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Arterial elasticity imaging: comparison of finite-element analysis models with high-resolution ultrasound speckle tracking.

Park DW, Richards MS, Rubin JM, Hamilton J, Kruger GH, Weitzel WF - Cardiovasc Ultrasound (2010)

Bottom Line: The nonlinear mechanical properties of internal organs and tissues may be measured with unparalleled precision using ultrasound imaging with phase-sensitive speckle tracking.The many potential applications of this important noninvasive diagnostic approach include measurement of arterial stiffness, which is associated with numerous major disease processes.Use of the pressure equalization technique during imaging resulted in average strain values of 26% and 18% at the top and sides, respectively, compared to 5% and 2%, at the top and sides, respectively, under physiologic pressure.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Internal Medicine, University of Michigan, Ann Arbor, Michigan, USA.

ABSTRACT

Background: The nonlinear mechanical properties of internal organs and tissues may be measured with unparalleled precision using ultrasound imaging with phase-sensitive speckle tracking. The many potential applications of this important noninvasive diagnostic approach include measurement of arterial stiffness, which is associated with numerous major disease processes. The accuracy of previous ultrasound measurements of arterial stiffness and vascular elasticity has been limited by the relatively low strain of nonlinear structures under normal physiologic pressure and the measurement assumption that the effect of the surrounding tissue modulus might be ignored in both physiologic and pressure equalized conditions.

Methods: This study performed high-resolution ultrasound imaging of the brachial artery in a healthy adult subject under normal physiologic pressure and the use of external pressure (pressure equalization) to increase strain. These ultrasound results were compared to measurements of arterial strain as determined by finite-element analysis models with and without a surrounding tissue, which was represented by homogenous material with fixed elastic modulus.

Results: Use of the pressure equalization technique during imaging resulted in average strain values of 26% and 18% at the top and sides, respectively, compared to 5% and 2%, at the top and sides, respectively, under physiologic pressure. In the artery model that included surrounding tissue, strain was 19% and 16% under pressure equalization versus 9% and 13% at the top and sides, respectively, under physiologic pressure. The model without surrounding tissue had slightly higher levels of strain under physiologic pressure compared to the other model, but the resulting strain values under pressure equalization were > 60% and did not correspond to experimental values.

Conclusions: Since pressure equalization may increase the dynamic range of strain imaging, the effect of the surrounding tissue on strain should be incorporated into models of arterial strain, particularly when the pressure equalization technique is used.

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Related in: MedlinePlus

Stress-strain curves for FEA modeling. Stress-strain relationship for bovine arterial wall (a) and surrounding tissue (b). The linear approximations of Young's modulus used in the finite-element analysis (FEA) model are summarized in Table 1.
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Figure 4: Stress-strain curves for FEA modeling. Stress-strain relationship for bovine arterial wall (a) and surrounding tissue (b). The linear approximations of Young's modulus used in the finite-element analysis (FEA) model are summarized in Table 1.

Mentions: Figure 4 provides the results of the bovine artery and surrounding tissue microelastometer experiments as stress-strain curves. It can be seen that although strain is nonlinear overall, it can be approximated as piecewise linear function over each of the physiologic and pressure equalization ranges. Table 1 gives the Young's modulus values determined for each pressure range, using Equation 2, where σ is the change in pressure in kilopascals inside the artery and ε is the strain. Figure 5(a) shows the boundary conditions and mesh on the artery model with surrounding tissue. Figure 5(b) shows the strain distribution in the tissue under physiologic pressure. As the internal pressure increases from 80 to 120 mmHg, the radius of the artery increases, but the thickness of the arterial wall decreases. From Figure 5(b) it can be seen that the lateral sides (left and right) of the artery expand outwards, while the axial edges (top and bottom) tend to move inward (indicated as a negative strain) toward the center of the artery. In the ultrasound experiment, the subject's upper arm rests flat on a table, and pressure equalization is achieved by using the transducer to apply pressure to the arm. Thus, the bottom of the surrounding tissue is constrained while pressure is applied to the top. Under conditions of normal physiologic blood pressure of 120/80 mmHg, the transmural arterial wall pressure increases from 80 (diastolic) to 120 (systolic) mmHg. Under these conditions the artery and tissue are already under a certain amount of strain, as can be seen from Figures 4(a) and (b), resulting in a certain amount of resistance against further expansion of the vessel. A specific arterial pressure results in a force on the internal lumen wall of the artery. This force results in a displacement, or expansion of the artery. Due to the base strain offset (pre-strain) imposed due to the physiologic pressure and non-linear elastic response (steeper Young's modulus), a small displacement change occurs as the physiologic pressure pulses. As the artery expands, the arterial wall and surrounding tissue are deformed, resulting in an increasing elastic force opposing the pressure induced force. Arterial deformation reaches equilibrium when the sum of the force vectors balance (= 0), which occurs relatively quickly due to the slope of the stress-strain curve. During the pressure equalization procedure used to illicit nonlinear behavior of the arterial wall [16], an external force is applied, which results in deformation of the artery and surrounding tissue. This deformation is again balanced by the reaction force due to the elasticity of the tissue. When the reaction force exceeds the pressure-induced force, the vessel collapses. As the physiologic pressure pulses, the pressure force exceeds the external force and the artery expands again until the forces are once again in equilibrium. Due to the external force, the base strain offset (pre-strain) is removed so the expansion occurs over an area of the stress-strain curve with a lower Young's modulus, meaning that a larger displacement is necessary to balance the forces.


Arterial elasticity imaging: comparison of finite-element analysis models with high-resolution ultrasound speckle tracking.

Park DW, Richards MS, Rubin JM, Hamilton J, Kruger GH, Weitzel WF - Cardiovasc Ultrasound (2010)

Stress-strain curves for FEA modeling. Stress-strain relationship for bovine arterial wall (a) and surrounding tissue (b). The linear approximations of Young's modulus used in the finite-element analysis (FEA) model are summarized in Table 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2908573&req=5

Figure 4: Stress-strain curves for FEA modeling. Stress-strain relationship for bovine arterial wall (a) and surrounding tissue (b). The linear approximations of Young's modulus used in the finite-element analysis (FEA) model are summarized in Table 1.
Mentions: Figure 4 provides the results of the bovine artery and surrounding tissue microelastometer experiments as stress-strain curves. It can be seen that although strain is nonlinear overall, it can be approximated as piecewise linear function over each of the physiologic and pressure equalization ranges. Table 1 gives the Young's modulus values determined for each pressure range, using Equation 2, where σ is the change in pressure in kilopascals inside the artery and ε is the strain. Figure 5(a) shows the boundary conditions and mesh on the artery model with surrounding tissue. Figure 5(b) shows the strain distribution in the tissue under physiologic pressure. As the internal pressure increases from 80 to 120 mmHg, the radius of the artery increases, but the thickness of the arterial wall decreases. From Figure 5(b) it can be seen that the lateral sides (left and right) of the artery expand outwards, while the axial edges (top and bottom) tend to move inward (indicated as a negative strain) toward the center of the artery. In the ultrasound experiment, the subject's upper arm rests flat on a table, and pressure equalization is achieved by using the transducer to apply pressure to the arm. Thus, the bottom of the surrounding tissue is constrained while pressure is applied to the top. Under conditions of normal physiologic blood pressure of 120/80 mmHg, the transmural arterial wall pressure increases from 80 (diastolic) to 120 (systolic) mmHg. Under these conditions the artery and tissue are already under a certain amount of strain, as can be seen from Figures 4(a) and (b), resulting in a certain amount of resistance against further expansion of the vessel. A specific arterial pressure results in a force on the internal lumen wall of the artery. This force results in a displacement, or expansion of the artery. Due to the base strain offset (pre-strain) imposed due to the physiologic pressure and non-linear elastic response (steeper Young's modulus), a small displacement change occurs as the physiologic pressure pulses. As the artery expands, the arterial wall and surrounding tissue are deformed, resulting in an increasing elastic force opposing the pressure induced force. Arterial deformation reaches equilibrium when the sum of the force vectors balance (= 0), which occurs relatively quickly due to the slope of the stress-strain curve. During the pressure equalization procedure used to illicit nonlinear behavior of the arterial wall [16], an external force is applied, which results in deformation of the artery and surrounding tissue. This deformation is again balanced by the reaction force due to the elasticity of the tissue. When the reaction force exceeds the pressure-induced force, the vessel collapses. As the physiologic pressure pulses, the pressure force exceeds the external force and the artery expands again until the forces are once again in equilibrium. Due to the external force, the base strain offset (pre-strain) is removed so the expansion occurs over an area of the stress-strain curve with a lower Young's modulus, meaning that a larger displacement is necessary to balance the forces.

Bottom Line: The nonlinear mechanical properties of internal organs and tissues may be measured with unparalleled precision using ultrasound imaging with phase-sensitive speckle tracking.The many potential applications of this important noninvasive diagnostic approach include measurement of arterial stiffness, which is associated with numerous major disease processes.Use of the pressure equalization technique during imaging resulted in average strain values of 26% and 18% at the top and sides, respectively, compared to 5% and 2%, at the top and sides, respectively, under physiologic pressure.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Internal Medicine, University of Michigan, Ann Arbor, Michigan, USA.

ABSTRACT

Background: The nonlinear mechanical properties of internal organs and tissues may be measured with unparalleled precision using ultrasound imaging with phase-sensitive speckle tracking. The many potential applications of this important noninvasive diagnostic approach include measurement of arterial stiffness, which is associated with numerous major disease processes. The accuracy of previous ultrasound measurements of arterial stiffness and vascular elasticity has been limited by the relatively low strain of nonlinear structures under normal physiologic pressure and the measurement assumption that the effect of the surrounding tissue modulus might be ignored in both physiologic and pressure equalized conditions.

Methods: This study performed high-resolution ultrasound imaging of the brachial artery in a healthy adult subject under normal physiologic pressure and the use of external pressure (pressure equalization) to increase strain. These ultrasound results were compared to measurements of arterial strain as determined by finite-element analysis models with and without a surrounding tissue, which was represented by homogenous material with fixed elastic modulus.

Results: Use of the pressure equalization technique during imaging resulted in average strain values of 26% and 18% at the top and sides, respectively, compared to 5% and 2%, at the top and sides, respectively, under physiologic pressure. In the artery model that included surrounding tissue, strain was 19% and 16% under pressure equalization versus 9% and 13% at the top and sides, respectively, under physiologic pressure. The model without surrounding tissue had slightly higher levels of strain under physiologic pressure compared to the other model, but the resulting strain values under pressure equalization were > 60% and did not correspond to experimental values.

Conclusions: Since pressure equalization may increase the dynamic range of strain imaging, the effect of the surrounding tissue on strain should be incorporated into models of arterial strain, particularly when the pressure equalization technique is used.

Show MeSH
Related in: MedlinePlus