Knowledge Base

Definition

The change in direction of the nose, center, tail-base point or Head direction line between two consecutive samples.

Calculation

You can calculate Turn angle in two ways, based on body points or the Head direction line.

Based on Body Points

Turn angle is calculated as the difference between two subsequent values for Heading of the specified body point:

• ΔHeading = Heading_k - Heading_k-1
• If ΔHeading < -180°, then Relative Turn angle = ΔHeading +360°.
• If ΔHeading ≥ +180°, then Relative Turn angle = ΔHeading -360°.
• Else Relative Turn angle = ΔHeading.

In the example below, there is a turn to the right (clockwise) at sample k. The heading HE_k-1 is positive, while HE_k is negative. As a result, the difference HE_k - HE_k-1 is negative. For the default axis orientation shown in the figure below, a clockwise turn corresponds to a negative Turn angle. A counter-clockwise turn corresponds to a positive Turn angle.

Based on Head Direction

Turn angle is calculated as the difference between two subsequent values for Head direction (see the figure below, left). This value is independent of the position of the body points:

• ΔHead direction = Head direction_k - Head direction_k-1
• If ΔHead direction < -180° then relative Turn angle = ΔHead direction +360°.
• If ΔHead direction ≥ +180° then relative Turn angle = ΔHead direction -360°.
• Else relative Turn angle = ΔHead direction.

The Turn angle based on head direction depends only on the samples k–1 and k, while the Turn angle based on a body point depends on the last three samples (k–2, k–1 and k).

Note: The Head direction line is calculated using the subject's contour. If you swap nose- and tail-base points, or interpolate those two points, the Head direction line is not recalculated using the contour, instead as the prolongation of the segment joining the nose-point and the center-point. Turn angle is then calculated based on those head direction lines.

Absolute vs. Relative Turn Angles

• Absolute Turn angle: The difference in direction is unsigned. Absolute Turn angle ranges from 0° to +180°.
• Relative Turn angle: The difference in direction is signed. With a default axis orientation, a clockwise turn is signed negative, and a counterclockwise is signed positive. Therefore, the Relative Turn angle ranges from -180° to +180°. Relative angles help you distinguish between clockwise turns and counterclockwise turns.

Absolute and Relative turn angles result in different averages. Consider for example two angles, -10° and +40°. The average relative turn angle is (-10°+40°)/2 = 15°. The average absolute turn angle is (10+40)/2 = 25°.

Tip: With the default axis orientation, a clockwise (right) turn means a negative turn angle. A counter-clockwise (left) turn means a positive angle. Whenever you use a coordinate system other than the default one, rotate the image to know the sign of the turn. For example, a right turn on a coordinate system with the x-axis flipped gets a positive value.

How to Specify Turn Angle

1. Click the Add button next to Turn angle and click the Turn angle tab. Select Absolute or Relative.
2. Select Head direction turn angle (body point is ignored) if you want to calculate turn angle based on the Head direction line.
3. Click the Body points tab. Select the body points for which you want to calculate the turn angle. By default, Center-point is selected. If your experiment is set to Only center-point detection or Color marker tracking, this tab is absent. Calculations are based on the center point. This tab is not available if you choose the option in step 2.
4. Complete the procedure to add the variable. See Calculate statistics: procedure.

Relative and absolute turn angle based on the change in direction of the Head direction line can be visualized in Integrated Visualization (Analysis > Results > Integrated Visualization). The first chart shows Relative turn angle, displaying positive and negative values for left and right turns of the head respectively. The second chart shows Absolute turn angle. These dependent variables can also be exported in the raw data file (Analysis > Export > Raw Data).

Relative Turn Angle and Axis Orientation

Relative Turn angle depends on the orientation of the x- and y-axes in the Arena Settings used for that trial. By default, the x-axis is horizontal and pointing to the right. A clockwise turn is scored as a negative value, and a counterclockwise turn is scored as a positive value. However, if the x-axis is pointing to the left, a clockwise turn is scored as a positive value, and a counterclockwise turn is scored as a negative value.

The sign of the Relative Turn angle (RTA) depends on the orientation of the x- and y-axes. The sign inside the circles indicates the sign of Heading (HE) values. When the difference HE_k - HE_k-1 is larger than +180° or smaller than -180°, the rules described in Heading apply.

If the axes are swapped, the reference line is now vertical and the Relative Turn angle is calculated relative to the vertical axis.

Notes

• The mean, standard deviation and variance are calculated with linear statistics.
• Turn angle is calculated in a way different from that in EthoVision 3. This is because Turn angle is based on Heading, which is set consistent with Head direction.
• Turn angle is very sensitive to small, random movements of the body points. When the animal sits still, Turn angle can get very high, unrealistic values. To remove such small movements from your data, smooth the tracks, then run analysis.
• Turn angle should not be confused with turn bias or turning rate. These are actually synonyms for the dependent variables Relative Angular velocity and Absolute Angular velocity, respectively.

Application

Assessing turn angles can be helpful for detecting stereotypic movements. In this case, consecutive turn angles tend to have large values (for example, in circling behavior of rodents), or show repeating patterns (for example, rocking or waving).

For better quantification of biases in the left/right direction, first filter the data with the Minimal Distance Moved method, to ignore points where the animal does not move significantly.

Cumulative Turn angles are used to calculate rotations. See Rotation.

Source: EthoVision XT 19 Help, Noldus Information Technology