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In silico medical device testing of
anatomically and mechanically
conforming patient-specific
spinal fusion cages designed by
full-scale topology optimisation
Thijs Smit
1
*, Niels Aage
2
, Daniel Haschtmann
3
,
Stephen J. Ferguson
1
and Benedikt Helgason
1
1
Institute for Biomechanics, ETH Zürich, Zürich, Switzerland,
2
Solid Mechanics, Technical University of
Denmark, Kongens Lyngby, Denmark,
3
Department of Spine Surgery and Neurosurgery, Schulthess
Klinik, Zürich, Switzerland
A full-scale topology optimisation formulation has been developed to automate
the design of cages used in instrumented transforaminal lumbar interbody fusion.
The method incorporates the mechanical response of the adjacent bone
structures in the optimisation process, yielding patient-specific spinal fusion
cages that both anatomically and mechanically conform to the patient,
effectively mitigating subsidence risk compared to generic, off-the-shelf
cages and patient-specific devices. In this study, in silico medical device
testing on a cohort of seven patients was performed to investigate the
effectiveness of the anatomically and mechanically conforming devices using
titanium and PEEK implant materials. A median reduction in the subsidence risk by
89% for titanium and 94% for PEEK implant materials was demonstrated
compared to an off-the-shelf implant. A median reduction of 75% was
achieved for a PEEK implant material compared to an anatomically
conforming implant. A credibility assessment of the computational model
used to predict the subsidence risk was provided according to the ASME
V&V40–2018 standard.
KEYWORDS
in silico, ASME V&V40, model credibility, medical device testing, topology optimisation,
patient-specific, finite element analysis, lumbar spinal fusion implant
Highlights
•A full-scale topology optimisation formulation to design anatomically and
mechanically conforming patient-specific spinal fusion implants was tested, in
silico, on a cohort of seven patients.
•The anatomically and mechanically conforming patient-specific spinal fusion cages
reduced the median subsidence risk by 89% for titanium and 94% for PEEK implant
materials compared to an off-the-shelf implant.
•The method was similarly effective for patients with low and high bone quality.
•The credibility of the in silico medical device testing procedure was evaluated
according to the ASME V&V40–2018 standard.
OPEN ACCESS
EDITED BY
Wenxin Niu,
Tongji University, China
REVIEWED BY
Alessandra Aldieri,
Polytechnic University of Turin, Italy
Fulvio Tartara,
University Hospital of Parma, Italy
*CORRESPONDENCE
Thijs Smit,
thsmit@ethz.ch
RECEIVED 01 December 2023
ACCEPTED 07 August 2024
PUBLISHED 10 September 2024
CITATION
Smit T, Aage N, Haschtmann D, Ferguson SJ and
Helgason B (2024) In silico medical device
testing of anatomically and mechanically
conforming patient-specific spinal fusion cages
designed by full-scale topology optimisation.
Front. Bioeng. Biotechnol. 12:1347961.
doi: 10.3389/fbioe.2024.1347961
COPYRIGHT
© 2024 Smit, Aage, Haschtmann, Ferguson and
Helgason. This is an open-access article
distributed under the terms of the Creative
Commons Attribution License (CC BY). The use,
distribution or reproduction in other forums is
permitted, provided the original author(s) and
the copyright owner(s) are credited and that the
original publication in this journal is cited, in
accordance with accepted academic practice.
No use, distribution or reproduction is
permitted which does not comply with these
terms.
Frontiers in Bioengineering and Biotechnology frontiersin.org01
TYPE Original Research
PUBLISHED 10 September 2024
DOI 10.3389/fbioe.2024.1347961
1 Introduction
Recent advancements in patient-specific computational models
enable in silico clinical trials to play an increasing role in the
development of medical devices. The benefits of in silico clinical
trials over conventional clinical trials include 1) cost and time
efficiency; 2) collecting data before animals or humans are
subjected to potential harm; 3) comparing multiple treatments
per patient; and 4) a broader or more in-depth analysis of
treatments (Viceconti et al., 2021); (Action, 2015).
In recent years, there has been a surge in the use of in silico
clinical trials, e.g., in the fields of pharmacology, cardiovascular
stents, diabetes treatment, and orthopaedics (Passini et al., 2017;
EMA, 2018;Sarrami-Foroushani et al., 2021;Schmitzer et al.,
2022;La Mattina et al., 2023). Looking specifically at in silico
clinical trials where finite element (FE) models were used, Kassab-
Bachi et al.studied the effect of geometric variability in the spine
on the biomechanical response, i.e., the intradiscal pressure and
the facet joint contact pressure in a cohort of 152 patients
(Kassab-Bachi et al., 2023), and Aldieri et al.investigated the
fracture risk of the proximal human femur (Aldieri et al., 2023)
with a focus on proving the credibility of the computational
models according to the ASME V&V40–2018 standard
(The American Society of Mechanical Engineers ASME, 2018).
With further development, in silico clinical trials will potentially
be accepted by regulatory agencies as supplementary material for
market approval applications and may be used as a (partial)
replacement of animal and human clinical trials (Viceconti
et al., 2016)(Viceconti et al., 2005).
The authors recently developed a topology optimisation (TO)
strategy that automates the design of cages used in instrumented
transforaminal lumbar interbody fusion (TLIF). The strategy
incorporates the mechanical response of the adjacent bone
structures in the optimisation process, with the goal to reduce
subsidence risk. This results in anatomically and mechanically
conforming devices (AMCDs) that successfully reduce the
subsidence risk compared to off-the-shelf (OTS) cages and
anatomically conforming devices (ACDs) (Smit et al., 2024)
(Smit, 2023). The optimisation and in silico testing process
have been automated further to facilitate in silico medical
device testing on multiple patients. Furthermore, the
optimization and testing procedures were modified with the
goal to increase the effectiveness of optimisation and improve
the credibility of the in silico testing process. As Viceconti et al.
suggested, the evaluation of the credibility of the computational
model should be considered early in the development of new in
silico methods using guidelines from regulatory agencies and
examples e.g. Viceconti et al. (2021).
Thus, the aim of this study was to perform in silico medical
device testing of AMCDs on a cohort of seven patients and compare
the AMCDs to OTS cages and ACDs, using titanium and PEEK
implant materials. The credibility assessment of the computer model
that was used in the subsidence risk prediction was carried out
according to the ASME V&V40–2018 standard. We hypothesized
that AMCDs reduce the subsidence risk over ACDs and OTS cages
for patients with a broad range of bone quality. Furthermore, we
hypothesised that PEEK cages have lower subsidence risk than
titanium cages and that there is a negative correlation between
the subsidence risk and bone quality.
2 Methods
2.1 Topology optimisation
Our newly developed TO strategy (Smit et al., 2024)(Smit, 2023)
to optimise spinal fusion cages was, in this work, slightly modified to
improve its effectiveness and to allow the optimisation of titanium
and PEEK implant materials. The computational domain Ω
comprised an implant domain (Ω
implant
), a bone domain (Ω
bone
),
and a rigid domain (Ω
rigid
), with Ω=Ω
implant
∪Ω
bone
∪Ω
rigid
(Figure 1A). Ω
bone
contains the bone structures and patient-specific
material properties. Ω
implant
was the design domain that was
subjected to optimisation in the TO process.
Domain Ω, with a size of 54 mm × 54 mm × 54 mm, was discretised
using a structured grid of 1.728 million hexahedral elements with an
isotropic element edge length of 0.45 mm. Resampling was performed
using SimpleITK version 2.1.1.2 (Lowekamp et al., 2013) to adjust the
CT scan resolution to match the resolution of Ωand to position the
Functional Spinal Unit (FSU) in the approximate centre of Ω.The
vertebrae were partially embedded in Ω
rigid
.
Six load cases (axial compression, lateral shear, posterior–anterior
shear, flexion, lateral bending, and axial rotation) were used in the TO
process. The applied loads were based on the study by Rohlmann et al.
(2008) and the OrthoLoad dataset (Bergmann and Damm, 2008)
(Figure 1C;Table 1). Loads were applied on nodes at the top of Ω.
Nodes on the bottom of Ωwere fixed in all directions. The load
magnitude for all patients was scaled with respect to the patient’s body
weight and the body weight of patient 1 (see Section 2.2), as was used in
the subsidence risk assessment (Han et al., 2013)(Zhang et al., 2017).
Similar to the TO formulation that was previously used (Smit et al.,
2024)(Smit, 2023), the compliance of the bone–implant system was
minimised for all load cases (optimisation objective), but to avoid the
overloading of the adjacent vertebrae, the maximum principal strains in
Ω
bone
were constrained (optimisation constraints). Constraining the
minimum principal strains was omitted because our previous work
indicated that this constraint was inactive (Smit et al., 2024)(Smit, 2023)
because the compression load from the implant is transferred to the
shear, orthogonal to the endplate, along the periphery of the implant. In
pure shear, the maximum and minimum principal strains have equal
magnitudes but opposite signs, indicating that the tensile limit is
reached first due to a lower threshold. Shearing is the dominant
loading mode in the endplates, which was confirmed by several
authors who identified shear failure of the vertebra endplates as the
dominant failure mode in subsidence (Cadman et al., 2016); (Au et al.,
2011). Furthermore, we use a local volume constraint on Ω
implant
to
create a porous implant structure. To promote manufacturability, the
minimum strut diameter was controlled using robust TO formulation.
No other manufacturing-specific constraints were added to make a
comparison between titanium and PEEK fair because these materials
have different manufacturability requirements.
The compliance minimisation problem with the maximum
principal strain constraint and local volume constraint in discrete
form is written as
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Smit et al. 10.3389/fbioe.2024.1347961
min
x
lc
k1
fxe
()
kin Ω
subject to
(1)
gxd
1≤0.0in Ωbone,(2)
vxd
≤0.0in Ωimplant,(3)
where lc represents the six load cases with k1...6, fis the
objective function (Equation 1), g1is the constraint on the
maximum principal strain response (Equation 2) for the
compression load case in the Ω
bone
, and vis the local volume
constraint (Equation 3)onΩ
implant
. The maximum principal
strain constraint on the compression load case was used as this
was the active constraint (Smit et al., 2024)(Smit, 2023) with a
maximum principal strain limited to 0.73% based on the work by
Bayraktar et al. (2004). The local volume constraint v(xd)followed
the implementation published by Wu et al. (2018). The local volume
constraint was applied on the dilated design xd, with a local volume
fraction of 0.35, a filter radius of 3.5, and p-mean penalty of 16.
Finally, Poisson´s ratio for Ω
implant
was set to 0.3 for titanium and
0.43 for PEEK. The E-modulus for the titanium implant was set to
110 GPa (Niinomi and Nakai, 2011), and for the PEEK implant, the
E-modulus was set to 3 GPa (Zhao et al., 2018). The optimisation
was run for 24 h on a computational cluster using 1,000 cores in
parallel. The final design should at least exhibit a discreteness
measure that is lower than 3%. This value is considered to be an
acceptable convergence to a solid/void design (Wang et al., 2011).
The resulting cage designs from the optimisation process have a
voxelised surface because of voxel-based discretisation. The final designs
were achieved by applying the “Iso volume”filter to the optimised cage
using a contour of 0.5 as the threshold and exporting to an .stl file using
vtk 9.1.0 (Schroeder et al., 1996). The resulting file was used in the
subsidence risk assessment Section 2.3 and Section 2.4.
FIGURE 1
Computational domain and load application for the TO and subsidence risk assessment domain. (A) Optimisation domain Ωwith Ω=Ω
implant
UΩ
bone
UΩ
rigid
. Support constraints, in all directions, were applied to the bottom of Ω(data from patient 2; see Section 2.2) (B) Subsidence risk assessment domain
with FL application and support constraint illustrated including the right-h anded orthogonal coordinate system (data from patient 1; see Section 2.2). (C)
Forces in black and moments in red were applied on top of the optimisation domain Ωin the xy-centre of Ω
rigid
.
TABLE 1 Spinal loads during daily living applied in the TO process, derived
from the study by Rohlmann et al. (2008) and the OrthoLoad dataset
(Bergmann and Damm, 2008) from a patient with similar weight to patient 1
(see Section 2.2) [table from Smit et al. (2024) and Smit (2023)].
Description Component Patient 1 Unit
Axial compression Fz−177 N
Posterior/anterior shear Fy27 N
Lateral shear Fx5N
Flexion Mx0.4 Nm
Lateral bending My0.5 Nm
Axial rotation Mz0.7 Nm
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2.2 Study patient datasets
Anonymised pre-operative computed tomography (CT)
scans with clinical resolution (voxel sizes of approximately
0.30 mm × 0.30 mm × 0.50 mm), from seven female patients,
were provided by the Schulthess Klinik, Zürich (Table 2). The
patients, who were diagnosed with degenerative
spondylolisthesis or degenerative disk disease, were treated
with a TLIF procedure. Patients with other spinal diseases
such as trauma, infection, or tumour were excluded. The CT
images from patients 1 and 2 were reused from a previous study
(Smit et al., 2024)(Smit, 2023), and all the patients provided
informed consent for the use of their data for research purposes.
The CT scans were calibrated using a phantom-less calibration
procedure (Lee et al., 2017). The vertebrae were segmented using
open-source software MITK-GEM (Pauchard et al., 2016).
T-scores, based on DXA scans, were only available for the
L4 level for three patients. Bone quantity was thus assessed by
calculating the integral volumetric bone mineral density (vBMD)
for each vertebra that was modelled, including the endplates and
cortical bone in accordance with the work by Kaiser et al. (2020)
(Table 2;Figure 2).
2.3 Finite element models
The model building process follows the workflow presented
by Smit et al. (2024) (Smit, 2023) but is briefly described here for
clarity and context. A commonly used, commercially available
OTS cage, for a TLIF procedure with a height of 9 mm, was
reengineered into a CAD model. The cages were placed anteriorly
and across the mid-line in an optimal position, restoring spinal
alignment as much as possible. The implant placement was
checked by a spine surgeon according to standard surgical
fusion techniques for the TLIF approach. The ACD and
AMCD design domains were created by matching the top and
bottom surfaces of the CAD model to the patient’sendplates.It
was assumed that the intervertebral disc and cartilaginous
endplates were removed during the surgery. The cages were
placed according to standard surgical fusion procedures, and
the implant position was checked by a spinal surgeon.
In the optimisation process (Section 2.1), daily living load cases
were applied, which cause strains in the bone structures within the
linear regime. The optimisation process was followed by the
subsidence risk assessment (Section 2.4) that was performed in
commercial FE analysis software where the cages were loaded with
hyper-physiological loading that can potentially lead to non-linear
material response, both in the implant and the bone structures.
In the subsidence risk assessment, 10-node tetrahedral elements
(C3D10M) were used to mesh the bone and implant structures with
an average edge length of 1.5 mm for the vertebrae and 0.5 mm for
the cages. The apparent density-to-modulus relationship from the
study by Ouyang et al. (1997) (Table 5) was used to assign material
properties to the bone elements in the FE mesh based on an internal
calibration of the CT grey levels to the apparent density. Poisson’s
ratio was set to 0.3, and the minimum value for Young’s modulus
was set to 25 MPa for the bone structures. The subsidence risk
assessment was performed in an explicit non-linear FE solver
(Abaqus 2021, Dassault Systèmes, Vélizy-Villacoublay, France),
assuming non-linear geometry and a general contact formulation.
The bone structures were modelled using a rate-independent
elasto–plastic material model, which captures the asymmetric
tension–compression post-yield behaviour of bone (Figure 3B)
(Bayraktar et al., 2004). A compressive follower load (FL) of
310 N for patient 1 was assumed based on the study by
Rohlmann et al. (2014) and the OrthoLoad dataset (Bergmann
TABLE 2 Patient data overview. BMI, body mass index; vBMD, volumetric bone mineral density; T-scores based on DXA scans when available. NA, not
available.
FSU ID Age Gender BMI Weight [kg] Level vBMD [g/cm
3
] T-score
1 66 Female 18.3 51 L4 0.16 −2.3
L5 0.15 NA
2 58 Female 25.6 75 L4 0.40 NA
L5 0.45 NA
3 57 Female 24.2 70 L4 0.16 NA
L5 0.17 NA
4 67 Female 41.6 100 L4 0.52 1.5
L5 0.54 NA
5 76 Female 22.9 64 L4 0.15 NA
L5 0.21 NA
6 76 Female 22.6 64 L4 0.21 NA
L5 0.27 NA
7 52 Female 24.3 60 L4 0.33 1.3
L5 0.31 NA
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and Damm, 2008). The magnitude of FL for all patients was scaled
with the patient’s body weight to the body weight of patient 1 and
subsequently distributed on the superior endplate of the superior
vertebra such that the direction of the load was as defined by
Rohlmann et al. (2009) (Figure 1B). The inferior endplate of the
inferior vertebra was constrained in all translations. The models
were solved on a computational cluster using 64 cores in parallel.
Poisson’s ratio was set to 0.3 and 0.43 for titanium and PEEK,
respectively. The material models for titanium and PEEK are shown
in Figure 3A.
2.4 Subsidence risk assessment
The maximum factor of fracture risk (FFR) was used as a
surrogate for subsidence risk. The maximum FFR is quantified as
the degree of overloading of the vertebrae using a maximum
principal strain limit of 1.5% and a minimum principal strain
limit of −2.0% (Soyka et al., 2016). For each element “i”in the
bone domain, the FFR (FFRi,Equation 4) and maximum FFR
(Equation 5)(Soyka et al., 2016) were calculated using
FFRimax εmax ,i
1.50%,εmin ,i
−2.00%
,(4)
Maximum FFR max FFRi
()
,(5)
where εmax ,i is the maximum principal strain of element i, in the
centroid of the element, and εmin ,i is the minimum principal strain of
element i, in the centroid of the element.
2.5 Computer model credibility assessment
Credibility assessments were performed following the ASME
V&V40–2018 standard. Note that the following applies to the
subsidence risk assessment of Section 2.3, 2.4. The process starts
with the definition of the question of interest (QoI). The next step
was to formulate the context of use (CoU) including the function and
scope of the computer model that was used in answering the
QoI (Table 3).
The model risk describes the possibility that the use of the
computer model leads to a decision causing harm to the patient.
The model risk is composed of the “model influence”and the
“decision consequence.”The model influence describes how
much influence the results of the computer model have on the
decision maker.
The model influence is defined to be MEDIUM because the
decision of the AMCD has lower subsidence risk than the ACD or
OTS, for a specific patient, is informed by the results from the
computer model, in combination with the observations and
judgment of the spinal surgeon.
The decision consequence is the significance of harm to the
patient in the case of an incorrect decision.
The decision consequence is defined to be LOW because
a worst-case incorrect decision would lead to a patient
being treated by an OTS cage, which is the current
standard practise.
The selection of computer model credibility activities is based on
the credibility requirements for the computational model that
FIGURE 2
Patients ordered based on the mean segment integral vBMD.
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should correspond with the model risk that was defined (Table 4).
Model credibility is defined as the trust in the predictive capability of
the computer model for the CoU, according to the
ASME V&V40–2018.
The ASME V&V40 standard suggests several credibility factors
that should be evaluated to demonstrate that the overall credibility of
the computational model agrees with that of the model
risk (Table 8).
A mesh convergence study of the bone structures was
performed by calculating changes in the maximum FFR for
gradually decreasing element edge length. Mesh convergence
of the implant structures was assessed by decreasing the
element edge length of the implant mesh while maintaining an
element edge length of 1.5 mm for the bone structures. The
maximum FFRs were calculated, as well as the percentage
difference in the maximum FFR between different meshes
((current−previous)
previous * 100). The simulations were run using patient
2 and the ACD in titanium. Furthermore, for the mesh
convergence study, a homogeneous Young’s modulus of
350 MPa for the bone structures was used.
The sensitivity analysis of the maximum FFR with respect to
the load magnitude was performed by calculating the variation in
the maximum FFR while applying variations (2.5% and 25%
change), positive or negative, to the applied load magnitude. The
sensitivity analysis of the maximum FFR to different apparent
density-to-modulus relationships was performed by calculating
the maximum FFR using two alternative relationships, from the
study by Kopperdahl and Keaveny (1998) and by Morgan et al.
(2003), with all other model parameters kept the same (Table 5).
The sensitivity of the maximum FFR with respect to the
constitutive model for the subsidence risk assessment was
investigated by additionally calculating the maximum FFR
with a linear constitutive model and a symmetric post-yield
behaviour for the bone structures with all other model inputs
equal. The sensitivity studies were conducted for patient 2 with
the ACD in titanium and the AMCD of patient 6 in PEEK.
Percentage differences were calculated compared to the base
model, and the maximum percentage differences were
reported. In our previous study, mechanical tests were
conducted, and the computer model was subsequently
FIGURE 3
Material models for implant materials and bone. (A) The yield and ultimate strain were assumed to be 0.7% and 10% (Nikiel et al., 2021) for titanium
and 1.3% and 45% for PEEK (Zhao et al., 2020), respectively. (B) For the bone elements, a tension yield strain εT
yof 0.73% and a compressive yield strain εC
y
of −1.04% were assumed (Bayraktar et al., 2004). After reaching the yield point, a post-yield modulus (Ep) of 5% of element’s elastic Young’s modulus (E)
was observed (Bayraktar et al., 2004). Subsidence risk was quantified using a maximum principal strain limit of 1.5% and a minimum principal strain
limit of −2.0% (Soyka et al., 2016) (Figure is not to scale).
TABLE 3 Definition of the question of interest (QoI) and the context of use (CoU).
QoI Do the new AMCDs reduce subsidence risk compared to ACDs and OTS implants?
CoU A patient-specific FE model (Section 2.3) will be used to quantify the subsidence risk under a hyper-physiological loading condition. The patient-
specific FE models are built using clinical CT scans including the FSU of interest. The subsidence risk assessment (Section 2.4) provides anestimate, for
a given patient and implant, of the factor of fracture risk (FFR). The resulting maximum FFR is used as a surrogate for subsidence risk and as an
outcome variable in a comparative study. Bench tests were performed to test the implant integrity and provide validation of the FE model (Smit et al.,
2024)(Smit, 2023). In a clinical setting, the surgeon would use the outcome of a patient-specific comparative study, together with other available
information, his/her judgement and experience, in the treatment planning.
TABLE 4 Model risk summary for this study following example 6 in ASME V&V40–2018.
Context of use Model influence Decision consequence Model risk
Patient-specific FE model used to assess the subsidence risk of an implant (Table 3) MEDIUM LOW LOW
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validated against them (Smit et al., 2024)(Smit, 2023).Amorein-
depth explanation of the credibility factors is provided in the
work by Viceconti et al. (2016) and Aldieri et al. (2023).
2.6 Statistical analysis
For statistical analysis, Spearman’s rank correlation coefficient
analysis was used to calculate the correlation coefficient rwith (−1<
r<1) between two variables. A Mann–Whitney Utest was used to
compare two samples with statistical significance assumed when p<
0.05. The small sample size in this study does not allow for reliable
normality testing (Taylor, 2017); therefore, statistical methods were
selected that allow for non-normally distributed data and are robust
on small datasets, e.g., the median was reported. SciPy version 1.11.1
(Virtanen et al., 2020) and Seaborn version 0.11.2 (Waskom, 2021)
were used to implement the statistical methods and data
visualisations.
3 Results
3.1 Optimised cages
The resulting AMCDs show a “box-like”design and are hollow
in the inside with patient-specific internal strut structures, similar as
found by Smit et al. (2024) and (Smit, 2023). The outside shape
conforms to the endplate shapes of the vertebrae. The designs satisfy
all the constraints and reached a discreteness parameter lower than
3%. The morphological details of the AMCDs are listed in Table 6.
The porosity and mean pore size diameter are very similar for the
titanium and PEEK implants, the reason being that the local volume
constraint, which controls the porosity and pore size distribution, is
an active constraint. Nevertheless, the internal structures and the
exact location of the pores are patient-specific. The fact that the local
volume constraint is effective in controlling the implant
morphology, independent of other constraints, enables it to tune
the porous internal structure of the implant to be favourable for
bone in-growth.
3.2 Subsidence risk assessment
Figure 4 highlights elements with FFR larger than 1, which
indicates mechanical overloading, for patient 1 for all three implant
types. The red elements are associated with the titanium implant and
the green elements with the PEEK implant. Figure 4 shows that the
titanium implant leads to a higher volume of overloaded elements
than the PEEK implant material by 15%, 5%, and 300%, for the OTS
cage, ACD, and AMCD, respectively. Furthermore, the two separate
concentrations in the superior vertebra compared to the evenly
distributed overloaded elements in the lower vertebra are explained
by the contact areas between the endplate and the OTS cage
(Figure 4A). The ACD and AMCD were endplate conforming
and show that the regions of overloaded elements were reduced
(Figures 4B, C).
The subsidence risk assessment provided the maximum FFR
data for the three implant groups in PEEK and titanium implant
materials for all patients (Figure 5A). In general, the subsidence risk
for ACDs was reduced, compared to the OTS cages, and the
subsidence risk for AMCDs was reduced, compared to the ACD,
for all patients.
Comparison of the maximum FFR results between PEEK and
titanium implant materials, for the three implant types, showed that
there was no statistical difference between the PEEK and titanium
TABLE 5 Apparent density-to-Young’s modulus relationships used in
sensitivity study with Ouyang et al. as baseline.
Density-to-Young’s modulus relationships
Ouyang et al. (1997) (baseline) E2383ρapp 1.88
Kopperdahl and Keaveny (1998) E2100ρapp −80
Morgan et al. (2003) E4730ρapp1.56
TABLE 6 Mean +/−standard deviation of porosity and pore diameter for
AMCDs.
Titanium implant PEEK implant
Porosity 58.47% ± 1.1% 59.44% ± 1.5%
Mean pore diameter 5.01 mm ± 0.54 mm 4.88 mm ± 0.43 mm
FIGURE 4
Elements with FFR >1 are highlighted with green for PEEK implant
material and red for titanium implant material. (A) OTS model. (B) ACD
model. (C) AMCD model. Data from patient 1.
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groups with p-values of 0.71, 0.95, and 0.53 for the OTS, ACD and
AMCD implant types, respectively. The negative correlations
between the maximum FFR and vBMD for the different implant
types are given in Figure 5A. As an illustration, the linear
correlations between the maximum FFR and vBMD indicate that,
for a patient with a mean vBMD of 0.25 g/cm
3
, the maximum FFR
values would be 14.8, 3.8, and 2.0 for the OTS cage, ACD, and
AMCD, respectively.
A comparison of the implant type and implant materials is given
in Figure 5B. This shows that the median maximum FFR reduction
between the OTS PEEK to AMCD PEEK, OTS Ti to AMCD Ti, and
ACD PEEK to AMCD PEEK is statistically significant with 94%,
89%, and 75%, respectively. The reduction in the maximum FFR for
the OTS cage to the ACD, ACD to AMCD, and OTS cage to AMCD
is not strongly significantly correlated with vBMD, with p-values of
0.18, 0.07, and 0.09 for the PEEK implant material and 0.12, 0.15,
and 0.09 for titanium, respectively.
3.3 Computer model credibility assessment
An element edge length of 1.5 mm was chosen for the bone
structures because subsequent decreases in element edge length
produced percentage differences in the maximum FFR lower
than the 5% threshold (Figure 6A). For the implant structures,
an element edge length of 0.5 mm was chosen, and the mesh
FIGURE 5
Results summarised: (A) Relationships between the maximum FFR and vBMD for the three implant groups. (B) Statistical significance of the reduction
between different groups formed by the implant type and implant material.
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convergence study indicated that variations had little influence on
the maximum FFR (Figure 6B).
Table 7 shows the results of the sensitivity studies. The
sensitivity of the maximum FFR with respect to variations in
load magnitude, different density-to-Young’s modulus
relationships, and different constitutive models is illustrated by
reporting the maximum percentage difference derivation from
the base case. Patient 2 is loaded in the linear loading regime
and shows little variation in the maximum FFR for the applied
variations. On the other hand, patient 6 shows a larger variation in
the maximum FFR because this patient is loaded in the non-linear
loading regime.
The credibility factors were assessed after the outputs of the
verification and validation (V&V) activities were obtained. The
robustness of the activities and level of rigour were evaluated
according to the guidelines and examples from the ASME
V&V40–2018 standard. This assessment is summarised in
columns “Rigour selected”and “Achieved credibility”in Table 8.
The quantities of interest considered in the verification and
validation study were the maximum FFR and the
force–displacement curve in the mechanical tests. Therefore, we
consider the quantities of interest relevant but not identical since the
maximum FFR cannot be calculated directly in mechanical testing of
samples. In the validation study, the range of applied forces is
physiological and, therefore, deemed relevant for the CoU. The
mechanical tests did not include the bone structures; therefore,
partial overlap between the validation and CoU is concluded.
4 Discussion
The aim of this study was to perform in silico medical device
testing of AMCDs, which were designed and optimised by our
recently developed full-scale TO strategy, and compare the
subsidence risk to OTS cages and ACDs. We performed the
study on seven patient datasets using titanium and PEEK
implant materials. We hypothesised that AMCDs would reduce
subsidence risk over OTS cages and ACDs. We found that AMCDs
reduce the subsidence risk compared to OTS cages and ACDs and
that the median reduction is statistically significant for OTS PEEK
compared to AMCD PEEK, OTS Ti to AMCD Ti, and ACD PEEK to
AMCD PEEK (Figure 5B). Similar results were published by
Chatham et al., who compared a custom-shaped cage with a
standard cage and found a significant reduction in stresses at the
bone–implant interface (Chatham et al., 2017); however, they did
not explore mechanically conforming devices.
Furthermore, we hypothesised that PEEK cages would have
lower subsidence risk than titanium cages; however, our data did not
show this to be the case. Other research studies confirm this
observation and conclude that the implant geometry has a larger
influence on subsidence risk than the implant material (Ferguson
et al., 2006;Chatham et al., 2017;Suh et al., 2017). However,
Carpenter et al.concluded in a computational study that PEEK
interbody cages produce strain states in the adjacent vertebra that
favour bone in-growth compared to titanium cages (Carpenter
et al., 2018).
Lastly, we hypothesised that there is a negative correlation
between subsidence risk, represented by the maximum FFR, and
bone quality. We found that this negative correlation exists and is
statistically significant for all three cage types (Figure 5A). This
finding is in line with that of the previous literature (Jost et al., 1998;
Schreiber et al., 2014;Tempel et al., 2015;Soliman et al., 2022). For
example, Tempel et al.concluded that the rate of subsidence
FIGURE 6
Results from the mesh convergence study. The maximum FFR value is indicated by the blue line, the percentage difference is indicated by the green
bars, and the 5% threshold is indicated by the black line. (A) Mesh convergence results for bone structures in the subsidence risk assessment. (B) Mesh
convergence results of implant structures in the subsidence risk assessment.
TABLE 7 Overview of the sensitivity study. The maximum percentage
difference deviation from the base case is reported. Variation load
magnitude: sensitivity of the maximum FFR with respect to the variation in
the load magnitude. Relationships: sensitivity of the maximum FFR
regarding different density-to-Young’s modulus relationships. Constitutive
model: sensitivity of the maximum FFR with respect to the constitutive
model.
Patient 26
Implant type ACD AMCD
Material Titanium PEEK
Variation load magnitude with 2.5% 0.2% 17.9%
Variation load magnitude with 25% 1.5% 76.5%
Density-to-Young’s modulus relationships −0.8% −0.1%
Constitutive models 0.0% 108%
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following lateral lumbar interbody fusion (LLIF) is negatively related
to BMD, and patients diagnosed with osteopenia (DXA T-score
of −1.0 or less) are at an increased risk of subsidence and revision
surgery. Soliman et al.showed a higher vertebral bone quality score
(a bone quality score derived from magnetic resonance imaging)
that was significantly associated with an increased risk of subsidence.
We investigated how effective the optimisation method is in
reducing the subsidence risk for patients with different bone
densities; however, no significant correlation was found between
the reduction for the maximum FFR and vBMD, suggesting that the
effectiveness of the method is not strongly related to the bone quality
of the patient. A possible explanation is the phenomena of sclerosis
or thickening of the bony endplate in combination with degenerative
disc disease (Velnar and Gradisnik, 2023), (Fields et al., 2018).
Polikeit et al.reported that a thickening of the endplate can shift the
load to the endplate, away from the vertebral body, reducing the
influence of vertebral vBMD (Polikeit et al., 2003).
Performing credibility activities enhances the understanding of
the behaviour of the computer model to assess the subsidence risk.
First, looking at the results for patient 2, the influence of the applied
variations had only a minor influence on the maximum FFR
(Table 7). This is important to know because the load that is
applied per patient in the present study is indirectly selected
through the weight of the patient and from a small dataset, and
therefore, small variations are likely compared to the in vivo
population-wide situation. The risk exists that the loads are
underestimated and lead to a significantly different AMCD
design, resulting in an underperforming implant. However, the
risk of implant failure is low since titanium implants are strong
compared to the loads they are subjected to in vivo. Looking at
patient 6, we observe a larger variation in the maximum FFR. The
reason is that this patient has relatively low bone quality. Therefore,
patient 6 is loaded in the non-linear loading regime, explaining the
variability. The constitutive model variation is shown to result in a
small influence when the model is operated in the linear regime.
When the model is operated in the non-linear regime, we see a large
influence on the maximum FFR, as is the case for patient 6. This
confirms the choice for a non-linear material model for the
subsidence risk assessment. The variations in the maximum FFR
by changing the density-to-Young’s modulus relationships are small
for both patients 2 and 6, and the relationship that is used in this
study is the worst case.
As in silico trials are increasingly used in research, the authors
found it useful to include extensive V&V activities according to the
ASME V&V40–2018 standard (The American Society of
Mechanical Engineers ASME, 2018). Although the standard was
followed as much as possible in our assessment of model credibility,
a certain degree of interpretation is involved in selecting the
credibility activities and judging the rigour and the achieved
credibility. We established the credibility of the model through
an assessment that involved evaluating the relevance of validation
activities and results in connection with the quantities of interest and
predefined CoU (Tables 3,8). Based on a review of the CoU, the
model risk, the credibility activities, and results, the computer model
for subsidence risk assessments is deemed sufficiently credible for
the CoU. Compared to the credibility assessment by Aldieri et al.
(2023), this study included less extensive mesh convergence and
sensitivities studies but a similar degree of validation using
mechanical test data with the exception of the use of human
cadaveric material. This corresponds to the difference in the
defined model risk, medium versus low for this study. Viceconti
et al. (2021) specifically pointed out that a newly developed in silico
computer model might be deemed credible for a CoU but has
minimal clinical applicability because the clinical environment,
where the computer model is intended to be used, is
misunderstood. Therefore, they recommend that authors,
reviewers, and editors should, at least, include the basic activities
from the categories, namely, verification, validation, and uncertainty
quantification, in any publication that includes
mechanistic modelling.
TABLE 8 Outcome of credibility assessment. Overview of the selected credibility activities according to The American Society of Mechanical (2018) in the
first column. The number of the corresponding paragraph numbers within the ASME V&V40–2018 standard is reported in brackets. The classification in the
“Rigour selected”column comes from the ASME V&V Standard. The last column refers to the credibility level that is achieved.
Activity categories Credibility factor Rigour
selected
Achieved
credibility
Verification Code (5.1.1) Referring to Dassault’s quality system b Medium
Calculation (5.1.2.1) Mesh convergence of the bone domain b Medium
Mesh convergence of the implant domain b Medium
Sensitivity of the maximum FFR to magnitude of load b Medium
Validation Computational model (5.2.1.2.1) Sensitivity of the maximum FFR of different density
relationships
b Medium
Sensitivity of the maximum FFR to constitutive model b Medium
Comparator (5.2.2.1 + 5.2.2.2) Bench test validation was provided by Smit et al. (2024) and
Smit (2023)
b-c-b-b-b-a-a-a-b Medium
Assessment (5.2.3) Assessment of the rigour and achieved credibility b-b-b-c-c High
Applicability Relevance to the quantity of
interest (5.3.1)
Section 3.3 a Low
Relevance to CoU (5.3.2) Section 3.3 b Medium
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A limitation in this study was the use of continuum modelling
and the surrogate measure, the maximum FFR, as a representation
of subsidence risk. Using continuum models, in the worst case, could
result in sub-optimal cage designs; however, several studies did show
that continuum models can accurately represent the mechanical
response of the trabecular structures (Verhulp et al., 2006;Eswaran
et al., 2009;Enns-Bray et al., 2018). Additionally, the vertebra
endplates distribute the loads that are applied on the cage and
reduce the influence of the continuum modelling assumption. The
FFR is a measure based on principal strains that is valid across a
range of bone densities (trabecular and cortical bone). Several
authors have adopted and validated principal strain-based
fracture criteria (Soyka et al., 2016)(Schileo et al., 2008)
(Helgason et al., 2009). On the other hand, stress-based fracture
criteria are often adopted in Molinari et al. (2021). Subsidence is a
predictor of revision surgery (Tempel et al., 2018)(Campbell et al.,
2020); however, the accuracy of the maximum FFR to predict
subsidence and/or revision surgery should be investigated in
future research, e.g., in a retrospective study. A retrospective
study can be performed with the combination of pre-operative
CT scans, post-operative radiographic information on implant
placement, and post-operative subsidence information.
Longitudinal information would provide a more direct link
between the maximum FFR and clinical outcomes. A second
limitation was that the credibility activities according to the
ASME V&V40–2018 standard likely need to be extended when
the subsidence risk assessment would be used in a regulatory filing
by including additional code verification activities, e.g., sensitivity
studies on solver parameters, and comparator validations.
Furthermore, the effect of cage height on the design was not
studied separately and should be addressed in future work. A
third limitation pertains to the stability or stiffness of the
bone–implant system, which is not specifically quantified in this
study. The stiffness of the bone–implant system is important since
achieving stability or stiffness of the bone–implant system is the
primary goal of a fusion surgery. A final limitation is the small
sample size and the single source of the CT scan data. In the future, a
larger sample size should be included to obtain a better
understanding of the effectiveness of the method.
5 Conclusion
In this in silico medical device testing study, we demonstrated
that anatomically and mechanically conforming devices achieved a
median reduction in subsidence risk by 89% for titanium and 94%
for PEEK, compared to off-the-shelf implants. Comparing an
anatomically and mechanically conforming cage to an
anatomically conforming cage, a median reduction of 75% is
achieved for PEEK implant material through additional
mechanical optimisation. We could not show a significant
dependency between the achieved reduction and bone quality. A
credibility assessment of the in silico medical device testing
procedure to assess subsidence risk was performed according to
ASME V&V40–2018, and the subsidence risk assessment was
deemed sufficiently credible for the context of use.
Data availability statement
The datasets presented in this study can be found in online
repositories. The names of the repository/repositories and accession
number(s) can be found at: https://github.com/thsmit/TopOpt_in_
PETSc_wrapped_in_Python.
Ethics statement
Written informed consent was obtained from the individual(s)
for the publication of any potentially identifiable images or data
included in this article.
Author contributions
TS: writing–original draft, visualisation, validation,
methodology, investigation, and conceptualisation. NA:
writing–review and editing and methodology. DH: writing–review
and editing, resources, and conceptualisation. SF: writing–review
and editing, supervision, and funding acquisition. BH:
writing–review and editing, supervision, methodology,
investigation, and conceptualisation.
Funding
The author(s) declare that financial support was received for
the research, authorship, and/or publication of this article. This
project received funding from the European Union’s Horizon
2020 research and innovation programme under the Marie
Sklodowska-Curie Grant Agreement No. 812765. Open access
funding by ETH Zurich.
Acknowledgments
The authors thank Dave O’Riordan (Schulthess Klinik, Zürich)
for his efforts to provide the CT data.
Conflict of interest
The authors declare that they have filed a patent application
based on the topology optimization method that is used in this work.
Publisher’s note
All claims expressed in this article are solely those of the authors
and do not necessarily represent those of their affiliated
organizations, or those of the publisher, the editors, and the
reviewers. Any product that may be evaluated in this article, or
claim that may be made by its manufacturer, is not guaranteed or
endorsed by the publisher.
Frontiers in Bioengineering and Biotechnology frontiersin.org11
Smit et al. 10.3389/fbioe.2024.1347961
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