500 GGDI and GGAI of the hip and knee graphs were used for the assessment of the mathematical properties of the indices. The analysis concluded that the indices consist R-Ideals, and therefore Rings. The numerical analysis of GGDI and GGAI proved that the numerical representation of deviation in units of dispersion consists a Ring algebraic structure, so these two indexes have all the properties of a Ring set.
This fact enables the GGDI and GGAI indexes to be used in parametic tests.
GGDI shares common ground with the Gait Profile Score (GPS). Both indexes are measuring subjects's deviation from the normal subjects mean values. However GPS calculates the root mean square difference of the right and left patient’s curves from the normal mean curves in degrees, therefore it does not address the fact that absolute deviation in degrees might be of different pathological severity* depending on the degrees that SD of normal subjects are showing at that specific instant.
GGDI is specially defined to address this issue by dividing at each instant the observed deviation with the normal subjects SD and transferring this information to the final value of the GGDI.
The above approach inherits another very significant property on the GGDIs & GGAIs.
We define this property as Comparability.
Comparability is the flexibility to directly compare the indexes of any gait graph to each other. This is feasible because all indexes share a common denominator, which is the familiar and easy to understand normal subjects SD. This option is not available when using any other indexes.
* In gait analysis deviations observed for the subject measured within one Standard Deviation of the normal subjects group, are considered non pathological or within the normal range, while larger deviations are considered increasingly pathological.