Chromosomal damage is likely the cause of the New Cancers that develop years later, and at least part of the problem with the Myelodysplasia Syndromes.  Some tissues are very sensitive to radiation, and the cells do not recover from treatment: bone cells die and bone becomes osteoporotic, salivary tissue also dies.  Most of the other symptoms of late effects probably come from damage to the irradiated blood vessels that service the tissues, resulting in those blood vessels undergoing premature aging, scarring, and arteriosclerosis.  The organs that rely upon these damaged vessels for their blood supply are compromised, and often undergo ischemic damage, or cannot function reliably.

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