Noninvasive in vivo determination of residual strains and stresses

Abstract

Vascular growth and remodeling during embryonic development are associated with blood flow and pressure induced stress distribution, in which residual strains and stresses play a central role. Residual strains are typically measured by performing in vitro tests on the excised vascular tissue. In this paper, we investigated the possibility of estimating residual strains and stresses using physiological pressure-radius data obtained through in vivo noninvasive measurement techniques, such as optical coherence tomography or ultrasound modalities. This analytical approach first tested with in vitro results using experimental data sets for three different arteries such as rabbit carotid artery, rabbit thoracic artery, and human carotid artery based on Fung's pseudostrain energy function and Delfino's exponential strain energy function (SEF). We also examined residual strains and stresses in the human swine iliac artery using the in vivo experimental ultrasound data sets corresponding to the systolic-to-diastolic region only. This allowed computation of the in vivo residual stress information for loading and unloading states separately. Residual strain parameters as well as the material parameters were successfully computed with high accuracy, where the relative errors are introduced in the range of 0-7.5%. Corresponding residual stress distributions demonstrated global errors all in acceptable ranges. A slight discrepancy was observed in the computed reduced axial force. Results of computations performed based on in vivo experimental data obtained from loading and unloading states of the artery exhibited alterations in material properties and residual strain parameters as well. Emerging noninvasive measurement techniques combined with the present analytical approach can be used to estimate residual strains and stresses in vascular tissues as a precursor for growth estimates. This approach is also validated with a finite element model of a general two-layered artery, where the material remodeling states and residual strain generation are investigated.