Conceptual and practical implications of breast tissue geometry: Toward a more effective, less toxic therapy
Conceptual and practical implications of breast tissue geometry: Toward a more effective, less toxic therapy
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DOI：
10.1634/theoncologist.10-6-370
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发表时间：
2005-06-01
期刊：
影响因子：
5.8
通讯作者：
Norton, L
中科院分区：
文献类型：
--
作者：
Norton, L
数学提供了对肿瘤发生的复杂过程的更好理解。基于Gompertzian现象和Norton-Simon假说，可以通过更大的化疗剂量率来增强细胞杀伤。1995年Bonadonna等人的研究和CALGB/Intergroup C9741研究的结果表明，剂量密集组患者的无病生存期和总生存期显著延长。由于Gompertzian动力学的适用性，人们的注意力已转向Gompertzian曲线的病因。乳腺肿瘤的尺寸，与生物学中的所有组织尺寸一样，可以通过分形计算。细胞密度较低的组织通常具有比具有较多细胞的组织更低的分形维数（即，较高的单元密度通常是由于较高的分形维数）。密度是细胞数除以组织体积。当允许生长时，具有较低分形维数的组织的密度迅速下降。然而，由于肿瘤具有更高的分形质量维数，因此随着其生长更大而保持高密度，从而导致更快的生长速率和更大的最终尺寸。乳腺浸润性导管腺癌的分形维数高（即，2.98），这导致与正常乳腺组织相比非常致密的组织（具有约2.25的分形维数）。正如预期的那样，较高的分形维数导致高增长率。
Mathematics provides greater understanding of the complex process of tumorigenesis.Based on the Gompertzian phenomenon and the Norton-Simon hypothesis, enhanced cell kill can be obtained through a greater chemotherapy dose rate. Results from the 1995 Bonadonna et al. study and the CALGB/Intergroup C9741 study demonstrated that patients in the dose-dense arms had significantly longer disease-free survival and overall survival.Because of the demonstrated applicability of Gompertzian kinetics, attention has been turned to the etiology of the Gompertzian curve. Breast tumor dimensions, as with all tissue dimensions in biology, can be calculated by fractals. A less cell-dense tissue usually has a lower fractal dimension than a tissue with more cells (i.e., a higher cell density is usually due to a higher fractal dimension). Density is the number of cells divided by the tissue volume. When allowed to grow, the density of a tissue with a lower fractal dimension drops quickly. However, a tumor, since it has a higher fractal mass dimension, maintains a high density as it grows bigger, resulting in a more rapid growth rate and a larger final size. Fractal dimensions of infiltrating ductal adenocarcinomas of the breast are high (i.e., 2.98), which results in a very dense tissue compared with normal breast tissue (with a fractal dimension of about 2.25). As expected, the higher fractal dimension results in a high rate of growth.