Research Papers

Noninvasive In Vivo Determination of Residual Strains and Stresses

[+] Author and Article Information
Samir Donmazov, Senol Piskin

Department of Mechanical Engineering,
Koç University,
Sariyer, Istanbul 34450, Turkey

Kerem Pekkan

Associate Professor
Department of Mechanical Engineering,
Koç University,
Rumelifeneri Kampüsü,
Sariyer, Istanbul 34450, Turkey;
Department of Biomedical Engineering,
Carnegie Mellon University,
Pittsburgh, PA 15219
e-mail: kpekkan@ku.edu.tr

1Corresponding author.

Manuscript received November 6, 2014; final manuscript received March 6, 2015; published online April 15, 2015. Assoc. Editor: Thao (Vicky) Nguyen.

J Biomech Eng 137(6), 061011 (Jun 01, 2015) (10 pages) Paper No: BIO-14-1551; doi: 10.1115/1.4030071 History: Received November 06, 2014; Revised March 06, 2015; Online April 15, 2015

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.

Copyright © 2015 by ASME
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Fig. 1

General geometrical representation of 3D vessel wall in zero-stress reference state, unloaded state(0), unloaded state(1), and subsequent loaded states under transmural pressure and axial forces

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Fig. 2

The two-layer microstructure finite element model of residual stress generation. Series of vessel cross sections representing: (a) the stress-free open configuration of the baseline rabbit carotid artery having an effective angle of 100 deg, (b) midvessel closure toward the fully closed unloaded state achieved by thrust elements pulling the open ends, (c) unloaded state(0), (d) unloaded state(1) with prestretch—only mesh shown, and (e) the loaded state(2)—section of vessel is shown. Material properties are then altered representing the vascular remodeling by (f) the remodeled loaded state(3) and its corresponding (g) remodeled unloaded configuration and (h) remodeled stress-free state resulting in an effective angle of 90 deg. Color and legends correspond to the magnitude of Cauchy stress distributions (mm Hg). Legend in (f) corresponds to vessel cross sections in (e) and (f), while legend in (b) corresponds to all other states.

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Fig. 3

Residual stress distribution through the arterial wall in unloaded state(0) and unloaded state(1) in (a) rabbit carotid artery, (b) rabbit thoracic, and (c) human carotid artery, respectively, compared with experimental results based on in vitro data given in (a) Ref. [22], (b) Ref. [4], and (c) Ref. [22]

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Fig. 4

Axial force distribution through the arterial wall in (a) rabbit carotid artery and (b) human carotid artery compared with results (Ref.) based on in vitro experiments [22]

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Fig. 5

Residual stress distribution through the arterial wall in unloaded state(0) and unloaded state(1) in swine iliac artery during the loading (L) and unloading (UL)




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