Calibration of the Differential Path Length Factor in the Modified Beer-Lambert Law (MBLL) Upon the Local Off-axis Diffuse Reflection Imaging (sDRI)

Abstract: The optical path length is required to calculate the regional change in hemoglobin concentration from the change of measured light absorbance. The partial path length factor (PPF) is generally used for path length estimation in diffuse reflectance imaging measurements. To noninvasively determine absolute concentrations of hemoglobin (Hb) in skin tissue by means of regular near infrared (NIR) light diffuse reflectance measurements, the modified Beer Lambert law is applied. The method was developed to inversely calculate the concentration of oxygenated hemoglobin (Hbo), deoxygenated hemoglobin (Hb) as well as an effective partial path length, which NIR light passes through in the tissue between source and detector. Applying four different skin equivalent phantoms that mimic superficial skin tissue, it is shown that the optical density is in quadratic relation with both oxygenated and deoxygenated hemoglobin concentrations, thereby validating the modified Beer Lambert law in the optical density range of 0.02 and 0.08. Based on this, the partial path length factor is found to be linearly proportional with the concentration of hemoglobin. The variation of the partial path length factor for both the oxygenated and deoxygenated hemoglobin is between 0.3 and 0.6. The results also showed that in the NIR mainly in the range (700nm–1200nm) the absorbance of the oxygenated hemoglobin is more stable than that of the deoxygenated hemoglobin. It is in agreement with the prediction made based on the optical density.