Compr.Analysis of mechanical waves accompanying nerve impulse
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- 1. ANALYSIS OF MECHANICAL WAVES ACCOMPANYING NERVE IMPULSE
Tiziano Modica SUPERVISORS: MASSIMO CUOMO, PROF. ENG. JRI
ENGELBRECHT, PHD DSC UNIVERSITY OF CATANIA DEPARTMENT OF CIVIL
ENGINEERING AND ARCHITECTURAL Masters Degree Thesis in Civil
Engineering Structural and Geotechnical CENTRE FOR NONLINEAR
STUDIES, INSTITUTE OF CYBERNETICS AT TALLINN UNIVERSITY OF
TECHNOLOGY, Tallinn - Estonia
- 2. Waves Monodimensional wave equation Fourier series 2 2 0 2 2
2 = 0 = cos + 0 = cos +
- 3. Dispersion Non dispersive medium = = Dispersive medium = ()
Anomalous and normal dispersion
- 4. Soliton Dispersion and nonlinearity interaction Kortewegde
Vries equation Schrdinger equation Boussinesq-type equations
- 5. Pseudospectral Method (PSM) Global method Stable and
accurate Boundary conditions Trigonometric functions
- 6. Aliasing Cutting high frequencies Increasing the number of
points
- 7. Gibbs phenomenon Oscillatory divergence Filtering
technique
- 8. 0 10 20 30 40 50 0 20 40 60 80 100 -0.2 0 0.2 0.4 x KdV
equation 3D plot T U 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Kortewegde
Vries equation PSM approximation Solitonic behaviour
- 9. From mathematical to biological models
- 10. Nerve pulse propagation Action Potential (AP)
All-or-nothing law Stable pulses Refractory period
Annihilation
- 11. Cell membrane Nernst equation selective permeability -70 mV
Na-K pump
- 12. Electrical experimental evidences Electrodiffusive
models
- 13. Hodgkin & Huxely 1952 Potential difference Ionic
currents Membrane conductance 22 2 2 = + + +
- 14. Mechanical experimental evidences Heat production Swelling
Curtailment
- 15. Heimburg & Jackson model 2005 1D sound propagation
equation Boussinesq-type equation with solitonic solution Melting
transition
- 16. Engelbrecht Peets Tamm model 2014 Nerve fibre considered as
a rod Navier-Bernoulli hypothesis Rayleigh-Love correction Bishops
model according to Porubov
- 17. Engelbrecht Peets Tamm model 2014 Inertial effects
Modelling of anomalous dispersion More consistent model 2 2 = 1 + +
2 2 2 + + 2 2 4 4 + 4 2 2 Nonlinear terms Dispersive / inertial
terms Solitonic initial condition Mixed derivatives
- 18. EPT model: numerical results
- 19. EPT model: numerical results H1=72.14 H2=100 P=6.5810-4
Q=2.24510-4 H1=72.14 H2=1 P=6.5810-4 Q=2.24510-4 P=Q=H1=H2=0
- 20. EPT model: numerical results H1=72.14 H2=100 P=6.5810-4
Q=2.24510-4 H1=72.14 H2=1 P=6.5810-4 Q=2.24510-4 P=Q=H1=H2=0 0 200
400 600 800 1000 1200 1400 1600 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Plot
at timestep 3900 space amplitude Full EPT equation (i.e. anomalous
dispersion) EPT normal dispersion Wave equation
- 21. Conclusions PSM is accurate and efficient, it can be used
to solve PDEs and neural models Pay attention to Gibbs phenomenon
and aliasing HH model is not complete, it explains only the
electric behaviour of AP propagation
- 22. Conclusions Heimburg & Jackson model explains the
mechanical changes but it has some problems in terms of cph and cgr
Engelbrecth Peets Tamm model solves Heimburg & Jackson models
problems
- 23. ConclusionsStill unsolved Mechanical model does not
represent annihilation How to Unificate HH model to EPT model?