## 2 Materials and Methods  
This study was conducted on 55 male rabbits (_Oryclogus cuniculus_), weighing 1.5 kg (\(\pm\)0.1 kg) and aged 2-3 months. The rabbits were fed a standard pelleted rabbit ration ad libitum with free drinking access. The rabbits were subdivided into five groups: a control group (9 rabbits) that did not receive irradiation or antioxidants; Group 1 (G1, 11 rabbits), which received Gallium-68 isotope irradiation; Group 2 (G2, 13 rabbits), which received _Angelica archangelica_ root powder water extraction for 7 days before irradiation; Group 3 (G3, 10 rabbits), which received _Ginkgo biloba_ for 7 days before irradiation; and Group 4 (G4, 12 rabbits), which received a combined dose of both antioxidants for 7 days with the same concentration, time, and duration as in Groups 2 and 3. The experimental design was approved by the ethical committee of Taif University. An injectable solution of the \({}^{68}\)Ga isotope was used, _Gallium Ga-68 dottoc_ (Rx), in a 30-mL multidose vial containing 18.5-148 MBq/mL (0.5-4.0 mCi/mL). The dose was calculated as 2 MBq/kg, identical to the isotopes used commercially in human diagnostic protocols. An intravenous application was used. Before the injections, the rabbits were hydrated with saline injections to ensure adequate isotope absorption. A suitable syringe was used to collect blood samples via the left ear vein, and the samples were then stored in heparinized tubes at -70 \({}^{\circ}\)C until the analysis procedure was conducted. _Angelica archangelica_ herb roots were commercially collected from a traditional herb dealer in Egypt. _Ginkgo biloba_ was delivered from public pharmacies as tablets in Saudi Arabia. _A. archangelica_ and _G. biloba_ protective doses were calculated based on a 0.11 g/kg body weight [17]. The derivative concentrations of hemoglobin were measured using a modified Beer-Lambert law. Spectrophotometrically, the four types of hemoglobin (oxyhemoglobin (HbO\({}_{2}\)), carboxyhemoglobin (HbCO), sulfhemoglobin (SHb), and methemoglobin (Met.HB) had characteristic pigment peaks. Four linear equations were obtained at wavelengths of 500, 569, 577, and 620 nm, respectively. A matrix instant solution of the four equations was carried out to calculate each derivative concentration separately. The millimolar extinction coefficients are presented in the following equations with the four unknown concentrations of hemoglobin pigments (C\({}_{\text{Hb-O2}}\), C\({}_{\text{Hb-CO}}\), C\({}_{\text{Met-Hb}}\), and C\({}_{\text{Hb-S}}\)) [19]:  
\[A^{500} =5.05\;\text{C}_{\text{HbO2}}+5.35\;\text{C}_{\text{HbCO}}\;+\;9.04\; \text{C}_{\text{Met-Hb}}+7.2\;\text{C}_{\text{SHb}} \tag{1}\] \[A^{569} =11.27\;\text{C}_{\text{HbO2}}+14.27\;\text{C}_{\text{HbCO}}\;+\;4.1\;\text{C}_{\text{Met-Hb}}+8.1\;\text{C}_{\text{SHb}}\] (2) \[A^{577} =15.37\;\text{C}_{\text{HbO2}}+10.0\;\text{C}_{\text{HbCO}}\;+\;4.1\;\text{C}_{\text{Met-Hb}}+8.1\;\text{C}_{\text{SHb}}\] (3) \[A^{620} =0.24\;\text{C}_{\text{HbO2}}+0.33\;\text{C}_{\text{HbCO}}\;+\;3.35\;\text{C}_{\text{Met-Hb}}+20.8\;\text{C}_{\text{SHb}} \tag{4}\]  
The above linear system of equations can be represented in matrix form as:  
\[\left[ \begin{array}{cccc}5.05&5.35&9.04&7.2\\ 11.27&14.27&4.10&8.1\\ 15.37&10.0&4.10&8.1\\ 0.24&0.33&3.35&20.8\end{array} \right]\cdot\left[ \begin{array}{c}\text{C}_{ \text{HbO2}}\\ \text{C}_{\text{HbCO}}\\ \text{C}_{\text{Met-Hb}}\\ \text{C}_{\text{SHb}}\end{array} \right]=\left[ \begin{array}{c}\text{A}^{500} \\ A^{569}\\ A^{577}\\ A_{620}\end{array} \right] \tag{5}\]  
Mathematically, this is a linear equation system and can be solved by the process of manipulation. The Gaussian elimination method was used to calculate the different derivative concentrations. Matrix calculations resulted in the following equations, which could be used to calculate each concentration separately, where A\({}_{500}\), A\({}_{569}\), A\({}_{577}\), and A\({}_{620}\) are the spectrophotometric absorbances of the hemoglobin solution at the wavelengths 500, 569, 577, and 620 nm, respectively.