Kinetics of Particle Decay in Spiny Dendrites

While anomalous switching slows down the transport of particles in dendrites (8.49), it leads to a higher rate of particle decay than in the Markovian case. This is illustrated in Fig. 8.5, where the decay of particles in the anomalous case (y = 0.1) is compared with that in the non-Markovian case (Gamma distribution) and the standard Markovian case (y = 1). One can see that the decrease of diffusion of particles toward the parent dendrite, decrease of the exponent y, leads to a faster decay of the total number of particles p t) = /(pi + /P2) From (8.48), p(t) t I e as t oo. This explains the effect of limited diffusion of Ca along dendrites 

1 Obtain the velocity of the invasion front (8.6) and the recovery front (8.7) for the tumor-host interaction model given by (8.1). 

2 Obtain the integro-differential equations for glioma invasion (8.12) from the balance equations (8.10). 

3 Find the Hamilton-Jacobi equation for the glioma invasion front (8.23) from (8.20) following the same procedure as in Sect. 4.6.1. 

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