Aortic Pressure Model
Biomedical engineers often design instrumentation to measure physiological processes, such as blood pressure. To do this they must develop mathematical models of the process. The following equation is a specific case of one model used to describe the blood pressure in the aorta during systole (the period following the closure of the heart’s aortic valve). The variable 1 represents time in seconds, and the dimensionless variable y represents
the pressure difference across the aortic valve, normalized by a constant reference pressure.
y(1) = e-St sin (9.71 + i)
Plot this function for 1 2: O.
Note that if t is a vector, the’ MATLAB functions exp ( – S*t) and sin (9 . 7*t + pi/2) will also be vectors the same size as t. Thus we must use element-by-element multiplication to compute y(1).
In addition, we must decide on’ the proper spacing to use for the vector t and its upper limit. The sine function sin(9.71 +n/2) oscillates with a frequency of 9.7 rad/sec, which is 9.7 (27r) = 1.5 Hz. Thus its period is 1/1.5 = 2/3 sec. The spacing of t should be a small fraction of the period .in order to generate enough ‘points to plot
the curve. Thus we select a spacing of 0.003 to give approximately 200 points per period.
The amplitude of the sine wave decays’ with time because the sine is multiplied by the decaying exponential e-8r The exponential’s initial value is eO = I, and it will be 2 percent of its initial value at 1 = 0.5 (because e-8(o.S) = 0.02) ..Thus we select the upper limit of t to be 0.5. The session is:
The plot is shown in Figure 2.3-4. Note that we do not see much of an oscillation despite the presence of a sine wave. This is because the period of the sine wave is greater than the time it takes for the exponential e-St to become essentially zero .