Cardiac output is the amount of blood that is pumped by the heart per unit time, measured in litres per minute. A normal adult's heart can easily pump 4.7 litres of blood per minute through the blood circulatory system.

 

A dye is injected into a main vein near the heart in order to measure a patient’s cardiac output without interrupting the flow of blood. The dye is drawn into the right side of the heart, pumped through the lungs and out from the left side of the heart into the aorta, where its concentration can be measured every few seconds as the blood flows past. 

 

The data in the graph on the next page show the response of a healthy, resting patient to an injection of 10 mg of dye. The x-axis values represent time in seconds after the dye injection and the y-axis values represent dye concentration in the blood in mg/litre.

 

Use the graph shown below to calculate* the patient’s cardiac output in litres of blood per minute.

 

Present your calculations* for the problem in the form of a report, which includes your answers to the following questions.

 

 

Q1   You may google or search from books to read about cardiac output. Present your findings in not more than a single A4 page (not more than 400 words). Diagrams may be included in your answer.

 

Q2   What connections do you see between your findings in Q1 and the problem above presented with given data?

 

Q3   Name a mathematical method and state the formula to estimate the area under the dye concentration curve. Show how it enables you to get the answer. The data could be read at intervals of 2 seconds.

 

Q4   How does your answer in Q3 enable you to perform the calculation?

 

Q5   Calculate the cardiac output in litres of blood per minute.

 

Q6   (a) In Q3 above, comment on the accuracy of your answer when the data were read at intervals of 1 second instead?

 

         (b) Is the relation represented in the graph above specially named as a function? Explain your answer.

 

Q2   What connections do you see between your findings in Q1 and the problem above presented with given data?

In this case we take the value of h from the graph. From the graph h = 2

Area under the dye concentration curve graph= 2/3(0+0+4(0.25+1.4+3.6+8.1+5.25+3.4+2.1)+2(0.75+2.25+6.9+5.8+4.6+2.5))=94.666667

Q5) Cardiac output in litres of blood per minute = 10/area *60
                                                                              = 10/94.66667 *60
                                                                              = 6.3380 litres/minute