When we collect fish muscle samples, some kinds of fishes have lots of intermuscular bones, especially less evolved fishes, and they are hard to remove.
Probably the simplest approach is to use acidification with 1M HCl to dissolve inorganic carbonate from the bone. This can be done after the samples have been dried or freeze-dried and ground to powder for analysis.
Some authors do find that this procedure does not significantly change the d13C value for fish muscle samples though, so it may not be necessary:
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Something to be careful of, is that the acid treatment will also affect the d14N and possibly other isotope ratios as well. If acidifying samples, it is advisable to analyse duplicate samples with and without the acid treatment.