  The quantification of the stiffness of tubular biological structures is often
obtained, both in vivo and in vitro, as the slope of total transmural hoop
stress plotted against hoop strain. Total hoop stress is typically estimated
using the "Laplace law." We show that this procedure is fundamentally flawed
for two reasons: Firstly, the Laplace law predicts total stress incorrectly for
biological vessels. Furthermore, because muscle and other biological tissue are
closely volume-preserving, quantifications of elastic modulus require the
removal of the contribution to total stress from incompressibility. We show
that this hydrostatic contribution to total stress has a strong
material-dependent nonlinear response to deformation that is difficult to
predict or measure. To address this difficulty, we propose a new practical
method to estimate a mechanically viable modulus of elasticity that can be
applied both in vivo and in vitro using the same measurements as current
methods, with care taken to record the reference state. To be insensitive to
incompressibility, our method is based on shear stress rather than hoop stress,
and provides a true measure of the elastic response without application of the
Laplace law. We demonstrate the accuracy of our method using a mathematical
model of tube inflation with multiple constitutive models. We also re-analyze
an in vivo study from the gastro-intestinal literature that applied the
standard approach and concluded that a drug-induced change in elastic modulus
depended on the protocol used to distend the esophageal lumen. Our new method
removes this protocol-dependent inconsistency in the previous result.
