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Journal of Computational Neuroscience

, Volume 37, Issue 2, pp 317–332 | Cite as

Compromised axonal functionality after neurodegeneration, concussion and/or traumatic brain injury

  • Pedro D. MaiaEmail author
  • J. Nathan Kutz
Article

Abstract

Axonal swellings are almost universal in neurodegenerative diseases of the central nervous system, including Alzheimer’s and Parkinson’s disease. Concussions and traumatic brain injuries can also produce cognitive and behavioral deficits by compromising neuronal morphology. Using a spike metric analysis, we characterize computationally the effects of such axonal varicosities on spike train propagation by comparing Poisson spike train classes before and after propagation through a prototypical axonal enlargement, or focused axonal swelling. Misclassification of spike train classes and low-pass filtering of firing rate activity increases with more pronounced axonal injury. We show that confusion matrices and a calculation of the loss of transmitted information provide a very practical way to characterize how injured neurons compromise the signal processing and faithful conductance of spike trains. The method demonstrates that (i) neural codes encoded with low firing rates are more robust to injury than those encoded with high firing rates, (ii) classification depends upon the length of the spike train used to encode information, and (iii) axonal injuries reduce the variance of spike trains within a given stimulus class. The work introduces a novel theoretical and computational framework to quantify the interplay between electrophysiological dynamics with focused axonal swellings generated by injury or other neurodegenerative processes. It further suggests how pharmacology and plasticity may play a role in recovery of neural computation. Ultimately, the work bridges vast experimental observations of in vitro morphological pathologies with post-traumatic cognitive and behavioral dysfunction.

Keywords

Neurodegenerative diseases Traumatic brain injury Concussion Alzheimer Parkinson Axonal Swellings Axonal Computation Spike train metrics 

Notes

Acknowledgments

We are especially grateful to Bingni Brunton, Steven Brunton, Borna Dabiri and Matthew Hemphill for discussions relating to the filtering and functionality of the injured axons. We also thank Eric Shea-Brown, Ben Lansdell and Alex Cayco-Gajic for helpful discussions relating to this work. Finally, we acknowledge our anonymous reviewers for pointing out other neurodegenerative diseases beyond TBI where our work could be potentially applied.

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Fainaru-Wada, M., & Fainaru, S. (2013). League of denial: The NFL, concussions, and the battle for truth. Crown Archetype.Google Scholar
  2. Faul, M., Xu, L., Wald, M.M., Coronado, V.G. (2010). Traumatic brain injury in the United States: emergency department visits, hospitalizations, and deaths. Atlanta (GA): centers for disease control and prevention, national center for injury prevention and control.Google Scholar
  3. Adle-Biassette, H., Chretien, F., Wingertsmann, L., Hery, C., Ereau T., Scaravilli, F., Tardieu, M., Gray, F. (1999). Neuropathology and Applied Neurobiology, 25, 123–133.PubMedCrossRefGoogle Scholar
  4. Altenberger, R., Lindsay, K.A., Ogden, J.M., Rosenberg, J.R. (2001). The interaction between membrane kinetics and membrane geometry in the transmission of action potentials in non-uniform excitable fibres: a finite element approach. Journal of Neuroscience Methods, 112, 101–117.PubMedCrossRefGoogle Scholar
  5. Antic, S., Wuskell, J.P., Loew, L., Zecevic, D. (2000). Functional profile of the giant metacerebral neuron of Helix aspersa: temporal and spatial dynamics of electrical activity in situ. The Journal of Physiology, 527, 55–69.PubMedCentralPubMedCrossRefGoogle Scholar
  6. Aronov, D., & Victor, J.D. (2005). Non-euclidean properties of spike train metric spaces. Physical Reviews E - Statistics Nonlin Soft Matter Physical, 69, 061905.CrossRefGoogle Scholar
  7. Bakkum, D.J., Frey, U., Radivojevic, M., Russel, T.L., Müller. J., Fiscella, M., Takahashi, H., Hierlemann, A. (2013). Nature communications, 4, 2181.PubMedCrossRefGoogle Scholar
  8. Blumbergs, P.C., Scott, G., Manavis, J., Wainwright, H., Simpson, D.A., McLean, A.J (1995). Topography of axonal injury as defined by amyloid precursor protein and the sector scoring method in mild and severe closed head injury. Journal of Neurotrauma, 12, 565–572.PubMedCrossRefGoogle Scholar
  9. Browne, K.D., Chen, X.H., Meaney, D.F., Smith, D.H. (2011). Mild traumatic brain injury and diffuse axonal injury, in Swine. Journal of Neurotrauma, 28(9), 1747–1755.PubMedCentralPubMedCrossRefGoogle Scholar
  10. Bucher, D., & Goaillard, J.M. (2011). Beyond faithful conduction: Short term dynamics, neuromodulation, and long-term regulation of spike propagation in the axon. Progress in Neurobiology, 94, 307–346.PubMedCentralPubMedCrossRefGoogle Scholar
  11. Chen, W.R., Shen, G.Y., Shepherd, G.M., Hines, M.L., Midtgaard, J. (2002). Multiple modes of action potential initiation and propagation in mitral cell primary dendrite. Journal of Neurophysiology, 88, 27552764.CrossRefGoogle Scholar
  12. Chen, Y.C., Smith, D.H., Meaney, D.F. (2009). In-Vitro approaches for studying blast-induced traumatic brain injury. Journal of Neurotrauma, 26(6), 861–876.PubMedCentralPubMedCrossRefGoogle Scholar
  13. Christman, C.W., Grady, M.S., Walker, S.A., Hol-Loway, K.L., Povlishock, J.T. (1994). Ultra-structural studies of diffuse axonal injury in humans. Journal of Neurotrauma, 11, 173–186.PubMedCrossRefGoogle Scholar
  14. Cheng, C.L., & Povlishock, J.T. (1988). The effect of traumatic brain injury on the visual system: a morphologic characterization of reactive axonal change. Journal of Neurotrauma, 5, 47–60.PubMedCrossRefGoogle Scholar
  15. Dayan, P., & Abbot, F.L. (2001). Theoretical Neuroscience. MIT Press.Google Scholar
  16. Coleman, M. (2005). Axon degeneration mechanisms: commonality amid diversity. Nature Reviews Neuroscience, 6(11), 889–898.PubMedCrossRefGoogle Scholar
  17. Debanne, D. (2004). Information processing in the axon. Nature Reviews Neuroscience, 5(4), 304–316.PubMedCrossRefGoogle Scholar
  18. Debanne, D., Campanac, E., Bialowas, A. (2011). Axon Physiology. Physiological Reviews, 91, 555–602.PubMedCrossRefGoogle Scholar
  19. Ermentrout, G.B., & Rinzel, J. (1996). Reflected waves in an inhomogeneous excitable medium. SIAM Journal on Applied Mathematics, 56(4), 1107–1128.CrossRefGoogle Scholar
  20. Ermentrout, G.B. (2010). Mathematical foundations of neuroscience: Springer.Google Scholar
  21. Ferguson, B., Matyszak, M.K., Esiri, M.M., Perry, V.H. (1997). Axonal damage in acute multiple sclerosis lesions. Brain, 120, 393–399.PubMedCrossRefGoogle Scholar
  22. Fitzhugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal, 1(6), 445–466.PubMedCentralPubMedCrossRefGoogle Scholar
  23. Galvin, J.E., Uryu, K., Lee, V.M., Trojanowski, J.Q. (1999). Axon pathology in parkinsons disease and lewy body dementia hippocampus contains α-, β-, and γ -synuclein. Proceedings of National Academy of Science (USA), 96, 13450–13455.CrossRefGoogle Scholar
  24. Gerstner, W. (2002). Spiking neuron models. Cambridge University Press.Google Scholar
  25. Goldstein, S.S., & Rall, W. (1974). Changes of action potential shape and velocity for changing core conductor geometry. Biophysical Journal, 14, 731–757.PubMedCentralPubMedCrossRefGoogle Scholar
  26. Grady, M.S., Mclaughlin, M.R., Christman, C.W., Valadaka, A.B., Flinger, C.L., Povlishock, J.T. (1993). The use of antibodies against neurofilament sub- units for the detection of diffuse axonal injury in humans. Journal of Neuropathology Experimentalis Neurologica, 52, 143–152.CrossRefGoogle Scholar
  27. Hemphill, M.A., Dabiri, B.E., Gabriele, S., Kerscher, L., Franck, C., Goss, J.A., Alford, P.W., Parker, K.K. (2011). A possible role for integrin signaling in diffuse axonal injury. PLos ONE, 6(7), 22899.CrossRefGoogle Scholar
  28. Hodgkin, A.L., & Huxley, A.F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117(4), 500–545.PubMedCentralPubMedGoogle Scholar
  29. Izhikevich, E.M. (2007). Dynamical systems in neuroscience: the geometry of excitability and bursting. MIT Press.Google Scholar
  30. Johnson, V.E., Stewart, W., Smith, D.H. (2013). Axonal pathology in traumatic brain injury. Experimental Neurology, 246, 35–43.PubMedCentralPubMedCrossRefGoogle Scholar
  31. Jorge, R.E., Acion, L., White, T., Tordesillas-Gutierrez, D., Pierson, R., Crespo-Facorro, B., Magnotta, V.A. (2012). White matter abnormalities in veterans with mild traumatic brain injury. American Journal of Psychiatry, 169(12), 1284–1291.PubMedCentralPubMedCrossRefGoogle Scholar
  32. Krstic, D., & Knusesl, I. (2012). Deciphering the mechanism underlying late-onset alzheimer disease. Nature Reviews Neuroscience, 9(1), 25–34.Google Scholar
  33. Khodorov, B.I., & Timin, E.N. (1975). Nerve impulse propagation along nonuniform fibres. Progress in Biophysics and Molecular Biology, 30(23), 145–184.PubMedGoogle Scholar
  34. Kutz, J.N. (2013). Data-driven modeling and scientific computing: Oxford Press.Google Scholar
  35. Liberski, P.P., & Budka, H. (1999). Neuroaxonal pathology in Creutzfeldt-Jakob disease. Acta Neuropathology (Berlim), 97, 329–334.CrossRefGoogle Scholar
  36. Lipton, M.L., Gellella, E., Lo, C., Gold, T., Ardekani, B.A., Shifteh, K., Bello, J.A., Branch, C.A. (2008). Journal of Neurotrauma, 25, 13351342.PubMedCrossRefGoogle Scholar
  37. Magdesian, M.H., Sanchez, F.S., Lopez, M., Thostrup, P., Durisic, N., Belkaid, W., Liazoghli, D., Grütter, P., Colman, R. (2012). Atomic force microscopy reveals important differences in axonal resistance to injury. Biophysical Journal, 103(3), 405–414.PubMedCentralPubMedCrossRefGoogle Scholar
  38. Maia, P.D., & Kutz, J.N. (2014). Identifying critical regions for spike propagation in axon segments. Journal of Computational Neuroscience, 36(2), 55–141.CrossRefGoogle Scholar
  39. Manor, Y., Koch, C., Segev, I. (1991). Effect of geometrical irregularities on propagation delay in axonal trees. Biophysical Journal, 60, 1424–1437.PubMedCentralPubMedCrossRefGoogle Scholar
  40. Maxwell, W.L., Povlishock, J.T., Graham, D.L. (1997). A mechanistic analysis of nondisruptive axonal injury:A review. Journal of Neurotrauma, 17(7), 419–440.CrossRefGoogle Scholar
  41. Millecamps, S., & Julien, J.P. (2013). Axonal transport deficits and neurodegenerative diseases. Nature Reviews Neuroscience, 14(161), 161–176.PubMedCrossRefGoogle Scholar
  42. Nagumo, S., Arimoto, Yoshizawa, S. (1962). An active pulse transmission line simulating nerve axon. Proceedings of the IRE, 50(10), 2061–2070.CrossRefGoogle Scholar
  43. Niogi, S.N., Mukherjee, P., Ghajar, J., Johnson, C., Kolster, R.A., Sarkar, R., Lee, H., Meeker, M., Zimmerman, R.D., Manley, G.T., Mccandliss, B.D. (2008). Extent of Microstructural White Matter Injury in Postconcussive Syndrome Correlates with Impaired Cognitive Reaction Time: A 3T Diffusion Tensor Imaging Study of Mild Traumatic Brain Injury. American Journal of Neuroradiology, 29(5), 967–973.PubMedCrossRefGoogle Scholar
  44. Parnas, I. (1972). Differential block at high frequency of branches of a single axon innervating two muscles. Journal of Neurophysiology, 35, 903–914.PubMedGoogle Scholar
  45. Parnas, I., Hochstein, S., Parnas, H. (1976). Theoretical analysis of parameters leading to frequency modulation along an inhomogeneous axon. Journal of Neurophysiology, 39(4).Google Scholar
  46. Parnas, I. (1979). Propagation in nonuniform neurites: form and function in axons. The neurosciences, edited by Schmitt, F.O. Worden F.G.Cambridge, MIT Press, 499–512.Google Scholar
  47. Ramon, F., Joyner, R.W, Moore, J.W. (1975). Propagation of action potentials in inhomogeneous axon regions. Federation proceedings, 34, 1357–1363.PubMedGoogle Scholar
  48. Rinzel, J. (1990). Mechanisms for nonuniform propagation along excitable cables. Annals of the New York Academy of Sciences, 591.Google Scholar
  49. Rubovitch, V., Ten-Bosch, M., Zohar, O., Harrison, C.R., Tempel-Brami, C., Stein, E., Hoffer, B.J., Balaban, C., Schreiber, S., Chiu, W.T., Pick, C.G. (2011). A mouse model of blast-induced mild traumatic brain injury. Experimental Neurology, 232(2), 280–289.PubMedCentralPubMedCrossRefGoogle Scholar
  50. Scott, A. (2002). Neuroscience: a mathematical primer: Springer.Google Scholar
  51. Segev, I., & Schneidman, E. (1999). Axons as computing devices: basic insights gained from models. The Journal of Physiology, 93, 263–270.Google Scholar
  52. Shepherd, G.M.G., & Harris, K. (1998). Three-dimensional structure and composition of CA3 to CA1 axons in rat hippocampal slices: implications for presynaptic connectivity and compartmentalization. Journal of Neuroscience, 18(20).Google Scholar
  53. Smith, D.H., Wolf, J.W., Lusardi, T.A., Lee, V.M.Y., Meaney, D.F. (1999). High tolerance and delayed elastic response of cultured axons to dynamic stretch injury. The Journal of Neuroscience, 19(11), 4263–4269.PubMedGoogle Scholar
  54. Smith, D.O. (1980). Mechanisms of action potential propagation failure at sites of axon branching in the crayfish. The Journal of Physiology, 301, 243–259.PubMedCentralPubMedGoogle Scholar
  55. Tang-Schomer, M.D., Johnson, V.E., Baas, P.W., Stewart, W., Smith, D.H (2012). Partial interruption of axonal transport due to microtubule breakage accounts for the formation of periodic varicosities after traumatic axonal injury. Experimental Neurology, 233, 364–372.PubMedCentralPubMedCrossRefGoogle Scholar
  56. Tang-Schomer, M.D., Patel, A.R., Bass, P.W., Smith, D.H (2010). Mechanical breaking of microtubules in axons during dynamic stretch injury underlies delayed elasticity, microtubule disassembly, and axon degeneration. The FASEB Journal, 24(5), 1401–1410.PubMedCentralCrossRefGoogle Scholar
  57. Trapp, B.D., Peterson, J., Ransohoff, R.M., Rudick, R., Mrk, S., B L. (1998). Axonal transection in the lesions of multiple sclerosis. The New England Journal of Medicine, 338, 278–285.Google Scholar
  58. Tsai, J., Grutzendler, J., Duff, K., Gan, W.B. (2004). Fibrillar amyloid deposition leads to local synaptic abnormalities and breakage of neuronal branches. Nature Neuroscience, 7, 1181–1183.PubMedCrossRefGoogle Scholar
  59. Victor, J.D. (2005). Spike train metrics. Current opinion in Neurobiology, 15, 585–592.PubMedCentralPubMedCrossRefGoogle Scholar
  60. Victor, J.D., & Purpura, K.P. (1997). Metric space analysis of spike trains: theory, algorithms and application. Network: Computational Neural Systems, 8, 127–164.CrossRefGoogle Scholar
  61. Wang, J., Hamm, R.J., Povlishock, J.T. (2011). Traumatic axonal injury in the optic nerve: evidence for axonal swelling, disconnection, dieback and reorganization. Journal of Neurotrauma, 28(7), 1185–1198.PubMedCentralPubMedCrossRefGoogle Scholar
  62. Xiong, Y., Mahmood, A., Chopp, M. (2013). Animal models of traumatic brain injury. Nature Reviews Neuroscience, 14(2), 128–142.PubMedCentralPubMedCrossRefGoogle Scholar
  63. Zhou, Y., & Bell, J. (1994). Study of propagation along nonuniform excitable fibers. Mathematical Biosciences, 119(2), 169–203.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA

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