The pleural membrane is modeled as a planar collection of interconnected randomly oriented line elements. By assuming that the line elements follow the strain field of a continuum, a strain-energy function is formulated. From the strain-energy function, an explicit stress-strain equation for large deformations is derived. In the linear approximation of the stress-strain equation the shear modulus and the area modulus of the membrane are respectively found to be 2.4 and 2.8 times the tension at the reference state. The stress-strain equation for large deformations is used to predict the displacement field around a circular hole in pleura. Good agreement is found between these predictions and measurements made on ablated pleura from dog lungs. From these theoretical and experimental results the conclusion is drawn that the pleura has a significant role in carrying shear forces and maintaining the lung's shape.
[1]
T A Wilson,et al.
A strain energy function for lung parenchyma.
,
1985,
Journal of biomechanical engineering.
[2]
I. S. Sokolnikoff.
Mathematical theory of elasticity
,
1946
.
[3]
J. E. Adkins,et al.
Large Elastic Deformations
,
1971
.
[4]
D. Stamenovic,et al.
The shear modulus of liquid foam
,
1984
.
[5]
Y. Lanir.
Constitutive equations for fibrous connective tissues.
,
1983,
Journal of biomechanics.
[6]
Heinrich v. Hayek,et al.
The human lung
,
1960
.
[7]
S. Lai-Fook,et al.
Improved measurements of shear modulus and pleural membrane tension of the lung.
,
1979,
Journal of applied physiology: respiratory, environmental and exercise physiology.
[8]
S. Lai-Fook,et al.
Lung parenchyma described as a prestressed compressible material.
,
1977,
Journal of biomechanics.