A Proof of Concept Study to Evaluate the Effectiveness of Tysabri in Relapsing Remitting Multiple Sclerosis (RRMS) Patient Bladder Function

Key Inclusion Criteria: Participants are eligible to be screened for this study if all of the following criteria are met: * Patient must meet all prescribing criteria for TYSABRI® and eligible for the TOUCH™ program. * If utilizing medications for symptoms of bladder dysfunction (such as incontinence, urgency etc), subjects will need to remain on a stable dose of medication(s) for at least one month prior to and for duration of study. * If utilizing medications that affect urinary output (e.g. anticholinergics, diuretics, etc.), subjects will need to remain on a stable dose of medication(s) for at least one month prior to study entry and for the duration of the study. * Able to provide written informed consent. * Patient must be willing to maintain current hydration habits and caffeine intake for the duration of the study. Participants will be selected for enrollment if all of the following criteria are met: * Screening Visit urinary incontinence defined as: \- Greater than or equal to 3 incontinence episodes per week or greater than or equal to 8 micturitions per day (both mean numbers). * Screening Visit score on the UDI-6 of more than or equal to 6. * Screening Visit EDSS 0 - 6.5 Key Exclusion Criteria: Candidates will be excluded from study screening if any of the following exclusion criteria exist: * Primary progressive, secondary progressive, or progressive relapsing MS. Primary progressive, secondary progressive or progressive relapsing multiple sclerosis are defined by Lublin and Reingold (Lublin and Reingold, 1996) or EDSS \>6.5. * Current or previous history of Progressive Multifocal Leukencephalopathy (PML). * A clinically significant infectious illness (e.g., cellulitis, abscess, pneumonia, septicemia) within 30 days. * History of recurrent or chronic urinary tract infection or a urinary tract infection within the preceding 30 days prior to Week 0 (diagnosis based on clinical history and Screening Visit urinalysis and urine culture). * Patients who have in-dwelling foley catheter or a suprapubic catheter. * Patients with a history of symptomatic benign prostatic hyperplasia (BPH) or a history of prostate cancer. * History of, or abnormal laboratory results indicative of, any significant cardiac, endocrinologic, hematologic, hepatic, immunologic, metabolic, urologic, pulmonary, gastrointestinal, dermatologic, psychiatric, renal, and/or other major disease, that, in the opinion of the investigator, would preclude the administration of natalizumab for the duration of the study. * Subject with history of malignancy within the past 2 years, with the exception of basal cell carcinoma that has been treated. * History of severe allergic or anaphylactic reactions or known drug hypersensitivity. * Any prior treatment with the following medications: Natalizumab (TYSABRI®) * Nursing mothers, pregnant women, and women planning to become pregnant while in study. * Any other reasons that, in the opinion of the Investigator and/or Sponsor, the subject is determined to be unsuitable for enrollment into this study. * Unwillingness or inability to comply with the requirements of this protocol including the presence of any condition (physical, mental, or social) that is likely to affect the subject's ability to comply with the study protocol. * History of alcohol or drug abuse within 2 years prior to randomization. * Female subjects who are not postmenopausal for at least 1 year, surgically sterile, or willing to use a medically acceptable method of birth control during the study. The rhythm method is not to be used as the sole method of contraception. Participants will be determined as screen failures if any of the following criteria apply: * Abnormal blood tests, performed at the screening visit, which exceed any of the limits defined below: 1. ALT/ SGPT, or AST/ SGOT more than three times the upper limit of normal (i.e., 3xULN). 2. Total white blood cell (WBC) count less than 2,300/mm3. 3. Platelet count less than 100,000/mm3. 4. Creatinine more than 2xULN. * Screening Visit urinary incontinence defined as less than 3 incontinence episodes per week or less than 8 micturitions per day (both mean numbers). * Screening Visit score on the UDI-6 of less than 6. * Screening Visit EDSS more than 6.5. NOTE: Other protocol defined inclusion/exclusion criteria may apply.