GGDI Calculation

The calculation steps needed to create the Gait Graph Deviation Index are described in the following section.

Gait Graph Deviation Index may also be refered as Motion Graph Deviation Index as explained here.

Step 1. Calculation of the Instant Gait Graph Deviation IGGDy(t)

The first step demands to calculate the Instant Gait Graph Deviation for the Right and Left limb which are used also for the creation of the Gait Deviation Graphs.

Instant Gait Graph Deviation in Y axis IGGDy(t) numerical values derive from the subtraction of the measured subjects’ Y values from the respective mean Normal Subjects Y values at each moment of the gait cycle (t).

Two series of values that define the Right and Left limb curves must be calculated for the Right and Left limb gait curves.

(Right) R IGGDy(t) = R y(t)- Normal y(t)

(Left) L IGGDy(t) = L y(t)- Normal y(t)

t=1 to 100% of the gait cycle

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

The values of the IGGDIyt) may be positive or negative. Their sign indicates the direction of the deviation. It depends on the subjects values weather they are lower or greater values from the normal mean. If for example all sagittal plane knee IGGDy(t) values throughout the gait cycle are positive (+), then the subject knee is more flexed than the normal subjects mean at all instances, while if some of the values are negative (-) then the subject's knee is more extended at these instants of the gait cycle.

Step 2. Calculation of the Instant Gait Graph Deviation Index IGGDI_(t)

The next step is to proceed in the calculation of the Instant Gait Graph Deviation Index IGGDI(t) for the Right and Left limb gait curves.

The formulas to calculate the IGGDI(t) are:

(Right) Instant Gait Graph Deviation Index R IGGDI_(t) = R IGGDy_(t) / Normal SD_(t)

(Left) Instant Gait Graph Deviation Index L IGGDI_(t) = L IGGDy_(t) / Normal SD_(t)

t=1 to 100% of the gait cycle

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

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

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

Step 3. Calculating the Weighted Instant Gait Graph Deviation Index WIGGDI(t)

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

Having established the way to measure the instant deviation severity as a ratio to the Normal SD, the next step is to establish a measurement for the overall gait graph deviation. The contribution of each IGGDI(t) to the total Deviation observed in the gait graph curve 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 IGGDI(t) with the weight factor we end up with the Weighted IGGDI(t) values (WIGGDI(t)).

Again, the series of values are calculated for the Right and Left limb gait curves.

(Right) Weighted IGGDI(t) R WIGGDI_(t) = R IGGDI(t) * Weight Factor

(Left) Weighted IGGDI(t) L WIGGDI_(t) = L IGGDI(t) * Weight Factor

t=1 to 100% of the gait cycle

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

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

Step 4. Calculating the GGDI+ and GGDI-

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

(Right) R GGDI- = sum(R WIGGDI-_(t)) R GGDI+ = sum(R WIGGDI+_(t))

(Left) L GGDI- = sum(L WIGGDI-_(t)) L GGDI+ = sum(L WIGGDI+_(t))

t=1 to 100% of the gait cycle

Note: The GGDI + and GGDI - values may be reported to document the amount of the deviation that is located above and the amount of the deviation that is located bellow the normal mean curve.

Step 5. Calculating the GGDItot or GGDI

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

(Right) R GGDItot = ABS(R GGDI-) + ABS(R GGDI+)

(Left) L GGDItot = ABS(L GGDI-) + ABS(L GGDI+)

t=1 to 100% of the gait cycle

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

This concludes the procedure of the GGDI calculation.

Figure 1. Classical Gait Analysis Graphs and Gait Deviation Graphs

together with the Right GGDI (blue) and Left GGDI (red) values imposed on the top of each graph.

Positive and Negative component values are referred in the parenthesis.

Note: Reason for Reporting Left & Right GGDI values together with GGDI+ and GGDI- values

In figure 1, on the right side graphs (Gait Deviation Graphs) you may notice that together with the Left and Right GGDI values the respective GGDI- and GGDI+ values are reported on the right top of each graph. These values are important for documenting the proportion of the deviation that is located above and bellow the normal mean curve thus discriminate deviations of equal GGDI. 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 GGDI Calculation MS EXCEL Example