Pollution in a Lake Example 2 Mercury in Fish Modeling Mercury in Fish Mercury

Pollution in a Lake Example 2 Mercury in Fish Modeling Mercury in Fish Mercury in Fish 1 Introduction - Fishing and Mercury in the Great Lakes Region Mercury, a heavy metal, is a dangerous neurotoxin that is very difficult to remove from the body It concentrates in the tissues of fish, particularly large predatory fish such as Northern Pike, Lake Trout, Bass, and Walleye The primary sources of mercury in the Great Lakes region Runoff of different minerals that are mined Incinerators that burn waste, especially batteries Most batteries no longer contain mercury Bacteria converts mercury into the highly soluable methyl mercury Enters fish by simply passing over their gills Larger fish consume small fish and concentrate mercury Joseph M. Mahaffy, h [email protected] i Lecture Notes – Linear Differential Equations — (37/64) Introduction Falling Cat 1 st Order Linear DEs Examples Pollution in a Lake Example 2 Mercury in Fish Modeling Mercury in Fish Mercury in Fish 2 Introduction - Mercury and Health Higher levels of Hg in fish may cause children problems in their developing neural system, resulting learning disorders Michigan Department of Health warns that young children and pregnant women should limit their consumption of fish, especially the larger predatory fishes Joseph M. Mahaffy, h [email protected] i Lecture Notes – Linear Differential Equations — (38/64) Introduction Falling Cat 1 st Order Linear DEs Examples Pollution in a Lake Example 2 Mercury in Fish Modeling Mercury in Fish Mercury in Fish 3 How Hg gets into fish Lyndsay Marie Doetzel, An investigation of the factors affecting mercury accumulation in lake trout, Salvelinus namaycush , in Northern Canada, University of Saskatchewan, Saskatoon, 2007 Joseph M. Mahaffy, h [email protected] i Lecture Notes – Linear Differential Equations — (39/64) Introduction Falling Cat 1 st Order Linear DEs Examples Pollution in a Lake Example 2 Mercury in Fish Modeling Mercury in Fish Mercury in Fish 4 Introduction - Mercury Buildup in Fish So why do fish build up the dangerous levels of Hg in their tissues? Hg is not easily removed from the system, so when ingested it tends to remain in the body Heavy metals are eliminated with chelating agents Mathematically, this build up is seen as the integral of the ingested Hg over the lifetime of the fish Thus, older and larger fish should have more Hg than the younger fish Joseph M. Mahaffy, h [email protected] i Lecture Notes – Linear Differential Equations — (40/64)

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Introduction Falling Cat 1 st Order Linear DEs Examples Pollution in a Lake Example 2 Mercury in Fish Modeling Mercury in Fish Modeling Mercury in Fish Modeling Mercury in Fish - Outline for the Model Classic model for growth of a fish (length) is the von Bertalanffy equation dL dt = b ( L * - L ) with L (0) = 0 Develop an allometric model relating weight to length, i.e., W = αL k Standard dimensional analysis gives an integer appropriate integer k Assumptions are made for accumulation of mercury (Hg) in the fish and a DE for the amount of Hg in the fish is formulated