V.A. Khokhlova,1,2 P.V. Yuldashev,2 W. Kreider,1

O.A. Sapozhnikov,1,2 M.R. Bailey,2 and L.A. Crum2

Nonlinear modeling as a metrology tool to characterize

high intensity focused ultrasound fields

2Department of AcousticsPhysics Faculty

Moscow State UniversityRussia

1Center for Industrial and Medical Ultrasound

Applied Physics LaboratoryUniversity of Washington

164th Meeting of the Acoustical Society of America, Kansas City, MO, 22 - 26 October 2012

• Introduction High Intensity Focused Ultrasound fields = nonlinear fields

• Metrology of nonlinear HIFU fieldscombined measurement and modeling approach,calibration in water, translation (derating) to tissue, enhancement of heating, predicting bioeffects

• HIFU treatment protocols based on nonlinear effectscontrolled mechanical and thermal bioeffects in the presence of shock

• Conclusions

Outline

Therapeutic applications of ultrasoundbasic concept

HIFU surgery:frequency0.7 – 4 MHzIntensity in situ :500 – 25 000 W/cм2

Major bioeffects of HIFUthermal: tissue heating due to absorption of ultrasound energythermal dose for necrosis:120-240 min at 43ºC1 c at 56ºC, 0.1 c at 59ºCmechanical: cavitation

shear stresses???

High Intensity Focused Ultrasound= nonlinear acoustic fields

Nonlinear propagation effects in HIFU fields

• ultrasound propagation speed of depends on local pressure• high pressure regions (compressions) travel faster

than low pressure regions (rarefactions)• harmonic wave transforms to sawtooth wave

)sin()0( 00 pxp 00

030

pcxsh - shock formation distance

p/p0

p0= 1 MPa, f0 = 1 MHz , xsh=15 cm p0= 10 MPa, f0 = 3 MHz , xsh= 5 mm

20

40

3

6 cfAH s

heat deposition at the shocks

~ 1 cm

10 MPa – 3 300 W/cm2

clinically relevant focal values

Nonlinear acoustics• peak positive and negative pressures (p+ ; p-)• shock amplitude (As)• narrower focal zone, enhanced heat deposition

HIFU fields in the presence of nonlinear effects:acoustic characterization and new bioeffects

Linear acoustics• focal pressure amplitude (pF)• broader focal zone

pF

5 mm

5 mm

5 mm

Different effects in tissue:thermal coagulation

boilingemulsificationshear stresses

immune response

Nonlinear effects and resulting shocks are important in HIFU metrologyas they result in enhanced heating and additional nonthermal bioeffects

p p

p

sA

Nonlinear modeling combined with measurements can be an effective tool to characterize outputs of HIFU transducers

calibration of HIFU fields in water

derating nonlinear water measurements to tissueestimating therapeutic dose delivered

developing treatment protocols

making HIFU more efficient and safe

optimizing treatment avoiding or using nonlinear effectsstudying new bioeffects

Characterization of HIFU fields in water: combined measurement and modeling approach

2D clinical phased array

1.2 MHz operational frequency128 mm diameter, 120 mm focus256 elements of 6.6 mm diameter each central hole for imaging

MR-guided HIFU system(Sonalleve 3.0T, Philips Healthcare)

examples: typical HIFU sources of different geometry

single element HIFU transducer

2.158 MHz operational frequency45 mm diameter, 45 mm focus

Model equations for High Intensity Focused Fields

KZK equation

nonlinearity absorptiondiffraction

nonlinear model with diffraction in parabolic approximation

pLpc

pcr

prrr

czp

abs

3

3

30

2

22

300

02

221

2

single elementtransducers

z

F

rae

2D axially symmetric KZK nonlinear models are simpler in modeling, but they are not applicable to all geometries and provide approximate results in the nearfield

20

00

fff

in tissue: power law of absorption with frequency

~ 1

Boundary condition to the KZK modeling

Initial pressure and apertureare chosen to match the measured low amplitude focal distributions

of the real source

a0

F

z

focal zone

a0 = 20 mm, F = 44.4 mm, G = 48

Real source is substituted by an “equivalent” uniformly vibrating

single element source

obtained from low amplitude measurements along the axis and in the focal plane :

M.S. Canney et al. Acoustic characterization of high intensity focused ultrasound fields: A combined measurement and modeling approach. JASA, 2008, 124(4), 2406-2420.

Nonlinear propagation effects and shock formation

in HIFU fieldsf0 = 2 MHz , d0 = F = 44 mm

water , 180 W acoustic powerinput: 7.8 W/cm2 / 4.8 bars at focus: 18 000 W/cm2 / 230 bars

spectrum

f/f0

axial peak pressure positive p+/p0 and negative p-/p0

z/F

one cycle of a HIFU waveform p/p0

0

20

40

60 measured waveform

65.554.543.532.521.5 *10-5

time, s

pressure, MPasource pressure: 0.4 MPa source intensity: 5 W/cm2

linearly estimatedfocal pressure: 18.5 MPafocal intensity: 11 500 W/cm2

FOPH frequency response

Modeling results are more accurate than measurements at high power outputs (due to bandwidth limitations of hydrophones) and can be applied to predict in situ fields

Validation of nonlinear modeling at high outputs in water

focal waveform modeling and measurements with FOPH hydrophones

Hydrophone bandwidth is critical (100 MHz versus 30 MHz) for measuring p+

Model equations for High Intensity Focused Fields

0/ czt

zF

y

x

a0 HIFU arrays

3D full diffraction nonlinear model

3

3

30

2

22

300

2

2

2

2

2

20

2

222

pc

pcz

pyp

xpc

zp

Westervelt equation:

nonlinearity absorptiondiffraction

3D full wave nonlinear models can accurately simulate the entire field of HIFU sources at high outputs, but they are very intensive computationally

P.V. Yuldashev, V.A. Khokhlova. Simulation of three-dimensional nonlinearfields of ultrasound therapeutic arrays.Acoustical Physics, 2011, 57(3), 334–343.

Boundary condition for the modelingobtained from measurements using acoustic holography

hydrophonewater

HIFU transducer

measurement plane

experimental arrangementfor reconstruction of vibration velocity at the surface of the transducer Philips MR-guided HIFU source

O.A. Sapozhnikov et al. Reconstruction of the normal velocity distribution on the surface of an ultrasonic transducer from the acoustic pressure measured on a reference surface. Acoustical Physics, 2003, v.49(3), 354–360.

2D multi element clinical phased arrayPhilips MR-guided HIFU source

W. Kreider et al. Acoustic measurements and holographic reconstruction of the Philips MR-guided HIFU source. 2nd Int. MR-guided Focused Ultrasound Symp 2010, p.79.

Boundary condition to the modelingreconstructed experimentally using acoustic holography

magnitude

phase

Array elements do not vibrate uniformly as ideal pistons

reconstructed 2D velocity distribution at the array surface

Hologram

3D acoustic field

Therapeutic array

Validation of linear/nonlinear modeling of the array fieldin water

focal waveforms modeled and measured with the FOPH hydrophone

-20

0

20

40

60b)

10 15 20

0

50

100

t

c)

10 15 20

0

50

100

t

d)

-5

0

5

p, MPa

a)

experimenthologram

Linear simulations of the array field using acoustic holography data

agree well with direct hydrophone measurements (dots)

linear pressure amplitude distribution on the axis of the array

Nonlinear waveforms with shock amplitudes of up to 100 MPa were modeled and measured

at the focus and agree very well

P.V. Yuldashev, V.A. Khokhlova. Simulation of three-dimensional nonlinear fields of ultrasound therapeutic arrays. Acoustical Physics, 2011, v.57(3), 334–343.

pF

p0, f0

2r0F

Nonlinear derating method

3000

02

0 pp

FcfrG F

strongly focused transducer

linear focusing gain

On-axis linear propagation curves for pressure amplitude (G = 40)

at the focus:

here L=F, F = 1 (example)

)exp()()( 00 Lwaterptissuep

)()( waterptissuep FF

deration to tissue

– absorption L – focal depth in tissue

at the source:

Equal pressure at the focus = equal pressures in the focal lobe (for high gain sources): nonlinear effects will be very similar in water and in tissue

0.25 0.50 0.75 1.00 1.250

10

20

30

40p/p0 water

tissue

x/F

0.95 1.00 1.0532

36

40

0.25 0.50 0.75 1.00 1.250

10

20

30

40p/p0 water

tissue

x/F

0.95 1.00 1.0532

36

40

Experimental validation of derating method:measurements behind ex vivo bovine liver

f0 = 2 MHzF = 2r0 = 45 mmG = pF / p0 = 48

liver, 27 mm thick

fiber optichydrophone

p0 = 0.29 MPa – waterp0 = 0.48 MPa – liver

measured focal waveform:water versus liver

= 0.7 dB/(cm MHz)p0(tissue) =p0(water)·exp( L)

0.0 0.2 0.4 0.6 0.8 1.0-10

0

10

20

30

40

50 FOPH (Water) FOPH (Liver) KZK (Liver)

time (s)

Pres

sure

(MPa

)

Focal waveforms measured, simulated, and derated from calibration in water agree very well.

Measurement of shock waves in tissue using FOPH

FOPH

Do shocks exist in HIFU fields in inhomogeneous tissue?

Measured shock waveform behind

2.5 cm thickex vivo porcine

body wall

Measured shock waveform behind

2.0 cm thickex vivo liver sample

Shock waves of up to 100 MPa amplitude are clinically relevant

intensity max 16 000 W/cm2

heat deposition max 56 000 W/cm3

peak negative pressure max 113 bars

boiling cavitation

In situ nonlinear field Gel phantom 7% BSA

peak positive pressure max 630 bars

0.0 0.2 0.4 0.6 0.80.5

1.0

1.5

2.0

2.5

3.0

3.5

experiment

maximum localizationmaximum asymmetry of the waveform

N

K(P+)

Nonlinear heating is much more localized than cavitation, heating due to shocks results in ms boiling. Time to boil agrees better with the modeling

Example

different peak amplitude and duty cycle = same average HIFU power

advantages of pulsing schemes with high peak pressures:

- enhanced heating by shocks- mechanical effect- time windows for imaging- visualization of bubbles

Shock waves, ms boiling, and pulsing schemes and in HIFU

lesions of different types

5 mm 5 mm

5 mm

As

nonlinear shock wave

Nonlinear acoustic effects are clinically relevant and critical in some current applications of HIFU

Nonlinear HIFU fields can be accurately characterized using a combined modeling and measurement approach

Newer bioeffects can be induced in tissue using strongly distorted nonlinear waves with shocks

Conclusions

AcknowledgementsWork supported by:

NIH EB007643