基于粒计算的腰椎-腰背肌系统生物力学负荷差异及其与疼痛指数的关联机制

doi:10.3877/cma.j.issn.2095-655X.2025.04.005

中华诊断学电子杂志 ›› 2025, Vol. 13 ›› Issue (04) : 242 -247. doi: 10.3877/cma.j.issn.2095-655X.2025.04.005

智能医学

基于粒计算的腰椎-腰背肌系统生物力学负荷差异及其与疼痛指数的关联机制

欧阳林¹^,^†(

), 欧阳川², 张清华¹, 朱巧珍¹, 陈鑫¹, 陈鼎伟¹, 杨立杰³

¹363000　漳州，第九〇九医院　厦门大学附属东南医院放射诊断科，厦门大学医学院医学影像研究所
²330000　南昌大学玛丽女王学院
³363000　漳州，闽南师范大学数学与统计学院

收稿日期:2025-05-23 出版日期:2025-11-26
通信作者: 欧阳林
基金资助:
福建省自然科学基金(L2023037)

The biomechanical load differences of the lumbar vertebrae-lumbar muscle system based on granular computing and their association mechanism with pain score

Lin Ouyang¹^,^†(), Chuan Ouyang², Qinghua Zhang¹, Qiaozhen Zhu¹, Xin Chen¹, Dingwei Chen¹, Lijie Yang³

¹Department of Radiology, the 909th Hospital (Dongnan Hospital Affiliated to Xiamen University), Institute of Medical Imaging, School of Medicine, Xiamen University, Zhangzhou 363000, China
²Queen Mary College, Nanchang University, Nanchang 330000, China
³School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China

Received:2025-05-23 Published:2025-11-26
Corresponding author: Lin Ouyang

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引用本文：

欧阳林, 欧阳川, 张清华, 朱巧珍, 陈鑫, 陈鼎伟, 杨立杰. 基于粒计算的腰椎-腰背肌系统生物力学负荷差异及其与疼痛指数的关联机制[J/OL]. 中华诊断学电子杂志, 2025, 13(04): 242-247.

Lin Ouyang, Chuan Ouyang, Qinghua Zhang, Qiaozhen Zhu, Xin Chen, Dingwei Chen, Lijie Yang. The biomechanical load differences of the lumbar vertebrae-lumbar muscle system based on granular computing and their association mechanism with pain score[J/OL]. Chinese Journal of Diagnostics(Electronic Edition), 2025, 13(04): 242-247.

目的

探讨下腰痛患者在直立与弯腰15°负重20 kg体位下，腰椎-腰背肌系统的生物力学负荷差异及其与疼痛指数(PS)的关联机制。

方法

选取2018年5月至2021年5月就诊于厦门大学附属东南医院放射诊断科诊断为下腰痛的1 400例患者，按年龄(21~30、31~40、41~50、51~60、61~70、71~80、81~90岁)和性别分层分组。通过生物力学环状应力原理构建数学物理解析型应力模型，分析不同性别、年龄及姿势(直立/弯腰15°负重20 kg)下L₃-L₄、L₄-L₅椎间盘应力PS分布。采用独立样本t检验比较男、女PS差异，Pearson相关分析PS与年龄的相关性，线性趋势检验PS与年龄的线性趋势，双因素方差分析比较男、女性别各年龄L₄-L₅与L₃-L₄椎间盘应力PS比值差异。

结果

在弯腰15°负重20 kg姿势下，各年龄段女性L₃-L₄与L₄-L₅椎间盘应力PS均高于男性，均差异有统计学意义(L₃-L₄：t＝297.51，58.77，70.40，36.57，54.39，73.86，31.40；均P<0.01。L₄-L₅：t＝60.00，49.19，31.28，64.42，180.81，38.69，64.35；均P<0.01)；在直立位，各年龄段女性L₃-L₄椎间盘应力PS高于男性(t＝78.31，28.29，71.04，26.55，24.40，23.87，28.38)，但L₄-L₅椎间盘应力PS低于男性(t＝43.24，40.98，29.14，4.61，10.20，67.22，12.62)，均差异有统计学意义(均P<0.01)。在直立位，女性年龄与L₃-L₄、L₄-L₅椎间盘应力PS均具有相关性，且存在显著的线性趋势(r＝0.914，r²＝0.835；r＝0.939，r²＝0.882；均P<0.01)。而男性在直立位与弯腰15°负重20 kg状态下，年龄与L₃-L₄椎间盘应力PS均具有相关性，且存在显著的线性趋势(r＝0.883，r²＝0.780；r＝0.973，r²＝0.947；均P<0.01)。男、女性别在直立位L₄-L₅与L₃-L₄椎间盘应力PS比值比较(1.410±0.004，1.180±0.004)，差异存在统计学意义(F＝1.265，P<0.01)。

结论

无论男女，L₃-L₄与L₄-L₅椎间盘应力PS与年龄呈显著正相关，提示随年龄增长，腰椎-腰背肌系统的生物力学负荷耐受能力逐渐下降。

关键词: 腰椎退行性病变, 腰痛, 粒计算, 应力, 年龄组

Objective

To explore the differences in biomechanical load of the lumbar vertebrae-lumbar muscle system and their association mechanism with pain score (PS) in patients with low back pain under 2 postures: upright and bending at 15° with a load of 20 kg.

Methods

A total of 1 400 patients diagnosed with low back pain at the Dongnan Hospital Affiliated to Xiamen University from May 2018 to May 2021 were selected and stratified and grouped according to age (21-30, 31-40, 41-50, 51-60, 61-70, 71-80, 81-90 years old) and gender. Based on the principle of biomechanical circular stress, a mathematical and physical analytical stress model was constructed to analyze the stress PS distribution of L₃-L₄ and L₄-L₅ intervertebral discs under different genders, ages and postures (upright/bending at 15° with a load of 20 kg). Independent sample t-test was used to compare the PS differences between male and female groups. Pearson correlation analysis was used to analyze the correlation between PS and age. Linear trend test was used to test the linear trend between PS and age. Two-factor analysis of variance was used to compare the differences in the PS ratio of intervertebral disc stress between L₄-L₅ and L₃-L₄ in each age group between males and females.

Results

Under the posture of bending 15° with a load of 20 kg, the stress PS of intervertebral discs at L₃-L₄ and L₄-L₅ in females were higher than those in males, and the differences were statistically significant (L₃-L₄: t=297.51, 58.77, 70.40, 36.57, 54.39, 73.86, 31.40, all P<0.01. L₄-L₅: t=60.00, 49.19, 31.28, 64.42, 180.81, 38.69, 64.35, all P<0.01) . In the upright position, the stress PS of the L₃-L₄ intervertebral discs in females were higher than those in males (t=78.31, 28.29, 71.04, 26.55, 24.40, 23.87, 28.38), but the stress PS of the L₄-L₅ intervertebral discs were lower than those in males (t=43.24, 40.98, 29.14, 4.61, 10.20, 67.22, 12.62), and the differences were statistically significant (all P<0.01). In the upright position, female age was correlated with the stress PS of intervertebral discs at L₃-L₄ and L₄-L₅, and there were significant linear trends (r=0.914, r²=0.835; r=0.939, r²=0.882; all P<0.01). However, for males in the upright position and the state of bending at 15°with a load of 20 kg, age was correlated with the stress PS of L₃-L₄ intervertebral discs, and there were significant linear trends (r=0.883, r²=0.780; r=0.973, r²=0.947; all P<0.01). The comparison of the PS ratio of intervertebral disc stress between L₄-L₅ and L₃-L₄ in the upright position between male and female genders (1.410±0.004, 1.180±0.004) showed a statistically significant difference (F=1.265, P<0.01).

Conclusion

Regardless of gender, the stress PS of L₃-L₄ and L₄-L₅ intervertebral discs is significantly positively correlated with age, suggesting that the biomechanical load tolerance capacity of the lumbar vertebrae-lumbar muscle system gradually decreases with age.

Key words: Disc degenerative change, Low back pain, Granular computing, Stress, Age groups

图1 腰背肌环状应力示意图注：Fc为L₃-L₄或L₄-L₅椎间盘合力；θ为Fc与椎间盘平面夹角(°)；p为椎间盘突出水平分量压力；σ_h为环状应力

表1 疼痛指数与临床症状的对应关系

腰背肌环状应力	<2	[2，4)	[4~6)	[6~8)	[8~10)	[10~12)	[12~14)	[14~16)	[16~18)	≥18
临床疼痛感觉	无痛感	稍有感觉	隐隐作痛	微痛	疼痛	过疼痛	非常疼痛	严重疼痛	疼痛难耐	剧痛
数字评定量表(分)	1	2	3	4	5	6	7	8	9	10
疼痛指数	1	2	3	4	5	6	7	8	9	10

表1 疼痛指数与临床症状的对应关系

腰背肌环状应力	<2	[2，4)	[4~6)	[6~8)	[8~10)	[10~12)	[12~14)	[14~16)	[16~18)	≥18
临床疼痛感觉	无痛感	稍有感觉	隐隐作痛	微痛	疼痛	过疼痛	非常疼痛	严重疼痛	疼痛难耐	剧痛
数字评定量表(分)	1	2	3	4	5	6	7	8	9	10
疼痛指数	1	2	3	4	5	6	7	8	9	10

表2 不同性别的下腰痛患者不同年龄段直立与弯腰15°负重20 kg时L₃-L₄的PS比较(

±s)

按年龄分层的群粒组(岁)	PS(直立)		t值	P值	PS(弯腰)		t值	P值
按年龄分层的群粒组(岁)	GM	GF	t值	P值	GM	GF	t值	P值
21~30	1.440±0.002	1.670±0.002	78.31	<0.01	4.910±0.002	5.610±0.001	297.51	<0.01
31~40	1.480±0.002	1.630±0.004	28.29	<0.01	4.900±0.003	5.190±0.004	58.77	<0.01
41~50	1.510±0.002	1.690±0.002	71.04	<0.01	4.960±0.003	5.210±0.002	70.40	<0.01
51~60	1.710±0.005	1.900±0.005	26.55	<0.01	5.060±0.005	5.270±0.003	36.57	<0.01
61~70	1.790±0.004	2.010±0.007	24.40	<0.01	5.120±0.003	5.370±0.003	54.39	<0.01
71~80	1.780±0.004	1.920±0.003	23.87	<0.01	5.130±0.004	5.530±0.003	73.86	<0.01
81~90	1.720±0.007	2.230±0.017	28.38	<0.01	5.200±0.007	5.690±0.014	31.40	<0.01

表2 不同性别的下腰痛患者不同年龄段直立与弯腰15°负重20 kg时L₃-L₄的PS比较(

±s)

按年龄分层的群粒组(岁)	PS(直立)		t值	P值	PS(弯腰)		t值	P值
按年龄分层的群粒组(岁)	GM	GF	t值	P值	GM	GF	t值	P值
21~30	1.440±0.002	1.670±0.002	78.31	<0.01	4.910±0.002	5.610±0.001	297.51	<0.01
31~40	1.480±0.002	1.630±0.004	28.29	<0.01	4.900±0.003	5.190±0.004	58.77	<0.01
41~50	1.510±0.002	1.690±0.002	71.04	<0.01	4.960±0.003	5.210±0.002	70.40	<0.01
51~60	1.710±0.005	1.900±0.005	26.55	<0.01	5.060±0.005	5.270±0.003	36.57	<0.01
61~70	1.790±0.004	2.010±0.007	24.40	<0.01	5.120±0.003	5.370±0.003	54.39	<0.01
71~80	1.780±0.004	1.920±0.003	23.87	<0.01	5.130±0.004	5.530±0.003	73.86	<0.01
81~90	1.720±0.007	2.230±0.017	28.38	<0.01	5.200±0.007	5.690±0.014	31.40	<0.01

表3 不同性别的下腰痛患者不同年龄段直立与弯腰15°负重20 kg时L₄-L₅的PS比较(

±s)

按年龄分层的群粒组(岁)	PS(直立)		t值	P值	PS(弯腰)		t值	P值
按年龄分层的群粒组(岁)	GM	GF	t值	P值	GM	GF	t值	P值
21~30	2.180±0.003	1.990±0.003	43.24	<0.01	5.110±0.002	5.310±0.002	60.00	<0.01
31~40	2.240±0.003	2.040±0.003	40.98	<0.01	5.120±0.003	5.320±0.003	49.19	<0.01
41~50	2.190±0.005	1.990±0.005	29.14	<0.01	5.120±0.005	5.320±0.005	31.28	<0.01
51~60	2.130±0.004	2.160±0.004	4.61	<0.01	5.140±0.004	5.490±0.003	64.42	<0.01
61~70	2.450±0.006	2.360±0.007	10.20	<0.01	5.090±0.001	5.350±0.001	180.81	<0.01
71~80	2.190±0.005	2.650±0.005	67.22	<0.01	5.120±0.004	5.380±0.005	38.69	<0.01
81~90	2.650±0.006	2.750±0.006	12.62	<0.01	5.200±0.006	5.710±0.006	64.35	<0.01

表3 不同性别的下腰痛患者不同年龄段直立与弯腰15°负重20 kg时L₄-L₅的PS比较(

±s)

按年龄分层的群粒组(岁)	PS(直立)		t值	P值	PS(弯腰)		t值	P值
按年龄分层的群粒组(岁)	GM	GF	t值	P值	GM	GF	t值	P值
21~30	2.180±0.003	1.990±0.003	43.24	<0.01	5.110±0.002	5.310±0.002	60.00	<0.01
31~40	2.240±0.003	2.040±0.003	40.98	<0.01	5.120±0.003	5.320±0.003	49.19	<0.01
41~50	2.190±0.005	1.990±0.005	29.14	<0.01	5.120±0.005	5.320±0.005	31.28	<0.01
51~60	2.130±0.004	2.160±0.004	4.61	<0.01	5.140±0.004	5.490±0.003	64.42	<0.01
61~70	2.450±0.006	2.360±0.007	10.20	<0.01	5.090±0.001	5.350±0.001	180.81	<0.01
71~80	2.190±0.005	2.650±0.005	67.22	<0.01	5.120±0.004	5.380±0.005	38.69	<0.01
81~90	2.650±0.006	2.750±0.006	12.62	<0.01	5.200±0.006	5.710±0.006	64.35	<0.01

图2 不同性别下腰痛患者在直立位与弯腰15°负重20 kg状态下年龄与PS的线性趋势检验注：图中各点代表各年龄段的平均PS。GF为女性亚群组；GM为男性亚群组；PS为疼痛指数

图3 各年龄段不同性别的下腰痛患者在直立位与弯腰15°负重20 kg状态下椎间盘应力PS比值注：GF为女性亚群组；GM为男性亚群组；PS为疼痛指数

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The biomechanical load differences of the lumbar vertebrae-lumbar muscle system based on granular computing and their association mechanism with pain score

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The biomechanical load differences of the lumbar vertebrae-lumbar muscle system based on granular computing and their association mechanism with pain score