Fleshy Substance In Bowels, Absence Of Blood. Suffering From Chronic Constipation, IBS. What Could It Be?

I have what seems to be a fleshy substance in my bowels. I have chronic constipation and IBS for over 20 years. I have stopped taking medicine for over 15 years because of the side effects. However in the last 4-5 years I have had to take a laxative to have a bowel movment once a week or every 2 weeks. Now, I am trying my best to maintain a diet that easy digestable. Soft foods, clear soups, and liquids. I have noticed on a couple occasions in the last two weeks that I have passed large amounts of fleshy substance in my bowels. No, blood involved and not the thin stomach linen. These are actually think pieces of what could be considered flesh or chicken liver type things. I do not eat meat, so it can not be meat waste. Do you have any suggestions or relevance to what this may be and what I can look into.