Final answer:
The substance most likely increased in the myocardial fibers of the deceased 80-year-old woman's heart, giving it a brown appearance, is lipofuscin, a byproduct of cellular aging. Therefore, the correct option is 1.
Step-by-step explanation:
The dark brown heart with light brown perinuclear pigment seen in the cardiac muscle fibers of an 80-year-old woman likely indicates the presence of lipofuscin. This is a pigment that accumulates as a byproduct of cellular aging, and it is commonly found in the myocardial fibers of the elderly. In contrast, amyloid would be associated with amyloidosis and has a different staining characteristic. Hemosiderin accumulation occurs with iron overload, and would not typically present as a light brown pigment. Bilirubin is associated with jaundice and does not accumulate in the myocardial fibers in this manner.