Abstract — We show that a 2 MHz HIFU

field can be measured in water and with high

spatial resolution by placing a small scatterer in

the field and sensing the scattered wave. We use a

bistatic configuration placing a hydrophone at a

safe distance. Glass and steel tips are fabricated

using simple techniques and evaluated. Tapered tip

geometry proves to be mechanically robust and

not prone to internal resonance or scattering

from other sites than the tip. Glass proves to be

superior to polished carbide steel in its ability t o

delay the initiation of cavitation, and relatively

easy to manufacture using common pipette

drawing technology. In our tests, a highly

nonlinear 2 MHz HIFU field is mapped in

degassed water with a 0.1 mm glass tip. The

fundamental, 2n d, 3rd, and 4th harmonics are

mapped with at least 25 dB dynamic range and are

comparable with numerical results. Numerical

simulations for nonlinear fields in water are

obtained using a well established KZK equation

based calculation.

I. INTRODUCTION

Conventional mapping of high intensity fields

produced by focused transducers is performed by

mechanically scanning a hydrophone through the

field. Unfortunately, repeated measurements at

typical medical HIFU (High Intensity Focused

Ultrasound) levels of thousands of Watts per

square centimeter risks damaging the hydrophone

by heating or by cavitation, even when very short

pulses are used. Furthermore, the resolution of the

field map is limited to the size of the active area

of the hydrophone, typically on the order of 0.5

mm and large compared to many wavelengths of

interest. For highly focused and intense acoustic

fields, power can be significant at the third or

fourth harmonic. For example, at frequencies of 2

or 3 MHz which are commonly used in HIFU

therapy, field feature sizes at the focus can be on

the order of 0.1 mm or smaller. Such features are

not present at low intensities most often used for

field mapping measurements, because the field is

much more linear at such intensities.

Field maps are essential for transducer

development and testing. High power densities

used in HIFU result in severe electrical and

thermal stresses and can lead to failure. Focal gain

is sensitive to imperfections, and partial

delamination between the matching layer and the

active element can produce significant reductions

in focal intensity. At low powers, this problem is

often discovered by measuring the beam

dimensions in the focal region. Government

regulatory compliance testing (primarily for

imaging devices) requires extensive field mapping.

While HIFU therapeutic devices are not yet

approved, field maps will likely be required of any

manufacturer to verify focal characteristics as

well as pre-focal fields to ensure the absence of

“hot spots” where they are not desired. Finally,

the need to compare theory with experiment and

numerical models with data motivates the

development of in situ techniques for measuring

HIFU fields.

II. APPROACH

The idea of measuring a strong field indirectly

by placing a known scatterer within it and

HIGH RESOLUTION MAPPING OF NONLINEAR MHZ ULTRASONIC FIELDS

USING A SCANNED SCATTERER

Peter Kaczkowski* and Bryan CunitzCenter for Industrial and Medical Ultrasound

Applied Physics Laboratory, University of WashingtonSeattle, WA 98105, USA

Vera Khokhlova, Oleg SapozhnikovMoscow State University

Moscow, Russia

measuring the scattered field using a receiver

safely outside the primary source field is not a

new one. Long used by practitioners in ultrasound

laboratories [1-5], the technique has mostly been

applied in a monostatic configuration, that is, one

in which the receiver is in the same location as

the source, and indeed is often the very same

transducer. We sought to measure harmonics of

the field to which the source transducer was not

sensitive due to the rather careful electrical and

mechanical impedance matching done near the

fundamental frequency to optimize HIFU

efficiency (e.g., to minimize transducer heating).

Thus, we chose to use a different transducer as

receiver.

Geometrical arrangement

The receiver we chose to test the approach was

a general purpose hydrophone manufactured by

Sonic Concepts, Woodinville, Washington, USA,

used for a wide range of measurements in our lab.

The transducer is made of PZT with a center

frequency of 5 MHz and has two matching layers,

thus providing a wide sensitivity bandwidth (here

we recorded in the 2 – 8 MHz band). The

transducer is a spherical cap with a diameter of

0.95 cm and a radius of curvature of 7.5 cm. The

setup geometry is diagrammed in Figure 1.

Figure 1. General arrangement of HIFU transducer,scattering tip, and receiver. A rigid frame holding bothscatterer and receiver is essential; the scatterer andreceiver must move as one. The calibration standardhydrophone is not shown; it is positioned at the samelocations as the scattering tip and detects the fielddirectly at safe amplitude settings.

Scatterer properties

To be effective at probing small spatial scales,

the scatterer must be both small and rigidly

supported. Generally, the scatterer must be

smaller than a wavelength; ideally, it behaves as a

Rayleigh scatterer. Consequently, it will scatter

broadly in angle and the choice of incident and

scattered field angles is not particularly

important. Furthermore, the scattered power is

proportional to (frequency)4 and this dependence

helps mitigate the decrease in power with

increasing harmonic number in a nonlinear field,

and can also be used to offset receiver sensitivity

falloff above its central frequency. A tapered tip

provides excellent mechanical support as well as

very little scattering from the taper for a

moderate range of angles. No appreciable pulse

lengthening was observed in the scattered signal

(for a short HIFU pulse) that would be due t o

scattering from points other than the tip.

A rigid frame ensures that the Green’s function

between scatterer and receiver is constant during a

scan, permitting absolute calibration of the

system using a reference hydrophone, or a

standard calibrated source, for each frequency of

interest. The frequency dependence of the system

is highly scatterer and receiver dependent; no

attempt was made to compute it in advance. The

rigid frame holds two hydrophones: the 1 cm

diameter 5 MHz focused PZT element with its

center of curvature centered on the scatterer (and

located outside the source field), and one 0.6 mm

active diameter PVDF needle hydrophone (NTR,

Seattle, WA). The latter is used for calibration by

replacement and is mounted facing the HIFU

source but with sufficient offset from the

scattering tip to keep it out of the HIFU field

during scattering measurements. The PVDF

hydrophone is only used at low intensities.

Tip fabrication techniques

We fabricated tapered rods of steel and glass

with tip diameters between 0.5 mm and 0.01 mm.

Carbide tool rod stock was sharpened by hand

using a grinder and successively finer emery paper.

Though the tip was relatively easy to make, we

were not able to prevent cavitation from

initiating with a few acoustic cycles, even at

moderate HIFU pressures. Glass has different

surface properties than steel, and inhibits

cavitation long enough (at least 10 cycles) t o

provide purely tip-scattered signals. We only

describe the manufacture of glass tips in detail.

Figure 2. A pipette puller is used to draw glass tubesinto extremely small diameter needles for use inbiological experiments. Here, a 5 mm diameter glass rodis held vertically by two chucks. A coiled heating elementis driven by a current source and heats it to a brightorange glow, softening the rod. The upper chuck is fixed,and the bottom one can be lowered by hand or byattaching a fixed weight. Several heat, draw, cool andcleave cycles are repeated to reach the desired tip size.

Glass can easily be drawn into extremely thin

fibers or tubes when heated. Using standard

laboratory borosilicate glass rod and a pipette

puller we fabricated tapered glass tips with face

diameters ranging from 0.01 mm to 1 mm.

Excellent results are achieved with tip face

diameter on the order of 0.1 mm. Figure 2 is a

photograph of a pipette puller.

The glass is heated, drawn, cooled and cleaved

several times to reach the desired tip diameter.

This process leads to tips such as the one depicted

in Figure 3. Cleaving is preferred to melting the

tip which creates a tiny ball; the ball tends t o

resonate. Tips are surprisingly robust; they are

not often damaged by cavitation, or, at least

calibration results do not change measurably. It is

possible that erosion of such small tips would not

cause much change in scattering properties as long

as the tip preserved its diameter. If the latter is

much smaller than the acoustic wavelength details

of the face shape do not measurably affect

scattering properties.

III. FIELD MAPPING PROCEDURE

Field mapping is done over a broad frequency band

by processing the scattered pressure waveform at

each spatial location of the scatterer. The

scattered waveform is collected by amplifying and

digitizing the receive hydrophone voltage during

the initial dozen cycles or so. At high intensities,

cavitation modifies the scattered signal

dramatically. Bubbles are not usually visible at the

tip; rather the waveform becomes completely

unstable. It is interesting to observe that the

instability typically appears near the same time

after the HIFU pulse begins, as long as adequate

time is given for bubbles to re-dissolve in the

highly degassed water. We use a 2 MHz HIFU

burst of 10 cycles at a repetition rate of 10 Hz.

The voltage waveform collected over a 2

microsecond window is processed by FFT, and

harmonic amplitudes are stored for each spatial

location.

Figure 3. Photographs of the same tip at variousmagnifications. Top: no magnification, scale is in cm.Middle: Tip magnified to X5. Bottom: tip magnified toX40; each minor division is 0.01mm.

Calibration of the system is performed by direct

comparison of field maps collected by the

scatterer system and by a conventional calibrated

PVDF needle hydrophone. This approach suffers

from the limited resolution of our PVDF needle,

but there are now hydrophones available with

active areas on the order of 0.1 mm (it would not

be prudent to use these in a HIFU field, however).

The calibration need only be done once for any

given tip and frame setting; we do not yet have a

sense for how rapidly tips erode and how often re-

calibration is needed.

IV. RESULTS AND CONCLUSIONS

We conducted a field map for a 2 MHz HIFU

source emitting a total acoustic power of 60 W

(Sonic Concepts model SU-101, RoC = 55 mm,

Diam = 35 mm). The tip diameter was about 0.1

mm, and the field map step size was set to 0.05

mm. Experimental field maps of the fundamental,

2nd, 3rd, and 4th harmonic fields plotted on a

logarithmic color scale are presented in Figure 5:

the speckle (noise) in the 4th harmonic data is at

25 dB below the peak. On a linear scale, the data

plots are nearly indistinguishable from numerical

simulations (labeled “Theory”) of the

experimental conditions using a KZK equation

method [6].

A simple method using a scanned tapered tip

scatterer can be used to measure MHz range HIFU

fields (including harmonics) at full power, in water

or other fluids without risk of damage to the

hydrophone which is placed outside the direct

HIFU field. Tapered glass tips are effective and

inexpensive to manufacture, and tend to suppress

cavitation due to their surface properties.

V. REFERENCES

[1] Bernier, C.A., L. Huntsman, and R. Martin, "Apractical approach to measuring an intravascularultrasonographic imaging system beam pattern", JUltrasound Med, 14(5): p. 367-73, May 1995.

[2] Parker, K.J., "The thermal pulse decay technique formeasuring ultrasonic absorption coefficients",JASA, 74(5): p. 1356-1361, 1983.

[3] Raum, K. and W.D. O'Brien, Jr., "Pulse-echo fielddistribution measurement technique for high-frequency ultrasound sources", IEEE Trans. UFFC,44(4): p. 810-815, 1997.

[4] Lizzi, F., "Private communication." 2002.[5] Szabo, T., "Private communication." 2003.[6] Khokhlova, V.A., et al., "Numerical modeling of

finite-amplitude sound beams: Shock formation inthe near field of a cw plane piston source", J.Acoust. Soc. Am., 110(1): p. 95-108, Jul 2001.

Figure 4. Top: Scanned scatterer data using a 0.1 mm tip, and a 2 MHz nonlinear HIFU field.Bottom: KZK simulations for the experimental conditions of the scan above.Spatial units are mm; the noise, visible as speckle in the 8 MHz data is 25 dB below peak.