A mathematical model that predicts the changes to the ultrasound frequ
ency spectrum after passing through human tissue and Albunex (a regist
ered trademark of Molecular Biosystems Inc, San Diego, CA) microsphere
s is proposed. Changes in backscattered intensity and mean frequency o
f the reflected signal can be estimated as a function of imaging geome
try, ultrasound frequency, and microsphere concentration and size dist
ribution. An important result is that the frequency shifts and the int
ensity variations are caused both by the microspheres in the path betw
een the transducer and the region of interest, and by the reflection p
roperties of the contrast agent in the region of interest. The model e
nables one to explain and predict clinically observed intensity effect
s such as the shadow effect in the right ventricle, and the fact that
received intensity increases with concentration up to a certain point
where it falls off. The effect of the removal of the larger microspher
es in the lungs is so significant that concentrations that give positi
ve frequency shifts with increasing concentration in the right ventric
le will give negative shifts in the left ventricle. The frequency shif
t is only a good indicator of concentration for ultrasound frequencies
below 4 MHz, while the intensity is very sensitive to the Albunex mic
rosphere concentration and the imaged depth at the higher frequencies.
It is also found that the periodic variation in heart muscle thicknes
s during the heart cycle will significantly affect the intensity and m
ean frequency of the backscattered ultrasound observed in the left ven
tricle, and in such a way as to give a periodic variation over the hea
rt cycle.