6.5 Residual Stress
275
to restore the geometry in the uncut specimen. In general, the cutting procedure
depends on the problem, the tools available, and the expertise of the investigator.
Unfortunately, tissue dissection suffers from important drawbacks that limit its
usefulness for determining residual stress in living organisms. Clearly, cutting is
an invasive process that generally would not be desirable in a clinical setting, and
the tissue of interest must be free of external loads and constraints. It is unlikely
that a surgeon would want to remove the heart from a patient’s chest, cut it to
estimate residual stress, and put it back just to improve the accuracy of wall stress
calculations. Moreover, determining residual stress patterns via dissection usually
entails computational modeling that requires knowing constitutive relations, which
vary from patient to patient. As we will see, barring a noninvasive way to determine
residual stress, estimates of stress in loaded tissues provided by patient-specific
models could contain significant errors.
In addition, even in a research laboratory, each cut may relieve only a portion of
the residual stress, leading to an important question: How many cuts are needed?
Sometimes just a few cuts can provide a reasonable estimate of stress at the tissue
level. But what about at microscopic levels, where most of the stress-generating
activity occurs? Suppose we dissociate a tissue into individual cells. Is that enough?
What about the stresses in actin fibers and microtubules? In an isolated cell, these
and other elements can be in various states of tension or compression, as long as the
net cytoskeletal force vanishes.
In theory, one can keep dissecting a tissue almost indefinitely. In this respect, the
definition of the term “residual stress” is somewhat arbitrary. Nevertheless, tissue
dissection provides a useful way to estimate residual stress in soft tissues. These
and other issues warrant additional study.
Example 6.6 At Betty’s urging, Barney volunteered to donate a portion of his aorta
to a study of residual stress in arteries. 6 When a length of aorta was removed from
his chest, the distance between two tissue labels shortened, indicating that the artery
was stretched axially in vivo. While in Barney, therefore, the vessel could be treated
as a circular tube subjected to blood pressure p i and axial stretch ratio λ.
To characterize residual stress in the isolated artery, a relatively thin slice was
dissected and cut transmurally. The section immediately opened into a circular
sector with geometry defined by the inner radius a 0 , outer radius b 0 , and opening
angle φ (Fig. 6.7).
To estimate wall stress, consider a first-approximation model for the aorta
consisting of a single layer of incompressible orthotropic tissue with the strainenergy density function (Chuong and Fung 1986)
6 No worries—Barney was fine after the artery was sewn up and re-implanted.
275
to restore the geometry in the uncut specimen. In general, the cutting procedure
depends on the problem, the tools available, and the expertise of the investigator.
Unfortunately, tissue dissection suffers from important drawbacks that limit its
usefulness for determining residual stress in living organisms. Clearly, cutting is
an invasive process that generally would not be desirable in a clinical setting, and
the tissue of interest must be free of external loads and constraints. It is unlikely
that a surgeon would want to remove the heart from a patient’s chest, cut it to
estimate residual stress, and put it back just to improve the accuracy of wall stress
calculations. Moreover, determining residual stress patterns via dissection usually
entails computational modeling that requires knowing constitutive relations, which
vary from patient to patient. As we will see, barring a noninvasive way to determine
residual stress, estimates of stress in loaded tissues provided by patient-specific
models could contain significant errors.
In addition, even in a research laboratory, each cut may relieve only a portion of
the residual stress, leading to an important question: How many cuts are needed?
Sometimes just a few cuts can provide a reasonable estimate of stress at the tissue
level. But what about at microscopic levels, where most of the stress-generating
activity occurs? Suppose we dissociate a tissue into individual cells. Is that enough?
What about the stresses in actin fibers and microtubules? In an isolated cell, these
and other elements can be in various states of tension or compression, as long as the
net cytoskeletal force vanishes.
In theory, one can keep dissecting a tissue almost indefinitely. In this respect, the
definition of the term “residual stress” is somewhat arbitrary. Nevertheless, tissue
dissection provides a useful way to estimate residual stress in soft tissues. These
and other issues warrant additional study.
Example 6.6 At Betty’s urging, Barney volunteered to donate a portion of his aorta
to a study of residual stress in arteries. 6 When a length of aorta was removed from
his chest, the distance between two tissue labels shortened, indicating that the artery
was stretched axially in vivo. While in Barney, therefore, the vessel could be treated
as a circular tube subjected to blood pressure p i and axial stretch ratio λ.
To characterize residual stress in the isolated artery, a relatively thin slice was
dissected and cut transmurally. The section immediately opened into a circular
sector with geometry defined by the inner radius a 0 , outer radius b 0 , and opening
angle φ (Fig. 6.7).
To estimate wall stress, consider a first-approximation model for the aorta
consisting of a single layer of incompressible orthotropic tissue with the strainenergy density function (Chuong and Fung 1986)
6 No worries—Barney was fine after the artery was sewn up and re-implanted.