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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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Computed flow-rate under pulsatile pressure. Transient flow rate under pulsatile pressure load with wall pre-stress.
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Figure 7: Computed flow-rate under pulsatile pressure. Transient flow rate under pulsatile pressure load with wall pre-stress.

Mentions: The transient flow rate computed for the pre-stressed artery by applying the pulsatile pressure pulse is shown in Figure 7. The numerically computed time averaged flow rate, 246 ml/min, was 30% higher than the measured flow rate of 188 ml/min as reported by Sinha-Roy et al., [13], for the tapered femoral artery. The measured flow rate of 188 ml/min was obtained using Doppler flow wire for the tapered femoral artery. The difference between the computed and measured value could be because of Doppler measurements, which are based on average peak velocity (APV) and have been reported to register a lower flow rate than actual [31-33].


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)

Computed flow-rate under pulsatile pressure. Transient flow rate under pulsatile pressure load with wall pre-stress.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 7: Computed flow-rate under pulsatile pressure. Transient flow rate under pulsatile pressure load with wall pre-stress.
Mentions: The transient flow rate computed for the pre-stressed artery by applying the pulsatile pressure pulse is shown in Figure 7. The numerically computed time averaged flow rate, 246 ml/min, was 30% higher than the measured flow rate of 188 ml/min as reported by Sinha-Roy et al., [13], for the tapered femoral artery. The measured flow rate of 188 ml/min was obtained using Doppler flow wire for the tapered femoral artery. The difference between the computed and measured value could be because of Doppler measurements, which are based on average peak velocity (APV) and have been reported to register a lower flow rate than actual [31-33].

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