# Calibrated Hydraulic Resistance Adjuncts for Carbon Dioxide Angiography Optimization
## 2 Materials and Methods  
### Experimental Setup  
For this research, 3 calibrated hydraulic resistance adjuncts have been assembled using different lengths of low internal diameter tubes (2F endovascular catheters) (Figure 2). The tube length ranged between 32 cm and 55 cm. The hydraulic resistances of the standard injection line (R\({}_{\text{line}}\)) and the adjuncts (R\({}_{\text{adj}}\)) have been experimentally evaluated by recording the exponential pressure decay of a known volume CO\({}_{2}\)-filled chamber; the complete measurement method is described in a previous paper [19]. The apparatus described in Figure 3 has been used to simulate the CO\({}_{2}\) angiographic process. The alternating pump (simulating the left ventricle) pushes a colored saline solution (blood) into the aorta through the aortic valve. The blood flows into the arterial tree and then into the venous system. From here, blood enters the atrium and then, through the mitral valve, to the ventricle. By regulating the stopcocks, it was possible to set the peripheral resistance and, therefore, the mean arterial pressure. Pulse pressure was settled by modulating the compliance of the aorta [20]. A pressure transducer (Edwards TruWave, Edwards Lifesciences Corp, Irvine, CA, USA) connected to a Dash 3000 acquisition unit (GE HealthCare, Chicago, IL, USA) and an electromagnetic flowmeter (Biotronex 610 square wave EMF, Biotronex Laboratory Inc, Silver Spring, MD, USA) were used to acquire the internal arterial pressure (P\({}_{\text{int}}\)) and flow (F\({}_{\text{a}}\)(t)). A settable frame rate digital TV camera (model acA 1300-75 gc, Basler, Ahrensburg, Germany) interfaced with a Matrox Concord Card (Matrox, Doral, QC, Canada) allowed to record videos of blood flow and bubble motion during the procedures. Arterial pressure,  
Figure 1: System to change the hydraulic resistance: (**a**) the stopcock allows the flow directly to the catheter, avoiding adjunct resistance; (**b**) the gas flows in the adjunct resistance and then the injection catheter. aortic flow, and video output were acquired simultaneously with the ANScovery system (Sparkbio Srl, Bologna, Italy) [21]. An automatic CO2 injector (Angiodroid Srl, Bologna, Italy) was used to inject fixed gas volumes (Vin) at constant pressures (Pin) inside the arterial tree through a standard gas injection line (mod CO200001, Angiodroid Srl, Bologna, Italy) with a 5F Cordis catheter (Cordis, Milpitas, CA, USA). Two 3-ways stopcocks at the beginning of the injection catheter permitted the insertion of the calibrated hydraulic resistance adjuncts (Figure 2). Signal analysis and imaging evaluation were performed with the ANScovery software (version 8.0). The target vessel network image is shown in Figure 4.  
The measured hydraulic resistance adjuncts' values were 28 mmHg/mL/s, 42 mmHg /mL/s, and 69 mmHg/mL/s, respectively. The hydraulic resistance (Rine) of the standard gas injection line, connections, and stopcocks was 5.5 mmHg/mL/s (1 mmHg/mL/s = 1.33\(\cdot\)10\({}^{8}\) N\(\cdot\)s\(\cdot\)m\({}^{-5}\)). So, 4 different conditions have been simulated, considering that the total resistance for each condition is given by summing Rine to Rad; (a) no adjunct resistance (only Rine); (b) Rine + 28 mmHg/mL/s; (c) Rine + 42 mmHg/mL/s; and (d) Rine + 69 mmHg/mL/s. The pulsatile behavior of the vascular simulator was set to produce 2 mL stroke volume each second in the target vessel, with a vascular pressure pulse of 150/80 mmHg (mean value 120 mmHg) and peak flow of 3.8 mL/s. The instantaneous flow signal was recorded before the injection point to avoid the noise of bubble passage through the electromagnetic probe. In all the subsequent measurements, an injection volume of 20 mL was set, and the  
Figure 2: Variable hydraulic resistance for two different conditions: (**a**) without any external adjunct resistance; (**b**) with the calibrated adjunct resistance. gas injection image was continuously observed and recorded from the pressure onset to the last injected bubble.