CT-based finite element modeling of a porcine femur: specimen-specific HU–modulus fitting and experimental displacement comparison

Finite element (FE) models have significantly advanced bioengineering by enabling the characterization of biological tissues, assessment of mechanical responses to loading, and development of prosthetic and biomedical applications. Porcine bone provides a relevant experimental model because of its similarities to human bone tissue. This study investigated the mechanical response of porcine femoral bone by comparing experimental compression data with finite element models derived from medical imaging. Computed tomography (CT) scans of a porcine femur were segmented to generate FE models with element-wise, piecewise-constant inhomogeneous isotropic material properties assigned from local Hounsfield Unit (HU) averages. Axial compression tests provided experimental load–displacement data, while stress and strain fields were obtained from the numerical models. The experimental and numerical displacement values differed by approximately 0.3%, 2%, and 1% for the cortical, cortical–trabecular, and trabecular regional comparisons, respectively. The numerical models additionally enabled characterization of stress and strain distributions and identification of regions of elevated mechanical response. These results demonstrate close specimen-specific agreement between the experimental displacement measurements and the CT-based FE predictions. However, because the HU–density–modulus coefficients were fitted using experimental data from the same femur, the reported agreement represents specimen-specific experimental-numerical consistency rather than independent validation, and transferability to other specimens or imaging protocols remains to be established.

The femur plays a crucial role in the structure and functionality of the human body, as it is the longest and strongest bone. In addition to its primary function as a weight-bearing and movement support in the lower body, the femur is intimately connected to the circulatory system by being an important site of blood cell production in the bone marrow (Joshi and Karande, 2023). However, various disorders can affect the health of the femur, with osteoporosis being one of the main problems. Osteoporosis weakens bone density, increasing the risk of fractures even in the face of minimal stress (Sollmann et al., 2021). To address these issues and improve quality of life, interdisciplinary approaches combining principles of biomechanics and medicine have been proposed (Li et al., 2020). Studies investigating the mechanical response of the femur to different loads and clinical situations contribute to a better understanding of how to prevent and treat problems related to this bone (Joshi and Karande, 2023; Argüello et al., 2019), (Díaz et al., 2017). These investigations are not only based on physical evidence but also employ numerical methods and computational models to simulate the behavior of the femur under various conditions (Day et al., 2022). This integration of knowledge remains vital to advance understanding of the complexities of the femur and its impact on the overall health of the individual (Argüello et al., 2019).

Given the inherent difficulties in accessing human anatomical components, analyses have been performed using bones from animals with human-like characteristics (Dahmen et al., 2015). In the case of femur-related studies, 4- to 6-month-old porcine models have emerged as a viable alternative due to their similarities to the human femur in terms of trabecular and cortical structure (Singh and Pandey, 2020). The parallel is evident in morphology and biomechanical properties. As in humans, porcine bones present a trabecular organization within, with interconnected internal branching. This trabecular arrangement allows them to have a reduced bone mass while maintaining the ability to withstand mechanical stresses (Joshi and Karande, 2023; Baca et al., 2008; Schileo et al., 2008). In addition, the outer cortical layer of bone also exhibits similarities in density and distribution, contributing to the overall robustness and strength of the femur (Sollmann et al., 2021; Feng et al., 2011). This similarity provides a valuable basis for studies seeking to better understand the responses of the human femur to different loads and to develop more effective approaches to the prevention and treatment of bone disorders (Argüello et al., 2019).

Studies have shown that porcine femurs share anatomical and mechanical similarities with human femurs, particularly in terms of bone density and elastic modulus (Ruess et al., 2012; Mejía Rodríguez et al., 2024). The trabecular and cortical structures in porcine bones exhibit comparable mechanical behavior, making them suitable for biomechanical investigations relevant to human applications. Previous research has reported elastic modulus values ranging from 4,000 MPa to 20,000 MPa for human cortical bone and 50 MPa–500 MPa for trabecular bone (Mejía Rodríguez et al., 2025). In comparison, porcine femurs exhibit ranges of 4,000 MPa–9500 MPa in cortical regions and 22 MPa–83 MPa in trabecular regions (Feng et al., 2011). Likewise, bone density in humans varies between 1.1 and 2.0 g/cm3, closely matching reported porcine values of 1.0–1.8 g/cm3 (Schileo et al., 2008). These similarities justify the use of porcine femurs as experimental surrogates for human bone mechanics in finite element analysis and biomechanical studies. Bone maturity is also a relevant factor when interpreting HU-based material assignment. During skeletal growth, porcine bone undergoes changes in mineralization, cortical thickness, porosity, collagen organization, and trabecular architecture, which can modify density, stiffness, and structural integrity independently of HU alone (Ruess et al., 2012; Mejía Rodríguez et al., 2024). Therefore, the present HU-density-modulus calibration should be interpreted for a five-to six-month-old porcine femur and should not be directly extrapolated to fully mature animals or to specimens at different growth stages without additional calibration.

The finite element analysis (FEA) of bones has become a great tool to predict the outcome of in vivo practices (Ruess et al., 2012; Maldonado-Moreno et al., 2024). Its introduction into the orthopedic field dates back to the early ‘70 s and since then, its use has been increasing in areas such as prosthesis design (Mejía Rodríguez et al., 2024; Mejía Rodríguez et al., 2025), to obtain structural data of bones and evaluate tissue deterioration over time (Dahmen et al., 2015; Castillo et al., 2025). Recently, finite element models, in addition to describing and characterizing tissues, corroborate or discard hypotheses related to the intervening forces in a certain region of the body, materials to be used in the prevention of tissue wear, and even the pressure exerted by inter-articular ligaments, faster and more efficiently (Chen et al., 2019; Naghibi et al., 2019; Zellmann et al., 2019).

Recent studies have further advanced the application of finite element analysis in understanding the mechanical behavior of the femur under different conditions. Studies have integrated muscle forces and friction contact into finite element models to predict stress and strain patterns in osteoarthritic femoral heads, highlighting the importance of biomechanical factors in load redistribution (Bini et al., 2019). Similarly, investigations on the topological organization of trabecular bone in normal, fractured, and osteoporotic samples have demonstrated how skeletal pathology alters the structural integrity of bone networks and influences mechanical performance (Reznikov et al., 2020). Additionally, critical evaluations of bone material properties have correlated cortical and cancellous bone anisotropy with apparent density, which is essential for realistic finite element modeling of the proximal femur (Wirtz et al., 2000). These studies reinforce the importance of accurately representing bone material properties and load conditions in computational models to enhance their predictive capabilities.

Recently, with advances in personalized medicine and medical imaging, finite element models have been made by obtaining patient data from X-rays, computed tomography (CT), micro-computed tomography (micro-CT), high-resolution peripheral computed tomography (HR-pQCT), and magnetic resonance imaging (MRI). From this information, a DICOM (Digital Imaging and Communications in Medicine) file is obtained that can be further processed by segmentation procedures to generate 3D reconstructions and finite element meshes of the study geometry (Puggelli et al., 2019; Hernández-Salazar et al., 2024). With the development of imaging technologies, progress has also been made in more accurate models obtained from micro-CT and HR-pQCT, which have proven to be very reliable, however, their quality is directly related to the amount of incident radiation on the specimen under study (Damm et al., 2019).

Bone is a hierarchically structured tissue with strong anisotropic properties. Cortical bone exhibits direction-dependent stiffness and is often modeled as orthotropic or transversely isotropic, while trabecular bone is commonly treated as isotropic but heterogeneous, depending on the level of analysis. A variety of constitutive models have been proposed, ranging from linear elasticity to elastoplasticity and damage-based formulations. The choice of constitutive model has a major impact on FEA predictions, yet in practice many imaging-based studies adopt simplified isotropic elastic models for computational tractability (Bahia et al., 2016). This simplification raises questions about predictive accuracy, particularly when such models are applied across regions of varying microstructure. However, more recent research has focused on manipulating organic tissue properties at the element or voxel level (Baca et al., 2008). This approach involves assigning specific mechanical properties to the scanned element based on its grayscale, which is expressed in Hounsfield units (HU) that, in turn, reflect the intensity of each pixel in the image (Zhu et al., 2018). HU quantify the radiological density and have shown a correlation with Young’s modulus of materials (Rho et al., 1995). While this imaging-to-FEA pipeline has been explored in both human and animal studies, its accuracy depends on empirical HU–density–modulus laws and assumptions of material behavior, both of which require validation against mechanical testing. Recent CT- and micro-CT-based finite element studies have further shown that image-derived models can reproduce experimentally measured strain fields and link computed strain or strain-gradient metrics with tissue-level bone adaptation under controlled axial loading (Horasan et al., 2024; Horasan et al., 2025). These studies support the use of imaging-based finite element (FE) models as a mechanistic bridge between local density, assigned material properties, and experimentally measured mechanical response, while also emphasizing the need for model calibration and sensitivity checks. Evidence from trabecular bone shows that bone volume fraction and fabric anisotropy are major determinants of stiffness (Maquer et al., 2015), underscoring the limitations of reducing image-derived heterogeneity to one isotropic modulus per element. Recent numerical and experimental orthopedic studies illustrate complementary validation strategies: lattice structures and hip endoprostheses have been evaluated through coupled computational and mechanical testing (Kharin et al., 2023); in situ X-ray CT has been used to quantify internal structural changes under compression (Akifyev et al., 2023); and numerical homogenization provides effective properties for heterogeneous microstructures (Andreassen and Andreasen, 2014).

This study addresses this gap by integrating CT-based segmentation and HU-derived modulus assignment with mechanical testing of porcine femoral specimens. Element-wise HU mapping is an established approach in CT-based FEA; therefore, the contribution of the present work is not the introduction of HU mapping itself, but its application as a specimen-specific workflow linking the same porcine femur CT data, fitted HU–density–modulus relations, and experimentally measured axial compression displacements. The resulting model is described here as an inhomogeneous isotropic continuum with piecewise-constant element properties, rather than as a continuous-gradient material formulation. This terminology better reflects the numerical implementation, in which each tetrahedral element receives one elastic modulus value from the local CT attenuation field. The workflow supports a direct experimental-numerical comparison for anatomically matched femoral regions, while the transferability of the fitted coefficients to other bones, scanners, and CT protocols remains a limitation requiring independent evaluation.

Bone preparation and mechanical test

We considered the right hind leg of a Pietrain porcine specimen Sus scrofa domesticus, aged between five and 6 months. The muscle tissue was removed from the piece, thus preserving the four parts of bone tissue. Then, manual cleaning of the bones was performed such as not to compromise their mechanical properties. The condition of the bones after cleaning is shown in Figure 1. This preparation process ensured that the bones were in optimal condition for subsequent analysis. After removal of surrounding soft tissue, the femur was wrapped in gauze moistened with 0.9% saline solution to prevent dehydration and placed in a sealed polyethylene bag. The specimen was stored at −20 °C until 24 h prior to testing, at which point it was thawed gradually at 4 °C. During specimen preparation and throughout mechanical testing, hydration was maintained by periodically reapplying saline to the surface. These procedures followed recommended bone preservation protocols (Szebényi et al., 2013; Simpson and Augat, 2015; Lee and Jasiuk, 2014), which minimize alterations to mechanical properties by maintaining moisture content and preventing microbial degradation.

The protocol for the compressive test was made following the tests in (Li et al., 2020) and (Szebényi et al., 2013), using approximately cylindrical specimens with different diameters and heights from each region, as shown in Figure 2. This study took into account the recommendations made in (Keaveny et al., 1997), where they determined that small specimens produce errors. The compressive test was conducted in a MTS Bionix 370.02 universal testing machine, at a speed of 2 mm/min, with a LVDT (Linear Variable Differential Transformer) at a sampling rate of 50 Hz. No digital filtering was applied during acquisition. A seating preload of 50 N was applied to (i) eliminate fixture slack, (ii) ensure full, repeatable contact between platens and specimen ends, and (iii) stabilize the LVDT zero before the main ramp. At the smallest cross-section among our cylinders, this preload corresponds to an apparent compressive stress < ∼1 MPa, i.e., well below the reported yield levels for porcine trabecular bone and orders of magnitude below cortical yield; thus, it is not expected to induce micro-damage. The specimens illustrated in Figure 2 were extracted from anatomically defined regions of the porcine femur. Bones 1–5 were obtained from the diaphyseal region by making transverse cuts at approximately 25 mm intervals along the shaft. These specimens had approximate transverse diameters ranging from 14 to 22 mm. Bones 6 and 7 were extracted from the epiphyseal regions and had approximate diameters of 25 mm and heights of approximately 25 mm. These values are reported as approximate bounding dimensions because the cross-sections were not perfectly circular after anatomical cutting.

In the experimental tests, only load–displacement data were recorded and analyzed. No experimental stress values were computed from the specimen geometry, as slight irregularities and taper can lead to significant errors in small bone samples. Instead, stresses were evaluated exclusively in the finite element model, where geometry was derived directly from the CT segmentation and therefore represented accurately. To minimize frictional effects between the specimen ends and the compression platens, the contact surfaces were polished, and a thin layer of synthetic lubricant (petroleum jelly) was applied before each test. Despite these precautions, a small residual friction effect may remain, as is common in unconfined compression tests. No explicit friction measurement was performed in the experimental phase. However, in the FE model, end contacts were idealized as frictionless to match the intended experimental conditions.

The experimental program was conducted on a single porcine femur, from which cylindrical specimens were extracted from anatomically consistent regions representing cortical, trabecular–cortical, and trabecular bone. To ensure spatial consistency, the location of each cylindrical specimen was planned using the CT-derived 3D model of the femur. Anatomical landmarks such as the femoral head, diaphyseal midpoint, and condyles were used to establish a reference coordinate system. Cortical specimens were extracted from the mid-diaphysis where cortical thickness was maximal and trabecular content minimal. Trabecular–cortical transition specimens were taken from metaphyseal regions, while trabecular specimens were extracted from the epiphyses. The anatomical regions identified in the segmented CT model were transferred to the physical bone using anatomical landmarks (femoral head, diaphyseal midpoint, and condyles) as reference points, ensuring that each specimen corresponded directly to the regions modeled in the finite element analysis. This alignment minimized variability due to positional differences and allowed one-to-one comparison between physical and numerical tests. The experimental dataset comprised seven coupons extracted from one biologically independent porcine femur. Bones 1–5 were obtained from predominantly diaphyseal/cortical regions, whereas Bones 6–7 were obtained from predominantly epiphyseal/trabecular regions. These coupons represent spatial samples from the same femur and are therefore not independent biological replicates. Accordingly, n = 1 refers to the number of biologically independent femora rather than to the number of tested coupons. Consequently, the present dataset cannot be used to estimate interindividual biological variability or population-level confidence intervals.

Medical imaging and bone segmentation

A computerized axial tomography of a fresh porcine leg was performed using a Toshiba Aquilion 64 CT scanner, with 12 slices/second contrast, thickness of 0.5 mm, and 64 simultaneous detector rows. The specimen was transported considering a controlled temperature to ensure the good condition of the bone tissue. A total of 832 slices were obtained in a DICOM file that was later processed in the software 3D Slicer (Fedorov et al., 2012; Carrasco-Lara et al., 2025). From the segmentation process, five meshes corresponding to each of the bones found in the scanned porcine leg were obtained. Then, each one of the meshes was stored separately and the mesh corresponding to the femur was fitted to match with the bone used in the mechanical compression tests. Figure 3 shows the segmentation process carried out from the DICOM data. The segmentation process provided anatomical reference for both the experimental and numerical phases of the study. Specifically, the segmented geometry was used to identify the anatomical regions from which the compression specimens were extracted and to generate the finite element model used for HU-based material mapping and mechanical analysis.

The inhomogeneous isotropic material model incorporated spatial variations in elastic modulus and density derived from the CT attenuation field. To evaluate the bulk density in bone tissue, it was calibrated between 189 and 1725 HU (Carrasco-Lara et al., 2025) for densities in the range (687–720 kg/m3) (Feng et al., 2011). These values are comparable to the results in (Day et al., 2022). For the models with cortical bone, the expression to evaluate the apparent density reads:

We then fitted the linear ρ c → E c relationship by minimizing the error between FE-predicted actuator displacement and the experimental load–displacement at the same load level (displacement-based fitting). The values of the linear elastic modulus E c, considered isotropic at the voxel level, were evaluated using the data extracted from the CT scans and the calculated bulk density as:

For the models with the trabecular bone, the fitting procedure yields the following expressions for the density ρ t and elastic modulus E t:

Formally, for each tissue class we solved with a (intercept) and b (slope) giving Equations 2, 4. Here S indexes the calibration specimens, u F E and u k exp are actuator displacements at the same applied load. Equations 1–4 should therefore be interpreted as specimen-specific empirical fitted relations. The HU-density conversion was initialized from CT calibration approaches reported for bone densitometry, and the modulus coefficients were then obtained by minimizing the displacement error in Equation 5. Similar HU/bone mineral density (BMD)-to-strength correlation procedures require calibration against experimental data and are commonly treated as scanner-, specimen-, and tissue-dependent (Schileo et al., 2008; Rho et al., 1995; Khan et al., 2014). Because the present dataset was obtained from one biologically independent femur, the available coupons represent spatial samples rather than independent biological replicates; therefore, no population-level sensitivity or uncertainty analysis was performed. The initialization of Equations 1–4 was based on CT-density and density-modulus relationships previously applied to porcine vertebral tissue and on quantitative CT calibration literature. Specifically, Rho et al. (Mejía Rodríguez et al., 2025) reported relationships among CT number, density, and mechanical properties for porcine cortical and trabecular bone; Schileo et al. (2008) and Taddei et al. (2007) used CT-derived density mapping in subject-specific femoral finite element models; and Kalender et al. (Kalender, 1992) provided phantom-based spinal QCT calibration. These sources were used as initialization and calibration frameworks, not as direct final coefficients. Their use for porcine femoral tissue is supported by reported similarities in density, cortical/trabecular organization, and mechanical behavior between porcine and human femora (Cone et al., 2017; McGovern et al., 2018), as well as recent porcine femur mechanical-property studies (McGovern et al., 2018; Markarian et al., 2026). The final coefficients were fitted to the present porcine femur compression data; therefore, Equations 1–4 should be interpreted as specimen-specific porcine femur relationships. As the modulus coefficients were obtained by minimizing the displacement error for the present specimen, the procedure is described as specimen-specific fitting rather than as a universally transferable calibration. The fitted relations were used to reproduce the mechanical response of the scanned porcine femur under the present CT protocol and experimental boundary conditions. Transferability to other femora, skeletal maturity stages, scanners, reconstruction kernels, or segmentation protocols has not been established and must be evaluated with independent specimens and scanner-specific calibration.

The density and elastic information were mapped from the CT scans to the corresponding mesh elements using Bonemat (Taddei et al., 2007). In this implementation, HU values sampled from the CT voxel grid inside each tetrahedral element were locally averaged and converted to a single elastic modulus through Equations 1–4. Boundary and partially overlapping voxels were therefore represented by the local HU average of the segmented element volume, while voxels outside the bone mask were excluded from bone material assignment. This procedure captures macroscopic spatial inhomogeneity at the element scale but does not resolve trabecular fabric anisotropy or sub-element mineral gradients (Hamamoto et al., 2023). Each element was modeled as linear isotropic elastic; consequently, the assembled model is spatially inhomogeneous and produces nonuniform stress and strain fields, but it does not represent material anisotropy at a material point. Figure 4a shows the final distribution of the elastic modulus for the femur in bone 1. Figure 4b represents a longitudinal cut of the bone, showing the internal variation of elastic modulus in the bone tissue.

Figure 4 illustrates the element-wise HU-to-modulus assignment obtained from the CT-based material mapping. Because the longitudinal section represents only one view of the three-dimensional material distribution, local modulus variations should be interpreted together with the underlying CT-derived HU distribution rather than as a homogeneous physiological modulus field (Markarian et al., 2026). To complement the modulus map, a radial HU profile for Bone 1 was extracted directly from the original CT image. The profile, shown in Figure 5, was obtained from a transverse slice near the mid-diaphysis along a line extending from the periosteal cortex to the medullary canal. HU values were sampled directly from the CT image using trilinear interpolation and normalized from 0 at the periosteal surface to 1 at the medullary canal. The profile shows a local maximum within the cortical wall and a decrease near the periosteal surface. This behavior was also observed by Markarian et al. (2026), and Hamamoto et al. (2023), and may be associated with partial-volume averaging at the external boundary, scatter-related artifacts, and local mineralization differences in immature porcine cortical bone. The profile should therefore be interpreted as a local CT attenuation measurement used to support the modulus distribution in Figure 4, not as an imposed radial material law. The observed radial heterogeneity is consistent with the modulus distribution presented in Figure 4, indicating that the local modulus variations reflect the measured CT data rather than an imposed radial material distribution.

Numerical model

The structural analysis was performed using a standard Galerkin finite element approximation in the volumetric reconstructions produced for each specimen, which correspond to the same geometries utilized in the experimental tests of the femur. The meshing process was performed for each model with the software Ansys 2022R2 (Aerssens et al., 1998), as depicted in Figure 6. The meshes consisted of second-order tetrahedral elements and, for bone 1, comprised a total of 13,326 nodes and 8,396 elements, giving a total of 39,978 degrees of freedom (DOF) for the entire model. Second-order tetrahedral elements were used because they conform efficiently to complex bone geometries. Hexahedral elements, while potentially more accurate in capturing stress gradients, are difficult to generate in anatomically irregular structures such as the femur. To assess structural mesh convergence, displacement convergence is presented in Table 1, with a variation that does not exceed 0.395%. Likewise, a quality check of the elements was made, ensuring that the distortion values remained below 0.95. Although mesh independence analyses were performed for all specimens, only the results for Bone 1 are presented because the remaining models exhibited similar convergence trends and resulted in comparable mesh densities. The meshes were imported into Bonemat, which mapped HU values from the CT voxel grid to each element by local averaging. Because the elastic property assigned to each element depends on this averaging, the material field is mesh dependent in principle; therefore, the convergence study should be interpreted as displacement convergence for the final mapped model.

To assess the mechanical response of the numerical models, axial loads of 1,000 N and 10,000 N were selected based on the experimentally measured load–displacement curves. The 1,000 N level lies within the loading range reached by the trabecular specimens, whereas 10,000 N lies within the experimental range of the cortical specimens. These load levels were used as reference points for comparison between the numerical and experimental displacement responses. The loads were applied at the top cross-section in the z-direction, as shown in Figure 7. Displacement constraints were imposed on the bottom cross section of the femur to avoid rigid body motion. These boundary conditions reproduce the axial compression experiments described in Section 2.1. In ANSYS, the FEA used a linear isotropic elastic model for each element. Young’s modulus was assigned from the local HU-based calibration and Poisson’s ratio was set to 0.30 for all elements. The top surface received the prescribed axial compressive distributed load, the lower surface was fixed in the loading direction and constrained to prevent rigid-body motion, and contact with the platens was idealized as frictionless to represent the lubricated experimental setup. The frictionless contact assumption is an idealization of the petroleum-jelly lubrication used experimentally. Any residual friction would partially restrain lateral expansion from Poisson’s effect and could slightly reduce the measured axial displacement. This effect may contribute to the small displacement differences (<2%) between FE and experimental results, but the close agreement suggests that residual friction was not the dominant source of error.

The inhomogeneous isotropic material model was implemented by assigning mechanical properties to each voxel based on the corresponding HU values from the CT scans. The transition between cortical and trabecular bone was defined through a continuous gradient function that interpolates the elastic modulus values across the interface. The transition layer thickness was determined by the HU threshold range, with values between 600 and 900 HU corresponding to intermediate regions where mechanical properties gradually shift between trabecular and cortical bone (Schileo et al., 2008). This voxel-based approach ensures a smooth variation of material properties, avoiding abrupt changes that could introduce numerical instabilities in the finite element model.

Experimental tests

The femur consists of high-stiffness zones with elastic modulus values ranging from 4,000 MPa to 9500 MPa in the diaphysis, and low-stiffness zones with elastic modulus values ranging from 83 MPa to 22 MPa in the epiphyses. Figure 8 shows the results of the load vs. displacement for the experimental tests of the bone specimens under compression, where the different behavior of trabecular and cortical bone can be observed. The experimental compression test results are detailed in Table 2 and 3, which present the maximum load and normal displacements. Each specimen was compressed until structural failure, defined by either a visible fracture or a clear load drop in the force-displacement curve. The maximum load reported corresponds to the peak of the curve immediately before failure.

Table 2 shows the results for the cortical bone sections, which are more compact and exhibit minimal deformation. The maximum load for these sections is 18,550.67 N, with a deformation of 0.604 mm in that specimen. In contrast, Table 3 presents the results for the trabecular bone sections, which have a less compact structure and therefore show greater deformation under load. The maximum load for the trabecular specimens is 1,300.69 N, with a deformation of 15.789 mm.

The experimental results highlight the pronounced mechanical contrast between cortical and trabecular bone regions in the porcine femur. Cortical specimens supported loads exceeding 18 kN with displacements below 1.7 mm, reflecting their high stiffness and load-bearing capacity. In contrast, trabecular specimens failed at loads near 1.3 kN with displacements over 13 mm, confirming their compliant nature and energy-absorbing role. These values are in close agreement with previously reported ranges for porcine femurs, where cortical elastic modulus is typically between 4 and 9 GPa and trabecular modulus ranges from 20 to 100 MPa (Feng et al., 2011). The experimental trends also mirror human femoral mechanics, supporting the use of porcine femurs as surrogates in biomechanical modeling. Variations among cortical specimens (e.g., Bone 5 exhibiting lower maximum load) may be attributable to differences in cross-sectional area, microstructural density, or preparation-induced microdefects. Because all seven coupons were obtained from a single biologically independent femur, the observed variability represents spatial variation within that femur and cannot be interpreted as interindividual biological variability. These results form the reference dataset used for specimen-specific fitting and experimental–numerical displacement comparison in Section 3.2.

Numerical model

Based on the characterization performed, we developed a numerical model to replicate the compression tests conducted on the bone specimens. The objective was to accurately model the experimental process and establish a suitable analysis method. This finite element model was created using the same parameters as the laboratory tests, with a focus on the spatially inhomogeneous isotropic stiffness distribution derived from HU-based Young’s modulus assignment. Two loads, 1,000 N and 10,000 N, were evaluated as scaled linear-elastic cases, and the distributed load was applied to the top surface while a fixed boundary condition was set at the bottom. Figure 9 shows the von Mises stress distribution for the model with bone 1 under a 10,000 N load, with a maximum value of 72.34 MPa.

The elastic moduli determined through FEA are presented in Table 4 and 5. The mechanical characteristics exhibited by the porcine femur align with the attributes commonly associated with both cancellous and compact bone structures. Specifically, the calculated elastic modulus values span a range indicative of cortical bone, varying from 4,080.31 MPa to 971.63 MPa. Meanwhile, the values reflecting combined trabecular and cortical behavior fall within the range of 2602.67 MPa–154.55 MPa. Furthermore, when considering solely the behavior attributed to the trabecular component, the elastic modulus values are confined within the interval of 83.5 MPa–21.0 MPa. The low minimum values reported for cortical models in Table 4 correspond to element-wise extrema within transition or partial-volume regions of the segmented model; they should not be interpreted as the bulk modulus of pure cortical tissue. The higher element-wise maxima and the experimental stiffness response remain within the broad range reported for porcine femoral cortical and trabecular bone, which is affected by age, anatomical region, testing mode, and strain rate (Feng et al., 2011; Szabo et al., 2024; Bonney et al., 2011).

The displacements investigated span three distinct segments of the porcine femur. These segments encompass cortical, trabecular-cortical, and trabecular tissues. After fitting the empirical coefficients of the material relations by minimizing the displacement differences for the present specimen, close agreement was obtained between the experimental and finite-element displacement values. These results indicate a resemblance to the findings reported by (Day et al., 2022). In their study, an elastic modulus of 65 MPa was assigned to the trabecular zone. In our study, the values lie within a range of 22 MPa–83 MPa, depending on bone characteristics.

Because the same specimen dataset was used to fit the HU–density–modulus coefficients, the displacement differences reported in Table 6 represent internal fitted-data agreement rather than independent validation. A limitation of this study is that all seven experimental coupons were obtained from one biologically independent porcine femur. Because n = 1 at the femur level, statistical confidence intervals for biological variability cannot be estimated from the present dataset. The reported error bounds are therefore limited to the numerical-experimental displacement differences in Table 6 and should be interpreted as specimen-specific experimental–numerical agreement rather than independent or population-level validation. The HU-density-modulus coefficients were obtained by displacement-error minimization for this specimen and should be considered specimen- and protocol-specific fitting coefficients, not transferable material laws. In addition, the local HU averaging used for element-wise material assignment makes the property field dependent on CT resolution, segmentation, and mesh density; the present convergence study evaluates displacement convergence for the final mapped model but does not independently quantify material-field convergence. Future work should include multiple femora, additional age groups, repeated CT protocols, perturbation of calibration coefficients and thresholds, and validation metrics beyond displacement, including strain fields and failure loads, to quantify biological variability and transferability.

This study presents a characterization of porcine femoral bone using the finite element method by integrating experimental compression data with CT-based medical imaging and element-wise material assignment. The reported elastic modulus values span approximately 971.63–4,080.31 MPa for the cortical region and 21.0–83.5 MPa for the trabecular region, reflecting the marked mechanical contrast between these tissues. Experimentally measured displacements were 0.578 mm for the cortical region, 1.581 mm for the cortical–trabecular region, and 14.721 mm for the trabecular region. The corresponding finite element values were 0.579, 1.610, and 14.522 mm, resulting in differences of approximately 0.3%, 2%, and 1%, respectively. These small differences indicate close experimental–numerical agreement for the present specimen. However, because the HU–density–modulus coefficients were fitted using displacement data from the same femur, this agreement should be interpreted as internal consistency of the fitted model rather than as independent validation.

The numerical model reproduced the spatial variation of CT attenuation by assigning one isotropic elastic modulus to each tetrahedral element from the corresponding local HU average. Consequently, the resulting material field is spatially inhomogeneous and piecewise constant at the element scale, while each individual element remains linear elastic and isotropic. The procedure therefore represents CT-derived macroscopic inhomogeneity but does not reproduce local material anisotropy, trabecular fabric, or sub-element mineral gradients. The fitted HU–density–modulus relations should also be regarded as specimen- and protocol-specific rather than as universally transferable material laws. Their applicability to other femora, skeletal maturity stages, CT scanners, reconstruction kernels, segmentation procedures, or mesh configurations has not yet been established and requires evaluation with independent experimental data.

The numerical analyses considered axial loads of 1,000 N and 10,000 N. The 1,000 N case was retained as a lower reference load, whereas the 10,000 N case was used for visualization of the higher-load structural response. Because a linear-elastic formulation was adopted, the two cases are related by proportional scaling and do not constitute independent constitutive assessments. In addition, the compressive resultant was distributed over the upper cross-section rather than imposed through a rigid platen with equal axial displacement. Although this loading condition was selected to approximate the experimental compression configuration, it does not reproduce the exact kinematic action of the experimental platen on an inhomogeneous end surface. Therefore, the reported stress and displacement fields should be interpreted within this boundary-condition assumption. The use of one biologically independent porcine femur, from which seven spatial coupons were obtained, also prevents assessment of interindividual biological variability and population-level statistical confidence.

Future work should extend the present workflow to multiple independent femora and different maturity groups, CT acquisition protocols, and anatomical regions. Separate datasets should be used for parameter fitting and independent model evaluation, together with additional comparison metrics such as experimentally measured strain fields, failure loads, and local deformation patterns. Material-field convergence could also be assessed by remapping HU values across different mesh resolutions, while future compression simulations could incorporate a rigid platen or reference-point coupling with prescribed axial displacement and comparison of the resulting reaction force with the experimental load–displacement response. With these additional verification steps, the proposed CT-to-FEA workflow may provide a useful basis for more robust subject-specific bone models and, in the longer term, contribute to applications in orthopedic biomechanics, implant design, fracture assessment, and patient-specific computational modeling.