Department of Medical Biotechnologies, University of Siena, Siena, Italy.
Clin Exp Rheumatol. 2013 May-Jun;31(3):389-93. Epub 2013 Feb 13.
We aimed to measure the fractal dimension on x-ray images and ultrasonographic parameters of the os calcis of bone from 4 districts in osteoporotic patients and in control subjects, in order to test the hypothesis that ultrasonographic parameters correlate to the fractal dimension obtained on x-ray images.
Fractal analysis on radiological images from 4 bone districts (proximal femur, calcaneus, metacarpus and 3rd phalanx) was performed in a study comparing ultrasonographic evaluation of the os calcis in severe osteoporotic patients and in control cases. We studied 86 x-ray-views from patients with severe reduction of ultrasound Stiffness Index and in healthy women. Ultrasound measurements of left os calcis were performed using the Lunar Achilles-Plus instrument. Fractal analysis was performed using the box-counting method.
In healthy subjects, fractal dimension, D, measure of structural complexity, resulted close to the topological dimension (no fractal structure), TD, in femur (1.99±0.03)and phalanx (1.96±0.03), D differed significantly from TD in calcaneus (D=1.90±0.02; p<0.001) and metacarpus (D=1.89±0.03, p<0.001). In osteoporotic subjects, in calcaneus and metacarpus, D was higher (1.94±0.03, 1.93±0.03, respectively) than in healthy subjects (1.90±0.02, 1.89±0.02, respectively, p<0.01). In all the subjects, fractal dimension and ultrasound broadband attenuation T-score correlated significantly in calcaneus and metacarpus (p<0.03 and p<0.02, respectively).
Parameters based on a combination of ultrasonic examination and fractal analysis on radiographic images may add useful structural information regarding the patients' skeleton using non invasive procedures.
我们旨在测量骨质疏松症患者和对照组 4 个骨区的 X 射线图像和跟骨超声参数的分形维数，以验证超声参数与 X 射线图像获得的分形维数相关的假设。
在一项比较严重骨质疏松症患者和对照组跟骨超声评估的研究中，对 4 个骨区（股骨近端、跟骨、掌骨和第 3 指骨）的放射学图像进行分形分析。我们研究了 86 例 X 射线图像，这些图像来自超声硬度指数严重降低的患者和健康女性。使用 Lunar Achilles-Plus 仪器对左跟骨进行超声测量。分形分析采用盒计数法。
在健康受试者中，结构复杂性的分形维数 D 接近拓扑维数（无分形结构），股骨（1.99±0.03）和指骨（1.96±0.03），跟骨（D=1.90±0.02；p<0.001）和掌骨（D=1.89±0.03，p<0.001）的 D 与 TD 显著不同。在骨质疏松症患者中，跟骨和掌骨的 D 较高（1.94±0.03，1.93±0.03），分别高于健康受试者（1.90±0.02，1.89±0.02，p<0.01）。在所有受试者中，跟骨和掌骨的分形维数与超声宽带衰减 T 评分显著相关（p<0.03 和 p<0.02）。
基于超声检查和放射学图像分形分析相结合的参数可能通过非侵入性程序为患者骨骼提供有用的结构信息。
