Safety and Efficacy of Desensitization Therapy in Sensitized Participants Awaiting Heart Transplantation

Inclusion Criteria: * Subject must be able to understand and provide informed consent; * Candidate (as recipient) for a primary heart transplant (single organ transplant); * Calculated panel reactive antibody (cPRA) of greater than 30% with a threshold using mean fluorescent intensity (MFI) of 3,000 or standard fluorescence intensity (SFI) of 60,000; * Status 1 (1A or 1B) enrollment and randomization to occur within 2 weeks after status 1 listing; * Female subject is either postmenopausal for at least 1 year before the screening visit, is surgically sterilized or if they are of childbearing potential, agree to practice 2 effective methods of contraception from the time of signing the informed consent form through 30 days after the last dose of bortezomib, or agree to completely abstain from heterosexual intercourse; * Male subjects, even if surgically sterilized (i.e., status postvasectomy) must agree to 1 of the following: practice effective barrier contraception during the entire study treatment period and through a minimum of 30 days after the last dose of study drug, or completely abstain from heterosexual intercourse; * Negative test for HIV (human immunodeficiency virus), HBsAg (hepatitis B surface antigen), HBcAb (hepatitis B core antibody), and HCV (hepatitis C virus) antibodies within 6 months prior to study entry. Exclusion Criteria: * Recipient of multiple solid organ or tissue transplants; * Prior history of organ transplantation; * Women of childbearing potential with a positive serum β-human chorionic gonadotropin (β-hCG) pregnancy test.Pregnancy testing is not required for postmenopausal or surgically sterilized women; * Currently breast-feeding a child or plans to become pregnant during the timeframe of the study follow-up period; * Subject has a hypersensitivity to VELCADE® (bortezomib), boron, or mannitol; * Active systemic infection at time of enrollment; * Any history of serologic positivity to HIV, HBsAg, HBcAb and HCV Ab; * History of malignancy except when noted by an oncology specialist that tumor recurrence is low based on tumor type, response to therapy and negative metastatic work-up; * Radiation therapy within 3 weeks before randomization. Enrollment of subjects who require concurrent radiotherapy (which must be localized in its field size) should be deferred until the radiotherapy is completed and 3 weeks have elapsed since the last date of therapy; * Subjects with a platelet count of less than 75,000 within 7 days prior to enrollment; * Subjects with an absolute neutrophil count (ANC) of less than 1,500 within 7 days prior to enrollment; * Subjects with \>1.5 x ULN (upper limit of normal) total bilirubin; * Subjects with any grade or history of neuropathy; * Any condition that, in the opinion of the investigator, would interfere with the subject's ability to comply with study requirements; * Participation in another interventional clinical trial or requiring treatment using un-marketed investigational drug(s) within 14 days of start of this trial and throughout the duration of this trial.