Ebook An Application Of The Finite Volume Method To The Bio-Heat-Transfer-Equation In Premature Infants
In Germany 7% of all newborn babies are preterm, corresponding to about 55,000 of about 800,000 newborn babies per year. Reasons for a premature birth may be diseases of the mother (e.g. high blood pressure, diabetes) or sudden complications like infections or shocks. But nevertheless for about half of all premature births no reason can be found. In order to protect premature infants against heat and water-losses to their surroundings, against infections and hypoxemia, incubators and open radiant warmers are widely used. A description of how these devices work and their history of development can be found in [11], an introduction to the general principles of thermoregulation of premature infants in [7].
To better understand the thermoregulation of premature infants in a certain micro-climate, thermoregulatory models and corresponding simulation tools have been developed. Using them it is possible to gain insight into the involved processes and the complexity of the whole thermoregulatory system. They are systematic tools for hyperthermia planning and for the improvement of warming therapy devices. They allow for clinical studies and for the prediction of physiological phenomena without exposing human beings to experiments. In a clinical setting, a sound simulation of the thermoregulation would allow for a proper tuning of the environmental parameter within the incubator with the goal to achieve the optimal living conditions for the specific newborn.
Hardware simulators (manikins, dummies) are an approach to model the thermoregulatory system. Because it is difficult to manufacture them and nearly impossible to adjust them to new parameters, quantitative models have been of keen interest to scientists and engineers for a long time. The work of Bußmann [4] is a milestone of physiological developments. It contains a synopsis of the physiological basics of thermoregulation and the development of a computer model to simulate the dynamic heat transfer processes of a preterm or newborn baby in an incubator.
The processes of molecular heat transfer, metabolic heat production and heat transfer due to blood flow are modelled as well as the heat losses over the skin by transepidermal water loss, radiation, and convection. Furthermore the control mechanisms thermogenesis without shivering and vasomotoric control of the skin are taken into account. Nevertheless the disadvantages of the model are obvious. The geometry of an infant is replaced by a non-realistic compartment model and only homogeneous temperature profiles can be computed.
The series of works by Fischer et al. [10], Fenner [8] and Wronna [20] has taken first steps towards a more realistic modeling. The work [16] presents the development of a numerical method for the time-accurate computation of the temperature distribution inside a premature infant. It is an essential improvement of the model presented in [4], because it allows for simulations in realistic 3-dimensional geometries. Furthermore the dynamic evolution of the temperature distributions can be computed. In addition not only incubator settings, but also the conditions of an open radiant warmer are modelled. Besides, the boundary conditions are modified and a new one for conduction is introduced.
The present paper is a brief summary of [16]. Section 2 describes the modeling and computer simulation of the real geometry of a premature infant by means of MRT-slices and the use of a CFD-grid-generator. In section 3 the mathematical model is outlined. It is an initial boundary value problem (IBVP) consisting of the bio-heat-transfer-equation (BHTE) supplemented by initial and boundary Neumann conditions.
The BHTE describes the temperature distribution inside the preterm baby taking into account the molecular heat transfer, metabolic heat production, heat transfer due to blood flow and respiratorical water loss. In order to solve the BHTE numerically, section 4 surveys the constituent parts of a finite volume method. First, finite volume methods are a natural choice for the numerical solution of the BHTE because they are directly applicable to its integral form. Second, the use of unstructured grids is necessary in order to cope with realistic geometries. Finite volume methods are formulated on general control volumes and hence can easily be employed on unstructured grids, indeed one can even say that they are especially designed for such grids. In section 5 numerical test runs using real life data are presented.
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