D1 Advanced Kinematic Analysis

Topic

Advanced kinematic analysis describes the movement of body segments in space and time without explicitly referencing the forces causing that movement. This description is constructed by reconstructing the trajectories of markers or anatomical points in three dimensions, using images captured simultaneously by multiple synchronized cameras. The reconstruction relies on projective geometry: each camera defines an optical ray extending from the image plane into the three-dimensional space where the movement occurs, and the 3D position of each marker is determined by the intersection of at least two such optical rays corresponding to the same marker as viewed from two different cameras.

Once reconstructed from the camera data, the 3D position of each marker is expressed as a time-varying trajectory of Cartesian coordinates; this trajectory is filtered to remove high-frequency noise introduced by the measurement process itself, while preserving the low-frequency range—up to approximately twenty cycles per second—where the relevant biomechanical information regarding the movement is concentrated. From these filtered positions, the velocity and acceleration of each marker are derived through successive numerical differentiation over time; acceleration is particularly sensitive to any residual noise in the signal, making the initial filtering of position data a critical step prior to differentiation.

Based on the filtered trajectories of markers located on adjacent body segments, joint kinematics describes how the relative orientation of a body segment changes over time with respect to the neighboring segment forming the joint. This relative orientation can be represented in two ways: via a sequence of three successive rotation angles, or through an alternative representation that avoids a specific problem inherent to such angles—namely, that certain orientation combinations cause two of the three rotation axes to align, temporarily causing the system to lose the ability to distinguish between rotations. The spatiotemporal gait parameters—step frequency, step length, walking speed, and cadence—are derived directly from these marker trajectories. To compare walking speed across species of vastly different body sizes, speed is combined with animal size to form a dimensionless number; this allows one to determine whether two animals of different sizes are moving in an equivalent manner relative to their own bodies.

The advanced kinematic analysis introduced earlier reveals a characteristic pattern in normal gait: the body's potential and kinetic energies are smoothly interchanged throughout each step, and temporal variability from one step to the next is very low, with a coefficient of variation of less than three percent. In the presence of pathology, however, spatiotemporal asymmetries arise between the two sides of the body, and temporal variability increases markedly; within the framework of advanced kinematic analysis, both changes—asymmetry and increased variability—serve as fundamental diagnostic markers of movement impairment.

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