# Calibrated Hydraulic Resistance Adjuncts for Carbon Dioxide Angiography Optimization
## 1 Introduction
The clinician knows that the instantaneous gas input flow (F\({}_{\text{g}}\)(t), mL/s) [17] corresponds to the instantaneous difference between the injector pressure (P\({}_{\text{inj}}\)) and the internal vascular cavity pressure (P\({}_{\text{int}}\)), divided by the hydraulic resistance (R\({}_{\text{es}}\)) of the injection line (Hagen-Poiseuille's Law [18]):  
\[\text{F}_{\text{g}}(\text{t})=\frac{\text{P}_{\text{inj}}-\text{P}_{\text{int} }(\text{t})}{\text{Res}}\left(\left[\text{mL/s}\right]\right) \tag{1}\]  
This formula shows how difficult it is to control the gas injection efficiently by acting only on the injection pressure because vascular cavity pressure pulsates, and the catheter used for diagnostic and interventional approaches has its hydraulic resistance (from 2 mmHg/(mL/s) up to 100 mmHg/(mL/s)) [5]. The problem is particularly evident in the case of low blood flow or small vessels with physiological pulsatile pressure (femoral arteries, foot arteries, and subclavian arteries). In these conditions, to have a desired low gas flow injection using catheters with internal channel suitable for a standard wire guide (0.035 in = 0.889 mm) and consequent low resistance (~5 mmHg/(mL/s)), it would be necessary to use injection pressure, only slightly higher than vascular one, with an instantaneous gas injection strongly dependent from the patient pressure pulsatility. Moreover, since the blood flow is pulsatile and in phase with the pressure, the result is a minimum gas injection flow corresponding to the maximum instantaneous blood flow, precisely the opposite of what is desired for optimal angiographic imaging. A possible solution to this problem is to use thinner catheters with higher resistance and pressure but with unaffordable procedural issues. A possible alternative is to use usual (low hydraulic resistance) catheters and connections, with standard wire guides and good maneuverability, with an adjunct appropriate calibrated hydraulic resistance tube (R\({}_{\text{adj}}\)) in series. This trick allows the gas input flow (F\({}_{\text{g}}\)(t)) to be more easily controlled and stabilized. A higher injection pressure (P\({}_{\text{inj}}\)) must be used without changing the standard diagnostic procedure and devices to compensate for the adjunct resistance effect on gas flow. To avoid an increased procedural complexity, the calibrated hydraulic resistance adjunct may be mounted in parallel with a low resistance stopcock to permit an easy passage from a high gas flow rate, used in large vascular cavities, to a low gas flow rate, used in small vascular vessels, without changing the injection line and catheter (Figure 1). This solution makes the gas injection rate more regular, especially in wide pulse arterial pressure cases. Gas bubbles are more regularly injected and distributed inside the vessel, with consequent possible imaging benefits. A higher hydraulic resistance also permits easier control of gaseous retrograde flow in the vessel, reducing the patient's pain. We tested this approach on a vascular simulator with transparent vessels to visually observe the effect of the adjunct resistances and also to clarify if it is better for imaging to have inside the target vessel many regularly distributed running bubbles obtained by an adjunct resistance device and higher injection pressure, or small volumes of gas fulfilled vascular sections followed by gas empty ones, obtained without adjunct resistance and low-pressure injection. Moreover, the records can clarify how the injection time courses (gas output delay and duration) change with and without resistance adjunct. Maybe other questions will arise from our results; they will be discussed and described in subsequent simulations and testing.