Health Effects

I believe this is what happening in the new health model:

1. The first thing to consider is the feed back loop:

       amyloid  ->  microglia  ->  microglia      ->
       source       cluster        release IL-1B
   
   
               ->  absorbed by  ->  triggers new    ->  back to beginning
              /    neurons          amyloid source
       IL-1B -
              \                   ->  releases  ->  causes
               ->  absorbed by   /    IL-6          neuron
                   astrocytes   -                   death
                                 \
                                  ->  releases  ->  protects and
                                      TNF-a         promotes recovery
                                                    of neurons
   

2. The wave of IL-1B is basically centered around the first amyloid source.
   
   
3. The first astrocytes to respond to the wave are the ones closest to the center.
   
   
4. Astrocytes can cluster around fibrous amyloid, so that locations of amyloid fiber can cause the greatest changes to neuron health, especially if they're near the center.
   
   
5. The diffusivity of TNF is greater than that of IL-6. (The diffusion coefficient for IL-6 is 10% less than for TNF.)
   
   
6. Also, TNF gets absorbed at a higher rate than IL-6. (I believe that this is because there are more TNF receptors than IL-6, but it also might be the case that the kinetic rates favor TNF.)
   
   
7. The new ODE for Neuron Health is

       dH          / IL-1B \          / IL-6 \         / TNF  \
       -- = e     ( ------- ) + e    ( ------ ) + e   ( ------ ) + rH(1-H)
       dt    IL-1B \ MAX1B /     IL-6 \ MAX6 /     TNF \ MAXT /
   

   • each "e" represesnts the health effects of that chemical
   • -1 < e < 1
   • negative values of e are detrimental
   • positive values of e are beneficial
   • each chemical listed represents the concentration of that chemical in the neuron
   • each "MAX" is the maximum amount of that chemical a neuron can absorb
   • "MAX" can also be thought of as the chemical level that causes maximum health effects to take place
   
   
8. The key to getting the localized neuronal death is in the interplay between IL-6 and TNF.
   
   
9. Because IL-6 diffuses more slowly than TNF and is absorbed at a lower rate, MAX6 needs to be smaller than MAXT and/or e for IL-6 needs to be greater in magnitude than TNF. This will lead to neuronal death occuring near astrocytes (near the center especially where amyloid fibers are present).
   
   
10. Because TNF diffuses faster than IL-6, it is able to protect and recover a region outside of the initial neuronal death. However this can only happen if the inequalities dealing with MAX's and e's aren't overwhelmingly in favor of IL-6. Thus, some balance needs to occur.
    
    
11. If the feedback loop discussed in (1) is not disrupted, I would expect complete death in the case where e for IL-6 is greater in magnitude than the sum of e for TNF and 0.5*r.
    
    
12. Because of (4), there can be a link between fiber deposits and dead neurons which is a plaque. Also, blocking astrocytes reduce the diffusivities of all chemicals in their vicinity which allows IL-6 and TNF to build up faster in these areas.