S. Negin Mortazavi

Mathematical Modeling of Mammary Ducts in Lactating Human Females

This work studies a model for milk transport through lactating human breast ducts and describes mathematically the mass transfer from alveolar sacs through the mammary ducts to the nipple. In this model, both the phenomena of diffusion in the sacs and conventional flow in ducts have been considered. The ensuing analysis reveals that there is an optimal range of bifurcation numbers leading to the easiest milk flow based on the minimum flow resistance. This model formulates certain difficult-to-measure values like diameter of the alveolar sacs and the total length of the milk path as a function of easy-to-measure properties such as milk fluid properties and macroscopic measurements of the breast. Alveolar dimensions from breast tissues of six lactating women are measured and reported in this paper. The theoretically calculated alveoli diameters for optimum milk flow (as a function of bifurcation numbers) show excellent match with our biological data on alveolar dimensions. Also, the mathematical model indicates that for minimum milk flow resistance the glandular tissue must be within a short distance from the base of the nipple, an observation that matches well with the latest anatomical and physiological research.

Mathematical analysis of mammary ducts in lactating human breast.

This work studies a simple model for milk transport through lactating human breast ducts, and describes mathematically the mass transfer from alveolar sacs through the mammary ducts to the nipple. In this model both the phenomena of diffusion in the sacs and conventional flow in ducts have been considered. The ensuing analysis reveals that there is an optimal range of bifurcation numbers leading to the easiest milk flow based on the minimum flow resistance. This model formulates certain difficult-to-measure values like diameter of the alveolar sacs, and the total length of the milk path as a function of easy-to-measure properties such as milk fluid properties and macroscopic measurements of the breast. Alveolar dimensions from breast tissues of six lactating women are measured and reported in this paper. The theoretically calculated alveoli diameters for optimum milk flow (as a function of bifurcation numbers) show excellent match with our biological data on alveolar dimensions. Also, the mathematical model indicates that for minimum milk flow resistance the glandular tissue must be within a short distance from the base of the nipple, an observation that matches well with the latest anatomical and physiological research.

Effect of porous media properties on heat transfer in triangular porous duct

This study presents an analysis of forced convection in a porous triangular channel. The flow is laminar, fully developed and assumed to have constant properties. The porous channel has an isotropic matrix and the boundary conditions are fixed with constant temperature. In this paper, accurate analytical solutions are presented to determine the effects of apex angle and porous media properties on the velocity and temperature distribution in a triangular channel along with the friction factor fRe, and Nusselt number NuT. The presentaion includes numerical features of the exact series solution using Brinkman’s model. Numerical results for dimensionless average temperature and velocity are presented for various porosities, permeabilities and apex angles.Copyright

Lactation in the Human Breast From a Fluid Dynamics Point of View

This study is a collaborative effort among lactation specialists and fluid dynamic engineers. The paper presents clinical results for suckling pressure pattern in lactating human breast as well as a 3D computational fluid dynamics (CFD) modeling of milk flow using these clinical inputs. The investigation starts with a careful, statistically representative measurement of suckling vacuum pressure, milk flow rate, and milk intake in a group of infants. The results from clinical data show that suckling action does not occur with constant suckling rate but changes in a rhythmic manner for infants. These pressure profiles are then used as the boundary condition for the CFD study using commercial ansys fluent software. For the geometric model of the ductal system of the human breast, this work takes advantage of a recent advance in the development of a validated phantom that has been produced as a ground truth for the imaging applications for the breast. The geometric model is introduced into CFD simulations with the aforementioned boundary conditions. The results for milk intake from the CFD simulation and clinical data were compared and cross validated. Also, the variation of milk intake versus suckling pressure are presented and analyzed. Both the clinical and CFD simulation show that the maximum milk flow rate is not related to the largest vacuum pressure or longest feeding duration indicating other factors influence the milk intake by infants.

Modeling of milk flow in mammary ducts in lactating human female breast

A transient laminar Newtonian three-dimensional CFD simulation has been studied for milk flow in a phantom model of the 6-generations human lactating breast branching system. Milk is extracted by the cyclic pattern of suction from the alveoli through the duct and to the nipple. The real negative (suction) pressure data are applied as an outlet boundary condition in nipple. In this study, the commercial CFD code (Fluent Inc., 2004) is employed for the numerical solution of the milk flow. The milk intake flow rate from simulation is compared to the real clinical data from published paper. The results are in good agreement. It is believed that the methodology of the lactating human breast branching modeling proposed here can provide potential guidelines for further clinical and research application.

Effect of inertia and viscosity force on heat transfer in triangular porous channels

The present investigation aims analytically at considering the fully developed forced convection in a fluid saturated triangular porous channel, with imposed heat flux at walls. The flow in the channel defined by the Brinkman-Forchheimer-extended Darcy equation which includes the inertial and viscous terms. The generalized momentum equation, along with energy equation were solved by applying the accurate analytical solutions based on the Galerkin Integral Method. The results show the effects of Darcy number, viscosity ratio, and inertia force on velocity and temperature profiles.

A Heat Transfer in Iso-Thermal Triangular Channel Filled With Porous Media

This study presents an analysis of forced convection in a porous triangular channel. The flow is laminar, fully developed and assumed to have constant properties. The porous channel has an isotropic matrix and the boundary conditions are fixed with a constant temperature. In this paper, accurate analytical solutions are presented to determine the effects of apex angle and porous media properties on the temperature distribution in a triangular channel along with the Nusselt number NuT.Copyright

Effect of Apex Angle on the Flow and Heat Transfer in Triangular Porous Ducts With Iso-Flux Boundary Conditions

This study presents an analysis of fully developed laminar flow in a porous triangular channel. The flow is assumed to have constant properties and the porous channel is an isotropic matrix. Very accurate analytical solutions are presented by Galerkin Integral method for iso-flux boundary conditions. In this paper, the effect of apex angle in the triangular channel is shown on the velocity and temperature distributions along with the friction factor fRe, and the Nusselt number NuH .Copyright