Final answer:
A BM core biopsy offers the most comprehensive insight into the architectural structure of bone marrow, crucial for diagnosing and assessing marrow-related disorders. Peripheral blood samples, BM crush particles, and BM aspirations provide information but lack the architectural context that a core biopsy presents.
Step-by-step explanation:
The sample that gives the most insight into the architectural arrangement of bone marrow in a patient is the BM core. This is because the bone marrow core biopsy provides a solid architecture of the marrow, thereby allowing for the assessment of marrow cellularity, stromal structures, and the presence or absence of fibrosis or tumor infiltration. Peripheral blood samples, BM crush particles, and BM aspirations can help in the diagnosis of various conditions but will not provide the same insight into the physical architecture of the marrow as a core biopsy would. For example, crush particles may give information about cells present but can lack architectural context, and aspirations may not always yield sufficient cellular material for diagnosis.