The Spirogram: Rate Of Change Of Air Volume In Lungs

**(S _{i}P_{j}A_{jk}) = S_{7}P_{5}A_{51}
Basic Sequences = 1275-5-51**

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The Spirogram: Rate Of Change Of Air Volume In Lungs

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1. 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 the following equation:
*V(t) = 3 + 0.05sin(160πt - π/2)*, where *t* is time measured in minutes and V(t) is the lung volume in liters.

(a) What is the formula for the rate of flow of air into the lungs at time *t*?

(b) What is the *peak inspiration flow*, that is, the maximum rate of flow of air during *inspiration* (breathing in)?

(c) What is the *mean inspiration flow*, that is, the average rate of flow of air during inspiration, from t = 0 to t = 1/160?

1(a)**The string**: S_{7}P_{5}A_{51} (physical change - rate of flow )
**The math**: Rate of flow = *dV(t)/dt = 8πcos(160πt - π/2)*------(1).

(b) Peak inspiration flow occurs when equation (1) is maximum. This occurs when

cos(160πt - π/2) = 1. So, *peak inspiration flow* = 8πL/min.

(c) Mean inspiration flow = integration of rate of flow from t = 0 to t =1/160

=*1/(1/160 -0)[∫ _{0}^{1/160} (8πcos(160πt - π/2)]*

=

=

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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