Marin Zach, Batchelder Kendra A, Toner Brian C, Guimond Lyne, Gerasimova-Chechkina Evgeniya, Harrow Amy R, Arneodo Alain, Khalil Andre
CompuMAINE Laboratory, Department of Mathematics & Statistics, University of Maine, Orono, ME, 04469, USA.
Laboratory of Physical Foundation of Strength, Institute of Continuous Media Mechanics UB RAS, Perm, Russia.
Med Phys. 2017 Apr;44(4):1324-1336. doi: 10.1002/mp.12120. Epub 2017 Mar 14.
The microenvironment of breast tumors plays a critical role in tumorigenesis. As long as the structural integrity of the microenvironment is upheld, the tumor is suppressed. If tissue structure is lost through disruptions in the normal cell cycle, the microenvironment may act as a tumor promoter. Therefore, the properties that distinguish between healthy and tumorous tissues may not be solely in the tumor characteristics but rather in surrounding non-tumor tissue. The goal of this paper was to show preliminary evidence that tissue disruption and loss of homeostasis in breast tissue microenvironment and breast bilateral asymmetry can be quantitatively and objectively assessed from mammography via a localized, wavelet-based analysis of the whole breast.
A wavelet-based multifractal formalism called the 2D Wavelet Transform Modulus Maxima (WTMM) method was used to quantitate density fluctuations from mammographic breast tissue via the Hurst exponent (H). Each entire mammogram was cut in hundreds of 360 × 360 pixel subregions in a gridding scheme of overlapping sliding windows, with each window boundary separated by 32 pixels. The 2D WTMM method was applied to each subregion individually. A data mining approach was set up to determine which metrics best discriminated between normal vs. cancer cases. These same metrics were then used, without modification, to discriminate between normal vs. benign and benign vs. cancer cases.
The density fluctuations in healthy mammographic breast tissue are either monofractal anti-correlated (H < 1/2) for fatty tissue or monofractal long-range correlated (H>1/2) for dense tissue. However, tissue regions with H~1/2, as well as left vs. right breast asymetries, were found preferably in tumorous (benign or cancer) breasts vs. normal breasts, as quantified via a combination metric yielding a P-value ~ 0.0006. No metric considered showed significant differences between cancer vs. benign breasts.
Since mammographic tissue regions associated with uncorrelated (H1/2) density fluctuations were predominantly in tumorous breasts, and since the underlying physical processes associated with a H1/2 signature are those of randomness, lack of spatial correlation, and free diffusion, it is hypothesized that this signature is also associated with tissue disruption and loss of tissue homeostasis.
乳腺肿瘤的微环境在肿瘤发生过程中起着关键作用。只要微环境的结构完整性得以维持，肿瘤就会受到抑制。如果组织结构因正常细胞周期的破坏而丧失，微环境可能会起到肿瘤促进作用。因此，区分健康组织和肿瘤组织的特性可能不仅仅在于肿瘤特征，还在于周围的非肿瘤组织。本文的目的是展示初步证据，即通过对整个乳房进行基于小波的局部分析，可以从乳房X光片中定量、客观地评估乳腺组织微环境中的组织破坏和稳态丧失以及双侧乳腺不对称性。
使用一种基于小波的多重分形形式主义，即二维小波变换模极大值（WTMM）方法，通过赫斯特指数（H）对乳房X光片中的乳腺组织密度波动进行定量分析。每张完整的乳房X光片按照重叠滑动窗口的网格化方案被切割成数百个360×360像素的子区域，每个窗口边界相隔32像素。二维WTMM方法分别应用于每个子区域。建立了一种数据挖掘方法来确定哪些指标能最好地区分正常病例和癌症病例。然后，这些相同的指标未经修改就被用于区分正常病例和良性病例以及良性病例和癌症病例。
健康乳房X光片中的乳腺组织密度波动，对于脂肪组织是单分形反相关的（H < 1/2），对于致密组织是单分形长程相关的（H > 1/2）。然而，通过产生P值约为0.0006的组合指标定量分析发现，H~1/2的组织区域以及左右乳房的不对称性在肿瘤性（良性或癌症）乳房中比在正常乳房中更为常见。所考虑的指标在癌症乳房和良性乳房之间均未显示出显著差异。
由于与不相关（H1/2）密度波动相关的乳房X光片组织区域主要存在于肿瘤性乳房中，并且由于与H1/2特征相关的潜在物理过程是随机性、缺乏空间相关性和自由扩散，因此推测这种特征也与组织破坏和组织稳态丧失有关。
