椎体截面的数理学原理分析与脊柱病变的探讨

The principles of mathematical analysis for vertebral sections and the research of spinal lesions

目的测量脊柱椎体终板截面的横径与矢径,利用数理学原理分析脊柱椎体—椎间盘受力传递规律,分析人体脊柱椎体—椎间盘的受力规律与临床病理联系。方法测量10具完整脊柱标本C2-S1各椎体上下截面的横径（L）、矢径（H）,运用几何学相似原理：椎体/椎间盘上下截面面积变化可近似用数学方程表达,S1/S2=（a^＊b）/（A^＊B）,S=π/4^＊L^＊H,分析椎体上下截面的结构规律;根据椎间盘的结构,利用物理学静水液压原理：F1/F2=S1/S2,分析椎间盘压力变化规律;根据数理学原理推测脊柱椎体—椎间盘的结构与力学规律。结果脊柱椎体截面的结构从C2下截面到L4下截面面积呈＂S＂形曲线递增,L4下截面面积最大,L4下截面到S1上截面递减;椎体—椎间盘间截面横径矢径决定其椎体截面面积、压力系数K,K=L^＊H。结论脊柱椎体—椎间盘自身结构决定了脊柱特有的力学传递与分布规律;建立数理学方程来认识脊柱的结构与力学传递规律能更直观的理解与观察脊柱力学特性与临床脊柱病变规律。

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.