Patients with lymphoma and breast cancer receiving chemotherapy regimens that include anthracycline drugs, such as doxorubicin, are at risk for developing cognitive and cardiac impairment. This potential cognitive impairment is refered to as "chemobrain" by some patients. We have demonstrated in mice that the drug mesna, which is used to prevent other complications of other chemotherapy drugs, prevents certain types of doxorubicin-induced damage of blood proteins. Blocking doxorubicin's damage of these blood proteins has blunted or prevented the subsequent markers of neurologic and cardiac injury in mice. This clinical trial will determine if mesna prevents doxorubicin-induced damage of blood proteins in cancer patients, and may establish if blood protein injury is the first step in anthracycline-induced cognitive and cardiac dysfunction and if using the drug mesna can blunt or prevent these changes in blood markers of injury for patients with cancer.