Studies in this area are little. However, with quick research I found an article found determined Tartrazine in urine samples ''A sensitive and specific enzyme immunoassay for detecting tartrazine in human urinary samples''
First, you have to check if they are matabolized in the body. for example, human body metabolizes aspartame (artificial sweetener), breaking it down into aspartic acid, methanol and phenylalanine. So, you can't check for its concentration in human urine.
I have attached a recent study analysed food colourants in foods and in urine samples. as they found olny Tartrazine in urine of children consuming food sources of that food colourant.
Best regards
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