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首页> 外文期刊>Frontiers in Physiology >The Quantitative Criteria Based on the Fractal Dimensions, Entropy, and Lacunarity for the Spatial Distribution of Cancer Cell Nuclei Enable Identification of Low or High Aggressive Prostate Carcinomas
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The Quantitative Criteria Based on the Fractal Dimensions, Entropy, and Lacunarity for the Spatial Distribution of Cancer Cell Nuclei Enable Identification of Low or High Aggressive Prostate Carcinomas

机译:基于分形维数,熵和腔隙度的癌细胞核空间分布定量标准可识别低度或高度侵袭性前列腺癌

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Background: Tumor grading, PSA concentration, and stage determine a risk of prostate cancer patients with accuracy of about 70%. An approach based on the fractal geometrical model was proposed to eliminate subjectivity from the evaluation of tumor aggressiveness and to improve the prediction. This study was undertaken to validate classes of equivalence for the spatial distribution of cancer cell nuclei in a larger, independent set of prostate carcinomas. Methods: The global fractal capacity D _(0), information D _(1)and correlation D _(2)dimension, the local fractal dimension (LFD) and the local connected fractal dimension (LCFD), Shannon entropy H and lacunarity λ were measured using computer algorithms in digitalized images of both the reference set ( n = 60) and the test set ( n = 208) of prostate carcinomas. Results: Prostate carcinomas were re-stratified into seven classes of equivalence. The cut-off D _(0)-values 1.5450, 1.5820, 1.6270, 1.6490, 1.6980, 1.7640 defined the classes from C1 to C7, respectively. The other measures but the D _(1)failed to define the same classes of equivalence. The pairs ( D _(0), LFD), ( D _(0), H ), ( D _(0), λ), ( D _(1), LFD), ( D _(1), H ), ( D _(1), λ) characterized the spatial distribution of cancer cell nuclei in each class. The co-application of those measures enabled the subordination of prostate carcinomas to one out of three clusters associated with different tumor aggressiveness. For D _(0)< 1.5820, LFD < 1.3, LCFD > 1.5, H < 0.7, and λ > 0.8, the class C1 or C2 contains low complexity low aggressive carcinomas exclusively. For D _(0)> 1.6980, LFD > 1.7644, LCFD > 1.7051, H > 0.9, and λ < 0.7, the class C6 or C7 contains high complexity high aggressive carcinomas. Conclusions: The cut-off D _(0)-values defining the classes of equivalence were validated in this study. The cluster analysis suggested that the number of the subjective Gleason grades and the number of the objective classes of equivalence could be decreased from seven to three without a loss of clinically relevant information. Two novel quantitative criteria based on the complexity and the diversity measures enabled the identification of low or high aggressive prostate carcinomas and should be verified in the future multicenter, randomized studies.
机译:背景:肿瘤分级,PSA浓度和分期确定前列腺癌患者的风险,准确度约为70%。提出了一种基于分形几何模型的方法,以消除肿瘤侵袭性评估中的主观性并改善预测。进行这项研究以验证在更大,独立的一组前列腺癌中癌细胞核空间分布的等价类。方法:整体分形容量D _(0),信息D _(1)和相关性D _(2)维度,局部分形维数(LFD)和局部连接分形维数(LCFD),香农熵H和色度λ使用计算机算法在前列腺癌的参考集(n = 60)和测试集(n = 208)的数字化图像中测量γ。结果:前列腺癌被重新划分为七个等价类。截止的D _(0)值1.5450、1.5820、1.6270、1.6490、1.6980、1.7640分别定义了从C1到C7的类别。除D _(1)之外的其他度量均未能定义相同的等价类。对(D _(0),LFD),(D _(0),H),(D _(0),λ),(D _(1),LFD),(D _(1),H ),(D _(1),λ)描述了每个类别中癌细胞核的空间分布。这些措施的共同应用使前列腺癌从属于与不同肿瘤侵袭性相关的三类之一。对于D _(0)<1.5820,LFD <1.3,LCFD> 1.5,H <0.7和λ> 0.8,C1或C2类仅包含低复杂度低侵袭性癌。对于D _(0)> 1.6980,LFD> 1.7644,LCFD> 1.7051,H> 0.9和λ<0.7,C6或C7类包含高复杂性高侵袭性癌。结论:本研究验证了定义等价类的截止D _(0)值。聚类分析表明,在不损失临床相关信息的情况下,主观格里森等级的数量和等效的客观等级的数量可以从七个减少到三个。基于复杂性和多样性措施的两个新颖的定量标准可以识别低度或高度侵袭性前列腺癌,并应在未来的多中心,随机研究中得到验证。

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