Page 319 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

296 BIOMECHANICS OF THE HUMAN BODY

12.4.1 Anatomical Model
The first step requires that we decide which joints and muscles will be included and how their
parameters will be obtained. For this lower limb model, a popular anatomical model is that developed
using SIMM (Musculographics Inc.) (Delp et al., 1990, and extended by Lloyd and Buchanan, 1996).
This model includes 12 musculotendon actuators, represented as line elements that wrap around bone
segments or other muscles. These are the rectus femoris (RF), vastus lateralis (VL), vastus intermedius
(VI), vastus medialis (VM), medial gastrocnemius (MG), lateral gastrocnemius (LG), semimembra-
nosus (SM), semitendinosus (ST), biceps femoris long (BFL) head, biceps femoris short (BFS) head,
tibialis anterior (TA), and soleus (Sol). Joint kinematics will be used as input for this anatomical model
to determine individual muscle tendon lengths and moment arms.

12.4.2 Muscle Activation Dynamics Model
The magnitudes of the EMG signals will change as the neural command calls for increased or
decreased muscular effort. Nevertheless, it is difficult to compare the absolute magnitude of an EMG
signal from one muscle to that of another because the magnitudes of the signals can vary depending
on many factors such as the gain of the amplifiers, the types of electrodes used, and the placements
of the electrodes. Thus, in order to use the EMG signals in a neuromusculoskeletal model, we must
first transform them into muscle activation. The muscle activation dynamics model transforms raw
EMG to muscle activation, and the whole process is shown in Fig. 12.7.
Firstly, the raw EMGs are high-pass-filtered using a forward and reverse pass fourth-order
Butterworth filter to remove movement artifact, then full wave rectified, normalized by peak rectified
EMG values obtained from maximum voluntary contraction (MVC) trials, and then low-pass-filtered
using a forward and reverse pass fourth-order Butterworth filter to account for the natural filtering
property of muscle.
After rectifying, normalizing, and filtering the raw EMG data, activation dynamics needs to be used
to characterize the time varying features of EMG. Muscle twitch response can be well represented by
a critically damped linear second-order differential system (Milner-Brown et al., 1973). This type of
response has been the basis for the differential equations to determine neural activation, u(t), from the
rectified, normalized, and filtered EMG input, e(t).
2
de t() de t()
ut() = M 2 + B + K et() (12.1)
dt dt
where M, B, and K are the constants that define the second-order differential system.
This differential equation can be expressed in discrete form by using backward differences
(Thelen et al., 1994; Lloyd and Buchanan, 1996).
−
ut() = α ⋅ e t d) − β 1 ⋅ ut −1 ) − β 2 ⋅ ut − 2 ) (12.2)
(
(
(
where d is the electromechanical delay, and α, β , and β are the coefficients that define the second-
2
1
order dynamics. To realize a positive stable solution of Eq. (12.1), a set of constraints are employed.
β = γ + γ 2
1
1
β = γ × γ
2 1 2
(12.3)
γ < 1
1
γ < 1
2
This equation can be seen as a recursive filter, where the neural activation depends not only
on the current level of neural activation but also on its recent history. This filter should have unit