ABSTRACT
Mathematical model for the tumor growth incorporating energy supply and requirement, angiogenesis efficiency and effect of elasticity of adjacent normal tissue to understand tumor biology and predict saturation status is rare to find. This study is conducted to address these issues. We propose mathematical expressions to explain alterations of tumor cell density (nT), microvessel density (MVD), and growth rate(r) during the development of brain tumors. We assume that nT increases during the growth of the tumor due to the increase of external pressure from the initial cell density (nT0); nT0 is same as the external normal tissue. The rate of increase in tumor cells (dNT/dt) depends on the rate of energy available for the creation of new cells and the energy required for a single cell division(?). Due to the increase of tumor cell density, hypoxia is developed, which up-regulates the secretion of vascular endothelial growth factor (VEGF) and new capillaries are generated. Therefore, the surface area density of capillaries (Acs) in tumors increases. Hence, we consider that Acs(t) ? nT(t). A modified logistic equation is developed. Temporal variations of nT(t), Acs(t), r(t) and tumor cell population ‘NT(t)’ are examined. The expressions of saturated cell density(nTM), saturated microvessel surface area density (AcsM) and tumor saturation time(Ts) are formulated. An important feature, tumor saturation factor ‘fTS’ is determined. When fTS<1, a tumor will saturate at Ts, and nTM depends solely on fTS.
ABSTRACT
Background: An increase in number of melanocytes in the basal cell layer of the epidermis is an important feature in many disorders of hyperpigmentation. In this study, we attempted an objective evaluation of the linear density of melanocytes and keratinocytes, along with other epidermal characteristics, in periorbital hyperpigmentation using immunohistochemistry and morphometric techniques. Methods: Melanocytes and epidermal parameters were assessed by digital morphometry in 30 newly diagnosed cases of periorbital hyperpigmentation and 14 controls from the post-auricular region. Melanocytes were labelled with the immunohistochemical stains, Melan-A and tyrosinase. We studied the linear keratinocyte density, mean linear melanocyte density, ratio of melanocytes to keratinocytes, the ratio between inner and outer epidermal length, maximum epidermal thickness and minimum epidermal thickness. Results: Melan-A expression of melanocytes showed strong positive correlation (r = 0.883) with the tyrosinase expression. Mean linear melanocyte density was 24/mm (range: 13–30/ mm) in cases and 17/mm (13–21/mm) in controls and this difference was statistically signifi cant (P < 0.001). The mean ratio of melanocyte to keratinocyte was 0.22 (0.12– 0.29) in cases and 0.16 (0.12–0.21) in controls; again, this difference was statistically signifi cant (P < 0.001). There was a mild negative correlation with linear keratinocyte density (r = −0.302) and the ratio between inner and outer epidermal length (r = −0.456). However, there were no differences in epidermal thicknesses. Limitations: There were fewer control biopsies than optimal, and they were not taken from the uninvolved periorbital region. Conclusion: Mean linear melanocyte density and the ratio of melanocytes to keratinocytes is increased in cases with periorbital hyperpigmentation. It is, therefore, likely that increased melanocyte density may be the key factor in the pathogenesis of periorbital hyperpigmentation.
ABSTRACT
Background: Vascular proliferation, inflammation and epidermal changes are important features in the pathogenesis of psoriasis. Aims: In this study we attempted an objective evaluation of these parameters using morphometry. Methods: Inflammation, microvessels and epidermal parameters were assessed in 50 newly diagnosed cases of psoriasis vulgaris (between 01 Nov 2008 and 31 Oct 2011) by morphometry. Parameters studied were microvessel density, microvessel caliber, inflammatory cell density in dermis, ratio between inner and outer epidermal length, maximum epidermal thickness, minimum epidermal thickness and difference between maximum epidermal thickness and minimum epidermal thickness. Results: Microvessel caliber showed moderate correlation (r = 0.645) and microvessel density, weak correlation (r = 0.226) with inflammatory cell density in dermis. Both these parameters also showed mild positive correlation with "ratio between inner and outer epidermal length". All parameters except minimum epidermal thickness showed mild positive correlation with inflammatory cell density in dermis. Conclusion: All microvessels and epidermal parameters showed positive correlation with dermal inflammation; and epidermal parameters exhibited positive correlation with micro-vascular dilation. It is likely that inflammation is a key factor in the pathogenesis of psoriasis.