Question: A spirogram is a device that records
A spirogram is a device that records on a graph the volume of air in a person’s lungs as a function of time. If a person undergoes spontaneous hyperventilation, the spirogram trace will closely approximate a sine curve. A typical trace is given by
where t is measured in minutes and V(t) is the lung volume in liters. (See Fig. 1.) Exercise refers to this function.
Figure 1:
The minute volume is defined as the total amount of air inspired (breathed in) during 1 minute. According to a standard text on respiratory physiology, when a person undergoes spontaneous hyperventilation, the peak inspiratory flow equals p times the minute volume, and the mean inspiratory flow equals twice the minute volume. Verify these assertions using the data from Exercise 57.
Exercise 57:
(a) Find a formula for the rate of flow of air into the lungs at time t.
(b) Find the maximum rate of flow of air during inspiration (breathing in). This quantity is called the peak inspiratory flow.
(c) Inspiration occurs during the time from t = 0 to t = 1/160. Find the average rate of flow of air during inspiration. This quantity is called the mean inspiratory flow.
Transcribed Image Text:
V(t) = 3+.05 sin 160mt 05 sin(16 -7). 2 Long volume (liters) 3 0 Inspiration Respiration Time (minutes) - 80 y = V(t) t
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