## Abstract

Biomechanical testing of long bones can be susceptible to errors and uncertainty due to malalignment of specimens with respect to the mechanical axis of the test frame. To solve this problem, we designed a novel, customizable alignment and potting fixture for long bone testing. The fixture consists of three-dimensional-printed components modeled from specimen-specific computed tomography (CT) scans to achieve a predetermined specimen alignment. We demonstrated the functionality of this fixture by comparing benchtop torsional test results to specimen-matched finite element models and found a strong correlation (R2 = 0.95, p < 0.001). Additional computational models were used to estimate the impact of malalignment on mechanical behavior in both torsion and axial compression. Results confirmed that torsion testing is relatively robust to alignment artifacts, with absolute percent errors less than 8% in all malalignment scenarios. In contrast, axial testing was highly sensitive to setup errors, experiencing absolute percent errors up to 50% with off-center malalignment and up to 170% with angular malalignment. This suggests that whenever appropriate, torsion tests should be used preferentially as a summary mechanical measure. When more challenging modes of loading are required, pretest clinical-resolution CT scanning can be effectively used to create potting fixtures that allow for precise preplanned specimen alignment. This may be particularly important for more sensitive biomechanical tests (e.g., axial compressive tests) that may be needed for industrial applications, such as orthopedic implant design.

## 1 Introduction

Benchtop cadaveric biomechanical testing is the gold standard for evaluating both the mechanical properties of bone and the performance of orthopedic implants. However, the bony geometries and mechanical properties of cadaveric specimens have inherent variability, which often limits the statistical power of findings and requires large sample sizes [1]. This issue can be readily circumvented with the use of synthetic bone models, but these surrogates are not always appropriate (e.g., modeling the mechanical behavior of cadaveric osteoporotic bone [13]). In these instances, cadaveric specimens still provide the best representation of the clinical experience, but best practices for minimizing variability in mechanical testing methods have been slow to emerge. In a recent literature review on experimental approaches to measure bone stiffness via compression testing, Zhao et al. found that all aspects of experimental protocols were variable, particularly the testing configuration [4].

Currently, there are no available standards for implementing repeatable specimen alignment protocols to determine the mechanical properties of long bones. The lack of a universally accepted approach is in part due to the difficulties associated with testing cadaveric bones. Challenges include the heterogeneity of specimen cohorts, residual soft tissue interfaces between the bone and test fixture, and in some instances, the low forces required to avoid specimen damage [4]. In addition, achieving consistent and accurate specimen alignment plays a key role in minimizing errors during biomechanical testing of cadavers [47].

Several animal studies have developed techniques and fixtures to ensure the repeatability and accuracy of specimen placement during biomechanical testing. For example, Bell et al. utilized a custom-designed breakaway mold to pot rat femora for mechanical testing of bone-implant anchorage [8]. This device centered the specimen and ensured that loading was directed perpendicular to the implant surface. Cheong et al. used microcomputed tomography (CT) scans of ovine tibiae in conjunction with a semi-automated algorithm to define principal components and subject-specific coordinate systems [9]. This allowed for pure bending and torsion during virtual mechanical testing; however, physical testing was never conducted, nor was the alignment of the virtually defined coordinate system to the machine's loading axis investigated.

To allow for direct comparisons between studies, researchers must conduct a clearly defined test through the use of a standard reference system and an alignment/potting fixture [10,11]. Unfortunately, many studies do not report the specimen alignment/potting protocol in sufficient detail for it to be replicated or assessed appropriately [1214]. Proper alignment is difficult to achieve in practice because cross-sectional profiles of bones are highly variable and there are gradual curvatures along the length of the bone [8]. Typically, alignment is based on identification of anatomical landmarks that define local coordinate systems and reference axes [9,10,15,16]. Sample alignment is performed under visual inspection, but it is challenging to ensure that a specimen's theoretical reference axis is positioned collinear to the test frame mechanical axis and this detail is commonly overlooked [3,14,17,18]. Currently, there are no accepted standards for implementing controlled, repeatable whole-bone specimen alignment [47].

Accordingly, the objective of this study was to utilize medical imaging software and additive manufacturing techniques to design an adaptable, specimen-specific potting fixture capable of creating a repeatable alignment between bone and test frame axes. To achieve this goal, we developed an inexpensive and easy-to-replicate alignment/potting fixture that can be utilized on any long bone. To assess the quantitative impact of specimen malalignment on the results of long-bone mechanical tests, we compared physical and virtual mechanical tests. Our hypothesis was that specimen malalignment would be associated with error in the inferred axial stiffness and torsional rigidity of long bones.

## 2 Methods

### 2.1 Specimens.

Three matched pairs of fresh-frozen cadaveric radii were utilized in this study (one male and two females; age range 83–89 years). All donors had confirmed osteopenia by dual-energy X-ray absorptiometry scanning of the lumbar spine (t-scores: −1.1, −1.4, and −2.0). These specimens showed no evidence of any deformities, pathological abnormalities, or prior surgery.

### 2.2 Finite Element Analysis

#### 2.2.1 CT Scanning Protocol.

Each forearm underwent clinical CT scanning in a Siemens Somatom Definition Edge scanner (Siemens Healthcare GmbH; Erlangen, Germany). An axial slice thickness of 0.5 mm, a pixel size of 0.625 mm, and a peak kilovoltage of 55 kVp were specified for each scan. A hydroxyapatite (HA) bone density calibration phantom (QRM-BDC/6; QRM GmbH) was included in each scan to convert radiodensity $ρHU$ (Hounsfield Unit, HU) to bone mineral density $ρQCT$ (quantitative computed tomography, QCT; mgHA/cm3).

Each CT scan was transferred for postprocessing using the digital imaging communications in medicine (DICOM) format. These DICOM files were imported into Mimics (v21.0; Materialize, Leuven, Belgium), which was used to transform the two-dimensional stacked image data sets into three-dimensional (3D) models (Figs. 1(a) and 1(b)). A predefined segmentation filter for bone (threshold range set to 226+ HU) was used to segment the hard tissue from the surrounding soft tissue (Fig. 1(b)). After the threshold-based segmentation, various other segmentation tools (slice edit, region grow, etc.) were used to isolate the radius in the scan (Fig. 1(c)). Each of the six 18-mm diameter cylindrical inserts in the phantom (0, 100, 200, 400, 600, and 800 mgHA/cm3) were also segmented for later calibration (see Sec. 2.2.4Material Assignment below).

Fig. 1
Fig. 1
Close modal

#### 2.2.3 Virtual Realignment Protocol.

As will be discussed in greater detail in Sec. 2.3Biomechanical Testing, the distal and proximal ends of each cadaveric radius were fixed in a urethane potting material to a depth equal to the widest portion of the distal radius. To replicate this condition in the virtual models, the distal and proximal ends of each radius model were cropped at the same levels. These surfaces were specified for boundary condition application.

Since the physical samples could only be potted once, deliberate malalignment was only introduced into the virtual models. In addition to the aligned configuration, in which the mechanical loading axis is aligned with the model's reference line, six other configurations were simulated: four off-centered configurations and two angular malalignment configuration. These models were configured to evaluate the effect of nonconcentricity (off-centered, but parallel) and angular malalignment between the mechanical axis of the bone and the test frame. The off-centered configuration was created by shifting the radius 10 mm anteriorly (A), posteriorly (P), medially (M), or laterally (L) relative to the mechanical loading axis (Fig. 2(a)). For the angular malalignment configuration, the distal surface was tilted 5 deg away from the reference line in the coronal (M-L angled) or sagittal plane (A-P angled) (Figs. 2(b) and 2(c)).

Fig. 2
Fig. 2
Close modal

#### 2.2.4 Material Assignment.

In CT images, there is a direct association between the local material radiodensity of the scanned object (mgHA/cm3) and the gray value assigned to each voxel [HU]. HU values scale linearly with density but can vary slightly based on the scanner settings used. Therefore, the calibration phantom was used to generate a quantitative calibration conversion equation, Eq. (1), that describes the relationship between radiodensity $ρHU$ [HU] and bone mineral density $ρQCT$ (mgHA/cm3) at the specified scan settings.
$ρQCT=0.8127ρHU+8.518$
(1)
Bone mineral density was then used to infer Young's modulus, $E (MPa)$, using a well-known conversion equation, Eq. (2), that was previously derived for human trabecular bone across multiple anatomic sites (vertebra, proximal tibia, greater trochanter, and femoral neck) [23]
$E=8.92*ρQCT1.83$
(2)

This material model was selected because the donors had documented osteopenia, which causes trabecularization of cortical bone [24,25]. These material assignment relationships, along with a Poisson's ratio of 0.3, were applied to all of the elements within each model using Mimics (Fig. 1(d)) [26].

#### 2.2.5 Meshing and Load Application.

All meshes were generated using 3-Matic (14.0; Materialize, Leuven, Belgium) and finite element analysis was executed using ANSYS Workbench Mechanical (ANSYS, Inc., Canonsburg, PA). In all models, the anatomic proximal cropped surface (elbow) was fixed. Physical tests were conducted with the radii in an inverted orientation, so in all models, the anatomic proximal surface was positioned below the anatomic distal surface (elbow below wrist). For the virtual torsion test, a 5-deg angular remote displacement about the axial reference line was applied to the anatomic distal cropped surface. A remote displacement was used to ensure that the angular displacement was applied about the reference axis (i.e., mechanical axis of the machine) and not the centroid of the anatomic distal cropped surface. For the virtual axial test, a compressive force of 250 N was applied at the anatomic distal cropped surface using a remote force boundary condition to ensure that the load was being applied through the reference axis. This load range was selected based on the forces that the articular radial surface experiences during light active motion [2731]. The maximum displacement [mm] and moment reaction (N-mm) along the z-axis were recorded.

A mesh convergence study was performed to ensure that the key outcome measure used for comparison to physical torsion testing (calculated moment reaction) would not be affected by changing the size of the mesh. The mesh size was reduced until the result showed less than one percent difference in the moment reaction from the previous tested mesh size. As a result, a quadratic tetrahedral element type with a maximum edge length of 0.75 mm was used (Fig. 1(d)). The models had a median of 1.05 × 106 elements.

### 2.3 Biomechanical Testing

#### 2.3.1 Alignment/Potting Fixture.

Custom 3D-printed alignment/potting fixtures were built to ensure precise alignment of each radius with the mechanical axis of the test frame. The alignment fixture contained a modular two-piece insert printed with polylactic acid (Micromake Kossel Delta 3D, Shandong, China), where the cavity created by the assembled insert matched the mid-diaphyseal region of each specimen (Figs. 3(a)3(c)). An outer universal sleeve was printed in Onyx (Mark II, Markforged Inc., MA) and similarly assembled to secure the insert (Fig. 3(d)). Once fully assembled, motion of the aligned bone was restricted to sliding on vertical stainless-steel rods, which were secured in an Onyx baseplate (Fig. 3(e)). All 3D rendered parts were designed in SolidWorks 2018 (Dassault Systemes SolidWorks Corps., MA). A detailed list of the 3D-printed parts and the fastening hardware can be found in the bill of materials in Digital Content I available in the Supplemental Materials on the ASME Digital Collection. A SolidWorks “Pack and Go” file containing the reference files needed to rebuild the assembly can be found in Digital Content II available in the Supplemental Materials on the ASME Digital Collection.

Fig. 3
Fig. 3
Close modal

#### 2.3.2 Specimen Preparation for Mechanical Testing.

On the day of testing, specimens were thawed and all soft tissue was carefully removed. Specimens were wrapped in saline-soaked gauze, vacuum sealed, and refrigerated at 4 °C while awaiting testing. Freezing and thawing prior to mechanical testing has been shown to have a negligible effect on bone stiffness [4]. Anterior–posterior and medial-lateral radiographs were obtained (SireMobil, Siemens, Munich, Germany). Proximal and distal epiphyses of each specimen were potted in urethane (Master Dyna-Cast, Freeman Manufacturing and Supply, Mount Joy, PA) using the alignment/potting fixture as described in Sec. 2.3.1 Alignment/Potting Fixture. The potting depth was equal to the widest portion of the distal end, which was predetermined in the virtual environment for each bone. The depth was marked on the physical specimen using a set of digital calipers and an ink pen.

Fig. 4
Fig. 4
Close modal

### 2.4 Data Processing and Statistics

#### 2.4.1 Biomechanical Testing.

All mechanical testing data were processed in matlab (R2016a; The MathWorks, Inc., MA). The total torsional stiffness ($k$) was calculated by averaging the slope of the linear portion of the torque versus angular displacement curve for the final five cycles in rotation. To account for the effects of the inherent stiffness of the test fixture, a test fixture compliance correction was applied. The fixture was tested in isolation to determine its stiffness in torsion ($kf$). Then, the specimen stiffness ($ks$) was calculated using a series spring assumption, as shown in Eq. (3)
$1k=1kf+1ks$
(3)

Specimen torsional stiffness, $ks$, was then converted to torsional rigidity, $KT$, by multiplying by the specimen gauge length: $KT=ksL$.

#### 2.4.2 Finite Element Model Analysis.

Virtual torsional rigidity ($KVT$) was calculated in the finite element models as follows:
$KVT=MLϕ$
(4)
where M is the z-direction moment reaction about the long axis, L is the specimen gauge length, and $ϕ$ is the angle of twist. Simulated axial tests were also performed. Virtual axial stiffness ($kVA$) was defined as
$kVA=Fδ$
(5)

where $F$ is the compressive load applied and $δ$ is the maximum total displacement in the model.

#### 2.4.3 Statistical Analysis.

All statistical analyses were performed in spss (v.24; IBM Corp., Armonk, NY). Pearson's correlations were used to assess associations between variables. Deviations from normality were assessed using Shapiro-Wilk testing. Between-groups comparisons of aligned versus malaligned configurations in the finite element models were assessed using nonparametric Friedman tests. Post hoc pairwise comparisons were performed with a Bonferroni correction for multiple comparisons. Statistical significance was determined at an alpha of 0.05.

## 3 Results

### 3.1 Physical/Virtual Specimen Alignment and Torsional Rigidity.

Initial verification of axis alignment between benchtop and virtual models was confirmed by superimposition of radiographs and model renderings (Fig. 5). Renderings of the virtual models, as viewed through the front and right planes in solidworks, were superimposed over the radiographs to align the global coordinate systems (z-axis on center with the alignment fixture). Without any manipulation of either image, the profile of the virtual models matched the profile of the corresponding radiograph of the clamped specimen, thus confirming that the fixture maintained the alignment that was created virtually. Excellent alignment registration was observed between the physical and virtual models in both views. For each donor, right-left radius pairs had similar torsional rigidities. The two female donors had a measured torsional rigidity 3.3 times lower than the male donor (specimens 2 and 3 versus 1; see Table 1).

Fig. 5
Fig. 5
Close modal
Table 1

Comparison of physical and virtual torsion test results for all cadaveric specimens and their corresponding virtual models with ideal alignment

Torsional rigidity (Nm2/deg)
SpecimenGage length (mm)Physical, KTVirtual, KVT
1 L181.50.2460.357
1R182.50.2370.352
2 L164.50.0790.089
2R167.00.0730.080
3 L180.50.0740.084
3R181.00.0630.075
Torsional rigidity (Nm2/deg)
SpecimenGage length (mm)Physical, KTVirtual, KVT
1 L181.50.2460.357
1R182.50.2370.352
2 L164.50.0790.089
2R167.00.0730.080
3 L180.50.0740.084
3R181.00.0630.075

The physical torsional rigidity values, $KT$, compared favorably with the predicted virtual torsional rigidity values, $KVT$, from the finite element models. A strong and statistically significant correlation between the physical torsional test results and virtual torsional test results was observed (R2 = 0.9536, p < 0.001). Relative error between the physical and virtual torsional rigidities was highest for the male donor.

### 3.2 Malalignment Sensitivity Study

#### 3.2.1 Virtual Torsional Rigidity.

The mean and standard deviation results for virtual torsional rigidity in all configurations are shown in Table 2. For the virtual torsion test, the absolute percent error in the inferred torsional rigidity for the four off-centered configurations relative to the perfectly aligned configuration is shown in Fig. 6 for each specimen. In all donors, the largest percent errors occurred when specimens were positioned off-centered by 10 mm in the anterior and medial directions, but these errors were less than 4% in all cases. The mean and standard deviation of the absolute percent errors in inferred rigidity in the four off-centered configurations (anterior, posterior, medial, and lateral) were 2.2% ± 2.5%, 0.7% ± 0.4%, 1.8% ± 2.2%, and 0.2% ± 0.3%, respectively. Overall, there were significant differences in $KVT$ associated with alignment, $X2$(4) = 10.953, p =0.027, but post hoc analysis revealed no significant individual pairwise comparisons between alignment groups after Bonferroni correction of the p values.

Fig. 6
Fig. 6
Close modal
Table 2

Mean and standard deviation results for the virtual torsional rigidity and virtual axial stiffness for all configurations including the significant individual pairwise comparisons between groups

Virtual test configurationVirtual axial stiffness (N/mm)Significant differenceVirtual torsional rigidity (Nm2/deg)Significant difference
Aligned1731 ± 833**,††,†††0.171 ± 0.138*
Anterior (off-centered)1198 ± 6330.176 ± 0.141
Lateral (off-centered)1953 ± 1087***,†0.172 ± 0.138
Posterior (off-centered)1872 ± 1085*0.172 ± 0.138
Medial (off-centered)1073 ± 598*,**,***0.176 ± 0.142
A-P Angled1633 ± 872††0.163 ± 0.135*
M-L Angled1575 ± 715†††0.160 ± 0.135
Virtual test configurationVirtual axial stiffness (N/mm)Significant differenceVirtual torsional rigidity (Nm2/deg)Significant difference
Aligned1731 ± 833**,††,†††0.171 ± 0.138*
Anterior (off-centered)1198 ± 6330.176 ± 0.141
Lateral (off-centered)1953 ± 1087***,†0.172 ± 0.138
Posterior (off-centered)1872 ± 1085*0.172 ± 0.138
Medial (off-centered)1073 ± 598*,**,***0.176 ± 0.142
A-P Angled1633 ± 872††0.163 ± 0.135*
M-L Angled1575 ± 715†††0.160 ± 0.135
a

*, **, ***, †, ††, ††† significant pairwise comparisons.

The absolute percent error in the inferred torsional rigidity for the angular malaligned cases relative to the aligned configuration is shown in Fig. 7(a) for each specimen. Errors were similar for rotations occurring in the coronal and sagittal planes. The mean and standard deviation of the absolute percent errors in inferred rigidity in the two angular malalignment configurations (coronal and sagittal) were 6.2% ± 2.7% and 8.0% ± 3.2%, respectively. Overall, there were significant differences in $KVT$ associated with alignment, $X2$(2) = 10.333, p =0.006. Posthoc analysis revealed a significant individual pairwise comparison between the sagittal and aligned groups (adjusted significance p =0.004).

Fig. 7
Fig. 7
Close modal

#### 3.2.2 Virtual Axial Stiffness.

The mean and standard deviation results for virtual axial stiffness in all configurations are shown in Table 2. For the simulated axial compression test, the absolute percent error in the inferred stiffness for the four off-centered configurations relative to the perfectly aligned configuration is shown in Fig. 6 for each specimen. Overall, the malalignment-induced percentage errors were an order of magnitude higher in axial compression testing than in torsional testing. As before, in all donors, the largest percent errors occurred when specimens were positioned off-centered in the anterior and medial directions. The mean and standard deviation of the absolute percent errors in inferred stiffness in the four off-centered configurations (anterior, posterior, medial, and lateral) were 32.5% ± 5.3%, 3.5% ±17.6%, 40.2% ± 6.4%, and 9.4% ± 15.2% , respectively. Overall, there were significant differences in axial stiffness associated with alignment, $X2$(4) = 20.800, p <0.001. Posthoc analysis revealed multiple significant individual pairwise comparisons, including medial-posterior, medial-aligned, medial-lateral, and anterior-lateral (adjusted significances p 0.035).

The absolute percent error in the inferred axial stiffness for the angular malalignment cases relative to the aligned configuration is shown in Fig. 7(b) for each specimen. Errors were similar for rotations occurring in the coronal and sagittal planes. The mean and standard deviation of the absolute percent errors in inferred stiffness in the two angular malalignment configurations (coronal and sagittal) were 129.1% ± 24.7% and 127.4% ± 17.5%, respectively. Overall, there were significant differences in axial stiffness associated with alignment, $X2$(2) = 9.000, p =0.011. Posthoc analysis revealed two significant individual pairwise comparisons between both angular malalignment cases and the aligned group (adjusted significances p 0.028).

## 4 Discussion

The results from this study confirmed our hypothesis that specimen malalignment is associated with error in biomechanical testing. In particular, we found that axial stiffness measures were very sensitive to malalignments between the specimen mechanical axis and the test frame axis, with average absolute errors up to 129%. Errors were highest when the offset produced bending in the same direction as the natural curvature of the radius. In contrast, torsional rigidity measures were more robust to deviations from ideal alignment, with errors <4% due to off-center malalignment and <15% due to angular malalignment. Our findings are consistent with previous reports that have emphasized the importance of achieving repeatable alignment of test samples in biomechanical testing. Cristofolini and Viceconti (2000) applied the anatomic reference system proposed by Ruff and Hayes (1983) to align cadaveric and composite tibiae for mechanical testing, but found that achieving ideal alignment was difficult in practice, with significant potential for error particularly in axial loading [3,16]. Even when each specimen was marked by a robust and consistent reference system, ensuring that this reference system was aligned with the test frame loading axis proved difficult. This suggests that whenever appropriate, torsion tests should be used preferentially as a summary mechanical measure, or as a supplement to axial compressive tests.

Limitations of this study include the small sample size of cadaveric specimens (only three donors) and limited available physical test data (torsion only) for comparison between physical and virtual tests. The virtual models are further limited by the use of a material assignment law that is not specific to mixed cortical/cancellous bone. Numerous scaling relations for radiodensity and Young's modulus are available in the literature for different species, anatomic sites, and bone types [37]. We chose Eq. (2) after evaluating the performance of three candidate scaling equations, one for human cortical bone, one for human trabecular bone, and one for nonosteoporotic human radii (Digital Content III available in the Supplemental Materials on the ASME Digital Collection) [23,38,39]. The nonosteoporotic human radii law overpredicted the rigidity of our radii, which we attribute to the structural and mechanical changes known to occur in osteopenic cortical bone [38]. Conversely, the cortical bone law underpredicted the rigidity for these low density, osteopenic bones [39]. The pooled trabecular law we ultimately chose, although not derived for osteopenic radii, showed very close correspondence between physical and virtual tests for the two female donors [23]. The larger error between the physical and virtual tests for the male donor was likely due to the less-advanced progression of osteopenic bone degeneration, leading to an underprediction of rigidity with the trabecular material assignment law.

## 5 Conclusions

Specimen malalignment can cause significant errors in biomechanical testing of whole bones. The results from this study highlight the importance of combining a consistent anatomic reference system with the use of a robust alignment protocol and potting fixture. Torsion testing is more robust to alignment artifacts than axial compressive testing, but all loading modes can be improved by ensuring the desired alignment between anatomic reference lines and the test frame. To achieve this optimal alignment, we have designed a customizable specimen alignment and potting fixture that guarantees the desired sample alignment through image-based pretest planning and 3D printing. Use of this method may be particularly important for more sensitive biomechanical tests (e.g., axial compressive tests) that may be needed for industrial applications, such as implant design and construct mechanical testing.

## Acknowledgment

The authors acknowledge Carolyn Persinger and Jaclyn Rissling for their support in obtaining and processing the clinical CT scans and Sarah Kauzmann for assistance with graphical design in Fig. 4.

## Funding Data

• National Science Foundation (Grant No. CMMI-1943287; Funder ID: 10.13039/100000001).

## Nomenclature

• CT =

computed tomography

•
• DICOM =

digital imaging communications in medicine

•
• E =

Young's modulus

•
• F =

•
• HA =

hydroxyapatite

•
• HU =

Hounsfield unit

•
• $k =$ =

total torsional stiffness

•
• $kf$ =

fixture torsional stiffness

•
• $ks$ =

specimen torsional stiffness

•
• $KT$ =

torsional rigidity

•
• $kVA$ =

axial stiffness

•
• $KVT$ =

virtual torsional rigidity

•
• L =

specimen gauge length

•
• M =

z-direction moment reaction

•
• QCT =

quantitative computed tomography

•
• $δ$ =

maximum total displacement

•
• $ϕ$ =

angle of twist

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