Inclusion Criteria:  Male and female subjects must be 18-65 years of age Diagnosis of primary progressive MS according to 2017 revised McDonald criteria (26) EDSS score at screening 3.0-6.5 that was not acquired within the last 6 months Stable disease state as evidenced by no significant change in EDSS (1 point or more) in the last 3 months Patients must have a suitably matched, banked UCB per section 5.3 Able to complete a written informed consent prior to any study assessments Patients of childbearing potential must practice effective contraception during the study, and be willing to continue contraception for at least 6 months after DUOC-01 dosing so that, in the opinion of the Investigator, they will not become pregnant during the course of the study. Patient is a good candidate for the trial, in the opinion of the Investigators Subjects on disease-modifying therapies upon entering the study must continue on these therapies as a concomitant treatment throughout the course of the study to minimize additional variables. However, changes in these disease-modifying therapies can occur at the clinician's discretion, if there are clinical reasons to do so, which would be documented.  Exclusion Criteria:  1. Prior organ, tissue, or stem cell transplant or cell therapy within 3 years of study entry 2. Diagnosis of a progressive neurological disorder other than MS 3. Active, chronic disease of the immune system other than MS 4. Any medical condition that the investigator deems as unsuitable with therapy 5. Inability to have an MRI brain scan, or lumbar puncture (i.e., claustrophobia, allergy to contrast, bleeding disorder, or on anticoagulation) 6. Intractable seizures 7. Chronic aspiration 8. Bleeding disorder 9. Evidence of HIV infection or HIV positive serology 10. Uncontrolled bacterial, viral, or fungal infection within 2 weeks of DUOC-01 administration, as defined by progression while on appropriate treatment 11. History of malignancy of any organ system within the past two years with the exception of basal cell carcinoma or squamous cell carcinoma of the skin that has been excised with clear margins. 12. Requirement of ventilatory support 13. Pregnant or breastfeeding or intention to become pregnant during the study 14. Active concurrent malignancy, or receiving concurrent radiotherapy, immunosuppressive medications for conditions other than MS, or cytotoxic chemotherapy 15. Patients with Suicidal Ideation in the past 6 months per screening on C-SSRS; patients with Suicidal Behavior in the past 2 years, except for Non-suicidal self-injurious behavior 16. Abnormal lab values: Total bilirubin>2.0 mg/dl unless due to Gilbert's syndrome AST or ALT > 5 times the ULN WBC <2.0x 103/μL ALC <0.5 x 103/ μL Serum creatinine >2x ULN eGFR <60 mg/mmol CD4 count <200 cells/mm3