GGAI Calculation

Step 1. Calculation of the Instant Gait Graph Asymmetry IGGAy(t)

The first step demands to calculate the Instant Gait Graph Asymmetry which has been described in the construction of the Gait Asymmetry Graph.

Instant Gait Graph Asymmetry IGGAy(t) numerical values derives from the subtraction of the measured Right side subject’s Y values from the respective Left side subject’s Y values at each moment of the gait cycle (t).

Instant Gait Graph Asymmetry IGGAy(t)= Right y(t)- Left y(t)

t=1 to 100% of the gait cycle

Note: Positive IGGAy+_(t) and Negative IGGAy-_(t) values

The values of the IGGAIy_(t) may be positive or negative. Their sign indicates the direction of the asymmetry. It depends on the right side subjects values weather they are lower or greater values than respective left side values. If for example all sagittal plane right knee IGGAy_(t) values throughout the gait cycle are positive (+), then the right knee is more flexed than the respective left knee at the respective instants, while if they are negative (-) then the right knee is more extended than the left at the respective instants.

Step 2. Calculation of the Instant Gait Graph Asymmetry Index IGGAI(t)

The next step is to proceed in the calculation of the Instant Gait Graph Asymmetry Index IGGAI(t).

The formulas to calculate the IGGAI(t) are:

Instant Gait Graph Asymmetry Index IGGAI_(t) = IGGAy_(t) / Normal SD_(t)

t=1 to 100% of the gait cycle

This calculation transforms each IGGAy(t) value of the gait graph into Normal SD units. These values are the building blocks of the Gait Asymmetry Index.

Note: Positive IGGAI+_(t) and Negative IGGAI-_(t) values

The sign of each IGGAI_(t) value can be positive or negative currying the sign of the IGGAy_(t) that was derived.

Step 3. Calculating the Weighted Instant Gait Graph Asymmetry Index WIGGAI(t)

Each IGGAI(t), has a partial contribution to the overall observed asymmetry on a gait graph.

Having established the way to measure the instant asymmetry severity as a ratio to the Normal SD, the next step is to establish a measurement for the overall gait graph asymmetry. The contribution of each IGGAI(t) to the total asymmetry observed in the gait graph curves can be calculated by applying a weight factor to each instant value.

Weight Factor calculation

The weight factor to be applied depends on the sampling frequency used to create the gait curves and can be calculated from the following formula:

Weight Factor = 1 / number of graph points

For example in a graph of a gait cycle that uses 50 points for the plot (i.e. one point every 2% of the gait cycle) the calculated weight factor is 1/50 = 0.02 . If the graph is plotted using 100 points then the weight factor is 1/100 = 0.01 etc.

After multiplying each IGGAI(t) with the weight factor we end up with the Weighted IGGAI(t) values (WIGGAI(t)).

Weighted IGGAI(t) WIGGAI_(t) = IGGAI(t) * Weight Factor

t=1 to 100% of the gait cycle

Note: Positive IGGAI+_(t) and Negative IGGAI-_(t) values

As explained above the sign of the IGGAI_(t) the series of values can be positive and negative, the resulted WIGGAI_(t) values are also currying the sign of the IGGAI_(t) thus being positive or negative.

Step 4. Calculating the GGAI+ and GGAI-

Summing separately all negative (WIGGAI-(t)) and all positive (WIGGAI-(t)) values, the Gait Graph Negative Asymmetry Index (GGDI-) and Gait Graph Positive Asymmetry Index (GGDI+) are created.

GGAI- = sum(R -WIGGAI_(t))

GGAI+ = sum(R +WIGGAI_(t))

t=1 to 100% of the gait cycle

Note: The GGAI + and GGA - values may be reported to document the amount of the asymmetry that right side curve is located above the left side curve and the amount of the asymmetry that right side curve is located bellow the left side curve.

Step 5. Calculating the GGAItot or GGAI

The final step is to combine the absolute values of the two sub-indexes to create the total Gait Graph Asymmetry Index GGAItot

GGAItot = ABS(GGDI-) + ABS(GGDI+)

t=1 to 100% of the gait cycle

GGAItot or GGAI number represents in a single value the overall asymmetry observed in the gait gait graph curves, expressed in units of SDs, taking in account all instant deviations.

This concludes the procedure of the GGAI calculation.

Figure 1. Classical Gait Analysis Graphs and Gait Asymmetry Graphs

together with the GGAI (green) value imposed on the top of each graph.

Positive and Negative component values are referred in the parenthesis.

Note: Reason for Reporting GGAI values together with GGAI+ and GGAI- values

In figure 1, on the right side graphs (Gait Asymmetry Graphs) you may notice that together with the GGAI values the respective GGAI- and GGAI+ values are reported on the right top of each graph. These values are important for documenting the amount of the asymmetry that the right side curve is located below the left side curve and the amount of asymmetry that the right side curve is located above the left side curve, thus discriminate asymmetries of equal GGAI. If this information is needed it may be also reported on the top right side of the Classical Gait Graphs.

Click here for a detailed EXCEL GGAI Calculation Example