![]() This study details an anatomically realistic anthropomorphic 3D model of the SSS based on high-resolution MR imaging of a healthy human adult female. Maximum Reynolds number was 174.9 and average Womersley number was 9.6, likely indicating presence of a laminar inertia-dominated oscillatory CSF flow field. Surface area of these features was 318.52, 112.2 and 232.1 cm 2 respectively. Volume of the dura mater, spinal cord and NR was 123.1, 19.9 and 5.8 cm 3. The final model had a total of 139,901 vertices with a total CSF volume within the SSS of 97.3 cm 3. Final model geometry and hydrodynamics were characterized in terms of axial distribution of Reynolds number, Womersley number, hydraulic diameter, cross-sectional area and perimeter. Model simplification and smoothing was performed to produce a final model with minimum vertices while maintaining minimum error between the original segmentation and final design. Key design criteria for each NR pair included the radicular line, descending angle, number of NR, attachment location along the spinal cord and exit through the dura mater. 31 pairs of semi-idealized dorsal and ventral nerve rootlets (NR) were added to the model based on anatomic reference to the magnetic resonance (MR) imaging and cadaveric measurements in the literature. An expert operator completed manual segmentation of the CSF space with detailed consideration of the anatomy. ![]() MethodsĪ subject-specific 3D model of the SSS was constructed based on high-resolution anatomic MRI. An accurate anthropomorphic representation of these features is needed for development of in vitro and numerical models of cerebrospinal fluid (CSF) dynamics that can be used to inform and optimize CSF-based therapeutics. ![]() contains another special case for you to consider.The spinal subarachnoid space (SSS) has a complex 3D fluid-filled geometry with multiple levels of anatomic complexity, the most salient features being the spinal cord and dorsal and ventral nerve rootlets. You can simplify your explanation by referring to the proof you created for opposite-handed triangles. Then use the construction from the previous activity to superpose an image of `triABC` onto `triDEF`.Īs you do this construction, describe it and explain why it works. On page 1 transform `triABC` so that the image is opposite-handed to `triDEF`. What's the simplest way you can transform `triABC` to make its image opposite-handed compared to `triDEF`? Why is it impossible to put two similarly-handed triangles into superposition using the same reflections you used for opposite-handed triangles? In this activity you'll do just that, but instead of creating an entirely new proof you'll find a easier way, by using the proof you've already created. ![]() But what if the two triangles are similarly handed? How can you construct/prove the SSS theorem for similarly-handed triangles? In all three of the examples `triABC` and `triDEF` were opposite-handed: one clockwise and one counter-clockwise. Other Cases for the SSS Theorem: In the previous activity, you used three examples to construct and prove the SSS Theorem. ![]()
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