ABSTRACT
BACKGROUND AND OBJECTIVE: Harmonious interactions of five representative organs: kidney, liver, heart, spleen, and lung, improve metastasis and cell divisions, and abnormal cell division causes cancer cell development. The research is processed through a mathematical approach based on win-win principle of five organs to generate medicine in blood vessel. The variations of solute medicine amount in blood vessel with respect to the flow rates of injected drugs are interpreted. The alterations of tumor cells density and tumor angiogenesis factor concentration are described according to the recovery of five organs' functions. METHODS: A compartmental analysis is applied to obtain medicine concentration in blood vessel by the functional recovery of five organs considering time level ti, the reaction rate coefficient Rj, and the medicine flow rate α. Random motility and chemotaxis in response to tumor angiogenesis factor gradients are comprised to derive mathematical governing equations for tumor cells motion and a finite volume method with time-changing is adopted to obtain numerical solutions due to the complexity of the governing equations. RESULTS: Drug concentration in blood vessel grows as heart reaction rate increases, and the medicine made through the functional enhancements of five representative organs is highly influential to restrain the activity of tumor angiogenesis factor. With the growth of medicine concentration in blood vessel according to the decline of reaction rate and medicine flow rate, tumor cells reacts hypersensitively at the moment of medicines injection and the density of tumor cells approached to zero. CONCLUSIONS: Consequently, reaction rate, time level, and medicine flow rate are crucial factors in the determination of medicine amount in blood vessel and to control tumor angiogenesis factor concentration, and harmonious balanced functions among five organs based on win-win principle contribute to control the activity of tumor cells.
Subject(s)
Angiogenesis Inducing Agents , Spleen , Liver , Kidney , LungABSTRACT
The thermoelastic behaviors of such as temperature distribution, displacements, and stresses in thermal barrier coatings (TBCs) are seriously influenced by top coat thickness and edge conditions, which were investigated based on the thermal and mechanical properties of plasma-sprayed TBCs. A couple of governing partial differential equations were derived based on the thermoelastic theory. Since the governing equations are too involved to solve analytically, a finite volume method was developed to obtain approximations. The thermoelastic characteristics of TBCs with the various thicknesses and microstructures were estimated through mathematical approaches with different edge conditions. The results demonstrated that the top coat thickness and the edge condition in theoretical analysis are crucial factors to be considered in controlling the thermoelastic characteristics of plasma-sprayed TBCs.
ABSTRACT
The thermoelastic characteristics of plasma-sprayed thermal barrier coatings (TBCs) have been analyzed using mathematical modeling. Two types of TBC model, cylinder and circular disk which are commercial plasma-sprayed TBCs, subjecting to symmetric temperature distribution to the radial and longitudinal directions, respectively, were taken into consideration. Based on the thermoelastic theories, a second order ordinary differential equation was derived for the cylinder model and a pair of partial differential equations were set up for the circular disk model. The analytic solution was obtained from the ordinary differential equation, while a finite volume method was developed for numerical solutions to the pair of partial differential equations due to the complexity of governing equations. The thermoelastic characteristics of TBC models, such as temperature distributions, displacements, and stresses, were displayed according to the obtained solutions. The rate of heat conduction in the section of the top coat is relatively slow in comparison with the substrate, and no profound difference appears in the temperature distribution between two TBC models. The highest longitudinal tensile stress is expressed at the bond coat of both models, and the substrate is under the compressive stresses to the circumferential direction. While the cylinder expands to the positive longitudinal direction only, the expansion in the circular disk occurs to both the positive and negative longitudinal directions. Relatively large displacement and stresses exhibit in the cylinder as compared with the circular disk. In the circular disk, the stresses to the radial direction undulate at each section, and the displacement profile displays that the width of the circular disk is slightly narrowed. The results demonstrate that the mechanical and thermal properties of the top and bond coats are the crucial factors to be considered in controlling the thermoelastic characteristics of plasma-sprayed TBCs.
ABSTRACT
During physical exertion the consumption rate increases and some cells suffer from the lack of oxygen. The time-wise evolution of hypoxia is analyzed mathematically under the condition the perfusion of each capillary is constant. The domain used contains multiple non-homogeneous capillaries of different solute out. Cells surrounding capillaries may consume or preserve more oxygen than are necessary at the beginning of new environment.
