8:45-9:00 Laura Ellwein,
North Carolina State University
Modeling Autonomic and Autoregulation of Blood Flow during Postural Change from Sitting to Standing
The "light-headedness" a person feels with a sudden posture change is caused by a lack of blood flow to the brain. In normal individuals it is overcome naturally via autonomic reflexes (ARF), which impact the entire body, and cerebral autoregulation (CA), a local control mechanism. The interaction between the two mechanisms is not well understood. To study these mechanisms we have developed a compartment model coupled with physiological models describing the ARF and CA during postural change from sitting to standing. To validate our mathematical model we use finger blood pressure and cerebral blood flow velocity data obtained non-invasively from a young subject. This model validation is carried out using nonlinear optimization methods.
9:05-9:20 Jimena Davis,
North Carolina State University
Comparison of Two Approximation Methods in the Estimation of Growth Rate Distributions in Size-Structured Mosquitofish Populations
In an effort to protect the environment, biologists are using mosquitofish in the place of chemicals to control mosquito populations in rice fields. While they have used mosquitofish in the place of pesticides for some time, they have not completely understood the control of the growth of mosquitofish populations. Biologists would like to be able to predict the growth and decline of the mosquitofish populations in order to determine the optimal amount of mosquitofish to use for control purposes. We will present the Sinko-Streifer population model modified as in the Growth Rate Distribution model of Banks-Botsford-Kappel-Wang. We will also present and compare the results of two approximation methods used in the inverse problem for estimation of distributions of growth rates in size-structured mosquitofish populations.
This work is supported by a DOE Computational Science Graduate Fellowship.
9:25-9:40 Karen Yokley,
North Carolina State Univerisity
Physiologically Based Model Development and Parameter
Nerves in the nasal cavity of rodents can be stimulated by the presence of inhaled irritants. In order to better understand how the nervous system responds to such chemicals, we have created a model to describe how the presence of irritants affects respiration in the rat. By combining and adapting two previous models, one that evaluates the relationship between inhaled acrylic acid vapor concentration and the tissue concentration in various regions of the nasal cavity and another which describes the baroreflex-feedback mechanism regulating human blood pressure, we created a system of equations that models the sensory irritant response. The adapted model focuses on the dosimetry of these reactive gases in the respiratory tract, with particular focus on the physiology of the upper respiratory tract, and on the neurological control of respiration rate due to signaling from the irritant-responsive nerves in the nasal cavity. Further, the model is evaluated and improved through optimization of particular parameters and through sensitivity analysis.
9:45-10:00 Xiaohua Teresa Jin,
University of South Carolina
Real Number Radio Channel Assignment for the Lattices
The channel assignment problem is to assign radio frequency channels to transmitters in a network, using a small span of channels and satisfying some frequency separations to avoid interference. Griggs (1992) formulated the corresponding integer graph L(2,1)-labeling problem, which has been the object of a considerable number of papers. We extend it and propose the real number graph labeling problem here, which allow the labels and the constraints ki to be nonnegative real numbers. An L(k1,k2,...,kp)-labeling of graph G is an assignment of nonnegative real numbers to the vertices of G with x ∈ V(G) labeled f(x), such that |f(u)-f(v)| ≥ ki if u and v are at distance i apart, where ki ∈ [0,∞). We denote by λ(G;k1,k2,...,kp) the minimum span over such labeling f ∈ L(k1,k2,...,kp)(G). We show λ(G;k1,k2) is a continuous and piecewise-linear function of k1,k2, and λ(G;k1,k2)=k2λ(G;k,1) for real numbers k1 ≥ 0, k2>0$ and k=k1/k2.
In a radio mobile network, large service areas are often covered by a network of nearly congruent polygonal cells, with each transmitter at the center of a cell that it covers.
All transmitters may be placed in the triangular lattice ΓT, the square lattice ΓS, or the hexagonal lattice ΓH.
We determine values of the minimum span λ(ΓT;k,1)$ for all k ≥ 4/5, have bounds for 0