New Model (Complex Interface)
4-20nm
Encapsulated Microbubbles
From Echocardiography to noninvasive blood pressure monitoring
and targeted drug delivery
2-10m
Kausik Sarkar

s
Interfacial Stress=f (Interfacial Strain,  , , E s,…)

Supported by UDRF, DOD,
NSF: CTS-0352829, CBET-0651912, CBET-0625599
NIH: 1R21HL081892-01A2
3P20RR016472-09S4
Transducer



Chatterjee & Sarkar, Ultrasound Med. Bio. 2003
Sarkar et al, J. Acoust. Soc. Am. 2005
Chatterjee et al, Ultrasound Med. Bio. 2005
Chatterjee et al, Phys. Fluids 2005
Sarkar et al Ultrasound Med Bio. 2009
Katiyar et al J. Colloids Int. Sc. 2009
Paul et al J. Acoust. Soc. Am. 2010
Ultrasound Contrast agents?
Transmitted Signal
Inject patients Gas bubbles
 Gas compressible
 Different sound speed
Scattered Signal

Surface stress
Surface shear viscosity
3
R 2
R
R 
(RR  R 2 )  PG0  0   4   4 s 2  P0  PA sint
2
R R
R
R
US forcing
inertia
Attenuation data
Bubble Size distribution
Determine s & 
Chatterjee & Sarkar, Ultrasound in Medicine and Biology 2003
Model Validity
Amphiphilic Molecule
(Lipids, proteins, or surfactants)
small
3a
With agent
Contrast microbubbles
Small bubble
Start simple…
 s   Is  ( s   s )(Is : Ds )Is  2 s Ds
http://adam.about.com/reports/High-blood-pressure.htm
http://adam.about.com/reports/High-blood-pressure.htm
Smallest capillaries (6) 
Find them
Surface tension
Surface strain rate
Surface dilatational viscosity
Dog’s left ventricle
complementary
receptor
Blood pressure:
force on the artery wall


Model
Newtonian rheology
Pressure Estimation
Echocardiography
Targeting ligands binding to

Surface shear elasticity s
Surface dilatational elasticity Es

Modified “Rayleigh-Plesset”
Molecular imaging &
Noninvasive Local Blood
Targeted drug/gene delivery
No agent
Interfacial tension 
Surface shear viscosity s
Surface dilatational viscosity s

Contrast
microbubbles
Good reflector of sound
s  s s
 Es 
Edwards et al (1991)
Evans & R Skalak (1980)
Interface rheology
Dhiman Chatterjee, Pankaj Jain,
Amit Katiyar, Shirshendu Paul, Daniel Russakow
 l l
Pg
2D “continuum” interface
Mechanical & Aerospace Engineering
George Washington University
10
m
liquid
gas
bubble ()

high curvature 1/R
Model fitted in linear
(small amplitude) regime
fexcitation
= fresponse
Pressure jump (surface tension) p 2/R

Air
1 micron air bubble dissolves in 20 ms!!
1 micron octafluoropropane bubble dissolves in  5s!!
Encapsulated bubbles: stable for hours

Octafluoropropane
C3F8 (OFP)
Can it predict nonlinear response?
Low solubility gas

Albunex (Molecular Biosystems, USA)
Levovist (Schering, Germany)

Imavist (Alliance Pharmaceuticals, USA)




Sonazoid (Nycomed, Norway)
Optison (Amersham, USA and Norway)
Definity (Lantheus Imaging, USA)
FDA approved for echocardiography
Subharmonic
fexcitation/2
Superharmonic
2fexcitation
1
Parameter Estimation - Find , s
Subharmonic Response
Church-Hoff
Sonazoid



Interfacial tension  = 0.60 N/m
Dilatational viscosity
Our strain softening interfacial models work well !!!
s = 0.0110-6 Ns/m
Interfacial tension too big


Should
decrease
Subharmonic as a function of excitation
Our
with surfactant!!!
(air-water = 0.070 N/m)
Does it work for pressure estimation?
Elasticity is missing!!
Church, J. Acoust. Soc. Am. 1995
Subharmonic response = function (ambient over-pressure Pov)
Hoff et al, J. Acoust. Soc. Am. 2000
Non-Newtonian interface rheology
Sarkar et al, J. Acoust. Soc. Am. (2005)
Noninvasive pressure measurement
Non-Newtonian Rheology
In Vitro experiments
Interfacial Elasticity


Organ level local blood pressure
 Portal hypertension
 Cancer vasculature

Dilatational elasticity Es
With change in area A
 Es
 R  2 
A
 E s    1
A
 Ru 

Subharmonic aided pressure estimation
(SHAPE)
Find , s, Es


=0.019N/m, Good!!
s =0.0110-6 Ns/m
Es =0.51N/m
Validation
 Subharmonic prediction wrong!!

Large forcing
Large oscillation

Linear elasticity



A 



0
45
90
135
180
catheter
NSF supported
Sonazoid (R0=3.2 μm)
Pa=0.8
MPa
• Behavior is complicated
2
E 0s
3 MHz
=0.019N/m
s =0.0110-6 Ns/m
Es0 =0.55N/m
=1.5
-12
Levovist
Definity
PRC
Sonazoid
Subharmonic from a single bubble


-9
Use model
Exponential elasticity E s  E0s exp    A 

-6
Subharmonic response
 Reduces with ambient pressure increase
 Use it to measure pressure
Bubble surface element
Strain softening
-3
Sarkar et al, J. Acoust. Soc. Am. (2005)
Non-linear Interfacial Elasticity

0
Ambient over-pressure (mmHg)
≡ Blood pressure variation
Subharmonic change (dB)

Subharmonic decrease (dB)

4
0
• Needs scrutiny
-2 2.46 MHz
2.65 MHz
2.73 MHz
-4 3.47 MHz
3.64 MHz
0
45
90
135
180
Ambient?over-pressure (mmHg)
How about free bubble
Works!!
Paul et al, J. Acoust. Soc. Am. (2010)
2
Subharmonic response
f0 
Resonance frequency
1/ 2
 
2 0
1  1 
 3k  1 

3k  patm  pov  
2   R02 
R0
 
Ambient pressure
Radius=2 μm
-10
f
f0
f / f0 <1.6
Ongoing Other Research
  
Move away 
  Decrease
 sub-resonance 
-15
f
f0
f / f0 > 2.0
-20
-25
1.5
1.67
1.75
2
1.6 < f / f0 < 2.0
2.25
f
f0
  
Approach 
  Increase
 sub-resonance 
  
Goes through 
  Non-monotonic
 sub-resonance 
Normalized frequency ( f / f0 )
13
Noninvasive pressure measurement
50
100
-2
-3
-4
-5
Pa =
Pa =
Pa =
Pa =
Pa =
-6
-7
-8
-9
150
10
0
R0 = 2 m & f /f0 = 1.5
0
50
2.85
2.90
3.00
3.10
3.20
bar
bar
bar
bar
bar
100
150
Ambient Pressure (mmHg)
Excitation pressure=0.3 0MPa
-2
0
-3
-4
-10
-5
-6
-20
-7
-8
-30
50
20
0
-9
f =2.8MHz=1.6 f0
f =2.98MHz=1.7 f0
f =3.15MHz=1.8 f0
f =3.33MHz=1.9 f0
45
90
100
Pa= 4.3 bar
Pa= 4.4 bar
Pa= 4.5 bar
Pa= 4.6 bar
Pa= 4.7 bar
Pa= 4.8 bar
-1
Subhamonic Increase (dB)
0
Subharmonic change (dB)
0
-1
Subhamonic Reduction (dB)
Subharmonic response (dB)
Excitation frequency
f

f0
pov   f 0  
Excitation pressure = 0.24 MPa
-5
15
150

20
15
10
5
5
0
135
50
Professor Sanku Mallik (Pharmacy NDSU)
R0= 2 & f /f0= 2.5
10
Radius=2
μm
0
Echogenic liposome
100
180Ambient Pressure (mmHg)
150
0
Ambient over-pressure (mmHg)
It can increase or decrease!!!!
NSF supported
Summary
Oxygen microbubble foam
Characterization



Professor Mark Borden (ME CU Boulder)
2D viscous and viscoelastic interfacial Rheology
Optimum design
lipid
shell
oxygen
Intravenous oxygen delivery for
acute hypoxia
water
 Measure bulk Rheology
 Measure mixing
Subharmonic aided pressure estimation (SHAPE)


Theoretically subharmonic can decrease or increase with pressure
More work is needed to understand it!!!!
 Encapsulation
 Size population
 Bubble destruction
Oxygen Microbubble Foam Injection:
Catheter
oxygen diffuses from OMBs to RBCs
 Numerical simulation of microphysics
 Compute rheology
O2
vein
OMB
RBC’s
Submitted to NSF for funding
3
Acknowledgement


Dr. Dhiman Chatterjee, IITM (India)
Pankaj Jain, Chase



Amit Katiyar,
Shirshendu Paul
Daniel Russakow

Professor Flemming Forsberg, Radiology, Thomas Jefferson

NSF




NIH

DOD

CBET-0352829
CBET-0651912
CBET-0625599
1R21HL081892-01A2

CBET-1033256
DMR-1005283

3P20RR016472-09S

4