Biomechanical analysis of variants of spinopelvic fixation of longitudinal sacral fractures by the finite element method Текст научной статьи по специальности «Медицинские технологии»

A.A. KULESHOV ET AL., 2023

biomechanical analysis of variants

of spinopelvic fixation of longitudinal sacral fractures by the finite element method

A.A. Kuleshov1, N.A. Aganesov1, M.S. Vetrilel, A.V. Dof, I.N. Lisyansky1, S.N. Makarov1

1National Medical Research Center of Traumatology and Orthopedics named after N.N. Priorov, Moscow, Russia 2Saratov National Research State University named after N.G. Chernyshevsky, Saratov, Russia

Objective. To analyze the strength of three types of spinopelvic fixation system configurations in longitudinal fracture of the sacrum by the finite element method.

Material and Methods. Biomechanical analysis was carried out by the finite element method. A three-dimensional model of a segment of the spinopelvic complex (SPC), including the pelvic bones, sacrum and L4 and L5 vertebrae, was created on the basis of the CT scan results of a healthy patient. Then, a longitudinal fracture of the sacrum was simulated on the developed model of the sacrum on the left side in zone 1 according to the Denis classification. Further, a comparative assessment of three variants of spinopelvic fixation systems with the help of biomechanical computer modeling was carried out: bilateral spinopelvic system L4—S2Alar, bilateral spinopelvic system L4—S2Alar with transverse connector installation, and bilateral spinopelvic system L4—S2Alar with L-shaped rod installation. The stability of fixation, as well as the amount of loads acting on the fixation elements and bone tissues were determined.

Results. As the rigidity of the structure increases by means of a transverse connector or an L-shaped rod, the load is redistributed between the screws located to the left and right of the fracture. The rigidity of the L4—S2Alar system with parallel, unconnected rods is much lower, which leads to a critical increase in loads on instrumentation and vertebrae.

Conclusion. Analysis of three variants of spinopelvic fixation of longitudinal fractures of the sacrum by finite element method revealed that bilateral spinopelvic system with pedicle screws installed in the L4 and L5 vertebrae and pelvic screws installed in the iliac bones through the lateral masses of S2, two on each side (L4—S2 Alar) and connected by two parallel rods (variant 1) is the least strong in comparison with the other variants. The strength of the fixation increases when the structure is supplemented with a transverse connector between the rods (variant 2). The L4—S2 Alar design with an L-shaped rod on the side of the longitudinal fracture of the sacrum (variant 3) proved to be the most strong.

Key Words: spinopelvic fixation, sacral fracture, pelvic fracture, spinopelvic dissociation, transpedicular fixation, biomechanical modeling. Please cite this paper as: Kuleshov AA, Aganesov NA, Vetrile MS, Doi AV, Lisyansky IN, Makarov SN. Biomechanical analysis of variants of spinopelvic fixation of longitudinal sacral fractures by the finite element method. Hir. Pozvonoc. 2023;20(1):28—35. In Russian. DOI: http://dx.doi.org/10.14531/ss20231.28-35.

Longitudinal fractures account for 90 % of all sacral injuries caused by a loss of pelvic ring integrity [1]. Such injuries usually occur due to high-energy shock loads (falls from height, road accidents, etc.) and often result in vertical displacement of half of the pelvis [2].

The fundamental issue in sacral fracture surgery is to relieve instability and restore pelvic ring integrity. To accomplish this task, different types of surgical hardware are used [3], including various configurations of pedicle screws and rods. There is no single approach to choosing a spinopelvic fixation variant currently, which provokes discussions in the literature [4, 5]. The related question

is about the mechanical reliability of the installed hardware and its configurations.

The objective is to analyze the strength of three types of spinopelvic fixation system configurations in longitudinal fractures of the sacrum using the finite element technique.

Material and Methods

Three variants of fixation system being used in real surgical treatment of a longitudinal fracture of the sacrum have been studied:

• bilateral spinopelvic system with pedicle screws installed into the L4 and L5 vertebrae and two pelvic screws

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installed into the iliac bones through the lateral masses of S2 on both sides (L4-S2Alar) connected by two parallel rods;

• bilateral spinopelvic system L4-S2Al-ar with additional installation of a transverse connector;

• bilateral spinopelvic system L4-S2Al-ar with installation of an L-shaped rod.

The analysis of the strength of each fixation variant was performed under biomechanical criteria of success assessment [6].

The staff of the Department of Computer Modeling in Biomedicine and Materials Science of the Saratov National Research State University named after N.G. Chernyshevsky performed biome-

chanical analysis by the finite element technique. A three-dimensional model of a segment of the spinopelvic complex (SPC), including the pelvic bones, sacrum, and L4 and L5 vertebrae, was created on the basis of the CT scan results of a patient without pathology of the mus-culoskeletal system. A longitudinal fracture of the sacrum was simulated on the developed model of the sacrum on the left side in zone 1 according to the Denis classification.

All three considered fixation variants imply the use of pedicle screws installed into the L4 and L5 vertebrae on both sides and pelvic screws installed through the lateral masses of the sacrum into the iliac bone (S2Alar), two on each side, and differ in the way the screws are connected to each other. In the first system variant (Fig. 1a), two parallel rods (not connected to each other) are installed into the screw heads. In the second system variant (Fig. 1b), two parallel rods are installed into the screw heads and connected to each other with a transverse connector. In the third system variant (Fig. 1c), an L-shaped rod is installed, which, with its vertical part, connects the L4 and L5 screws and the pelvic screws on the side of the fracture. As for its horizontal part, it passes along the posterior surface of the sacrum to the opposite side from the fracture and is installed into the lower pelvic screw on the opposite side from the fracture. The L4 and L5 screws and the upper pelvic screw on the opposite side from the fracture are connected with a second rod.

Then, a comparative assessment of the considered fixation variants was performed using biomechanical computer modeling with the finite element technique. The fixation stability, as well as the amount of loads acting on the fixation elements and bone tissues were determined. The problem of the statics of a deformable solid body had been solved with the aim of determination of the stress-strain state of the "SPC segment - implants" system under the action of external surface loads (forces and moments). The surfaces of the

acetabulum were rigidly fixed to prevent their displacement.

During modeling, the effect of six types of external loads was studied [1, 6, 7], the descriptions of which are given in Table 1 and Fig 2. The studied loads simulate the effects of human body weight as well as muscle forces during turns and rotations of the body. It should be noted that this biomechanical model simulates the state of bone tissues and their interaction with implants immediately after surgery. It does not presuppose the study of their long-term interaction, including the remodeling of bone tissue and its adaptation to external loads and implantable systems.

In biomechanical modeling, all materials were considered to be linearly elastic and isotropic [5, 6]. The data concerning the mechanical characteristics

of bone tissues, intervertebral discs, and implants, as well as their junction coupling, were adopted from the literature [5].

When evaluating the stability and strength of each of the considered fixation variants, the strength parameters of cortical (tensile strength up to 161 MPa) and trabecular (tensile strength up to 15 MPa) bone tissues and implants (Ti6Al4V ELI Titanium Alloy with tensile strength up to 1,300 MPa) were considered [8-12].

The fixation stability was evaluated by the displacements of the fixed SPC segment under external loads. As for strength, it was estimated by means of internal forces (equivalent stresses) arising in the vertebrae, bone fragments of the sacrum and implants under the studied loads.

Fig. 1

Three-dimensional models of variants of the arrangement of the spinopelvic fixator in case of a longitudinal fracture of the sacrum: a - bilateral spinopelvic system L4-S2Alar; b - bilateral spinopelvic system L4-S2Alar with the installation of a transverse connector; c - bilateral spinopelvic system L4-S2Alar with installation of an L-shaped rod

Fig. 2

The effect of external loads on the "SPC segment - implants": a - load in the standing position (vertically to the upper endplate of the L4 vertebra in the direction of the L5 vertebra); b - load moment of 10 N*m (tilt to the left); c - the location of the model relative to the coordinate system

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aa kuleshov et al. biomechanical analysis of variants of spinopelvic fixation of longitudinal sacral fracture

Table 1

Types and magnitudes of loads under study

Standing position Tilt forward Tilt backward Tilt to the right Tilt to the left Rotation around an axis

Force of 600 N Force of 600 N and Force of 600 N and Force of 600 N and Force of 600 N and Force of 600 N and

moment of 10 N*m moment of -10 N*m moment of -10 N*m moment of 10 N*m moment of 10 N*m

around the x-axis around the x-axis around the y-axis around the y-axis around the z-axis

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Fig. 3

The field of complete displacements in the standing position: a - variant 1; b - variant 2; c - variant 3

Results and Discussion

Fig. 3 and 4 illustrate typical fields of calculated complete displacements in modules and equivalent stresses. Complete displacements were calculated for each

point as the distance passed from the initial location to the final position reached during the deformation.

The use of a transverse connector between the rods (variant 2) and an L-shaped rod (variant 3), significantly

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stabilizes fixation (the first biomechanical criterion of success [6]), and reduces displacement in the fixed segment (Table 2). Similar displacement values under similar loads were found in the study of A.V. Dol et al. [5]. According to this paper, the greatest displacements were achieved when tilting forward.

It should be noted that in variants 2 and 3, in comparison with the first one, the equivalent stresses on the lower right screw grow considerably and the stresses on the upper left pedicle screw reduce, as shown in Figs. 5-7. So we can conclude that with an increase in the rigidity of the system by means of a transverse connector or/and an L-shaped rod, the load is redistributed between the screws placed to the left and right of the fracture. In other words, the left bone fragment of the sacrum is also maintained by the right part of the fixing system in the second and third fixation variants. Meanwhile, the rigidity of the system of the first fixation variant is not enough to hold the fragments, which results in a critical enhanced load on the surgical hardware (Table 3).

In this case, the most loaded element of the fixation system is the left rod, which is also illustrated in Figs. 5-7. These conclusions are applicable to all the loads under consideration.

The analysis of equivalent stresses in implants was performed to identify their highest values and compare them with the tensile strength (safety factor is equal to 3) [13]. The implants are made of titanium alloy, whose tensile strength is 1,300 MPa. Therefore, the permissible stress is no more than 433 MPa. The analysis of the equivalent stress values from Table 3 indicates that variants 2 and 3 meet the strength criterion (the second biomechanical criterion of success [6]).

aa kuleshov et al. biomechanical analysis of variants of spinopelvic fixation of longitudinal sacral fracture

Fig. 4

The field of equivalent stresses in the standing position: a - variant 1; b - variant 2; c - variant 3

Table 2 Maximum complete displacements in the model for three fixation variants, mm

Variants Standing position Tilt forward Tilt backward Tilt to the right Tilt to the left Rotation around the vertical axis

1 6.2 8.1 4.2 6.8 6.1 6.2

2 4.0 5.2 2.7 4.4 3.8 4.0

3 4.0 5.4 2.5 4.3 3.9 4.4

Meanwhile, variant 1 does not meet this criterion for most of the loads studied (Table 3).

For all fixation variants, there are no stress in the bone tissues of the sacrum that can destroy them (Tables 4, 5). It should be noted that fixation variants 2 and 3 promoted the achievement of lower equivalent stresses in implants and bone tissues with all the studied loading variants.

It can be concluded that variants 2 and 3 are optimal in terms of biome-chanics and the application of biome-chanical parameters for evaluating fixation success. Concurrently, the third variant is advantageous since its execu-

tion identified lower levels of equivalent stress than variants 1 and 2.

Conclusion

Analysis of three variants of spinopelvic fixation of longitudinal fractures of the sacrum by finite element technique showed that the bilateral spinopelvic system with pedicle screws installed in the L4 and L5 vertebrae and pelvic screws installed in the iliac bones through the lateral masses of S2, two on each side (L4-S2 Alar), and connected by two parallel rods (variant 1) is the weakest in comparison with the other variants. The fixation strength is enhanced when the

system is supplemented with a transverse connector between the rods (variant 2). The L4-S2 Alar system with an L-shaped rod on the side of the longitudinal fracture of the sacrum (variant 3) proved to be the strongest.

The study had no sponsors.

The authors declare that they have no conflict of interest.

The study was approved by the local ethical committees of the institutions.

All authors contributed significantly to the research and preparation of the article, read and approved the final version before publication.

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Table 3

Maximum equivalent stresses in implants for three fixation variants, MPa

Table 4

Maximum equivalent stresses in trabecular bone of sacral fragments for three fixation variants, MPa

Variants Standing position Tilt forward Tilt backward Tilt to the right Tilt to the left Rotation around

the vertical axis

1 11 12 11 11 12 8

2 11 11 10 12 9 7

I3 10 10 7 11 14 8

Table 5

Maximum equivalent stresses in the cortical bone of sacral fragments for three fixation variants, MPa

Variants Standing position Tilt forward Tilt backward Tilt to the right Tilt to the left Rotation around

the vertical axis

1 82 104 58 81 82 77

2 82 105 58 81 83 79

3 71 96 45 70 72 70

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aa kuleshov et al. biomechanical analysis of variants of spinopelvic fixation of longitudinal sacral fracture

References

1. Beckmann N, Cai C. CT characteristics of traumatic sacral fractures in association 9. Goldstein SA. The mechanical properties of trabecular bone: depen-

with pelvic ring injuries: correlation using the Young-Burgess classification system. dence on anatomic location and function. J Biomech. 1987;20:1055-1061.

Emerg Radiol. 2017;24:255-262. DOI: 10.1007/s10140-016-1476-0. DOI: 10.1016/0021-9290(87)90023-6.

2. Nonne D, Capone A, Sanna F, Busnelli L, Russo AL, Marongiu G, Dess G, 10. Havaldar R, Pilli SC, Putti BB. Insights into the effects of tensile and

Ferreli A. Suicidal jumper's fracture - sacral fractures and spinopelvic instability: compressive loadings on human femur bone. Adv Biomed Res. 2014;3:101.

a case series. J Med Case Rep. 2018;12:186. DOI: 10.1186/s13256-018-1668-1. DOI: 10.4103/2277-9175.129375.

3. Zakirov RI, Ahtyamov IF. Surgery of unstable pelvic ring injuries. Trends, issues and 11. Misch CE, Qu Z, Bidez MW. Mechanical properties of trabecular bone in the human

perspectives. N.N. Priorov Journal of Traumatology and Orthopedics. 2021 ;28(4):31 -38. mandible: implications for dental implant treatment planning and surgical placement.

DOI: 10.17816/vto34523. J Oral Maxillofac Surg. 1999;57:700-706. DOI: 10.1016/s0278-2391(99)90437-8.

4. Donchenko SV, Slinyakov LYu, Chernyaev AV. Treatment of unstable Pelvic ring 12. Titanium Alloys in Medical Applications [Electronic resource]. URL: https://www.azom.

injuries with vertebropelvi transpedicular fixation. Traumatology and Orthopedics of com/article.aspx?ArticleID=1794 (access date 26.07.2022).

Russia. 2013;(4):67-74. DOI: 10.21823/2311-2905-2013-4-67-74. 13. GOST R 52857.1-2007. Vessels and apparatus. Norms and methods of strength calcula-

5. Dol AV, Ivanov DV, Kazhanov IV, Kirillova IV, Kossovich LYu, Mikityuk SI, tion. General requirements.

Petrov AV. Biomechanical modeling of surgical reconstructive treatment variants of

unilateral sacral fractures. Russian Journal of Biomechanics. 2019;23(4):537-548. DOI:

10.15593/RZhBiomeh/2019.4.04.

6. Ivanov DV. Biomechanical support for the physician's decision when choos- Address correspondence to:

ing a treatment option based on quantitative success criteria. Izvestiya of Sara- Kuleshov Aleksandr Alekseyevich

tov University. Mathematics. Mechanics. Informatics. 2022;22(1):62-89. DOI National Medical Research Center for Traumatology and Orthopedics

10.18500/1816-9791-2022-22-1-62-89. n.a. N.N. Priorov,

7. Joukar A, Shah A, Kiapour A, Vosoughi AS, Duhon B, Agarwal AK, Elgafy H, 10 Priorova str., Moscow 127299, Russia,

Ebraheim N, Goel VK. Sex specific sacroiliac joint biomechanics during stand- [email protected]

ing upright: a finite element study. Spine. 2018;43:E1053-E1060. DOI: 10.1097/

BRS.0000000000002623. Received 25.10.2022

8. Karlov AV, Shakhov VP. External Fixation Systems and Regulatory Mechanisms of Review completed 11.01.2023

Optimal Biomechanics. Tomsk, 2001. Passed for printing 16.01.2023

Aleksandr Alekseyevich Kuleshov, DMSc, trauma orthopedist, head of Vertebrology Department, National Medical Research Center for Traumatology and Orthopedics n.a. N.N. Priorov, 10Priorova str., Moscow, 127299, Russia, ORCID: 0000-0002-9526-8274, [email protected];

Nikolay Aleksandrovich Aganesov, trauma orthopedist, National Medical Research Center for Traumatology and Orthopedics n. a. N.N. Priorov, 10 Priorova str., Moscow, 127299, Russia, ORCID: 0000-0001-5383-6862, [email protected];

Marchel Stepanovich Vetrile, MD, PhD, trauma orthopedist, deputy director for science, National Medical Research Center for Traumatology and Orthopedics n.a. N.N Priorov, 10 Priorova str., Moscow, 127299, Russia, ORCID: 0000-0001-6689-5220, [email protected];

Aleksandr Viktorovich Dol, PhD in Mathematics and Physics, assistant professor, leading engineer of the Department of Computer Modeling in Biomedicine and Materials Science, Saratov National Research State University n.a. N.G. Chernyshevsky, 80 Astrakhanskaya str., Saratov, 410012, Russia, ORCID: 0000-0001-58421615, [email protected];

Igor Nikolayevich Lisyansky, MD, PhD, trauma orthopedist, National Medical Research Center for Traumatology and Orthopedics n.a. N.N. Priorov, 10 Priorova str., Moscow, 127299, Russia, ORCID: 0000-0002-2479-4381, [email protected];

Sergey Nikolayevich Makarov, MD, PhD, trauma orthopedist, National Medical Research Center for Traumatology and Orthopedics n. a. N.N. Priorov, 10 Priorova str., Moscow, 127299, Russia, ORCID: 0000-0003-0406-1997, [email protected].

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