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Constitutive Modeling and Numerical Simulation of Axonal Swelling at Large Deformation and Its Effects on Action Potential Propagation

Dehghany Dahaj, Mohammad | 2021

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 54782 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Naghdabadi, Reza; Sohrabpour, Saeed
  7. Abstract:
  8. Brain diseases like Parkinson’s, ischemia and trauma are among major causes of death worldwide. Axonal swelling is the hallmark of most of these diseases. It is frequently observed that the axonal swelling will not remain homogeneous and shape transformations like forming multiple beads along the axon (or beading) may happen. These focal large swellings can alter or even block the passing action potentials along the axon and hence may have serious cognitive consequences. This research deals with theoretical and numerical modeling of axonal swellings. The proposed model has two parts: the central axoplasm and the surrounding cortical membrane. Instable large deformations, water diffusion, chemical reactions, active deformations are among the main physics governing the swelling process. These physics are highly coupled together and thus the problem is intrinsically multiphysics. Therefore, we employ continuum thermodynamics framework to extract the governing equations of the system in a consistent way. The obtained equations are highly nonlinear and coupled and thus must be solved numerically. To this end, we utilize nonlinear finite element (FE) method.In this thesis, axonal swelling due to osmotic shocks, actomyosin disruptions and low levels of metabolic energy is studied. It is shown that kinetics of axonal swelling is surface limited and this swelling happens mainly in the radial direction. In addition, the proposed model indicates that membrane tension is the primary cause for beading instability. For this instability, the beading wavenumbers vary between 0.2 and 0.55 which is in close agreement with the experimental range 0.3 to 0.6. The present study, furthermore, explores axonal cytotoxic swelling. It is observed that the model can accurately capture this swelling as well. With the developed framework, finally, we study Gibbs-Donnan equilibrium of the axon due to inhibition of the ionic pumps. This study shows that at Gibbs-Donnan equilibrium, the axonal area can increase by 180%.In conclusion, the present research can significantly enhance our understanding of the axonal swelling process. This better understanding can help in preventing or even treating the responsible brain pathological states. Furthermore, the current work can serve as a basis for future research works in the new important field of brain cell mechanics
  9. Keywords:
  10. Finite Element Method ; Axons Diameter ; Continuum Thermodynamics ; Beading Instability ; Osmotic Swelling ; Cytotoxic Swelling ; Large Deformation

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