From what I've read,
Bioavailability is the degree to which food nutrients are available for absorption and utilization in the body.
How would you explain this with an example?
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Bioavailability is a concept which applies to nutrients and drugs which pass through first-pass metabolism, i.e. orally (and to some extent nasally) consumed substances. Anything absorbed in the gut first passes through the liver before reaching the rest of the circulation, and both the gut and liver may metabolise it to some extent. The liver in specific has the powerful Cytochrome P450 system, a huge variety of enzymes to break down all sorts of substances, although in some cases it can actually produce more active or even toxic forms instead of breaking them down.
This can lead to drastic reductions in the amount available in the systemic circulation after oral administration. E.g. propanolol (a beta blocker) needs to be given in 100mg doses orally while intravenously (avoiding first-pass metabolism) only 5mg are needed.