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The quantification of the stiffness of tubular biological structures is oftenobtained, both in vivo and in vitro, as the slope of total transmural hoopstress plotted against hoop strain. Total hoop stress is typically estimatedusing the "Laplace law." We show that this procedure is fundamentally flawedfor two reasons: Firstly, the Laplace law predicts total stress incorrectly forbiological vessels. Furthermore, because muscle and other biological tissue areclosely volume-preserving, quantifications of elastic modulus require theremoval of the contribution to total stress from incompressibility. We showthat this hydrostatic contribution to total stress has a strongmaterial-dependent nonlinear response to deformation that is difficult topredict or measure. To address this difficulty, we propose a new practicalmethod to estimate a mechanically viable modulus of elasticity that can beapplied both in vivo and in vitro using the same measurements as currentmethods, with care taken to record the reference state. To be insensitive toincompressibility, our method is based on shear stress rather than hoop stress,and provides a true measure of the elastic response without application of theLaplace law. We demonstrate the accuracy of our method using a mathematicalmodel of tube inflation with multiple constitutive models. We also re-analyzean in vivo study from the gastro-intestinal literature that applied thestandard approach and concluded that a drug-induced change in elastic modulusdepended on the protocol used to distend the esophageal lumen. Our new methodremoves this protocol-dependent inconsistency in the previous result.

The Invalidity of the Laplace Law for Biological Vessels and of Estimating Elastic Modulus from Total Stress vs. Strain: a New Practical Method