Neckel Lab - CatWalk Methods

The gait analysis of rodents is a tricky business. They never walk in straight lines, they never listen when we ask "slow down," they just go (or more often, don't go). It is up to us to take the self selected behaviors of the rats and compare them. Of course the pre-injury behaviors are wildly different from post-injury, which are then different following treatment. So we have developed an array of techniques to compare these different gaits more accurately.

Coordinate Frame

In traditional gait analysis measurements are based off of a world coordinate frame - an X/Y grid on the floor. Steps are measured as the change in X from point A to B, base of support as the change in Y, speed calculated from a start to a finish, and so forth. We quickly came to accept that our rats either didn't know or didn't care about the grid they were walking on. They would stop whenever they liked, walk in a direction that wasn't parallel to the world coordinate frame grid, or worse yet, slightly change their direction as they walked. Instead of training our animals to walk the way our tools needed them to (straight lines parallel to the world coordinate frame), we built better tools to measure how the rats wanted to walk. Luckily for us, all we needed was a little bit of linear algebra. Instead of measuring gait in the world coordinate frame we rotate and translate all measures into the body coordinate frame of the animal. That way no matter what the rat decides to do in the device, strides are anterior/posterior changes, base of support are medial/lateral changes, and velocity is the rate at which the ground passes under the center of mass.

Body Coordinate Frame Compared to the World Coordinate Frame

Nonlinear Regression

Our lab compares post-injury functional deficits and recovery to pre-injury locomotor measures such as stride length, cycle time, duty factor, and velocity. This comparison process is not exactly straightforward, as most of these measures change depending on velocity. Thus, we must determine a method of accurately comparing these measures regardless of velocity. By using nonlinear regression techniques we can analyze the post- injury recovery process more accurately. Nonlinear regression analysis was chosen because we could place mathematical boundaries matching physiological limitations while accurately predicting the velocity dependence of a particular locomotor measurement.

Once each group of data had a nonlinear regression model, comparisons were made using an F test to determine whether the groups were statistically different or not. Using this regression analysis technique, we determined significant differences between pre-injury and post-injury data in stride length and duty factor, along with the left hind limb's cycle time [see our paper].

Over time, the rats' gait changes, with some limbs spontaneously recovering. By looking at the individual limbs' velocity dependent locomotor measures, we can compare changes in step parameters to other limbs or over time. In our experience, over time the right forelimb shows spontaneous recovery, with the hind limbs showing changes away from pre-injury values. We interpret this as a compensatory technique. The less impaired limbs, with their greater range of motion, strength, and control, adjust their gait to enable the more impaired right forelimb to take a more normal step.

3D Paw Placements

Non linear regression is a great tool to express how stride length is dependent on velocity. But the length of a stride is not the only relevant aspect, the location in body space is equally important. With our rotated coordinates we can easily measure if a stride is more medial or anterior pre/post injury and pre/post treatment. This paw placement is also dependent on velocity, because, of course it is. In order to see how the 2D paw location is different at different velocities we simply plotted our data in 3D. And instead of looking at means with confidence intervals we felt that we were better served by comparing models of the smallest irregular cone that contains 95% of our data. This cone was found by first fitting all the prints within a narrow velocity window with a 95% confidence ellipse. By sweeping through all velocities we then were able to model how our ellipse parameters changed. When we used this technique on our pre-injury data we found that rats place their forepaws more medially and anteriorly at higher velocities. We also found that rats were more consistent with their placement at higher velocities. After SCI rats lose this level of control on placement and consistency. Interestingly we found evidence that over time the more impaired limb has some measure of spontaneous recovery while the other limbs develop compensatory techniques [see our paper].