A three-dimensional (3D) finite-element model of the L3–S1 lumbar segment was developed based on imaging data of a healthy 31-year-old male volunteer. This study was approved by the Ethics Committee of the Sixth Medical Center of the General Hospital of the Chinese People’s Liberation Army [Ethics approval No. HZKY-PJ-2025-1]. The model simulated the biomechanical behavior following UBE across various combinations of BMI stratification, osteoporosis, and disc degeneration. Geometry and meshing were performed in ANSYS APDL 13.0 (ANSYS Inc., United States), following the parameterization protocol of Viceconti et al. (2005). The model comprised: Vertebral bodies include cancellous bone, cortical shell, and cartilaginous endplates; Posterior elements include spinous processes, pedicles, transverse processes, and articular facets; Intervertebral discs include annulus fibrosus and nucleus pulposus; Ligaments include anterior longitudinal ligament (ALL), posterior longitudinal ligament (PLL), ligamentum flavum (LF), supraspinous ligament (SSL), interspinous ligament (ISL), intertransverse ligament (ITL), and facet joint capsule (FJC). The overall modeling workflow is summarized in Figure 1.

Material properties for all anatomical components were assigned from published sources (Table 1) (Polikeit et al., 2003; Schweitzer et al., 2007; Bresnahan et al., 2009). The intervertebral disc was modeled as a composite, with annulus fibrosus and nucleus pulposus occupying 56% (674 mm²) and 44% (539 mm²) of its cross-sectional area, respectively. The annulus fibrosus was modeled as an anisotropic material to reflect its lamellar architecture, while the nucleus pulposus was treated as quasi-incompressible. Facet joints were defined as low-friction sliding contacts (coefficient of friction = 0.1), permitting limited relative motion between articular surfaces. Cartilaginous interfaces were specified as bonded contacts. Ligaments were modeled as nonlinear, tension-only elements using second-order reduced-integration formulations.

To apply loads and extract responses, remote points were placed on the superior surfaces of the L3–S1 vertebral bodies, facilitating the application of moments and the measurement of outcome metrics such as ROM.

Mesh generation was conducted in ANSYS Workbench using second-order tetrahedral elements. Element sizes ranging from 1 to 5 mm were tested, and von Mises stress in the L4–L5 nucleus pulposus under a 10 N·m flexion moment was evaluated for mesh sensitivity (Karpiński et al., 2017). Reducing the element size from 2 to 1 mm altered the stress by only 1.45%, satisfying the accuracy criterion; therefore, a 2 mm mesh was adopted for all subsequent simulations. The final mesh comprised 127,622 elements.

Mesh independence was further verified under a combined load of 500 N axial compression and 6 N·m flexion/extension moments (Wilke et al., 1994). Convergence was defined as a change of less than 5% in the target stress between successive refinements, with the relative variation calculated accordingly. Δ % = σ n − σ n − 1 σ n − 1 × 100   %

Stress values stabilized (variation <5%) once the mesh comprised approximately 1.276 × 10⁵ elements; accordingly, this mesh was chosen for subsequent simulations (Figure 2).

Disc degeneration was simulated according to the Pfirrmann and Thompson grading systems by proportionally reducing the disc height and the area of the nucleus pulposus. Grades I–II were classified as normal, grade III as mild degeneration, and grades IV–V as severe degeneration. Using the validated baseline L3–S1 finite-element model (Zhang and Han, 2023), disc height was reduced by 20% for mild and 60% for severe degeneration; the corresponding loss of nucleus pulposus volume was replaced with annulus fibrosus tissue to conserve total disc volume. Concurrently, the material properties of the endplates and disc tissues were adjusted to reflect endplate sclerosis and other degenerative changes.

Osteoporosis was modeled by reducing bone mineral density (BMD) in both cortical and cancellous bone, thereby reflecting the systemic nature of the disease (Kang et al., 2022). Both bone types were represented as anisotropic materials, with distinct elastic moduli assigned to healthy and osteoporotic conditions. In the osteoporotic model, elastic moduli were uniformly decreased to mirror the reduced stiffness associated with lower BMD. Detailed material properties for both disc-degeneration and osteoporosis scenarios are summarized in Table 2.

The L4–L5 segment was used to simulate UBE decompression. Through two ipsilateral portals, a 6.9-mm endoscopic trephine created a medial laminotomy with full-thickness flavectomy and limited medial facet trimming to decompress the ipsilateral side, then undercut the spinous base and contralateral lamina to the lateral recess for contralateral decompression; facet cartilage was minimally debrided with subchondral bone preserved, and ≥50% of the bony facet was retained (Sellier et al., 2024). The surgical resections and decompression corridor were parameterized to reflect the clinical pathway and qualitatively checked for anatomical correspondence. The procedural steps and surgical trajectory are depicted in Figure 3.

Loading conditions were designed to reflect both BMI-dependent body weight and standardized boundary constraints. Based on a reference height of 1.75 m, four body-mass scenarios (70, 80, 90, and 100 kg) were modeled, corresponding to BMIs of 22.86, 26.12, 29.39, and 32.65 kg/m², respectively. For each case, a vertical compressive load equivalent to two-thirds of body weight (457, 523, 588, and 653 N) was applied to the superior surface of L3 to simulate physiological axial loading (Zhang et al., 2024).

Two distinct load cases were defined and used consistently throughout the study: Scheme Validation: 150 N axial preload applied on L3 and ±10 N·m pure moments to reproduce standard in-vitro validation conditions. Scheme Primary simulations: BMI-mapped axial compression (two-thirds body weight; 457/523/588/653 N) applied on L3 and ±10 N·m pure moments; no additional 150 N preload was added. The inferior surface of S1 was fully constrained for both schemes.

The inferior surface of S1 was fully constrained in all degrees of freedom. In Scheme Validation, a 150 N axial preload was applied on L3 prior to the ±10 N·m moments. In Scheme Primary simulations, the BMI-mapped axial compression replaced any additional preload. (Yamamoto et al., 1989; Chen et al., 2001). Pure moments of ±10 N·m were then imposed through remote points to simulate six principal motions: flexion, extension, left and right lateral bending, and left and right axial rotation.

This unified loading scheme ensured consistency across BMI groups and allowed direct comparison of range of motion (ROM), intradiscal pressure (IDP), and facet-joint stress under identical boundary conditions (Karpiński et al., 2019).

To ensure predictive stability and biomechanical reliability, we validated the segmental ROM for the intact (M0), osteoporosis (OP), and disc-degeneration (DD) models against established experimental and numerical studies (Cai et al., 2020).

Outcome measures included segmental ROM (°), intradiscal pressure (IDP, MPa) at the nucleus pulposus (pressure surrogate), and tissue von Mises stress (MPa) at the facet joints and endplates Additionally, we evaluated the distribution and magnitude of disc stress-concentration zones for each loading scenario (Figure 6).

The independent biomechanical effects of BMI, osteoporosis, and intervertebral disc degeneration are summarized below.

1. BMI: Each incremental increase in BMI elevated nucleus pulposus pressure (NP pressure; IDP) by approximately 9%–12% in non-degenerated discs and shifted loads posteriorly; in degenerated discs, NP pressure remained lower overall, whereas annular (disc-internal) stress and facet-joint von Mises stress increased, indicating an amplifying effect of body weight on load transfer.

A multifactorial assessment of BMI, osteoporosis, and disc degeneration yielded two primary observations:

1. Nonlinear Synergistic Amplification: Under high BMI (32.65 kg/m²) combined with severe osteoporosis and severe degeneration, posterior-element loading increased non-additively. Peak facet-joint von Mises stress rose from 1.02 MPa to 2.47 MPa, exceeding the sum of single-factor effects and indicating pronounced nonlinear amplification.

Decompressive UBE removes portions of the lamina and ligamentum flavum, reducing posterior-column bending stiffness and shifting greater moments to remaining structures. Our simulations confirmed a decrease in flexion-extension stiffness of lumbar segments following decompression. Montanari et al. similarly reported that two-level laminectomy in vitro markedly increased lumbar flexion ROM and disc strain, as loss of posterior support forced anterior discs and posterior facets to bear higher bending loads (Montanari et al., 2024). An elevated BMI further exacerbates this load transfer: increased body weight raises axial spinal loads, thereby imposing additional stress onto the anterior column. Takatalo et al. demonstrated in a finite-element study that obesity significantly increased lumbar segmental mobility and intradiscal pressure compared to normal weight (Takatalo et al., 2013). Epidemiological data link higher BMI to accelerated degeneration of discs and facets, thereby increasing lumbar stenosis and spondylolisthesis risk (Schuller et al., 2011). Schuller, Charles, and Steib et al. found that 71.4% of patients with L4–L5 degenerative spondylolisthesis were overweight (BMI >25), attributing slips in part to obesity-induced overload (Alexiou and Voulgaris, 2013). Consistent with these findings, our model demonstrated that under high BMI, bending loads after UBE are predominantly borne by the anterior column and facet joints, underscoring the amplifying effect of obesity on postoperative load redistribution.

Prior biomechanical studies have predominantly employed univariate designs, examining obesity, osteoporosis, or disc degeneration in isolation. Obesity is a well-established risk factor that increases lumbar loading, elevates IDP, and accelerates degeneration. Similarly, osteoporosis characterized by reduced bone mineral density—weakens spinal load-bearing capacity, yielding greater displacements and stress responses under equivalent loading or surgical conditions (Zou et al., 2024). Han et al. used finite element analysis to compare disc degeneration in normal versus osteoporotic spines, demonstrating that degeneration in osteoporotic models redistributes loads—decreasing stresses in cortical bone and endplates while increasing stresses in cancellous bone and posterior facets. Cai et al. simulated graded L4–L5 degeneration, finding that severe degeneration reduced segmental ROM by up to ≈75% (e.g., axial rotation) while increasing adjacent-segment ROM, IDP, annulus-fibrosus stress (0.4–2.6 MPa), and neighboring facet-joint loads. Although these single-factor investigations clarified individual influences, they failed to account for non-linear superposition when pathological factors coexist. In contrast, our study represents the first attempt to incorporate elevated BMI, osteoporosis, and disc degeneration within a unified finite-element framework, thereby capturing their synergistic effects on L4–L5 biomechanics and providing a more clinically representative model.

Besides, most prior studies have not incorporated the biomechanical impact of the surgical pathway itself. Most finite element and in vitro investigations simulate the intact preoperative spine, with little consideration of decompressive alterations. For example, stand-alone laminectomy often compromises segmental stability and can precipitate vertebral slippage (Simon et al., 2022), whereas tubular minimally invasive decompression preserves portions of the posterior column—maintaining global stability but subjecting remaining structures to elevated local stresses (Dhar et al., 2024). In a recent finite-element comparison of percutaneous transforaminal endoscopic discectomy (PTED) versus unilateral biportal endoscopy (UBE) at L4–L5, Zou, et al. reported that both techniques minimally affected overall ROM and disc stress, with UBE exhibiting local stability loss only under specific motions (e.g., L4–L5 maximal displacement rose by ≈ 16–18% during lateral bending and peak stress increased by ≈ 11.7% in left axial rotation). Overall, biomechanical models that explicitly simulate the surgical pathway remain scarce.

By integrating three common clinical pathologies—elevated BMI, osteoporosis, and disc degeneration—into a finite-element model that includes postoperative decompressive anatomy, this study systematically deciphers the layered mechanisms governing L4–L5 stability and load response after UBE. Our results validate the Introduction’s hypothesis that the coexistence of these factors induces stress imbalance and latent instability after UBE. Individually, each pathology alters segmental mobility and internal stress; in combination, they interact nonlinearly, creating a “pseudo-stability” that conventional assessments may overlook. These findings underscore the need for comprehensive preoperative evaluation and postoperative management that account for multiple risk factors, distinguishing apparent stability from internal stress overload. This paradigm offers a theoretical foundation for personalized rehabilitation, re-herniation prevention, and individualized patient care. This work co-frames BMI, degeneration, and osteoporosis in a unified, procedure-concordant FE model to minimize cross-study heterogeneity, and delivers practical guidance for BMI ≥30 with low bone mass and advanced degeneration—namely avoid early end-range axial rotation/lateral bending, implement time-bound weight control, and initiate/schedule anti-osteoporotic therapy.

In light of our findings, several clinical implications emerge. First, patients with high BMI, osteoporosis, or severe disc degeneration demonstrated a greater tendency toward postoperative instability after UBE. This suggests that these risk factors should be carefully evaluated in preoperative planning, and whenever possible, optimized through weight reduction and osteoporosis management prior to surgery. Second, the observed “pseudo-stability” phenomenon indicates that conventional kinematic assessments may underestimate hidden stress overload, particularly in obese or osteoporotic patients with advanced degeneration. Clinicians should therefore exercise caution when interpreting preserved or mildly reduced ROM on imaging, as this may mask substantial internal biomechanical risks. Third, our results highlight the importance of tailored postoperative rehabilitation. Specifically, strategies such as core muscle strengthening, sustained weight control, and pharmacological or lifestyle interventions to improve bone density may help mitigate stress overload, prevent recurrent instability, and reduce the likelihood of adjacent-segment degeneration.

Although finite-element analysis has been widely used in spinal biomechanics since the 1970s and offers low susceptibility to external variables with strong controllability, its fundamentally static nature cannot fully replicate complex neuromuscular control (Ribeiro et al., 2024). Our simulations were performed under quasi-static loads (BMI-matched axial compression plus ±10 N·m pure moments) to provide stable, comparable end-range responses across 24 combinations; however, this design does not capture time-dependent tissue behavior, muscle activation patterns, or repetitive daily activities. Moreover, the current model is based on the lumbar geometry of a single healthy male, limiting generalizability across sex, body habitus, and age. Consequently, the absolute magnitudes of ROM, IDP, and facet stress should be interpreted with caution and not read as task-specific values (e.g., walking, lifting) nor as implying fatigue or cumulative damage; the intended interpretation is trend-level—under the modeled conditions, higher BMI and the presence of osteoporosis or severe degeneration are associated with reduced post-UBE segmental stability and increased local tissue loading. To broaden realism and quantify variability, future work will (i) generate multi-subject models from CT datasets spanning age/sex morphologies, (ii) perform probabilistic/parametric analyses that vary key geometric and material parameters within reported ranges, (iii) couple musculoskeletal estimates of muscle forces to subject-specific anatomies, and (iv) incorporate fatigue behavior with representative cyclic load histories (e.g., repeated flexion–extension and axial-rotation, and a walking-like pattern). Finally, validation against longitudinal clinical outcomes will be crucial to develop individualized, dynamic biomechanical assessments.