Parenchyma basically means breast tissue and asymmetry means that there is a difference in the breasts density (one breast more dense than the other). Sometimes breast tissue can become more prominent during certain times in a menstrual cycle related to hormone fluctuation.
A breast density,whether it's palpable or not, could mean a lot of things and doesn't necessarily point to cancer.You don't say what your radiologist has recommended,but usually a diagnostic mammogram is needed to focus on the area of density so a diagnosis can be made.Very often the density will disappears upon compression indicating that it could have simply been tissue that folded over on itself..If the density remains,then further investigation might be required.
Best wishes and hoping that all goes well for you....
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