Introduction

Stress fractures are prevalent in both humans and animals who engage in athletic activities. The most common site of stress fracture in Thoroughbred racehorses is the metacarpophalangeal joint (MCP). This joint is subjected to high-magnitude and high-rate cyclic loads in racehorses during training and racing, resulting in repeated high compressive loads on the joint surface1. Post-mortem examination of specimens from the third metacarpal bone (MC3) has revealed trabecular bone sclerosis or densification, microcracks in the SCB and calcified cartilage of the PSG and the condyles2,3,4. Metacarpal SCB fatigue damage may progress to at least two types of injury: condylar fractures and palmar osteochondral disease of the condyles (POD)5,6. Although the pathogenesis of parasagittal condylar fractures is well characterized, further research is needed to determine which specific characteristics of SCB microdamage are most predictive of imminent fracture risk or progression to non-fatal palmar osteochondral disease (POD). Improved understanding of these precursors is critical for early identification of high-risk horses and the prevention of catastrophic MC3 fractures.

Identifying horses at risk of fracture is challenging; hence, the significant interest in advanced imaging methods that have the potential to detect early pathological changes associated with fracture. Computed tomography (CT) is one of the most practical imaging modalities now available due to the ability to rapidly obtain images of all four fetlock joints in the standing sedated horse7. Although unable to detect microdamage, CT can reveal changes in the bone shape and the distribution of bone mineral density (BMD), including lytic (low BMD) and sclerotic (high BMD) volumes. Focal lytic SCB is associated with microdamage and targeted bone resorption, which are common in the palmar aspect of the metacarpal/tarsal condyles and PSGs in Thoroughbred racehorses8. However, it is currently not possible to determine which patterns of lytic and sclerotic areas are most likely to progress to fatal fractures9,10.

While clinical images provide valuable information regarding joint shape, tissue microstructure and bone mineral density, estimating bone’s resistance to cyclic loading requires knowledge of the strains applied to each area within the bone during galloping. Because it is difficult to place sensors within the SCB to measure load, finite element (FE) models provide a non-invasive tool for assessing the distribution of external loads within the bone. While our previous microCT-based FE models accurately predicted strain distribution and locations of impact-induced microfractures in the equine SCB at a tissue level within cartilage-bone plugs11,12, there are very few studies that have assessed the mechanical behaviour of SCB at a joint scale. Previous work investigated cartilage stresses in the metacarpophalangeal joint, but bone was assumed as a rigid material1. Another study estimated bone stresses in the P1-MC3 joint where injury is less common in racehorses13. There are no studies that have evaluated SCB intra-tissue strains and stresses at the MC3-proximal sesamoid joint. Most importantly, the evaluation of stresses and strains within the SCB of live horses will provide valuable information regarding the mechanism and prediction of fracture.

While developing joint-specific three-dimensional finite element (FE) models provides detailed insight into joint mechanics, the process is time-consuming and computationally intensive. Previous studies have demonstrated that slice-based FE models, particularly those using peripheral quantitative computed tomography (pQCT) images, can effectively estimate local mechanical behavior and enhance fracture risk assessment in clinical settings14,15. Based on this evidence, we hypothesised that slice-based FE models could also be a suitable approach for evaluating SCB stresses and strains in racehorse joints. While earlier slice-based models were typically 2D and used a plane-strain assumption, i.e., no deformation in the out-of-plane direction, our study accounts for out-of-plane deformations associated with cartilage loading by extruding single oblique CT slices to a thickness of 20 mm, enabling three-dimensional deformation while maintaining the efficiency of a slice-based modeling approach. This study aimed to validate an extruded slice-based finite-element approach by comparing its biomechanical predictions with those from full 3D joint-specific models of the equine distal MC3, while examining reductions in development time and computational cost. The overall goal of our work is to develop a fast CT-based FE model pipeline for investigating stresses and strains in live racehorses, to ultimately enhance fracture risk prediction. Thus, our specific aims in the present study were first, to develop joint-specific 3D FE models using standing CT images for three trained racehorses, each presenting distinct SCB conditions common in racehorses as identified by their CT images: (1) biaxial sclerotic condylar SCB with no visible lesions, (2) focal lytic SCB with associated sclerosis in the PSG, and (3) focal lytic SCB with associated sclerosis in the condyles, and to validate these models against cartilage contact pressures reported in the existing literature; and second, to develop joint-specific slice-based FE models using a single oblique dorsal CT slice through the identified condition in CT images, whether lesion or sclerosis, and compare them against the 3D models; and finally, to determine the sensitivity of the slice-based FE models predictions to variations in the model inputs and parameters.

Methods

Figure 1 illustrates the overall workflow of the current study and the development of 3D and slice-based CT FE models for each joint. CT images of three horse in a standing position were co-registered, aligned and adjusted into galloping position. The 3D segmentation and FE mesh development was performed for each horse (Fig. 1E, F, I, J). A single dorsal oblique CT slice was extracted from the segmented aligned galloping position (Fig. 1F), approximately 10 mm palmar to the transverse ridge, where we have also performed extensive studies of bone plugs previously16,17,18,19. However, if there was a lesion present in other sites on the condyles, the slice was taken through the centre of the lesion. Lesion sites typically occurred within the palmar condylar region, only a few millimeters from this reference plane. The single slice was then extruded to generate a volume, referred to as a slice-based FE model in this study (Fig. 1H-J). Two FE models were developed for each joint, one using 3D volume and the other using the single slice.

Fig. 1
figure 1

Workflow for generating 3D- and slice-based finite element (FE) models of equine limbs. (A) A standing computed tomography (CT) scan was performed on both equine thoracic limbs using a standing CT scanner. (B) The right thoracic limbs are isolated from the scans. (C) CT images were aligned and co-registered to a common coordinate system. (D) The proximal sesamoid bones (PSBs) and P1 bones were rotated around the joint centre to simulate the galloping posture (rotation of 49°). (E) Segmentation of third metacarpal (MC3), PSBs, articular cartilage (AC), and intersesamoidean ligament/flexor tendon (ISL/FT). (F) Material properties based on bone density were mapped to MC3 and the 3D finite element mesh is created. (G) A dorsal oblique CT slice was taken from the distopalmar section of the joint, the location of the extracted slice is indicated by a dashed line in D and F. (H) The selected CT slice was extruded to a thickness of 20 mm for slice-based modelling; anatomical landmarks are indicated here as sagittal ridge (SR, white arrow), lateral and medial condyles (dashed arrows) and lateral and medial parasagittal grooves (PSGs, solid arrows). These landmarks are also shown in (Fig. 2A and D). (I) A finite element mesh of the slice-based model was generated with bone, cartilage, and ligament structures. (J) Boundary conditions and loading are applied to the slice-based model for biomechanical simulations.

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CT imaging

CT images of three live Thoroughbred racehorses were obtained from a clinical data base with the following SCB conditions: (1) BS in both lateral and medial condyles, (2) lytic SCB underlying the lateral PSG with associated surrounding sclerosis, LGL, and (3) lytic SCB in the condylar region, BCL (Fig. 2A-C). MC3 joints were scanned using a standing CT scanner (Asto CT Inc., Middleton, WI, USA). The dimensions of the scanning protocol were 0.7324 × 0.7324 × 0.5555, and exposure of 160kVp and 8 mA at 1 s per 360-degree revolution using 24 detector rows with a variable helical pitch, typically 0.55. Slice acquisition rate was 36 slices/sec with an image acquisition matrix of 1024 × 1024 and a resolution at isocentre of 0.75 mm.

Fig. 2
figure 2

Dorsal oblique computed tomography (CT) slices of the distal third metacarpal bone (MC3) and corresponding three-dimensional (3D) finite element (FE)–predicted articular cartilage (AC) pressure distributions. (A–C) Dorsal oblique CT slices of distal MC3 illustrating three subchondral bone (SCB) conditions: bilateral sclerosis (BS), a lateral parasagittal groove lesion with surrounding sclerosis (LGL, black arrow), and bilateral condylar lesions (BCL, black arrows). Dashed rectangles denote the ROI used for stress and strain analyses: a 50 mm mediolateral width centred at the apex of the PSG, i.e. SR, a 20 mm depth of superficial SCB from the joint surface proximally, and a 1 mm depth in the dorsopalmar direction (normal to the view). (D–F) 3D FE-predicted AC pressure (MPa) distributions generated by the proximal sesamoid bones (PSBs) over the MC3–PSB interface. The solid black lines in D–F indicate the precise dorsal oblique slice locations from which the CT images in A–C were obtained, showing how the internal SCB morphology corresponds to the predicted surface pressure distribution. Numbers 1–5 in A and D denote anatomical landmarks described in the text and also shown in (Fig. 1H): (1) lateral condyle (LC), (2) lateral PSB groove (LPSG), (3) sagittal ridge (SR), (4) medial PSB groove (MPSG), and (5) medial condyle (MC). (G) Sagittal view illustrating the distopalmar viewing direction (black arrow) in D–F and the dorsal oblique slice location. The colour bar indicates pressure magnitude (MPa).

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Aligning and registration

The DICOM images were imported into image processing software (Simpleware, Synopsys, USA) to identify the right and left thoracic limbs of each Thoroughbred horse using markers set during the scans. Only right thoracic limbs were used in the current study. The joint images were co-registered to one joint so that the oblique dorsal plane, the main plane of interest in the current study, was aligned with the horizontal axis. To align the images, the “Landmark only” option in Simpleware was used, and further visual inspection was performed to ensure the alignment was accurate by inspecting the direction of sagittal ridge and condylar surfaces. Since the original scans were taken with the horses in a standing position, the proximal sesamoid bones (PSBs) were rotated around the joint centre to match the midstance galloping position20. A code was developed in MATLAB (R2020a, MathWorks Inc., USA) to read the aligned sagittal DICOM images of the limbs and map a circle to the joint surface from the transverse ridge (TR) to the palmar part of the joint. Then, a copy of the images was rotated in 2D around the centre of this circle for 49 degrees (Fig. 1C-D), i.e., the approximate fetlock angle compared to the standing position. The position of each PSB was also adjusted with respect to the TR to match those reported in the literature20.

Segmentation

To develop the 3D FE model, the distal MC3, articular cartilage, PSBs, intersesamoidian ligament/flexor tendons (ISL/FT) as well as P1 bone were segmented from CT images based on their greyscale value (Fig. 1D). Due to the limited contrast within the joint space, fully automatic segmentation was not feasible. Therefore, semi-automatic segmentation was required, involving frequent visual inspections, particularly in regions with surface joint lesions where the grayscale values were similar to those of the joint space. A combination of smoothing, thresholding, mask splitting, and morphological operations were used to complete the segmentation. To develop the slice-based FE model, a single CT oblique dorsal slice was extracted. CT images were acquired with voxel dimensions of 0.7324 × 0.7324 × 0.5555 mm (X, Y, Z), corresponding to a reconstructed slice thickness of 0.5555 mm. Following registration and rotation to match a weight-bearing galloping position, the single oblique slice used for the slice-based models was resampled from this dataset, yielding an effective thickness of ~ 0.56 mm. Each slice was then extruded to a depth of 20 mm for FE analysis. (Fig. 1H-J). Python scripts were executed within Simpleware’s integrated scripting environment to automate most processing steps, including slice extrusion, mesh generation, and refinement, and material mapping, with final segmentation of lesions verified via visual inspection (Synopsys, 2023). Changes in strains and stresses in the SCB were less than 5% when slice thickness was increased to 30 mm, indicating that this thickness was sufficient to provide adequate distance from the bone dorsopalmar boundaries.

Loading conditions

To simulate the compression exerted by the flexor tendons (FT) on the palmar aspect of the proximal sesamoid bones during midstance, an approximate load of 7kN was applied to the ISL surface. An equivalent pressure was calculated based on the ISL surface area of each model. Since the response was found to be linear, the results could be adjusted proportionally by multiplying them by the applied load.

Boundary conditions

Three-dimensional models

The distal end of P1 and the proximal end of MC3 were fully constrained (Fig. 1F).

Slice-based models

To replicate the in-situ boundary conditions, we constrained the bone proximopalmarly and distodorsally, while allowing the cartilage margins to expand freely, representing their natural lateral expansion within the joint. The proximal end of MC3 was fully constrained. To check that this fixed boundary was not influencing stresses too close to the SCB, we extended the model proximally by 50 mm of additional bone, so the proximal boundary behaved like part of a longer, continuous shaft rather than a cut face. We then evaluated the effect of this extension, as well as varying the SCB elastic modulus from 500 to 50,000 MPa (i.e., 0.1× to 10× the average SCB modulus). Across these tests, stress and strain within the superficial 20 mm of SCB, the primary analysis region, changed by no more than 5.5%. Therefore, for the remaining slice-based models we constrained only the proximal face of the bone in all directions.

Material properties

MC3 bone

We created heterogeneous FE models by mapping bone mineral density (BMD)-based elastic modulus (E) using a previously established equation from a study on SCB specimens from lateral condyles19:

E = − 8196.7 + 5,880.6ρ, R2 = 0.34, P = 0.0044, (n = 22).

where ρ represents actual density (ranging from 1.7 to 1.9 g/cm3). This equation was also applied to regions of lytic bone, with the elastic modulus extrapolated linearly based on the local density within the lesion. Actual density was obtained from a calibration phantom that converted Hounsfield Unit (HU) density to actual density. We assumed a Poisson’s ratio of 0.3 for bone21.

Proximal sesamoid bones (PSBs)

An initial elastic modulus of 4,000 MPa was assigned to PSBs, which was the median value when the same material properties were mapped as MC3.

Articular cartilage (AC)

A neo-Hookean hyperplastic model was assigned to the AC with a shear modulus, G = 40 MPa, and a Poisson’s ratio of 0.4999. This model accurately predicted the instantaneous response of cartilage of cartilage explants under impact loading11,22,23,24.

Intersesamoidian ligament (ISL)

Initial homogeneous material properties were assigned similar to articular cartilage elastic material properties, i.e. E = 300 MPa and v = 0.49, in both 3D and slice-based models (Malekipour 2016).

FE mesh

The mesh volume was generated in Simpleware for all segmented areas in both 3D and slice-based models using linear tetrahedral elements (C3D4). Articular cartilage elements were further converted to hybrid elements in ABAQUS (6.14–2, Simulia, USA). A mesh convergence study was conducted using a slice-based model and the final element size was set to 0.6 mm within the 20 mm superficial SCB of MC3, i.e. the main area of interest, and 1 mm for the remaining part of the MC3 in both the 3D and slice-based models. Additionally, the FE results were tested for MC3 linear versus second order modified tetrahedral (C3D10M) elements, and results did not change by more than 1.5% at this refinement level. The sensitivity to the number of material divisions in Simpleware was also investigated, and the strains and stresses did not change by more than 1% when the number of subsets decreased from 50 to 20. As a result, a subset of 20 was chosen for the remaining models.

FE analysis

FE models were analyzed in ABAQUS/Standard (Simulia, Providence, RI, USA), and output data were exported to MATLAB for post-processing. Model outputs included AC pressure, and maximum and minimum principal stresses and strains (εt: maximum principal – tensile; εc: minimum principal – compressive; σVM: von Mises stress) for the SCB. Analyses were conducted within a defined region of interest (ROI) extending 1 mm in the dorsopalmar direction, 50 mm mediolaterally (centered at the apex of the PSG), and 20 mm proximally from the joint surface into the superficial SCB (Fig. 2A–C, dashed rectangles: 50 × 20 × 1 mm³). Comparisons were made across consecutive 3 mm-wide mediolateral subregions (3 × 20 × 1 mm³) based on nodal coordinates. Landmarks corresponding to the lateral condyle (LC), medial condyle (MC), sagittal ridge (SR), and parasagittal grooves (PSGs) were manually identified on the CT images and mapped onto the pressure profiles according to their spatial coordinates (Fig. 1H).

For each subregion, peak (90th percentile) stress and strain values were calculated. Principal strain (absolute values), and von Mises stress magnitudes were compared between 3D and slice-based models, and the orientations of principal strains were examined to assess directional consistency between models.

Additionally, the volume of highly strained bone was determined by summing the volume of all elements exhibiting either tensile or compressive strain exceeding the peak tensile or compressive strain within the analyzed SCB cuboid (VHR). This volume was further normalised by dividing by the entire volume of the ROI to be more comparable between horses (VNHR, %). Principal strain and stress directions were also compared across all models. Computation times were obtained from ABAQUS/Standard solver message files. CPU time represents the total central processing unit (CPU) time used by the solver, while wall-clock time indicates the actual elapsed computation time, including all input/output operations.

Sensitivity analysis

We evaluated the sensitivity of slice-based FE-predicted strains and stresses within ROI, corresponding to the 20 mm most superficial SCB, spanning 50 mm mediolaterally and 1 mm in thickness (Fig. 2A-C). Sensitivity analyses included ± 50% changes to the material properties of the AC, PSBs, and ISL, as well as a mediolateral shift of one PSB by one pixel to simulate segmentation error. This geometric perturbation also altered AC thickness locally, particularly at the PSG, which was a primary area of interest. Additionally, we examined the influence of AC Poisson’s ratio by testing two values: 0.49 and 0.3. The baseline model assumed a Poisson’s ratio of 0.4999 for AC to reflect its near-incompressible behavior under impact loading (~ 0.5), while allowing convergence in ABAQUS/Standard. To assess sensitivity to this assumption, we first reduced the Poisson’s ratio slightly to 0.49, to determine whether a small change from the near-incompressible limit would influence the stress and strain outputs. We then tested a lower value of 0.3, representing more compressible or degenerated cartilage. This is consistent with previous experimental and FE modeling studies, which report that osteoarthritic cartilage exhibits increased compressibility and reduced effective Poisson’s ratios due to structural matrix deterioration and fluid loss25,26,27. A maximum difference of 10% in output variables (strains and stresses) between baseline and sensitivity models was considered acceptable, following previously published thresholds1,28.

Results

The histograms in Fig. 3 summarise the distribution of elastic modulus (ESCB​) values assigned to elements within the distal MC3 region of each horse, illustrating the heterogeneity of material stiffness within the distal MC3 condyles for three horses. Because both the 3D and slice-based models used the same density-to-modulus mapping, their histograms overlapped; therefore, only the slice-based data are shown. The E of analysed ROIs ranged from 460.6 to 3,447 MPa across the three condyles (Fig. 3, x-axis). The BS horse model showed a distribution of E skewed toward higher values (Fig. 3A), indicating a denser material distribution, as expected. In contrast, the BCL horse displayed a wider range of densities with a peak over the lower modulus, indicating the presence of lytic bone.

Fig. 3
figure 3

Histogram of element-level elastic modulus (E, MPa) values assigned to the distal third metacarpal (MC3) models of each horse: bilateral sclerosis (BS), lateral parasagittal groove lesion (LGL), and bilateral condylar lesions (BCL). The y-axis indicates the number of finite-element mesh elements within each modulus range, and the x-axis shows the corresponding E value (MPa). The BS model exhibits a higher proportion of stiff elements consistent with subchondral sclerosis, whereas the LGL and BCL models display broader distributions reflecting localised or mixed sclerosis and lysis. Both 3D and slice-based models exhibited similar distributions; therefore, only the slice-based results are displayed to avoid redundancy.

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The average CPU time for slice-based models was 16,984 ± 15,339 s, compared to 71,139 ± 69,862 s for full 3D models. Similarly, the average wall-clock time was significantly lower for slice-based models (3,037 ± 2,564 s) than for 3D models (14,245 ± 10,552 s). Although all models had comparable mesh densities, minor variations in lesion geometry and material partitioning changed the total number of equations solved, contributing to differences in CPU time. As analyses were executed on a remote HPC system, variability in wall-clock time likely reflected dynamic resource allocation and I/O scheduling rather than model configuration. The most time-intensive component of the 3D workflow was the segmentation of bone structures and joint spaces, especially in lesion-affected areas where manual input and repeated visual inspection were required. This increased processing time and introduced inter-subject variability in segmentation quality. On average, 3D segmentation could take several hours and was more prone to operator error. In contrast, the slice-based segmentation workflow was largely automated following the development of custom Python scripts within Simpleware’s scripting environment (Synopsys, 2023). Only brief visual verification (∼10 min) was needed. Subsequent steps including extrusion, mesh generation, and refinement, were also scripted, allowing model generation to be completed within minutes after initial setup.

3D FE analysis

The applied load through ISL generated average AC pressures of 12.6 ± 3.1 MPa. In all three 3D models (Fig. 2D–F), pressure was highest in the palmar region of the joint, with negligible pressures observed at the sagittal ridge. These pressure distributions were consistent across horses with varying subchondral bone (SCB) conditions identified on CT (Fig. 2A-C). The solid black lines in Fig. 2D–F indicate the locations of the dorsal oblique slices shown in Fig. 2A–C and mark the precise planes from which AC pressure was extracted for comparison in Fig. 4.

Fig. 4
figure 4

Finite element (FE)-predicted articular cartilage (AC) pressure profiles plotted along the lateromedial width of the distal MC3, extracted through the slice locations indicated by the solid black lines in (Fig. 2D–F). (A–C) Pressure profiles from slice-based (solid line) and 3D (dashed line) FE models for the BS, LGL, and BCL horses, respectively. The top panels show the sagittal model orientation (left) and the dorsal-oblique slice used for profile extraction (centre). Computed tomography (CT) images (right) indicate lesion sites (white dashed boxes) for the lateral-groove lesion (LGL) and bilateral-condylar lesion (BCL) models, corresponding to the dashed rectangles on the plots marking the anatomical lesion positions. A broader peak in the pressure profile represents the redistribution of load across the condylar surface surrounding the lesion. Due to x-axis normalization, lesion positions may appear spatially similar across models despite anatomical differences (e.g., PSG vs. condylar lesions).

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Comparison of AC pressure slice-based and 3D models

Across the lateromedial direction (Fig. 4), AC pressure profiles showed close agreement between the slice-based and 3D FE models. Both models predicted peak pressures in the condylar regions and minimal pressures over the sagittal ridge, with an RMSE of 1.82 ± 0.46 MPa (average ± SD) for AC pressure across the three horses.

In the BCL horse, which had lesions in both condyles, redistribution of AC pressure was observed mainly over the medial lesion (~ 8 mm diameter), which was larger than the lateral lesion (~ 4 mm). Pressures were higher over the surrounding sclerotic SCB and lower over the lesion itself (13.2 MPa vs. 10 MPa, Fig. 4C). Additionally, in horses with subchondral lesions, the AC pressure profiles exhibited broader peaks, indicating load redistribution across the condylar surface adjacent to the lesions.

SCB intra-tissue stress/strain

Both the 3D and slice-based FE models showed similar overall patterns of stress, especially in the superficial SCB close to the AC (Fig. 5). Peak strains across the mediolateral ROIs were also similar between 3D and slice-based FE models (Fig. 6) across all three horses (BS, LGL, and BCL). Both models identified peak tensile (εt) and compressive (εc​) strains in the lateral and medial PSGs and the LC and MC, and minimal strains over the SR. However, the slice-based models underestimated strain magnitudes in most areas especially in the BS horse, with a percent difference of 11.38 ± 4.83 and 11.83 ± 6.77 for tensile and compressive strains, respectively. Similarly, both models predicted similar patterns for the volume of SCB at high-risk of initial failure (Fig. 6). However, the 3D model predicted a greater highly strained bone volume, especially in the BS horse, compared to the slice-based model (Fig. 6). Furthermore, both models showed that regions with lesions in the LGL and BCL horses experienced elevated strains compared to the BS horse without SCB injury, indicating that the presence of lesions altered the strain patterns and/or characteristics of these bones and produced high strains that promoted lesion development. Across the SCB depth, both models predicted high tensile and compressive peak strains near the articular cartilage-SCB interface, and the strain values decreased towards the deeper layers of the SCB across all horses (Fig. 7). Figure 8 shows the principal strain directions within the ROI for each horse. Across all horses, compressive (minimum principal) strains were directed mainly perpendicular to the articular surface, and tensile (maximum principal) strains ran tangentially along it, indicating that compressive and tensile loading in the SCB act normal and parallel to the joint surface. The BS horse showed a uniform and symmetric pattern of strain directions. In contrast, the LGL horse displayed asymmetry, with strain directions deflecting around the lateral lesion while remaining aligned medially. The BCL horse showed more divergence, with strain directions fanning around both condylar lesions, indicating load redistribution. Similar orientation patterns were observed in both the 3-D and slice-based models.

Fig. 5
figure 5

Finite-element (FE)–predicted von Mises stress in the dorsal-oblique slice through the distal third metacarpal bone (MC3), corresponding to the slice plane indicated in (Fig. 1D,F). The corresponding CT slices for each horse are shown in (Fig. 2A–C). Top row (A–C): 3-D FE models; bottom row (D–F): slice-based FE models for the bilateral sclerosis (BS), lateral parasagittal-groove lesion (LGL), and biaxial condylar-lesion (BCL) horses, respectively. Stress distribution is displayed using a consistent colour scale (MPa), with red denoting higher stress and blue denoting lower stress.

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Fig. 6
figure 6

Comparison of tensile strain (εt​), compressive strain (εc​), and maximum principal stress (σt) and volume of bone with strains exceeding 90th percentile (VNHR, %) between 3D (blue lines) and slice-based (red lines) finite element (FE) models across three conditions: no lesion (BS), lateral parasagittal groove lesion (LGL), and bicondylar palmar osteochondral disease lesion (BCL) in the equine third metacarpal bone (MC3). Each graph represents values sampled across consecutive 3 mm-wide mediolateral regions of interest (ROIs). Vertical dashed lines indicating anatomical landmarks of lateral condyle (LC), lateral parasagittal groove (LPSG), sagittal ridge (SR), medial parasagittal groove (MPSG), and medial condyle (MC) for each joint. Both tensile and compressive strains are plotted as positive magnitudes.

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Fig. 7
figure 7

Comparison of tensile (A, left) and compressive (B, right) strain distributions between 3D (blue) and slice-based (red) finite element (FE) models across the subchondral bone (SCB) depth within the simulated dorsal-oblique slice. Strains represent 90th percentile values within 3 mm-wide mediolateral subdivisions corresponding to the lateral condyle (LC), lateral parasagittal groove (LPSG), medial parasagittal groove (MPSG), and medial condyle (MC). The plotted SCB depth spans ~ 0–16 mm (rather than 0–20 mm) because the sagittal ridge (SR) region, showing minimal strain, was excluded. Peak strains occurred near the distal (most superficial) SCB surface, particularly in regions of lytic bone. The y-axis represents SCB depth, with 0 mm at the AC–SCB interface (distal) and 16 mm at the deepest SCB (proximal).”

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Fig. 8
figure 8

(A–C) Dorsal oblique CT slices of the distal third metacarpal bone (MC3) from three horses showing bilateral sclerosis (BS, A), a lateral parasagittal groove lesion (LGL, B), and biaxial condylar lesions (BCL, C). Dashed rectangles denote the region of interest (ROI; 50 mm width, 20 mm depth, 1 mm thickness); arrows indicate lesion sites. Distal is oriented toward the top and proximal toward the bottom of each image. (D–F) Maximum (red) and minimum (black) principal strain directions within the ROI for each horse. Arrow orientation indicates the principal strain direction, and arrow length represents its relative magnitude. Compressive (minimum) principal strains are directed predominantly perpendicular to the articular surface, whereas tensile (maximum) principal strains are oriented tangentially. Patterns of principal strain direction were consistent between the slice-based and 3-D FE models.

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Sensitivity analysis

The sensitivity analysis demonstrated that variations in the Poisson’s ratio of the articular cartilage (AC) had the most pronounced effect on the FE model outputs. When the Poisson’s ratio was reduced from 0.4999 to 0.3, peak tensile stress increased by 23.5%, while tensile and compressive strains increased by 15.9% and 17.2%, respectively (Table 1). Changes in the shear modulus of AC (GAC) produced more moderate effects, with strain and stress changes remaining below 6%. Alterations to the elastic modulus of the PSBs and transverse properties of the ISL caused stress differences of up to 8.8%, particularly affecting tensile stresses. However, most other parameter changes, including assumptions on ligament isotropy and PSBs positioning, resulted in less than 5% variation in stress outputs. Specifically, shifting the PSBs medially or laterally by one pixel (affecting AC thickness by 0.7 mm) caused tensile stress changes of only 5.5%. Overall, the slice-based FE models exhibited strong robustness, with most stress and strain variations staying within acceptable margins, indicating resilience to minor segmentation errors and variability in material property assumptions.

Table 1 Percent change in peak (90th percentile) tensile and compressive strains and stresses and von mises stress within a defined SCB region of 8 mm depth, 50 mm mediolateral width and 1 mm thickness, based of slice-based FE models.
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Discussion

The pressure distribution patterns predicted by our 3D finite element models, with elevated palmar pressures and minimal loading along the sagittal ridge, are qualitatively consistent with the ex vivo measurements in Easton29 (Fig. 2.7), where a calibrated Tekscan pressure-mapping sensor was inserted at MC3 joint, under gallop-equivalent loading. This agreement supports the validity of our loading configuration and boundary conditions. Additionally, the strong agreement between the slice-based and 3D models, particularly in predicting the overall stress and strain patterns and the location of highly strained bone volume, supports the use of slice-based models as a valid, efficient alternative for identifying SCB regions with elevated risk of stress fracture.

Peak pressures in the 3D models aligned well with previous studies that report similar cartilage contact pressures under galloping loads using pressure sensors and FE models1,30. Unlike most previous models that either applied load directly to the MC331 or assumed the bone to be rigid1, our models simulated a more physiological load transfer through the ISL and PSBs to the SCB. This approach enables investigation of stress distribution patterns that correspond to common sites of fatigue microdamage in the superficial SCB and the sites of pathology in the specimens modelled, specifically in the condylar and PSG superficial SCB, while identifying negligible loads at the SR. The low stress observed at the SR highlights its lower susceptibility to fatigue failure under these conditions5,6. Identifying the condyles and PSGs as areas of elevated stress provides valuable insight into the biomechanical factors contributing to injury risk.

The differences between the slice-based and 3D FE-predicted strains in our study are smaller (~ 12%) than the 50% difference reported in other studies comparing simplified and complex FE models32,33. Differences between the 3D- and slice-based models can be attributed to the ability of 3D models to more fully capture complex geometry, load distribution, and stress concentration effects. This may explain the larger volume of highly strained bone in the 3D models, particularly in the BS horse, where the smaller overall bone volume made the difference more pronounced (Fig. 6, VNHR). Additionally, the orientation of principal strain directions provides further insight into joint loading. In all models, compressive strains acted predominantly perpendicular to, whereas tensile strains were tangential to the articular surface. In horses with focal lesions (LGL and BCL), principal strain directions deviated around the lesions, demonstrating how weakened bone regions redistribute the local load. Nevertheless, the overall patterns of stress and strain were similar in the distal SCB close to the AC-SCB interface between the 3D and slice-based models, suggesting that both models effectively identified high-risk areas within the joint. Additionally, accurate determination of the SCB elastic modulus for FE modelling is inherently challenging due to its high variability and heterogeneity, suggesting that the relative differences between the models may be of less importance34,35. Instead, the similarity in stress and strain distribution patterns is more important for identifying horses with elevated imminent risk of stress fracture.

This study also identified the Poisson’s ratio of AC as the most influential factor affecting SCB stress and strain in slice-based FE models of the equine MC3 joint. This finding highlights the importance of accurately modeling cartilage incompressibility and lateral deformation, which is better represented in our semi-3D framework than in simplified 2D plane-strain assumptions. Under high-rate galloping loads, AC behaves like an incompressible material, protecting the SCB through hydrostatic pressurization. When νAC was reduced to 0.3, mimicking degenerative cartilage25, SCB strains increased by ~ 16%, consistent with prior FE modelling studies36,37,38,39. In contrast, variations in PSB and ISL stiffness, or minor segmentation inaccuracies (one-pixel shifts corresponding to ~ 0.7 mm changes in AC thickness), had minimal impact (< 9% and < 6% changes, respectively), confirming model robustness.

Taken together, these findings highlight that slice-based FE models can match the overall predictive patterns of full 3D models while being approximately four times faster to develop, far easier to implement, and robust to minor segmentation or parameter variations. This efficiency and reliability make the slice-based approach a practical tool for large-scale or clinical applications, enabling rapid assessment of joint load distribution and early identification of animals at risk of SCB injury.

We chose to extract the CT slice for the slice-based FE models from the areas with pathologic changes such as subchondral sclerosis or lysis rather than the exact same site in all models. These are the common sites of subchondral fatigue injury and microdamage in Thoroughbred racehorses4, and therefore most relevant to assessing fracture risk. However, structural change may not always arise from the same site in the palmar aspect of MC3. For example, PSG subchondral focal osteolysis is often more proximal/palmar than POD lysis. Therefore, the CT slice used to develop each slice-based model was tailored to the specific lesion location in each horse to preserve physiological relevance. Because each slice was selected using consistent anatomical landmarks at the distal condylar region and compared directly with its corresponding 3D model from the same joint, this approach maintained biomechanical relevance while minimizing methodological bias due to minor positional differences among specimens.

The elastic modulus assigned to the PSBs (4,000 MPa) is consistent with the experimentally measured compressive stiffness of total PSB specimens (2.7 ± 0.5 GPa; Pearce et al., 2022). Sensitivity analysis showed < 9% variation in FE results when PSB stiffness was altered, confirming that this parameter had minimal influence on model outcomes. In this study, we modelled SCB using an E–BMD relationship derived from subchondral bone regions of the distal MC3 showing mild sclerosis19. This provided a biologically representative estimate of mechanical behaviour in the subchondral region. Lesion sites were assigned moduli from the lower-density range of this relationship, consistent with previously reported values for osteolytic lesions40, providing a conservative yet realistic representation of local stiffness reduction. Additionally, due to CT resolution and segmentation constraints, only larger lesion, typically greater than 6 mm in diameter, could be modelled reliably. This was primarily because of low contrast in CT images and partial volume effects at the lesion edges, which likely led to an overestimation of the density of small lesions, making accurate segmentation challenging, even with a fine mesh size. Importantly, this limitation means that the current modelling framework is more sensitive to focal lytic and sclerotic changes associated with palmar osteochondral disease (POD) or larger areas of bone lysis that can precede parasagittal condylar fractures but is limited with smaller areas of lysis often observed underlying the parasagittal groove. Additinally, this limitation arises from image resolution rather than the modelling framework itself and reflects a constraint also encountered in clinical imaging of subchondral pathology. While separate segmentation of lytic and sclerotic volumes could allow for more accurate assignment of subvolume material properties, this might result in abrupt, non-physiological changes between the lesion and the surrounding SCB. Future models incorporating higher-contrast CT images, improved segmentation methods, or an E–BMD relationship specifically accounting for specimens with such lesions40, may enable more accurate modelling of smaller lesions.

Another limitation of the current study is that we did not have access to joint-specific load data applied through the ISL for each case. Additionally, the exclusion of surrounding soft tissues, such as muscles and tendons, may reduce the precision of the biomechanical interactions modelled between bones, ligaments, and cartilage. As a result, both the 3D- and slice-based approaches are constrained by uncertainties in material properties, imaging resolution, and joint-specific load application, and these limitations should be considered when interpreting the results. In particular, these factors hinder accurate comparisons of strain magnitudes between horses, making it difficult to draw precise conclusions about which horse experienced higher strain and to establish correlations between mechanical strains and bone adaptation or bone homeostatic failure with microdamage accumulation. Although the number of specimens was limited (n = 3), we showed good agreement across a range of typical pathologies in racehorses. Additionally, the model comparisons consistently reproduced AC surface pressures reported in previous experimental measurements (Easton, 2012) and showed stress- and strain-pattern trends corresponding to common regions of POD and fracture, supporting the validity of the approach. The present work, therefore, represents a methodological validation; future studies will undertake experimental testing to confirm model predictions. Future work could focus on comparing slice-based FE model predictions with clinical outcomes to assess their utility in identifying early markers of joint pathology and injury risk. Inclusion of longitudinal CT imaging and validation of model predictions with experimental data could provide more accurate mechanical strain estimates, ultimately aiding in a better understanding of the mechanisms of bone adaptation and stress fractures. Nevertheless, our results on overall stress/strain patterns remain realistic, as they effectively identify common failure locations and areas of damage.

Conclusion

Our findings suggest that slice-based models can be a valuable tool for rapidly assessing biomechanical behaviour in equine joints, especially when precise material properties are difficult to obtain. Our CT-based FE models identified the superficial SCB in both PSGs and the MC3 condyles as locations with the highest risk of initial failure.