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Spinal Cord Boundary Conditions Affect Brain Tissue Strains in Impact Simulations

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Brain and spinal cord injuries have devastating consequences on quality of life but are challenging to assess experimentally due to the traumatic nature of such injuries. Finite element human body models (HBM) have been developed to investigate injury but are limited by a lack of biofidelic spinal cord implementation. In many HBM, brain models terminate with a fixed boundary condition at the brain stem. The goals of this study were to implement a comprehensive representation of the spinal cord into a contemporary head and neck HBM, and quantify the effect of the spinal cord on brain deformation during simulated impacts. Spinal cord tissue geometries were developed, based on 3D medical imaging and literature data, meshed, and implemented into the GHBMC 50th percentile male model. The model was evaluated in frontal, lateral, rear, and oblique impact conditions, and the resulting maximum principal strains in the brain tissue were compared, with and without the spinal cord. A new cumulative strain curve metric was proposed to quantify brain strain distribution. Presence of the spinal cord increased brain tissue strains in all simulated cases, owing to a more compliant boundary condition, highlighting the importance of the spinal cord to assess brain response during impact.

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  1. Barker, J. B., and D. S. Cronin. Multilevel validation of a male neck finite element model with active musculature. J. Biomech. Eng. 143:1, 2021.

    Article  Google Scholar 

  2. Barker, J. B., D. S. Cronin, and R. W. Nightingale. Lower cervical spine motion segment computational model validation: kinematic and kinetic response for quasi-static and dynamic loading. J. Biomech. Eng.139:061009, 2017.

    Article  Google Scholar 

  3. Bruneau, D. A., and D. S. Cronin. Brain response of a computational head model for prescribed skull kinematics and simulated football helmet impact boundary conditions. J. Mech. Behav. Biomed. Mater.115:104299, 2021.

    Article  PubMed  Google Scholar 

  4. Bruneau, D. Investigation of Head and Brain Response in Football Helmet Impacts using a Finite Element Model of the Head and Neck with Active Muscle by, 2019.

  5. Centers for Disease Control and Prevention. Surveillance Report of Traumatic Brain Injury-related Emergency Department Visits, Hospitalizations, and Deaths-United States, 2014. Centers Dis. Control Prev. U.S. Dep. Heal. Hum. Serv. 24, 2019.

  6. Ceylan, D., N. Tatarli, T. Abdullaev, A. Seker, S. D. Yildiz, E. Keles, D. Konya, and Y. Bayri. The denticulate ligament: Anatomical properties, functional and clinical significance. Acta Neurochir. 154:1229–1234, 2012.

    Article  PubMed  Google Scholar 

  7. Chen, R., B. Shi, X. Zheng, Z. Zhou, A. Jin, Z. Ding, L. V. Hai, and H. Zhang. Anatomic study and clinical significance of the dorsal meningovertebral ligaments of the thoracic dura mater. Spine. 40:692–698, 2015.

    Article  PubMed  Google Scholar 

  8. Fernandes, F. A. O., D. Tchepel, R. J. A. de Sousa, and M. Ptak. Development and validation of a new finite element human head model: Yet another head model (YEAHM). Eng. Comput. 35:477–496, 2018.

    Article  Google Scholar 

  9. Fountas, K. N., E. Z. Kapsalaki, J. Jackson, R. L. Vogel, and J. S. Robinson. Cervical spinal cord-smaller than considered? Spine. 23(1513–1516):1998, 1976.

    Google Scholar 

  10. Gayzik, F. S., D. P. Moreno, C. P. Geer, S. D. Wuertzer, R. S. Martin, and J. D. Stitzel. Development of a full body CAD dataset for computational modeling: a multi-modality approach. Ann. Biomed. Eng. 39:2568–2583, 2011.

    Article  CAS  PubMed  Google Scholar 

  11. Gayzik, S., D. Moreno, N. Vavalle, A. Rhyne, and J. Stitzel. Development of the Global Human Body Models Consortium mid-sized male full body model. Inj. Biomech. Res. 1:39–12, 2011.

    Google Scholar 

  12. Horgan, T. J., and M. D. Gilchrist. The creation of three-dimensional finite element models for simulating head impact biomechanics. Int. J. Crashworthiness. 8:353–366, 2003.

    Article  Google Scholar 

  13. Iwamoto, M., Y. Nakahira, and H. Kimpara. Development and Validation of the Total HUman Model for Safety (THUMS) toward further understanding of occupant injury mechanisms in precrash and during crash. Traffic Inj. Prev. 16:S36–S48, 2015.

    Article  PubMed  Google Scholar 

  14. Jannesar, S., M. Allen, S. Mills, A. Gibbons, J. C. Bresnahan, E. A. Salegio, and C. J. Sparrey. Compressive mechanical characterization of non-human primate spinal cord white matter. Acta Biomater. 74:260–269, 2018.

    Article  PubMed  Google Scholar 

  15. Jin, X., J. B. Lee, L. Y. Leung, L. Zhang, K. H. Yang, and A. I. King. Biomechanical Response of the Bovine Pia-Arachnoid Complex to Tensile Loading at Varying Strain Rates, 2006.

  16. Kameyama, T., Y. Hashizume, and G. Sobue. Morphologic Features of the Normal Human Cadaveric Spinal Cord. Spine. 21:1285–1290, 1996.

    Article  CAS  PubMed  Google Scholar 

  17. Kato, F., Y. Yukawa, K. Suda, M. Yamagata, and T. Ueta. Normal morphology, age-related changes and abnormal findings of the cervical spine Part II: Magnetic resonance imaging of over 1,200 asymptomatic subjects. Eur. Spine J. 21:1499–1507, 2012.

    Article  PubMed  PubMed Central  Google Scholar 

  18. Kato, D., Y. Nakahira, N. Atsumi, and M. Iwamoto. Development of human-body model THUMS version 6 containing muscle controllers and application to injury analysis in frontal collision after brake deceleration. Conf. Proc. Int. Res. Counc. Biomech. Inj. IRCOBI 2018-Sep:207–223, 2018.

  19. Kimpara, H., Y. Nakahira, M. Iwamoto, K. Miki, K. Ichihara, S. I. Kawano, and T. Taguchi. Investigation of Anteroposterior Head-Neck Responses during Severe Frontal Impacts Using a Brain-Spinal Cord Complex FE Model. SAE Tech. Pap. 2006-Nov:509–544, 2006.

  20. Ko, H. Y., J. H. Park, Y. B. Shin, and S. Y. Baek. Gross quantitative measurements of spinal cord segments in human. Spinal Cord. 42:35–40, 2004.

    Article  PubMed  Google Scholar 

  21. Kraan, G. A., T. H. Smit, and P. V. J. M. Hoogland. Extraforaminal ligaments of the cervical spinal nerves in humans. Spine J. 11:1128–1134, 2011.

    Article  PubMed  Google Scholar 

  22. Lasswell, T. L., D. S. Cronin, J. B. Medley, and P. Rasoulinejad. Incorporating ligament laxity in a finite element model for the upper cervical spine. Spine J. 17:1755–1764, 2017.

    Article  PubMed  Google Scholar 

  23. Liu, Y., X. Zhou, J. Ma, Y. Ge, and X. Cao. The diameters and number of nerve fibers in spinal nerve roots. J. Spinal Cord Med. 38:532–537, 2015.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Mao, H., L. Zhang, B. Jiang, V. V. Genthikatti, X. Jin, F. Zhu, R. Makwana, A. Gill, G. Jandir, A. Singh, and K. H. Yang. Development of a finite element human head model partially validated with thirty five experimental cases. J. Biomech. Eng. 135:1, 2013.

    Article  Google Scholar 

  25. Mattucci, S. Strain rate dependent properties of younger human cervical spine ligaments. J. Mech. Behav. Biomed. Mater. 10:216–226, 2012.

    Article  PubMed  Google Scholar 

  26. Meaney, D. F., B. Morrison, and C. D. Bass. The mechanics of traumatic brain injury: A review of what we know and what we need to know for reducing its societal burden. J. Biomech. Eng. 136:1, 2014.

    Article  Google Scholar 

  27. Melvin, J. W., and N. Yoganandan. Biomechanics of Brain Injury: A Historical Perspective. In: Accidental Injury, New York: Springer, 2015, pp. 221–245.

    Chapter  Google Scholar 

  28. Miller, L. E., J. E. Urban, M. E. Kelley, A. K. Powers, C. T. Whitlow, J. A. Maldjian, S. Rowson, and J. D. Stitzel. Evaluation of brain response during head impact in youth athletes using an anatomically accurate finite element model. J. Neurotrauma. 36:1561–1570, 2019.

    Article  PubMed  PubMed Central  Google Scholar 

  29. Miller, L. E., J. E. Urban, and J. D. Stitzel. Development and validation of an atlas-based finite element brain model. Biomech. Model. Mechanobiol. 15:1201–1214, 2016.

    Article  PubMed  PubMed Central  Google Scholar 

  30. Okada, Y., T. Ikata, S. Katoh, and H. Yamada. Morphologic analysis of the cervical spinal cord, dural tube, and spinal canal by magnetic resonance imaging in normal adults and patients with cervical spondylotic myelopathy. Spine. 19:2331–2335, 1994.

    Article  CAS  PubMed  Google Scholar 

  31. Östh, J., M. Mendoza-Vazquez, A. Linder, M. Y. Svensson, and K. Brolin. The VIVA OpenHBM finite element 50th percentile female occupant model: Whole body model development and kinematic validation. Conf. Proc. Int. Res. Counc. Biomech. Inj. IRCOBI 2017-Sep, pp. 443–466, 2017.

  32. Östh, J., M. Mendoza-Vazquez, M. Y. Svensson, A. Linder, and K. Brolin. Development of a 50th percentile female human body model. 2016 IRCOBI Conf. Proc. - Int. Res. Counc. Biomech. Inj. pp. 573–575, 2016.

  33. Polak, K., M. Czyz, K. Ścigała, W. Jarmundowicz, and R. Bedziński. Biomechanical characteristics of the porcine denticulate ligament in different vertebral levels of the cervical spine-Preliminary results of an experimental study. J. Mech. Behav. Biomed. Mater. 34:165–170, 2014.

    Article  PubMed  Google Scholar 

  34. Post, A., A. Oeur, B. Hoshizaki, and M. D. Gilchrist. An examination of American football helmets using brain deformation metrics associated with concussion. Mater. Des. 45:653–662, 2013.

    Article  Google Scholar 

  35. Richardson, M. G., and R. N. Wissler. Density of lumbar cerebrospinal fluid in pregnant and nonpregnant humans. Anesthesiology. 85:326–330, 1996.

    Article  CAS  PubMed  Google Scholar 

  36. Rowson, S., and S. M. Duma. Brain injury prediction: Assessing the combined probability of concussion using linear and rotational head acceleration. Ann. Biomed. Eng. 41:873–882, 2013.

    Article  PubMed  PubMed Central  Google Scholar 

  37. Rycman, A., S. McLachlin, and D. S. Cronin. A hyper-viscoelastic continuum-level finite element model of the spinal cord assessed for transverse indentation and impact loading. Front. Bioeng. Biotechnol. 9:1, 2021.

    Article  Google Scholar 

  38. Rycman, A., S. McLachlin, and D. S. Cronin. Comparison of numerical methods for cerebrospinal fluid representation and fluid–structure interaction during transverse impact of a finite element spinal cord model. Int. J. Numer. Method. Biomed. Eng. 2022.

    Article  PubMed  Google Scholar 

  39. Shetye, S. S., M. M. Deault, and C. M. Puttlitz. Biaxial response of ovine spinal cord dura mater. J. Mech. Behav. Biomed. Mater. 34:146–153, 2014.

    Article  PubMed  PubMed Central  Google Scholar 

  40. Shi, B., X. Zheng, S. Min, Z. Zhou, Z. Ding, and A. Jin. The morphology and clinical significance of the dorsal meningovertebra ligaments in the cervical epidural space. Spine J. 14:2733–2739, 2014.

    Article  PubMed  Google Scholar 

  41. Tardieu, G. G., C. Fisahn, M. Loukas, M. Moisi, J. Chapman, R. J. Oskouian, and R. S. Tubbs. The Epidural Ligaments (of Hofmann): A Comprehensive Review of the Literature. Cureus. 8:1, 2016.

    Google Scholar 

  42. Taylor, C., J. M. Bell, M. J. Breiding, and L. Xu. Traumatic Brain Injury-Related Emergency Department Visits, Hospitalizations, and Deaths-United States, 2007 and 2013 Surveillance Summaries Centers for Disease Control and Prevention MMWR Editorial and Production Sta. Morb. Mortal. Wkly. Rep. 66:1–8, 2017.

    Google Scholar 

  43. Thunnissen, J., J. Wismans, C. L. Ewing, and D. J. Thomas. Human Volunteer Head-Neck Response in Frontal Flexion: A New Analysis. 1995.

    Article  Google Scholar 

  44. Toyota Motor Corporation, and I. Toyota Central R&D Labs. Total Human Model for Safety (THUMS) Documentation. 2021.

  45. Tubbs, R. S., G. Salter, P. A. Grabb, and W. J. Oakes. The denticulate ligament: Anatomy and functional significance. J. Neurosurg. 94:271–275, 2001.

    CAS  PubMed  Google Scholar 

  46. Wadhwani, S., P. Loughenbury, and R. Soames. The Anterior Dural (Hofmann) Ligaments. Spine (Phila. Pa. 1976). 29:623–627, 2004.

  47. Wedekind, C., and M. Lippert-Grüner. Long-term outcome in severe traumatic brain injury is significantly influenced by brainstem in involvement. Brain Inj. 19:681–684, 2005.

    Article  CAS  PubMed  Google Scholar 

  48. Wismans, J., H. Van Oorschot, and H. J. Woltring. Omni-directional human head-neck response. 1986.

    Article  Google Scholar 

  49. Wismans, J., M. Philippens, E. Van Oorschot, D. Kallieris, and R. Mattern. Comparison of human volunteer and cadaver head-neck response in frontal flexion. 1987.

    Article  Google Scholar 

  50. Wismans, J., and C. H. Spenny. Performance requirements for mechanical necks in lateral flexion. 1983.

    Article  Google Scholar 

  51. Yang, K. H., J. Hu, N. A. White, A. I. King, C. C. Chou, and P. Prasad. Development of Numerical Models for Injury Biomechanics Research: A Review of 50 Years of Publications in the Stapp Car Crash Conference. SAE Tech. Pap. 2006 Nov, 2006.

  52. Zhang, L., K. H. Yang, R. Dwarampudi, K. Omori, T. Li, K. Chang, W. N. Hardy, T. B. Khalil, and A. I. King. Recent Advances in Brain Injury Research: A New Human Head Model Development and Validation. SAE Tech. Pap. 45:, 2001.

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The authors gratefully acknowledge funding from the Natural Sciences and Engineering Research Council of Canada, Stellantis Canada, General Motors of Canada, Honda Development and Manufacturing of America, and the Global Human Body Models Consortium; and Compute Canada for the computational resources needed to undertake the research.

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The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Correspondence to Duane S. Cronin.

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Rycman, A., McLachlin, S.D. & Cronin, D.S. Spinal Cord Boundary Conditions Affect Brain Tissue Strains in Impact Simulations. Ann Biomed Eng 51, 783–793 (2023).

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