Stress-strain analysis and the lung

Abstract

Stress is the magnitude and direction of forces acting on a body, and strain is the magnitude and direction of deformations. Constitutive equations define the relationship between stress and strain for any material. If the material can be considered homogeneous, isotropic, and elastic--that is, if the mechanical properties are uniform and independent of direction and the deformations are reversible--the constitutive equations are greatly simplified and problems of physiological interest become more tractable. Material properties may be expressed as linear elastic constants or a strain energy function. Strain energy is most suitable for large-deformation nonlinear elasticity, but such analyses are extremely complex. Theoretically, linear elasticity is limited to very small deformations, but its applicability can be expanded by considering perturbations from an initial prestressed state, but using material properties that are functions of the initial conditions. Two independent elastic constants, the bulk modulus for volume change and the shear modulus for shape change, are required to define the material properties. For problems in which the geometry of the body and the applied forces are too complex to allow an analytic solution, the body may be broken up into many small, simple elements, and the resulting matrix of equations may be simultaneously solved by a computer. The disadvantage of this finite-element analysis, in addition to its inherent complexity, is that solutions are in terms of numbers rather than equations, and determining the effect of parameters requires that a number of sample problems be solved. Nevertheless, because of its immense power, this technique has an important place in lung mechanics.