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Mathematics. Mechanics. Informatics

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Ivanov D. V. Biomechanical support for the physician’s decision when choosing a treatment option based on quantitative success criteria. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2022, vol. 22, iss. 1, pp. 62-89. DOI: 10.18500/1816-9791-2022-22-1-62-89, EDN: ZYXHTD

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Biomechanical support for the physician’s decision when choosing a treatment option based on quantitative success criteria

Ivanov Dmitry V., Saratov State University

Preoperative planning for the treatment of the consequences of diseases and injuries of the spino-pelvic complex surgical treatment is a mandatory procedure and should ensure the selection of implants, modes and techniques for their installation, as well as the reconstruction of the optimal biomechanics of the operated segment. For each individual patient, the surgeon chooses a treatment variant based on his qualitative and quantitative individual parameters. Therefore, the task of developing some measurable characteristics (criteria) seems to be urgent, with the help of which it would be possible to choose a successful variant for each specific patient. In surgery of the spino-pelvic complex pathologies, it is customary to use questionnaires of the patient’s quality of life to assess the long-term treatment results. During preoperative planning, surgeons also calculate geometric parameters to assess the degree of deformity and select the necessary correction. At the same time, a geometrically and anatomically correctly planned operation may not be successful in terms of assessing the strength of implanted structures and the “bone-implant” system as a whole. This paper presents the results of the development and testing of criteria for assessing the success of surgical reconstructive treatment of the consequences of the spino-pelvic complex diseases and injuries. Three groups of criteria have been identified: geometric, biomechanical, and clinical. Geometric and biomechanical criteria make it possible to obtain short-term postoperative prognosis. The use of clinical success criteria makes it possible to formulate long-term postoperative prognosis. The criteria for assessing success do not offer the surgeon any new treatment variant, but only provide a tool for quantitative comparison of the treatment variants that are considered by him and the choice of successful ones among them. The criteria for evaluating the success of treatment are implemented in the Smart Plan Ortho preoperative planning system developed at Saratov University, which provides a full cycle of preoperative planning in accordance with the planning–modeling–forecast methodology.

The work was supported by the Advanced Research Foundation.
  1. R. M. Tikhilov, I. I. Shubnyakov, D. G. Pliev, eds. Rukovodstvo po khirurgii tazobedrennogo sustava [Guide to Hip Surgery: in 2 vols.]. Vol. 2. St. Petersburg, RNIITO im. R. R. Vredena, 2015. 356 p. (in Russian).
  2. Dictionary of the Russian Language (Ozhegov) online. Available at: https://slovarozhegova.ru/ (accessed 04 August 2021) (in Russian).
  3. Werner D. A. T., Grotle M., Gulati S., Austevoll I. M., Madsbu M. A., Lønne G., Solberg T. K. Can a Successful Outcome After Surgery for Lumbar Disc Herniation Be Defined by the Oswestry Disability Index Raw Score? Global Spine Journal, 2020, vol. 10, iss. 1, pp. 47–54. https://doi.org/10.1177/2192568219851480
  4. Mjaset C., Zwart J. A., Goedmakers C. M. W., Smith T. R., Solberg T. K., Grotle M. Criteria for success after surgery for cervical radiculopathy-estimates for a substantial amount of improvement in core outcome measures. The Spine Journal, 2020, vol. 20, iss. 9, pp. 1413–1421. https://doi.org/10.1016/j.spinee.2020.05.549
  5. Alhaug O. K., Dolatowski F. C., Solberg T. K., Lønne G. Criteria for failure and worsening after surgery for lumbar spinal stenosis: A prospective national spine registry observational study. The Spine Journal, 2021, vol. 21, iss. 9, pp. 1489–1496. https://doi.org/10.1016/j.spinee.2021.04.008
  6. Duval-Beaupere G., Schmidt C., Cosson P. A Barycentremetric study of the sagittal shape of spine and pelvis: The conditions required for an economic standing position. Annals of Biomedical Engineering, 1992, vol. 20, iss. 4, pp. 451–462. https://doi.org/10.1007/BF02368136
  7. Le Huec J. C., Hasegawa K. Normative values for the spine shape parameters using 3D standing analysis from a database of 268 asymptomatic Caucasian and Japanese subjects. European Spine Journal, 2016, vol. 25, iss. 11, pp. 3630–3637. https://doi.org/10.1007/s00586-016-4485-5
  8. Schwab F., Lafage V., Patel A., Farcy J.-P. Sagittal plane considerations and the pelvis in the adult patient. Spine, 2009, vol. 34, iss. 17, pp. 1828–1833. https://doi.org/10.1097/brs. 0b013e3181a13c08
  9. Krutko A. V. Sagittal’nyi balans. Garmoniya v formulakh. Spravochnaya informatsiya dlya prakticheskikh raschetov [Sagittal Balance. Harmony in Formulas, Background Information for Practical Calculations]. Novosibirsk, ANO “Klinika NIITO”, 2016. 67 p. (in Russian).
  10. Tikhilov R. M., Nikolaev N. S., Shubnyakov I. I., Myasoedov A. A., Boyarov A. A., Efimov A. V., Syundyukov A. R. Difficulties of total hip replacement in patients with ankylosing spondylitis (case report). Traumatology and Orthopedics of Russia, 2016, vol. 22, no. 2, pp. 70–79 (in Russian). https://doi.org/10.21823/2311-2905-2016-0-2-70-79
  11. Makirov S. K., Yuz A. A., Jahaf M. T. Method of assessing the parameters of the sagittal spinal pelvic balance. Hirurgia pozvonocnika (Spine Surgery), 2015, vol. 12, no. 3, pp. 55–63 (in Russian). https://doi.org/10.14531/ss2015.3.55-63
  12. Kudyashev A. L., Hominets V. V., Teremshonok A. V., Korostelev K. E., Nagorny E. B., Dol A. V., Ivanov D. V., Kirillova I. V., Kossovich L. Yu. Biomechanical background for the formation of proximal junctional kyphosis after the transpedicular fixation of the lumbarian spine. Russian Journal of Biomechanics, 2017, vol. 21, iss. 3, pp. 270–279. https://doi.org/10.15593/RZhBiomeh/2017.3.07
  13. Kim Y. J., Lenke L. G., Bridwell K. H., Kim J., Cho S. K., Cheh G., Yoon J. Proximal junctional kyphosis in adolescent idiopathic scoliosis after 3 different types of posterior segmental spinal instrumentation and fusions: Incidence and risk factor analysis of 410 cases. Spine, 2007, vol. 32, iss. 24, pp. 2731–2738. https://doi.org/10.1097/BRS.0b013e31815a7ead
  14. Le Huec J. C., Charosky S., Barrey C., Rigal J., Aunoble S. Sagittal imbalance cascade for simple degenerative spine and consequences: Algorithm of decision for appropriate treatment. European Spine Journal, 2011, vol. 20, suppl. 5, pp. 699–703. https://doi.org/10.1007/s00586-011-1938-8
  15. Johnson R. D., Valore A., Villaminar A., Comisso M., Balsano M. Sagittal balance and pelvic parameters — a paradigm shift in spinal surgery. Journal of Clinical Neuroscience, 2013, vol. 20, iss. 2, pp. 191–196. https://doi.org/10.1016/j.jocn.2012.05.023
  16. Kotelnikov A. O., Riabykh S. O., Burtsev A. V. Hip-spine syndrome: The problem from the biomechanical point of view. Genij Ortopedii, 2019, vol. 25, no. 4, pp. 541–549 (in Russian). https://doi.org/10.18019/1028-4427-2019-25-4-541-549
  17. Burtsev A. V., Ryabykh S. O., Kotelnikov A. O., Gubin A. V. Clinical issues of the sagittal balance in adults. Genij Ortopedii, 2017, vol. 23, no. 2, pp. 228–235 (in Russian). https://doi.org/10.18019/1028-4427-2017-23-2-228-235
  18. Ivanov D. V., Kirillova I. V., Kossovich L. Yu., Likhachev S. V., Polienko A. V., Kharlamov A. V., Shulga A. E. Comparative analysis of the SpinoMeter mobile application and Surgimap system for measuring the sagittal balance parameters: Inter-observer reliability test. Genij Ortopedii, 2021, vol. 27, no. 1, pp. 74–79 (in Russian). https://doi.org/10.18019/1028-4427-2021-27-1-74-79
  19. Pan C., Wang G., Sun J. Correlation between the apex of lumbar lordosis and pelvic incidence in asymptomatic adult. European Spine Journal, 2020, vol. 29, iss. 3, pp. 420–427. https://doi.org/10.1007/s00586-019-06183-y
  20. Legaye J., Duval-Beaupere G. Sagittal plane alignment of the spine and gravity: A radiological and clinical evaluation. Acta Orthopaedica Belgica, 2005, vol. 71, iss. 2, pp. 213–220.
  21. Vialle R., Levassor N., Rillardon L., Templier A., Skalli W., Guigui P. Radiographic analysis of the sagittal alignment and balance of the spine in asymptomatic subjects. Journal of Bone & Joint Surgery, 2005, vol. 87, iss. 2, pp. 260–267. https://doi.org/10.2106/JBJS.D.02043
  22. Hyun S.-J., Han S., Kim Y. B., Kim Y. J., Kang G.-B., Cheong J.-Y. Predictive formula of ideal lumbar lordosis and lower lumbar lordosis determined by individual pelvic incidence in asymptomatic elderly population. European Spine Journal, 2019, vol. 28, iss. 9, pp. 1906–1913. https://doi.org/10.1007/s00586-019-05955-w
  23. Sullivan T. B., Marino N., Reighard F. G., Newton P. O. Relationship between lumbar lordosis and pelvic incidence in the adolescent patient: Normal cohort analysis and literature comparison. Spine Deformity, 2018, vol. 6, iss. 5, pp. 529–536. https://doi.org/10.1016/j. jspd.2018.02.002
  24. Manoharan S. R., Joshi D., Owen M., Theiss S. M., Deinlein D. Relationship of Cervical Sagittal Vertical Alignment After Sagittal Balance Correction in Adult Spinal Deformity: A Retrospective Radiographic Study. International Journal of Spine Surgery, 2018, vol. 12, no. 2, pp. 269–275. https://doi.org/10.14444/5033
  25. Yeh K.-T., Lee R.-P., Chen I.-H., Yu T.-C., Liu K.-L., Peng C.-H., Wang J.-H., Wu W.-T. Correlation of Functional Outcomes and Sagittal Alignment After Long Instrumented Fusion for Degenerative Thoracolumbar Spinal Disease. Spine, 2018, vol. 43, iss. 19, pp. 1355–1362. https://doi.org/10.1097/BRS.0000000000002471
  26. Than K. D., Park P., Fu K.-M., Nguyen S., Wang M. Y., Chou D., Nunley P. D., Anand N., Fessler R. G., Shaffrey C. I., Bess S., Akbarnia B. A., Deviren V., Uribe J. S., La Marca F., Kanter A. S., Okonkwo D. O., Mundis G. M., Mummaneni P. V. Clinical and radiographic parameters associated with best versus worst clinical outcomes in minimally invasive spinal deformity surgery. Journal of Neurosurgery, 2016, vol. 25, iss. 1, pp. 21–25. https://doi.org/10.3171/2015.12.SPINE15999
  27. Kao F.-C., Huang Y.-J., Chiu P.-Y., Hsieh M.-K., Tsai T.-T. Factors predicting the surgical risk of osteoporotic vertebral compression fractures. Journal of Clinical Medicine, 2019, vol. 8, no. 4, pp. 501. https://doi.org/10.3390/jcm8040501
  28. Kornilov N. V., Voitovich A. V., Mashkov V. M., Einstein G. G. Khirurgicheskoe lechenie degenerativno-distroficheskikh porazheniy tazobedrennogo sustava [Surgical Treatment of Degenerative-Dystrophic Lesions of the Hip Joint]. St. Petersburg, LITO Sintez, 1997. 292 p. (in Russian).
  29. Tian J.-L., Sun L., Hu R.-Y., Han W., Tian X.-B. Correlation of Cup Inclination Angle with Liner Wear for Metal-on-polyethylene in Hip Primary Arthroplasty. Orthopaedic Surgery, 2017, vol. 9, iss. 2, pp. 186–190. https://doi.org/doi:10.1111/os.12337
  30. Mas Y., Gracia L., Ibarz E., Gabarre S., Pena D., Herrera A. Finite element simulation and clinical follow-up of lumbar spine biomechanics with dynamic fixations. PLoS ONE, 2017, vol. 12, no. 11, e0188328. https://doi.org/10.1371/journal.pone.0188328
  31. Chun K., Yang I., Kim N., Cho D. Effect of Device Rigidity and Physiological Loading on Spinal Kinematics after Dynamic Stabilization: An In-Vitro Biomechanical Study. Journal of Korean Neurosurgical Society, 2015, vol. 58, no. 5, pp. 412–418. https://doi.org/10.3340/jkns.2015.58.5.412
  32. Clair S. St., Tan J. S., Lieberman I. Oblique lumbar interbody fixation: A biomechanical study in human spines. Journal of Spinal Disorders and Techniques, 2012, vol. 25, iss. 4, pp. 183–189. https://doi.org/10.1097/BSD.0b013e318211fc6b
  33. Niosi C. A., Zhu Q. A., Wilson D. C., Keynan O., Wilson D. R., Oxland T. R. Biomechanical characterization of the three-dimensional kinematic behaviour of the Dynesys dynamic stabilization system: An in vitro study. European Spine Journal, 2006, vol. 15, iss. 6, pp. 913–922. https://doi.org/10.1007/s00586-005-0948-9
  34. White III A. A., Panjabi M. M. Clinical Biomechanics of the Spine. 2nd ed. New York, J. B. LIPPINCOTT Company, 1990. 722 р.
  35. Brown T., Hansen R. J., Yorra A. J. Some mechanical tests on the lumbosacral spine with particular reference to the intervertebral discs; A preliminary report. The Journal of Bone and Joint Surgery. American volume, 1957, vol. 39-A, iss. 5, pp. 1135–1164.
  36. Inoue N., Espinoza Or´ıas A. A. Biomechanics of intervertebral disk degeneration. Orthopedic Clinics of North America, 2011, vol. 42, iss. 4, pp. 487–499. https://doi.org/10.1016/j.ocl.2011.07.001
  37. Hansson T. H., Keller T. S., Panjabi M. M. A study of the compressive properties of lumbar vertebral trabeculae: Effects of tissue characteristics. Spine, 1987, vol. 12, iss. 1, pp. 56–62. https://doi.org/10.1097/00007632-198701000-00011
  38. Baikov E. S., Baikalov A. A. Relationship between biomechanical and biochemical parameters of spinal motion segments and recurrent lumbar disc herniation. Hirurgia pozvonocnika (Spine Surgery), 2017, vol. 14, no. 4, pp. 61–68 (in Russian). https://doi.org/10.14531/ss2017.4.61-68
  39. Natarajan R. N., Watanabe K., Hasegawa K. Biomechanical analysis of a long-segment fusion in a lumbar spine — a finite element model study. Journal of Biomechanical Engineering, 2018, vol. 140, iss. 9, pp. 1–7. https://doi.org/10.1115/1.4039989
  40. Shin J. K., Lim B. Y., Goh T. S., Son S. M., Kim H.-S., Lee J. S., Lee C.-S. Effect of the screw type (S2-alar-iliac and iliac), screw length, and screw head angle on the risk of screw and adjacent bone failures after a spinopelvic fixation technique: A finite element analysis. PLoS ONE, 2018, vol. 13, no. 8, pp. 296–301. https://doi.org/10.1371/journal.pone.0201801
  41. Duan Y., Wang H. H., Jin A. M., Zhang L., Min S. X., Liu C. L., Qiu S. J., Shu X. Q. Finite element analysis of posterior cervical fixation. Orthopaedics & Traumatology: Surgery & Research, 2015, vol. 101, iss. 1, pp. 23–29. https://doi.org/10.1016/j.otsr.2014.11.007
  42. Kudiashev A. L., Khominets V. V., Teremshonok A. V., Nagorny E. B., Stadnichenko S. Yu., Dol A. V., Ivanov D. V., Kirillova I. V., Kossovich L. Yu., Kovtun A. L. Biomechanical modeling in surgical treatment of a patient with true lumbar spondylolisthesis. Hirurgia pozvonocnika (Spine Surgery), 2018, vol. 15, no. 4, pp. 87–94 (in Russian). https://doi.org/10.14531/2018.4.87-94
  43. La Barbera L., Galbusera F., Villa T., Costa F., Wilke H.-J. ASTM F1717 standard for the preclinical evaluation of posterior spinal fixators: Can we improve it? Journal of Engineering in Medicine, 2014, vol. 228, iss. 10, pp. 1014–1026. https://doi.org/10.1177/0954411914554244
  44. Su Y.-S., Ren D., Wang P.-С. Comparison of biomechanical properties of single- and two-segment fusion for denis type B spinal fractures. Orthopaedic Surgery, 2013, vol. 5, iss. 4, pp. 266–273. https://doi.org/10.1111/os.12068
  45. Vessels and apparatus. Norms and methods of strength calculation. General requirements. Moscow, Standartinform, 2008. 26 p. (in Russian).
  46. 316LS/316LVM Surgical Stainless Steel Bar — ASTM F138. Available at: https://www.upmet.com/products/stainless-steel/316lslvm (accessed 17 August 2018).
  47. Ti6Al4V ELI Titanium Alloy. Available at: https://www.arcam.com/wp-content/uploads/Arcam-Ti6Al4V-ELI-Titanium-Alloy.pdf (accessed 17 August 2018).
  48. Havaldar R., Pilli S. C., Putti B. B. Insights into the effects of tensile and compressive loadings on human femur bone. Advanced Biomedical Research, 2014, vol. 3, pp. 101. https://doi.org/10.4103/2277-9175.129375
  49. Karlov A. V., Shakhov V. P. Sistemy vneshnei fiksatsii i reguliatornye mekhanizmy optimal’noi biomekhaniki [External Fixation Systems and Regulatory Mechanisms for Optimal Biomechanics]. Tomsk, STT, 2001. 477 p. (in Russian).
  50. Misch C. E., Qu Z., Bidez M. W. Mechanical properties of trabecular bone in the human mandible: Implications for dental implant treatment planning and surgical placement. Journal of Oral and Maxillofacial Surgery, 1999, vol. 57, iss. 6, pp. 700–706. https://doi.org/10.1016/s0278-2391(99)90437-8
  51. Goldstein S. A. The mechanical properties of trabecular bone: Dependence on anatomic location and function. Journal of Biomechanics, 1987, vol. 20, iss. 11, pp. 1055–1061. https://doi.org/10.1016/0021-9290(87)90023-6
  52. Gushcha A. O., Yusupova A. R. Evaluation of outcomes of surgical treatment for degenerative diseases of the spine. Hirurgia pozvonocnika (Spine Surgery), 2017, vol. 14, no. 4, pp. 85–94 (in Russian). https://doi.org/10.14531/ss2017.4.85-94
  53. Byvaltsev V. A., Belykh E. G., Alekseeva N. V., Sorokovikov V. A. Primenenie shkal i anket v obsledovanii patsientov s degenerativnym porazheniem poiasnichnogo otdela pozvonochnika: metodicheskie rekomendatsii [The Use of Scales and Questionnaires in the Examination of Patients with Degenerative Lesions of the Lumbar Spine: Guidelines]. Irkutsk, FGBU “NTsRVKh” SO RAMN, 2013. 32 p. (in Russian).
  54. Cao P., Hao W., Zhang L., Zhang Q., Liu X., Li M. Safety and Efficacy Studies of Vertebroplasty with Dual Injections for the Treatment of Osteoporotic Vertebral Compression Fractures: Preliminary Report. Academic Radiology, 2020, vol. 27, iss. 8, pp. e224–e231. https://doi.org/10.1016/j.acra.2019.09.023
  55. Cook C. E., Learman K. E., O’Halloran B. J., Showalter C. R., Kabbaz V. J., Goode A. P., Wright A. A. Wright Which Prognostic Factors for Low Back Pain Are Generic Predictors of Outcome Across a Range of Recovery Domains? PTJ: Physical Therapy & Rehabilitation Journal, 2013, vol. 93, iss. 1, pp. 32–40. https://doi.org/10.2522/ptj.20120216
  56. Cheng L., Cai H., Yu Y., Li W., Li Q., Liu Z. Modified Full-Endoscopic Interlaminar Discectomy via an Inferior Endplate Approach for Lumbar Disc Herniation: Retrospective 3-Year Results from 321 Patients. World Neurosurgery, 2020, vol. 141, pp. e537–e544. https://doi.org/10.1016/j.wneu.2020.05.234
  57. Marouby S., Coulomb R., Maury E., Assi C., Mares O., Kouyoumdjian P. Prospective Evaluation of Spino-Pelvic Parameters with Clinical Correlation in Patients Operated with an Anterior Lumbar Interbody Fusion. Asian Spine Journal, 2020, vol. 14, no. 1, pp. 88–96. https://doi.org/10.31616/asj.2019.0041
  58. Staartjes V. E., Vergroesen P. A., Zeilstra D. J., Schroder M. L. Identifying subsets of patients with single-level degenerative disc disease for lumbar fusion: The value of prognostic tests in surgical decision making. The Spine Journal, 2018, vol. 18, iss. 4, pp. 558–566. https://doi.org/10.1016/j.spinee.2017.08.242
  59. Vieli M., Staartjes V. E., Eversdjik H. A. J., De Wispelaere M. P., Oosterhuis J. W. A., Schroder M. L. Safety and Efficacy of Anterior Lumbar Interbody Fusion for Discogenic Chronic Low Back Pain in a Short-stay Setting: Data From a Prospective Registry. Cureus, 2019, vol. 11, no. 8. e5332. https://doi.org/10.7759/cureus.5332
  60. Ertzgaard P., Nene A., Kiekens C., Burns A. S. A review and evaluation of patient-reported outcome measures for spasticity in persons with spinal cord damage: Recommendations from the Ability Network — an international initiative. The Journal of Spinal Cord Medicine, 2020, vol. 43, iss. 6, pp. 813–823. https://doi.org/10.1080/10790268.2019.1575533
  61. Amirdjanova V. N., Goryachev D. V., Korshunov N. I., Rebrov A. P., Sorotskaya V.N. SF-36 questionnaire population quality of life indices. Nauchno-prakticheskaya revmatologiya [Rheumatology Science and Practice], 2008, vol. 46, no. 1, pp. 36–48 (in Russian).
  62. Gary K. W., Cao Y., Burns S. P., McDonald S. D., Krause J. S. Employment, health outcomes, and life satisfaction after spinal cord injury: Comparison of veterans and nonveterans. Spinal Cord, 2020, vol. 58, no. 1, pp. 3–10. https://doi.org/10.1038/s41393-019-0334-9
  63. Kolesnikov S. V., Diachkova G. V., Kamshilov B. V., Kolesnikova E. S. Evaluation of clinical and functional status of patients following total hip replacement. Genij Ortopedii, 2019, vol. 25, no. 1, pp. 32–37 (in Russian). https://doi.org/10.18019/1028-4427-2019-25-1-32-37
  64. Wright J. G., Rudicel S., Feinstein A. R. Ask patients what they want. Evaluation of individual complaints before total hip replacement. The Journal of Bone and Joint Surgery, 1994, vol. 76, no. 2, pp. 229–234.
  65. Dulaev A. K., Kazhanov I. V., Presnov R. A., Mikityuk S. I. Triangular osteosynthesis of fractures of the sacrum in vertically unstable pelvic ring injuries. Polytrauma, 2018, no. 2, pp. 17–34 (in Russian).
  66. Fairbank J. C., Pynsent P. B. The Oswestry Disability Index. Spine, 2000, vol. 25, iss. 22, pp. 2940–2952. https://doi.org/10.1097/00007632-200011150-00017
  67. Solberg T., Johnsen L. G., Nygaard Ø. P., Grotle M. Can we define success criteria for lumbar disc surgery? Estimates for a substantial amount of improvement in core outcome measures. Acta Orthopaedica, 2013, vol. 84, iss. 2, pp. 196–201. https://doi.org/10.3109/17453674.2013.786634
  68. Jaeschke R., Singer J., Guyatt G. H. Measurement of health status: Ascertaining the minimal clinically important difference. Controlled Clinical Trials, 1989, vol. 10, iss. 4, pp. 407–415. https://doi.org/10.1016/0197-2456(89)90005-6
  69. Copay A. G., Subach B. R., Glassman S. D., Polly D. W., Schuler T. C. Understanding the minimum clinically important difference: A review of concepts and methods. The Spine Journal, 2007, vol. 7, iss. 5, pp. 541–546. https://doi.org/10.1016/j.spinee.2007.01.008
  70. Donnik A. M., Ivanov D. V., Kossovich L. Yu., Levchenko K. K., Kireev S. I., Morozov K. M., Ostrovsky N. V., Zaretskov V. V., Likhachev S. V. Creation of Three-Dimensional Solid-State Models of a Spine with Transpedicular Fixation Using a Specialized Software. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2019, vol. 19, iss. 4, pp. 424–438 (in Russian). https://doi.org/10.18500/1816-9791-2019-19-4-424-438
  71. Donnik A. M., Ivanov D. V., Kireev S. I., Kossovich L. Yu., Ostrovsky N. V., Norkin I. A., Levchenko K. K., Likhachev S. V. Extracting Clinically Relevant Data from Biomechanical Modeling of Surgical Treatment Options for Spinal Injury in Damaged Vertebrae Th10, Th11. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2019, vol. 19, iss. 4, pp. 439–453 (in Russian). https://doi.org/10.18500/1816-9791-2019-19-4-439-453
  72. Dol A. V., Dol E. S., Ivanov D. V. Biomechanical modeling of surgical reconstructive treatment of spinal spondylolisthesis at L4–L5 level. Russian Journal of Biomechanics, 2018, vol. 22, no. 1, pp. 25–36. https://doi.org/10.15593/RJBiomech/2018.1.03
  73. Beskrovny A. S., Bessonov L. V., Golyadkina A. A., Dol A. V., Ivanov D. V., Kirillova I. V., Kossovich L. Yu., Sidorenko D. A. Development of a decision support system in traumatology and orthopedics. Biomechanics as a tool for preoperative planning. Russian Journal of Biomechanics, 2021, vol. 25, no. 2, pp. 99–112. https://doi.org/10.15593/RJBiomech/2021.2.01
  74. Dol A. V., Ivanov D. V., Kazhanov I. V., Kirillova I. V., Kossovich L. Yu., Mikityuk S. I., Petrov A. V. Biomechanical modeling of surgical reconstructive treatment options for unilateral sacral fractures. Russian Journal of Biomechanics, 2019, vol. 23, no. 4, pp. 459–468. https://doi.org/10.15593/RJBiomech/2019.4.04
  75. Denisov A. O., Shilnikov V. A., Barns S. A. Coxa-vertebral syndrome and its significance in hip arthroplasty (review). Traumatology and Orthopedics of Russia, 2012, vol. 18, no. 1, pp. 121–127 (in Russian). https://doi.org/10.21823/2311-2905-2012-0-1-144-149