Lead has proven toxicity and a number of adverse effects on the human body, and the...

 

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Lead has proven toxicity and a number of adverse effects on the human body, and the effects are more acute in children. Sources of lead contamination and uptake in the United States, for example, are mainly due to food and water. After ingestion, lead goes to the blood and then gets transported rapidly to tissue and bones. A three-compartment model is schematically depicted below. 3 Bone X3 (t) k13x1 1 H K31x3 1 Lead input Blood x (t) K10 = 0.211 K20 = 0.0162 K10x1 Urine K12x1 K21x2 K12 k21 2 Tissue x (t) a. Write down the model equations for the rate of change of mass of lead in the three compartments where x (t) is the amount of lead in compartment i and is measured in micrograms. K20X Hair, nails, k20x2 sweat, etc. b. Using the following values of rate constants (all with units 1/day), solve (numerically) and plot the solutions x (t), x (t), x3 (t), labeling the curves and axes clearly. Assume the lead input is measured to be 1 = 49.3 g/day. Include your code. = 0.111 = 0.0124 K13 = 0.0039 k31 = 3.5 x 10-5 Lead has proven toxicity and a number of adverse effects on the human body, and the effects are more acute in children. Sources of lead contamination and uptake in the United States, for example, are mainly due to food and water. After ingestion, lead goes to the blood and then gets transported rapidly to tissue and bones. A three-compartment model is schematically depicted below. 3 Bone X3 (t) k13x1 1 H K31x3 1 Lead input Blood x (t) K10 = 0.211 K20 = 0.0162 K10x1 Urine K12x1 K21x2 K12 k21 2 Tissue x (t) a. Write down the model equations for the rate of change of mass of lead in the three compartments where x (t) is the amount of lead in compartment i and is measured in micrograms. K20X Hair, nails, k20x2 sweat, etc. b. Using the following values of rate constants (all with units 1/day), solve (numerically) and plot the solutions x (t), x (t), x3 (t), labeling the curves and axes clearly. Assume the lead input is measured to be 1 = 49.3 g/day. Include your code. = 0.111 = 0.0124 K13 = 0.0039 k31 = 3.5 x 10-5