How Is This Acid Base Map Established?
The curves are rather obtained clinically, statistically evaluating diagnose, symptoms and results of clinical lab tests.
Metabolic curve follows malfunctioning metabolism keeping too low ( m. acidosis ) or too high ( m. alkalosis ) level of bicarbonate.
Respiratury curves follows states of too intense breathing ( r. alkalosis ) or too shallow breathing ( r. acidosis ), because of too low respectively high level of carbon dioxide partial pressure, caused by abnormal breathing.
Note that the $K_{\ce{H, CO2}}$ Henry constant  or CO2 is $\pu{29.41 atm/(mol/L)}$. the value will be higher because of the body temperature, can be corrected by temperature dependent $\ce{CO2}$ solubility.
$$\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}+\log\left(\frac{[\mathrm{Base}]}{[\mathrm{Acid}]}\right)=\mathrm{p} K_{\mathrm{a}}+\log\left(\frac{[\ce{HCO3-}] \cdot K_{\ce{H, CO2}}}{p_{\ce{CO2}} }\right)$$
Where pKa of carbonic acid is 6.35, if counting the total $\ce{CO2}$ concentration.
There are 3 variables ( $\mathrm{pH}$, $p$, $\ce{[HCO3-]}$ ) and 2 degrees of freedom. $\mathrm{p}$ is controlled by breathing, $\ce{[HCO3-]}$ is controlled by metabolism. $\mathrm{pH}$ is result.