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Research Papers

Deformations and End Effects in Isolated Blood Vessel Testing

[+] Author and Article Information
Kenneth L. Monson1

Department of Mechanical Engineering, University of Utah, 50 South Central Campus Drive, MEB 2132, Salt Lake City, UT 84112ken.monson@utah.edu

Vishwas Mathur

Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112

David A. Powell

Department of Mechanical Engineering, Stanford University, Stanford, CA 94305

1

Corresponding author

J Biomech Eng 133(1), 011005 (Dec 23, 2010) (6 pages) doi:10.1115/1.4002935 History: Received June 28, 2010; Revised October 13, 2010; Posted November 02, 2010; Published December 23, 2010; Online December 23, 2010

Blood vessels are commonly studied in isolation to define their mechanical and biological properties under controlled conditions. While sections of the wall are sometimes tested, vessels are most often attached to needles and examined in their natural cylindrical configuration where combinations of internal pressure and axial force can be applied to mimic in vivo conditions. Attachments to needles, however, constrain natural vessel response, resulting in a complex state of deformation that is not easily determined. As a result, measurements are usually limited to the midsection of a specimen where end effects do not extend and the deformation is homogeneous. To our knowledge, however, the boundaries of this uninfluenced midsection region have not been explored. The objective of this study was to define the extent of these end effects as a function of vessel geometry and material properties, loading conditions, and needle diameter. A computational fiber framework was used to model the response of a nonlinear anisotropic cylindrical tube, constrained radially at its ends, under conditions of axial extension and internal pressure. Individual fiber constitutive response was defined using a Fung-type strain energy function. While quantitative results depend on specific parameter values, simulations demonstrate that axial stretch is always highest near the constraint and reduces to a minimum in the uninfluenced midsection region. Circumferential stretch displays the opposite behavior. As a general rule, the length of the region disturbed by a needle constraint increases with the difference between the diameter of the needle and the equilibrium diameter of the blood vessel for the imposed loading conditions. The reported findings increase the understanding of specimen deformation in isolated vessel experiments, specifically defining considerations important to identifying a midsection region appropriate for measurement.

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Figures

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Figure 1

Needle-to-needle and midsection axial stretch values during a constant pressure (13 kPa) axial extension test. The arrow shows the path of the midsection axial stretch as pressure is increased from 0 kPa to 13 kPa, but needle position is constant. The vessel reference length was ∼2.5 mm.

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Figure 2

Predicted vessel geometry and associated axial stretch ratio for the baseline geometry loaded at 13 kPa and successively increasing values of the n-t-n stretch (1.0, 1.05, 1.10, and 1.15 from left to right)

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Figure 3

Axial and circumferential stretch ratios as functions of position along the vessel axis (data from half of the vessel shown due to symmetry; 0.0 is axial center). Pressure was constant at 13 kPa, while the n-t-n stretch varied between 1.0 and 1.15 (labels). Midsection boundaries for a threshold difference of 0.01 are plotted.

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Figure 4

(a) Axial and (b) circumferential stretch ratios as functions of vessel length for cases having pressures of 6 kPa, 13 kPa, or 20 kPa and n-t-n ratios of 1.0 or 1.15

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Figure 5

(a) Axial and (b) circumferential stretch ratios as functions of axial position for vessels with diameters ranging from 0.52 mm to 1.04 mm. All specimens having a length of 6.075 mm were pressurized at 13 kPa and were stretched axially to n-t-n ratios of either 1.0 or 1.15.

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Figure 6

(a) Axial and (b) circumferential stretch ratios as functions of axial position for vessels having lengths of 4.05 mm, 6.08 mm, and 8.10 mm. All cases were pressurized at 13 kPa and stretched axially to n-t-n ratios of 1.0 or 1.15.

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Figure 7

(a) Axial and (b) circumferential stretch ratios as functions of axial position for vessels constrained by needles having diameters equal to 0.8, 0.9, or 1.0 times the specimen diameter. All vessels had lengths of 4.05 mm, were pressurized at 13 kPa, and were stretched axially to n-t-n ratios of 1.0 or 1.15.

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Figure 8

(a) Axial and (b) circumferential stretch ratios as functions of axial position for vessels with variations in material parameters c1 and c2. All cases utilized the baseline geometry, had a n-t-n axial stretch of 1.15, and were pressurized at 13 kPa.

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