The principles of mathematical analysis for vertebral sections and the research of spinal lesions
LIU Xiao-yong, YANG Hui-lin, LUO Zong-ping
Chinese Journal of Clinical Anatomy ›› 2016, Vol. 34 ›› Issue (4) : 439-443.
The principles of mathematical analysis for vertebral sections and the research of spinal lesions
Objective To analyze stress transmission rule of spinal vertebral body - intervertebral disc with mathematical and physical principles; to analyze the correlation between stress transmission rule of spinal vertebral body - intervertebral disc and clinical pathology. Methods The transverse diameter (L) and sagittal diameter (H) of the upper and lower sections on each vertebral body of C2~S1 in 10 intact spinal specimens were measured. Similarity principle of geometry was used: the area changes of upper and lower sections of vertebral body/intervertebral disc could be expressed in mathematical equations S1/S2=(a*b)/(A*B) and S=π/4*L*H to analyze the structure law of upper and lower sections of vertebral bodies; According to the structure of the intervertebral disc, principle of hydrostatic pressure F1/F2=S1/S2 was used to analyze the law of intervertebral disc pressure change. Results With regard to the spinal vertebral body section structure, the area increased in a S-shaped curve from the lower section of C2 to lower section of L4. The section area decreased from the lower section of L4 to the upper section of S1. The transverse diameter and sagittal diameter of the vertebral body - intervertebral disc determined the section area of the vertebral body and pressure coefficient K, K=L*H. Conclusion The structure of spinal vertebral body-intervertebral disc itself determines the specific mechanical transmission and distribution characteristics of the spine; Establishment of mathematical equations to recognize the structure and mechanical transmission law of the spine can help more intuitively understand and observe spinal mechanical characteristics and patterns of clinical spinal lesions.
Spine / Vertebral body / Intervertebral disc / Transverse diameter / Sagittal diameter / Mathematics and physics
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