Skip to main content

Advertisement

SpringerLink
Log in

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

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Fainaru-Wada, M., & Fainaru, S. (2013). League of denial: The NFL, concussions, and the battle for truth. Crown Archetype.

  • 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.

  • 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.

    Article  CAS  PubMed  Google Scholar 

  • 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.

    Article  CAS  PubMed  Google Scholar 

  • 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.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Aronov, D., & Victor, J.D. (2005). Non-euclidean properties of spike train metric spaces. Physical Reviews E - Statistics Nonlin Soft Matter Physical, 69, 061905.

    Article  Google Scholar 

  • Bakkum, D.J., Frey, U., Radivojevic, M., Russel, T.L., Müller. J., Fiscella, M., Takahashi, H., Hierlemann, A. (2013). Nature communications, 4, 2181.

    Article  PubMed  Google Scholar 

  • 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.

    Article  CAS  PubMed  Google Scholar 

  • 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.

    Article  PubMed Central  PubMed  Google Scholar 

  • 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.

    Article  PubMed Central  PubMed  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  PubMed Central  PubMed  Google Scholar 

  • 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.

    Article  CAS  PubMed  Google Scholar 

  • 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.

    Article  CAS  PubMed  Google Scholar 

  • Dayan, P., & Abbot, F.L. (2001). Theoretical Neuroscience. MIT Press.

  • Coleman, M. (2005). Axon degeneration mechanisms: commonality amid diversity. Nature Reviews Neuroscience, 6(11), 889–898.

    Article  CAS  PubMed  Google Scholar 

  • Debanne, D. (2004). Information processing in the axon. Nature Reviews Neuroscience, 5(4), 304–316.

    Article  CAS  PubMed  Google Scholar 

  • Debanne, D., Campanac, E., Bialowas, A. (2011). Axon Physiology. Physiological Reviews, 91, 555–602.

    Article  CAS  PubMed  Google Scholar 

  • Ermentrout, G.B., & Rinzel, J. (1996). Reflected waves in an inhomogeneous excitable medium. SIAM Journal on Applied Mathematics, 56(4), 1107–1128.

    Article  Google Scholar 

  • Ermentrout, G.B. (2010). Mathematical foundations of neuroscience: Springer.

  • Ferguson, B., Matyszak, M.K., Esiri, M.M., Perry, V.H. (1997). Axonal damage in acute multiple sclerosis lesions. Brain, 120, 393–399.

    Article  PubMed  Google Scholar 

  • Fitzhugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal, 1(6), 445–466.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • Gerstner, W. (2002). Spiking neuron models. Cambridge University Press.

  • Goldstein, S.S., & Rall, W. (1974). Changes of action potential shape and velocity for changing core conductor geometry. Biophysical Journal, 14, 731–757.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    CAS  PubMed Central  PubMed  Google Scholar 

  • Izhikevich, E.M. (2007). Dynamical systems in neuroscience: the geometry of excitability and bursting. MIT Press.

  • Johnson, V.E., Stewart, W., Smith, D.H. (2013). Axonal pathology in traumatic brain injury. Experimental Neurology, 246, 35–43.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • 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.

    Article  PubMed Central  PubMed  Google Scholar 

  • Krstic, D., & Knusesl, I. (2012). Deciphering the mechanism underlying late-onset alzheimer disease. Nature Reviews Neuroscience, 9(1), 25–34.

    Google Scholar 

  • Khodorov, B.I., & Timin, E.N. (1975). Nerve impulse propagation along nonuniform fibres. Progress in Biophysics and Molecular Biology, 30(23), 145–184.

    CAS  PubMed  Google Scholar 

  • Kutz, J.N. (2013). Data-driven modeling and scientific computing: Oxford Press.

  • Liberski, P.P., & Budka, H. (1999). Neuroaxonal pathology in Creutzfeldt-Jakob disease. Acta Neuropathology (Berlim), 97, 329–334.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Maia, P.D., & Kutz, J.N. (2014). Identifying critical regions for spike propagation in axon segments. Journal of Computational Neuroscience, 36(2), 55–141.

    Article  Google Scholar 

  • Manor, Y., Koch, C., Segev, I. (1991). Effect of geometrical irregularities on propagation delay in axonal trees. Biophysical Journal, 60, 1424–1437.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Millecamps, S., & Julien, J.P. (2013). Axonal transport deficits and neurodegenerative diseases. Nature Reviews Neuroscience, 14(161), 161–176.

    Article  CAS  PubMed  Google Scholar 

  • Nagumo, S., Arimoto, Yoshizawa, S. (1962). An active pulse transmission line simulating nerve axon. Proceedings of the IRE, 50(10), 2061–2070.

    Article  Google Scholar 

  • 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.

    Article  CAS  PubMed  Google Scholar 

  • Parnas, I. (1972). Differential block at high frequency of branches of a single axon innervating two muscles. Journal of Neurophysiology, 35, 903–914.

    CAS  PubMed  Google Scholar 

  • Parnas, I., Hochstein, S., Parnas, H. (1976). Theoretical analysis of parameters leading to frequency modulation along an inhomogeneous axon. Journal of Neurophysiology, 39(4).

  • 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.

  • Ramon, F., Joyner, R.W, Moore, J.W. (1975). Propagation of action potentials in inhomogeneous axon regions. Federation proceedings, 34, 1357–1363.

    CAS  PubMed  Google Scholar 

  • Rinzel, J. (1990). Mechanisms for nonuniform propagation along excitable cables. Annals of the New York Academy of Sciences, 591.

  • 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.

    Article  PubMed Central  PubMed  Google Scholar 

  • Scott, A. (2002). Neuroscience: a mathematical primer: Springer.

  • Segev, I., & Schneidman, E. (1999). Axons as computing devices: basic insights gained from models. The Journal of Physiology, 93, 263–270.

    CAS  Google Scholar 

  • 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).

  • 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.

    CAS  PubMed  Google Scholar 

  • 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.

    CAS  PubMed Central  PubMed  Google Scholar 

  • 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.

    Article  PubMed Central  PubMed  Google Scholar 

  • 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.

    Article  CAS  PubMed Central  Google Scholar 

  • 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.

  • 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.

    Article  CAS  PubMed  Google Scholar 

  • Victor, J.D. (2005). Spike train metrics. Current opinion in Neurobiology, 15, 585–592.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Victor, J.D., & Purpura, K.P. (1997). Metric space analysis of spike trains: theory, algorithms and application. Network: Computational Neural Systems, 8, 127–164.

    Article  Google Scholar 

  • 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.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Xiong, Y., Mahmood, A., Chopp, M. (2013). Animal models of traumatic brain injury. Nature Reviews Neuroscience, 14(2), 128–142.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Zhou, Y., & Bell, J. (1994). Study of propagation along nonuniform excitable fibers. Mathematical Biosciences, 119(2), 169–203.

    Article  CAS  PubMed  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, University of Washington, 98195-3925, Seattle, WA, USA

    Pedro D. Maia & J. Nathan Kutz

Authors
  1. Pedro D. Maia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Nathan Kutz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pedro D. Maia.

Additional information

Action Editor: Jonathan David Victor

Grants or other notes about the article that should go on the front page should be placed here. General acknowledgments should be placed at the end of the article.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maia, P.D., Kutz, J.N. Compromised axonal functionality after neurodegeneration, concussion and/or traumatic brain injury. J Comput Neurosci 37, 317–332 (2014). https://doi.org/10.1007/s10827-014-0504-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-014-0504-x

Keywords

Search

Navigation