### Questions about geometry & area(x)

Posted:

**Fri Sep 11, 2015 2:44 am**I'm having some trouble understanding how area(x) is calculated in the morphology of my model. My basic understanding is that when a morphology is imported into NEURON, it is specified using the pt3dadd function, which specifies the segments as truncated cones/frusta. Furthermore, despite having many pt3dadd data points, this seems to get reduced when using the d_lambda rule to compartmentalize the model (e.g. 49 pt3dadd data points in one section of my model became reduced to 11 compartments). My first question, is how diameters are computed (i.e. based on the diameters declared by the pt3dadd function) for these "merged" compartments? When calculating the average diameter for the pt3dadd data points that merged into one compartment, I see that it does not exactly equate to the diameter that is now listed in that segment.

Secondly, since the segments in my model are presumably truncated cones, I expected that the equation of the lateral surface area of a truncated cone should equate to the surface area computed by area(x). However I noticed that for a single segment, this value is larger than when using area(x). Of course, this discrepancy (obviously) becomes amplified when computing this for an entire dendritic tree (e.g. in one dendritic tree the value computed using the equation for the lateral surface area of a truncated cone was almost 60um^2 larger than when using area(x)). On the other hand, if using the equation for the lateral surface area of a cylinder the difference becomes smaller (e.g. in the same dendritic tree, the value computed using the equation for the lateral surface area of a cylinder was only 5um^2 smaller than when using area(x)). I have also read that area(x) calculates the integral of the surface area, which, apparently, does not necessarily equate to the normal equations of surface area(?). With this in mind, I have a couple more questions:

Does area(x) in fact calculate the integral of the surface area, and, if so, why is this measure more suitable to use than the normal surface area equation?

Does area(x) distinguish between when it should be calculating a segment as a truncated cone or a cylinder? If not, and it assumes that all segments are cylinders, this may explain why the lateral surface area of a cylinder provided a closer answer to what was computed by area(x).

Several ways of calculating surface area in the segments:

oc>access dend[3]

oc>nseg

11

oc>div = 1/nseg // Find the proportion of the first segment along dend[3]

oc>div

0.090909091

oc>PI*((sqrt(((L*div)^2)+((diam(0)/2)-(diam(div)/2))^2))*((diam(0)/2)+(diam(div)/2))) // Lateral surface area of a truncated cone

86.692146

oc>PI*diam(div)*L*div // Lateral surface area of a cylinder

85.888932

oc>area(div) // Integral of the surface area(?)

85.893665

Any help is much appreciated,

Alex GM

Secondly, since the segments in my model are presumably truncated cones, I expected that the equation of the lateral surface area of a truncated cone should equate to the surface area computed by area(x). However I noticed that for a single segment, this value is larger than when using area(x). Of course, this discrepancy (obviously) becomes amplified when computing this for an entire dendritic tree (e.g. in one dendritic tree the value computed using the equation for the lateral surface area of a truncated cone was almost 60um^2 larger than when using area(x)). On the other hand, if using the equation for the lateral surface area of a cylinder the difference becomes smaller (e.g. in the same dendritic tree, the value computed using the equation for the lateral surface area of a cylinder was only 5um^2 smaller than when using area(x)). I have also read that area(x) calculates the integral of the surface area, which, apparently, does not necessarily equate to the normal equations of surface area(?). With this in mind, I have a couple more questions:

Does area(x) in fact calculate the integral of the surface area, and, if so, why is this measure more suitable to use than the normal surface area equation?

Does area(x) distinguish between when it should be calculating a segment as a truncated cone or a cylinder? If not, and it assumes that all segments are cylinders, this may explain why the lateral surface area of a cylinder provided a closer answer to what was computed by area(x).

Several ways of calculating surface area in the segments:

oc>access dend[3]

oc>nseg

11

oc>div = 1/nseg // Find the proportion of the first segment along dend[3]

oc>div

0.090909091

oc>PI*((sqrt(((L*div)^2)+((diam(0)/2)-(diam(div)/2))^2))*((diam(0)/2)+(diam(div)/2))) // Lateral surface area of a truncated cone

86.692146

oc>PI*diam(div)*L*div // Lateral surface area of a cylinder

85.888932

oc>area(div) // Integral of the surface area(?)

85.893665

Any help is much appreciated,

Alex GM