# Reconstruction of the Physiological Behavior of Real and Synthetic Vessels in Controlled Conditions
## 2 Materials and Methods
### Experimental Conditions  
Changes in the diameter and displacement of the walls of the iliac arteries were investigated and compared with vascular prostheses made of expanded polytetrafluoroethylene (ePTFE) with a specified length of 100 mm, diameter of 8 mm, and wall thickness of 1 mm. The analysis encompassed iliac arteries sharing identical dimensions (length of 100 mm and diameter of 8 mm). The study received approval from the local Institutional Review Board (2069/2012) of the Medical University of Vienna. To validate the accuracy of the experimental setup, vision data were juxtaposed with clinical data obtained using the ultrasound 2D- Speckle tracking technique (2 DSTT) (GE Vivid 7, GE Healthcare, Pittsburgh, PA, USA), equipped with software for strain analysis (EchoPac PC, GE Medical System, Pittsburgh, PA, USA, [[https://www.gehealthcare.com/products/ultrasound/vivid/echopac](https://www.gehealthcare.com/products/ultrasound/vivid/echopac)]([https://www.gehealthcare.com/products/ultrasound/vivid/echopac](https://www.gehealthcare.com/products/ultrasound/vivid/echopac)), accessed on 16 February 2024). To verify the area change percentage (ACP) and vessel shape (VS), flow construction was performed with various parameters: pulsatile nature heart rates (FP)--60, 75, 90, 105, and 120 min\({}^{-1}\)--and different stroke volumes (volumes (EV): 70, 85, 100 and 115 mL) using non-commercial fluid for one cycle. The movement of the vessel wall was analyzed using 2 DSTT, and it was ascertained whether the changes recorded with VS replicated the wall changes recorded with 2 DSTT. Furthermore, current studies indicate that pulsatile flow plays a crucial role in the evaluation of pathological states, e.g., aneurysms [23]. For standardization, the changes in vessel diameter recorded by the ACP were compared with clinical data collected during patient examinations using the 2 DSTT approach. Figure 2: An artificial circulatory phantom (ACP): (**a**) iliac artery; (**b**) expanded polytetrafluoroethylene arterial (ePTFE) vascular prosthesis. Six ACP iliac arteries were compared with data from six healthy patients diagnosed with 2 DSTT using the same type of arteries and hemodynamic conditions as in the ACP. To further standardize the results for ACP patients and healthy subjects, tests were conducted under the conditions of heart rates (75 min\({}^{-1}\) and 90 min\({}^{-1}\)) and stroke volume (EV = 70 mL). Medical data were then compared with the ACP results obtained under the same hemodynamic conditions. Ultimately, 120 cases were studied for iliac arteries and 120 cases for the ePTFE vascular prostheses. The diameter change (Dc) (Equation (1)) and wall displacement (Wd) (Equation (2)) were calculated using the following equations:  
\[\text{Dc}=\text{Ddynamic(x,y,z)}-\text{Dstatic(x,y,z)} \tag{1}\]  
where:  
Dc--vessel's diameter change [mm]. Dstatic(x,y,z)--vessel's diameter, recorded under static conditions [mm]. Ddynamic(x,y,z)--the maximal vessel's diameter under dynamic conditions [mm]. \[\text{Wd}=\text{Wdynamic (xp',yp',zp')}-\text{Wstatic (xp,yp,zp)} \tag{2}\]  
where:  
Wd--vessel's wall displacement [mm]. Wstatic (xp,yp,zp)--spatial configuration of vessel's wall in relation to its central axis, recorded under static conditions [mm]. Wdynamic (xp',yp',zp')--spatial configuration of vessel's wall in relation to its central axis, recorded under dynamic conditions [mm]. Moreover, tortuosity (Tortuosity index T\({}_{i}\) (Equation (3)); Tortuosity (T) (Equation (4)) was applied to verify the correct operation of the WD parameter measurement. \[\text{T}_{i}=\text{L/C} \tag{3}\]  
where:  
T\({}_{i}\)--totruosity index [-]. L--the linear distance of the vessel's segment [mm]. C--the distance between vessel's start and endpoint [mm]. \[\text{T}=1-\text{d/1} \tag{4}\]  
where:  
T--totruosity [-]. d--the linear distance of the centerline [-]. L--the distance along the centerline [-]. Furthermore, a modification of the tortuosity (modified tortuosity index (Mti) (Equation (5))) presented in the literature was proposed.