Final answer:
The causal organism for the symptoms and MRI findings in a 21-year-old woman with AIDS is Bartonella henselae, which can cause bacillary angiomatosis and bacillary peliosis in immunocompromised individuals.
Step-by-step explanation:
The most likely causal organism for the condition described in a 21-year-old woman with AIDS, who has a rash on her extremalies, back, and trunk, and MRI findings of cystic blood-filled spaces in the liver and spleen, is Bartonella henselae. This organism is known to cause bacillary angiomatosis (BA) in immunocompromised patients, which is characterized by the proliferation of blood vessels resulting in tumor-like masses in the skin and internal organs. Another condition caused by this organism in such patients is bacillary peliosis (BP), which includes the presence of multiple cyst-like, blood-filled cavities in the liver and spleen. The correct answer to the presented question would be C) Bartonella henselae.