**2.2.1 Principle of the stretch reflex**

When muscle is stretched, it reflexively contracts in response. This kind of muscle response is called the stretch reflex. The stretch reflex is the target of the pendulum test. Fig. 3 shows the conceptual pathway of the stretch reflex. When muscle is stretched by some factor, receptor (called muscle spindle) detects it as a stimulus and transmit it as an afferent signal up to the spinal cord i.e., the α-motoneuron. The spinal cord receives the signal and sends a command (efferent signal) to effector (muscle) to restore this stretched state to the original state. These processes are executed unconsciously. Afferent fiber and efferent fiber function respectively as the transmission pathways for the afferent signal and efferent signal, which are both transmitted as impulses.

Fig. 3. Path of stretch reflex.

The reflex pathway described above (receptor → spinal cord → effector) is called a reflex arc. The stretch reflex is generated not only by passive muscle stretching, but also in response to conscious stretching of a muscle. The pendulum test is a test to estimate the sensitivity with which the reflex arc responds to the stimulus of knee flexion (extension of the quadriceps femoris muscle). The knee joint motion in this case is induced unconsciously by adding external force with the subject in a resting state for ease of estimation.

### **2.2.2 Structure of the spindle and its functions**

Muscle is made up of many extrafusal muscle fibers arranged in parallel. Both ends of each muscle spindle are attached to one of these extrafusal muscle fibers. The muscle spindle is covered with a capsule, as shown in Fig. 4. In the capsule, there exist two types of intrafusal muscle fibers, called nuclear bag intrafusal muscle fiber and nuclear chain intrafusal muscle fiber. Stretching of the extrafusal muscle fiber affects the nuclear bag intrafusal muscle fiber and nuclear chain intrafusal muscle fiber, and stretch velocity and displacement, respectively, are detected. The detection sensitivities of the stretch velocity and displacement are regulated by efferent commands that are sent from phasic γ-motoneuron and tonic γ-motoneuron present in the spinal cord, respectively. The two kinds of detected information are consolidated into the afferent signal within the muscle spindle and transmitted to the spinal cord through Group Ia afferent fiber. Group II afferent fiber that send only nuclear chain intrafusal muscle fiber information to the spinal cord is also present, but they have a little influence on the stretch reflex in the pendulum test, and so it is not shown in the figure.

The afferent signal of Group Ia fiber is given as follows as the impulse frequency *f*<sup>s</sup> (primary approximation) (Harvey & Matthews, 1961).

$$f\_{\rm s} = k\_{\rm 1s}x + k\_{\rm 2s}f\_{\rm 3s} + k\_{\rm 1d}\dot{x} + k\_{\rm 2d}f\_{\rm 3d} \tag{1}$$

Here, *x* is extrafusal muscle fiber (muscle) displacement, *f*γd and *f*γs are the respective impulse frequencies from the brain to phasic and tonic γ-motoneurons, and *k*1s, *k*1d, *k*2s, and *k*2d are constants. As shown in the above equation, there are two types of components in stimuli detected by the muscle spindle in the stretch reflex: a stretch velocity component expressed by the first and second terms, and a muscle displacement component expressed by the third and fourth terms.

Fig. 4. Structure of muscle spindle.

22 Advanced Topics in Measurements

When muscle is stretched, it reflexively contracts in response. This kind of muscle response is called the stretch reflex. The stretch reflex is the target of the pendulum test. Fig. 3 shows the conceptual pathway of the stretch reflex. When muscle is stretched by some factor, receptor (called muscle spindle) detects it as a stimulus and transmit it as an afferent signal up to the spinal cord i.e., the α-motoneuron. The spinal cord receives the signal and sends a command (efferent signal) to effector (muscle) to restore this stretched state to the original state. These processes are executed unconsciously. Afferent fiber and efferent fiber function respectively as the transmission pathways for the afferent signal and efferent signal, which

> spinal cord (α-motoneuron)

The reflex pathway described above (receptor → spinal cord → effector) is called a reflex arc. The stretch reflex is generated not only by passive muscle stretching, but also in response to conscious stretching of a muscle. The pendulum test is a test to estimate the sensitivity with which the reflex arc responds to the stimulus of knee flexion (extension of the quadriceps femoris muscle). The knee joint motion in this case is induced unconsciously

Muscle is made up of many extrafusal muscle fibers arranged in parallel. Both ends of each muscle spindle are attached to one of these extrafusal muscle fibers. The muscle spindle is covered with a capsule, as shown in Fig. 4. In the capsule, there exist two types of intrafusal muscle fibers, called nuclear bag intrafusal muscle fiber and nuclear chain intrafusal muscle fiber. Stretching of the extrafusal muscle fiber affects the nuclear bag intrafusal muscle fiber and nuclear chain intrafusal muscle fiber, and stretch velocity and displacement, respectively, are detected. The detection sensitivities of the stretch velocity and displacement are regulated by efferent commands that are sent from phasic γ-motoneuron and tonic γ-motoneuron present in the spinal cord, respectively. The two kinds of detected information are consolidated into the afferent signal within the muscle spindle and transmitted to the spinal cord through Group Ia afferent fiber. Group II afferent fiber that send only nuclear chain intrafusal muscle fiber information to the spinal cord is also present,

by adding external force with the subject in a resting state for ease of estimation.

afferent nerve efferent nerve

effector (muscle)

contractile force (muscle contraction)

receptor (muscle spindle)

stimulation (muscle stretch)

**2.2.2 Structure of the spindle and its functions** 

**2.2 Physiology of the stretch reflex 2.2.1 Principle of the stretch reflex** 

are both transmitted as impulses.

Fig. 3. Path of stretch reflex.
