Thermal Modeling of the Human Lactating Breast

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2018-05

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Abstract

In this work, the lactating human breast has been studied mathematically from the bio-heat transfer point of view in one and three dimensional cases. The effect of the milk in the milk production system and milk transportation system of the breast on the bio-heat transfer has been considered in the form of the convective heat transfer through the breast tissue. In the one dimensional case, the related bio-heat transfer equation has been solved analytically and numerically and the results showed a good agreement after validating with other studies in the literature. The effect of the external heat flux at the outer surface and the indirect effect of the infant’s periodic suckling pressure on the temperature distribution of the breast tissue has been investigated. In the three dimensional case, expanding the one dimensional form of the bio-heat equation is required to model the bio-heat transfer in the lactating breast three dimensionally. However, due to the complexity of the analytical solution in three dimensional equations, the governing equations are solved numerically by using ANSYS Fluent. In order to have an accurate bio-heat model in the ANSYS Fluent, a three dimensional model of the milk flow within the breast is required initially since the bio-heat transfer of the lactating breast is coupled with the milk flow through the tissue. The breast tissue is assumed as porous tissue since it is a fatty tissue full of bifurcated tree shape milk ducts, alveoli sacs and mammary glands. Up to 7 lobes with 8 bifurcation levels and each level as a porous medium with different porosities are considered. Existing clinical data of the infant’s suckling pressure pattern have been used as the boundary conditions in the three dimensional simulations. The porous model has been cross-validated with clinical data and previous non-porous simulation model. Based on the clinical data of milk intake rate and suckling pressure from 15 infants, an appropriate range for permeability of the breast tissue is obtained. The developed porous media model of the lactating breast from fluid dynamic point of view, is used to simulate the three dimensional thermal model of the lactating breast and results for different related factors such as infant’s suckling pressure over the breastfeeding stages, changing milk viscosity during the breastfeeding period, and different heat fluxes applied on the breast skin are presented. As a result, a pattern to improve the breastfeeding by using the heating pad is introduced.

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Heat—Transmission, Lactation, Breast milk, Porous materials—Thermal properties, Breastfeeding

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