Mathematics and nutrition science

SUMMARY: Mathematicians and nutrition scientists model and analyze numerous aspects of nutrition and diet.

Nutrition is the system of providing food to an organism as well as the science of food and eating. Nutrition science is an interdisciplinary field that involves a wide variety of disciplines, including mathematics, statistics, culinary science, physiology, genetics, biochemistry, psychology, medical sciences, sociology, anthropology, and ethnography. Mathematical and statistical methods are widely used to describe and analyze different nutrients in food, determine their impact on nutrition and health, develop eating plans, assess public opinion, and inform public policy. Meal-planning and nutritional labels are often used in classroom mathematical problems.

Taxonomies of Human Nutrients

The understanding of what balanced nutrition means is a difficult and controversial subject, with many schools of scientific thought, cultural traditions, and governing bodies proposing different ways of eating. Many people may be familiar with the U.S. Department of Agriculture’s food pyramid, which was introduced in the 1990s to replace the older four food groups model. There are similar guidelines produced in many countries, using a mix of scientific research and expert opinion. One measurement scale for a nutrient is the time it takes for its lack to manifest itself in health problems. Lack of energy-providing nutrients, such as fats, proteins, and carbohydrates, is felt within hours as hunger and causes symptoms within days. A disbalance of macrominerals, such as potassium and calcium, as well as some vitamins has been shown to lead to specific diseases and is felt within weeks to months.

For example, physician James Lind published an influential treatise on scurvy in 1753, based in part on his controlled experiments with British sailors. Lack of some other vitamins and minerals can take years to manifest. Flavonoids are found in plants, changing coloration, smell, and taste. Researchers hypothesize that flavonoids regulate organism responses, such as inflammations and allergies, as well as reactions to carcinogens, bacteria, and viruses. Most studies of flavonoids in human nutrition are only decades old. Probiotics are live microorganisms most frequently eaten with fermented food. They may affect the immune system, blood pressure, inflammation, and cancer. Prebiotics are food items, such as inulin in chicory roots, that promote the growth of microorganisms in the digestive tract. Water participates in most systems and processes in the body, playing roles such as a solvent for other substances and entering chemical reactions.

Researching and Modeling Nutrition

Data collection and quantitative analysis are used for a variety of purposes in nutrition science. For example, they are used to investigate the effects of nutritional deficiencies, optimize diets for long-term health and longevity, study the effectiveness of weight-loss plans, and establish causal links between political policy changes and nutrition and health effects. Qualitative methods like case studies and ethnographic studies are insufficient to establish cause, though they may highlight key variables. One critical principle of scientific studies that seek to make causal connections is isolating a small number of variables to systematically manipulate, while controlling the rest. Because nutrients interact with all systems in the body—with other organisms living in the body, with each other, and with behaviors other than eating—the complexity of the resulting system can make this approach difficult. Further, the effects of some types of nutrients take years or even decades to uncover, or they may occur in only a small number of people. Studying these would require extensive longitudinal studies or very large sample sizes to be statistically valid, which may have significant practical and ethical barriers. Finally, individual differences in reactions to nutrition changes may be large and non-random, depending on genetics, culture, and daily habits, which means that averaging the effects of nutritional interventions may overlook important effects on small minorities, such as allergic reactions.

Mathematicians and nutrition scientists use mathematical modeling and simulation to investigate the functions of systems and to experiment with the conditional responses of multiple variables. Increases in computing power have made complex modeling a feasible alternative to traditional scientific experimentation. Problems are drawn from areas of concern, such as obesity, diabetes, cancer, and toxicology. Many models rely on collection of kinetic body data to develop accurate models of physiological processes, such as bioperiodicity and membrane transport, which is also possible because of advances in medical imaging and other technology. Computational approaches are used to estimate distributions of parameters, evaluate linear integrators and other functions, manipulate multiple variables in stochastic models, and create visualizations. Mathematical or statistical approaches, such as neural networks, graph theory, and cluster analysis, have also been used to model data or systems and to make connections.

Genetically modified foods are a controversial subject in nutrition. Typical reasons for altering food are for resistance to pests or disease or for nutritional benefits. The Swiss-developed “golden rice” has higher levels of vitamin A than standard rice strains, which would theoretically benefit third world countries where rice is a staple food and vitamin A deficiencies are common. Some support the use of such foods to combat hunger in areas of the world with chronic shortages and endemic malnutrition. Others cite the unknown long-term effects, such as spontaneous cross-pollination with unmodified organisms, as well as the ethical implications. Mathematicians and scientists have helped to create genetically modified foods and have investigated many questions related to them. For example, informaticists have used combinatorial reduction rules to create a model to detect unknown, genetically modified organisms. Others research and model aspects such as the likelihoods of positive and negative ecological outcomes, pathogenicity, public acceptance, and impacts on international trade using probabilistic and statistical methods, simulation, differential equations, and a wide variety of computerized modeling techniques.

Diets and Meal Planning

A diet is the description of types and quantities of nutrients consumed. Because organisms vary in ways other than food intake, dietary variables are typically studied in their relationships with other variables—either direct proportionality or more complex functions. Different cultures have varied proportions of nutrients in their diets, as well as certain prohibitions. For example, Aleuts traditionally eat a large amount of meat, consuming about eight times more protein than South American agricultural tribes. Japanese and Mediterranean diets are often cited for emphasis on certain fats, fruits, vegetables, and carbohydrates. Both Jewish and Muslim traditions forbid certain types of foods. People may also choose diets for specific goals, such as weight loss or control of medical conditions like diabetes or high blood pressure, often with little scientific evidence of effectiveness—though scientists are seeking ways to validate or refute such claims. Globalization has made different types of diets and foods increasingly known and accessible to people everywhere.

Software for planning least-cost nutritional meals was developed for mainframe computers in the early 1960s and evolved during the 1970s to include food preferences options. Later research in the 1980s and the evolution of personal computing led to new software that used mathematical programming to optimize and maximize menu planning for different variables, including nutrition, allergies, and preferences. Internet-based software and algorithms, such as that used by the weight-loss company Weight Watchers with their Weight Watchers Online program, now allows people to track and plan menus based on a variety of criteria, often dynamically linked to databases with recipes, past behavior, and weight or measurement tracking. Large institutions, such as schools and hospitals, may use software that includes inventory and other supply variables.

Nutrition and Mathematical Problem Solving

There are studies directly linking nutrition and success in mathematics. One group of researchers found that providing a balanced breakfast before the morning mathematics class raised test scores more than any other variable they analyzed, such as changes in teaching methods. Different cultures have different beliefs of what constitutes “brain food.” Certain types of fat, vitamins B and C, and monosaccharides have been shown to increase memory and speed of computation within time periods from minutes to days from increased consumption. More complex cognitive effects of food, such as connections between gluten or lactose sensitivity and attention, are being investigated.

Math and Weight Loss

The Harvard Medical School offered a simple mathematical model for weight loss involving both an increase in exercise and a reduction in daily calorie intake. For all its physical and mental benefits, exercise alone was a time-intensive way for a person to meet their weight-loss goals. To eliminate one pound of fat from the human body requires the expenditure of 3,500 calories. It may take the average person several days to perform enough exercise to meet this threshold. A more practical approach was to reduce daily caloric intake while increasing the number of calories burned. As a mile jogged expended 100 calories, a run of 35 miles equated to one pound's worth of calories. A person jogging four miles a day, for five days in a week, would need over three weeks to accomplish this caloric goal. The same person that reduced 250 calories a day from their diet would achieve the same caloric reduction in two weeks. Combining both practices, exercise and caloric reduction, the target of 3,500 calories burned could be attained in slightly over a week.

Bibliography

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