Arterial blood CO2 content, division and partial pressure My lecturer cites Boron and Boulpaep's Medical Physiology (2nd edition) for the following claims:


the total $\ce{CO2}$ content of arterial blood is $26.4$ mmol/L or $48\%$ v/v (not sure if these numbers convert)
including $90\%$ as bicarbonate, $5\%$
as dissolved gas and 5% as carbamino compounds (specifically
carbaminohaemoglobin)
the arterial partial pressure of $\ce{CO2}$ is $40$mmHg


How does one get from the arterial partial pressure value to determining these proportions and figures?

What I've tried: Henry solubility constant for $\ce{CO2}$ in water, equilibrium constants for the hydration of $\ce{CO2}$, ionisation of carbonic acid, assumed carbaminohaemoglobin formation went to completion and only consumed $\ce{CO2(aq)}$. Still don't seem to completely match my lecturer's figures.
Even when Douglas equation has been criticized is the best approach I know to calculate CO2 content. You can calculate plasma CO2 content and total blood CO2 content

Douglas 1988 (DOI: 10.1152/jappl.1988.65.1.473)