Page 143 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

120 BIOMECHANICS OF THE HUMAN BODY

(e.g., rectus abdominis, external and internal oblique, and transverse abdominis), which act as actu-
ators of the mobile rib cage. The geometry parameters of the model components (e.g., rib length and
angle corresponding to the cephacaudal direction, muscle fiber orientation, and muscle length and
position) and their variation with lung volumes were derived from the literature (Ratnovsky et al.,
2003) and observation of cadavers. Assuming a quasi-static equilibrium at each lung volume sets of
force balance equations were constructed (Ratnovsky et al., 2005). The model input parameters were
mouth pressure, lung volume and the forces of the sternomastoid, external intercostals, external
oblique, and rectus abdominis that were computed from EMG measurements (Ratnovsky et al., 2003).
The instantaneous work done by each of the respiratory muscle during breathing was calculated
as the product of the instantaneous force and the corresponding length change at any lung volume.
The overall work performed by each of the respiratory muscle during a given breathing phase of
inspiration or expiration was calculated from the area under the curve of the instantaneous work
(Ratnovsky et al., 2005). The results show that the inspiratory muscles performed work even at rel-
atively low efforts, while the expiratory muscles produced work only at high expiratory efforts
(i.e., average value increased from 0 to 1 mJ). The work of the diaphragm was found to be significantly
higher than those of the external intercostals and sternomastoid muscles. However, the diaphragm
work decreased as lung volume increased, while the work done by the sternomastoid and external
intercostals increased with lung volume.

5.4.3 Three-Dimensional Chest Wall Model
A three-dimensional model of the canine chest wall geometry was developed for finite element
analysis of the forces of the intercostal muscles (Loring and Woodbridge, 1991). Accurate dimen-
sions were used to construct the geometry of the ribs and sternum as well as the orientation of the
external, internal, and parasternal intercostal muscles. The forces of the intercostal muscles were
applied first at a single intercostal space and then over the entire rib cage. In the first case the action
of both the external and internal intercostal muscles was to draw the ribs together. However, in the
second case the result was a prominent motion of the sternum and all ribs in the direction consistent
with the traditional view of intercostal muscle action. The external intercostal forces had an inspira-
tory effect with cephalad motion of the sternum and a “pump-handle” motion of the ribs, while the
internal intercostal forces had an expiratory effect.
A similar finite element model for the human chest wall was also developed in order to simulate
the action of the respiratory muscles (Loring, 1992). The external, internal, parasternal intercostal,
levator costae, and cervical accessory muscles were modeled with forces whose position and orien-
tations were consistent with the distribution of the muscles in two human cadavers. All muscle forces
were equivalent to approximately one-fifth of the maximal stress of a tetanized skeletal muscle. The
model predictions revealed that the external intercostal, internal intercostal, and cervical accessory
muscles cause large displacements of the sternum and large pump handle rotations of the ribs about
their spinal ends, but cause minor lateral movements of the lateral portions of the ribs. On the other
hand, the parasternal and the levator costae cause prominent upward and outward displacements of
the lateral portion of the ribs, expanding the transverse diameter of the rib cage and cause only a
small downward displacement of the sternum.

REFERENCES

Abraham, K. A., H. Feingold, D. D. Fuller, M. Jenkins, J. H. Mateika, and R. F. Fregosi. 2002. Respiratory-related
activation of human abdominal muscles during exercise. J Physiol. 541(Pt 2):653–663.
Agostoni, E., and W. O. Fenn. 1960. Velocity of muscle shortening as a limiting factor in respiratory air flow.
J Appl Physiol. 15:349–353.
Ambrosino, N., C. Opasich, P. Crotti, F. Cobelli, L. Tavazzi, and C. Rampulla. 1994. Breathing pattern, ventila-
tory drive and respiratory muscle strength in patients with chronic heart failure. Eur Respir J. 7(1):17–22.