1.5 micrometer (radius) scattering	15 micrometer (radius) scattering

Air Resonance radius 1.5 = 2.1 MHz      Air Resonance radius 15 = 210 kHz
(typical capillary contrastor)		(brain tissue contrast agent)

________________________________________________________________________
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
 . . . . . . . .  For a gas with c = 343 m/s (air) . . . . . . . . . . .
. . . . . . . .         (hard sphere in air)      . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	
ka =  1    gives    f =  36 MHz		ka =  1    gives    f = 3.6 MHz
ka =  2    gives    f =  73 MHz		ka =  2    gives    f = 7.3 MHz
-------------------------------		-------------------------------	
ka =  5    gives    f = 180 MHz		ka =  5    gives    f =  18 MHz
-------------------------------		-------------------------------	
ka = 10    gives    f = 360 MHz		ka = 10    gives    f =  36 MHz


1   MHz    gives   ka  = 0.027		1   MHz    gives   ka  =  0.27
2   MHz    gives   ka  = 0.055		2   MHz    gives   ka  =  0.55
-------------------------------		-------------------------------	
10  MHz    gives   ka  = 0.27		10  MHz    gives   ka  =  2.7 		
-------------------------------		-------------------------------	
100 MHz    gives   ka  = 2.7		100 MHz    gives   ka  =  27		





 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
=========================================================================
=============    For a fluid with c = 1500 m/s (water)  =================
=============         (for an air bubble in water)       ================
=========================================================================


ka =  1    gives  f =   160 MHz		ka =  1    gives    f =  16 MHz	
ka =  2    gives  f =   320 MHz		ka =  2    gives    f =  32 MHz	
-------------------------------		-------------------------------	
ka =  5    gives  f =   800 MHz		ka =  5    gives    f =  80 MHz	
-------------------------------		-------------------------------	
ka = 10    gives  f = 1,600 MHz		ka = 10    gives    f = 160 MHz	


1   MHz    gives   ka =  0.0063		1   MHz    gives   ka  =  0.063  	
2   MHz    gives   ka =  0.013		2   MHz    gives   ka  =  0.13  	
-------------------------------		-------------------------------	
10  MHz    gives   ka =  0.063 		10  MHz    gives   ka  =  0.63  	
-------------------------------		-------------------------------	
100 MHz    gives   ka =  0.63  		100 MHz    gives   ka  =  6.3  		







ka_i  =  2 pi (radius in microns) (freq in MHz) / (c in meters/sec)
f_i   =  (c in meters/sec) (ka) / 2 pi (radius in microns)
ka    =  (2 pi / wavelength in microns) * (radius in microns)