Timing within the activity envelope and shape of the activity envelope

The narrow window method (slice technique) was used to determine the normalised amplitude relative to MVC and the normalised frequency of each activity envelope. The narrow window (100 samples) around the peak activation was assumed to capture a stationary signal each activity envelope. Therefore, if it is true, the amplitude and frequency of the peak activation would be consistent. However, when the shape of the activity envelope has an inconsistent pattern, the window may have a risk to capture the different point of the peak activation each activity envelope. Therefore, the shape of the activity envelope was to determine whether it affected the amplitude and frequency of the peak activation. There are three possible types of the shapes of the activity envelope given as below (Figure 5 – 11). In order to define the shape of the activity envelope (SOA), firstly the three components

(including onset, peak and offset) of the activity envelope were defined and then each component were normalised relative to the beginning of the gait cycle.

B

A C

Onset Offset Onset Offset Onset Offset

Peak Peak Peak

Figure 5 – 11 : Pattern of the shape of the activity envelope (SOA)

Onset : activation time of the activity envelope. Peak : largest amplitude point of the activity envelope.

Offset : inactivation time of the activity envelope. A : OnPk (Onset to Peak) > PkOff (Peak to Offset).

B : OnPk (Onset to Peak) = PkOff (Peak to Offset). C : OnPk (Onset to Peak) < PkOff (Peak to offset).

1st gait cycle 2nd gait cycle 3rd gait cycle

Right heel strike Right heel strike Right heel strike Right heel strike

OnPk OnPk OnPk

Figure 5 – 12 : Timing between onset and peak within an activity envelope

The time between normalised onset (%Onset) and peak (%Peak) relative to right heel strike within an activity envelope was defined as OnPk (Figure 5 – 12) (5 – 6).

• OnPk =%Peak−%Onset --- (5 – 6)

1st gait cycle 2nd gait cycle 3rd gait cycle

Right heel strike Right heel strike Right heel strike Right heel strike

PkOff PkOff PkOff

Figure 5 – 13 : Timing between peak and offset within an activity envelope

The time between normalised peak (%Peak) and offset (%Offset) relative to right heel strike within an activity envelope was defined as PkOff (Figure 5 – 12) (5 – 7).

• PkOff =%Offset−%Peak --- (5 – 7)

1st gait cycle 2nd gait cycle 3rd gait cycle

Right heel strike Right heel strike Right heel strike Right heel strike

OnOff OnOff OnOff

Figure 5 – 14 : Timing between onset and offset within an activity envelope

The time between normalised onset (%Onset) and offset (%Offset) relative to right heel strike within an activity envelope was defined as OnOff (Figure 5 – 13) (5 – 8).

• OnOff =%Offset−%Onset --- (5 – 8)

1st gait cycle 2nd gait cycle 3rd gait cycle

Right heel strike Right heel strike Right heel strike Right heel strike OnPk

Figure 5 – 15 : Shape of the activity envelope (SOA)

After calculating the component parts of the activity envelope, timing (OnPk) between normalised onset and peak points of the activity envelope relative to right heel strike was divided by timing (PkOff) between normalised peak and offset points of the activity envelope relative to right heel strike. This ratio defined the shape of the activity envelope (SOA) (Figure 5 – 15) (5 – 9).

• SOA=OnPk/PkOff --- (5 – 9)

V. Interval timing within a gait cycle (OnOn, PkPk, and OffOff)

In previous sections, timing of the activity envelope (%Onset, %Peak and %Offset) and components of the activity envelope (OnPk, PkOff, OnOff, and shape of the activity envelope (SOA)) were determined during consecutive gait cycles was defined. However, the length of

time between activity envelopes within a gait cycle was not determined. The interval timing within each gait cycles was defined as the time difference between the first activity envelope (1^st AE) and second activity envelope (2^nd AE) within a gait cycle with respect to three points of the activity envelope. Therefore, each point of the activity envelope was calculated within a gait cycle (Figure 5 – 16, 17, and 18) (5 – 10), (5 – 11), and (5 – 12).

1st gait cycle 2nd gait cycle 3rd gait cycle

Right heel strike Right heel strike Right heel strike Right heel strike

%Onset

Figure 5 – 16 : Timing between onset (1^st activity envelope) and onset (2^nd activity envelope) within a gait cycle

• OnOn = %Onset₂ – %Onset₁ --- (5 – 10)

%Onset1 is the normalised onset point relative to right heel strike of the first activity envelope (1^st AE) within one gait cycle. %Onset₂ is the normalised onset point relative to right heel strike of the second activity envelope (2^nd AE) within one gait cycle.

1st

1st gait cycle 2nd gait cycle 3rd gait cycle

Right heel strike Right heel strike Right heel strike Right heel strike

%Peak

Figure 5 – 17 : Timing between peak (1^st activity envelope) and peak (2^nd activity envelope) within a gait cycle

• PkPk = %Peak₂ – %Peak₁ --- (5 – 11)

%Peak1 is the normalised peak point relative to right heel strike of the first activity envelope (1^st AE) within one gait cycle. %Peak₂ is the normalised peak point relative to right heel strike of the second activity envelope (2^nd AE) within one gait cycle.

1st

1st gait cycle 2nd gait cycle 3rd gait cycle

Right heel strike Right heel strike Right heel strike Right heel strike

%Offset

Figure 5 – 18 : Timing between offset (1^st activity envelope) and offset (2^nd activity envelope) within a gait cycle

• OffOff = %Offset₂ – %Offset₁ --- (5 – 12)

%Offset1 is the normalised offset point relative to right heel strike of the first activity envelope

(1^st AE) within one gait cycle. %Offset₂ is the normalised offset point relative to right heel strike of the second activity envelope (2^nd AE) within one gait cycle.

5.2.8. Statistical analysis

The surface EMG signal was recorded from paraspinal muscles during steady state walking.

Several parameters defined above were used to characterise the pattern of muscle activity of paraspinal muscles during steady state walking. The first aim of this study was to evaluate the consistency of muscle activation of paraspinal muscles within a subject within a minute. A second aim of this study was to evaluate the consistency of muscle activation of paraspinal muscles between subjects over a 10 minute. A third aim of this study was to determine the pattern of activity of paraspinal muscles difference between sides at the same level of the spine and between three levels of the spine on the same side. In order to achieve these steps, a series of statistical test were carried out and are detailed below (I. ~ IV.). A significance level of 0.05 was accepted as representing a significant change for this study. Two statistical programs (Minitab^® for Windows, version 14, Minitab Inc., State College, PA, US)(SPSS for Windows, Version 13, SPSS Inc., Chicago, Illinois, US) were used to do all statistical analyses below.