**2.2.3 Phasic stretch reflex and tonic stretch reflex**

Commands to control the lower extremities are transmitted from the brain to muscle via the spinal cord. They are broadly divided into commands for flexion and extension, commands for maintaining of posture and commands for adjusting of the muscle spindle sensitivity. The first commands are generated only consciously, the second and third ones are generated consciously and/or unconsciously. Measurements of knee joint motion in the pendulum test are however done under the unconscious state of the subjects, and so the commands in this case are only unconscious ones to maintain posture and adjust the muscle spindle sensitivity. Consequently, the presence or absence of the efferent command toward the muscle and its strength during the pendulum test are determined only by these unconscious commands.

Fig. 5 shows the reflex arcs in the pendulum test schematically with a focus on the quadriceps femoris muscle. It includes phasic γ-motoneuron, tonic γ-motoneuron and αmotoneuron that play principal roles in the stretch reflex. The upper part enclosed by the solid line is the spinal cord. Signals *f*e and *f*i are commands to determine the posture, and represent frequencies of the impulses from the brain to the α-motoneuron and presynaptic inhibition part, respectively. The presynaptic inhibition part usually suppresses afferent signal from the muscle spindle so that it does not reach the α-motoneuron. Signals *f*γd and *f*γ<sup>s</sup> are commands to adjust the muscle spindle sensitivity, and represent frequencies of the impulses from the brain to the phasic γ-motoneuron and tonic γ-motoneuron, respectively.

Precise Measurement System

3.3, may be listed as follows.

b. Magnetic-type goniometer

device, and has no wearable parts.

large non-linearity and hysteresis.

scale of the system, etc. e. Accelerometer

simultaneously. f. Gyroscope

for Knee Joint Motion During the Pendulum Test Using Two Linear Accelerometers 25

Measurements of physical movement have long been done focused on gait analysis. Recently, various types of advanced measurement technology are used in the field of sports science. Among them, sensors and measurement systems thought to be applicable to measurements of lower extremity motion, including sensors for pendulums described in 3.2-

This is a fixed rotation axis sensor that uses a rotating variable resistor. The rotation angle is detected as an electrical potential proportional to it. It has high reliability. On the other hand, it is unsuitable for measurement of high-speed movement, because large torque is

This is a fixed rotation sensor with multiple magnetic pole and magnetic elements arranged along its circumference. It detects an electrical potential proportional to the rotation angle. It has high reliability and high accuracy. It requires a little torque since it is a non-contact-type

This sensor was developed for angle measurements of complex joints (Nicol, 1989). It is not affected by movement of the joint axes, with the basic axis and movement axis set on either end of a bar-shaped resistor that changes electrical resistance with changes in shape. The angle between the two axes is measured as change in the resistance value. It has both rather

Many marking points are attached to the surface of the subject's body, and images are made while the subject is moving (Fong et al., 2011). The subject is completely unrestricted. The angles at multiple points can be measured simultaneously. Its application is limited to experimental use for reasons of large filming space requirement, low time resolution, large

This sensor detects the movement of an object along a single axis as an acceleration signal, using a built-in strain gauge or similar element set. It is applicable to detection of accelerations in a wide range of fields, and various types have been developed from perspectives such as model type, accuracy, and stability. It does not restrict the movement of subjects, because a sensor only needs to be attached to one side of a joint even for joint movement measurements. It can also measure angle and angular acceleration

Ultra-small devices have been developed using the Coriolis force and piezoelectricity based on micro-electro-mechanical systems (MEMS) technology (Tong & Granat, 1999). Currently,

To summarize, the requirements for knee joint motion measurement systems suitable for the pendulum test in clinical practice include: (1) sufficient accuracy; (2) low susceptibility to effects from the motion of the knee joint axis; (3) no restriction of the knee joint when worn; (4) ability to be attached simply and stably; and (5) ability to obtain waveforms of angle,

**3. Detection of knee joint motion using acceleration sensors** 

c. Distribution constant-type electrogoniometer ("flexible goniometer")

d. Marking point measurement (or motion capture system)

however, stability and reliability remain problematic.

**3.1 Accelerometers as biosensors of knee joint motion** 

a. Electrogoniometer (commonly called potentiometer)

required to drive contact points and they are abrasive.

In normal subjects, *f*e, *f*γd, *f*γs have rather small values and *f*i has rather large value, so that the α-motoneuron does not fire and no reflex occurs. Consequently, the knee joint motion at pendulum test becomes a free oscillation. On the contrary, in subjects having injuries of central nervous system, more than one of *f*e, *f*γd, *f*γs have rather large values and/or *f*i has rather small value, so that the α-motoneuron fires and the stretch reflex occurs in the knee joint. Consequently, the knee joint motion is forced to disturb from free oscillation by the contractile force. In the following, we call such an oscillation forced oscillation.

The forced oscillation is classified into two types (William, 1998). One is a forced oscillation that is caused by stretch velocity component included in the afferent signal from the muscle spindle to the α-motoneuron. The value of the contractile force induced by such a component becomes maximum at the time when stretch velocity of the quadriceps femoris muscle reaches about maximum value. We call the reflex caused by such a component phasic reflex. The other is a forced oscillation that is caused by displacement component in the afferent signal from the muscle spindle. The contractile force in this case has maximum value at the time when the displacement of the muscle is about maximum. We call the reflex caused by such a component tonic reflex.

Fig. 5. Reflex arc.

As mentioned above, two types of reflexes can occur in the reflex arc composed of spindle, GIa fiber, presynaptic inhibition, α-motoneuron, α fiber and muscle. Evaluation of these reflexes therefore requires consideration of not only the size of the reflex but also the timing of their generation. Naturally, therefore, measurements of knee joint motion used in analyzing these reflexes demand high accuracy.
