# Veins Depth Estimation Using Diffused Reflectance Parameter
## 1 Introduction  
The process of Intravenous (IV) catheterization is the first and most important step in any medication to hospitalized patients. In this process, catheters are passed into the patient's subcutaneous veins for medication or nutrition delivery. In general, before the catheter insertion veins are localized, to select the appropriate vein for medication or blood sampling. This task is conducted by trained health professionals, who finds the veins either by sight or by simply feeling with hand. Each year in USA only, around 25 million catheters are placed into the patients [1]. Around 80% of all indoor and numerous outdoor patients require catheters for the injection of medication and blood sampling [2, 3].  
There are a lot of complications in veins' localization that a staff may face. These are caused by many physical differences which includes skin color, vessels depth, burn marks, hair, tattoos etc. Since vein localization process becomes challenging, sometimes it may increase the risk of multiple attempts, incorrect catheterization, vein rupture, bruising of skin and nerve injury. According to studies [4], more than 2 attempts on average, per patient, are required for successful placement of an IV catheter. More than one attempt may lead to severe pain and trauma like condition for the patients (especially infants). Another consequence may lead to veins rupture. This may cause the transfer of medication to the tissues adjacent to the place of catheter. Furthermore, in some cases extravasation may happen that could lead to a surgical intervention [5]. The subcutaneous veins existing in the hypodermis layer of skin, are used for the usual catheterization and blood testing process. The NIR imaging technique is found to be the best technique for vein visualization among other imaging techniques. The absorption coefficient of Hemoglobin (Hb) in NIR spectrum is high as compared to the skin tissues. Therefore, veins appear darker in NIR images contributing to the better skin/vein distinction [6; 7]. Furthermore, the nature of NIR light is non ionizing. This make it suitable for application to the skin of patients, multiple times with no damaging effects on the patient [8]. There are few NIR imaging methods and devices proposed for veins localization to date. None of them, to the best of our knowledge, offer the measurement of vessel's depth [9]. In order to avoid incorrect IV placements, veins depth information is vital. The amount of subcutaneous fat varies from patient to patient, making the subcutaneous veins depth variable. The medical staff faces difficulty in veins depth estimation, especially in the cases of obese patients. This paper is an extension of the work presented in [10], in which a novel technique for veins depth estimation using measured reflectance parameter was introduced. A four-layered skin model is presented, which incorporates the veins with varying depth (1.6 to 4.5 mm) in the fourth layer. State of the art Monte Carlo simulations are used to simulate light propagation within skin. Since the subcutaneous veins lie in hypodermis layer of skin, the width of this layer is increased steadily with increment 0.1 mm in each iteration. As output, diffused reflectance parameter 'Rd' for each iteration is recorded. In order to calculate the blood vessels depth, the recorded diffused reflectance is used in the anticipated mathematical model. The comparative plots are presented between the vein's depth, calculated analytically using the proposed model and the actual depth readings used in Monte Carlo simulations. Furthermore, for the sensitivity analysis of the model, the veins depth is calculated with the \(\pm\)5% change in the sum of absorption and scattering coefficients of all layers. Results are plotted along with the analytical calculated veins depth.