Homework #3: BME 2210
Due as a single PDF file ICON submission by Friday, September 28, 2018 by 5:00 PM
 1. Using Matlab, plot the following ultrasound pressure wave as a function of x for t =1
??(??, ??) = ??0??-∝??cos(???? - ????)
 where α = 0.15 neper/m, where neper is a dimensionless quantity, ?? = 1 rad/cm, ω = 1
 rad/s, and P0 = 15 N/m2. Submit your “.m” file as well as the resulting graph labeled
appropriately.
%% Plot of attenuated acoustic pressure wave


2. An ultrasound imaging system is used to create a B-mode image of a soft-tissue sample. We
want an image that extends to a depth of 30 cm from the transducer. Assume that 175
A-mode lines are used to create the B-mode image.
a) How much time is required to acquire the data for each A-mode line?
 
b) What is the maximum possible B-mode image refresh rate, in frames per second?
 
c) Using the same refresh rate calculated above, what is the maximum depth possible if all
A-mode lines are acquired simultaneously?
 
3. Answer the following showing your work:
a) If the attenuation coefficient of the heart muscle ??ℎ?? = 0.185 (???? ∙ ??????)-1, calculate
the distance at which the signal amplitude of a 2-MHz ultrasound beam will be reduced
by half traveling through heart muscle.
b) You have two transducers available, a 25-MHz transducer and a 3-MHz transducer.
Which transducer should you use to perform an echocardiogram, and why (show your
work)?
 
4. An ultrasound beam incident at an angle of 15° from fat tissue into muscle tissue, calculate
the angle of refraction using the table below?

5. Using the table above and in the figure shown below, the transducer is stimulated with a
 A B
 Fat 

Transducer

short pulse resulting in a short burst of pressure traveling through the sequence of materials
 shown in figure. Assume that no echoes are returned at the transducer-tissue interface. The
 transducer is operating at 3 MHz frequency, measured from the transducer edge, A = 3 cm
 and B = 5 cm. Use specific sound speeds in the corresponding materials.
 a) Assuming perpendicular incidence and that the system is setup to equalize the amplitude
 of all the returned signals (don’t account for attenuation and reflection/transmittance at
 interfaces), sketch the timing of the first echoes (signals) received by the transducer
 from interfaces A, and B.
 
b) Now accounting for attenuation and reflection/transmittance at interfaces calculate the
 actual amplitudes of the pulses from interfaces A and B relative to the incident
 amplitude.