refactor various files

S2/Neuro/VL/NeuroVL2.typ

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+#import "../preamble.typ": *
+ 
+#show: conf.with(num: 1)
+
+= Membrane Potential
+
+Outside the cells in the brain there is salt.
+Inside there is potassium.
+
+== Prerequisites for a Neuron to fire
+
+_Watch the embedded movie._
+
+There are different potentials build up in the membrane.
+
++ The charge is in equillibrium. But there is a gradient of Pr and Cl
++ Cloride will diffuse $==>$ on that side there are too many negative charges
++ The negative charge pushes the potassium to this side
++ Finally a potassium gradient stabilizes
+
+Why is the resulting potential negative?
+
+== Nernst and general Nernst eqation 
+$
+	V_(x) = (R T) / (z F) ln ([X]_(o) ) / ([X]_(i) ) \
+	V_(x) = (R T) / (z F) ln (P_("K") [K]_(o) + P_("Cl") ["Cl"]_(o) + ...  ) / (P_("K") [K]_(i) + P_("Cl") ["Cl"]_(i) + ... ) \
+
+$
+
+When the permeability for the potassium is low then the other ones play a bigger role.
+Potential is only there when permeability is existing.
+
+Q: What is similar to a low pass filter.
+
+In reality there are multiple conducters connected in parralel. Also the conductivity of the Na and K channles are changable.
+
+Q: What does a conductivity of $oo$ mean?
+
+= Hodgkin and Huxley
+
+Q: What have they done?
+A: They used squids to measure the axons, because they are $1"mm"$ thick
+
+Types of Neuronal Recording Methods
+- EEG (on top of the head)
+- ECoG (small hole in the head)
+- Extracellular (needles in the brain)
+- Intra cellular (needles in the cell of the brain)
+
+== Action Potential
+
++ The cell gets excited
++ Chainreaction of channel opening and gradient stabilisation
+	- Sodium channels open
+	- K chanels open
+	- Na channels become refactory
+	- ...
++ Refactory period
++ ...
+
+#highlight[TODO: continue the steps]
+
+Currents can add up to trigger an AP. THe refactory period is the time after an AP when Na channles are inactive. The firing rate is increaed with a highter input strenght.
+
+The lenght of the potiential depends on the type of cell. Then the refactory period is also longer. \
+The maximum firing rate is limited by the absolute refactory period.
+
+== The actual model
+
+$
+	I_("inj") = I_(C) + sum I_(k) (t) , space C = Q/u , space I_(C) = C (dif u) / (dif t) = C (dif V) / (dif t) \
+	I_(x) = I_(x) \
+	C (dif V_m ) / (dif t) = - sum I_(k) +  I_("inj") (t) \
+	sum I_k = g_("Na") (V_m - V_("Na") )+ g_(K)  (V_m - V_(K) )+ g_(L) (V_(m) - V_(L)  )\
+	C (dif V_m ) / (dif t) = - g_("Na") (V_m - V_("Na") )- g_(K)  (V_m - V_(K) )- g_(L) (V_(m) - V_(L)  ) + I_("inj") (t) \
+$
+
+Now the Equation becomes time dependent
+
+$
+	C (dif V_m ) / (dif t) = - macron(g)_("Na") m^(3) h  (V_m - V_("Na") )- macron(g)_(K) n  (V_m - V_(K) )- macron(g)_(L) (V_(m) - V_(L)  ) + I_("inj") (t). \
+	dot(x)= - (1) / (tau_(x)  u_(b))  A .
+$
+
+Capacitance is a biological constant.
+
+== Voltabe clamp method
+
+With this method it is possible to stimulate a cell and measure the floating current at the same time.
+
+There are substances to kill certain types of channels in the cell. If done so the graph of the potential changes.
+
+Also there is a method to measuer individual channels and their current they leave through.The AP is a positive feedback loop.
+
+The sodium channels cannot immeadiately open again. It takes about 1ms for them to open again. When measuring one always measurers multiple fibres (Suberposition).
+
+In the heart there are calcium channels.
+
+_Max firing frequency is about $1"kHz"$_
+
+== Propagation of AP
+
+There are multiple Methods of propagation the AP. One is to recreate the AP along the way (this takes time but is faster with higher diameter of the axon).
+
+The other method is the saltatory "jumpy" conduction. This is much faster and the AP jumps between the isolations.
+
+