A typical volume of blood in the human body is about L. A certain percentage of that volume (called the hematocrit) consists of red blood cells (RBCs); typically the hematocrit is about in males. Suppose that a surgery takes four hours and a male patient bleeds L of blood. During surgery the patient’s blood volume is maintained at L by injection of saline solution, which mixes quickly with the blood but dilutes it so that the hematocrit decreases as time passes. A procedure called acute normovolemic hemodilution (ANH) has been developed to minimize RBC loss during surgery. In this procedure blood is extracted from the patient before the operation and replaced with saline solution. This dilutes the patient’s blood, resulting in fewer RBCs being lost during the bleeding. The extracted blood is then returned to the patient after surgery. Only a certain amount of blood can be extracted, however, because the RBC concentration can never be allowed to drop below during surgery. What is the maximum amount of blood that can be extracted in the ANH procedure for the surgery described in this project? What is the RBC loss without the ANH procedure? What is the loss if the procedure is carried out with the volume calculated in Problem 1?
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
A typical volume of blood in the human body is about L. A certain percentage of that volume (called the hematocrit) consists of red blood cells (RBCs); typically the hematocrit is about in males. Suppose that a surgery takes four hours and a male patient bleeds L of blood. During surgery the patient’s blood volume is maintained at L by injection of saline solution, which mixes quickly with the blood but dilutes it so that the hematocrit decreases as time passes.
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A procedure called acute normovolemic hemodilution (ANH) has been developed to minimize RBC loss during surgery. In this procedure blood is extracted from the patient before the operation and replaced with saline solution. This dilutes the patient’s blood, resulting in fewer RBCs being lost during the bleeding. The extracted blood is then returned to the patient after surgery. Only a certain amount of blood can be extracted, however, because the RBC concentration can never be allowed to drop below during surgery. What is the maximum amount of blood that can be extracted in the ANH procedure for the surgery described in this project?
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What is the RBC loss without the ANH procedure? What is the loss if the procedure is carried out with the volume calculated in Problem 1?
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