Design and optimisation of patient-specific porous femoral stems

Abstract

Background

Total hip replacement surgery is a well-established intervention that restores joint function and provides excellent outcomes for patients. In some cases, bone resorption caused by stress shielding leads to implant loosening. Stress shielding occurs because implants are much stiffer than bone and transmit a significant proportion of the load, leaving the surrounding bone to carry less load compared to an intact femur.

Methods

To address stress shielding, we aimed to design patient-specific additively manufactured porous femoral stems with reduced stiffness. Diamond lattice structure test specimens of varying porosities were manufactured and tested to measure elastic moduli and yield strengths. These properties were used in subsequent implant optimisation based on finite element analysis. Four implant templates were created based on the region of the implant that was assigned porous material. These templates were referred to as fully porous (FP), proximally porous with a solid distal end (PP), solid distal shell (DS), and fully solid shell (SS). In addition, the elastic modulus within the porous region was assigned either a linear or a radial distribution, resulting in eight possible implant designs.

Results

Optimisation yielded six distinct solutions, which were evaluated based on the reduction in stress shielding and micromotion at the bone implant interface. While all implant designs reduced stress shielding compared to a solid implant, only the PP and SS stems were predicted to pass the standard fatigue test for femoral stems (ISO 7206-4). Implant-bone micromotion was conducive for bone implant integration for all designs, with the potential exception of the fully porous stem. Of the implants that were predicted to pass the fatigue test, the linear proximal porous stem resulted in the largest reduction in stress shielding (9.5% for walking, 8.1% for stair climbing).

Conclusions

Based on patient-specific computational models, the porous region of the stems influenced the reduction of stress shielding compared to fully solid stems. Considering implant fatigue failure and bone-implant micromotion, the PP and SS templates were found to be the most suitable design approaches to address femoral bone stress shielding after total hip replacement. Further investigation is required to fully comprehend the implications of porous femoral stems on long-term implant stability.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13018-025-06389-5.

Background

Osteoarthritis (OA) is a common musculoskeletal condition affecting over 500 million people globally [1] and the leading cause of joint replacement surgery [2]. Despite their success, implant longevity is limited, which can necessitate a more complex and costly revision surgery [3]. In Australia, 5.8% of cementless primary total hip replacements (THRs) are revised within 15 years after surgery [2]. A predominant reason for revision is component loosening which affects the femoral component in 20.8% of cases [2].

Non-cemented femoral stems are often made of titanium which has a significantly higher stiffness compared to the surrounding bone (Cancellous bone: 0.02–6 GPa, cortical bone: 3–30 GPa, solid titanium: 100–120 GPa) [4]. After implantation the joint load is partially transmitted through the implant reducing the loading in the bone significantly compared to the pre-implantation state, which is known as stress shielding [5, 6]. Reduced load exposure can lead to bone resorption, the clinically relevant manifestation of stress shielding, contributing to implant loosening [7].

In recent years, fully porous biomaterials have been explored to mitigate the effects of stress shielding. The advancement of additive manufacturing technologies such as electron beam melting (EBM) or selective laser melting (SLM) provide the opportunity to generate custom porous implants with reduced stiffness [8]. Porous structures can be based on repeating cubic cells, also known as unit cells [4]. Lattice structures that consist of interconnected beams (beam-based) can cover a wide range of mechanical properties and be designed to match those of bone tissue [4]. Diamond lattice structures have been studied for the application in medical devices due to their biomimetic properties and have the capacity to enable bone ingrowth and enhance biological fixation of the implant [8].

Porous joint replacement designs, that have been proposed in the literature, can be broadly grouped into three categories of porosity distribution: uniform, graded and optimised. Uniform distributions are characterised by a single unit cell design used throughout the entire porous implant region, while graded and optimised designs have changing porosity parameters [9]. The latter is based on an optimisation algorithm which allows for custom designs based on patient-specific bone material properties [9]. While some studies investigated the effects of different material property distribution strategies, in most cases only one design approach is considered in the analyses [10, 11]. Comparisons of porosity distributions and their effect on applying them in different regions of the implant are currently lacking. To quantify the achieved stress shielding reduction, some studies compare bone stress or strain, or strain energy density between intact and implanted bone [9]. Thus far, octahedral shear strain (OSS) has not been considered in the analysis of porous femoral stems, despite Piccinini et al. showing that OSS performed best as a stimulus for bone remodelling prediction in continuum finite element modelling (FEM) [12].

The aim of this study was to develop an optimisation approach for the design of a custom porous femoral stem using diamond lattice structures. This approach aimed to minimise bone resorption caused by stress shielding considering octahedral shear strain in the femur resulting from daily activities while also considering the fatigue strength of the femoral stem. Stress shielding reduction and micromotion were evaluated for varying porous implant regions and stiffness distributions to evaluate performance and to identify the most suitable design approach for patient-specific femoral stems with improved long-term stability.

Methods

The methods in this study were broadly summarised into three parts: determining material properties of lattice structures, optimising porous femoral stem designs, and evaluating the performance of the resulting optimised porous femoral stems.

Determining material properties of lattice structures

To determine the elastic modulus and yield strength of diamond lattice structures, we additively manufactured and tested 15 Titanium (Ti6Al4V) samples. The design of our samples was constrained by three parameters. Firstly, pore size was limited to a maximum of 800 µm because pore sizes larger than this may inhibit bone tissue growth into the implant [13–15]. Secondly, the porosities of the samples were set to be between 30 and 70% because this range has been approved by the FDA for porous coatings in hip replacements [16]. Finally, the minimum strut diameter was limited to 0.25 mm by the manufacturer. Samples with a unit cell size of 1.2 mm and porosities of 31%, 44%, 56%, and 68% met all requirements and were selected for testing (Fig. 1, Table 1). Each specimen comprised 1000 unit cells (10 unit cells × 10 unit cells × 10 unit cells) in size and was tested in compression in accordance with ISO 13314 using a universal material testing machine (INSTRON Universal Testing Machine 5569A, Norwood, MA, USA) [17].

Fig. 1.

Additively manufactured samples with A 31% B 44% C 56% D 68% porosity

Table 1.

Design parameters of additively manufactured and tested diamond lattice samples

Porosity (%)	Strut diameter (mm)	Pore size (mm)	Number of samples
44	0.48	0.49	5
56	0.41	0.57	5
68	0.34	0.64	5

As specified in the standard, one sample of each porosity (44%, 56% and 68%) was tested without a hysteresis loop to determine the required values for the hysteresis test protocol. The four remaining samples were tested using the hysteresis protocol and mean values were reported. Stress–strain curves calculated from the force–displacement data were plotted and elastic modulus and compressive offset strength (yield strength) were determined as per ISO 13314 [17]. Samples with a porosity of 31% could not be tested to failure due to limited load cell capacity with a maximum axial load of 10,000 N. As per ISO standard specifications, to determine the elastic modulus and compressive offset strength (yield strength) testing to failure was required. To estimate the material properties of the low porosity samples (31% porosity), the elastic modulus and yield strength were extrapolated from the mean values of the remaining three data points retrieved for porosities of 44%, 56% and 68%. The obtained material properties for diamond lattice structures with porosities between 31 and 68% were used in the optimisation to define the elastic modulus range within the porous implant region.

Porous femoral stem optimisation

Finite element models

Three finite element (FE) models were created to perform the optimisation. The first was an FE model of the intact femur to obtain the baseline octahedral shear strain (OSS) in the bone during activities of daily living before implantation. The second model represented a femur implanted with a femoral stem whose material properties were changed during the iterative optimisation process. The third FE model comprised only the femoral stem and simulated the ISO 7206–04 protocol for cyclic testing [18] within each iteration of the optimisation process (Fig. 2). The porous regions of the femoral stem were modelled as continuum material to reduce processing time for the iterative optimisation process. The previously experimentally determined mechanical properties of diamond lattice structures were applied. The implant was meshed using 2 mm tetrahedral elements (C3D4; Hypermesh 2021.2, Altair Engineering Inc., Troy, MI, USA).

Fig. 2.

Finite element model for femoral stem fatigue testing as per ISO 7206-4

The femur geometry was generated using a computed tomography (CT—Siemens, Munich, Germany; Resolution: 0.285 mm, 0.285 mm, 0.5 mm, Tube voltage, kVp = 120 kV, XRayTubeCurrent = 350 mA, Exposure = 1000 mAs, ExposureTime = 1000 ms) scan of a cadaveric human femur (female, age 77). The reported resolution and scanning parameters were within the range reported in various validated studies on femur segmentation [19]. The scanned femur bone was frozen shortly after the donor’s death. The bone was kept frozen until CT scanning which is a widely accepted method for preservation of bone mechanical properties as shown in previous studies [20, 21]. The use of the CT scan was approved by the University of Melbourne Human Ethics Advisory Group (22159). The bone was segmented (Mimics, Materialise NV, Leuven, Belgium), meshed using 2 mm tetrahedral elements and mesh quality was evaluated (C3D4; Hypermesh 2021.2, Altair Engineering Inc., Troy, MI, USA; accepted aspect ratio < 4.4). The bone was modelled as continuum material. Bone material properties were calculated from CT data using published relationships between Hounsfield units and Young's modulus (Mimics, Materialise NV, Leuven, Belgium). First, bone mineral density was calculated from the Hounsfield units () of bone and the HU of a CT calibration phantom (model M091, CIRS Inc, Norfolk, VA, USA) of known densities that was CT scanned together with the femur (Eq. 1). The Young’s moduli of elements (E) were calculated based on the density (Eq. 2) [22]. A total of 52 distinct elastic moduli ranging from 100 MPa to 20 GPa were assigned to bone elements. Peak femoral head loads and simplified muscle loads that occur during walking (Table 2) and stair climbing (Table 3) were applied to the model assuming a body weight of 75 kg [23–25]. Bone and implant surfaces were tied in all directions and the distal end of the FE model was fixed in three dimensions.

1

2

Table 2.

First loading condition applied to the intact and implanted femur during optimisation

	Force (N)				Point coordinates (mm)
		X	Y	Z		X	Y	Z
	Hip Load	− 535.7	− 342.5	− 1747.2	P0	0	0	0
	F1	426.3	31.6	635.8	P1	− 61.2	− 7.3	− 11.0
	F2	− 3.7	− 5.1	− 139.7
	F3	52.9	85.3	97
	F6	− 6.6	136.0	− 682.8	P2	− 53.9	− 7.4	− 56.7

Peak hip load acting on the femoral head during stair climbing walking and corresponding simplified muscle forces (F1-F6) acting on the femur at the same time point in the gait cycle of peak loading during walking. [18, 23, 24].

Table 3.

Second loading condition applied to the intact femur and implanted femur during optimisation

	Force (N)				Point (mm)
		X	Y	Z		X	Y	Z
	Hip Load	− 712.3	− 656.7	− 1999.6	P0	0	0	0
	F1	515.2	211.7	624.0	P1	− 61.2	− 7.3	− 11.0
	F2	− 1.5	− 2.2	− 47.8
	F3	22.8	36.0	21.3
	F4	− 3.7	− 5.9	− 123.5
	F5	77.2	22.1	94.1
	F6	− 16.2	164.6	− 993.0	P2	− 53.9	− 7.4	− 56.7
	F7	− 64.7	291.1	− 1963.2	P3	− 34.5	8.8	− 106.2

Peak hip load acting on the femoral head during stair climbing and corresponding simplified muscle forces (F1-F7) acting on the femur at the same time point in the gait cycle of peak loading during stair climbing [18, 23, 24].

Optimisation process

Prior to optimisation, four implant templates were created based on the same implant geometry. The templates differed from each other only in the region of the implant that was assigned porous material in the form of diamond lattice structures (Fig. 3). The implant neck was kept solid in all four templates to maintain the highest possible neck strength. Based on the porous regions, these implants were referred to as fully porous (FP), proximally porous with a solid distal end (PP), a solid distal shell (DS) and finally a fully solid shell (SS) with a proximal opening for bone cell migration (Fig. 3). The DS design was fully porous in the proximal region of the implant and the inner part of the distal end. A shell of 1 mm thickness surrounded the distal porous section. In contrast, the SS design had a porous core and a solid shell throughout the entire length of the implant, except for an opening in the anterior and posterior proximal part. During each iteration of the optimiser, only the elements within the porous region of each template were assigned new material properties. The optimiser aimed to find the distribution of elastic moduli within the porous regions of each of the templates that resulted in minimal stress shielding while preventing failure.

Fig. 3.

Four implant templates based on porous region: A FP B PP, C DS, D SS

A set of sample points based on the given porous implant region was used to optimise the elastic modulus () at the centroid of each tetrahedral element. Two types of distributions were compared for their stress shielding reduction capacity, namely linear (Eq. 3) and radial (Eq. 4):

3

4

where , and were the coordinates of the centroid of the element within the implant’s porous space. The values and were the half widths of the implant in x and y directions, respectively, corresponding to the implant cross section passing through _, , (Fig. 4). With each iteration of the optimisation, the elastic moduli at the sampling point were adjusted. The coefficients , , and were calculated from the elastic moduli at the sampling points. Then either Eq. (3) or Eq. (4), depending on the choice of linear or radial distribution, was used to calculate the elastic moduli for each element in the porous region of the implant.

Fig. 4.

Schematic representation of the implant cross-section passing through the centroid of the i^th element (, , )

The sampling points were spread furthest away from each other, depending on the type of distribution. For the linear distribution, the furthest four points within the bounding box of the porous region were selected (Fig. 5A). For the radial distribution, two sampling points were selected from the x–y plane in the centre of the porous implant region. The selected points were furthest away from each other. The third point was the most distal centre point within the porous region of the implant (Fig. 5B). The distribution equations were applied instead of an element-wise optimisation for two main reasons: (1) To achieve smoother transitions between unit cells and therefore avoid large stress concentrations at the unit cell intersections. (2) Only three or four input variables (elasticity moduli at the sampling points) were required for optimisation, resulting in reduced computation time compared to using an input variable for each element. The four templates and two distributions resulted in eight possible configurations for the optimised implant design.

Fig. 5.

Sample point selection for porous implant region for A linear distribution, and B radial distribution

The cost function (Eq. 5) used in the optimisation process quantified the difference between the pre-implantation OSS and the post-implantation OSS for elements representing bone, considering peak loads during walking and stair climbing. In addition, the cost function included a penalty term to consider material failure in the porous implant region.

5

where, was the number of elements representing bone in the implanted femur. and were the OSS of the i^th element in bone for the implanted femur under peak load occurring during walking and stair climbing, respectively. and were the OSS of the same element (i^th element) in bone for the intact femur under peak load occurring during walking and stair climbing, respectively. As the values of the first two terms describing the differences in OSS between an intact and implanted femur were extremely small (10^–3 -10^–4), they were multiplied by 1000 to ensure numerical stability and facilitate the convergence of the optimisation. was the number of elements within the implant predicted to fail during a fatigue test described in the ISO 7206–4 standard. To predict the elements that failed during the fatigue test, we used the Soderberg fatigue criterion to calculate a safety factor for each element (Eq. 6):

6

where was the safety factor of the element, and and were the amplitude and mean of the von Mises stresses respectively of each element in the implant. The von Mises stresses of the element in the implant were calculated for a maximum load of 2300 N and a minimum load of 300 N applied to the FE model simulating the ISO 7206-4 setup to calculate and :

7

8

Yield strength was calculated for each element based on the elastic modulus of the element. The relationship between elastic modulus and yield strength was determined from the compression testing of the selected diamond lattice structures and linear interpolation. Fatigue strength was estimated to be 0.3 * based on a previous study on the fatigue properties of diamond lattice structures [26].

From both a clinical and regulatory perspective, survival under fatigue testing (ISO 7206-4) needed to take precedence over minimising stress shielding. An implant that reduces stress shielding but fails early in service is not viable. To prioritise implant fatigue strength over stress shielding reduction, the penalty component of the cost function was set to be significantly higher than the other components of the cost function, even when only a single element was predicted to fail during the fatigue test. The penalty component was 100 for a single failed element, whereas the rest of the cost function was typically less than 1 or occasionally single-digit number. This hierarchical approach to setting up the cost function caused the optimiser to prioritise implant survival over stress shielding.

The cost function was optimised using an in-built MATLAB optimisation algorithm, namely ‘patternsearch’ (MATLAB, MathWorks, Inc., Natick (MA), USA). The lower and upper bound were set for the elastic modulus based on the experimentally determined mechanical properties of diamond lattice structures as described above. As the implant stiffness was iteratively adjusted, the total cost was calculated until convergence (Fig. 6).

Fig. 6.

Flowchart of the implant design and optimisation process (optimisation process within dashed lines)

Performance evaluation

The performance of each of the optimised implants was evaluated using two measures. The first was based on the changes in stress shielding between a solid implant and each of the optimised porous implants. The second was based on micromotion at the implant-bone interface for each of the different implant designs.

The changes in stress shielding were quantified by comparing octahedral shear strains in bone elements between the intact femur, the femur with a solid implant, and the femurs with each of the optimised porous implants. The following two equations were utilised:

9

where is the mean difference in OSS between the intact and implanted femur and quantifies the level of stress shielding. OSS was calculated for each element for the intact femur () and the same element in the implanted femur (). is the number of bone elements within one of the Gruen zones [27] or the sum of all elements within all of the Gruen zones, depending on which region is being calculated for.

10

where is the stress shielding associated with the solid implant and is the stress shielding associated with a porous implant. is the reduction in stress shielding achieved by the porous implant compared to the solid implant described as a percentage of the stress shielding associated with the solid implant ().

Micromotion at the implant-bone interface was evaluated under peak loading during walking. To analyse interface micromotion before osseointegration, a friction surface contact was applied to the FE model between implant and bone. Since the coefficients of friction (COF) reported in the literature varied widely (0.1–0.6) [11, 28–30], micromotion was analysed and compared for COF of 0.1, 0.2, 0.3 and 0.4. The tangential motions between each node on the implant surface and its nearest neighbour on the bone were calculated. The mean and maximum micromotion between bone and implant were calculated for each porous stem design.

Results

Lattice mechanical properties

Given the design constraints mentioned earlier, the minimum and maximum achievable elastic modulus for diamond lattice structures were 3110 MPa and 7970 MPa, respectively (Fig. 7A). The elastic modulus decreased linearly with increasing porosity. Yield strength increased linearly with increasing elastic modulus (Fig. 7B). This linear relationship was used to calculate the yield strength of each element within the porous region of the implant in the iterative optimisation process. The lower and upper bounds for the elasticity modulus of the sampling points were set to 3110 MPa and 7970 MPa, respectively.

Fig. 7.

Mechanical properties of lattice A elastic modulus over porosity, B yield strength over elastic modulus

Optimised porous implants

The femoral stem optimisation based on the eight configurations resulted in six unique solutions for the optimised implant design (Fig. 8, Table 4). The linear fully porous configuration and the radial fully porous configurations both converged on the same uniform distribution, with all the porous elements assigned the maximum elastic modulus (7970 MPa). Conversely, the linear solid shell configuration and the radial solid shell configurations both converged on the same uniform distribution, with all the porous elements assigned the minimum elastic modulus (3110 MPa). The other four configurations, based on proximal porous and distal shell templates with linear and radial distributions, converged on non-uniform distributions of elastic moduli. Except for the solid shell template, where the porous elements converged to the maximum porosity (lowest elastic modulus), all other configurations resulted in porosities of most elements converging to relatively low porosities (elastic modulus ≥ 5023 MPa for all elements). Only the four implant designs based on the proximal porous and solid shell templates were predicted to pass the ISO 13314 fatigue test. All other implants were predicted to fail (see number of failed elements in Table 4).

Fig. 8.

Optimised stiffness distribution A LFP/RFP, B LPP, C RPP, D LSS/RSS E) LDS, F) RDS

Table 4.

Optimisation results for eight implant design configurations

Design	Iterations until convergence	Stiffness range (MPa)	Average stiffness (MPa)	Number of failed elements in implant under fatigue loading (location of failed elements)
Linear fully porous (LFP)	185	7970	7970	17 (medial and lateral at half length of the implant)
Radial fully porous (RFP)	153	7970	7970	17 (medial and lateral at half length of the implant)
Linear proximal porous (LPP)	158	7757–7970	7872	0
Radial proximal porous (RPP)	154	5478–7970	7580	0
Linear distal shell (LDS)	274	7720–7911	7852	1 (medial distal end of proximal porous implant region)
Radial distal shell (RDS)	291	5023–7970	6719	1 (medial distal end of proximal porous implant region)
Linear solid shell (LSS)	296	3110	3110	0
Radial solid shell (RSS)	205	3110	3110	0

In the linearly distributed designs based on the proximal porous and distal solid templates (LPP, LDS) the stiffness generally decreased medially. For the LDS design this was more apparent throughout the full length of the implant, while in the LPP design, the stiffness also decreased proximally. The radially distributed designs (RPP, RDS) resulted in stiffer outer shells with softer cores. For the RDS design, the stiffness increased distally which was also observed in the RPP design although to a much lower degree (Fig. 8).

Stress shielding

Compared to the solid implant, all eight optimised porous implant configurations resulted in octahedral shear strains (OSS) in the implanted bone that more closely resembled those observed in the intact bone. This demonstrates that all eight porous implants were able to reduce stress shielding when compared to the solid implant (Table 5). In general, implants with larger porous regions showed more reduction in bone stress shielding. The type of stiffness distribution (linear or radial) within the porous implant region had a comparatively small impact on stress shielding. The change in octahedral shear strain () was larger for the solid implant compared to all of the porous implant designs in each of the Gruen zones 1–7 (Fig. 9). The difference between solid and porous implants was more apparent in the proximal part of the femur than in the distal part (Fig. 9). The Fully Porous (FP) design was found to reduce bone stress shielding more than other designs, particularly in the more distal Gruen zones (2–6). The solid shell design had the smallest reductions in stress shielding in all of the Gruen zones (Fig. 9). The performance of the proximal porous (PP) and distal shell (DS) designs were similar, and bone reductions to stress shielding were highest in the proximal regions.

Table 5.

Stress shielding reduction for optimised porous implant designs compared to solid implant

Design	Stress shielding reduction (SSR, Eq. 10) (%)
	Walking	Stair climbing
Linear fully porous (LFP)	13.1	11.2
Radial fully porous (RFP)	13.1	11.2
Linear proximal porous (LPP)	9.5	8.1
Radial proximal porous (RPP)	8.9	7.7
Linear distal shell (LDS)	9.2	7.9
Radial distal shell (RDS)	9.5	8.1
Linear solid shell (LSS)	3.1	3.6
Radial solid shell (RSS)	3.1	3.6

Fig. 9.

Decrease in octahedral shear strain after implantation compared to the intact femur

Micromotion

Micromotion at the bone-implant interface decreased with increasing coefficient of friction assigned to the surface-interaction in the finite element model (Fig. 10). At the lowest COF of 0.1, the peak micromotion near the neck region of a fully porous implant exceeded the upper threshold (150 µm) for potential bone ingrowth. The predicted mean micromotion for all implant designs was optimal for bone ingrowth (< 50 µm) irrespective of the coefficient of friction assigned to the bone-implant interface. The RDS design had higher peak micromotion than other proximally porous designs. The differences in micromotion between the different implant designs decreased with increasing COF. The micromotion at the implant-bone interface was higher in the more proximal areas, particularly on the medial side (Fig. 11). This area corresponds approximately to Gruen zone 7 for COF of 0.4 and includes Gruen zone 6 for a COF of 0.1.

Fig. 10.

Micromotion for each stem for varying COF A peak micromotion B mean micromotion

Fig. 11.

Micromotion at bone-implant interface for the six unique implant designs

Discussion

This work investigated the potential of patient-specific porous femoral stems to reduce bone stress shielding caused by total hip replacements. In contrast to previous studies where one specific porous design or a specified porous implant region with varying distribution strategies was presented [9], the current study investigated four assigned porous implant regions and two stiffness distribution strategies. There is no consensus in the literature for quantifying stress shielding. While some studies have used stress-based criteria, others have used strain-based criteria [9]. The current study is unique in its use of an octahedral shear strain (OSS) based quantification of stress shielding. OSS was selected because it has been shown to be a suitable mechanical stimulus for predicting bone remodelling in finite element models that treat bone as a continuum [12]. Our results demonstrate that it is possible to design a porous femoral stem that is capable of reducing stress shielding, is likely to pass the ISO 7206-4 fatigue test and to promote bone ingrowth.

Femoral stems were optimised to reduce the difference in OSS between intact and implanted bone by altering the implant’s stiffness within a defined porous region. Two solutions with uniform stiffness distributions and four solutions with linear and radial stiffness distributions were obtained. The uniformly porous designs included the fully porous (FP) solution with the lowest porosity and the solid shell (SS) designs with the highest porosity. While the latter fulfilled the strength requirement based on the Soderberg failure criterion, the former was found to experience fatigue failure. Linear and radial stiffness distributions in the proximally porous (PP) and distal shell (DS) designs tended towards higher stiffness in the distal end (Fig. 8). Additionally, radial distributions resulted in greater variation of included elastic moduli (Table 4). By using four different defined porous implant regions and two stiffness distribution equations, six distinct solutions were obtained.

Differences in bone strain between the implanted and the intact femur () for porous designs were compared to those of a conventional solid design. In general, a larger porous region led to a greater reduction in stress shielding. The FP design resulted in the greatest reduction in stress shielding (Table 5). Despite the internal structure of the SS design being fully porous, the reduction in stress shielding was less than 4% compared to the solid stem (Table 5). Despite the larger porous region in the DS design compared to the PP design, both exhibited similar performance in terms of stress shielding (Table 5, Fig. 9). The type of distribution, linear or radial, only resulted in minor differences in stress shielding. The SS and PP designs were the only ones that did not fail.

In addition to the reduction in stress shielding, introducing porosity in implants may improve osseointegration. Osseointegration requires the micromotions between bone and implant surfaces to be below the critical threshold for bone tissue formation. While small micromotions (< 50 µm) are favourable for bone on/ingrowth, excessive micromotions (> 150 µm) will inhibit osseointegration due to the formation of fibrous tissue [31]. The magnitude of maximum and mean micromotions varied depending on the applied coefficient of friction (COF), as well as the porous implant design. The calculated micromotions were highest for the FP design and lowest for the SS design. These differences were more prevalent for a lower COF. With increasing COF, the differences in predicted micromotion between the designs decreased. The radial distal shell (RDS) design was found to have higher peak micromotion compared to the linear distal shell (LDS), linear proximal porous (LPP) and radial proximal porous (RPP) designs. The higher peak micromotions in the RDS design may arise from the lower porosity in the areas of the implant that are in direct contact with the bone. The areas that experience higher micromotion corresponded to the Gruen zones 7 and 6 that have been found to be more prone to bone resorption [6, 32]. The proximal part of the bone appears to be at higher risk of excessive micromotion, but only in the fully porous design does micromotion exceed the critical threshold of 150 µm. We advise a cautious approach to interpreting these results, given that the COF at the bone-implant interface is not accurately known and is likely to vary across the interface and change over time [33].

In recent years, a variety of porous orthopaedic implant designs have been proposed to reduce stress shielding, including optimised porosity distributions [9]. Out of these studies, not all considered fatigue strength in their porous femoral stem designs. Among the studies that considered fatigue in their designs, implant porosity was optimised to achieve different objectives. In one study, researchers aimed to achieve minimal stiffness with an acceptable safety factor [34]. Others aimed to achieve maximum implant compliance [35], or maximum bone stress [36]. Other studies aimed for minimal bone loss based on strain energy density [32, 37]. Quantification of bone resorption is a common metric to evaluate implant performance [9]. One study calculated bone remodelling based on strain energy density in the bone and reported up to 75% reduction of bone loss based in comparison to a solid implant [32]. In contrast, this study showed a reduction of stress shielding of only 3 – 13% compared to the solid implant was achieved. However, bone loss may be challenging to reliably predict due to the lack of validation of bone remodelling algorithms for human bones [33]. Therefore, in the current study, a relative comparison between bone strains was preferred over the minimisation of total bone loss under the assumption that pre-implantation bone strains are the most favourable for maintaining bone density. Besides bone loss, some studies consider interface failure caused by micromotion at the implant-bone interface in their optimisation algorithm [32, 35, 37]. In contrast, in the current study, the performance of various designs was evaluated based on the achieved stress shielding reduction, as well as potential micromotions with varying COF. The decreasing micromotions observed with increasing COF may indicate reduced bone-implant micromotions under the assumption that bone tissue formation post-implantation gradually increases friction.

Despite the valuable insights offered by this study, there are certain limitations that should be considered when interpreting the results. This investigation was conducted for a single implant type and geometry, likely impacting the resulting reduction in bone stress shielding. As shown in a previous study, the type of stem in combination with reduced implant stiffness, impacts the strain transfer between implant and bone [38]. In addition, the geometry and material properties of a single femur specimen were considered in this study. To address this, a future study aims to incorporate a larger sample size to investigate the potential reductions for a representative patient cohort. Additionally, there were limitations in the bone-implant FE approach to allow for manageable computation time for the iterative optimisation process. This includes the applied forces and boundary conditions which were based on previous studies [23, 24, 39], not considering patient-specific factors such as body weight. The elements used in the finite element model may lead to lower accuracy of stress and strain distribution. A 4-node linear tetrahedron element (C3D4) mesh with an edge length of 2 mm was applied for femur bone and implant. Other studies have used smaller edge lengths of 1 mm and 10-node tetrahedron elements (C3D10) [34, 40], while in another study, the authors suggested 2 mm edge length to represent cancellous bone, 4 mm to represent cortical bone and 0.8 mm to represent the femoral stem implant [41]. However, the analysis focused on comparative outcomes between intact and implanted bone rather than absolute values. Therefore, despite the models not capturing the full complexity of the bone-implant interactions, the assumptions made remained consistent between models and meaningful comparisons could be extracted.

Another limitation is how the porous implants were represented in the FE models. Due to the computational load when modelling porous structures, the porous structures were modelled as continuum materials in the current study. This approach fails to quantify stress concentrations, particularly in the struts of the lattice structures, leading to a potential underestimation of maximum stress. Despite the use of the Soderberg fatigue failure criterion in the optimisation, which is considered the most conservative compared to other criteria such as Goodman or Gerber, the representation of the porous material as continuum material may lead to an overestimation of the safety factor. In addition to this, the mechanical properties used in the optimisation were based on a limited number of samples and inter-/extrapolated values from the linear sample data. Further experimental studies are required to increase the available data on the mechanical properties of diamond lattice structures and to evaluate whether the continuum material model allows for accurate representation of the implant behaviour after additive manufacturing. Future work should also explore more accurate representations of lattice structures without extensively increasing computation time. Considering the desired osseointegration of porous bone interfacing implants, other relevant parameters of porous materials should be considered in future designs. For instance, tortuosity impacts the permeability and therefore bone cell migration into porous scaffold structures [42]. Given that adjusting porosity parameters, such as tortuosity, results in geometrical changes, the stiffness of the porous material will inevitably change. Therefore, future work may explore the incorporation of tortuosity into the presented design framework.

The optimisation approach described in the current study only considered the changes in OSS at a point in time immediately after implantation and therefore does not consider any bone remodelling that may take place subsequently. Time-dependent modelling could be used to understand the long-term changes in bone density and its effect on bone-implant interactions. Future studies could also consider the effects of using low stiffness material alloys, improved post-manufacturing treatment methods, and porous structures that exhibit more favourable strength-to-stiffness ratios, factors that may further reduce stress shielding, improve bone-implant integration, and extend implant longevity.

Conclusion

In this study, custom porous femoral stems were designed based on eight configurations, aiming to minimise stress shielding while considering implant fatigue strength. Six unique design solutions were reached. Finite element modelling predicted that all six designs would reduce stress shielding by 3–13% when compared to a solid implant, but that only three of the designs have the potential to pass the ISO 7206-4 fatigue test. These three designs comprised the two proximally porous designs and the solid shell design. All three of these designs also exhibited micromotion at the bone implant interface that was conducive to bone ingrowth. Therefore, considering stress shielding, implant fatigue strength and bone ingrowth, the proximal porous and solid shell designs were the most promising. However, further experimental studies are needed to evaluate whether 3D printed full-scale implants behave as predicted in the current study.

Supplementary Information

Below is the link to the electronic supplementary material.

Abbreviations

COF

Coefficient of friction

CT

Computed tomography

DS

Distal shell

EBM

Electron beam melting

FDA

U.S. Food and Drug Administration

FE

Finite element

FEM

Finite element modelling

FP

Fully porous

HU

Hounsfield unit

ISO

International Organization for Standardization

LDS

Linear distal shell

LFP

Linear fully porous

LPP

Linear proximal porous

LSS

Linear solid shell

OA

Osteoarthritis

OSS

Octahedral shear strain

PP

Proximal porous

RDS

Radial distal shell

RFP

Radial fully porous

RPP

Radial proximal porous

RSS

Radial solid shell

SLM

Selective laser melting

SS

Solid shell

THR

Total hip replacement

Author contributions

SS, HG and PL contributed to the study design and revision of the manuscript. SS and HG conducted the computational analysis and interpreted the resulting data. SS conceptualised and executed the study, analysed the data and drafted the manuscript. All authors read and approved the final manuscript.

Funding

This study was funded by an Australian Research Council (ARC) Industrial Transformation Research Program (IC180100024).

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

Femur CT scan usage approved by the University of Melbourne Human Ethics Advisory Group (22159).

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.