How Is This Acid Base Map Established? In the Acid-base map -shown below- each line denoted as an isohydric line shows the pairs of $ PCO_{2}$ &amp; $ [HCO_{3}^{-}] $ that give a certain $ pH $. So each line connects the values of $ PCO_{2}$ &amp; $ [HCO_{3}^{-}] $ that give a value of $ pH $ that is constant across that line..
The 7.4 line shows the isohydric line of physiological pH,the central ellipse shows the normal range.
I understand the Henderson–Hasselbalch equation:
$\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}+\log _{10}\left(\frac{[\mathrm{Base}]}{[\mathrm{Acid}]}\right)$
What I would like to know is how this map established either experimentally or mathematically or both preferably.
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.