Filament Tracer algorithms

There are two different algorithms that Imaris Filament Tracer offers for calculating the dimensions of the spine head (see figure 2.4G). The original algorithm, known as Shortest Distance (SD), measures the distance between the seed point and the edges of the spine, takes the minimum, and builds a sphere with that radius as the model of the spine head. The alternative algorithm, Approximate Circle (AC), which Bitplane offered in response to a request from the Edwards group, estimates the volume of the spine head from cross section areas in various Z-planes and builds a sphere with that volume (figure 2.5). In the Imaris documentation (Bitplane, 2013), Bitplane state that SD is suitable for spines with roughly spherical heads, but less suitable for spines with large irregular heads, where it tends to underestimate the volume. AC does a better job of large irregular spine heads, but tends to overestimate volume in confocal images

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For cases where the centre axis is closer to the centre of diameter mask (blue hatched area), the difference between the options is smaller.

Shortest Distance from distance map

The Shortest Distance from Distance Map option considers the radius as the shortest distance from the seed point (yellow disk) to the edge of the filament mask (blue line), in any (x,y,z) direction.

This method is typically less sensitive to diameter overestimation due to axial (z) blur. It is recommended when the centre axis is overall well centred on the structure and the real structure has a roughly circular cross- section.

Approximate circle of cross section area

The Approximate Circle of cross section Area option is recommended when the centre axis position is not well centred in a large diameter structure e.g large irregular spine heads. The area of the green circle is equal to the cross-section area determined in the threshold step.

© Bitplane 2012

For cases where the centre axis is closer to the centre of diameter mask (blue hatched area), the difference between the options is smaller.

Shortest Distance from distance map

The Shortest Distance from Distance Map option considers the radius as the shortest distance from the seed point (yellow disk) to the edge of the filament mask (blue line), in any (x,y,z) direction.

This method is typically less sensitive to diameter overestimation due to axial (z) blur. It is recommended when the centre axis is overall well centred on the structure and the real structure has a roughly circular cross- section.

Approximate circle of cross section area

The Approximate Circle of cross section Area option is recommended when the centre axis position is not well centred in a large diameter structure e.g large irregular spine heads. The area of the green circle is equal to the cross-section area determined in the threshold step.

Filament Wizard Buttons Button Back

Shortest#

Distance#

Approximate#Circle#

Figure 2.5. Schematic diagrams illustrating the two alternative algorithms that can be chosen when using Imaris Filament Tracer to model a spine head. From the Imaris Reference Manual (Bitplane, 2013).

because of blurring in the Z-axis. AC is also less sensitive than SD to the exact

placement of the seed point, so less vulnerable to unconscious biassing by the analyst.

In order to understand the relative characteristics of these two algorithms, I compared them both with a manual method of estimating spine head size. Taking one of my confocal images, I used ImageJ to obtain a line profile across the head of each of 25 contiguous spines, then fitted a Gaussian curve to each profile and used full-width half-maximum (FWHM) as an estimate of diameter. Scatter plots comparing these with results from Imaris using either algorithm (figure 2.6) suggest that the diameter

0.0 0.4 0.8 1.2 0 20 40 60 80 X (µm) In te nsi ty 0.0 0.4 0.8 1.2 0.0 0.4 0.8 1.2 Approximate Circle

Head diam (Imaris) (µm)

H ea d di am (I ma ge J) (µ m) 0.0 0.4 0.8 1.2 0.0 0.4 0.8 1.2 Shortest Distance

Head diam (Imaris) (µm)

A

B"

C"

F"

E"

D

***"

Figure 2.6. Comparison of different methods of estimating spine head diameter. A: a single slice from a confocal stack showing a spine from an example

experiment. A line is drawn across the spine head in ImageJ, and an intensity profile is collected. Scale bar 1 µm. B and C: same section of dendrite as in A, modelled with Imaris filament tracer’s AC or SD algorithm. Arrowhead marks the spine also shown in A. D: A gaussian distribution (blue line) fitted to the intensity profile (red line) from the spine in A. FWHM (grey verticals) is used as an estimate of spine head diameter. E: scatter plot comparing head sizes of 25 spines

estimated using the ImageJ line profile method shown in A and D, with head sizes estimated using Imaris filament tracer’s AC algorithm. Grey dotted line of

equality is shown for reference. Blue dotted regression line is also shown

(R2_{=0.43, p=0.00041). F: as E but comparison is with Imaris filament tracer’s SD}

estimates from AC are much better correlated with those from the line profile than are the estimates from SD. It is also clear from figure 2.6 that AC tends to overestimate and SD tends to underestimate head diameter compared with ImageJ.

Of course I do not mean to imply that the line profile estimate is more accurate than Imaris – in fact the opposite is probably true, because Imaris models the spines in 3 dimensions taking account of the whole confocal stack, whereas the line profile method uses only a single line through a single confocal slice, discarding the vast majority of the information in the spine image. However, the line profile method is a useful indicator of how big a spine might seem to a human analyst looking at a confocal stack, and the fairly strong correlation with AC but not with SD is an argument in favour of using the AC algorithm.

Another argument in favour of using AC is that head diameter and volume estimates produced by SD are very “stepped” i.e. there are a small number of possible values, not a continuous range as with AC. A careful look at figure 2.6F reveals groups of points that are aligned vertically because SD assigned them an identical value.

However, SD gives estimates (derived from my set of uncaging and control

experiments) for mean head volume of spines in CA1 which approximately agree with results from EM work (Harris and Stevens, 1989), whereas the same spines analysed with AC produce a mean spine head volume which is larger than (nearly double) the EM results (table 2.1). Several factors might contribute to this discrepancy:

a) There is probably a sampling bias deriving from choices about which spines to model in Imaris; small spines tend to be faint and might not be clearly visible in the image, and Imaris is sometimes unable to model very small or faint spines.

b) AC tends to overestimate spine head diameter, an effect which is magnified in the estimates of volume (because volume is related to diameter cubed).

c) It is possible that the process of preparing tissue for EM has an effect on spine size. Although the resolution of EM is far higher than confocal microscopy, this does not necessarily mean that measurements from EM are a more accurate reflection of the dimensions of spines in living tissue.

In my PhD project the main experimental readout is change in spine head size over time. Hence I am much more interested in accurately measuring relative change than I am in measuring absolute spine head size, and for the reasons given above I am more confident in AC than SD to provide that. Therefore the analyses in my results chapters are all done using the AC algorithm.