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

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

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Dye concentration in the blood is one of the ways to determine the cardiac output of a person and itwas the method used in this problem. Based on the graph, the dye
concentration gradually rises to its peak which happens at about 15 seconds before it starts to decrease. In dye dilution, the dye would be injected into the right side of the heart and the concentration of dye would be measured at the aorta. After leaving the aorta, it circulates through the body before returning to the point of injection. The continual repetition of this cycle
would result in the dye being circulated better in the body and this would gradually result in the peak as seen in thegraph given.

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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.

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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.

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Cardiac output represents the volume of blood that is delivered to the body in one minute, and is therefore, an important factor in the determination of the effectiveness of the heart to deliver blood to the rest of the body and it may point out issues such as pre heart failure occurrence or inadequate circulation of blood through the body. The equation for

Cardiac output = stroke volume × heart rate

Heart rate refers to the number of times the heart beats per minute and the resting heart rate of an individual could be affected by a variety of factors such as stress levels, level of physical activeness as well as genetics. Increase in heart rate increases cardiac output as the volume of blood released into the body increases with respect to it. Stroke volume is the amount of blood your heart pumps each time it beats, and your heart rate is the number of times your heart beats per minute. A healthy heart with a normal cardiac output pumps about 5 to 6 litres of blood every minute when a person is resting.

The increasing of left ventricle dimensions, reduced systemic peripheral resistance and a
greater blood volume account for increases in resting, submaximal and maximal stroke volume, typically, after an endurance training programme.

One method of determining cardiac output is the thermodilution method. It adapts the
indicatordilution principle to injectates that cause changes in blood temperature detected
downstream The thermodilution (TD) method blood temperature detected downstream. ¾ an injectate of known volume and temperature is injected into the right atrium and the cooled blood traverses a thermistor in a major vessel branch downstream over a duration of time.

Another method is the dye dilution method. It is based on injecting a known quantity of a dye at one site into the circulatory system, and withdrawing blood at a distal site for determination of a concentration curve of the dye. The dye dilution method is one of the most accurate methods of determining cardiac output during exercise. The error of a single calculation of cardiac output values at rest and during exercise is less than 5%. This method does not allow measurement of 'beat to beat' changes, and requires a cardiac output that is stable for approximately 10 s during exercise and 30 s at rest.

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

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

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From Q3, we get the area under the dye concentration curve. The area under the curve represents the product of x-axis multiply by y(x) axis giving the unit s/mg/L. We can now simply divided the value (from Q3) by amount of dye present(10mg) to find out the cardiac output in litres of blood per minute

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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.

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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.

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(a) The answer will be more accurate when the data is read at intervals of 1 second instead. Parabolas are used to approximate each part of the curve and if the interval is halved, the gaps between the original curve and the parabola will be drawn shorter which allows a better fit. Thus, the coordinates that are drawn out will be closer to the original curve, improving the accuracy of the results.

(b) Yes, the relation shown in the graph is specially named as a function. A function is an equation that shows the relationship between a dependent variable, which in this case is y(x) and an independent variable, x. Also, to determine if the relation is a function, a vertical line can be drawn through the graph. If the relation is not a function, the graph will have at least 2 points with the same x-coordinate but with different y-coordinates. Since this relation does not have at least 2 of the same x-coordinates and a different y-coordinates when a vertical line is drawn, this relation shown in the graph is a function.

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

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

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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.

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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.

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Simpson’s rule can be used to estimate the area under the dye concentration.
We will use parabolas to approximate each part of the curve.

n= even no. of equal-width strips
h=width of the strips

Using the formula b-a/n =h, we get that n=14 as data is read at intervals of 2
seconds(h=2).