Question

Problem 4 Sodium is the primary cation in extracellular fluids (ECF) in humans. These fluids, such as blood plasma and ECF in other tissues, bathe cells and carry out transport functions (e.g. delivering nutrients and removing waste products). Although the system for maintaining optimal salt and water balance in the body is a complex one, one of the primary ways in which the human body keeps track of loss of body water is through osmoreceptors in the hypothalamus, which respond to tonicity changes in the ECF. A relative loss of body water will cause sodium concentration to rise higher than normal, a condition known as hypernatremia. This ordinarily results in thirst. Conversely, an excess of body water caused by drinking will result in too little sodium in the blood (hyponatremia). When this condition is detected by the hypothalamus, the hormone vasopressin is suppressed, leading to increased loss of water through the urine and a restoration of the blood sodium concentrations. Sodium homeostasis is a very complicated system, but we can approximate it using the following relations: - Sodium from dietary intake goes to the intestines. Sodium is transported from the intestines to the ECF - Sodium is absorbed from the ECF by the tissues, and returned by the tissues to the ECF Sodium is excreted from the ECF into urine. Draw a block diagram of the system above using the following notation: - xi: sod - X2: sodium concentration in the ECF - X3: sodium concentration in the tissues - X4: sodium concentration in the urine - ft): sodium intake from diet (input) - kj: rate constant, where i is the source block, and j is the destination block a) (10 points) ium concentration in the intestines b) Write the state equations, where the state variables are the sodium concentrations in each compartment. k2i and k42 can be omitted. The step after urine can be omitted. Hint: For example, sodium flux from xi to x2 is xik12. (10 points) c) Write the state equations and output equation in matrix form. Assume that the amount of sodium in the urine is the output. (You don't need to solve the equations.) (10 points)

Answer 1

Hypothalamus stimulates thirst 2 arterial pressure/angiotensin al Atrial Natriuretic Protein inhibits renin secretes Na+ Macula Densa cells nhibits renin sense osmolarity wichinhibits Na reuptake in ADH from post. pituitary Water uptake in CD Nat Too high (hypernatremia) CAUSES OF Na Homeostasis Diet Water retention Diuretics Hypoaldosteronism Excessive ADH Too low (hyponatremia) -Nause Less ADH from post. pituitary Stimulates JG cells/renin ptake in DCT Macula Densa cells sense osmolarity Juxtaglomerular UG) Cells Angio Renin