Page 138 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

BIOMECHANICS OF THE RESPIRATORY MUSCLES 115

and the change in muscle length is assumed to be exponential, similar to those of connective tissues,
while the characteristic equation of the contractile element combines the tension-length and the
force-velocity relationships of the muscle with the neural input signal (Winter and Bagley, 1987).
Hill’s muscle model was implemented in a study aimed to determine the forces generated by four
respiratory muscles from both sides of the chest wall (e.g., sternomastoid, external intercostals, rectus
abdominis, and external oblique) during different respiratory maneuvers (Hill, 1938; Ratnovsky et al.,
2003; Winter, 1990). The constant parameters for the model were extracted either from the literatures
or were measured from cadavers. Linear extrapolation was done to determine the variation in
respiratory muscles length at lung volume different than RV, FRC, and TLC during respiration. EMG
signal is depicted from the vicinity near the electrode, and it represents the electrical activity of a
skeletal muscle with a typical width of 5 cm and length of up to 30 cm. Therefore, for the wide muscles
(e.g., external intercostal and external oblique) it was assumed that a muscle unit in the vicinity of
the electrodes contributes to the EMG signal. Thus, the total muscle force from these muscles was
calculated as the sum of all the parallel units. The averaged forces developed by the abdominal mus-
cles, the sternomastoid muscles, and the fibers of the external intercostal muscles in one intercostal
space during low breathing efforts (i.e., expiration from 50 to 60 percent VC to 30 to 40 percent VC
or inspiration from 30 to 40 percent VC to 50 to 60 percent VC) were about 10 N, 2 N, and 8 N,
respectively. At high respiratory effort (i.e., expiring from 90 to 80 percent VC to RV and inspiring
from RV to 80 percent VC) these forces increased to about 40 to 60 N, 12 N, and 30 N, respectively.
The coordinated performance of respiratory muscles from both sides of the chest wall induces its
displacement during lung ventilation. Lung ventilation efficacy, therefore, may be influenced from
imbalance in the function of the muscles between the two sides. In healthy subjects a highly sym-
metrical performance both in terms of the value of the forces and the recruitment of the muscles was
observed in four respiratory muscles (Ratnovsky et al., 2003).
The same model was also employed to study the forces developed by the external oblique, ster-
nomastoid, and external intercostal muscles in emphysematous patients after a single-lung transplant
surgery (Ratnovsky and Elad, 2005). Forces developed by the muscles on the side of the transplanted
lung were compared with those of the other side, which has the diseased lung. The averaged values
for maximal forces at any breathing effort calculated from the muscles located at the side of the
transplanted lung were higher (0.66, 56, and 18 N at low breathing efforts and 7.3, 228, and 22 N at
high breathing efforts for the sternomastoid, external intercostal, and external oblique, respectively)
than those calculated for muscles on the side of the native (i.e., diseased) lung (0.56, 20.22, and 3 N at
low breathing efforts and 5.64, 132, and 6 N at high breathing efforts, respectively).

5.4 MODELS OF CHEST WALL MECHANICS

The human chest wall is a complex structure, and the contribution of its different components to effi-
cient respiration has been the subject of numerous mechanical and mathematical models.

5.4.1 One-Dimensional Chest Wall Model
In early models, the chest wall was simulated as one compartment of the rib cage with a single
degree of freedom (Fig. 5.2). It was described as a single cylinder containing three moving, massless
bodies that represent the rib cage, the diaphragm, and the abdomen (Primiano, 1982). An electrical
analog was used to examine the following limited cases: (1) a very stiff rib cage (as in adult normal
breathing) that moves relative to the skeleton as a single unit; (2) a very flaccid rib cage (represent-
ing a quadriplegic patient); and (3) Mueller maneuver, which is defined by a complete obstruction
of the airway opening, such that lung volume can change only by compressing the gas in the lungs.
A pneumatic analog of the inspiratory musculature was used in a quasi-static mechanical model
(Fig. 5.3) in order to examine theoretically the forces that act on the rib cage and the influence of lung
volume changes on the area of apposition of the diaphragm to the rib cage (Macklem et al., 1983).