Boussinesq Solitons as Propagators of Neural Signals

We consider certain approximation for determining the equation of motion for nerve signals by using the model of the lipid melting of membranes. The nerve pulses are found to display nonlinearity and dispersion during the melting transition. In this simplified model the nonlinear equation early proposed by Heimburg and coworkers transformed to the well known integrable Boussinesq non linear equation. Under specific values of the parametric space this system shows the existence of singular and regular soliton like structures. After their collisions the mutual creation and annihilation (each other) of nerve signals along the nerve, during their propagation, has been observed.Keywords: Boussinesq equation, singular solitons, single neurons, neural code.

Local Temperature Rises Influence In Vivo Electroporation Pore Development: A Numerical Stratum Corneum Lipid Phase Transition Model

Electroporation is an approach used to enhance transdermal transport of large molecules in which the skin is exposed to a series of electric pulses. Electroporation temporarily destabilizes the structure of the outer skin layer, the stratum corneum, by creating microscopic pores through which agents, ordinarily unable to pass into the skin, are able to pass through this outer barrier. Long duration electroporation pulses can cause localized temperature rises, which result in thermotropic phase transitions within the lipid bilayer matrix of the stratum corneum. This paper focuses on electroporation pore development resulting from localized Joule heating. This study presents a theoretical model of electroporation, which incorporates stratum corneum lipid melting with electrical and thermal energy equations. A transient finite volume model is developed representing electroporation of in vivo human skin, in which stratum corneum lipid phase transitions are modeled as a series of melting processes. The results confirm that applied voltage to the skin results in high current densities within the less resistive regions of the stratum corneum. The model captures highly localized Joule heating within the stratum corneum and subsequent temperature rises, which propagate radially outward. Electroporation pore development resulting from the decrease in resistance associated with lipid melting is captured by the lipid phase transition model. As the effective pore radius grows, current density and subsequent Joule heating values decrease.