Fig. 4

Comparison of the observed distribution of breast tumor locations from (Morris & Kwong, 2004) with the fractional probability of at least one hot spot in the different regions of the breast assuming a Poisson distribution of microvessels in 2D. In our simulation, the sampling circles had a radius of 200 μm. A hot spot was defined as a sampling circle with at least 5 microvessels. The overall cross section of the breast was assumed to be a circle with a radius of 7 cm. The fraction of tissue in the upper outer quadrant (UOQ), upper inner quadrant (UIQ), lower outer quadrant (LOQ), lower inner quadrant (LIQ), and central (nipple) region were assumed to be 0.38, 0.14, 0.24, 0.19, and 0.05, respectively. (Since the fraction of breast tissue in the different regions of the breast has not been measured, these numbers are based on estimates from Dr. Karen Lane, a breast surgeon at the University of California Irvine Medical Center.) To test our model, we used the two published 2D mean microvessel densities of 1 (Carpenter et al., 2011) and 61 (El-Gohary et al., 2009) microvessels/mm². We modulated the microvessel density in various regions of the breast according to the total hemoglobin concentration measured by near infrared diffuse optical spectroscopy in different regions of the left breast of postmenopausal women (Shah et al., 2004), i.e., we used the following values for the total hemoglobin: h(UOQ) = 16 μM, h(LOQ) = 12 μM, h(LIQ) = 13 μM, h(UIQ) = 15 μM, and h(AR) = 19 μM