Spine Model for Vibration Analysis - Computational Biomechanics of the Musculoskeletal System - page 181

T12-L1 carrying a mass of 40 kg, and reported a first-order resonant frequency of 23.5 Hz in axial
mode under a 30-N preload. In addition, the static facet contact force in the sagittal plane was 2.1%
of the 400-N compressive load for the same model. These results agree with other published results,
for example 1%~5% from Shirazi-Adl and Drouin (1987).
In order to investigate the resonant frequency characteristics of the human spine, different
numbers of spinal segments were analyzed using FE modal analysis. Table 15.2 lists the resonant
frequencies of FE models with one and two motion segments, L1-L5, L1-S1, and T12-Pelvis, and
other published results (Pope et al. 1987; Panjabi et al. 1986; Sandover and Dupuis 1987; Kong and
Goel 2003; Kasra, Shirazi-Adl, and Drouin 1992; Goel, Park, and Kong 1994).
The resonant frequencies of the one motion segment FE models of T12-L1 and L2-L3 in the verti-
cal direction, carrying a mass of 40 kg, are 25.7 and 26.7 Hz, respectively. The frequency of the two
segment L3-L5 model is 19.6 Hz. The frequencies of the entire lumbar spine of L1-L5 and L1-S1
in the vertical direction, carrying a distributed mass of 40 kg, are 11.5 and 9.12 Hz. The resonant

table 15.2
resonant Frequencies of Finite element models in the vertical direction for different
Spinal motion Segments

Spinal motion Segments resonant Frequency (hz) references notes

Kasra, Shirazi-Adl,
and Drouin (1992)

T12-L1 23.5 Experimental study

T12-L1 25.7 40 kg upper body

One motion segment L2-L3 26.0 Kasra, Shirazi-Adl,

and Drouin (1992)

L2-L3 26.7 40 kg upper body

L3-L4 27.7 Kong and Goel (2003)

Goel, Park, and
Kong (1994)

L4-S1 17.5 40 kg upper body

Two motion segments L4-S1 16.4 40 kg upper body

L3-L5 18.0 Kong and Goel (2003)

L3-L5 19.6 40 kg upper body

L1-L5 12.2 Kong and Goel (2003)

Lumbar spine

L1-L5 11.5 40 kg upper body

L1-S1 10.6 Kong and Goel (2003)

Lumbosacrum

L1-S1 9.12 40 kg upper body

Whole thoraco-lumbar
spine

T1-S1 8.40 Kong and Goel (2003) With rib cage

H-S1 8.32 Kong and Goel (2003) With rib cage

H-S1 8.91 Kong and Goel (2003) With muscle and rib

cage Head to sacrum

H-S1 6.82 Kong and Goel (2003) With preload and rib

cage

Lower thorax to
sacrum

T12-S1 7.68 40 kg upper body

T12-Pelvis 8.23 30 kg upper body

Lower thorax to pelvis T12-Pelvis 7.17 40 kg upper body

T12-Pelvis 5.84 60 kg upper body

Pope et al. (1987);
Panjabi et al. (1986);
Sandover and Dupuis
(1987)

4~6 Experimental study

Human body

4~8 Kong and Goel (2003)