Page 290 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

VIBRATION, MECHANICAL SHOCK, AND IMPACT 267

of the specific bone. Cortical bone is the dominant constituent of the long bones (e.g., femur, tibia),
while trabecular bone, which is more elastic and energy absorbent, is the dominant constituent of the
vertebrae (Gomez et al., 2002). The shear viscosity and bulk elasticity of soft tissue are from a model for
the response in vivo of a human thigh to the vibration of a small-diameter piston (von Gierke et al., 1952).
The nonlinear mechanical properties of biological tissues have been studied extensively in vitro,
including deviations from Hooke’s law (Fung, 1993; Haut, 2002).

Mechanical Impedance of Muscle Tissue. The (input) mechanical impedance is the complex ratio
between the dynamic force applied to the body and the velocity at the interface where vibration enters
the body. The real and imaginary parts of the mechanical impedance of human muscle in vivo are
shown as a function of frequency in Fig. 11.3 (von Gierke et al., 1952). In this diagram the measured
resistance (open circles) and reactance (diamonds) are compared with the predictions of a model, from
which some tissue properties may be derived (see Table 11.1). It should be noted that the mechanical
stiffness and resistance of soft tissues approximately triple in magnitude when the static compression
of the surface increases by a factor of three. The relationship, however, is not linear.

10 6 5 C

Resistance and reactance (dyn.s/cm) 10 4 3 Reactance Resistance A B
10

10

10

10 2
10 10 2 10 3 10 4 10 5 10 6
Frequency (Hz)
FIGURE 11.3 Mechanical resistance and reactance of soft thigh tissue
(2 cm in diameter) in vivo from 10 Hz to 1 MHz. The measured values
(open circles—resistance; diamonds—reactance) are compared with the
calculated resistance and reactance of a 2-cm-diameter sphere vibrating in
a viscous, elastic compressible medium with properties similar to soft human
tissue (continuous lines, curves A). The resistance is also shown for the
sphere vibrating in a frictionless compressible fluid (acoustic compression
wave, curve B) and an incompressible viscous fluid (curve C). (von Gierke
et al., 1952.)

Apparent Mass of Seated Persons. The apparent mass is often used to describe the response of
the body at the point of stimulation rather than the mechanical impedance, and is the complex
ratio between the dynamic force applied to the body and the acceleration at the interface where
vibration enters the body. It is commonly expressed as a function of frequency, and is equal to the
static weight of a subject in the limiting case of zero frequency when the legs are supported to move