PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Andrew Belmonte, Hope Shaffer.

Title:The misuse of the Laplace Law for estimating stiffness of biological vessels and an alternative method
Seminar:Seminar on Mathematics in the Bio and Geo Sciences
Speaker:Francesco Costanzo, Dept of Engineering Science & Mechanics, Penn State
Abstract:
Because elastic properties of muscle such as modulus of elasticity, or "stiffness" are affected by disease, age, medical interventions (e.g., surgery) and therapy, there is a need to experimentally estimate material properties of vessels in the human body both in vitro and in vivo. Stiffness of the wall muscle of the lumen in the gastrointestinal (GI) tract is commonly quantified in vitro by measuring the deformations of excised luminal segments in response to applied transmural pressure increases and extensional loads. To measure stiffness in vivo, transmural pressure increases are often estimated using manometry where accessible. In both applications, total wall averaged hoop stress is plotted against a strain measure and the slope interpreted as an elastic modulus. Hoop stress is often estimated using the "Laplace law," a static force balance in the limit of an infinitesimally thin vessel wall. We show that the Laplace law predicts the total stress incorrectly in the esophagus and, by extension, in most GI and cardiovascular vessels, as a result of the generally small relative transmural pressure differences required to distend relatively thick luminal wall layers of soft biological tissue. Furthermore, because muscle and other biological tissue are closely volume-preserving, mechanically sensible quantifications of stiffness require the removal of the hydrostatic contribution to total stress due to incompressibility in order to estimate a modulus of elasticity by quantifying stress vs. strain. 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 practical method for estimating a mechanically viable effective 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.

Room Reservation Information

Room Number:MB106
Date:08 / 31 / 2011
Time:01:00pm - 02:00pm