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Pulsatile arterial wall-blood flow interaction with wall pre-stress computed using an inverse algorithm.

Das A, Paul A, Taylor MD, Banerjee RK - Biomed Eng Online (2015)

Bottom Line: Under physiologic pulsatile pressure applied to the pre-stressed artery, the time averaged longitudinal stress was found to be 42.5% higher than the circumferential stresses.The results of this study are similar to the results reported by Zhang et al., (2005) for the left anterior descending coronary artery.The wall stresses were higher in magnitude in the longitudinal direction, under physiologic pressure after incorporating the effect of in-vivo axial stretch and pressure loading.

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ABSTRACT

Background: The computation of arterial wall deformation and stresses under physiologic conditions requires a coupled compliant arterial wall-blood flow interaction model. The in-vivo arterial wall motion is constrained by tethering from the surrounding tissues. This tethering, together with the average in-vivo pressure, results in wall pre-stress. For an accurate simulation of the physiologic conditions, it is important to incorporate the wall pre-stress in the computational model. The computation of wall pre-stress is complex, as the un-loaded and un-tethered arterial shape with residual stress is unknown. In this study, the arterial wall deformation and stresses in a canine femoral artery under pulsatile pressure was computed after incorporating the wall pre-stresses. A nonlinear least square optimization based inverse algorithm was developed to compute the in-vivo wall pre-stress.

Methods: First, the proposed inverse algorithm was used to obtain the un-loaded and un-tethered arterial geometry from the unstressed in-vivo geometry. Then, the un-loaded, and un-tethered arterial geometry was pre-stressed by applying a mean in-vivo pressure of 104.5 mmHg and an axial stretch of 48% from the un-tethered length. Finally, the physiologic pressure pulse was applied at the inlet and the outlet of the pre-stressed configuration to calculate the in-vivo deformation and stresses. The wall material properties were modeled with an incompressible, Mooney-Rivlin model derived from previously published experimental stress-strain data (Attinger et al., 1968).

Results: The un-loaded and un-tethered artery geometry computed by the inverse algorithm had a length, inner diameter and thickness of 35.14 mm, 3.10 mm and 0.435 mm, respectively. The pre-stressed arterial wall geometry was obtained by applying the in-vivo axial-stretch and average in-vivo pressure to the un-loaded and un-tethered geometry. The length of the pre-stressed artery, 51.99 mm, was within 0.01 mm (0.019%) of the in-vivo length of 52.0 mm; the inner diameter of 3.603 mm was within 0.003 mm (0.08%) of the corresponding in-vivo diameter of 3.6 mm, and the thickness of 0.269 mm was within 0.0015 mm (0.55%) of the in-vivo thickness of 0.27 mm. Under physiologic pulsatile pressure applied to the pre-stressed artery, the time averaged longitudinal stress was found to be 42.5% higher than the circumferential stresses. The results of this study are similar to the results reported by Zhang et al., (2005) for the left anterior descending coronary artery.

Conclusions: An inverse method was adopted to compute physiologic pre-stress in the arterial wall before conducting pulsatile hemodynamic calculations. The wall stresses were higher in magnitude in the longitudinal direction, under physiologic pressure after incorporating the effect of in-vivo axial stretch and pressure loading.

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Application of the inverse algorithm to a patient-specific artery. Intermediate steps of the inverse algorithm. A) Lumen surface in form of triangular mesh of STL triangles obtained by geometry reconstruction. B) Arterial wall geometry in form of STL-mesh of surface triangles. C) Finite element mesh of the wall geometry using 8 node (or 20 node) hexahedral elements. D) Constraints imposed on the arterial wall motion in each shrink and fit iteration. Rigid contact surface superimposed on the outer arterial wall surface and extended at the ends, to maintain arterial shape during the longitudinal (axial) shrink or stretch operation. Contact surface meshed with 4-noded quadrilateral elements. Only in-plane radial motion in dr-dθ plane allowed for the nodes of the inlet and outlet surfaces. Additionally, nodes of the outlets are allowed to move in dz direction during longitudinal stretch or shrink operation.
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Figure 9: Application of the inverse algorithm to a patient-specific artery. Intermediate steps of the inverse algorithm. A) Lumen surface in form of triangular mesh of STL triangles obtained by geometry reconstruction. B) Arterial wall geometry in form of STL-mesh of surface triangles. C) Finite element mesh of the wall geometry using 8 node (or 20 node) hexahedral elements. D) Constraints imposed on the arterial wall motion in each shrink and fit iteration. Rigid contact surface superimposed on the outer arterial wall surface and extended at the ends, to maintain arterial shape during the longitudinal (axial) shrink or stretch operation. Contact surface meshed with 4-noded quadrilateral elements. Only in-plane radial motion in dr-dθ plane allowed for the nodes of the inlet and outlet surfaces. Additionally, nodes of the outlets are allowed to move in dz direction during longitudinal stretch or shrink operation.

Mentions: In addition to the idealized axisymmetric geometry, the algorithm was tested for a 3D patient-specific arterial geometry. This was done to test the proposed steps (Figure 3) as described in the methods section, for a patient-specific case. The intermediate steps of the inverse algorithm for a patient-specific artery are shown in Figure 9. Specifically, Figure 9A shows the lumen boundary, which in the patient-specific case will be obtained from image reconstruction. As shown in Figure 1A, for the straight artery case, this surface is simply a cylindrical surface. Similarly, Figure 9B shows the arterial wall geometry obtained by adding wall thickness using nodal normal defined by Eq. 1. The corresponding wall geometry for the straight artery case (Figure 1C) was constructed by adapting the same procedure. Next, the finite element mesh used by the longitudinal and radial shrink operators for the patient-specific case is presented in Figure 9C, whereas Figure 1D shows the same for the straight artery. Finally, the boundary conditions and constraints imposed on the finite element mesh for the patient-specific case and the straight artery case are shown in Figure 9C and 1D, respectively. The complete pressure-flow analysis using blood-arterial wall interaction for such a patient-specific case will be presented in future.


Pulsatile arterial wall-blood flow interaction with wall pre-stress computed using an inverse algorithm.

Das A, Paul A, Taylor MD, Banerjee RK - Biomed Eng Online (2015)

Application of the inverse algorithm to a patient-specific artery. Intermediate steps of the inverse algorithm. A) Lumen surface in form of triangular mesh of STL triangles obtained by geometry reconstruction. B) Arterial wall geometry in form of STL-mesh of surface triangles. C) Finite element mesh of the wall geometry using 8 node (or 20 node) hexahedral elements. D) Constraints imposed on the arterial wall motion in each shrink and fit iteration. Rigid contact surface superimposed on the outer arterial wall surface and extended at the ends, to maintain arterial shape during the longitudinal (axial) shrink or stretch operation. Contact surface meshed with 4-noded quadrilateral elements. Only in-plane radial motion in dr-dθ plane allowed for the nodes of the inlet and outlet surfaces. Additionally, nodes of the outlets are allowed to move in dz direction during longitudinal stretch or shrink operation.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4306109&req=5

Figure 9: Application of the inverse algorithm to a patient-specific artery. Intermediate steps of the inverse algorithm. A) Lumen surface in form of triangular mesh of STL triangles obtained by geometry reconstruction. B) Arterial wall geometry in form of STL-mesh of surface triangles. C) Finite element mesh of the wall geometry using 8 node (or 20 node) hexahedral elements. D) Constraints imposed on the arterial wall motion in each shrink and fit iteration. Rigid contact surface superimposed on the outer arterial wall surface and extended at the ends, to maintain arterial shape during the longitudinal (axial) shrink or stretch operation. Contact surface meshed with 4-noded quadrilateral elements. Only in-plane radial motion in dr-dθ plane allowed for the nodes of the inlet and outlet surfaces. Additionally, nodes of the outlets are allowed to move in dz direction during longitudinal stretch or shrink operation.
Mentions: In addition to the idealized axisymmetric geometry, the algorithm was tested for a 3D patient-specific arterial geometry. This was done to test the proposed steps (Figure 3) as described in the methods section, for a patient-specific case. The intermediate steps of the inverse algorithm for a patient-specific artery are shown in Figure 9. Specifically, Figure 9A shows the lumen boundary, which in the patient-specific case will be obtained from image reconstruction. As shown in Figure 1A, for the straight artery case, this surface is simply a cylindrical surface. Similarly, Figure 9B shows the arterial wall geometry obtained by adding wall thickness using nodal normal defined by Eq. 1. The corresponding wall geometry for the straight artery case (Figure 1C) was constructed by adapting the same procedure. Next, the finite element mesh used by the longitudinal and radial shrink operators for the patient-specific case is presented in Figure 9C, whereas Figure 1D shows the same for the straight artery. Finally, the boundary conditions and constraints imposed on the finite element mesh for the patient-specific case and the straight artery case are shown in Figure 9C and 1D, respectively. The complete pressure-flow analysis using blood-arterial wall interaction for such a patient-specific case will be presented in future.

Bottom Line: Under physiologic pulsatile pressure applied to the pre-stressed artery, the time averaged longitudinal stress was found to be 42.5% higher than the circumferential stresses.The results of this study are similar to the results reported by Zhang et al., (2005) for the left anterior descending coronary artery.The wall stresses were higher in magnitude in the longitudinal direction, under physiologic pressure after incorporating the effect of in-vivo axial stretch and pressure loading.

View Article: PubMed Central - HTML - PubMed

ABSTRACT

Background: The computation of arterial wall deformation and stresses under physiologic conditions requires a coupled compliant arterial wall-blood flow interaction model. The in-vivo arterial wall motion is constrained by tethering from the surrounding tissues. This tethering, together with the average in-vivo pressure, results in wall pre-stress. For an accurate simulation of the physiologic conditions, it is important to incorporate the wall pre-stress in the computational model. The computation of wall pre-stress is complex, as the un-loaded and un-tethered arterial shape with residual stress is unknown. In this study, the arterial wall deformation and stresses in a canine femoral artery under pulsatile pressure was computed after incorporating the wall pre-stresses. A nonlinear least square optimization based inverse algorithm was developed to compute the in-vivo wall pre-stress.

Methods: First, the proposed inverse algorithm was used to obtain the un-loaded and un-tethered arterial geometry from the unstressed in-vivo geometry. Then, the un-loaded, and un-tethered arterial geometry was pre-stressed by applying a mean in-vivo pressure of 104.5 mmHg and an axial stretch of 48% from the un-tethered length. Finally, the physiologic pressure pulse was applied at the inlet and the outlet of the pre-stressed configuration to calculate the in-vivo deformation and stresses. The wall material properties were modeled with an incompressible, Mooney-Rivlin model derived from previously published experimental stress-strain data (Attinger et al., 1968).

Results: The un-loaded and un-tethered artery geometry computed by the inverse algorithm had a length, inner diameter and thickness of 35.14 mm, 3.10 mm and 0.435 mm, respectively. The pre-stressed arterial wall geometry was obtained by applying the in-vivo axial-stretch and average in-vivo pressure to the un-loaded and un-tethered geometry. The length of the pre-stressed artery, 51.99 mm, was within 0.01 mm (0.019%) of the in-vivo length of 52.0 mm; the inner diameter of 3.603 mm was within 0.003 mm (0.08%) of the corresponding in-vivo diameter of 3.6 mm, and the thickness of 0.269 mm was within 0.0015 mm (0.55%) of the in-vivo thickness of 0.27 mm. Under physiologic pulsatile pressure applied to the pre-stressed artery, the time averaged longitudinal stress was found to be 42.5% higher than the circumferential stresses. The results of this study are similar to the results reported by Zhang et al., (2005) for the left anterior descending coronary artery.

Conclusions: An inverse method was adopted to compute physiologic pre-stress in the arterial wall before conducting pulsatile hemodynamic calculations. The wall stresses were higher in magnitude in the longitudinal direction, under physiologic pressure after incorporating the effect of in-vivo axial stretch and pressure loading.

Show MeSH
Related in: MedlinePlus