This is a phase I/IIa, randomized, double-blind, two-arms, two-dose administration, placebo controlled, two-way crossover clinical trial in which 10 patients from 18 to 65 years of age affected with chronic traumatic spinal cord will enter the study with the objective to assess the safety and to obtain efficacy data in intrathecal administration of expanded Wharton's jelly mesenchymal stem cells.

This is a phase I/IIa, randomized, double-blind, two-arms, two-dose administration, placebo controlled, clinical trial in which 10 patients from 18 to 65 years of age affected with chronic traumatic spinal cord will enter the study with the objective to assess the safety and to obtain efficacy data in intrathecal administration (L3 level) of expanded Wharton's jelly mesenchymal stem cells. Following the administration patients will remain for 24 h at the hospital and thereafter will be discharged. For the first period, the follow-up is planned at day 7 and at 1, 3 and 6 months. At month 6, the patients will be treated in a crossover way (second period) and will follow the same schedule for the follow-up. First clinical trial evaluation will be performed at 12 month follow-up. From 12 to 18 month after the first infusion, patients will be randomized again to active treatment or placebo (double-blind) in order to assess the safety and efficacy of a second dose at 12 month follow-up. Thereafter, patients will be followed up at 24 and 36 months as part of a long-term follow-up.

Inclusion Criteria:

1. Single spinal cord injury lesion caused by trauma
2. Affected cord segments between T2 and T11, confirmed by magnetic resonance
3. Complete paraplegia (ASIA A)
4. Chronic disease state (between 12 months and 5 years after the injury)
5. Patients from 18 to 65 years of age, both sexes
6. Life expectancy > 2 years
7. Confidence that the patient will attend the follow-up visits.
8. Given informed consent in writing
9. Patient is able to understand the study and its procedures

Exclusion Criteria:

1. Mechanic ventilation
2. Lesion affecting multiple levels
3. Lesion length superior to 3 spinal cord segments, assessed by magnetic resonance
4. Penetrating trauma affecting the spinal cord
5. Positive serology to HIV, HBV, HCV and or syphilis
6. Pregnant woman or without proper anticonceptive measures according to the investigator, or breath feeding
7. Use of metal implants that complicates the MRI interpretation
8. Planned spinal surgery within subsequent 24 month after entering the trial
9. Intrathecal medication or immunosuppressive drugs the previous 60 days.
10. Neurodegenerative diseases
11. Significant abnormal laboratory tests that contraindicates patient's participation in the study.
12. Neoplasia within the previous 5 years, or without complete remission
13. Patient with difficulty for communicating
14. Participation in another clinical trial or treated with an investigational medicinal product the previous 60 days
15. Contraindication for lumbar punction
16. Other pathologic conditions or circumstances that could complicate the participation of the patient in the study according to medical criteria
17. The patient does not accept to be followed-up for a period that could exceed the clinical trial length