Knowledge Base

Gait Formulas

A gait formula starts at Initial Contact (IC) of the left hind paw after all paws have been placed at least once. The Step Cycle then runs until the next IC of the left hind paw. In the Support tab of the Run Statistics, each Step Cycle is put on a separate row.

Support Formula

During each Step Cycle paws are subsequently raised and placed, leading to different numbers of paws on the ground. The Step Cycle can be subdivided into a number (often 8) of subsequent sections during which different numbers of paws are touching the ground. The Support formula provides the number of paws on the ground during each section, for example:

• 2 — 3 — 2 — 3 — 2 — 3 — 2 — 3
• 4 — 3 — 2 — 3 — 4 — 3 — 2 — 3
• 1 — 2 — 1 — 2 — 1 — 2 — 1 — 2

Note that the Support formula does not describe which paws are on the ground, nor how long each section is in relation to the total Step Cycle.

Footfall Formula

The Footfall formula supplies some of the information which is missing in the Support formula, namely information on which paws are touching the floor during each section, but without information about the relative length of these sections.

The Footfall formula uses an alphanumeric notation in CatWalk, as follows:

• 0 — No paw touching the ground
• I — One paw touching the ground
  • ILH — Left hind paw on the ground
  • ILF — Left front paw on the ground
  • IRF — Right front paw on the ground
  • IRH — Right hind paw on the ground
• II — Two paws touching the ground
  • IIG — Girdle pairs
    • IIGF — Front paws on the ground
    • IIGH — Hind paws on the ground
  • IIL — Ipsilateral pairs
    • IILL — Left side on the ground
    • IILR — Right side on the ground
  • IID — Diagonal pairs
    • IIDL — Left front paw and right hind paw on the ground
    • IIDR — Right front paw and left hind paw on the ground
• III — One paw off the ground
  • IIILH — Left hind paw off the ground
  • IIILF — Left front paw off the ground
  • IIIRF — Right front paw off the ground
  • IIIRH — Right hind paw off the ground
• IV — Four paws on the ground

A possible footfall formula is then as follows:

IIILF - IIDR - IIIRH - IILL - IIIRF - IIDL - IIILH - IILR

These labels allow us to refer to specific combinations of placed paws and to assign durations (relative to that of the total Step Cycle) to them for further analysis. Especially interesting is the total duration spent in I's combined, and the total in IIG's and/or IIL's combined, as these are unstable (the mass-midpoint of the animal is far from the point(s) of support).

Circular Distributions

This section describes the computation of descriptive statistics for circular distributions of data such as phase lags during locomotion. It provides a very short summary of chapter 26 from Biostatistical Analysis by Zar (1998). Special statistical tests are available for circular distributions; see Zar (1998), Chapter 27.

Tip: Open the Excel file Calculate Circular Statistics of Phase Dispersions and Couplings.xlsx, found under C:\Program Files\Noldus\CatWalk XT 10\Documentation. Enter the values of Phase Dispersions and Couplings obtained in runs or trials to see how the main statistics are computed.

The Circular Mean

If we have a sample consisting of phase lags (periodic on the range 0–100), the mean of these phase lags is an estimate of the average phase lag angle in the sampled population. To compute the sample mean phase lag, we first consider the rectangular coordinates of the mean phase lag, then compute the length of the mean vector R. The Circular Mean (CStat Mean (%) in CatWalk XT) is derived from the cosine and sine of the resulting angle.

Interpreting the Mean and R

CatWalk XT reports the CStat Mean as a percentage of the step cycle duration. For Phase Dispersions, it ranges from -50% to +50%. For Couplings, it ranges from 0% to 100%.

The value R ranges from 0 to 1. Both CStat Mean and R are important: they can be interpreted as a vector with length R and a direction equal to the mean angle. The vector starts at the midpoint of a circle with a radius of 1.00 and ends at the mass midpoint of the phase lag values positioned on the circle itself.

• X and Y are the average x- and y-coordinates of the data points in a 2D space.
• The angle formed by the vector is halfway between the two data points.
• The length of the vector describes the dispersion of the data points around the mean.