Knowledge Base

What Are Phase Dispersions?

Phase Dispersion is a parameter that describes the temporal relationship between the placement of two paws in a single Step Cycle and tells you something about the coordination between those two paws.

Perfectly Balanced Walk

In a perfectly balanced walking pattern, there should be no differences between one side of the body or the body axis in comparison with the opposite side or axis.

When Can We Notice Differences in Walk

The difference between one and another side of the body will occur for example in a situation with antalgic gait in which the animal tries to put the painful paw on the ground for the shortest duration possible. This can be achieved by placing the uninjured paw on the ground earlier than normally. The changes of phase dispersion value of this paw pair are revealing an abnormality in movement - limping.

Phase Dispersions also play an important role when we want to distinguish different gaits like walking, trotting, and galloping.

Phase Dispersions in Detail

Phase Dispersion is the moment of Initial Contact of a target paw, expressed as a percentage of the Step Cycle time of an anchor paw.

The Step Cycle of every individual paw starts with the first initial contact of the paw, continues through the whole stand phase and the swing phase of the paw, and ends at the moment of another initial contact of the paw.

In CatWalk XT, 6 pairs of paws are displayed. Within diagonal pairs (RF-LH, LF-RH) and ipsilateral pairs (RF-RH, LF-LH), the anchor is always one of the front paws. Within girdle pairs (LF-RF, LH-RH), the anchor paw is always one of the left paws.

What Is Cstat and What Does It Tell Us?

Cstat is an average calculated according to Circular statistics. Circular data has a periodical nature. For example, months of the year are circular. The first month, January, is closer to the twelfth month of the previous year, December, than it is to the sixth month, June.

In contrast, most familiar statistics assume that variables are linear, where the lowest value is the farthest from the highest value.

Example of Circular Statistics

Consider a flower which bursts in December or January. If we calculate the average bursting time for this flower using linear statistics, we would get a value suggesting that most flowers burst in June, which is obviously not a correct conclusion. Circular statistics, on the other hand, takes into account that December is actually close to January because of the periodical nature of the months and calculates the correct average bursting time.

How Does Cstat Apply to Phase Dispersions?

Circular statistics applies to Phase Dispersions because of the periodical Step Cycle of a paw.

The values of Phase Dispersions vary from -50% to 75%. A positive value indicates that the Initial Contact of the target paw happened soon after the initial contact of the anchor paw, while a negative value reflects that the Initial Contact of the target happened later, just before the next Step Cycle of the anchor paw.

Examples of Phase Dispersions

If the Initial Contact of the target paw is at 0.22s of the anchor's Step Cycle, the Phase Dispersion is 50% (0.22 / 0.44 * 100). This represents the target paw initiating contact at halfway through the Step Cycle of the anchor paw (Kloos et al., 2005).

If the Initial Contact of the target paw is at 0.22s of the Step Cycle of the anchor paw and the Step Cycle is 0.28s, the value of Phase Dispersion exceeds 75% (0.22 / 0.28 * 100 = 78.5%). In this case, the target paw is assigned to the next Step Cycle of the anchor paw, resulting in a Phase Dispersion value of -25% (-0.06 / 0.24 * 100). This occurs when the Initial Contact of the target paw is closer to the start of the next Step Cycle of the anchor paw than to the first one (Kloos et al., 2005).

Phase Dispersions in Publications

Many researchers use Phase Dispersions values as an important input in their research. Below are some examples.

Study of Spinal Cord Injury in Rats

Kloos et al. (2005) used Phase Dispersions to study inter-paw coordination in rats with spinal cord injury (SCI). If we look at the diagonal paw pair of a normal animal at a moderate speed, the target paw typically moves synchronously with the anchor paw, meaning that the Initial Contact occurs simultaneously. This results in a Phase Dispersions value of 0%. When observing the girdle pairs, the Phase Dispersions value is usually 50%. After the injury, researchers found that inter-paw coordination followed different patterns, depending on the severity of SCI.

Research in Rats with Femoral Nerve Injury

Heinzel et al. (2020) conducted research on functional recovery in rats with femoral nerve injury. They observed ipsilateral, diagonal, and girdle pairs and found increased Phase Dispersions values for the hind girdle, right ipsilateral, and left diagonal pair, which were most noticeable immediately after surgery. The values returned to normal at around 5 to 6 weeks after surgery.

Study in Mice with Multiple Sclerosis

Bernardes et al. (2017) investigated walking impairment in exercised and non-exercised mice with multiple sclerosis. Looking at the Phase Dispersions values for diagonal paw pairs and other results, they concluded that previously exercised animals still showed decreased inter-paw coordination.

Summary

Phase Dispersions values enable us to gain an important view on what is happening within the placement of two paws before and after injury and treatment. They are calculated with the help of circular statistics due to the periodical Step Cycle of the paw. The values of Phase Dispersions are presented as a percentage based on the Initial Contact of a target paw within the Step Cycle time of an anchor paw.

Researchers around the world use CatWalk XT and its parameters to investigate and observe gait behavior in detail. Phase Dispersions provide an excellent insight into inter-limb coordination.

References

• Batka, R. J.; Brown, T. J.; McMillan, K. P.; Meadows, R. M.; Jones, K. J.; and Haulcomb, M. M. (2014). The need for speed in rodent locomotion analyses. Anat Rec (Hoboken), 297(10), 1839-1864.
• Bernardes, D. and Oliveira, A. L. R. (2017). Comprehensive catwalk gait analysis in a chronic model of multiple sclerosis subjected to treadmill exercise training. BMC Neurology, 17, 160.
• Boix, J.; von Hieber, D.; and Connor, B. (2018). Gait Analysis for Early Detection of Motor Symptoms in the 6-OHDA Rat Model of Parkinson's Disease. Frontiers in Behavioral Neuroscience.
• CatWalk XT manual.
• Heinzel, J. C.; Hercher, D.; and Redl, H. (2020). The course of recovery of locomotor function over a 10-week observation period in a rat model of femoral nerve resection and autograft repair. Brain and Behavior, p. e01580.
• Kameda, T.; Kaneuchi, Y.; Sekiguchi, M.; and Konno, S. (2017). Measurement of mechanical withdrawal thresholds and gait analysis using the catwalk method in a nucleus pulposus-applied rodent model. J. Exp. Orthop, 4, 31.
• Kloos, A. D.; Fisher, L. C.; Detloff, M. R.; Hassenzahl, D. L.; and Basso, D. M. (2005). Stepwise motor and all-or-none sensory recovery is associated with nonlinear sparing after incremental spinal cord injury in rats. Exp Neurol, 191, 251-265.

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Download the original PDF: Whitepaper - Phase dispersions (PDF)