## This page explains why EvF systems will (should?) always give different answers to von Frey filaments. It's slightly mathematical so here's a summary:

• The force range of the filaments used for mice usually runs from 0.07g to 6g, so the highest force applied is 6/.07 = 85 times the lowest one. But the filaments all have different diameters and mechanical nociceptive threshold is linearly related to diameter. This contracts the scale of "nociceptive stimulus" by a factor of nearly 3. So the 6g filament only really applies 31 times as much nociceptive stimulus as the 0.07g filament.

• We should not therefore expect any EvF, with a probe of fixed diameter, to make measurements that compare directly with filaments. At 6g, the EvF really will apply 85 times as much nociceptive stimulus as at 0.07g. Measurements of both hypo and hyperalgesia, made with EvF, will therefore show smaller differences, on a scale of grams force, from baseline threshold than measurements made with filaments. THIS DOES NOT MEAN that filaments are more "sensitive". If the repeatability (or scatter, or sigma) of the data is the same then both measures are equally valid; they are just on different scales.

## Von Frey filaments are simple in design...but complicated in use:

They are straight "springy" nylon rods of differing diameters (and slightly different lengths), supplied in sets. Each one buckles (elastically) at a force determined mainly by its diameter, but also influenced by its length. The nociceptive stimulus generated is not simple to analyse because, as they buckle, the contact area changes from a circle to something like a semi-circular line (depending on how much the tissue has deformed).

The force range of a set typically runs from 0.008gf to 300gf, so it's suitable for both mice and rats. To use, one would test first with a filament close to the expected threshold value (eg 2g). If the mouse responded, one would then test with the next filament down (1.4g). If it didn't respond, one would try the next filament up (2g) and so on until five changes in direction have been recorded. A mathematical algorithm called the up-down method is then used to derive the theoretical threshold. ## Here's a graph of the forces applied by a typical set of von Frey filaments, plotted against their diameter. These are the filaments typically used in mouse testing: 0.07g -6g. If they were all the same length, this graph would be a smooth curve (as the buckling force of an elastic column is related to the third power of the diameter). But, as the manufacturer is constrained by the diameters of filament material available, the force progression required (for the up-down method) is arrived at by varying the length as well (because a longer filament buckles at a lower force than a short one of the same diameter). That's why the graph is "lumpy".

## But the changing diameter of the filaments complicates the stimulus applied:

Pressure = Force/Area so you might expect that, if you doubled the diameter of a probe, you would need to apply four times the force to achieve the same nociceptive stimulus.

Apparently not so: it's well accepted that the increase in force required is linearly related to the  DIAMETER of the probe, not its area.  ## So a 10mm probe will require 5 times the force to achieve the same nociceptive threshold as the 2mm probe in the image above. ## Here's the same graph (blue dots) but with the force values "adjusted" for the increase in diameter of the higher force filaments (orange dots).

The correction has been made relative to the smallest one in the series (0.07g). It doesn't matter where the base line point is, the effect is the same effect but with different numbers. So it's important to remember that the scale for the orange dots is no longer an absolute force scale, it's a "nociceptive stimulus scale". The important point is that the 6g filament only applies 31 (2.2/0.07) times as much nociceptive force as the 0.07g filament, not 86 (6/0.07) times as much.

## This is the important conclusion from this page. Filaments and EvF systems can both provide valid data (providing the EvF is correctly designed) but the two measures are not directly comparable. There is also the matter of the Weber Fraction, which for a filament set varies considerably:

Animals (including humans) don't notice very small changes in the level of a stimulus. The smallest increment, expressed as a ratio, is known as The Weber Fraction. So if a human, for instance, can detect 10N with a particular probe and can then just detect 15N as being "a bit more force"  then the Weber fraction would be 15/10 = 1.5. As it's a constant ratio, the next increment they would theoretically be able to detect would be 15 *1.5 = 22.5N. And so on.

These increments, 10N, 15N and 22.5N are therefore a scale of convenient testing points (for this particular case) to detect differences. Which is what filaments do.

The up-down method recommends  that the Weber fraction is about equal to the standard deviation of the data (so you sort of need to know the answer before you start) but that it can vary up and down by up to 50%. But as you can see from this graph, the effective Weber fraction of the filaments varies a lot more than that. In particular, there's barely any difference in nociceptive stimulus between the 0.4 and 0.6g filaments (because the filament diameter has changed so much). This is another reason why filaments may give a different answer to EvF; the filament scale is quite distorted in some parts of its range.