates after 14 days of cell seeding compared to the EBM plates. This can be partially explained by the surface topography of the commercial bone plates. However, further investigation is required to elucidate the role that ion release and wettability have on cell interactions.

Surface hardness also has an important role on cell attachment and proliferation and differentiation. Several studies reported that harder substrates promote osteogenesis and increase cell attachment [31, 32]. The results show that EBM plates present higher surface hardness (326.9 ± 3.35) than commercial plates (275.98 ± 7.75), both exhibiting significantly higher values compared to cortical bone hardness (i.e. ~ 50 HV) [33].

This paper presents an integrated strategy combining topology optimization and additive manufacturing to produce bone fixation plates minimising the stress-shielding phenomena. From the results, it is possible to conclude the following: