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New mathematical model equations for O^sub 2^ and CO^sub 2^ saturations of hemoglobin (S ^sub HbO^ ^sub 2^ and S ^sub HbCO^ ^sub 2^) are developed here from the equilibrium binding of O^sub 2^ and CO^sub 2^ with hemoglobin inside RBCs. They are in the form of an invertible Hill-type equation with the apparent Hill coefficients ^sub K^ ^sub HbO^ ^sub 2^ and K ^sub HbCO^ ^sub 2^ in...