Introduction

Adjacent segment diseases (ASDs) are prevalent after lumbar fusion surgery [1]. Alterations in the kinetics of a motion segment likely paly a causal role in the mechanobiology of disc degeneration [2]. As far as postoperative ASDs are concerned, these changes may come as a result of surgically induced modifications in thoraco-lumbo-pelvic kinematics, spinal anatomy, and paraspinal muscle cross-sectional areas [3,4,5]. With no noninvasive in vivo technique available, in vitro setups [6] and force-controlled passive finite element (FE) models [7,8,9] have emerged as alternative measures to investigate the postoperative alterations in the spine biomechanics. Neglecting the crucial role of muscle forces before and after surgical interventions, however, casts doubt on the reliability of these results [10, 11]. In response, musculoskeletal (MS) models of the spine that incorporate the muscle activation have been considered when studying the effects of fusion surgery on spine kinetics [12,13,14,15].

Previous MS model studies have investigated the role of surgically induced alterations in the segmental lordosis, spinal anatomy, segmental kinematics, lumbopelvic rhythm (ratio of total lumbar rotation divided to pelvis rotation [16]), and muscle cross-sectional areas as well as the preoperative segmental conditions on the postoperative adjacent segment kinetics [12,13,14,15]. Despite their consideration of muscle forces, these MS models nevertheless idealize passive spinal motion segments to different degrees as frictionless spherical joints, bushing elements, or shear-deformable beams with nonlinear properties. As such, they can only predict the overall segmental compression and shear loads; they fail to determine the disc compression/shear loads, ligament/facet forces, internal stresses/strains. As a remedy, hybrid models have been introduced to combine the advantages of geometrically detailed passive FE models and active musculature in MS models [17,18,19,20]. In this approach, muscle forces are first calculated using a MS model with idealized motion segments and subsequently applied in a feedforward manner onto a detailed passive FE model to determine joint load-sharing and internal stresses. This hybrid simulation, however, is cumbersome in requiring multiple rounds of analyses and corrective iterations between these two distinct models. Moreover, errors in the predicted force in muscles and passive tissues are inevitable because of the quite dissimilar passive representations in these two models and the complex load- and motion-dependent nonlinearities of the passive spine [10, 21].

Recently, we developed and validated a fully coupled MS-FE thoraco-lumbo-pelvic (T12–S1) model in which the detailed active and passive structures are both present together within a single model [21]. The present study aims to use this model to evaluate the alterations in adjacent segment kinetics following a single-level (L4–L5) solid fusion surgery. Two distinct simulations are carried out for each of the preoperative and postoperative conditions. These four simulations represent patients having: (1) an intact (healthy) or a preoperative condition with normal or mild degeneration that does not noticeably affect spinal kinematics, (2) a preoperative high-grade L4–L5 degenerated segment with substantial loss of disc height and motions, (3) a postoperative fused L4–L5 segment with fixed lumbopelvic rhythm (LPR) with respect to the intact condition (where the lost motion at the fused segment is compensated by adjacent segments) based on clinical observations [22], and (4) a postoperative fused segment with altered LPR (where the lost motion at the fused segment is compensated by the pelvis alone) based on some other observations [23]. Surgically induced changes in segmental and pelvis kinematics as well as muscle cross-sectional areas (due to intraoperative iatrogenic injuries) are considered while simulating three static daily activities. Using such a model could substantially improve our understanding of the biomechanical etiology of ASDs. It is hypothesized that different postoperative lumbopelvic (with fixed or altered rhythm) and preoperative (intact or degenerated) scenarios affect adjacent segment kinetics to quite different degrees.

Methods

Preoperative intact model

An intact preoperative L4-L5 disc condition is simulated. This represents an intact (healthy) or a preoperative condition with normal or low-grade degeneration that does not affect spinal kinematics. A previously developed coupled 3D MS-FE model consisting of the pelvis, thorax, lumbar vertebrae, intervertebral discs (nucleus and annulus as a composite of a homogeneous matrix reinforced by collagen fiber networks), ligaments, facet joints, and 56 local and global muscle fascicles with their wrapping effects is used (Fig. 1) [21]. The FE model is reconstructed in ABAQUS (version 6.12, Simulia Inc., Providence, RI, USA). For the annulus matrix, material properties are modified based on findings of a recent study [24]; a compressible Mooney–Rivlin hyperelastic model (C1 = 0.18, C2 = 0.045, D = 0.2). Annulus collagen fibers are represented with 14 distinct membrane layers reinforced with rebar elements distributed throughout the annulus matrix [10] (at ± 30° with nonlinear properties [25]). Facet joints are modeled via surface-to-surface contacts (frictionless) having a gap limit of 1.25 mm [10]. Ligaments are considered as uniaxial tension elements having nonlinear properties [25]. Each nucleus is modeled as an incompressible fluid-filled cavity [10]. The trunk weight of ~ 344 N (corresponding to a body mass of ~ 68 kg) is partitioned among upper arms (~ 36 N), forearms/hands (~ 29 N), head (46 N), and T1–L5 segments (~ 233 N) that are applied via rigid elements at their centers of mass [10]. For each activity in neutral upright standing and flexion postures (“Simulated tasks” section), the measured sagittal rotations of thorax and pelvis [26, 27] as well as the estimated individual lumbar rotations [27,28,29] are prescribed into the model. Sum of cubed muscle stresses was minimized through an optimization approach to determine muscle forces using an in-house code [21].

Fig. 1
figure 1

The intact 3D musculoskeletal finite element (MS-FE) spine model and its musculature in the sagittal (left view) and coronal (front view) planes. Local muscles: ICPL: iliocostalis lumborum pars lumborum, LGPL: longissimus thoracis pars lumborum, MF: multifidus, QL: quadratus lumborum, and IP: iliopsoas. Global muscles: ICPT: iliocostalis lumborum pars thoracic and LGPT: longissimus thoracis pars thoracic. Abdominal muscles include: IO: internal oblique, EO: external oblique, and RA: rectus abdominis. Ligaments: the anterior longitudinal (ALL), posterior longitudinal (PLL), capsular (CL), intertransverse (ITL), ligamentum flavum (LF), supraspinous (SSL), interspinous (ISL), fascia (L4 and L5 to ilium), and iliolumbar (IL, L5 to ilium) ligaments. Vertebrae are not shown in the coronal view

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Preoperative degenerated model

A severely degenerated and narrowed L4–L5 disc is considered in the preoperative state. Fat infiltration in muscles is represented by reducing physiological cross-sectional areas (PCSAs) of paraspinal muscles; 14 and 11% for, respectively, multifidus and erector spinae at all fascicles crossing over the L4–L5 [5, 30]. The L4–L5 disc degeneration is modeled by reducing the disc height by ~ 60%, eliminating the nucleus incompressibility by setting its bulk modulus to 10 MPa, and offsetting the force–deformation curves of ligaments and fibers to account for their slackness while preserving annulus ground material properties unchanged [31,32,33,34,35]. In vivo imaging data indicate that, compared to healthy individuals, LPR decreases (i.e., the contribution of the pelvis to the forward trunk flexion increases) in these patients [36, 37]. Furthermore, MR images [38] show that the loss of motion at the degenerated (i.e., stiffened) L4–L5 segment is compensated by the hypermobility of motion segments at the thoracolumbar junction. Therefore, LPR is reduced by 20% and the reduced motion at the degenerated L4–L5 segment is compensated by larger motion at the T12–L2 segments.

Postoperative fused models

Simulations of fusion are considered only for the preoperative intact model (“Preoperative intact model” section) since nearly similar postoperative models are expected for the preoperative degenerated state [12]. The fused model has a rigidly connected L4 and L5 vertebrae. Prescribed kinematics at vertebrae and pelvis as well as injured muscle PCSAs are also as follows:

Postoperative alterations in kinematics

When the L4–L5 vertebrae are rigidly fused, the remaining segments postoperatively undergo greater rotations in order to accommodate the same posture and upper trunk flexion angle as in the preoperative condition. Based on in vivo imaging data, two approaches are adapted. First, the postoperative LPR is kept unchanged and therefore the lost L4–L5 motion is produced by the T12–L4 and L5–S1 segments. To simulate this condition, the individual lumbar rotations are recalculated based on pre- and postoperative upright X-ray measurements [22]. Second, and according to another in vivo study [23], the lost motion at the L4–L5 segment after fusion is compensated by the pelvis alone.

Alterations in muscle areas

Intraoperative injuries to paraspinal muscles are modeled based on our MR image measurements [5, 30]; the PCSAs of multifidus and erector spinae fascicles crossing over the L4–L5 segment are reduced in postoperative models by 26% and 11%, respectively.

Simulated tasks

Three regular static sagittal-symmetric daily activities in the standing are considered: one in the upright posture and two in forward trunk flexions of 40° (mid-flexion) and 80° (deep-flexion) [22, 27, 38].

Results

Changes in adjacent segment kinetics after the fusion surgery were computed that depended on the postoperative lumbopelvic kinematics and preoperative L4-L5 disc condition (Figs. 2, 3, 4, 5, 6, 7 and 8, Table 1). A substantial change (assumed here to be > 25%), as compared to the preoperative intact or degenerated states, in model outputs highlights an increase in the risk to initiate/accelerate postoperative ASDs [12]. The predicted postoperative alterations in adjacent segment gross compression and shear forces as well as global/local/total muscle forces (Figs. 2 and 3) were found, under the same load-kinematics, in overall agreement with our earlier modeling results using a MS model with segments idealized by nonlinear beams. Novel results on adjacent segment IDPs (Fig. 4), intervertebral disc compression/shear loads (Fig. 5), vector sum of all ligament/facet forces (Fig. 6), and stresses/strains in the disc (Figs. 7 and 8) that could not be predicted by the earlier MS model are therefore the focus of the present study. Postoperative alterations in adjacent level disc shear forces (Fig. 5b), facet/ligament forces (Fig. 6), and annulus stresses/strains (Figs. 7 and 8) were relatively greater than those found in disc IDPs (Fig. 4) and compression forces (Fig. 5a). Adjacent segment kinetics at the lower (L5–S1) and upper (L3–L4) segments altered to different degrees following the surgery.

Table 1 Changes (%) in adjacent segment IDP, disc compression and shear loads, maximal annulus principal stress, posterior collagen fiber strain as well as vector sum of ligament forces and facet contact forces in fused/degenerated states relative to intact state (left section) and in fused states relative to degenerated state (right section) in upright and flexed postures. Magnitude of changes is depicted by five color-coded levels (see the legend below). Ligament forces for intact and degenerated states were ~ 0 in upright standing at both upper and lower levels and in flexion 40° at upper level. Therefore, their relative changes are depicted with (−). Note that large relative changes (%) at upper level facet forces can be seen in fused models in flexion 80° as compared to preoperative degenerated state despite the fact that their absolute changes are < 80 N (Fig. 6b)
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Fig. 2
figure 2

Sum of bilateral forces (N) in a global (ICPT and LGPT), b local (ICPL, LGPL, IP, MF, and QL), and c all muscles

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Fig. 3
figure 3

Overall segmental compression (left) and shear (right) forces (N) at adjacent levels (L3–L4 and L5–S1) for different pre- and postoperative conditions in the upright and flexed postures

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Fig. 4
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Intradiscal pressure (IDP) (MPa) at adjacent levels (L3–L4 and L5–S1) for different pre- and postoperative conditions in the upright and flexed postures

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Fig. 5
figure 5

Disc compression (left) and shear (right) forces (N) at adjacent levels (L3–L4 and L5–S1) for different pre- and postoperative conditions in the upright and flexed postures

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Fig. 6
figure 6

Vector sum of forces in all ligaments (N) (left) and on bilateral facet articular surfaces (FJFs) (N) (right) at adjacent levels (L3–L4 and L5–S1) for different pre- and postoperative conditions in the upright and flexed postures

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Fig. 7
figure 7

Absolute maximal principal stress in the disc annulus ground substance (MPa) (left) and maximum tensile strain in the disc posterior fibers (%) (right) adjacent levels (L3–L4 and L5–S1) for different pre- and postoperative conditions in the upright and flexed postures

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Fig. 8
figure 8

Contour plots of maximal principal stresses (MPa) in the disc annulus for different pre- and postoperative conditions in the flexed posture of 80°

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Degenerated versus intact models (pre-operation)

In the upright standing, predictions of the degenerated and intact models were close with changes generally negligible and < 10% (Figs. 2, 3, 4, 5, 6 and 7, Table 1). In flexion tasks, however, the degenerated model predicted overall substantially smaller global (Fig. 2a) and larger local (Fig. 2b) muscle forces, smaller disc shear forces (Fig. 5b, Table 1), smaller ligament forces (Fig. 6a, Table 1), smaller upper adjacent segment facet forces and larger lower segment facet forces (Fig. 6b, Table 1) specially at the greater flexion angle. Changes in total muscle forces (Fig. 2c), adjacent level IDPs (Fig. 4, Table 1), and disc compression forces (Fig. 5a, Table 1) were less pronounced (< 25%) in the degenerated model. Maximum principal stresses in the annulus ground substance (Figs. 7a and 8) and collagen fiber strains (Fig. 7b) remained almost unchanged with alteration generally < 10% (Table 1).

Fused model (post-operation)

In the upright standing, predictions of the fused model were generally close to those of both preoperative intact and degenerated models (Figs. 2, 3, 4, 5, 6 and 7 and Table 1). In flexion tasks with a fixed LPR, ligament forces and disc annulus stress/fiber strain substantially increased (Figs. 6, 7 and 8, Table 1). In contrast, and as a result of these increases in passive tissue load-bearing contribution, sum of total muscle forces (Fig. 2c) and, hence, segmental compression (Fig. 3a) decreased. However, alterations in adjacent disc IDPs and compression forces (Figs. 4 and 5a, Table 1) were overall less pronounced (< 25% almost everywhere). Adjacent level disc shear forces generally substantially increased especially when compared to the degenerated model (Fig. 5b and Table 1). Adjacent level facet forces were much larger at the lower level where they increased at the smaller flexion angle, whereas decreased at the larger flexion angle (Fig. 6b and Table 1).

In altered LPR models, alterations generally disappeared (Figs. 2, 3, 4, 5, 6, 7 and 8, Table 1) except for global muscle forces (Fig. 2a) and facet forces compared to both preoperative states (Fig. 6b, Table 1), disc shear forces at upper level compared to the preoperative degenerated state (Fig. 5b, Table 1), and ligament forces at large flexions as compared to preoperative degenerated state (Fig. 6a, Table 1).

Discussion

A fully coupled MS–FE spine model was used to investigate, for the first time, the effects of alterations in spinal kinematics and muscle cross-sectional areas on adjacent segment biomechanics following a single-level L4–L5 solid fusion surgery. Unlike previous passive FE models [7,8,9, 39, 40], this model incorporated musculature and associated distinct pre- and postoperative role of muscle activations in spinal loads. Moreover, a preoperative high-grade L4–L5 degenerated segment with substantial loss of disc height and motions was considered. Different postoperative lumbopelvic (fixed or altered lumbopelvic rhythm) and preoperative (intact or degenerated) scenarios affected adjacent segment kinetics to different degrees (hypothesis confirmed) (Table 1). Postoperative alterations in spine kinematics were found as the primary factor affecting spine biomechanics. The extent of changes is depended also on the segment (upper versus lower) and preoperative condition (intact versus degenerated disc). Postoperative relative alterations in adjacent level disc shear forces (Table 1 and Fig. 5b), facet/ligament forces (Table 1 and Fig. 6), and annulus stresses/strains (Table 1, Figs. 7 and 8) were greater than those found in disc IDPs (Table 1 and Fig. 4) and disc compression forces (Table 1 and Fig. 5a). Such large changes likely play a role in the biomechanical etiology of ASDs.

Previous in silico biomechanical studies frequently considered passive FE models under idealized constant moments and compressive follower loads that remained identical in both pre- and postoperative conditions [7,8,9, 39, 40]. Foregoing loads actually resemble those in in vitro loading protocols rather than physiological in vivo tasks. Based on the loading protocol considered in these passive FE models (i.e., stiffness, flexibility, hybrid loading), adjacent segment IDPs and disc annulus stresses were found to either increase or remain unchanged. Segmental shear, disc shear, facet forces as well as their postoperative alterations could not accurately be predicted given the idealized nature of the compressive follower load applied [12]. In contrast, our current coupled MS-FE model simulations highlight the importance of postoperative alterations in adjacent segment shear forces that also affect facet contact loads. In accordance, clinical studies have identified listhesis and facet hypertrophy as some of the main causes of ASDs [41, 42]. Postoperative alterations in the disc compression and IDP were found less pronounced in our MS-FE model (Table 1).

Due to larger rotations at adjacent segments, forces in deeper posterior ligaments (ISL and SSL) were predicted to be much larger in the simulated fused model with fixed LPR. Fusion surgery also increased the collagen fiber strains and annulus matrix stresses (Table 1). These changes could contribute to the degradation and failure of soft tissues that may ultimately result in proximal junctional kyphosis (PJK) [43] and disc prolapse [44]. Moreover, there was an increase in disc shear forces especially when compared to the preoperative degenerated state. Animal and in vitro studies have indicated that shear loading [45, 46] and hyperflexion [47] can cause disc degeneration. It therefore appears that, by substantial increases in internal forces, stresses, and strains, alterations in spine kinematics after a fusion surgery expose adjacent level discs, facets, and posterior ligaments to further risk of biomechanical damages and ASDs.

In the MS model with a detailed FE passive spine (i.e., the MS-FE model), some limitations are noteworthy. Simulations were not subject-specific; pre- and postoperative generic models were reconstructed based on the CT images of a cadaver specimen [48] and driven by population-based data on the trunk musculature and passive material properties. As such and for more accurate estimations, the model should be personalized in both passive and active components [49]. Prescribed input vertebral kinematics were also based on limited population-based mean data reported in the literature. Two extreme scenarios were considered in post-fusion simulations (e.g., patients with fixed or altered postoperative lumbopelvic rhythm with respect to preoperative conditions) when compensating the eliminated motion at the fused segment while under identical trunk RoM preoperative and postoperative. Contradictory results on changes in the adjacent segment motions have been reported in the literature (e.g., increased/decreased/unchanged adjacent segment motion) [4]. However, in many of these studies, the overall trunk range of motion is not similar pre- and post-surgery. Besides, the severity of disc degeneration at the operated level could influence postoperative motions. Despite its effects on adjacent segment kinetics, available literature on changes in pelvis rotations after fusion remains limited [23]. The effects of changes in segmental lordosis or overall spinal configuration/anatomy were not considered in this study. Finally, our model employed an optimization method to estimate muscle forces; the central nervous system may adapt a different control strategy that could also differ in pre- and postoperative conditions.

Conclusion

Postoperative alterations in adjacent disc shear forces, facet/ligament forces, and annulus stresses/strains were much greater than those found in disc IDPs and compression forces. These changes that differed between the upper (L3–L4) and lower (L5-S1) adjacent segments were due primarily to postoperative alterations in lumbosacral segmental rotations. Postoperative changes in these lumbosacral angles should hence be minimized.