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Bulging Brains

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Abstract

Brain swelling is a serious condition associated with an accumulation of fluid inside the brain that can be caused by trauma, stroke, infection, or tumors. It increases the pressure inside the skull and reduces blood and oxygen supply. To relieve the intracranial pressure, neurosurgeons remove part of the skull and allow the swollen brain to bulge outward, a procedure known as decompressive craniectomy. Decompressive craniectomy has been preformed for more than a century; yet, its effects on the swollen brain remain poorly understood. Here we characterize the deformation, strain, and stretch in bulging brains using the nonlinear field theories of mechanics. Our study shows that even small swelling volumes of 28 to 56 ml induce maximum principal strains in excess of 30 %. For radially outward-pointing axons, we observe maximal normal stretches of 1.3 deep inside the bulge and maximal tangential stretches of 1.3 around the craniectomy edge. While the stretch magnitude varies with opening site and swelling region, our study suggests that the locations of maximum stretch are universally shared amongst all bulging brains. Our model has the potential to inform neurosurgeons and rationalize the shape and position of the skull opening, with the ultimate goal to reduce brain damage and improve the structural and functional outcomes of decompressive craniectomy in trauma patients.

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References

  1. Abaqus 6.14. Analysis user’s manual. SIMULIA. Dassault Systèmes (2014)

  2. Bain, A.C., Meaney, D.F.: Tissue-level thresholds for axonal damage in an experimental model of central nervous system white matter injury. J. Biomech. Eng. 122, 615–622 (2000)

    Article  Google Scholar 

  3. Barber, J.R.: The solution of elasticity problems for the half-space by the method of Green and Collins. Appl. Sci. Res. 40, 135–157 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  4. Brauna, J., Guob, J., Lutzkendorf, R., Stadler, J., Papazoglou, S., Hirsch, S., Sack, I., Bernarding, J.: High-resolution mechanical imaging of the human brain by three-dimensional multifrequency magnetic resonance elastography at 7T. NeuroImage 90, 308–314 (2014)

    Article  Google Scholar 

  5. Budday, S., Nay, R., de Rooij, R., Steinmann, P., Wyrobek, T., Ovaert, O.C., Kuhl, E.: Mechanical properties of gray and white matter brain tissue by indentation. J. Mech. Behav. Biomed. Mater. 46, 318–330 (2015)

    Article  Google Scholar 

  6. Budday, S., Sommer, G., Birkl, C., Langkammer, C., Haybäck, J., Kohnert, J., Bauer, M., Paulsen, F., Steinmann, P., Kuhl, E., Holzapfel, G.: Mechanical characterization of human brain tissue. Acta Biomater. (2017), accepted for publication

  7. Cloots, R.J.H., van Dommelen, J.A.W., Nyberg, T., Kleiven, S., Geers, M.G.D.: Micromechanics of diffuse axonal injury: influence of axonal orientation and anisotropy. Biomech. Model. Mechanobiol. 10, 413–422 (2011)

    Article  Google Scholar 

  8. Cooper, D.J., Rosenfeld, J.V., Murray, L., Arabi, Y.M., Davies, A.R., D’Urso, P., Kossmann, T., Ponsford, J., Seppelt, I., Reilly, P., Wolfe, R.: Decompressive craniectomy in diffuse traumatic brain injury. N. Engl. J. Med. 364, 1493–1502 (2011)

    Article  Google Scholar 

  9. Cotton, R.T., Pearce, C.W., Young, P.G., Kota, N., Leung, A.C., Bagchi, A., Qidwai, S.M.: Development of a geometrically accurate and adaptable finite element head model for impact simulation: the naval research laboratory-simpleware head model. Comput. Methods Biomech. Biomed. Eng. 19, 101–113 (2016)

    Article  Google Scholar 

  10. de Rooij, R., Kuhl, E.: Constitutive modeling of brain tissue: current perspectives. Appl. Mech. Rev. 68, 010801 (2016)

    Article  Google Scholar 

  11. ElSayed, T., Mota, A., Fraternali, F., Ortiz, M.: Biomechanics of traumatic brain injury. Comput. Methods Appl. Mech. Eng. 197, 4692–4701 (2008)

    Article  ADS  MATH  Google Scholar 

  12. Fletcher, T.L., Kolias, A.G., Hutchinson, P.J.A., Sutcliffe, M.P.F.: Development of a finite element model of decompressive craniectomy. PLoS ONE 9, e102131 (2014)

    Article  ADS  Google Scholar 

  13. Fletcher, T.L., Kolias, A.G., Hutchinson, P.J.A., Sutcliffe, M.P.F.: An improved method for assessing brain deformation after decompressive craniectomy. PLoS ONE 9, e110408 (2014)

    Article  ADS  Google Scholar 

  14. Fletcher, T.L., Kolias, A.G., Adams, H., Hutchinson, P.J.A., Sutcliffe, M.P.F.: Modelling of brain deformation after decompressive craniectomy. Ann. Biomed. Eng. (2016). doi:10.1007/s10439-016-1667-7

    Google Scholar 

  15. Franceschini, G., Bigoni, D., Regitnig, P., Holzapfel, G.A.: Brain tissue deforms similarly to filled elastomers and follows consolidation theory. J. Mech. Phys. Solids 54, 2592–2620 (2006)

    Article  ADS  MATH  Google Scholar 

  16. Gao, C.P., Ang, B.T.: Biomechanical modeling of decompressive craniectomy in traumatic brain injury. Acta Neurochir., Suppl. 102, 279–282 (2008)

    Article  Google Scholar 

  17. Goriely, A., Budday, S., Kuhl, E.: Neuromechanics: from neurons to brain. Adv. Appl. Mech. 48, 79–139 (2015)

    Article  Google Scholar 

  18. Goriely, A., Geers, M.G.D., Holzapfel, G.A., Jayamohan, J., Jerusalem, A., Sivaloganathan, S., Squier, W., van Dommelen, J.A.W., Waters, S., Kuhl, E.: Mechanics of the brain: perspectives, challenges, and opportunities. Biomech. Model. Mechanobiol. 14, 931–965 (2015)

    Article  Google Scholar 

  19. Goriely, A., Weickenmeier, J., Kuhl, E.: Stress singularities in swelling soft solids. Phys. Rev. Lett. 117, 138001 (2016)

    Article  ADS  Google Scholar 

  20. Hernandez, F., Wu, L.C., Yip, M.C., Laksari, K., Hoffmann, A.R., Lopez, J.R., Grant, G.A., Kleiven, S., Camarillo, D.B.: Six degree-of-freedom measurements of human mild traumatic brain injury. Ann. Biomed. Eng. 43, 1918–1934 (2015)

    Article  Google Scholar 

  21. Hernandez, F., Giordano, C., Kleiven, S., Camarillo, D.B.: Coronal head rotation, falx cerebri displacement, and corpus callosum strain are related and implicated in sport-related MTBI. J. Neurotrauma 33, A34–A35 (2016)

    Google Scholar 

  22. Holzapfel, G.A.: Nonlinear Solid Mechanics: A Continuum Approach for Engineering. John Wiley & Sons, New York (2000)

    MATH  Google Scholar 

  23. Hutchinson, P.J., Corteen, E., Czosnyka, M., Mendelow, A.D., Menon, D.K., Mitchell, P., Murray, G., Pickard, J.D., Rickels, E., Sahuquillo, J., Servadei, F., Teasdale, G.M., Timofeev, I., Unterberg, A., Kirkpatrick, P.J.: Decompressive craniectomy in traumatic brain injury: the randomized multicenter RESCUEicp study. Acta Neurochir., Suppl. 96, 17–20 (2006)

    Article  Google Scholar 

  24. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1987)

    MATH  Google Scholar 

  25. Jones, H.R., Burns, T.M., Aminoff, M.J., Pomeroy, S.L.: Netter Collection of Medical Illustrations: Nervous System: Part I, Brain, vol. 7. Saunders Elsevier, Philadelphia (2013)

    Google Scholar 

  26. Kaster, T., Sack, I., Samani, A.: Measurement of the hyperelastic properties of ex vivo brain tissue slices. J. Biomech. 44, 1158–1163 (2011)

    Article  Google Scholar 

  27. Kolias, A.G., Kirkpatrick, P.J., Hutchinson, P.: Decompressive craniectomy: past, present and future. Nat. Rev. Neurol. 9, 405–415 (2013)

    Article  Google Scholar 

  28. Kruse, S.A., Rose, G.H., Glaser, K.J., Manduca, A., Felmlee, J.P., Jack, C.R., Ehman, R.L.: Magnetic resonance elastography of the brain. NeuroImage 39, 231–237 (2008)

    Article  Google Scholar 

  29. Lang, G., Stewart, P.S., Vella, D., Waters, S.L., Goriely, A.: Is the Donnan effect sufficient to explain swelling in brain tissue slices? J. R. Soc. Interface 11, 20140123 (2014)

    Article  Google Scholar 

  30. Li, X., van Holst, H., Kleiven, S.: Decompressive craniectomy causes significant strain increase in axonal fiber tracts. J. Clin. Neurosci. 20, 509–513 (2013)

    Article  Google Scholar 

  31. Mihai, L.A., Chin, L.K., Janmey, P.A., Goriely, A.: A hyperelastic constitutive model for compression stiffening applicable to brain and fat tissues. J. R. Soc. Interface 12, 20150486 (2015)

    Article  Google Scholar 

  32. Mooney, M.: A theory of large elastic deformation. J. Appl. Phys. 11, 582–592 (1940)

    Article  ADS  MATH  Google Scholar 

  33. Ogden, R.W.: Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. Lond. A 326, 565–584 (1972)

    Article  ADS  MATH  Google Scholar 

  34. Pogoda, K., Chin, L.K., Georges, P.C., Byfield, F.R.J., Bucki, R., Kim, R., Weaver, M., Wells, R.G., Marcinkiewicz, C., Janmey, P.A.: Compression stiffening of brain and its effect on mechanosensing by glioma cells. New J. Phys. 16, 075002 (2014)

    Article  ADS  Google Scholar 

  35. Quinn, T.M., Taylor, J.J., Magarik, J.A., Vought, E., Kindy, M.S., Ellegala, D.B.: Decompressive craniectomy: technical note. Acta Neurol. Scand. 123, 239–244 (2011)

    Article  Google Scholar 

  36. Rivlin, R.S.: Large elastic deformations of isotropic materials. IV. Further developments of the general theory. Philos. Trans. R. Soc. Lond. 241, 379–397 (1948)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Rowson, S., Duma, S.M., Beckwirth, J.G., Chu, J.J., Greenwald, R.M., Crisco, J.J., Brolinson, P.G., Duhaime, A.C., McAllister, T.W., Maerlender, A.C.: Rotational head kinematics in football impacts: an injury risk function for concussion. Ann. Biomed. Eng. 40, 1–13 (2012)

    Article  Google Scholar 

  38. Saggar, M., Quintin, E.M., Kienitz, E., Bott, N.T., Sun, Z., Hong, W.C., Chien, Y., Liu, N., Dougherty, R.F., Royalty, A., Hawthorne, G., Reiss, A.L.: Pictionary-based fMRI paradigm to study the neural correlates of spontaneous improvisation and figural creativity. Sci. Rep. 5, 10894 (2015)

    Article  ADS  Google Scholar 

  39. Stiver, S.I.: Complications of decompressive craniectomy for traumatic brain injury. Neurosurg. Focus 26, E7 (2009)

    Article  Google Scholar 

  40. Tagliaferri, F., Zani, G., Iaccarino, C., Ferro, S., Ridolfi, L., Basaglia, N., Hutchinson, P., Servadei, F.: Decompressive craniotomies, facts and fiction: a retrospective analysis of 526 cases. Acta Neurochir. 154, 916–919 (2012)

    Article  Google Scholar 

  41. Tang-Schomer, M.D., Patel, A.R., Baas, P.W., Smith, D.H.: Mechanical breaking of microtubules in axons during dynamic stretch injury underlies delayed elasticity, microtubule disassembly, and axon degeneration. FASEB J. 24, 1401–1410 (2010)

    Article  Google Scholar 

  42. van den Bedem, H., Kuhl, E.: Tau-ism: the Yin and Yang of microtubule sliding, detachment, and rupture. Biophys. J. 109, 2215–2217 (2015)

    Article  Google Scholar 

  43. von Holst, H., Li, X.: Decompressive craniectomy (DC) at the non-injured side of the brain has the potential to improve patient outcome as measured with computational simulation. Acta Neurochir. 156, 1961–1967 (2014)

    Article  Google Scholar 

  44. von Holst, H., Li, X., Kleiven, S.: Increased strain levels and water content in brain tissue after decompressive craniectomy. Acta Neurochir. 154, 1583–1593 (2012)

    Article  Google Scholar 

  45. Weickenmeier, J., Kuhl, E., Goriely, A.: The mechanics of decompressive craniectomy: bulging in idealized geometries. J. Mech. Phys. Solids 96, 572–590 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  46. Weickenmeier, J., Butler, C., Young, P.G., Goriely, A., Kuhl, E.: The mechanics of decompressive craniectomy: personalized simulations. Comput. Methods Appl. Mech. Eng. (2017). doi:10.1016/j.cma.2016.08.011

    Google Scholar 

  47. Wright, R.M., Ramesh, K.T.: An axonal strain injury criterion for traumatic brain injury. Biomech. Model. Mechanobiol. 11, 245–260 (2011)

    Article  Google Scholar 

  48. Young, P.G., Beresford-West, T.B.H., Coward, S.R.L., Notarberardino, B., Walker, B., Abdul-Aziz, A.: An efficient approach to converting 3D image data into highly accurate computational models. Philos. Trans. R. Soc. Lond. A 366, 3155–3173 (2008)

    Article  ADS  Google Scholar 

  49. Zhang, L., Yang, K.H., King, A.I.: A proposed injury threshold for mild traumatic brain injury. J. Biomech. Eng. 126, 226–236 (2004)

    Article  Google Scholar 

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Acknowledgements

We thank Allan L. Reiss and his group for providing the MRI scans. This work was supported by the Timoshenko Scholar Award to Alain Goriely and by the Humboldt Research Award and the National Institutes of Health grant U01 HL119578 to Ellen Kuhl.

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Weickenmeier, J., Saez, P., Butler, C.A.M. et al. Bulging Brains. J Elast 129, 197–212 (2017). https://doi.org/10.1007/s10659-016-9606-1

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