# Photoacoustic Imaging in Oxygen Detection
## 2 Photoacoustic Imaging in sO\({}_{2}\) Measurement  
As discussed, yielding strong optical contrast is one facet in which PAI is superior to UI. The most typical case here is hemoglobin absorption. Hemoglobin, as the most important protein that delivers oxygen from respiratory organs to the rest of the body, can either be bound to oxygen molecules, forming oxyhemoglobin (HbO\({}_{2}\)), or desaturated with oxygen and form deoxyhemoglobin (HbR). These two forms of hemoglobin have different peak absorptions between 500-600 nm wavelength range as well as 700-900 nm wavelength range (Figure 1) and thus can be differentiated using spectral method [16]. The generated heat due to the absorption produces ultrasonic waves that can be acquired by a single or a series of transducers and be used to calculate the oxygen saturation in blood. This has been one of the most important and popular applications of PAI. Moreover, as can be seen from Figure 1, HbO\({}_{2}\) and HbR are the two major endogenous absorbers, which provide strong photoacoustic signals for sO\({}_{2}\) measurement. Basically, the blood absorption coefficient \(\mu_{a}(\lambda_{i})\) can be expressed as  
\[\mu_{a}(\lambda_{i})=\varepsilon_{HbR}(\lambda_{i})[HbR]+\varepsilon_{HbO_{2}} (\lambda_{i})[HbO_{2}], \tag{1}\]where \(\varepsilon_{HbR}(\lambda_{i})\) and \(\varepsilon_{HbO_{2}}(\lambda_{i})\) are the molar extinction coefficients (cm\({}^{-1}\)M\({}^{-1}\)) of HbR and HbO\({}_{2}\) at a certain wavelength \(\lambda_{i}\), and \([HbR]\) and \([HbO_{2}]\) are the concentrations of them, respectively. Since the strength of photoacoustic signal \(\phi(\lambda_{i},\ x,y,z)\) is proportional to the local illumined energy deposition, \(\mu_{a}(\lambda_{i})\) in Equation (1) can be replaced by \(\phi(\lambda_{i},\ x,y,z)\) and thus we can calculate and get the two concentrations as follows,  
\[\left[ \begin{array}{c}HbR\\ HbO_{2}\end{array} \right]_{(x,y,z)}=\left(M^{T}M\right)^{-1}M^{T}\phi(x,y,z)K, \tag{2}\]  
in which  
\[\text{M}=\left[ \begin{array}{cc}\varepsilon_{HbR}(\lambda_{1})&\varepsilon_ {HbO_{2}}(\lambda_{1})\\ \vdots&\vdots\\ \varepsilon_{HbR}(\lambda_{n})&\varepsilon_{HbO_{2}}(\lambda_{n})\end{array}  \right],\phi(x,y,z)=\left[ \begin{array}{c}\phi(\lambda_{1},\ x,y,z)\\ \vdots\\ \phi(\lambda_{n},\ x,y,z)\end{array} \right]\]  
Here, \(K\) is an unknown coefficient that is influenced by the local optical fluence as light passes through the skin, which is wavelength dependent, and by the different ultrasonic parameters [17]. Thus, the SO\({}_{2}\) can be calculated as  
\[\text{sO}_{2(x,y,z)}=\frac{[HbO_{2}]_{(x,y,z)}}{[HbO_{2}]_{(x,y,z)}+[HbR]_{(x,y,z)}}, \tag{3}\]  
Several factors during this process may induce error, reducing measurement accuracy, subsequently increasing uncertainty. These factors include the unknown coefficient K, number of wavelengths applied during the experiment which will affect the accuracy of least-squares fitting, accuracy of molar extinction coefficients at different wavelengths, and the detection component which is directly related with the signal strength. [PERSON] et al. investigated the principle of measuring sO\({}_{2}\) by photoacoustic microscopy with using four wavelengths between 500-600 nm range [18] The results were compared with those from optical absorption calculated ones measured by a spectrophotometer in the 700-1000 nm range, and they were agreed with each other with a systematic difference of 4%. In order to improve the precision and the reliability of spectral measurement of blood oxygen saturation, [PERSON] et al. [19] found that a specific wavelength combination of 660 nm and 805 nm responded more significantly to the changes in blood sO\({}_{2}\), and can detect sO\({}_{2}\) between 88-100% range. This makes it capable of detecting mixed and venous sO\({}_{2}\) and to some extent superior to traditional oximetry [20] that using 750 nm and 850 nm, which is mostly used to measure arterial sO\({}_{2}\).