Conceptual and Practical Implications of Breast Tissue Geometry: Toward a More Effective, Less Toxic Therapy

Abstract

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.

Modified Gompertz Equation for Electrotherapy Murine Tumor Growth Kinetics: Predictions and New Hypotheses

“…The linear fits of these two regions suggest that the slope of the curve for REG-II is 1.37 times higher than that for REG-I, a fact that corroborates that the TV regression rate is proportional to the rate of growth, in agreement with the NortonSimon hypothesis [39]. Prior to this study, we think that these rates are equal.…”

Early Detection of Recurrent Disease by FDG-PET/CT Leads to Management Changes in Patients With Squamous Cell Cancer of the Head and Neck

“…There is considerable variation among patients with respect to likelihood of recurrence and duration of survival, even after accounting for stage and tumor volume, probably because of biological factors [17]. According to the Gompertzian theory, the log kill is greater in small-volume tumors than in those of larger volume; thus, it is reasonable to speculate that the survival benefit can be compounded if the disease is detected early [18]. Despite corroborative data in the literature [6, 19 -24], the use of PET/HRCT in the follow-up of patients with HNSCC following definitive therapy remains contentious, mainly based on the lack of prospective trials comparing a predefined PET-based follow-up strategy with the conventional approach to address management implications.…”

Weekly epirubicin plus docetaxel as first-line treatment in metastatic breast cancer

“…Furthermore, weekly administration of chemotherapy in a dose-dense schedule is understood to have an anti-angiogenesis effect, constricting the blood supply to tumours and restricting their growth. Thus, the weekly schedule was designed to allow administration of a total dose of drug greater than or equal to that administered with the conventional 3-week schedule, to enhance cumulative cytotoxic activity while reducing the toxicity of the treatment, providing greater therapeutic benefit together with a more favourable tolerability profile (Norton, 1988(Norton, , 2005Burstein et al, 2000;Stammler et al, 2001;Wenzel et al, 2002).…”

“…A weekly schedule could maintain peak blood concentrations below the threshold value of medullar toxicity. This results in a more favourable safety profile, and facilitates maintenance of the correct dosing schedule and completion of the administration cycles (Norton, 1988(Norton, , 2005Burstein et al, 2000;Stammler et al, 2001;Wenzel et al, 2002).…”