The RT-SSS algorithm was explicitly applied to oxygenated and deoxygenated hemoglobin measurements using two wavelengths. From Eqs. (4) to (6), each absorbance change at wavelengths and measured with and was written as Display Formula
(8)with Display Formula
(12)where and represent the molecular extinction coefficient at wavelength for oxygenated and deoxygenated hemoglobins, respectively. Also and are the change in concentration of oxygenated and deoxygenated hemoglobins, respectively. Here, was assumed to be independent of the wavelength in the case of human measurement. When and are given, the deep and scalp hemoglobin signals are separated by solving Eq. (8) for four unknowns of , , and since the elements of the matrix on the left-hand side of Eq. (8) are directly measurable at each time, . The literature values of for hemoglobin can be used. The value of for the human forehead was estimated to be by stanching the scalp blood flow, and the errors in the calculated hemoglobin caused by the variation in the value of were also estimated in the previous paper on MD-ICA.7 Because the concept of RT-SSS is almost the same as that of MD-ICA, the effect of the variation of must also be almost the same.