10.3.6 Temporal integration of the dose and cumulative-load update

Once the elementary temporal dose for each interval has been calculated, the cumulative exertion load is obtained by processing all activity intervals in sequence. Each interval is characterized by its duration, the relative exertion in each biomechanical channel, and the functional muscle group that must act.

Integration does not consist solely of adding all the doses generated since the beginning of the activity. Previously accumulated exposure loses some of its value through recovery, including during intervals in which a new dose is generated. Two operations are therefore performed successively in each interval:

• Recovery corresponding to the interval duration is applied to the load previously accumulated by all muscle groups.

• The new temporal dose is added exclusively to the active functional muscle group.

To represent this process, the cumulative load of each muscle group is divided into a fast-recovery load component and a slow-recovery load component. For joint a, biomechanical channel c, functional muscle group m, and interval k, both components are updated as follows:

\[D_{a,c,m,k}^{rap} = \rho_{rap}\left( {\Delta t}_{k} \right)D_{a,c,m,k - 1}^{rap} + \omega_{rap}I_{a,c,m,k}\Delta D_{c}(t_{k})\]

Equation 19

\[D_{a,c,m,k}^{len} = \rho_{len}\left( {\Delta t}_{k} \right)D_{a,c,m,k - 1}^{len} + \omega_{len}I_{a,c,m,k}\Delta D_{c}(t_{k})\]

Equation 20

where:

• \(D_{a,c,m,k}^{rap}\) and \(D_{a,c,m,k}^{len}\ \) are the fast and slow load components at the end of interval k.

• \(\rho_{rap}\left( {\Delta t}_{k} \right)\ \) and \(\rho_{len}\left( {\Delta t}_{k} \right)\) are the retention factors for the two components during the interval. Their values range from 0 to 1.

• \(\omega_{rap}\) and \(\omega_{len}\) are the proportions of the new dose assigned to each component and satisfy \(\omega_{rap}\)+\(\omega_{len}\) = 1.

• \(I_{a,c,m,k}\ \) equals 1 when m is the active muscle group during the interval and 0 for the remaining groups.

• \(\Delta D_{c}(t_{k})\) is the elementary temporal dose generated during the interval.

The cumulative load of the muscle group at the end of the interval is the sum of its two components:

\[D_{a,c,m,k}^{} = D_{a,c,m,k}^{rap} + D_{a,c,m,k}^{len}\]

Equation 21

At the beginning of the activity, both components equal zero. In each interval, recovery is applied to all muscle groups that retain cumulative load, including those that are not active at that time. The new dose is then distributed between the fast and slow components of the active muscle group.

Accumulation and recovery can therefore occur simultaneously. When the new dose is greater than the reduction produced by recovery, the net load increases. When the dose is small or zero and recovery predominates, the load decreases. The cumulative load does not therefore have to increase continuously.

If the exertion changes direction and requires the action of an antagonist group, the new dose is assigned to that group. The previously active group stops receiving dose but retains its own state and continues to recover. In this way, the time histories of the different functional muscle groups remain separate.

Cumulative load can be consulted at the end of the activity or at any intermediate time. Its time course identifies periods in which exposure increases most rapidly, periods in which appreciable recovery occurs, and the channels or muscle groups that concentrate the greatest temporal demand.

If recovery were not considered, the ρ factors would equal 1 and the procedure would reduce to a sum of the elementary doses. The specific form and parameters of the recovery factors are described in the next section.