نوع مقاله: مقاله کامل پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد مهندسی مکانیک، گروه تبدیل انرژی، دانشکده‌ی مهندسی مکانیک، دانشگاه صنعتی خواجه نصیرالدین طوسی، تهران، ایران

2 استادیار، گروه تبدیل انرژی، دانشکده‌ی مهندسی مکانیک، دانشگاه صنعتی خواجه نصیرالدین طوسی، تهران، ایران

چکیده

در ستون فقرات، دیسک‌های بین مهره­ای نقش انعطاف­پذیری، انتقال بار و استهلاک انرژی در ضربات ناشی از بارگذاری را بر عهده دارند. افزایش سن و اعمال بارگذاری­های نامناسب منجر به انحطاط (دژنره شدن) دیسک­های بین مهره­ای می­شود. بررسی پارامترهای بیومکانیکی دیسک سالم و دژنره‌شده در سطوح مختلف جهت کشف مکانیزم­های مربوط به دژنره شدن دیسک و یافتن راه‌کارهای درمانی موثر از اهمیت بالایی برخوردار است. در این پژوهش، یک دیسک بین مهره­ای ناحیه‌ی گردنی ستون فقرات به همراه دو مهره‌ی مجاور آن (C5 و C6) با استفاده از روش مقطع­نگاری رایانه­ای (سی­تی اسکن) به یک مدل سه‌بعدی دقیق تبدیل شده است. برای تعریف دقیق خواص بیومکانیکی دیسک و مهره‌ها از دو مدل پوروویسکوالاستیک و پوروالاستیک استفاده شده است. در این دو مدل، ساختار دیسک و مهره به صورت متخلخل در نظر گرفته شده و هم‌چنین خواص ماتریس جامد دیسک و مهره و جریان سیال (آب) درون آن‌ها به عنوان یک عامل اساسی در عمل‌کرد ستون مهره­ها نیز مد نظر قرار داده شده است. خاصیت ویسکوالاستیک فاز جامد دیسک با استفاده از تست آزمایشگاهی ریلکسیشن (آسودگی از تنش) روی نمونه‌ی دیسک گوسفندی و برازش داده­های تنش بر حسب زمان، به مدل عمومی ماکسول دوشاخه­ای استخراج گردیده است. پاسخ­های وابسته به زمان دیسک بین مهره‌ای سالم و دیسک­های دژنره‌شده در سه سطح مختلف (خفیف، متوسط و شدید) در بارگذاری ریلکسیشن، با استفاده از روش المان محدود مورد بررسی قرار گرفته است. نتایج نشان می­دهند که در فرایند ریلکسیشن، با افزایش میزان دژنره شدن دیسک، سرعت جریان سیال درون آن کاهش یافته و این امر منجر به کاهش انعطاف­پذیری دیسک تحت بارگذاری می­گردد. هم‌چنین با بررسی نتایج مشاهده می­شود که تنش ریلکسیشن دیسک­ دژنره‌شده‌ی سطح 3 (شدید) نسبت به دیسک بین مهره­­ای سالم تا حدود 16% افزایش یافته است. بررسی میزان بیرون­زدگی دیسک­های دژنره‌شده و دیسک سالم تحت بارگذاری، نشان می­دهد که با افزایش میزان دژنره شدن دیسک، میزان بیرون­زدگی آن نیز افزایش می‌یابد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Assessing Time-Dependent Response of Intact and Degenerated Cervical Intervertebral Discs by Employing a Poroviscoelastic Model based on Experimental Relaxation Data

نویسندگان [English]

  • Mahdieh Mosayebi 1
  • Afsaneh Mojra 2

1 M.Sc. Student, Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran

2 Assistant Professor, Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran

چکیده [English]

Intervertebral disc (IVD) provides flexibility and shock absorption for the spine in the load transmission procedure. Disc degeneration may occur as a result of aging and inappropriate types of loading. Assessing biomechanical parameters of intact IVD in comparison to the degenerated disc with different grades of degeneration can facilitate the detection procedure and planning for suitable therapeutic treatment. In the present study, a real three-dimensional model of cercival IVD ( -  with adjacent vertebrae is constructed by using computed tomography (CT-scan) images. In order to accurately define mechanical properties, the disc and the vertebrae are modelled as poroviscoelastic and poroelastic materials, respectively. A porous medium approach is adopted to consider the considerable water content of both media alongside the solid matrix. For the solid phase of the IVD, the related viscoelastic parameters are extracted from an experimental test on a sheep lumbar intervertebral disc and stress vs. time data are fitted to the generalized Maxwell model with two Maxwell arms. By employing the finite element method, time-dependent response of the intact IVD and three different levels of the degenerated IVD (mild, moderate and severe) are studied in a relaxation test. Results indicate that during relaxation procedure, intradiscal fluid velocity decreases as a result of disc degeneration. This may oppositely affect the flexibility of IVD in the load bearing. It is also observed that stress relaxation of the severe degenerated IVD almost increases up to 16% relative to the intact IVD. Assessing the amount of disc bulging under load application shows enhancement for the degenerated disc compared to the intact disc.

کلیدواژه‌ها [English]

  • intervertebral disc
  • relaxation test
  • poroviscoelastic model
  • disc degeneration
  • finite element method

[1]   Schroeder et al., “Osmoviscoelastic finite element model of the intervertebral disc,” Eur. Spine J., vol. 15, no. 3, pp. 361-371, Mar., 2006.

[2]   P.E. Riches et al., “The internal mechanics of the intervertebral disc under cyclic loading,” J. Biomech., vol.35,no.9,pp.1263-1271,Sept 2002.

[3]   A. Gloria et al., “Dynamic-mechanical properties of a novel composite intervertebral disc prosthesis,” J. Mater. Sci.: Mater. Med., vol. 18, no. 11, pp. 2159-2165, Nov., 2007.

[4]   Q. Bao et al., “The artificial disc: theory, design and materials,” Biomaterials, vol. 17, no. 12, pp. 1157-1167, Sept., 1996.

[5]    H. Schmidt et al., “The risk of disc
prolapses with complex loading in different degrees of disc degeneration-a finite element analysis,” Clin. Biomech., vol. 22, no. 9, pp. 988-998, Nov., 2007.

[6]     R. N. Natarajan et al., “Modeling changes in
intervertebral disc mechanics with degeneration,” J. Bone Joint Surg. Am., vol. 88, pp. 36-40, Apr., 2006.

[7]   M. Nikkhoo et al., “A poroelastic finite
element model to describe the time-dependent response of lumbar intervertebral disc,” J. Med. Imaging Health Inf., vol. 1, no. 3, pp. 246-251, Sept., 2011.

[8]   M. Nikkhoo et al., “Dynamic Responses of Intervertebral Disc during Static Creep and Dynamic Cyclic Loading: A Parametric Poroelastic Finite Element Analysis,” Biomed. Eng. App. Bas. And Com., vol. 25, no. 1, pp. 1350013-1350022, 2013.

[9]   D. R. Wagner and J. C. Lotz, “Theoretical model
and experimental results for the nonlinear elastic
behavior of human annulus fibrosus,” J. Orthop. Res., vol. 22, no. 4, pp. 901-909, Jul., 2004.

[10]  D. D. Sun and K. W. Leong, “A nonlinear hyperelastic mixture theory model for anisotropy, transport, and swelling of annulus fibrosus,” Ann. Biomed. Eng., vol. 32, pp. 92-102, 2004.

[11]  J. L. Wang et al., “Viscoelastic finite-element
analysis of a lumbar motion segment in combined
compression and sagittal flexion: effect of loading rate,” Spine, vol. 25, no. 3, pp. 310-318, Feb., 2000.

[12]C. J. Massey et al., “Effects of aging and degeneration on the human intervertebral disc during the diurnal cycle: a finite element study,” J. Orthop. Res., vol. 30, no. 1, pp. 122-130, Jan., 2012.

[13]M. Nikkhoo et al., “A poroelastic finite
element model to describe the time-dependent response of lumbar intervertebral disc,” J. Med. Imaging Health Inf., vol. 1, no. 3, pp. 246-251, Sept., 2011.

[14]  H. Schmidt et al., “Response analysis of the lumbar spine during regular daily activities-a finite element analysis,” J. Biomech., vol. 43, no. 10, pp. 1849-1856, 2010.

[15]  H. Schmidt et al., “Finite element study
of human lumbar disc nucleus replacements,” Comp. Methods Biomech. Biomed. Eng., vol. 17, no. 16, pp. 1762-1776, 2014.

[16]  F. Galbusera et al., “Comparison of four methods to simulate swelling in poroelastic fnite element models of intervertebral discs,” J. Mech. Behav. Biomed. Mater., pp. 1234-1241, Apr., 2011.

[17]   K. S. Emanuel et al., “Osmosis and viscoelasticity both contribute to time-dependent behaviour of the intervertebral disc under compressive load: A caprine in vitro study,” J. Biomech., vol. 70, pp. 10-15, 2018.

[18]A. T. Dimitriadis et al., “Intervertebral disc
changes after 1 h of running: a study on athletes,” J. Int. Med. Res., vol. 39, pp. 569-579, 2011.

[19]   J. Nazari et al., “Feasibility of Magnetic resonance imaging (MRI) in obtaining nucleus pulposus (NP) water content with changing postures,” Mag. Resonan. Imaging, vol. 33, pp. 459-464, 2015.

[20]  P. Velísková et al., “Computational study of the role of fluid content and flow on the lumbar
disc response in cyclic compression: Replication of in vitro and in vivo conditions,” J. Biomech., vol. 70, pp. 16-25, 2018.

[21]   M. H. Krag et al., “Body height change during upright and recumbent posture,” Spine J., vol. 15, no. 3, pp. 202-207, Mar., 1990.

[22]   M. A. Adams et al., “Diurnal changes in spinal mechanics and their clinical significance,” J. Bone Jt. Surgery, Br. Vol., vol. 72, no. 2, pp. 266-270, Mar., 1990.

[23]   J. Kraemer et al., “Water and electrolyte content of human intervertebral discs under variable load,” Spine J., vol. 10, no. 1, pp. 69-71, Jan., 1985.

[24]   J. P. Callaghan and S. M. McGill, “Intervertebral disc herniation: studies on a porcine model exposed to highly repetitive flexion/extension motion with compressive force,” Clin. Biomech., vol. 16, no. 1, pp. 28-37, Jan., 2001.

[25]  R. J. Parkinson and J. P. Callaghan, “The role of
dynamic flexion in spine injury is altered by increasing dynamic load magnitude,” Clin. Biomech., vol. 24, no. 2, pp. 148-154, Feb., 2009.

[26]   M. Nikkhoo et al., “Biomechanical response of intact, degenerated and repaired intervertebral discs under impact loading – Ex-vivo and In-Silico investigation,” J. Biomech., vol. 70, pp. 26-32, Jan., 2018.

[27]R. Fan et al., “Effects of resting modes on human lumbar spines with different levels of degenerated intervertebral discs: a finite element investigation,” BMC Musculoskeletal Disord., vol. 16, pp. 221-236, Aug., 2015.

[28]   M. Adams, N. Bogduk, K. Burton, P. Dolan, “The Biomechanics of Back Pain,” Churchill Livingstone, Philadelphia, USA, 2006.

[29]   Y. Schroder, “Putting pressure on the spine: An osmoviscoelastic FE model of the intervertebral Disc,” Ph.D. thesis, Eindhoven University of Technology, 2008.

[30]   H. J. Wilke et al., “Validity and interobserver agreement of a new radiographic grading system or intervertebral disc degeneration: part I. lumbar spine,” Eur. Spine J., vol. 15, no. 6, pp. 720-730, Jun., 2006.

[31]   H. Xu et al., “Biomechanical comparison of posterior lumbar interbody fusion and transforaminal lumbar interbody fusion by finite element analysis,” J. Neurosurg., vol. 72, pp. 21-27, Aug., 2013.

[32]   C. J. Massey et al., “Effects of aging and degeneration on the human intervertebral disc during the diurnal cycle: a finite element study,” J. Orthop. Res., vol. 30, no. 1, pp. 122-130, Jan., 2012.

[33]   H. Schmidt et al., “The risk of disc prolapses with complex loading in different degrees of disc degeneration-a finite element analysis,” Clin. Biomech., vol. 22, no. 9, pp. 988-998, Nov., 2007.

[34]   F. Galbusera et al., “The mechanical response of the lumbar spine to different combinations of disc degenerative changes investigated using randomized poroelastic finite element models,” Eur. Spine J., vol. 20, no. 4, pp. 563-571, 2011.

[35]F. Galbusera et al., “The effect of degenerative
morphological changes of the intervertebral disc on the lumbar spine biomechanics: a poroelastic finite element investigation,” Comp. Methods
Biomech. Biomed. Eng., vol. 14, no. 8, pp. 729-739, 2011.

[36]       A.R. Makwana et al., “Towards a micromechanical model of intervertebral disc degeneration under cyclic loading,” Biomed. Biotechnol. Eng., vol. 3, no. IMEC2014-39174, pp. V003T03A012- V003T03A019, Nov., 2014.  

[37]   W. N. Findley et al., “Linear Viscoelastic Constitutive Equations,” in Creep and Relaxation of Nonlinear Viscoelastic Materials, New York, Dover Publications, 1976, ch. 5, pp. 50–69.

[38]  B. R. Simon et al., “Structural Models for Human
Spinal Motion Segments Based on a Poroelastic View of the Intervertebral Disk,” J. Biomech. Eng., vol. 107, no. 4, pp. 327-335, Nov., 1985.

[39]  J. M. Gere, “Tension, Compression, and Shear,” in Mechanics of Materials, Thomson Learning, 6th ed., 2004, ch. 1, pp. 6–24.

[40]D. A. Nield and A. Bejan, “Mechanics of Fluid Flow through a Porous Medium,” in Convection in Porous Media, Springer, 3rd ed., New York, 2006, ch. 1, pp. 4–17.