The influence of stent-graft spatial configuration on blood hemodynamic in Abdominal Aortic Aneurysm

Andrzej Polańczyk, MSc

Ireneusz Zbiciński, PhD, DSc

*Department of Heat and Mass Transfer, Faculty of Process and Environmental Engineering, Technical University of Lodz, Poland

e-mail address: andrzej@polanczyk.eu

Abstract The aim of this study was to estimate whether spatial configuration of an endovascular prosthesis can affect blood flow hemodynamic. An implant is a synthetic material graft foreign to our body which may initiate immunological reaction that comprises activation of macrophages and aggregation of blood plates. These may eventually lead to graft rejection. In this paper we concentrated on physical parameters that influence hemodynamic of blood flow through an abdominal aorta with endovascular prosthesis inside. Computational fluid dynamics (CFD) was used to estimate the behavior of blood flow in the endovascular prosthesis. 3D models of stent-grafts placed in Abdominal Aortic Aneurysm were prepared with the use of AngioCT data. Next, the ANSYS FLUENT 12.1 software was used to stimulate blood flow. The results of our study showed that spatial configuration of a stent-graft (narrows and angular bends) has an influence on blood velocity reduction and an increase risk of endovascular prosthesis occlusion. An increase in hematocrit value in area of narrows and angular bends of a stent-graft bifurcation leads to reduction in blood flow rate and wall shear stress and an increase in viscosity value in this area and as result. increase the risk of thrombosis.

Key words

CFD simulations, endovascular prosthesis, angular bends, stent-graft, CT, Abdominal Aortic Aneurysm.

1. Introduction Patients with Abdominal Aortic Aneurysm (AAA) belong to a group of high death risk. AAA is one of an urgent problem in medicine connected with postoperative complications after a stent-graft placement. Latest techniques of imaging e.g. ultrasonography, computer tomography or magnetic resonance enable a quick diagnosis of patients with AAA suspicion (Polanczyk et al 2010). One method of AAA treating is a surgical intervention with the use of endovascular prosthesis. Wall shear stresses (WSS) induced by flowing blood in places of aneurysm appearance may rupture aneurismal lesion. Therefore, an endovascular prosthesis counteracts the probability of aneurysm rupture. This technique is less invasive, however, it aggravates the risk of post-operative complications (Chong et al 2005).

Narrowness or angular bends in a bifurcated part of an artery may appeared after a stent-graft placement. This may led to disturbance in proper blood flow in a vascular system and thrombus development, resulted from small cross-section of blood flow appearance. In order to minimize post-operative complications after a stent-graft placement to AAA, researchers strive to constant modernization and creation of new solutions in the production of a stent-grafts (Owens 2006). Therefore, thorough computational analysis of this problem may become helpful.

2. Aim The purpose of this article was to determine how spatial configuration of a stent-graft, narrows and angular bends, may influence permeability of endovascular prosthesis. Calculations were based on CFD model of blood flow through abdominal part of aorta with a stent-graft inside.

3. Material and Methods Computational Fluid Dynamic (CFD) was used to examine the influence of endovascular prosthesis inserted into AAA. AngioCT data from patients, at the age 50±10 years, were used to preparation of a 3D model of a stent-graft. 3DDoctor software was used to generate spatial configuration of a stent-graft placed in Abdominal Aortic Aneurysm. Gambit 2.2.30 software was used to prepare geometry for blood flow calculation through investigated geometries. Tetrahedral elements were applied for the process of discretization. Boundary layer was used to increase accuracy of simulations. The number of mesh elements for particular endovascular prosthesis depended on its complication and was at a range of 400.000÷500.000. ANSYS FLUENT 12.1 software was used to carried out CFD simulations. The investigated 3D geometry of an endovascular prosthesis had one inlet at the top and two outlets at the bottom (Fig.1). The edges of analyzed domains were treated as a rigid walls. In a human's circular system blood flow has a pulsating character. To get closer to real conditions of blood flow, pulsating character of blood flow as a boundary condition at the inlet of analyzing 3D geometries was assumed. Mechanical properties of blood depend on red cells concentration in blood, which is described as hematocirt (Htc) (eq.1). Htc represents volumetric concentration of erythrocytes in volume of whole human blood (Bebenek 1999). (1)

where: Ve - volumetric concentration of erythrocytes in analyzed blood, m3, Vb - volume of blood, m3, To observe changes in hemodynamic of blood flow, Htc values were changed at the range of 30%÷60%.

Fig.1. A diagram of a blood flow through endovascular prosthesis in Abdominal Aortic

Aneurysm calculation. Blood density was defined as constant value of 1040 kg/m3 (Hoskins 2008). However, studies that ignored the red blood cell (RBC) contributions, which is roughly 30–55% by volume in

vivo, may be inadequate for extrapolating to in vivo conditions (Munn et al. 1996). Because of the high cell number and particulate nature of RBCs, whole blood exhibits non-Newtonian rheology. Blood belongs to non-Newtonian liquids group diluted with increase value of shear velocity γ. Because of that Quemada's model was used to describe rheological properties of blood (eq.2).

(2)

where: ηp - plasma viscosity, Pas, K - inner viscosity of erythrocytes, -, (eq.3) Htc - hematocrit, -,

(3)

where: k0, k∞ - parameters describing blood behavior, -, γ - shear velocity, 1/s, γc - boundary shear velocity, 1/s. Parameters k0, k∞ describing inner viscosity of erythrocytes, respectively for neutral and infinity shear velocity (Marcinkowska-Gapińska et al. 2007). Blood flow simulation were carried out for unsteady conditions of pulsating character of blood flow. This operation enabled us to got closer to real blood flow in human body. The time used to calculation was 1 second to be sure that it includes whole one heart cycle. We assumed that heart beats with constant frequency, at a range of 70÷80 times per minute. Therefore, we did not consider longer time of calculation.

4. Results and discussion Distribution of blood flow velocity, viscosity and wall shear stress during blood flow simulation through AAA with endovascular prosthesis inside was analyzed.

4.1. Blood flow rate Figure 2 shows distribution of velocity vectors for one of investigated objects during blood flow for different Htc value in function of time. We may observe that with increasing value of Htc in a branch with narrowness, flow rate decreased in comparison with a branch without narrowness. Respectively branch without narrowness became a main duct with use of which blood was distributed to lower part of human body.

[ml/s]

H=30%

H=40%

H=50%

H=60%

Fig.2. Blood flow rate contours for 0.10s period of time for Htc=30%, Htc=40%, Htc=50%

and Htc=60%. Increased value of Htc was connected with higher value of viscosity that involved higher drag forces. Therefore it was noticed that the branch without narrowing (Fig.4) had much higher values of flow compare with the branch with a narrow place (Fig.3). Figure 3 shows distribution of blood flow rate in function of increasing Htc value in the branch with narrowness. The highest value of flow rate for all analyzed cases was observed at 0.18 second of blood flow. We assume that this phenomena correlates with the heart cycle as near to this time period heart contrition appears.

Fig.3. Velocity distribution in branch with narrowness.

Fig.4. Velocity distribution in branch without narrowness.

In our study flow rate distribution was also different in a vessel with or without narrowness. It was observed that with increasing value of Htc, flow rate in branch with narrowness was decreasing. This supports the fact that branch without narrowness became a main duct responsible for directing blood to lower part of human body. Therefore, lower value of blood flow rate in a function of higher Htc was observed in narrowness (Fig.5).

Fig.5. Velocity distribution in narrowness of stent-graft's branch.

Table 1 shows changes of blood flow rate through endovascular prosthesis for Htc value ranging from 30%÷60%. Our results showed that with increasing value of Htc blood flow rate increased for both branches with or without narrowness. For Htc=30% average value of blood flow rate observed for branch with narrowness was 57% higher compared with a branch without narrowness. With increasing value of Htc differences in blood flow rate increased either. For Htc=60% average value of differences increased up to 63%. Table 1. Change of flow rate in function of hematocrit.

N. Hematocrit

Htc [-]

Change of

flow rate [%]

1 30 57

2 40 59

3 50 61

4 60 63

4.2. Blood viscosity Blood viscosity distribution enables to predict places with high risk of thrombus appearance. Figure 6 shows distribution of blood viscosity for 0.10 second period of time for Htc ranging from 30% to 60%.

[Pa s]

H=30%

H=40%

H=50%

H=60%

Fig.6. Blood viscosity contours for 0.10s period of time for Htc=30%, Htc=40%, Htc=50%

and Htc=60%.. We assumed, in our calculations, that blood is non-Newtonian liquid with increasing shear velocity. We observed that for increasing value of Htc (form 30% to 60%) value of blood viscosity increased in a branch with narrowness (Fig.7). Moreover, it correlated with lower value of blood flow rate followed by increased drag forces.

Fig.7. Blood viscosity distribution in branch with narrowness.

In our work comparison of two cases with and without branch narrowness showed that for place without narrowness blood viscosity decreased and simultaneously Htc value increased which was correlated with flow distribution. Higher flow rate that reduced blood viscosity appeared in a branch without narrowness (Fig.8).

Fig.8. Blood viscosity distribution in branch without narrowness.

Therefore, in narrowness increasing value of blood viscosity in a function of higher Htc was observed (Fig.9).

Fig.9. Blood viscosity distribution in narrowness of stent-graft's branch.

Table 2 shows changes of blood viscosity for blood flow through endovascular prosthesis for Htc value at a range of 30%÷60%. It is was noticed that differences in blood viscosity for both branches with and without narrowness, increased with increasing value of Htc. For Htc=30% average value of blood viscosity observed for branch with narrowness was 5% higher compare with branch without narrowness. Furthermore, blood viscosity increased when Htc value increased. For Htc=60% average value of differences increased up to 12%. Table 2. Change in blood viscosity in function of hematocrit.

N. Hematocrit

Htc [-]

Change of

viscosity [%]

1 30 5

2 40 7

3 50 10

4 60 12

4.3. Wall shear stress One of the most important parameters which should be considered when analyzing blood flow through an endovascular prosthesis is wall shear stress (WSS). Figure 10 shows WSS distribution for 0.10 second period of time for Htc ranging from 30%÷60%. It was observed that with increasing value of Htc average value of WSS for branch with narrowness decreased. On the contrary in a branch without narrowness higher values of WSS was accompanied by higher values of blood flow rate.

[Pa]

H=30%

H=40%

H=50%

H=60%

Fig.10. Wall shear stress (WSS) contours for 0.10s period of time for Htc=30%, Htc=40%,

Htc=50% and Htc=60%.. In our study higher values of WSS were observed for areas with lower viscosity, and similarly, higher flow rate. Opposite to that lower values of WSS were observed for lower blood flow rate and higher viscosity. Moreover, higher values of Htc in a branch without narrowing showed much higher values of WSS which correlated with increased blood flow and increased viscosity distribution (Fig.11) However, with increasing value of WSS flow rate was also higher which was opposite to blood viscosity that decreased. Therefore, in areas of low shear velocity were observed low WSS values.

Fig.11. Wall shear stress distribution in branch with narrowness.

Our stimulations showed that for a branch without narrowness WSS value was higher when compared with a branch without narrowness. Moreover, higher value of WSS it correlated with blood flow rate and viscosity distribution. For a branch without narrowness blood flow rate was higher and viscosity had lower values comparing with a branch without narrowness (Fig.12).

Fig.12. Wall shear stress distribution in branch without narrowness.

Therefore, in narrowness decreasing value of WSS in a function of higher Htc was observed (Fig.13). WSS shows areas where probability of blood coagulation is higher. Lower value of WSS involves lower force acting on vein's wall, what involves higher viscosity.

Fig.13. Wall shear stress distribution in narrowness of stent-graft's branch.

Table 3 shows changes in WSS for blood flow through endovascular prosthesis for Htc value ranging between 30%÷60%. Our results indicated increasing value of Htc involves higher differences of WSS between branches with and without narrowness. The average value of WSS observed for Htc=30% for a branch without narrowness was 37% higher than in a branch with narrowness. Moreover, with increased value of Htc WSS differences also increased. For Htc=60% average value of differences increased up to 45%. Table 3. Change of WSS in function of hematocrit.

N. Hematocrit

Htc [-]

Change of

WSSS [%]

1 30 37

2 40 40

3 50 43

4 60 45

5. Conclusions This article presents estimation of an effect of spatial configuration of endovascular prosthesis inside Abdominal Aortic Aneurysm on blood flow. Our results indicated that spatial configuration of a stent-graft (narrows and angular bends) has an influence on blood velocity reduction in vessels and an increased risk of endovascular prosthesis occlusion. An increase in hematocrit value in an area of narrows and angular bends of a stent-graft bifurcation led to reduction in blood flow rate and wall shear stress and an increase in viscosity value in this area which increase the risk of thrombosis.

Acknowledgement The study was supported by Grant No. 2011/35. from the Technical University of Lodz.

Notation Htc hematocrit, parameter of erythrocytes content in blood [-] K inner viscosity of erythrocytes [-] k0 parameters describing blood behavior [-] k∞ parameters describing blood behavior [-] γ shear velocity [1/s] γc boundary shear velocity [1/s] η blood viscosity [Pas] ηp plasma viscosity [Pas] τ shear stress [Pa]

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