The conus medullaris (Latin for "medullary cone") is the tapered, lower end of the spinal cord. It occurs near lumbar vertebral levels 1 (L1) and 2 (L2), occasionally lower. The upper end of the conus medullaris is usually not well defined.
After the spinal cord tapers out, the spinal nerves continue to branch out diagonally, forming the cauda equina.
The pia mater that surrounds the spinal cord, however, projects directly downward, forming a slender filament called the filum terminale, which connects the conus medullaris to the back of the coccyx. The filum terminale provides a connection between the conus medullaris and the coccyx which stabilizes the entire spinal cord.
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https://www.hindawi.com/journals/ari/2014/351769/ c. D. Moussallem, h. El masri, c. El-yahchouchi, f. Abou fakher, and a. Ibrahim, “relationship of the lumbar lordosis angle to the level of termination of the conus medullaris and thecal sac,” anatomy research international, vol. 2014, article id 351769, 4 pages, 2014. Doi:10.1155/2014/351769
https://www.ncbi.nlm.nih.gov/pmc/articles/pmc3280119/ wong jj, dufton j, mior sa. Spontaneous conus medullaris infarction in a 79 year-old female with cardiovascular risk factors: a case report. The journal of the canadian chiropractic association. 2012;56(1):58-65.