Nutrients have been recognized as essential for maximum growth, successful reproduction, and infection prevention since the 1940s; since that time, the lion's share of nutrient research has focused on defining their role in these processes. Around 1990, however, a major shift began in the way that researchers viewed some nutrients particularly the vitamins. This shift was motivated by the discovery that modest declines in vitamin nutritional status are associated with an increased risk of ill-health and disease (such as neural tube defects, heart disease, and cancer), especially in those populations or individuals who are genetically predisposed. In an effort to expand upon this new understanding of nutrient action, nutritionists are increasingly turning their focus to the mathematical modeling of nutrient kinetic data. The availability of suitably-tagged (isotope) nutrients (such as B-carotene, vitamin A, folate, among others), sensitive analytical methods to trace them in humans (mass spectrometry and accelerator mass spectrometry), and powerful software (capable of solving and manipulating differential equations efficiently and accurately), has allowed researchers to construct mathematical models aimed at characterizing the dynamic and kinetic behavior of key nutrients in vivo in humans at an unparalleled level of detail.

This volume is the proceedings of the 7th Mathematical Modeling in Experimental Nutrition Conference held at Penn State University July 29 until August 1, 2000. The book addresses the determination of optimal intakes of nutrients and food components to provide lifelong health and reduce incidence of disease. Mathematical modelling provides a means of rigorously defining the functions of a system and using a variety of conditions to stimulate responses. This volume presents the newest advances in modelling and related experimental techniques required to meet the new challenges currently facing nutrition and biological science.

This book developed from a series of conferences to facilitate the application of mathematical modeling to experimental nutrition. As nutrition science moves from prevention of gross deficiencies to identifying requirements for optimum long term health, more sophisticated methods of nutritional assessment will be needed. Collection and evaluation of kinetic data may be one such method.This books opens with chapters giving specific examples of the application of modeling techniques to vitamin A, carotenoids, folate, vitamin b-6, glycogen phosphorylase, transthyretin, amino acids, and energy metabolism. Obtaining kinetic data on internal processes is a major challenge; therefore, the text includes chapters on the use of microdialysis and ultrafiltration, use of membrane vesicles, and culture of mammary tissue.Many of the authors use the Simulation, Analysis and Modeling program which allows compartmental models to be described without specifying the required differential equations. The final sections of the book, however, present some more mathematical descriptions of physiological processes, including bioperiodicity, metabolic control, and membrane transport; discussions of some computational aspects of modeling such as parameter distributions, linear integrators and identifiability; and alternative mathematical approaches such as neural networks and graph theory. - Specific, detailed examples of applications of modeling to vitamins, proteins, amino acids, and energy metabolism - Novel methods for collecting kinetic data--microdialysis, ultrafiltration, membrane vesicles, and the culture of mammary tissue - Mathematical treatment of complex metabolic processes including bioperiodicity, metabolic control, and membrane transport - Computational approaches to distribution of kinetic parameters, evaluation of linear integrators, and identifiability - Alternative mathematical approaches--neural networks and graph theory - Detailed descriptions of the application of modeling to a variety of nutrients

Mathematical and Statistical Approaches in Food Science and Technology offers an accessible guide to applying statistical and mathematical technologies in the food science field whilst also addressing the theoretical foundations. Using clear examples and case-studies by way of practical illustration, the book is more than just a theoretical guide for non-statisticians, and may therefore be used by scientists, students and food industry professionals at different levels and with varying degrees of statistical skill.

A concise guide to representing complex Earth systems using simple dynamic models Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus. Mathematical Modeling of Earth's Dynamical Systems helps earth scientists develop a philosophical framework and strong foundations for conceptualizing complex geologic systems. Step-by-step lessons for representing complex Earth systems as dynamical models Explains geologic processes in terms of fundamental laws of physics and chemistry Numerical solutions to differential equations through the finite difference technique A philosophical approach to quantitative problem-solving Various examples of processes and systems, including the evolution of sandy coastlines, the global carbon cycle, and much more Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html

Highlighting effective, analytical functions that have been found useful for the comparison of alternative management techniques to maximize water and nutrient resources, this reference describes the application of viable mathematical models in data analysis to increase crop growth and yields. Featuring solutions to various differential equations, the book covers the characteristics of the functions related to the phenomenological growth model. Including more than 1300 literature citations, display equations, tables, and figures and outlining an approach to mathematical crop modeling, Mathematical Models of Crop Growth and Yield will prove an invaluable resource.

The primary purpose of each of the subsequent chapters of this book is to promulgate quantitative approaches concerned with elucidating mechanisms in a particular area of the nutrition of ruminants, pigs, poultry, fish or pets. Given the diverse scientific backgrounds of the contributors of each chapter (the chapters in the book are arranged according to subject area), the imposition of a rigid format for presenting mathematical material has been eschewed, though basic mathematical conventions are adhered to.

Mathematical modeling in the form of differential equations is a branch of applied mathematics that includes topics from physics, engineering, environmental and computer science. The mathematical model is an approximate description of real processes. Mathematical modeling can be thought of as a three step process: 1) Physical situation; 2) Mathematical formulation; 3) Solution by purely operations of the mathematical problem; 4) Physical interpretation of the mathematical solution. Over the centuries, Step 2 took on a life of its own. Mathematics was studied on its own, devoid of any contact with a physical problem; this is known as pure mathematics. Applied mathematics and mathematical modeling deals with all three steps. Improvements of approximations or their extensions to more general situations may increase the complexity of mathematical models significantly. Before the 18th century, applied mathematics and its methods received the close attention of the best mathematicians who were driven by a desire to develop approximate descriptions of natural phenomena. The goal of asymptotic and perturbation methods is to find useful, approximate solutions to difficult problems that arise from the desire to understand a physical process. Exact solutions are usually either impossible to obtain or too complicated to be useful. Approximate, useful solutions are often tested by comparison with experiments or observations rather than by rigorous mathematical methods. Hence, the authors will not be concerned with rigorous proofs in this book. The derivation of approximate solutions can be done in two different ways. First, one can find an approximate set of equations that can be solved, or, one can find an approximate solution of a set of equations. Usually one must do both. Models of natural science show that the possibilities of applying differential equations for solving problems in the disciplines of the natural scientific cycle are quite wide. This book represents a unique blend of the traditional analytical and numerical methods enriched by the authors developments and applications to ocean and atmospheric sciences. The overall viewpoint taken is a theoretical, unified approach to the study of both the atmosphere and the oceans. One of the key features in this book is the combination of approximate forms of the basic mathematical equations of mathematical modeling with careful and precise analysis. The approximations are required to make any progress possible, while precision is needed to make the progress meaningful. This combination is often the most elusive for student to appreciate. This book aims to highlight this issue by means of accurate derivation of mathematical models with precise analysis and MATLAB applications. This book is meant for undergraduate and graduate students interested in applied mathematics, differential equations and mathematical modeling of real world problems. This book might also be interested in experts working in the field of physics concerning the ocean and atmosphere.

Kinetic models are becoming standard tools in the research of biological systems. They are used to represent hypotheses, analyze data, and design experiments to maximize the information obtained from a study. Kinetic Models of Trace Element and Mineral Metabolism During Development describes models for calcium, chromium, copper, iron, iodide, lead, mercury, selenium, zinc, and others in health and disease.