To understand this, we should think about the pathology. Firstly, the breast has 3 major tissues: duct, lobule and interstitium. Secondly, BC has a variety of pathological types: intraductal carcinoma, infiltrating ductal carcinoma, medullary carcinoma, mucinous carcinoma, tubular carcinoma, lobular carcinoma in situ, infiltrating lobular carcinoma, inflammatory breast cancer and Paget's disease.

This sentence seems to describe carcinomas originated from ductal tissue, which can infiltrate the interstitium (stroma). In that case, the original ductal carcinoma is surrounded by infitrative mass, so we can see ductal spread inside the infitrative mass, and of course remote ducts.

For your reference, in this case, we should use the term 'infiltration' instead of 'invasion' (these are different) AND we'd better use the term 'mass' instead of 'tumor' (to avoid confusion breat cancer per se). We can use interstitium or stroma for 間質, but stroma is generally used in clinical settings.