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Rat Cerebellum volume
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This Use Case places cerebellar neurons (different types: specific simplified 
geometric features with anisotropic properties and specific density) into a 
layered-volume of the cerebellum.
This Use Case can be found in
*Online Use Cases/Circuit Building/Cells placement/Rat cerebellum volume*.

     .. image:: images/schema.png
        :width: 373px

     .. image:: images/cerebellum.png
        :width: 743px

     .. image:: images/placement_flow_chart.png
        :width: 1829px

Approach: the desired number of cells are progressively placed following a 
random direction from the previous cell with a distance step guaranteeing that
they do not overlap. A “reset” starting point occurs when the entire
surrounding is occupied. This algorithm is computationally efficient, which is 
fundamental for high-density volumes, but still keeps a strong random component 
to achieve a realistic distribution of the pairwise inter-neuron distances. 
The PC Layer is almost a planar grid in-between GRL and ML, with an inter-soma 
distance along the x-axis constrained by the requirement that adjacent 
dendritic trees must not overlap.

**Inputs:** by a simple GUI, the basic parameters can be entered by the user

•	Base sizes (x and z) of the cerebellar volume to be built
•	Plot option enabling
•	Save option enabling

Expert users can modify more parameters from `scaffold_params.py` 
(in `/storage`):

•	Neuron types (with ID)
•	Simplified geometric features for each neuron type: radius of the soma, and eventually dendritic field extensions (direction-dependent) if the constraints of not-overlapping cells are taken into account
•	Density for each neuron type, and eventually the ratio of the density values when compagin different types.

**Output:**

•	hdf5 matrix with 5 columns (saved in /storage)
•	Neuron ID (unique)
•	Neuron type ID (from 1 to 7)
•	3D coordinates (soma center) of each neuron (x, y, and z)

Monitoring: sparseness in the subvolume by computing the distribution of 
pairwise distances (monitoring_positioning.py in /storage)

Moreover, a 3D basic visualization is depicted (somas of each neuron, using a different color for each neuron type).


**Additional information:**

•	The whole Use Case should take about 10 minutes for a volume base of 400 x 400 µm.
•	No log in to any other computer required.




**EXAMPLE**

 -	x = 400 µm, z = 400 µm (→ DCN 200 x 200 µm)
 -	y = 930 µm (600+ 150+30+150 µm), i.e. thickness DCN + GRL+ PCL + ML

 TOT #NEURONS: 96.887

 Glomeruli (N=7073, radius =1.5 µm, in GRL excluded the upper 10 µm)

 -	3D dist = 206 ± 89 µm - Gaussian
 -	Min = 4; max =558 µm

 Granule cells (N=88229, radius = 2.5 µm, in the whole GRL)

 -	3D dist = 210 ± 90 µm- Gaussian
 -	Min =    ; max =     µm

 Golgi cells (N=219, radius = 8 µm, in GRL excluded the bottom 10 µm)

 -	3D dist = 214 ± 91 µm – Gaussian
 -	Min = 26; max =504 µm

 Purkinje cells (N=78, radius = 7.5 µm, in PCL, planar grid)

 -	3D dist = 250 ± 121 µm
 -	Min = 15; max =544 µm


 Basket cells (N=603, radius = 6 µm, in the ML lower half)

 -	3D dist = 208 ± 96 µm - Gaussian
 -	Min = 13; max = 534 µm

 Stellate cells (N=603, radius = 4 µm, in the ML upper half)

 -	3D dist = 201 ±94 µm - Gaussian
 -	Min = 9; max = 534 µm

 Deep Cerebellar projection Neurons (N=12, radius=10 µm, in the Deep Nucleus)

 -	3D dist = 269 ± 155 µm
 -	Min = 44; max = 566 µm


     .. image:: images/golgi_placement.png
        :width: 388px

     .. image:: images/gloms_placement.png
        :width: 388px

     .. image:: images/pc_placement.png
        :width: 394px

     .. image:: images/basket_placement.png
        :width: 394px

     .. image:: images/stellate_placement.png
        :width: 394px

     .. image:: images/dcn_placement.png
        :width: 388px