A Buoyancy Method for the Measurement of Total Ultrasound Power Generated by HIFU Transducers

Ultrasound in Med. & Biol., Vol. 34, No. 8, pp. 1327–1342, 2008 Crown Copyright © 2008 Published by Elsevier Inc. on behalf of World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/08/$–see front matter

doi:10.1016/j.ultrasmedbio.2008.01.008

● Original Contribution A BUOYANCY METHOD FOR THE MEASUREMENT OF TOTAL ULTRASOUND POWER GENERATED BY HIFU TRANSDUCERS ADAM SHAW Quality of Life Division, National Physical Laboratory, Teddington, Middlesex, United Kingdom (Received 21 September 2007; revised 30 October 2007; in final form 15 January 2008)

Abstract—Total acoustic output power is a key parameter for most ultrasonic medical equipment and especially for high intensity focused ultrasound (HIFU) systems, which treat certain cancers and other conditions by the noninvasive thermal ablation of the affected tissue. In planar unfocused fields, the use of a radiation force balance has been considered the most accurate method of measuring ultrasound power. However, radiation force is not strictly dependent on the ultrasound power but, rather, on the wave momentum resolved in one direction. Consequently, measurements based on radiation force become progressively less accurate as the ultrasound wave deviates further from a true plane-wave. HIFU transducers can be very strongly focused with F-numbers less than one: under these conditions, the uncertainty associated with use of the radiation force method becomes very significant. In this article, a new method for determining power is described in detail. Instead of radiation force, the new method relies on measuring the change in buoyancy caused by thermal expansion of castor oil inside a target suspended in a water bath. The change in volume is proportional to the incident energy and is independent of focusing or the angle of incidence of the ultrasound. The principles and theory behind the new method are laid out and the characteristics and construction of an appropriate target are examined and the results of validation tests are presented. The uncertainties of the method are calculated to be approximately ⴞ3.4% in the current implementation, with the potential to reduce these further. The new technique has several important advantages over the radiation force method and offers the potential to be an alternative primary standard method. (E-mail: [email protected]) Crown Copyright © 2008 Published by Elsevier Inc. on behalf of World Federation for Ultrasound in Medicine & Biology. Key Words: Ultrasound, Output power, Calibration, Calorimetry, Buoyancy, HIFU, FUS.

This radiation force method relies on the principle that when a travelling ultrasound wave is incident on an object or “target”, which partially reflects or absorbs the incident wave, the target experiences a force equal to the change in the momentum flux associated with the wave. Many commercial radiation force balances have been built and sold throughout the world and are used to measure the output from all types of therapeutic and diagnostic ultrasound equipment, covering the frequency range 0.75 MHz to 15 MHz and the power range 1 mW to 20 W. Leading national laboratories, have obtained excellent agreement in comparisons with each other using their primary standard radiation force balances and typically quote uncertainties in the region of ⫾3% to 4% (Tsciegg et al. 1983; Beissner et al. 1996; Beissner 2002). However, these comparisons have always used unfocused transducers operating at power levels below 20 W. HIFU transducers are generally strongly focused and operate up to 200 W or more. Two types of target are commonly used: a flat absorbing target held parallel to the transducer face or a

INTRODUCTION High intensity focused ultrasound (HIFU) is finding increasing use as a technique for treating certain cancers and other conditions by the noninvasive thermal ablation of the affected tissue. The total ultrasound output power of a HIFU system is a key quantity related to the delivered dose during clinical treatment. Traditionally, the use of a radiation force balance has been considered the most accurate method of measuring ultrasound power: it is described in detail in the literature (for example Greenspan et al. 1978; Benjavic and Carson 1980; Stewart 1982; Tsciegg et al. 1983; Livett 1984; Davidson 1991; Beissner et al. 1996; Beissner 1999a, 1999b, and 2002; Hekkenberg et al. 2000;2001, Hekkenberg et al. 2006; Sutton et al. 2003) and in IEC standard 61161 (IEC61161 (2006)).

Address correspondence to: Adam Shaw, Quality of Life Division, National Physical laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, UK. E-mail: [email protected] 1327

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Table 1. Ratio of results using reflecting target to results using absorbing target obtained during the European comparison

PTB NPL

1 MHz

2 MHz

5 MHz

10 MHz

1.015 1.026

1.003 1.023

0.984 1.002

0.949 0.976

right-angled convex conical target held with its axis perpendicular to the transducer face. In both these cases, simple theory predicts that the force, Fm, experienced by the target depends on the incident power, Pm and the speed of sound in the propagating medium (normally water), c: Fm ⫽

Pm . c

(1)

This equation is so widely used that it is easy to lose sight of the many assumptions that lie behind it and how those assumptions affect the uncertainty that should be attributed to the calculated value for total power. There is evidence that, even in the well controlled intercomparisons carried out by leading laboratories, some aspects of the uncertainties are not as well controlled as they might be. In Beissner et al. (1996), the National Physical Laboratory (NPL) and the Physikalische-Technische Bundesanstalt (PTB) report measurement made with both of these common target types. The ratio of the radiation conductance determined using the reflecting target to that determined using the absorbing target is given in Table 1. There is clear decreasing trend with frequency at both laboratories and the difference between the two target types is similar to the quoted uncertainties at 1 MHz and 10 MHz. Other observations at NPL also confirm that there are small significant differences between target types. The most likely explanation lies in the wave generated by the transducer. The simple theory assumes that the wave is planar, i.e., the wavefront is parallel to the transducer face and propagates in the forward direction. In real life, such perfection is not achievable even for a simple plane piston transducer and so the actual force will differ from the expected force by an amount which depends on the type of target, the type of transducer and the distance between them. Beissner (1987) has studied the force produced by idealised nonplane waves on an absorbing target and has derived a formula for calculating the “plane-wave correction” as a function of ka for a circular plane-piston transducer, where k is the acoustic wave number and a is the transducer radius. However, the reflecting target is more complicated and has not been studied. Shaw (2006) points out that the plane-wave approximation can introduce large measurement errors when

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making radiation force measurements in focused fields. In a focused field, the relationship between force and power is different to that in Equation (1). For a spherically focused bowl transducer incident on a totally absorbing target, IEC61161 (2006) gives the relationship in eqn 2, where ␥ is the half-angle subtended by the transducer and is calculated from the transducer radius, a, and the radius of curvature, Rc: ␥ ⫽ arcsin(a/Rc). Fm ⫽

P 1 ⫹ cos␥ c 2

(2)

This is a limiting case derived from an analytical field model (Beissner 1984). However, it can be derived separately using a simple ray acoustics model (Shou 1998) so it is of interest to consider a ray acoustics model for a conical reflecting target as shown in Fig. 1. For a ray incident at angle ␪, the change in vertical momentum on reflection is proportional to (cos(90o ⫺ 2␪) ⫹ cos␪). Integrating over all rays emerging from the transducer, we arrive at the relationship given in by IEC61161 (2006). Fm ⫽

P (1 ⫹ cos2␥) ⫾ (2␥ ⫺ sin2␥) c 4(1 ⫺ cos␥)

(3)

In eqn 3, the plus sign in the numerator applies when the tip of the cone lies between the center of curvature and the transducer, which is the case of practical interest. The ratio c Fm/P can now be calculated for an absorber and a right-angled cone using eqns 2 and 3, respectively. This is plotted in Fig. 2 as a function of the nominal F-number (Rc/2a) and clearly shows that the focusing errors are significant when using a conical target even in rather weakly focused fields and increase rapidly as the F-number decreases. For HIFU transducers, where F-numbers less than one are common, it is clear that the use of

Fig. 1. Ray acoustic model for a right-angled conical target in a focused field.

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assumptions, the change in volume should be proportional to the incident energy (product of power and time) and is independent of the angle of incidence of the ultrasound. In the current article, this buoyancy method will be explored in more detail. First, the principles and theory are laid out and the characteristics and construction of an appropriate target are examined. Then, the results of validation tests are presented and the uncertainties of the method are calculated and compared with those for radiation force. Finally, the advantages and disadvantages of the technique are discussed. Fig. 2. Relative error due to focusing for right-angled cone and absorbing targets.

conical reflecting targets should be avoided. However, it is also clear that there is significantly increased uncertainty from this source even when using a perfect absorbing target. A further difficulty with using an absorbing target is the risk of thermal damage to the target due the very high intensities generated. There are therefore two requirements to be addressed: the development of a high quality absorbing radiation force balance target that can survive exposure to very high power ultrasound fields; and the development of a method that overcomes the inherent limitation of the radiation force method in strongly focused fields. Maruvada et al. (2007) have explored the use of “brush” targets but their recommended procedure involves a “pulsed-mode” approach where the full voltage is applied to the transducer for only limited periods (roughly 100 ms tonebursts repeated every 1000 ms, giving a 10-fold reduction in the output power. One method to prevent excessive heat buildup is to use an absorbing fluid instead of a solid material so that heat is dissipated by convection and streaming currents within the target. A radiation force target filled with castor oil has been described previously by Shaw (2006) and calibrated against the portable power standard (Hekkenberg et al. 2006) using unfocused physiotherapy transducers at applied power levels between 1 and 15 W. The ratio of measured power to applied power was 1.04 at 1 MHz and 0.99 at 3 MHz both with an uncertainty of ⫾6%. The same target was also tested at incident powers up to 140 W at 1.08 MHz and shown to be linear to within ⫾3% over this range. Internal convection was observed during insonation but no signs of any damage were seen. In this same article, a new method for determining power was proposed which, instead of radiation force, relies on measuring the change in buoyancy caused by thermal expansion of the oil inside the target. Subject to certain

PRINCIPLES The principles of the buoyancy technique are briefly described by Shaw (2006): it is essentially a form of calorimetry where the change in the average temperature of the medium is inferred from its change in volume. Calorimetry is a general method that is commonly used to measure absorbed energy. Typically, the method measures the temperature rise in a known amount of material and assumes that the temperature of the material is uniform (or at least changes uniformly). If the heat capacity of the material is known, the amount of energy absorbed, ⌬J, is calculated from: ⌬J ⫽ MC⌬T

(4)

where M is the mass of material, C is its specific heat capacity and ⌬T is temperature increase. It can often be a relatively slow technique since time is required to establish thermal equilibrium and this in turn means that there is time for energy to be lost to the container or the outside environment. The use of multiple thermal sensors can cater better for nonuniform heating distributions provided that the number of sensors is adequate and that their presence does not affect the absorption process. It has been proposed previously for the measurement of ultrasound power or intensity (Wells 1963; Mikhailov 1964; Lloyd 1967; van den Ende 1969; Herman and Stewart, 1973; Zapf et al. 1976; Torr and Watmough 1977; Delchar and Melvin, 1994). To do this in a HIFU field where the ⫺6 dB focal diameter may be 1 mm or less would require an extremely high sensor density. The change in volume of liquid with temperature is of course well known and was the basis of most common thermometers until the invention of thermistors. Using the absorbing medium as its own thermometer provides an infinite sensor density without the risk of additional interactions and sources of uncertainty. In the proposed method, the ultrasound transducer and an oil-filled target are immersed in a water bath. The target is suspended from a balance and is positioned to intercept the whole of the ultrasound field generated by

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dVi(Ti) dVi(Ti) dTi ⫽ dt dT dt ⫽ Vi(Ti)Ei(Ti) ⫽ Vi(Ti)Ei(Ti) ⫽ Fig. 3. Typical weight vs. time sequence. The radiation force is determined from the difference between the paired open and closed symbols immediately before each transition.

dTi Wi(Ti) Li ⫽ ⫹ dt M iCi(Ti) M iCi(Ti) ⫽

Wi(Ti) ⫹ Li Vi(Ti)␳i(Ti)Ci(Ti)

冋

Wi(Ti) ⫹ Li Vi(Ti)␳i(Ti)Ci(Ti)

册

Ei(Ti) [W (T ) ⫹ Li] ␳i(Ti)Ci(Ti) i i

(7)

Now the rate of change of volume, V, of the whole target is given by summing over all elements: dV ⫽ dt

the transducer. An example weight versus time sequence is shown in Fig. 3 for an incident power of approximately 15 W: the ultrasound is absorbed resulting in an instantaneous radiation force and a progressive heating of the castor oil. Heating causes either the volume or the internal pressure to increase. Since the target is designed with a thin entry membrane, which is transparent to ultrasound and is intentionally not under tension, the pressure of the oil remains constant and its volume is free to expand. The change in volume results, according to Archimedes’ principle, in an additional buoyancy force acting vertically on the target and so the weight registered by the balance decreases. This stepwise decrease following each on-period can be seen by looking at consecutive off-periods in Fig. 4 and it can be determined from the weight versus time sequence. Considering a mass element, i, of the fluid with mass Mi at temperature Ti:

dTi dt

⫽

兺 i

Ei(Ti)

兺 ␳ (T )C (T ) 关W (T ) ⫹ L 兴 i

i

⫽

provided

dVi(Ti) dt

E ␳c

i

i

冋兺

i

Wi(Ti) ⫹

i

i

i

i

兺L i

册

i

E is constant w.r.t. temperature; ␳c ⫽

E ␳c

冋兺

Wi(Ti) ⫹ 0

i

册

provided that no other heat flows in or out of the oil; dV E ⫽ W dt ␳C

(8)

provided that all the ultrasound energy is absorbed in the oil. In practice, it is difficult to determine the rate of change of volume accurately during insonation since the

(5)

where Wi is the ultrasound energy absorbed in the element and Li is the rate of heat flow into the element from neighbouring elements. By definition, the coefficient of volume expansion, E, is given by: E(T) ⫽

1 dV(T) V(T) dT

(6)

and so (provided that the pressure in the oil remains constant) the rate of change of volume of the element is given by:

Fig. 4. Close up of the off-periods of a typical weight vs. time sequence. The buoyancy force is determined from the difference between the paired open and closed symbols half-way through each on-period.

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target is disturbed by the radiation force and by streaming and convection currents. It is more reliable to determine the net change in volume shortly after the end of the insonation period, t0, which amounts to integrating the equation over the duration of insonation to get: t0

⌬V ⫽

兰 dt dt dV

0 t0

(9)

兰

E Wdt ⫽ ␳C 0

Assuming that the ultrasound power is constant during the insonation period, t0, and that the density, ␳w, of the water in the water bath is uniform and constant, the change in mass displayed by the balance will be: ⌬M ⫽ ␳w⌬V ⌬M ⫽

␳wE Wt ␳C 0

(10) (11)

and the sensitivity, S, defined as the change in buoyancy per unit absorbed energy is given by: S⫽

⌬M ␳wE ⫽ Wt0 ␳C

(12)

which is independent of the volume of the target. So, for a known insonation period, the change in the indicated mass is directly proportional to the ultrasound power subject to the following assumptions: 1. The ratio E/␳c is constant over the range of temperature occurring inside the target at the time the buoyancy change is measured following insonation. It does not matter if the local temperature temporarily exceeds the range where this ratio is constant. 2. The heat lost from the oil to the container or the surrounding water is much less than the absorbed energy. 3. Other sources of heat are much less than the absorbed energy. 4. The ultrasound energy incident on the target is completely absorbed in the oil. 5. The water bath remains at a constant temperature and density. 6. The pressure of the oil remains nearly constant. 7. To determine power, as opposed to integrated energy, the power output of the transducer should be constant. CONSTRUCTION AND CHARACTERISTICS A larger and improved version of the target described previously has been constructed (Fig. 5). It con-

Fig. 5. Schematic diagram of castor oil target.

sists of a Perspex cylinder with an inner diameter of 12 cm and a length of 15 cm; the cylinder is filled with laboratory grade castor oil (absorption coefficient 0.8 dB cm⫺1 MHz⫺1.7) supplied by Fisher Scientific. The end of the cylinder facing the transducer is sealed with a plastic saran wrap membrane of measured thickness 10 ␮m, the far end with a 5 mm thick Perspex plate. The reflectivity of the entry membrane was measured to be less than ⫺30 dB up to 2 MHz and less than ⫺22 dB up to 5 MHz. To provide additional thermal insulation between the heated oil and the walls of the target, an open thin-walled chamber is fitted internally. The far end of the inner chamber is fitted with two pieces of Aptflex F36 absorber (Precision Acoustics Ltd, Dorchester, UK) each 2.5 mm thick: at 1 MHz the reflection loss was measured to be ⫺25 dB and the transmission loss ⫺23 dB cm⫺1 at 1 MHz. These absorbers are surrounded by castor oil to ensure rapid thermal equilibration with fluid. The entire target can be suspended directly from a balance or can be fitted to a cradle that allows the transducer to be fitted vertically above the target. The balance used was a Sartorius LP1200S balance of resolution 1 mg and capacity of 1200 g: the displayed mass was read continuously via an RS232 interface and analysed in Excel. A brass weight is attached to the target to ensure it remains negatively buoyant and is stable in the water; liquid crystal thermometers are fitted to the outside of the inner chamber to indicate the general temperature of the oil and monitor changes. Figure 6 shows the target fitted to its cradle and suspended from the balance; a HIFU transducer is mounted above the target. In the photograph, the inner chamber is fitted with a metal concave reflecting base; this was later replaced with absorbing layers described. The density, expansivity and heat capacity of castor oil (Eur. Pharm. Grade, produced by Acros Organics,

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Balance (with concealed underpan hook ) Shelf on aluminium framework

Volume 34, Number 8, 2008

Specific heat capacity was measured using a Perkin Elmer (Perkin Elmer, Waltham, MA, USA) differential scanning calorimeter (model DSC7). The temperature variation is shown in Table 2 and was found to fit the linear relationship: Cp(T) ⫽ (2043.0 ⫹ 3.0T) J kg⫺1 C⫺1.

Support rods

Transducer

Cradle

Target

Water tank

Fig. 6. Photograph of target and balance assembly.

Geel, Belgium) were measured as a function of temperature by the thermophysical properties group at NPL. Density was measured using Archimedes’ principle applied to a silica glass block of known volume immersed in the oil. The temperature variation is shown in Table 2 and was found to fit the linear relationship:

␳(T) ⫽ (972.7 ⫺ 0.678T) kg m⫺3.

(13)

where T is the temperature in °C. The uncertainty in the density is less than ⫾1% at the 95% confidence level.

(14)

The uncertainty is estimated to be ⫾3.4% at the 95% confidence level. The buoyancy sensitivity changes with temperature at a rate of less than 0.025%/°C so, for practical purposes, a temperature independent value of 0.350 mg J⫺1 ⫾ 3.7% is appropriate for the sensitivity, where the major source of uncertainty is due to the determination of the specific heat capacity of the castor oil. The sensitivity was also determined experimentally by measuring the rate of change of weight of a container of castor oil, which was heated electrically whilst suspended in a tank of water. The volume of the container was approximately 500 mL and heat was provided by passing current through a 30 cm length of nichrome (NiCr) wire. The ends of the wire were attached to two 2 mm plugs mounted in the base of the container and it was twisted into a spiral to fit conveniently inside the container. An acetate liner was placed inside the container close to, but not touching, the wall to minimise heat loss; the container was filled with castor oil and sealed with cling film, which was left unstretched to allow the oil volume to change freely. A loose acetate sheet was positioned close to the cling film to reduce heat loss. The container was suspended in water from the

Table 2. Density of water and density and specific heat capacity of Acros Organics castor oil in the range 10 to 60oC

Temperature o C

Density g/ml

Volume expansivity 1/K

10 15 20 25 30 35 40 45 50 55 60

0.9659 0.9625 0.9591 0.9557 0.9524 0.9490 0.9456 0.9422 0.9388 0.9354 0.9320

7.02x10⫺4 7.05x10⫺4 7.07x10⫺4 7.10x10⫺4 7.12x10⫺4 7.15x10⫺4 7.17x10⫺4 7.20x10⫺4 7.23x10⫺4 7.25x10⫺4 7.28x10⫺4

2.073 2.088 2.103 2.119 2.134 2.149 2.164 2.179 2.194 2.209 2.224

2.003 2.010 2.017 2.025 2.032 2.039 2.046 2.053 2.060 2.067 2.073

3.507x10⫺4 3.506x10⫺4 3.506x10⫺4 3.506x10⫺4 3.506x10⫺4 3.506x10⫺4 3.506x10⫺4 3.507x10⫺4 3.508x10⫺4 3.510x10⫺4 3.511x10⫺4

0.9997 0.9991 0.9982 0.9970 0.9956 0.9939 0.9921 0.9900 0.9877 0.9853 0.9826

1.0%

1.0%

3.4%

3.5%

3.7%

0.1%

95% uncertainty

SHC J/g/K

VHC J/ml/K

Volume sensitivity ml/J

Water density g/ml

Buoyancy sensitivity at 23oC mg/J

Buoyancy sensitivity at T mg/J

0.3496 0.3496 0.3495 0.3495 0.3495 0.3495 0.3496 0.3496 0.3497 0.3499 0.3500 Average 0.3495 3.7%

0.3505 0.3501 0.3497 0.3493 0.3489 0.3484 0.3478 0.3473 0.3467 0.3460 0.3453 3.7%

Also tabulated for castor oil are the derived volume expansion coefficient and volumetric heat capacity, the volume increase per absorbed Joule and the buoyancy increase per absorbed Joule in water at a fixed temperature of 23oC. The final column shows the buoyancy increase per absorbed Joule in water at the same temperature as the castor oil. The final row shows the uncertainty at a confidence level of approximately 95%.

Buoyancy method measurement ● A. SHAW

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Fig. 7. Example of weight and rate of change of weight of castor oil target subject to four 15 s periods of heating at approximately 40 W. Heating periods start at 30, 60, 90 and 120 s.

same balance used for acoustical power measurements, and electrical power was delivered via two flexible cables connected to the 2 mm sockets on the base of the container. Care was taken to minimise the strain in these cables. These cables were connected to a dc power supply; current and voltage were measured using a Keithley 2000 and Keithley 2001 DVM (Keithley, Cleveland, OH, USA), respectively: the uncertainty in each is less than 0.1% according to the instrument specifications. In the absence of a heating current, the resistance of the NiCr coil was 9.95 ⍀ and the resistance of the electrical leads was 0.10 ⍀. It was necessary to measure both current and voltage because the resistance of the coil was load-dependent: it increased to 10.03 ⍀ when 10 V (equivalent to approximately 10 W) was applied, and to 10.11 ⍀ when 20 V (approximately 40 W) was applied. According to Kaye and Laby (online edition), the resistivity of NiCr increases by approximately 0.009%/K, so an increase of 0.16 ⍀ implies that the temperature of the wire is about 180° K above room temperature. Due to this large temperature increase, it can be expected that there will be significant storage of thermal energy in and around the wire when it is first connected to the power supply and it will take some time for new equilibrium conditions around the wire to be established. From observation of the changing electrical resistance, this equilibrium took about 5 s to establish; after this time, the rate of energy flow into the bulk of the oil will be nearly constant and so the rate of change of buoyancy will be constant. The whole assembly, including the balance, was placed in a draught-proof enclosure and mounted on a granite slab to minimise disturbances.

The sensitivity (defined as the rate of change of weight per unit electrical power, which is equivalent to the definition of the change in buoyancy per unit absorbed energy given earlier) was determined from the difference between the slope during the middle 5 s of each on-period and the average of the slopes before and after that on-period (this compensates for the small changes in the slope during the off-periods caused by the gradual build up of heat in the target). Figure 7 shows on the right-hand vertical axis an example of the variation of displayed weight versus time for four 15 s periods of heating at approximately 40 W. Also shown on the left-hand axis, is the calculated rate of change of weight. It was measured at nominal electrical powers between 10 W and 40 W, which is consistent with the lower range of power levels required for HIFU fields: higher powers were not possible with the available power supply and the high wire temperatures achieved are a concern even at 40 W input power. These results are shown in Table 3 for oil from two producers. The first results from Acros Organics can be directly compared with the sensitivity values calculated from the measured properties of the same type of castor oil shown in Table 2 and agree to better than 4%, which is just within the combined uncertainties. The second results 11 months later show a significant increase of 2.5%. The results for the Fisher Scientific (Fisher Scientific, Loughborough, UK) oil (which by this time had been used inside a target for approximately 1 year) were intermediate. With a standard error of the mean at 0.7%, allowing a coverage factor of 2 and an additional uncertainty of 0.2% for the measurement of electrical power, we arrive at an uncer-

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Table 3. Sensitivity determined from electrical heating at nominal powers of 10, 20 and 40 W. Standard uncertainty includes random uncertainties and systematic uncertainty of 0.2% for electrical power measurement Acros Organics September 2006 Nominal power (W) 10 10 10 10 20 20 40 40 Mean and seom

Acros Organics August 2007

Fisher Scientific August 2007

Sensitivity (mg/s)/W

Standard uncertainty

Sensitivity (mg/s)/W

Standard uncertainty

Sensitivity (mg/s)/W

Standard uncertainty

0.3310 0.3429 0.3254 0.3328 0.3336 0.3352 0.3447 0.3423

1.0% 0.9% 0.8% 1.4% 0.4% 0.5% 0.3% 0.3%

0.3371 0.3435 0.3401 0.3467 0.3493 0.3494

0.5% 0.7% 0.5% 0.4% 0.3% 0.3%

0.3373 0.3399 0.3444 -

1.0% 0.3% 0.5% -

0.3360

0.7%

0.3444

0.6%

0.3405

0.7%

Zoil ⫺ Zwater Zoil ⫹ Zwater

tainty of less than 1.5% in the sensitivity. This is less than half the uncertainty from the measured properties of castor oil shown in Table 2. SOURCES OF UNCERTAINTIES In this section, the major sources of uncertainty are discussed and evaluated. The most fundamental of these is the determination of sensitivity, as this will affect any target design. Most of the other sources are dependent on specific details of the design: most importantly, target diameter and length. It is worth remembering that, in determining the uncertainty in a specified measured quantity (or measurand), it is important to be clear about precisely what quantity is required. Here we could consider at least three possible measurands: the total ultrasound power radiated by the transducer, the total ultrasound power reaching a specified surface (typically, a plane at some distance from the transducer and parallel to its front edge), or the total ultrasound power intercepted by the target. In the following discussion, it is the ultrasound power reaching the plane at the same distance as the entry membrane of the target which is of concern. Sensitivity The determination of the sensitivity of the method (defined as weight change per unit absorbed energy) has been discussed earlier. It may be calculated in two different ways: either from knowledge of the expansivity, heat capacity and density of castor oil, giving an uncertainty of 3.7%; or experimentally by direct electrical heating of a volume of castor oil, giving a much lower uncertainty of 1.5%. Clearly, the latter is preferable. Window Losses The pressure reflection coefficient of an ideal water/ castor oil interface in the absence of a window materials is given by:

(15)

where Z is the product of speed of sound and density for the specified medium. Using a value of 1490 m s⫺1 for the speed of sound in castor oil (Kaye and Laby, online edition) and 959 kg m⫺3 for density, the pressure reflection coefficient for such an interface would be 2.1% at 20°C, giving an energy reflection coefficient of only 0.04%. Consequently, the major source of reflection is the membrane of the acoustic window. For the target described in this article, the window was made of polyvinylidene chloride film (saran wrap) of thickness 10 ␮m. The reflection coefficient was measured using the materials characterisation facility at NPL and is shown in Table 4: the reflected energy is less than 1% up to 6 MHz. According to Kaye and Laby (online edition), the attenuation coefficient of polyvinylidene chloride is 207 Np m⫺1 at 2.5 MHz, so the transmission loss of the film is estimated to be 0.0071 dB MHz⫺1. The absorbed

Table 4. Reflection coefficient from saran wrap acoustic window Frequency (MHz)

Reflection coefficient (dB)

Pressure reflection coefficient

Energy reflection coefficient

Energy absorption coefficient

1 2 3 4 5 6 7

⫺36.0 ⫺31.0 ⫺26.1 ⫺24.1 ⫺21.9 ⫺20.7 ⫺19.5

1.6% 2.8% 4.9% 6.2% 8.0% 9.2% 10.6%

0.1% 0.1% 0.3% 0.4% 0.7% 0.9% 1.2%

0.2% 0.3% 0.5% 0.7% 0.8% 1.0% 1.1%

Values for energy reflection and absorption are rounded up to the next 0.1%.

Buoyancy method measurement ● A. SHAW

Table 5. Absorption coefficient of castor oil and F36 absorber as a function of temperature

10

2.5 mm radius 5 mm radius 10 mm radius 20 mm radius 50 mm radius

9

target:transducer ratio

8 7

1335

Temperature(oC)

6

Absorption coefficient for castor oil at 1 MHz(dB cm⫺1 MHz⫺1.8)

Absorption coefficient for F36 at 1 MHz (dB cm⫺1 MHz⫺1)

1.38 0.83 0.50 0.32

16.0 23.0 30.0 37.0

5

10 20 30 40

4 3 2 1.5 1 0

0

5

10

15

20

25

30

ka

Fig. 8. The minimum target size given as the quotient of bunfoc/a at a separation of 5 mm.

energy fraction is also shown in Table 4: it is less than 1% up to 6 MHz. Missed Energy Only acoustic energy intercepted by the target contributes to the increase in buoyancy. If the specified measurand is the ultrasound power intercepted by the target, the uncertainty contribution is zero by definition. When considering the radiated power or the power reaching a specified surface, this uncertainty contribution is partly related to the diameter of the target and partly to the diameter, frequency and geometry of the transducer. It is essentially equivalent to the situation when using the radiation force method with an absorbing target, and this is dealt with in part in IEC61161 (2006). This standard specifies, for the case of an unfocused plane piston transducer, the minimum target radius that intercepts at least 98% of the radiated energy: the specified minimum

10

2.5 mm radius 5 mm radius 10 mm radius 20 mm radius 50 mm radius

9

target:transducer ratio

8 7

radius, bunfoc, in an unfocused field as plotted as a multiple of the transducer radius, a, in Figs. 8 and 9 for separations of 5 mm and 15 mm. It depends on the transducer radius, a, and the acoustic wavelength, ␭ and the separation, z; an additional “safety net” value of 1.5 times the transducer radius is given in IEC61161 (2006). This value of 1.5 is often referred to in the literature as if it is sufficient to ensure that the target radius is more than 1.5 times the radius of the transducer. However, it is clear from Figs. 8 and 9 that, especially for small transducers, a much larger target is often required. In a focused field, it is reasonable to assume that a smaller target could be used. IEC61161 (2006) does not discuss this but Maruvada et al. (2007) suggest an equivalent specification based on simple ray acoustics. They assume that bunfoc is equal to 1.5a but their idea can be expressed more generally as: b foc ⫽ bunfoc ⫻

Rc ⫺ z . Rc

(16)

So we assume for the purposes of this article and without experimental investigation, that the uncertainty contribution due to missed energy is equal to 2% for a target of radius bfoc. For larger targets, the uncertainty contribution will be reduced and we will assume, again without experimental investigation, that the uncertainty for a buoyancy target of radius b is the same as for an absorbing radiation force target and is given by 2% ⫻

6

冋 册

冋 册

bunfoc Rc ⫺ z ⫻ b Rc

(17)

provided that b ⱖ bfoc.

5 4 3 2 1.5 1 0

0

5

10

15

20

25

30

ka

Fig. 9. The minimum target size given as the quotient of bunfoc/a at a separation of 15 mm.

Transmitted Energy The absorption coefficients of castor oil and F36 are strong functions of temperature as shown in Table 5. This is an important practical consideration when repeated measurements at high powers are made because of the progressive heat build up inside the target. A 15 cm length of castor oil attenuates 1 MHz ultrasound by 12 dB at 20°C and only by 5 dB at 40°C: ideally, the

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Fraction escaping (15cm oil/reflector) 0.2

20 deg C 25 deg C 30 deg C 35 deg C 40 deg C

0.18

Fraction escaping

0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

Frequency (MHz)

Fig. 10. Fractional power escaping a 15 cm long target with rear reflector as a function of frequency and temperature.

transmission loss of the target should be at least 20 dB. One possible solution is simply to have a longer target but to achieve 20 dB at 1 MHz would require a length of 60 cm at 40°C, which would be impractical. Another possible solution is to cool the target before use: however, this would be inconvenient and the target would require repeated re-cooling. A further option is to place an acoustic reflector at the rear of the target: this doubles the oil path length and reduces the fraction of the energy, which is reflected back out of the target (Fig. 10); the reflector works well at room temperature but the increased path length is clearly insufficient at higher temperatures and lower frequencies. Use of the F36 absorbing layers, which has an absorption coefficient that increases with temperature by 0.7 dB cm⫺1 MHz⫺1 °C⫺1 (Zeqiri and Bickley, 2000), allows a more compact target

Fraction transmitted (15cm oil/5mm F36) 0.2

20 deg C 25 deg C 30 deg C 35 deg C 40 deg C

0.18

Fraction escaping

0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

Frequency (MHz)

Fig. 11. Fractional power escaping a 15 cm long target with rear F36 absorber as a function of frequency and temperature.

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to be used with an overall transmission coefficient that is almost independent of temperature (Fig. 11). The energy transmitted through the target depends on the absorption coefficient of castor oil, ␣oil, the length of the oil path, L, the absorption coefficient of the backing material, ␣F36 and its thickness, d. For L ⫽ 15 cm and d ⫽ 5 mm, the transmission loss is 23.5 dB at 1 MHz so, for a well collimated beam propagating parallel to the axis of the target, less than 0.5% of the energy is transmitted. Note that for divergent beams or beams with significant divergent components, energy can also be transmitted through the sides of the target. This type of loss is not quantified here, where the prime concern is with measurement of focused fields, although it would be a consideration for plane transducers of small ka value. Heat Loss Heat is lost to the water by conduction through the side walls of the target, the rear surface and the acoustic window at the front of the target. This heat loss leads to a reduction in volume and, consequently, an increase in the weight of the target. Provided it remains nearly constant through a single insonation, heat loss per se does not give rise to any errors because the extrapolation algorithm compensates for any constant rate of drift in the weight. Uncertainty only arises when the rate of loss following an insonation is different to the rate of loss before. So the design of the target should ensure that changes in the rate of heat loss occur on a much longer timescale than the insonation period. To achieve this, loss through the walls and rear surface has been reduced by the use of an inner chamber, which provides a nearly static region of oil at least 5 mm thick around these surfaces. The acoustic window is necessarily very thin, but the effect of absorption within the oil is to produce a flow of warmed oil that moves away from the window, so that the temperature increase of the oil adjacent to the window is reduced. Nevertheless, heat loss through this window is likely to be greater than through the walls. An empirical evaluation of the uncertainty due to heat loss can be ascertained from the electrical heating example in Fig. 7. During the unheated periods (say at 25, 55, and 85 and 115 s) the rate of change of weight is close to zero. By 145 s, the rate of change is 0.4 mg s⫺1. This indicates that it takes at least 2 min for the internal temperature increase due to the first heating cycle to be reflected in a change in the rate of heat loss: much longer than the time typically used for a single insonation (5 to 20 s). The uncertainty from this source can also be estimated: the average rate of change of weight during the heating cycles is approximately ⫺14 mg s⫺1, and the change in heat loss between cycles is equivalent to 0.1 mg s⫺1 for each cycle. It therefore seems reasonable

Buoyancy method measurement ● A. SHAW

to take half of this as the uncertainty in the mean rate of change, which is equivalent to 0.4%. Heat Capacity of Internal Components The combined weight of the internal chamber is approximately 65 g and the F36 absorber is approximately 40 g. Precise values for the heat capacities are not known but inspection of Kaye and Laby (online edition) shows that, for both materials, a reasonable value for heat capacity is 1400 J kg⫺1 K⫺1. The estimated volume expansivity is 2 ⫻ 10⫺4 for the chamber and 4 ⫻ 10⫺4 for the F36. The total heat capacity of 2 litres of castor oil is approximately 4000 J K⫺1; the total heat capacity of the internal chamber and F36 are 90 and 55 J K⫺1, respectively. Consequently, assuming that the inside of the target is raised to a uniform temperature, approximately 96.5% of the input energy is stored in the oil and 3.5% in the other components, reducing the change in volume of the oil proportionately. These other components will expand of course but, since the volume expansivity of both is lower than that of castor oil, there will still be a reduction in the total volume change of approximately 2%. This results in a significant bias in the final power value, as well as an uncertainty. The heat capacity of the Perspex case of the target is ignored in this calculation because the effect of the internal chamber is to keep the heated oil away from the wall. This means that the time for the wall to reach equilibrium with the bulk of the oil is much longer than the typical insonation time. As discussed in the section on heat loss, these slow changes do not contribute significantly to uncertainty. Change of Depth Originally, the target was supported by three brass rods of diameter 2 mm. A change in the water level of 1 mm gives rise to a buoyancy force on these rods equal to 9.4 mg, equivalent to approximately 30 J. This would be a significant uncertainty at low power levels, so the brass rods were replaced with steel wire of diameter 0.5 mm, reducing the effect to approximately 2 J mm⫺1. Occasionally, nylon filament of diameter 0.1 mm was used instead, equivalent to approximately 0.1 J mm⫺1. Spread over typically four insonations in a measurement set, it seems reasonable to allocate an uncertainty of 0.5 J to each insonation due to this effect as a worst case. A second consideration that changing hydrostatic pressure leads to a change in the volume of the oil. Typical compressibility, K, of oil is 1.6 GPa and, for a change in hydrostatic pressure p, the volume change is given by:

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⌬V ⫽

⫺pV . K

(18)

The change in buoyancy due to a change of 1 mm in the water depth (a pressure change of 100 N m⫺2) is therefore less than 0.01 mg (equivalent to 0.03 J) and can be ignored. Surface Tension We have not been able to quantify any effect clearly attributable to surface tension. Although surface tension can be important when low powers are measured if the meniscus changes during the measurement (Rooney 1973), previous experience with radiation force balances at NPL has not indicated a surface tension effect when using targets suspended from single nylon filaments of diameter 0.05 mm even at power levels around 10 mW. This suggests that, as an upper limit, the uncertainty in this configuration is equivalent to less than 0.1 mW or 7 ␮g. The effect for three wires of diameter 0.5 mm might be expected to be 10 times larger for each wire, coming to approximately 0.2 mg in total. Water Temperature At normal room temperature, the density of water changes by approximately 0.03% K⫺1 (see Table 2) so the contribution, assuming an uncertainty in the water temperature of 2°K, is 0.06%. A potentially much larger contribution arises from the change in temperature of the water during insonation, directly due to transducer heating. As an example, consider a transducer with an efficiency of 50%, delivering 100 W of acoustic energy for 10 s. The acoustic energy is 1 kJ and the wasted electrical energy is also 1 kJ. Suppose all of this wasted electrical energy is lost to a water bath of volume 20 litres (with a total heat capacity of 84 kJ K⫺1): the average water temperature will increase by 0.012° K and the density will decrease by 0.003 kg m⫺3. The reduction in buoyancy due to the changing water temperature for a 2 litre target is equivalent to 6 mg. This should be compared with the increase in buoyancy of 340 mg due to the heating of the oil, giving rise to an uncertainty of 1.7%. This is perhaps an overestimate because HIFU transducers are generally more than 50% efficient and because it assumes that water heats uniformly during each insonation period, whereas the water next to the transducer will in reality heat more rapidly than the water around the target. In addition, similar to the discussion on heat loss previously, changes that occur over much longer timescales than a single insonation do not result in a significant uncertainty. Consequently, a contribution of 1% is taken for this source of uncertainty.

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Table 6. Estimated systematic uncertainty budget for exposure to 1 MHz ultrasound at a power level of 50 W for 10 s Source

Bias

Sensitivity Window losses Missed Transmitted Heat loss Internal components Change of depth Surface tension Water temperature Extrapolation Total Total

Uncertainty 1.5% 0.3%

⫺2.6%

0.7% 0.6% 0.4% 2% 0.1%* 0.1%* 1% 0.6%* 2.9%

⫺2.6%

3.4%

⫺0.6% ⫺2%

Comment

Includes reflection and absorption losses ka⫽ 125 so bunfoc ⬇ a

0.5 J uncertainty 0.2 mg uncertainty 1 mg uncertainty Expressed as a rectangular semirange. Expressed as 95% confidence level Gaussian equivalent

Individual uncertainty contributions are evaluated as the semi-range of a rectangular distribution. * Percent uncertainty is inversely proportional to delivered energy.

Extrapolation Algorithm The uncertainty due to the extrapolation algorithm is determined statistically by carrying out a sequence of nominally identical measurements and calculating the standard error of the mean with an appropriate coverage factor. However, an additional systematic component equal to the resolution of the balance, 1 mg in this case, is assumed. Overall Uncertainty The uncertainty is dependent on frequency, power level, transducer geometry and target design. As an example, Table 6 shows the estimated uncertainty for a 1 MHz focused bowl transducer of diameter 60 mm and radius of curvature 120 mm; the target is 12 cm in diameter and 15 cm long with 5 mm of F36 absorber close to the rear surface; the distance between the target and the transducer face is 30 mm. The output power is

Volume 34, Number 8, 2008

50 W and each insonation lasts 10 s, giving an energy output of 500 J per insonation and an anticipated buoyancy change of 170 mg. Some sources of uncertainty are also expected to introduce a bias in the final result. VALIDATION Direct Comparison With Radiation Force. With the new target, the buoyancy method has been compared directly with the radiation force technique for unfocused transducers between 1 and 15 W. The transducers were physiotherapy transducers of nominal diameter 25 mm and frequencies of 1 and 3 MHz made by Enraf (Enraf, Aartselaar, Belgium). A sensitivity of 0.341 mg J⫺1 was assumed (see entry for Fisher Scientific in Table 3) when determining the ultrasound power by the buoyancy method. The transducers were positioned vertically above the target and firing downwards; they were placed approximately 5 mm from the target and the target was tilted by approximately 5° to avoid coherent reflection from the membrane. Results are given in Table 7: the uncertainty in each method is 4% and on average results by the buoyancy method were 2.1% less than by the radiation force method at 1 MHz and 1.6% less at 3 MHz. These differences are smaller than the estimated uncertainties in either method; they are also comparable to the predicted bias (Table 6) of ⫺2.6% at 1 MHz due to the heat capacity of the other internal components and the fraction of transmitted energy. Angle Independence To test the angle-independence of the buoyancy method, it was used at 1 MHz only with the transducer directed horizontally at the entry membrane of the target (which was oriented with axis of the target horizontal). Nominal powers of 3, 5 and 10 W were generated using the same drive settings used in the vertical configuration. These results (Table 8) were virtually identical to the vertical configuration confirming that the method is can be used at any orientation. However, one disadvantage of

Table 7. Calibration of the buoyancy method at 1 and 3 MHz in the vertical configuration 1 MHz Power by radiation force (W) 3.40 ⫾ 4% 5.05 ⫾ 4% 8.36 ⫾ 4% 10.07 ⫾ 4% 15.03 ⫾ 4% Average ratio

3 MHz

Power by buoyancy (W)

Ratio

Power by radiation force (W)

Power by buoyancy (W)

Ratio

3.31 ⫾ 4% 4.91 ⫾ 4% 8.17 ⫾ 4% 9.89 ⫾ 4% 14.84 ⫾ 4%

0.975 0.972 0.978 0.982 0.987

1.01 ⫾ 4% 3.04 ⫾ 4% 5.06 ⫾ 4% 10.03 ⫾ 4% 14.98 ⫾ 4%

0.98 ⫾ 8% 3.06 ⫾ 4% 4.99 ⫾ 4% 9.87 ⫾ 4% 14.64 ⫾ 4%

0.965 1.006 0.986 0.984 0.977

0.979

Average ratio

0.984

Buoyancy method measurement ● A. SHAW

Table 8. Calibration of the buoyancy method at 1 MHz in the horizontal configuration 1 MHz - horizontal Power by radiation force (W) 3.40 ⫾ 4% 5.05 ⫾ 4% 10.07 ⫾ 4% Average ratio

Power by buoyancy (W)

Ratio

3.34 ⫾ 4% 4.95 ⫾ 4% 9.88 ⫾ 4%

0.983 0.979 0.981 0.981

the horizontal configuration is that the target is free to swing following the impulse of the radiation force. The resulting oscillations take some time to settle down and an off-period of between 30 and 60 s was required. Linearity The linearity of the buoyancy method was reported in Shaw (2006). It was tested by measuring both the radiation force and the buoyancy change resulting from exposure to 1.08 MHz ultrasound generated by a HIFU transducer at power levels between 4 and 140 W for durations of 10 s (Fig. 12). The diameter of the transducer used was 65 mm and the focal distance was 118 mm, giving an F-number of 1.8. From Fig. 2, the radiation force method should underestimate the true power by a 2% to 3%, however, no correction for this was made for this focusing effect as the purpose of the study was simply to determine linearity and not sensitivity. The slope of the best fit line through these data points was 3.56 mg W⫺1, corresponding to 0.356 mg J⫺1, and the standard deviation of the measurement points from this best fit line was 2.1%. There is no obvious pattern to the deviations form the best fit line, indicating that the method is linear to at least 140 W.

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Use on a Clinical System A number of evaluations were carried out using the Chongqing HAIFU system at the HIFU unit in the Churchill Hospital, Oxford. This is an extracorporeal system in which the transducer is mounted in a waterfilled bellows below the patient bed and the transducers are interchangeable. The aims were to test whether the target would survive exposure to high, clinical levels of ultrasound and to investigate the buoyancy method further. The force balance was mounted on a framework placed on the patient bed and a water tank with a 12 ␮m mylar base was used to isolate the system from the bellows to prevent contamination of the water supply to the HIFU unit in the event of a target rupture. It is relevant to consider how the measurement of both radiation force and buoyancy change are affected by the relative positions of the transducer, tank base and target: ● ●

●

All ultrasound energy converted to streaming momentum between transducer and base of tank is blocked. For the radiation force method most of the energy converted to streaming momentum between the base of the tank and the target is detected as incident power. For the buoyancy method, none of the energy converted to streaming momentum between the base of the tank and the target is detected as power.

Figures 13 and 14 show results for output power up to 230 W for two different transducers at a frequency of 0.8 MHz. No focusing correction has been applied to the radiation force results: the radiation force has been converted to a power by multiplying by the speed of sound. Focusing corrections can be calculated and are 1.16 and 1.06 for the respective cases. The mean ratios in the two cases are approximately 1.12 and 1.06, which are similar to the calculated focusing corrections. There also seems

0.8 MHz, F=0.75 1.2 1.15 1.1

Ratio

1.05 1 0.95 0.9 0.85 0.8

Fig. 12. Linearity of buoyancy method. Buoyancy change is plotted as a function of transducer output power for exposures of 10 s duration. Output power is simply calculated as the radiation force multiplied by the speed of sound in water, ignoring errors due to focusing, which will be approximately constant at all output levels.

0

50

100

150

200

250

Pow er (W )

Fig. 13. Ratio of power measured by buoyancy method to power measured by radiation force for transducer of F-number ⫽ 0.75. Error bars are twice the standard error on the ratio of the means.

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Fig. 14. Ratio of power measured by buoyancy method to power measured by radiation force for transducer of F-number ⫽ 1.125. Error bars are twice the standard error on the ratio of the means.

to be a trend of increasing ratio with increasing power: however, we cannot say with confidence whether this is real or what the cause of this trend is. It may be related to streaming and nonlinear loss in the water path but will require further investigation. The relatively large variation on some of the datapoints in Fig. 14 are probably due to small bubbles dislodging from the target. In other tests, powers up to 350 W were measured to check for cavitation in the oil. Under extreme conditions, bubbles could be generated but they were only observed at 0.8 MHz at power levels above 300 W with the focus placed just inside the target and with initial oil temperatures above 35°C. Streams of bubbles were generated under these conditions but were reabsorbed if the target was allowed to cool. No long-term change to the target performance was observed. In any event, these conditions should not arise in practice as it is intended that the focus should be placed substantially inside the oil volume. Damage to the acoustic window should be anticipated following prolonged exposure close to the focus although, when tested at 350 W, the membrane survived even with the focus was placed directly on it. DISCUSSION This article has presented in detail an alternative method for the measurement of ultrasound power. The method is based on measuring the buoyancy change caused by thermal expansion of a target filled with castor oil. It is a calorimetric method that is independent of the widely used radiation force technique. However, in the specific implementation described here, measurements using both of these independent principles can be made simultaneously allowing direct comparison. The most important advantage of this new method over the radiation force technique is that it responds

Volume 34, Number 8, 2008

directly to ultrasound power and not to the wave momentum: it is, therefore, independent of the direction of propagation of the ultrasound. The radiation force technique is only strictly accurate in the plane wave approximation and, as has been shown, deviations from this behaviour result in measurement errors. For the case of strongly focused transducers such as those often used for HIFU, the errors can be very significant. A further advantage is that it is insensitive to streaming currents caused by absorption of the ultrasound in the water path: at higher frequencies, streaming becomes the dominant source of uncertainty for the radiation force technique. Indeed, the ability to measure radiation force and buoyancy change simultaneously offers a method for studying directly the forces on a radiation force target due to streaming. These two advantages are so significant that it is logical to suggest that the buoyancy method may be a better primary standard than the existing radiation force balances at National Measurement Institutes (NMIs) around the world. Interestingly, such a primary standard could be traceable to standards for mass and temperature (if the sensitivity is determined from the thermal characteristics of castor oil) or to electrical standards (if the sensitivity is determined by electrical calibration). Of these two options, the second seems preferable because it offers smaller uncertainties and it allows for regular monitoring and recalibration of the target. Although superceded by a modulated radiation force technique (Greenspan et al. 1978), calorimetry traceable to electrical standards has been used at the U.S. National Bureau of Standards in the past as a reference ultrasound power measurement technique (Zapf et al. 1976). In their implementation, a fluid was pumped through two identical cells, one which was exposed to ultrasound and one heated electrically. A feedback system adjusted the heater current so that the temperature increase at the outlet of each of the two cells was identical: an overall uncertainty in the region of 4% was obtained. However, the system in question was complex, requiring that the two cells and the flow rate through them were closely matched, and several minutes insonation was required to establish equilibrium conditions. For HIFU equipment, extended insonation is often not possible as it may result in thermal damage to the transducer; in addition the wide range of transducer shape and size means that a single geometry of insonation cell is not always optimal. The proposed buoyancy method offers the benefits of simplicity with regard to ancillary equipment, almost instantaneous response and the ability to optimise target design easily without affecting the sensitivity (or calibration) of the measurement. Nevertheless, the freedom from sensitivity to vibration and environmental noise is an attractive aspect of

Buoyancy method measurement ● A. SHAW

more conventional calorimetry, which the buoyancy method does not share. This article has been mostly concerned with measurement of HIFU transducers; the uncertainties associated with the buoyancy method have been analysed and are estimated to be 3.4% for an example HIFU configuration at 1 MHz: this is comparable to the uncertainties quoted by leading NMIs for well collimated, unfocused fields. It is instructive to examine the major sources of uncertainty for the buoyancy technique and consider whether they can be reduced further. The single largest contribution comes from the thermal capacity of the other internal components of the target. This can be reduced by using a larger volume of oil and reducing the mass of the other components. Increasing the diameter and length of the target to 20 cm nearly quadruples the internal volume; halving the mass of the internal components is easily achieved by using thinner material for the inner chamber: reducing this contribution from 2% to less than 0.3%. The same increase in dimensions will reduce the transmitted energy by 4 dB at 1 MHz from 0.6% to 0.25% and the missed energy from 0.7% to 0.4%. Heat loss should be reduced also but is already small. Increasing the target volume will make the method more sensitive to changes in water temperature, so the water volume should be doubled also to compensate. However, if necessary, the transducer could be partly isolated from the rest of the water tank by fitting a shroud around the outside of the transducer case. The effect can also be reduced by orienting the measurement set up so that the transducer is above the target (as in Fig. 6) or by using a horizontal arrangement. It seems reasonable to assume that this contribution could be reduced from 1% to 0.5%, albeit at the expense of some inconvenience. The uncertainty due to the balance resolution can be reduced from 0.6% to 0.06% by using 0.1 mg balance. Overall, these changes would reduce the uncertainty from 3.4% to 2.6%. This means that even strongly focused transducers could be measured as accurately as simple well-collimated transducers can be measured at present. Further improvement in uncertainty is dependent on reducing the uncertainty in determining the sensitivity value. In principle, this should be possible and will be the subject of future study. An important criticism of the method relates to the use of castor oil. Since castor oil is a natural material, it is perhaps subject to more variation in its properties than man-made materials and its properties might change over time due, for instance, to oxidation, water uptake or exposure to light: indeed, Table 3 has shown evidence of small but significant differences due to supplier and age. There are two answers to this criticism. First, the principle of the method does not require that castor oil is used and it may be that there is a more suitable fluid available;

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we have not looked for one but the main limiting factor is likely to be identifying one with a sufficiently low impedance mismatch to water. Second, and more immediately applicable, is that targets can be made with a built-in calibration facility consisting of an electrical heating element similar to that described in the section on construction and characteristics. In this way, it is straightforward to determine the sensitivity using readily available calibrated electrical measurement equipment and to monitor changes over time. As has been shown, this is the most accurate method of determining the sensitivity. The fact that the sensitivity of the buoyancy method is not dependent on the direction of incidence of the ultrasound allows power to be measured accurately from almost any transducer geometry provided that the target is designed to an appropriate size and shape. For instance, an intravascular device that generates a radially symmetric cylindrical ultrasound field can be measured with a cylindrical target that has a lumen along its axis and where the acoustic window is the wall of the lumen. CONCLUSIONS This article has described in detail a new method for the measurement of ultrasound power based on measuring the buoyancy change caused by thermal expansion of a target filled with castor oil. It is a calorimetric method that is not related to the widely used radiation force technique. A target and measuring system has been built for the calibration of focused transducers in the frequency range above 0.8 MHz and at powers between 1 W and at least 300 W. Sources of uncertainties have been analysed and typical overall uncertainties at 1 MHz are estimated to be 3.4%. The technique has been compared with the radiation force method using reference unfocused transducers up to 15 W and, using focused transducers, up to 300 W. Unlike radiation force, which is related to wave momentum and is therefore directional, the new buoyancy method responds directly to absorbed energy and is direction-independent. This makes it a more accurate measure of incident ultrasound power in fields that deviate from ideal plane-wave behaviour. It also allows the method to be used in a horizontal configuration, which is often more convenient than the vertical arrangement normally required for gravimetric radiation force balances. With relatively minor modifications to the target and balance system, the new method could achieve uncertainties below 3% at 1 MHz. This is the same as is achievable by National Measurement Institutes using the radiation force method and there is the potential to reduce these uncertainties further. It is, therefore, sug-

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gested that the buoyancy method should be developed as a primary standard technique to supplement or replace existing primary standard radiation force balances. Acknowledgments—The author gratefully acknowledges the financial support of the National Measurement System Programmes Unit of the UK Department for Innovation, Universities and Skills. The author is particularly indebted to colleagues at NPL; to Prof. Gail ter Haar and the therapeutic ultrasound team at the Royal Marsden Hospital, Sutton; and to Dr. Tom Leslie, Prof. Feng Wu and the rest of the team at the HIFU Unit at the Churchill Hospital, Oxford.

REFERENCES Beissner K. Minimum target size in radiation force measurements. J Acoust Soc Am 1984;76:1505–1510. Beissner K. Radiation force calculations. Acustica 1987;62:255–263. Beissner K, Oosterbahn WA, Hekkenberg RT, Shaw A. European intercomparison of ultrasonic power measurement. Acustica 1996; 82:450 – 458. Beissner K. Primary measurement of ultrasonic power and dissemination of ultrasonic power reference values by means of standard transducers. Metrologia 1999;36:313–320. Beissner K. Summary of a European comparison of ultrasonic power measurements. Metrologia 1999;36:327–330. Beissner K. Report on the CIPM key comparison CCAUV.U-K1 (ultrasonic power). CIPM, Paris, 2002. (available for download from http://www.bipm.org/utils/common/pdf/final_reports/AUV/U-K1/ CCAUV.U-K1.pdf) Accessed September 2007. Banjavic RA, Carson PL. Report of task II - Radiation force balance system - construction and use. National Electrical Manufacturers Association report 1980. Davidson, F. Ultrasonic power balances. In: Preston RC, ed. Output measurements for medical ultrasound. London: Springer Verlag, 1991:75– 89. Delchar TA, Melvin RJ. A calorimeter for ultrasound total power measurements. Meas Sci Technol 1994;5:1533–1537. Greenspan M, Breckenridge FR, Tschiegg CE. Ultrasonic transducer power output by modulated radiation pressure. J Acoust Soc Am 1978;63:1031–1038. Hekkenberg RT, Beissner K, Zeqiri B. Therapy-level ultrasonic power measurement. Final Technical report SMT4-CT96-2139, European Commission, BCR Information, Report EUR18828 2000. Hekkenberg RT, Beissner K, Zeqiri B, Bezemer RA, Hodnett M. Validated ultrasonic power measurements up to 20 W. Ultrasound Med Biol 2001;27:427– 438. Hekkenberg R, Richards A, Beissner K, Zeqiri B, Bezemer R, Hodnett M, Prout G, Cantrall C. Transfer standard device to improve the traceable calibration of physiotherapy ultrasound machines. Ultrasound Med Biol 2006;32:1423–1429.

Volume 34, Number 8, 2008 Herman BA, Stewart HF. An ultrasonic radiation calorimeter. J Acoust Soc Am 1973;53:341. IEC61161:2006 Ed. 2. Ultrasonics - Power measurement - Radiation force balances and performance requirements. International Electrotechnical Commission, Geneva 2006. Kaye GWC, Laby TH. Table of physical and chemical constants. Online edition at www.kayelaby.npl.co.uk. Accessed September 2007. Livett A J. The determination of acoustic output power by means of the radiation pressure balance. PhD thesis, University of London 1984. Lloyd EA. Energy measurement. In: Brown B, Gordon D, eds Ultrasonic techniques in biology and medicine. London: Iliffe, 1967:59. Maruvada S, Harris GR, Herman BA, King RL. Acoustic power calibration of high-intensity focused ultrasound transducers using a radiation force technique. J Acoust Soc Am 2007;121:1434 –1439. Mikhailov IG. Methods of measuring the absolute intensity of ultrasonic waves in liquids and solids. Ultrasonics 1964;2:129 –133. Rooney JA. Determination of acoustic power outputs in the microwattmilliwatt range. Ultrasound Med Biol 1973;1:13–16. Shaw A. How to measure HIFU output power properly. In: Clement GT, McDannold NJ, Hynynen K, eds. Therapeutic ultrasound. Proceedings of the 5th International Symposium on Therapeutic Ultrasound (AIP Conference Proceedings). Vol. 829. Melville, NY: American Institute of Physics. 2006;628 – 632. Shou W, Wang Y, Qian D. Calculation for radiation force of focused ultrasound and experiment measuring HIFU power.[in Chinese] Technical Acoustics 1998;17:145. Stewart HF. Ultrasonic measurement techniques. In: Repacholi MH, Benwell DA, eds. Essentials of medical ultrasound. Totowa, NJ: Humana Press, 1982:77–116. Sutton YC, Shaw A, Zeqiri B. Measurement of ultrasonic power using an acoustically absorbing well. Ultrasound Med Biol 2003;29: 1507–1513. Torr GR, Watmough DJ. A constant-flow calorimeter for the measurement of acoustic power at megahertz frequencies. Phys Med Biol 1977;22:444 – 450. Tschiegg CE, Greenspan M, Eitzen DG. Ultrasonic continuous-wave beam-power measurements: International intercomparison. J Res Nat Bureau Stand 1983;88:91–103. Van Den Ende H. A radiation power calorimeter and a radiation force meter for small ultrasonic beams. Med Biol Eng Comput 1969;7: 411– 417. Wells PNT, Bullen MA, Follet DH, Freundlich HF, Angell James J. The dosimetry of small ultrasonic beams. Ultrasonics 1963;1:106 – 110. Zeqiri B, Bickley CJ. A new anechoic material for medical ultrasonic applications. Ultrasound Med Biol 2000;26:481– 485. Zapf TL, Harvey ME, Larsen NT, Stoltenberg RE. Ultrasonic calorimeter for beam power measurements. Natl. Bur. Stand. (U.S.) Tech. Note 686 1976;3.