Study of Lisdexamfetamine Sulfate to Treat Cognitive Dysfunction in Multiple Sclerosis

Inclusion Criteria: * Males/Females who are ≥ 18 years old and \< 55 years old and are capable of understanding and complying with the protocol, including speaking and writing fluent English and having at least a 9th grade education. * Have a diagnosis of either Relapsing Remitting or Secondary Progressive MS, as per revised McDonald's Criteria (68). * Have not received steroids in last thirty (30) days or a relapse in the last ninety (90) days, and whose MS is considered stable. * Presence of cognitive dysfunction characterized by slowed processing speed as indicated by a score of -1.5 SD below age/education matched norms on the SDMT or the PASAT. * An Expanded Disability Status Scale (EDSS) of ≤ 6.5 * Have given written informed consent prior to any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to his/her future medical care. * Are capable of performing the requirements of a NP test battery including at least 20/70 near visual acuity by near vision chart, with correction allowed. * If female, must neither be pregnant nor breast-feeding and must either (a) be \> 12 months post-menopausal or surgically sterilized, or (b) agree to use an acceptable method of birth control for the duration of the study. Abstinence will not be considered an acceptable method of birth control. Exclusion Criteria: * Have cognitive deficits caused by concomitant medication usage or other significant neurological/psychological disease e.g. Alzheimer's disease, Parkinson's disease, stroke, transient ischemic attack, Vascular Dementia, Huntington's disease, traumatic brain injury or chronic CNS infection * Have evidence of other medical cause(s) of cognitive impairment * Have evidence of major depression as determined by a positive BDIFS and clinician interview * Have uncontrolled or labile hypertension, tachycardia, cardiovascular or cerebrovascular disease * Have demonstrated a hypersensitivity to amphetamines in the past * The following concomitant medications are not permitted to be used within 28 days of enrollment or during the study * Monoamine Oxidase Inhibitors * Inhaled Beta2-agonists * Sympathomimetics * Antipsychotic agents * Modafinil * Tricyclic Antidepressants * Anticonvulsants other than gabapentin and pregabalin * The following medications are permitted if the patient has been on a stable dose for ≥ 6 weeks: * Short acting benzodiazepines, qhs administration only * Gabapentin and pregabalin Cholinesterase inhibitors other than donepezil, galantamine, and rivastigmine * Memantine * Anti-spasmodics * Selective serotonin reuptake inhibitors and serotonin-norepinephrine reuptake inhibitors.