Ultrasound in Med. & Biol., Vol. 40, No. 4, pp. 775–787, 2014 Copyright Ó 2014 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/$ - see front matter
http://dx.doi.org/10.1016/j.ultrasmedbio.2013.10.017
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Original Contribution MEASURING ABSOLUTE BLOOD PRESSURE USING MICROBUBBLES CHARLES TREMBLAY-DARVEAU,* ROSS WILLIAMS,y and PETER N. BURNSy * Department of Medical Biophysics, University of Toronto at Sunnybrook Health Sciences Centre, Toronto, Ontario, Canada; and y Sunnybrook Health Sciences Centre, Toronto, Ontario, Canada (Received 15 July 2013; revised 15 October 2013; in final form 21 October 2013)
Abstract—Gas microbubbles are highly compressible, which makes them very efficient sound scatterers. As another consequence of their high compressibility, the radii of the microbubbles are affected by the pressure of the fluid around them, which changes their resonance frequency. Although the pressures present within the human body cause only minor variations in the radii of uncoated microbubbles (0.2% per 10 mmHg) and, therefore, very small variations in the resonance frequency (1 kHz per 10 mmHg), it was found in the work described here, through both simulations and in vitro measurements, that large changes in resonance frequency can occur in phospholipid-coated microbubbles for small blood pressure variations because of the exotic buckling dynamics of phospholipid monolayers (up to 240 kHz per 10 mmHg). This method should allow non-invasive measurement of the gauge blood pressure in deep blood vessels as long as the microbubble physical properties are well controlled. (E-mail: [email protected]) Ó 2014 World Federation for Ultrasound in Medicine & Biology. Key Words: Microbubble imaging, Blood pressure, Acoustic spectroscopy.
by Fairbank and Scully (1977), who noted that the scattering properties of unshelled microbubbles are also affected by static fluid pressure and, therefore, could provide a direct way to measure local blood pressure deep within the body using ultrasound. Fairbank and Scully (1977) reported that increasing the static pressure effectively compresses the microbubble, which shifts the resonance frequency of microbubbles upward. Notably, a small shift in the resonance frequency of unshelled microbubbles was observed for 30- to 40-mm diameter microbubbles and hydrostatic pressure changes of about 0.2 atm. Ishihara et al. (1988) validated this later in a similar experiment. Non-invasive measurement of the gauge pressure within the body would have many clinical applications. It would be especially groundbreaking in the case of early diagnosis of portal vein hypertension. Portal vein hypertension is a common complication of liver cirrhosis, in which the vascular resistance of the portal-hepatic bed is drastically increased because of fibrosis. This causes an increase in pressure within the portal vein from 5– 10 mmHg in healthy individuals to .12 mmHg. The pressure in the portal vein cannot be measured with usual sphygmomanometry techniques. Although it is possible in theory to catheterize through the jugular vein and inferior vena cava and then puncture through the liver to
INTRODUCTION Intravascular contrast agents are well established as a means of improving conventional medical imaging techniques. For example, paramagnetic particles (e.g., iron oxide, gadolinium) can be used in magnetic resonance imaging because of their high magnetic susceptibility. In ultrasound, micron-size gas spheres of high compressibility coated by a thin shell, commonly referred to as microbubbles, are used. Microbubbles (1–10 mm in diameter) are similar in size to red blood cells (6–8 mm) and, therefore, do not diffuse through the walls of blood vessels, making them true intravascular agents. When microbubbles are injected, blood echoes become brighter on a B-mode image as a result of the coupling of the radial motion of the microbubble wall with the surrounding liquid, considerably increasing the backscattered signal. Microbubbles behave as non-linear scatterers, even when driven at low acoustic pressures, and emit signals at integer (harmonic) and fractional (sub-harmonic, ultra-harmonic) multiples of the insonation frequency. Another consequence of their high compressibility has been suggested
Address correspondence to: Charles Tremblay-Darveau, Sunnybrook Health Sciences Centre, 2075 Bayview Avenue, Toronto, ON M4N 3M5, Canada. E-mail: [email protected] 775
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access the portal circulation to measure local blood pressure with a manometer, such a procedure is extremely invasive and places the patient at high risk. A noninvasive way to measure blood pressure (i.e., gauge pressure) with a pressure resolution of 10 mmHg within non-limb vessels would have important value in the diagnosis of portal vein hypertension. Unfortunately, the resonance frequency shift of unshelled microbubbles for 10 mmHg is on the order of 1 kHz, which is too small for clinical application to portal vein hypertension diagnosis, even considering the resolution improvement achieved with a dual-frequency system (Leighton et al. 1997; Newhouse and Shankar 1984; Shankar et al. 1986). Recent literature suggests that some microbubble coatings can strongly affect the response to blood pressure. Shi et al. (1999), Forsberg et al. (2005), Andersen and Jensen (2010a, 2010b) and Li et al. (2012) recently observed that sub-harmonic emissions (i.e., the echo scattered at half of the insonification frequency) of phospholipid microbubbles are dependent on blood pressure. In particular, Frinking et al. (2009, 2010) found experimentally that phospholipid microbubbles increase their sub-harmonic power considerably when the ambient over-pressure forces the bubble to enter a surface tensionfree state (e.g., buckling). On the basis of these results, it has been suggested that the amplitude of the subharmonic mode might be a useful indicator of the local relative blood pressure. Yet the gauge pressure, and not the relative pressure, is needed to diagnose portal vein hypertension. It has been reported by Marmottant et al. (2005) that buckling dynamics also strongly affect the compressibility of phospholipid microbubbles, making the resonance frequencies of these bubbles more sensitive than those of microbubbles with simple shell models, such as a viscoelastic shell. In this study, we found that the resolution of the Fairbank and Scully (1977) method for measuring gauge blood pressure, in the light of an understanding of the effects of buckling phospholipid shells, can considerably be improved such that the required 10 mmHg resolution for portal vein hypertension diagnosis can be reached. Two different models were compared to illustrate the effect of shell elasticity on bubble sensitivity to ambient pressure: a viscoelastic surface tension model (de Jong et al. 1994) and a buckling surface tension model (Marmottant et al. 2005), which apply to a protein shell and a phospholipid shell, respectively. A summary of uncoated and shelled microbubbles, the linearized properties of microbubbles and the full numerical solutions of the Marmottant equation for the parameters of interest is presented. These simulations predict a significant improvement in the sensitivity of phospholipid microbubbles to blood pressure, which is investigated in vitro for Optison (a commercial protein-shelled microbubble)
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and for generic phospholipid microbubbles. We also found that inhomogeneity of physical properties (size, elasticity, surface tension at rest) can affect the reproducibility of blood pressure measurements by introducing a systematic bias in estimation of the resonance frequency. The extent of homogeneity in the microbubble radius distribution required to minimize statistical variability was investigated through simulations. Relevant technologies for the production of microbubbles that satisfy these requirements are discussed. THEORY Rayleigh-Plesset equation and shell models The phenomenon of stable cavitation of a vaporfilled bubble was initially explained by Rayleigh (1917) and Plesset (1949), as the result of the application of Newton’s third law to a spherical interface. This initial form of the Rayleigh-Plesset equation neglected the effects of viscosity and the compressibility of the surrounding medium, which were later introduced by Keller and Miksis (1980). Whereas the Rayleigh-Plesset equation explains the response of free gas bubbles (Plesset 1949; Rayleigh 1917), many models compete to describe the behavior of shelled microbubbles. Notably, the models of de Jong et al. (1994), Church (1995), Hoff et al. (2000), Khismatullin and Nadim (2002), Chatterjee and Sarkar (2003), Allen and Rashid (2004), Sarkar et al. (2005), Marmottant et al. (2005), Doinikov and Dayton (2007), Stride (2008) and Tsiglifis and Pelekasis (2008) use different assumptions and different levels of complexity to represent the effect of the shell on microbubble oscillations. De Jong et al. (1994) proposed the addition of two ad hoc terms to the Rayleigh-Plesset equation to compensate for shell friction, ks, and elasticity, c0, such that the equation becomes :: : 2 : Ro 3k oÞ rl RR 132R 5 po 12sðR 123kc R R R oÞ (1) 22sðR 12co R1o 2R1 R :
:
24mRl R24kRs2R2Po 2PðtÞ where R(t) is the instantaneous microbubble radius, R0 is the equilibrium radius, k is the polytropic constant, rl is the liquid density, ml is the liquid viscosity, P0 is the static fluid pressure, s(R) is the bubble-liquid interface surface tension and P(t) is any other applied pressure field (e.g., ultrasound). This model describes many fundamental properties of shelled microbubbles, such as an increase in resonance frequency and damping, and it is accurate for simpler shells such as protein. However, because the shell properties used are analogues of Hooke’s law and Newton’s viscous law (Doinikov and Bouakaz 2011), it
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cannot explain more complex phenomena such as compression-only and expansion-only behavior. Doinikov and Bouakaz (2011) stated that non-linear shell properties must be used to predict more accurately non-linear microbubble behaviors such as compressiononly oscillations. In particular, phospholipid shells increase the lifetime of microbubbles by reducing the surface tension between the gas core and the liquid, which limits gas diffusion. In Marmottant’s model (Marmottant et al. 2005), the previously ad hoc elasticity term is now included in a bubble radius-dependent surface tension interaction and, therefore, radius-dependent shell elasticity: 1 dsðRÞ ceff ðRÞ 5 R0 2 dR R0 The surface tension of a phospholipid interface is strongly dependent on the effective area of the molecule (Petriat et al. 2004); it buckles if the molecular density reaches a threshold value (corresponding to a high compression state), whereas it ruptures if stretched past a fixed threshold. Under this assumption, the surface tension of a microbubble coated with a phospholipid monolayer is 8 0 if R,Rbuck > > < 2 if Rbuck ,R,Rr (2) sðRÞ 5 co RRbuck 21 > > : sw if R.Rr where Rbuck and Rr are the buckling and rupture radii of the phospholipid microbubble, respectively. The radial equation of motion is :: : 2 R 3k 3k : o rl RR 132R 5 po 12s 12 c R R R :
:
24mRl R24kRs2R 22sðRÞ R
(3)
2Po 2PðtÞ For very small oscillations, it has been found (Marmottant et al. 2005) that eqn (3) reduces to the de Jong model. Modeling quasi-static compression of microbubbles The quasi-static compression of a bubble caused by blood pressure can be modeled using purely thermodynamic concepts, namely, the polytropic gas law and pressure equilibrium. Equating the pressure forces inside of the bubble at different compression states yields 23k 01 Þ 2Pv Po1 12sðR R01 Pg;e; ðPo1 Þ R01 5 5 (4) 2sðR Þ Pg;e ðPo2 Þ R02 Po2 1 02 2Pv R02
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Fig. 1. Compression of a 3-mm-radius microbubble by static pressure. The equilibrium radius at increasing ambient pressure was solved using eqn (4) for both a viscoelastic shell (solid line) and a free gas microbubble (dashed line).
where indices 1 and 2 refer to different states of compression of the microbubble, and Pv is the partial pressure of the gas. This equation does not have an analytic solution, but can be easily solved numerically (a solution is provided in Fig. 1). The microbubble shell coating usually reduces the effect of static pressure compressions by making the bubble stiffer, but as seen in Figure 1, this causes only small deviations in radius from the unshelled microbubble model (assuming the values from der Meer et al. [2007] for shell elasticity, c). Linear model of effect of blood pressure on microbubble resonance Although simulations must be used to understand the exact non-linear effect of blood pressure on the Rayleigh-Plesset equation, linearization can be used to understand the effect of blood pressure variation on the first-order behavior of microbubbles. In such a scheme, an ansatz solution to the Rayleigh-Plesset equation is assumed to be R(t) 5 R0(1 1 x(t) 1 O(x(t)2)), where x(t) 5 1 (dimensionless) and x(t)2 or higher-order terms are then considered negligible. It is well known (der Meer et al. 2007) that a driven damped harmonic oscillator solution is recovered: ::
:
x þ uo dx þ u2o x 5 PðtÞ rR2 o
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðu2o 2u2 Þ þðduuo Þ2 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 4ceff ðRo Þ 2ð3k21Þsw 1 uo 5 rR2 3kPo þ Ro þ Ro XðuÞ 5 rR1 2 o
PðuÞ
o
d 5 uocRo þ R24mrul o þ R34krus o o
o
(5)
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Here, X(u) is the Fourier transform of x(t), u0 is the natural resonance frequency and d is the total damping in the system. The static pressure has both explicit (in P0) and implicit (caused by compression of the equilibrium radius R0) contributions to the resonance frequency. Most of the shell’s effect on resonance frequency arises directly through the elasticity parameter. For a microbubble following the de Jong model, the coating merely increases the net elasticity, ceff, therefore adding a constant shift to the resonance frequency, whereas the shell viscosity increases the overall damping of the system. As in unshelled bubbles, gas dynamics will be responsible for the dependence of resonance frequency on the static pressure-dependent behavior of microbubbles with a viscoelastic shell. Because a 10 mmHg variation in blood pressure typically compresses a microbubble by about 0.2% of the bubble’s rest radius, the resonance frequency of a microbubble of constant shell elasticity is only weakly affected by blood pressure (6 kHz per 10 mmHg). In contrast, the elasticity of the phospholipid coating depends on the bubble radius. According to the Marmottant model, the elasticity, ceff 5 A(ds/dA), of a lipid-coated bubble is a strong function of bubble radius. An increase in static pressure compresses the bubble, decreasing its equilibrium radius. As long as the bubble’s equilibrium radius stays far from the buckling radius, it will behave similarly to a viscoelastic bubble (changes in ceff will be small), and therefore, the resonance frequency will increase slowly because of gas dynamics. When P0 is high enough, the bubble will undergo buckling, reducing the effective elasticity of its shell to zero and considerably reducing the resonance frequency. Within this transition region, the bubble offers a much more sensitive manometer than protein-shelled microbubbles. Assuming the bubble elastic properties illustrated in Figure 2a and a 3.0-mm radius at rest, the 0–120 mmHg region is the viscoelastic regime, the 120–173 mmHg region is the buckling transition and
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the 173–350 mmHg region is the buckled-state regime (Fig. 2b). The microbubble resonance frequency undergoes a steep change in the transitional region, varying between 1.9 and 1.22 MHz over a pressure change of only 25 mmHg, and the buckling bubble is roughly 40–120 times more sensitive to hydrostatic pressure (250 kHz per 10 mmHg) than the viscoelastic microbubble within these limits. The value of the critical hydrostatic pressure forcing the bubble into a buckled state depends on the surface tension at no over-pressure (i.e., a bubble whose radius at rest is closer to the buckling radius will buckle at lower over-pressure). Therefore, if the surface tension parameter could be controlled in microbubble populations, this could provide a method to tune the bubble to a desired pressure range. It is true that blood pressure changes microbubble size; a 10 mmHg variation in blood pressure will compress microbubbles by about 6–20 nm (assuming a 3-mm rest radius). For this reason, simpler microbubbles, such as unshelled and protein-shelled bubbles, respond only very weakly to blood pressure (6 kHz per 10 mmHg). However, microbubbles with a phospholipid shell respond strongly to blood pressure changes because of the non-linearity of their shell properties (250 kHz per 10 mmHg). METHODS Linearization predicts that viscoelastic shell bubbles respond very weakly to blood pressure, whereas phospholipid-coated microbubbles considerably lower their resonance frequency with increasing blood pressure because of buckling. It is unclear if this effect, as predicted by theory, occurs under more realistic experimental conditions when considering the non-linear scattering properties of microbubbles (for instance, by using acoustic pressure amplitudes higher than the perturbation model).
Fig. 2. Elasticity (a) and resonance frequency (b) versus hydrostatic pressure for a viscoelastic shell (dashed line) and a buckling phospholipid shell bubble (solid line). Drastic changes in elasticity occur when static pressure forces the microbubble to enter a transitional state. This causes a steep drop in the resonance frequency estimated using the linear model (eqn [5]).
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Simulation of effect of blood pressure on bubble resonance The Rayleigh-Plesset equation is solved for the radial response, R(t), to an acoustic pressure pulse, Pac(t), using MATLAB (The MathWorks, Natick, MA, USA) for both viscoelastic (eqn [1] with microbubble parameters from der Meer et al. [2007]) and phospholipid (eqn [3]) microbubbles. The pulse sequence used is a series of 50 narrowband pulses of 17 cycles spanning the frequency range 1.0 to 5.9 MHz. The acoustic pressure, or driving pressure, Pac(t), is left as a variable ranging from 1 to 350 kPa to study the non-linear hydrostatic pressure-dependent behavior of microbubbles. To avoid the discontinuity in ceff(R) occurring in the Marmottant model (Marmottant et al. 2005) at the buckling radius, a quadratic transition zone of constant second derivative with respect to radius was used at the transition, an approach initially proposed by Sijl (2009). The scattered pressure, Pscatt, is calculated using conservation of mass/ momentum assumptions (refer to Leighton 1994): :: : r r 2 2 Pscatt r; t2 5 RðtÞ R ðtÞ12RðtÞRðtÞ (6) c r To extract the amplitude of each harmonic, Pscatt is Fourier transformed, producing a spectrum of sharp peaks at harmonic and sub-harmonic frequencies (as a result of narrowband excitation). The amplitude of each peak is extracted using bandpass filters.
In vitro measurement of effect of blood pressure on microbubble resonance The resonant pressure response of microbubbles was determined experimentally using a spectroscopic approach. The experiment was performed using a spherically focused single-element transducer centered at 3.5 MHz, with a 1.91-cm diameter, a 2.54-cm focal length and an 85% fractional bandwidth (Panametrics-NDTC381, Olympus, Quebec, QC, Canada). The microbubbles were imaged through a thin, acoustically transparent Mylar window. The pressure chamber (3.7 cm wide, 3.7 cm high and 1.3 cm long) was connected to a manometer and an adjustable pressure reservoir. The dimensions of the pressure chamber are large enough such that boundary condition effects should be negligible (Leighton 2011). A 60-mL syringe filled with water at room temperature and gas equilibrium was connected to the system and was slowly compressed or expanded to adjust the pressure (refer to Fig. 3). The frequency response was measured up to 150 mmHg static pressure, beyond which the microbubbles become unstable. The pressure was then returned to atmospheric pressure to verify if the variation in resonance frequency with respect to pressure was reversible. The static fluid pressure was
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Fig. 3. Experimental setup used for measurement of the hydrostatic pressure-dependent response of microbubble populations. A 3.5-MHz 85% bandwidth spherically focused transducer was used at low acoustic amplitude. The transducer and the acoustic cell were submerged in water.
kept fixed during each measurement. As in the simulation, a series of narrowband pulses, consisting of 50 pulses of 17 cycles covering the range 1 to 5.9 MHz, were produced using an arbitrary waveform generator (AWG520, Tektronix, Beaverton, OR, USA) and a power amplifier (RPR-4000, Ritec, Warwick, RI, USA). A low acoustic pressure (65 kPa at the center frequency) was used. The signal was time gated at the focus of the transducer. Enough measurements were compounded to minimize the effect of statistical speckle (SNR [signalto-noise ratio]z1.91Nmeasurements ). A slowly rotating magnetic stirrer ensured that each measurement was independent. In addition to the speckle effect, backscatter spectroscopy measurements are limited by the bandwidth of the transducer. Each transducer has a particular frequency response curve, or transfer function (H), which affects both the transmitted (HT 5 Ptransmitted/Vinput) and received (HR 5 Vreceived/Pinput) signals. Under the reciprocity approximation, it can be shown that HT f HR, where the proportionality constant is known as the reciprocity factor (Sijl 2009). The reciprocity approximation is ensured by keeping the applied voltage to the transducer low. To decouple the microbubble scattered spectrum from the transducer transfer function, the backscattered reflection, Vcalib(u), from a quartz plate was measured. Under linear signal propagation conditions, the transfer function of the bubble is HB(u) 5 V(u)/ Vcalib(u), where V(u) is the received bubble response. The experiment was conducted using two different types of microbubbles: Optison microbubbles and generic phospholipid microbubbles. Optison microbubbles (GE Healthcare, Burnaby, BC, Canada) are clinical octafluoropropane gas microbubbles with an albumin shell.
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The generic phospholipid microbubbles were obtained as follows. A surfactant solution of 1,2-distearoyl-sn-glycero-3-phosphocholine and polyoxyethylene (40) stearate was prepared according to the recipe in Feshitan et al. (2009). The solution was then sonicated in a saturated perfluorobutane atmosphere, creating microbubbles varying between 1 and 10 mm in diameter and filled with perfluorobutane. In addition, as sonicated microbubbles typically have a wide range of radii and shell properties, a centrifuge (Legend RT, Sorvall, Newtown, CT, USA) is used to reduce the spread of the microbubble size distribution. Feshitan et al. (2009) described a method for isolating microbubbles by size using a centrifuge. The technique, similar to decantation (Goertz et al. 2007), exploits the simple idea that bubbles slowly float under the effect of gravity and that larger bubbles float faster. The slowly rising motion of bubbles in water is described by Stokes flow theory (low Reynold’s number model). The buoyancy velocity, mb, is estimated using ub 5
2ðrw 2rb Þ 2 R gc 9hw
(7)
where ru is mass density of water, hu is the dynamic viscosity of water, R is the bubble’s radius and gc is the centrifugal acceleration. To extract microbubbles of a particular size, a first slow centrifugation (1 min at 55 g) was used to remove the larger bubbles. A second faster centrifugation (1 min at 92 g) was then performed on the supernatant from the first centrifugation. The recovered precipitate contains the size-filtered microbubbles. A Coulter counter (Multisizer III, Beckman Coulter, Mississauga, ON, Canada) was used to quantify the size distribution and concentration for both the native and size-filtered microbubble populations. The radial size distributions of the populations used are illustrated in Figure 4. Linear simulation of effect of size distribution in microbubble populations In a realistic clinical setup, the echoes observed are produced by an ensemble of microbubbles of different radii and shell properties (e.g., surface tension at rest) instead of single microbubbles. This introduces further complexity because of the inherent statistics of microbubble populations. In particular, it is expected that increasing the spread in the size distribution of microbubbles (PR) should affect the resonance frequency of the echo produced by an ensemble of microbubbles. Statistical simulation is used to quantify the effect of size distribution (independent of surface tension variation). The echoes from various bubble populations were computed using the linear response equation (5). By use of central
Volume 40, Number 4, 2014 0.015 Optison Lipid shell (unfiltered) Lipid shell (centrifuge filtered)
Number [%]
780
0.01
0.005
0 0
1
2
3
4
5
6
Radius [µm]
Fig. 4. Size distributions measured with a Coulter counter for Optison (thin line), phospholipid centrifuge-filtered (dashed line) and phospholipid native sonicated (thick line) microbubbles. The coefficient of variation (CoV 5 sR/mR) achieved was 0.63, 0.72 and 0.41 for the Optison, phospholipid native and phospholipid centrifuged populations, respectively.
limit statistics, the expected scattered pressure amplitude is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pX 2 (8) jPi ðuk Þj jPðuk Þj 5 4 i where P2i ðuk Þ is the Fourier amplitude of the scattered pressure from microbubble i at frequency uk. Spatial populations of microbubbles were simulated by randomly attributing a spatial location to each bubble (affecting the phase of the scattered pressure). The radius was assigned according to a Gaussian probability distribution function with mean mR and standard deviation sR. An elastic shell model was used to study the effect of radius probability distribution, independent of surface tension effects. The coefficient of variation (CoV 5 sR/mR, dimensionless) was also introduced to normalize and quantify the spread of the microbubble size distributions.
RESULTS Simulation of effect of blood pressure on bubble resonance A viscoelastic bubble exhibits both elastic (constant elastic modulus) and viscous behavior. A simulation of a viscoelastic bubble, according to the de Jong model, is provided in Figure 5 for the pressure response to a series of narrowband pulses. The same effects as those predicted by the linear theory are observed: the resonance frequency is slowly shifted toward higher values as static pressure is increased (6 kHz per 10 mmHg, as illustrated in Fig. 7a). In addition, the resonance frequency weakly increases with increasing acoustic pressure, which causes small deviations (4% to 10%) from the linear model prediction of the resonance frequency resulting from
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Fig. 5. Simulation of the variation in echo pressure amplitude (each color scale normalized to its own maximum) with respect to static pressure of a viscoelastic bubble for both fundamental (left) and second harmonic (right) using the full equation of motion (3-mm radius, c 5 0.54 N/m). The microbubbles were driven using 17-cycle pulses with varying center frequencies (x-axis) and acoustic pressure, Pac (y-axis). The resonance frequency of the fundamental increases slowly with static fluid pressure. Acoustic pressure has only a weak effect on the resonance frequency.
non-linear effects. The second harmonic (i.e., the echo at twice the insonification frequency) scattered by the microbubbles becomes stronger as the acoustic pressure is increased. For fixed pressure, the second harmonic is maximum if the driving frequency lies between ½f0 and f0. In resemblance to the fundamental, this value also slowly increases with static fluid pressure. In contrast, phospholipid bubbles cannot be considered as purely viscoelastic at large driving pressures because they buckle and rupture at specific radius thresholds, and so the full Marmottant surface tension model must be used. Simulations of the Marmottant equation of motion with respect to frequency, acoustic pressure and static fluid pressure are provided in Figures 6 and 7b. At low acoustic pressures, simulations agree well with linear theory; the resonance frequency decreases quickly (410 kHz per 10 mmHg) as the transition regime is reached. At moderate acoustic pressures, the resonance frequency is considerably downshifted because the finite oscillations of bubbles reach the buckling radius (Figs. 6
and Fig. 7b). Such behavior is not predicted by linear theory, but a qualitative explanation is that as a bubble stays a fraction of its oscillation in the buckled state, it experiences a lower net elasticity c over a full cycle. This effect causes the microbubble to become a very poor manometer (5 kHz per 10 mmHg, refer to Fig. 7) if Pac is increased over a fixed threshold. In the studied case, a shift is observed for acoustic pressures as low as 40 kPa because the elastic regime covers a very narrow radius span. This result seems to agree with the experimental observations of Overvelde et al. (2010) that an increase in acoustic pressure also decreases the resonance frequency in microbubbles with non-linear shell properties. The linear approximation used in Figure 2 is valid only for low acoustic pressures (,40 kPa in this case), where finite oscillation effects can be safely neglected. Incidentally, the second harmonic response is maximal when the bubble is driven roughly at half of the fundamental resonance frequency of an unshelled microbubble for moderate to high acoustic pressures (Fig. 6). Finite
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Fig. 6. Simulation of the fluid static pressure-dependent response from a buckling bubble. The hydrostatic pressures used are 0 mmHg (non-buckled), 38 mmHg (transition) and 413 mmHg (buckled). R0 5 2.94 mm, Rbuck 5 2.92 mm, c0 5 2.55 N/m, z 5 5 kN/m. At low acoustic pressure, increasing the static pressure forces the bubble into a buckled state, causing a steep decrease in resonance frequency. Further increase in acoustic pressure can also cause a microbubble, initially in the elastic regime at rest, to buckle over its oscillation cycle, which also lowers the net resonance frequency (refer to P0 5 0 mmHg).
Fig. 7. Simulation of the effect of pulse pressure on the response of phospholipid microbubbles to static fluid pressure. (a) Viscoelastic model: At low acoustic pressure (Pac 5 3 kPa, solid), the resonance frequency changes by 0.008 MHz per 10 mmHg, whereas it changes by 0.006 MHz per 10 mmHg at Pac 5 350 kPa (dashed line). (b) Phospholipid microbubble: At low driving pressures, the microbubble responds well to pressure (0.41 MHz per 10 mmHg at Pac 5 3 kPa and 0.30 MHz per 10 mmHg at Pac 5 30 kPa). Finite oscillation effects cause the microbubble to become a poor manometer over a certain driving pressure (0.005 MHz per 10 mmHg at 40 kPa in this case), at which the microbubble starts to buckle within each oscillation. R0 5 2.94 mm, Rbuck 5 2.92 mm, c0 5 2.55 N/m, z 5 5 kN/m.
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buckling is always dominant at these acoustic pressures, which reduces the resonance frequency close to that of an unshelled microbubble. If the hydrostatic pressure is such that the bubble rest radius is within the transitional regime, a strong second harmonic component exists at very low acoustic pressure (1–10 kPa). Because second harmonics are usually very weak at such low acoustic pressure, this emission peak can be used as a selective marker for transitional buckling. In vitro measurement of effect of blood pressure on microbubble resonance Pulse-echo spectroscopy was performed on phospholipid- and protein-shelled microbubbles (using populations of different size distributions) for different hydrostatic pressures. The resonance frequency was extracted from the resonance spectra and plotted against hydrostatic pressure (Fig. 8). The standard error on the mean resonance frequency (error bars in Fig. 8) was estimated by propagating the error of the resonance spectrum to the maximum value. The error on the resonance frequency is associated with the uncertainty in determining the resonance frequency of a low-quality-factor resonance peak from the averaged speckle noise. The resonance frequency of both size-filtered and non-size-filtered phospholipid microbubble populations was significantly reduced as static pressure was increased (p-value 5 0.02 between 16 and 77 mmHg for the centrifuged populations and p-value 5 0.005 between 3 and 103 mmHg for the native microbubble population). The mean variations
Resonance Frequency [MHz]
4.6 4.4
Native generic phospholipid Centrifuged generic phospholipid Optison
*
4.2
*
4 3.8 3.6
783
in resonance frequency were 0.24 6 0.09 and 0.11 6 0.03 MHz per 10 mmHg for the size-filtered and native populations, respectively, in the region 0 to 52 mmHg (refer to Fig. 8 and Table 1). This dependency eventually reaches a plateau for large hydrostatic pressures, which is expected because all bubbles should buckle at high enough static pressures. As a result, the sensitivity is lowered to 0.08 6 0.02 and 0.07 6 0.02 MHz per 10 mmHg for the size-filtered and native populations, respectively, if a 0 to 100 mmHg region is considered. No significant shift in the resonance frequency of protein microbubbles was detected (p 5 0.48). All pvalues (two-tailed) were estimated using an unpaired ttest. Shell effects dominated the static pressure response of phospholipid microbubbles such that the resonance frequency shifts observed were well within the target pressure range, even for polydisperse microbubbles. This confirms that phospholipid-shelled microbubbles are much more sensitive to blood pressure than proteinshelled microbubbles. Moreover, as the hydrostatic pressure was relaxed to ambient pressure, the resonance frequencies for both native and centrifuge-filtered lipid microbubbles were restored to values slightly higher than their initial values. This suggests that the effect of hydrostatic pressure on the bubble is reversible. The echo spectra from phospholipid microbubbles were measured for increasing values of acoustic pressure. As acoustic pressure was progressively increased from 111 to 225 kPa, the resonance frequency peak shifted from 4 to 2.3 MHz (see Fig. 9). This shift, also present in simulations, occurs because the microbubble experiences part of its oscillation in a buckled state if subjected to a moderate acoustic pressure. This result agrees qualitatively with the observations of Overvelde et al. (2010), and indicates that the acoustic pressure, beyond a certain insonification amplitude threshold, affects the response from phospholipid microbubbles. The measured threshold is higher (between 111 and 225 kPa) than the predicted value from simulations (40 kPa). This
3.4
Table 1. Sensitivity of resonance frequencies of different bubble populations to static pressure variations*
3.2 3
0
20
40 60 80 100 120 Additional static pressure [mmHg]
140
160
Fig. 8. Experimental pulse-echo measurement of the variation in resonance frequency as a function of static pressure for different microbubble shells. The variation in resonance frequency between 3 and 103 mmHg was statistically significant for the native microbubbles (p 5 0.005) and also significant for centrifuge-filtered microbubbles (p 5 0.02) between 16 and 77 mmHg, but not statistically significant for Optison (p 5 0.48) for the interval 0 to 107 mmHg. Error bars with asterisks were obtained after the pressure in the cell was relaxed. The trend line for each population is also a solid line. Number of replicates 5 250.
Resonance frequency shift (MHz per 10 mmHg) Microbubble type
0 to 52 mmHg region
0 to 113 mmHg region
Optison Generic phospholipid centrifuged Generic phospholipid native
0.00 6 0.02 –0.24 6 0.09 –0.11 6 0.03
–0.008 6 0.011 –0.08 6 0.02 –0.07 6 0.02
* Values were obtained from data in Figure 8. Although the proposed technique is sensitive enough for application in portal vein pressure measurements, it still suffers from some reproducibility issues related to large experimental errors.
Fundamental Response [A.u.]
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120
Pac = 65 kPa Pac = 111 kPa
100
P
ac
= 225 kPa
Pac = 335 kPa
80 60 40 20
2
3
4
5
Excitation frequency [MHz]
6
Fig. 9. Variation in backscattered response (fundamental) as a function of the driving frequency from filtered microbubbles with increasing acoustic pressure. The resonance frequency is shifted toward lower values because of the buckling of phospholipid bubbles. The peak negative acoustic pressures used were 65 kPa (solid line), 111 kPa (dashed line), 225 kPa (dotted line) and 335 kPa (dashed-dotted line). Number of replicates 5 500.
difference is reasonable considering that very little is known about the actual value of surface tension at rest within the microbubble population, which directly affects the buckling radius. Effect of size distribution in microbubble populations on blood pressure measurement The dependence of resonance frequency on static pressure is not identical for centrifuge size-filtered and native microbubbles in Figure 8, introducing the important question of reproducibility between different population measurements. At 0 mmHg, the centrifuge-filtered bubbles had a higher resonance frequency than native microbubbles, with a steeper dependence on blood pressure. As static pressure was increased between 25 and 100 mmHg, however, resonance frequency dropped faster
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for native phospholipid microbubbles than for centrifugefiltered microbubbles. It is expected that these variations were due to the statistical spread of the bubble radius and shell properties, such as surface tension. All commercially available ultrasound contrast agents contain microbubbles of different sizes (probability distribution function PDFR) and shell properties (in particular the surface tension at rest, with probability distribution PDFS). As seen in Figure 8, increasing the spread in the size distribution of microbubbles in particular (through PDFR) affects the resonance frequency of microbubbles. The resonance frequency of a microbubble is specific to its radius and will decrease with an increase in microbubble radius. This distorts the resonance peak and shifts the resonance frequency as a population becomes more polydisperse. Shifts in resonance frequency cause systematic errors in static pressure measurements. A bubble population echo spectrum is also smeared by compounding peaks of different center frequencies, which artificially decreases the quality factor (Q 5 f0/FWHMf) of the resonance peak. A less defined resonance peak causes an increase in the random error of the resonance frequency measurement, thereby reducing our accuracy in measuring pressure. It is expected that these effects should become negligible as microbubbles are made more uniform in their radii. To determine the extent of homogeneity in the radius size distribution required to minimize these statistical effects, the linear echoes from populations of 1000 microbubbles following Gaussian radius distributions (PDFR f exp [-(R – mR)2/2s2R ]) centered around mR 5 2, 4 and 6 mm were calculated for increasing values of the standard deviation. As seen in Figure 10(a, c), the quality factor, Q, was found to decrease quickly as the CoV of the bubble population increased. A CoV of 0.06 will cause the quality factor to decrease by 25%, which causes significant broadening of the resonance peak. Shifts in the resonance frequency of 1% are observed at CoVs . 0.10. On the basis of these simulation results,
Fig. 10. Effect of bubble size distribution on the scattered signal by changing the standard deviation of a Gaussian population size distribution with 4.0-mm mean radius. The shift in resonance frequency (b) and decrease in quality factor (c) were computed from the scattered pressure (a) for microbubble populations of increasing coefficient of variation (CoV) and various mean radii.
Absolute BP measurement using microbubbles d C. TREMBLAY-DARVEAU et al.
a CoV of 0.10 is required to avoid systematic error due to the shift of the resonance frequency, and a CoV of 0.06 should be targeted to minimize the statistical error associated with resonance peak broadening due to microbubble radius distribution. DISCUSSION It has been found through both simulation and experiment that buckling-type phospholipid microbubble resonance frequencies are much more dependent on hydrostatic pressure than those of simpler viscoelastic shells such as protein microbubbles. The variation in resonance frequency for phospholipid microbubbles is high enough for realistic application to portal vein hypertension diagnosis. Most of the static pressure effects on phospholipid microbubbles are attributed to the shell dynamics (radiusdependent elasticity, in particular), as opposed to the gas dynamics, of viscoelastic microbubbles. In particular, this occurs because of the non-linearity of the surface tension function, s(R), which causes large variations in the shell’s elasticity (ceff(R) 5 ½R0[ds/R]│R0 ). We may infer that other strongly non-linear shells, such as nanoparticle-coated microbubbles (Stride et al. 2008), could present an analogous sensitivity to blood pressure. Our results also indicate that changes in the resonance frequency of lipid-shelled microbubbles are reversible. Moreover, although it was previously known that the sub-harmonic amplitude of phospholipid microbubbles can be used to measure blood pressure (Forsberg et al. 2005; Frinking et al. 2009, 2010), the absolute blood pressure can be measured only by tracking changes in the resonance frequency (directly related to shell elasticity), as indicated in this work. In particular, eqn (5) can be inverted for P0 as long as the physical properties of the microbubbles (e.g., surface tension, radius) are known. At the moment, clinically available microbubble contrast agents are produced mainly by sonication, a method with poor reproducibility, which results in a highly variable size distribution (CoV .. 0.10) and, as a consequence, causes large variations in resonance frequency. Although it reduces the CoV, centrifugation of the microbubbles is not selective enough to reach the 6% threshold (a CoV of 0.41 was achieved in this study). To overcome this limitation, a three-inlet microfluidic system can instead be used to produce almost monodisperse microbubbles (Seo et al. 2010). Perfluorocarbon gas is injected at high throughput in the central channel, and the aqueous shell solution is injected through both upper and lower channels. The microfluidic microbubbles are formed in a small nozzle at the intersection of the inlets, where both immiscible phases mix. Depending on the flow rate and size of the nozzle used, the bubbles will have different diameters and coefficients of variation.
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According to Seo et al. (2010), the coefficients obtained are always smaller than 0.06. In addition, two bubbles of identical size may respond very differently to the same acoustic pulse depending on the concentration of the surfactants in their shells (Sijl 2009), which directly affects shell surface tension. It is expected that within a population, the concentration of surfactant will vary for each bubble, and therefore, we should expect each of them to have a slightly different buckling radius. The extent of the statistical fluctuations of buckling radius within a bubble population remains to be quantified experimentally. The phospholipid concentration of a single microbubble might also be affected by ultrasound exposure through mechanisms such as lipid shedding (O’Brien et al. 2011). The behavior of phospholipid-shelled microbubbles may also differ in blood compared with simpler in vitro media such as water and saline. A self-assembly process that would allow control of surface tension for bubble populations has been proposed by Marmottant et al. (2005). It has been observed that bubbles at rest, even in a saturated atmosphere, deflate quickly after being created, but become much more stable as the buckling radius is reached. Gas diffusion outward from the microbubble occurs because the gas pressure inside of the bubble is always higher than the partial gas pressure of the surrounding liquid due to surface tension (a quantitative formulation of this phenomenon was given by Epstein and Plesset [1950]). It is therefore expected that within an old population (possibly a matter of minutes), bubbles are expected to shrink very close to their buckling radius, no matter their initial radius or surface tension at rest. Bubbles close to their buckling radius are very sensitive to any additional static pressure applied, which could explain why an entire population with a polydisperse size distribution of microbubbles seems to buckle at low static pressure (Fig. 8) and potentially provides a way to control the buckling radius in microbubble populations. Even considering the current intrinsic limitations of microbubble populations of polydisperse radii and surface tension at rest, a significant shift in the resonance frequency with increasing hydrostatic pressure was observed for phospholipid-shelled microbubbles. The sensitivity of these microbubbles to hydrostatic pressure is also expected to improve as microbubble physical properties become more controlled and optimized. As long as the physical properties of the microbubbles are known, the blood pressure could then be estimated directly using eqn (5). This method could be adapted to clinical scanners and provide a non-invasive blood pressure measurement deep in the body (where conventional sphygmomanometry techniques cannot be used). In particular, the proposed method would have important value
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in the diagnosis of portal vein hyper-pressure, where the gold standard for diagnosis of portal hypertension relies solely on the symptoms (Child-Pugh score) and not directly on pressure values, making any early diagnosis of the disease very difficult. CONCLUSIONS It has been found that hydrostatic pressure affects the resonance frequencies of phospholipid-shelled microbubbles more than viscoelastic-shelled microbubbles, because of the buckling dynamics of phospholipid monolayers. This remains valid as long as the acoustic pressure is kept below a fixed threshold (between 111 and 225 kPa in this case), above which the bubble will start to undergo periodic buckling because of finite size oscillations. Experiments suggest that the method should be sensitive enough for clinical application, in particular in portal vein hypertension diagnosis, because maximal variations in the resonance frequency ranging from 0.07 6 0.02 to 0.24 6 0.09 MHz per 10 mmHg have been measured for phospholipid microbubbles, whereas no significant shift has been observed for protein microbubbles. Current measurements of the resonance frequency from bubble populations (CoVs . 0.10) suffer from poor reproducibility because the inhomogeneity of the properties within a microbubble population causes bias in the net resonance frequency measured. In particular, it has been found that reproducibility can be improved by reducing the variability in microbubble radii below a CoV of 0.06. Such a CoV could be achieved using a microfluidic-based system to produce microbubbles, instead of the sonicationbased technique currently used. Acknowledgments—This work has been supported by the Natural Sciences and Engineering Research Council of Canada, the Ontario Graduate Scholarship Program and the University of Toronto. We thank Don Plewes, Richard Cobbold, Ahthavan Sureshkumar, Brendan Lloyd, Emmanuel Cherin, David Goertz, Peter Bevan, Nikita Reznik, John Hudson, Kogee Leung and Minseok Seo for illuminating discussions as well as the support given in the completion of this project.
REFERENCES Allen J, Rashid M. Dynamics of a hyperelastic gas-filled spherical shell in a viscous fluid. J Appl Mech 2004;71:195–200. Andersen K, Jensen J. Impact of acoustic pressure on ambient pressure estimation using ultrasound contrast agent. Ultrasonics 2010a;50: 294–299. Andersen KS, Jensen JA. Non-invasive estimation of blood pressure using ultrasound contrast agents. Physics Procedia 2010b;3:245–253. Chatterjee D, Sarkar K. A Newtonian rheological model for the interface of microbubble contrast agents. Ultrasound Med Biol 2003;29: 1749–1757. Church C. The effects of an elastic solid surface layer on the radial pulsations of gas bubbles. J. Acoust Soc Am 1995;97:1510–1521. De Jong N, Cornet R, Lancee C. Higher harmonics of vibrating gasfilled microspheres: Part 1. Simulations. Ultrasonics 1994;32: 447–453.
Volume 40, Number 4, 2014 Der Meer SV, Dollet B, Voormolen M, Chin C, Bouakaz A, Jong ND, Versluis M, Lohse D. Microbubble spectroscopy of ultrasound contrast agents. J Acoust Soc Am 2007;121:648–656. Doinikov A, Bouakaz A. Review of shell models for contrast agent microbubbles. IEEE Trans Ultrason Ferroelectr Freq Control 2011;58:981–993. Doinikov A, Dayton P. Maxwell rheological model for lipid-shelled ultrasound microbubble contrast agents. J Acoust Soc Am 2007; 121:3331–3340. Epstein P, Plesset M. On the stability of gas bubbles in liquid gas solutions. J Chem Phys 1950;18:1505–1509. Fairbank W, Scully M. A new noninvasive technique for cardiac pressure measurement: Resonant scattering of ultrasound from bubbles. IEEE Trans Biomed Eng 1977;107–110. BME-24. Feshitan J, Chen C, Kwan J, Borden M. Microbubble size isolation by differential centrifugation. J Colloid Interface Sci 2009;329: 316–324. Forsberg F, Liu J, Shi W, Furuse J, Shimizu M, Goldberg B. In vivo pressure estimation using subharmonic contrast microbubble signals: Proof of concept. IEEE Trans Ultrason Ferroelectr Freq Control 2005;52:581–583. Frinking P, Gaud E, Arditi M. Compression-only behavior and subharmonic scattering of phospholipid-shell microbubbles. In: Proceedings, 2009 IEEE International Ultrasonics Symposium, Rome, Italy, 20–23 September 2009. New York: IEEE, 2009:263–266. Frinking P, Gaud E, Brochot J, Arditi M. Subharmonic scattering of phospholipid-shell microbubbles at low acoustic pressure amplitudes. IEEE Trans Ultrason Ferroelectr Freq Control 2010;57: 1762–1771. Goertz D, de Jong N, van der Steen A. Attenuation and size distribution measurements of DefinityÔ and manipulated DefinityÔ populations. Ultrasound Med Biol 2007;33:1376–1388. Hoff L, Sontum P, Hovem J. Oscillations of polymeric microbubbles: Effect of the encapsulating shell. J Acoust Soc Am 2000;107: 2272–2280. Ishihara K, Kitabatake A, Tanouchi J, Fujii K, Uematsu M, Yoshida Y, Kamada T, Tamura T, Chihara K, Shirae K. New approach to noninvasive manometry based on pressure dependent resonant shift of elastic microcapsules in ultrasonic frequency characteristics. Jpn J Appl Phys Suppl 1988;27:125–127. Keller J, Miksis M. Bubble oscillations of large amplitude. J Acoust Soc Am 1980;68:628–633. Khismatullin D, Nadim A. Radial oscillations of encapsulated microbubbles in viscoelastic liquids. Phys Fluids 2002;14:3534–3557. Leighton T. The acoustic bubble. London: Academic Press; 1994. p. 151–159. Leighton T. The inertial terms in equations of motion for bubbles in tubular vessels or between plates. J Acoust Soc Am 2011;130: 3333–3338. Leighton T, Ramble D, Phelps A. The detection of tethered and rising bubbles using multiple acoustic techniques. J Acoust Soc Am 1997;101:2626–2635. Li F, Wang L, Fan Y, Li D. Simulation of noninvasive blood pressure estimation using ultrasound contrast agent microbubbles. IEEE Trans Ultrason Ferroelectr Freq Control 2012;59:715–726. Marmottant P, van der Meer S, Emmer M, Versluis M, de Jong N, Hilgenfeldt S, Lohse D. A model for large amplitude oscillations of coated bubbles accounting for buckling and rupture. J Acoust Soc Am 2005;118:3499–3505. Newhouse V, Shankar P. Bubble size measurements using the nonlinear mixing of two frequencies. J Acoust Soc Am 1984;75:1473–1477. O’Brien J, Ovenden N, Stride E. Accounting for the stability of microbubbles to multi-pulse excitation using a lipid-shedding model. J Acoust Soc Am 2011;130:EL180–EL185. Overvelde M, Garbin V, Sijl J, Dollet B, de Jong N, Lohse D, Versluis M. Nonlinear shell behavior of phospholipid-coated microbubbles. Ultrasound Med Biol 2010;36:2080–2092. Petriat F, Roux E, Leroux J, Giasson S. Study of molecular interactions between a phospholipidic layer and a pH-sensitive polymer using the Langmuir balance technique. Langmuir 2004;20: 1393–1400.
Absolute BP measurement using microbubbles d C. TREMBLAY-DARVEAU et al. Plesset M. The dynamics of cavitation bubbles. J Appl Mech 1949; 277–282. Rayleigh J. On the pressure development in a liquid during the collapse of a spherical cavity. Philos Mag 1917;34:94–98. Sarkar K, Shi W, Chatterjee D, Forsberg F. Characterization of ultrasound contrast microbubbles using in vitro experiments and viscous and viscoelastic interface models for encapsulation. J Acoust Soc Am 2005;118:539–550. Seo M, Gorelikov I, Williams R, Matsuura N. Microfluidic assembly of monodisperse, nanoparticle-incorporated perfluorocarbon microbubbles for medical imaging and therapy. Langmuir 2010;26: 13855–13860. Shankar P, Chapelon J, Newhouse V. Fluid pressure measurement using bubbles insonified by two frequencies. Ultrasonics 1986;24:333–336.
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Shi W, Forsberg F, Raichlen J, Needleman L, Goldberg B. Pressure dependence of subharmonic signals from contrast microbubbles. Ultrasound Med Biol 1999;25:275–283. Sijl J. Ultrasound contrast agents: Optical and acoustical characterization. Enschede: Jeroen Sijl, Physics of Fluids, University of Twente; 2009. p. 1–137. Stride E. The influence of surface adsorption on microbubble dynamics. Philos Trans R Soc A 2008;366:2103–2115. Stride E, Pancholi K, Edirisinghe M, Samarasinghe S. Increasing the nonlinear character of microbubble oscillations at low acoustic pressures. J R Soc Interface 2008;5:807–811. Tsiglifis K, Pelekasis N. Nonlinear radial oscillations of encapsulated microbubbles subject to ultrasound: The effect of membrane constitutive law. J Acoust Soc Am 2008;123:4059–4070.
http://dx.doi.org/10.1016/j.ultrasmedbio.2013.10.017
d
Original Contribution MEASURING ABSOLUTE BLOOD PRESSURE USING MICROBUBBLES CHARLES TREMBLAY-DARVEAU,* ROSS WILLIAMS,y and PETER N. BURNSy * Department of Medical Biophysics, University of Toronto at Sunnybrook Health Sciences Centre, Toronto, Ontario, Canada; and y Sunnybrook Health Sciences Centre, Toronto, Ontario, Canada (Received 15 July 2013; revised 15 October 2013; in final form 21 October 2013)
Abstract—Gas microbubbles are highly compressible, which makes them very efficient sound scatterers. As another consequence of their high compressibility, the radii of the microbubbles are affected by the pressure of the fluid around them, which changes their resonance frequency. Although the pressures present within the human body cause only minor variations in the radii of uncoated microbubbles (0.2% per 10 mmHg) and, therefore, very small variations in the resonance frequency (1 kHz per 10 mmHg), it was found in the work described here, through both simulations and in vitro measurements, that large changes in resonance frequency can occur in phospholipid-coated microbubbles for small blood pressure variations because of the exotic buckling dynamics of phospholipid monolayers (up to 240 kHz per 10 mmHg). This method should allow non-invasive measurement of the gauge blood pressure in deep blood vessels as long as the microbubble physical properties are well controlled. (E-mail: [email protected]) Ó 2014 World Federation for Ultrasound in Medicine & Biology. Key Words: Microbubble imaging, Blood pressure, Acoustic spectroscopy.
by Fairbank and Scully (1977), who noted that the scattering properties of unshelled microbubbles are also affected by static fluid pressure and, therefore, could provide a direct way to measure local blood pressure deep within the body using ultrasound. Fairbank and Scully (1977) reported that increasing the static pressure effectively compresses the microbubble, which shifts the resonance frequency of microbubbles upward. Notably, a small shift in the resonance frequency of unshelled microbubbles was observed for 30- to 40-mm diameter microbubbles and hydrostatic pressure changes of about 0.2 atm. Ishihara et al. (1988) validated this later in a similar experiment. Non-invasive measurement of the gauge pressure within the body would have many clinical applications. It would be especially groundbreaking in the case of early diagnosis of portal vein hypertension. Portal vein hypertension is a common complication of liver cirrhosis, in which the vascular resistance of the portal-hepatic bed is drastically increased because of fibrosis. This causes an increase in pressure within the portal vein from 5– 10 mmHg in healthy individuals to .12 mmHg. The pressure in the portal vein cannot be measured with usual sphygmomanometry techniques. Although it is possible in theory to catheterize through the jugular vein and inferior vena cava and then puncture through the liver to
INTRODUCTION Intravascular contrast agents are well established as a means of improving conventional medical imaging techniques. For example, paramagnetic particles (e.g., iron oxide, gadolinium) can be used in magnetic resonance imaging because of their high magnetic susceptibility. In ultrasound, micron-size gas spheres of high compressibility coated by a thin shell, commonly referred to as microbubbles, are used. Microbubbles (1–10 mm in diameter) are similar in size to red blood cells (6–8 mm) and, therefore, do not diffuse through the walls of blood vessels, making them true intravascular agents. When microbubbles are injected, blood echoes become brighter on a B-mode image as a result of the coupling of the radial motion of the microbubble wall with the surrounding liquid, considerably increasing the backscattered signal. Microbubbles behave as non-linear scatterers, even when driven at low acoustic pressures, and emit signals at integer (harmonic) and fractional (sub-harmonic, ultra-harmonic) multiples of the insonation frequency. Another consequence of their high compressibility has been suggested
Address correspondence to: Charles Tremblay-Darveau, Sunnybrook Health Sciences Centre, 2075 Bayview Avenue, Toronto, ON M4N 3M5, Canada. E-mail: [email protected] 775
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access the portal circulation to measure local blood pressure with a manometer, such a procedure is extremely invasive and places the patient at high risk. A noninvasive way to measure blood pressure (i.e., gauge pressure) with a pressure resolution of 10 mmHg within non-limb vessels would have important value in the diagnosis of portal vein hypertension. Unfortunately, the resonance frequency shift of unshelled microbubbles for 10 mmHg is on the order of 1 kHz, which is too small for clinical application to portal vein hypertension diagnosis, even considering the resolution improvement achieved with a dual-frequency system (Leighton et al. 1997; Newhouse and Shankar 1984; Shankar et al. 1986). Recent literature suggests that some microbubble coatings can strongly affect the response to blood pressure. Shi et al. (1999), Forsberg et al. (2005), Andersen and Jensen (2010a, 2010b) and Li et al. (2012) recently observed that sub-harmonic emissions (i.e., the echo scattered at half of the insonification frequency) of phospholipid microbubbles are dependent on blood pressure. In particular, Frinking et al. (2009, 2010) found experimentally that phospholipid microbubbles increase their sub-harmonic power considerably when the ambient over-pressure forces the bubble to enter a surface tensionfree state (e.g., buckling). On the basis of these results, it has been suggested that the amplitude of the subharmonic mode might be a useful indicator of the local relative blood pressure. Yet the gauge pressure, and not the relative pressure, is needed to diagnose portal vein hypertension. It has been reported by Marmottant et al. (2005) that buckling dynamics also strongly affect the compressibility of phospholipid microbubbles, making the resonance frequencies of these bubbles more sensitive than those of microbubbles with simple shell models, such as a viscoelastic shell. In this study, we found that the resolution of the Fairbank and Scully (1977) method for measuring gauge blood pressure, in the light of an understanding of the effects of buckling phospholipid shells, can considerably be improved such that the required 10 mmHg resolution for portal vein hypertension diagnosis can be reached. Two different models were compared to illustrate the effect of shell elasticity on bubble sensitivity to ambient pressure: a viscoelastic surface tension model (de Jong et al. 1994) and a buckling surface tension model (Marmottant et al. 2005), which apply to a protein shell and a phospholipid shell, respectively. A summary of uncoated and shelled microbubbles, the linearized properties of microbubbles and the full numerical solutions of the Marmottant equation for the parameters of interest is presented. These simulations predict a significant improvement in the sensitivity of phospholipid microbubbles to blood pressure, which is investigated in vitro for Optison (a commercial protein-shelled microbubble)
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and for generic phospholipid microbubbles. We also found that inhomogeneity of physical properties (size, elasticity, surface tension at rest) can affect the reproducibility of blood pressure measurements by introducing a systematic bias in estimation of the resonance frequency. The extent of homogeneity in the microbubble radius distribution required to minimize statistical variability was investigated through simulations. Relevant technologies for the production of microbubbles that satisfy these requirements are discussed. THEORY Rayleigh-Plesset equation and shell models The phenomenon of stable cavitation of a vaporfilled bubble was initially explained by Rayleigh (1917) and Plesset (1949), as the result of the application of Newton’s third law to a spherical interface. This initial form of the Rayleigh-Plesset equation neglected the effects of viscosity and the compressibility of the surrounding medium, which were later introduced by Keller and Miksis (1980). Whereas the Rayleigh-Plesset equation explains the response of free gas bubbles (Plesset 1949; Rayleigh 1917), many models compete to describe the behavior of shelled microbubbles. Notably, the models of de Jong et al. (1994), Church (1995), Hoff et al. (2000), Khismatullin and Nadim (2002), Chatterjee and Sarkar (2003), Allen and Rashid (2004), Sarkar et al. (2005), Marmottant et al. (2005), Doinikov and Dayton (2007), Stride (2008) and Tsiglifis and Pelekasis (2008) use different assumptions and different levels of complexity to represent the effect of the shell on microbubble oscillations. De Jong et al. (1994) proposed the addition of two ad hoc terms to the Rayleigh-Plesset equation to compensate for shell friction, ks, and elasticity, c0, such that the equation becomes :: : 2 : Ro 3k oÞ rl RR 132R 5 po 12sðR 123kc R R R oÞ (1) 22sðR 12co R1o 2R1 R :
:
24mRl R24kRs2R2Po 2PðtÞ where R(t) is the instantaneous microbubble radius, R0 is the equilibrium radius, k is the polytropic constant, rl is the liquid density, ml is the liquid viscosity, P0 is the static fluid pressure, s(R) is the bubble-liquid interface surface tension and P(t) is any other applied pressure field (e.g., ultrasound). This model describes many fundamental properties of shelled microbubbles, such as an increase in resonance frequency and damping, and it is accurate for simpler shells such as protein. However, because the shell properties used are analogues of Hooke’s law and Newton’s viscous law (Doinikov and Bouakaz 2011), it
Absolute BP measurement using microbubbles d C. TREMBLAY-DARVEAU et al.
cannot explain more complex phenomena such as compression-only and expansion-only behavior. Doinikov and Bouakaz (2011) stated that non-linear shell properties must be used to predict more accurately non-linear microbubble behaviors such as compressiononly oscillations. In particular, phospholipid shells increase the lifetime of microbubbles by reducing the surface tension between the gas core and the liquid, which limits gas diffusion. In Marmottant’s model (Marmottant et al. 2005), the previously ad hoc elasticity term is now included in a bubble radius-dependent surface tension interaction and, therefore, radius-dependent shell elasticity: 1 dsðRÞ ceff ðRÞ 5 R0 2 dR R0 The surface tension of a phospholipid interface is strongly dependent on the effective area of the molecule (Petriat et al. 2004); it buckles if the molecular density reaches a threshold value (corresponding to a high compression state), whereas it ruptures if stretched past a fixed threshold. Under this assumption, the surface tension of a microbubble coated with a phospholipid monolayer is 8 0 if R,Rbuck > > < 2 if Rbuck ,R,Rr (2) sðRÞ 5 co RRbuck 21 > > : sw if R.Rr where Rbuck and Rr are the buckling and rupture radii of the phospholipid microbubble, respectively. The radial equation of motion is :: : 2 R 3k 3k : o rl RR 132R 5 po 12s 12 c R R R :
:
24mRl R24kRs2R 22sðRÞ R
(3)
2Po 2PðtÞ For very small oscillations, it has been found (Marmottant et al. 2005) that eqn (3) reduces to the de Jong model. Modeling quasi-static compression of microbubbles The quasi-static compression of a bubble caused by blood pressure can be modeled using purely thermodynamic concepts, namely, the polytropic gas law and pressure equilibrium. Equating the pressure forces inside of the bubble at different compression states yields 23k 01 Þ 2Pv Po1 12sðR R01 Pg;e; ðPo1 Þ R01 5 5 (4) 2sðR Þ Pg;e ðPo2 Þ R02 Po2 1 02 2Pv R02
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Fig. 1. Compression of a 3-mm-radius microbubble by static pressure. The equilibrium radius at increasing ambient pressure was solved using eqn (4) for both a viscoelastic shell (solid line) and a free gas microbubble (dashed line).
where indices 1 and 2 refer to different states of compression of the microbubble, and Pv is the partial pressure of the gas. This equation does not have an analytic solution, but can be easily solved numerically (a solution is provided in Fig. 1). The microbubble shell coating usually reduces the effect of static pressure compressions by making the bubble stiffer, but as seen in Figure 1, this causes only small deviations in radius from the unshelled microbubble model (assuming the values from der Meer et al. [2007] for shell elasticity, c). Linear model of effect of blood pressure on microbubble resonance Although simulations must be used to understand the exact non-linear effect of blood pressure on the Rayleigh-Plesset equation, linearization can be used to understand the effect of blood pressure variation on the first-order behavior of microbubbles. In such a scheme, an ansatz solution to the Rayleigh-Plesset equation is assumed to be R(t) 5 R0(1 1 x(t) 1 O(x(t)2)), where x(t) 5 1 (dimensionless) and x(t)2 or higher-order terms are then considered negligible. It is well known (der Meer et al. 2007) that a driven damped harmonic oscillator solution is recovered: ::
:
x þ uo dx þ u2o x 5 PðtÞ rR2 o
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðu2o 2u2 Þ þðduuo Þ2 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 4ceff ðRo Þ 2ð3k21Þsw 1 uo 5 rR2 3kPo þ Ro þ Ro XðuÞ 5 rR1 2 o
PðuÞ
o
d 5 uocRo þ R24mrul o þ R34krus o o
o
(5)
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Here, X(u) is the Fourier transform of x(t), u0 is the natural resonance frequency and d is the total damping in the system. The static pressure has both explicit (in P0) and implicit (caused by compression of the equilibrium radius R0) contributions to the resonance frequency. Most of the shell’s effect on resonance frequency arises directly through the elasticity parameter. For a microbubble following the de Jong model, the coating merely increases the net elasticity, ceff, therefore adding a constant shift to the resonance frequency, whereas the shell viscosity increases the overall damping of the system. As in unshelled bubbles, gas dynamics will be responsible for the dependence of resonance frequency on the static pressure-dependent behavior of microbubbles with a viscoelastic shell. Because a 10 mmHg variation in blood pressure typically compresses a microbubble by about 0.2% of the bubble’s rest radius, the resonance frequency of a microbubble of constant shell elasticity is only weakly affected by blood pressure (6 kHz per 10 mmHg). In contrast, the elasticity of the phospholipid coating depends on the bubble radius. According to the Marmottant model, the elasticity, ceff 5 A(ds/dA), of a lipid-coated bubble is a strong function of bubble radius. An increase in static pressure compresses the bubble, decreasing its equilibrium radius. As long as the bubble’s equilibrium radius stays far from the buckling radius, it will behave similarly to a viscoelastic bubble (changes in ceff will be small), and therefore, the resonance frequency will increase slowly because of gas dynamics. When P0 is high enough, the bubble will undergo buckling, reducing the effective elasticity of its shell to zero and considerably reducing the resonance frequency. Within this transition region, the bubble offers a much more sensitive manometer than protein-shelled microbubbles. Assuming the bubble elastic properties illustrated in Figure 2a and a 3.0-mm radius at rest, the 0–120 mmHg region is the viscoelastic regime, the 120–173 mmHg region is the buckling transition and
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the 173–350 mmHg region is the buckled-state regime (Fig. 2b). The microbubble resonance frequency undergoes a steep change in the transitional region, varying between 1.9 and 1.22 MHz over a pressure change of only 25 mmHg, and the buckling bubble is roughly 40–120 times more sensitive to hydrostatic pressure (250 kHz per 10 mmHg) than the viscoelastic microbubble within these limits. The value of the critical hydrostatic pressure forcing the bubble into a buckled state depends on the surface tension at no over-pressure (i.e., a bubble whose radius at rest is closer to the buckling radius will buckle at lower over-pressure). Therefore, if the surface tension parameter could be controlled in microbubble populations, this could provide a method to tune the bubble to a desired pressure range. It is true that blood pressure changes microbubble size; a 10 mmHg variation in blood pressure will compress microbubbles by about 6–20 nm (assuming a 3-mm rest radius). For this reason, simpler microbubbles, such as unshelled and protein-shelled bubbles, respond only very weakly to blood pressure (6 kHz per 10 mmHg). However, microbubbles with a phospholipid shell respond strongly to blood pressure changes because of the non-linearity of their shell properties (250 kHz per 10 mmHg). METHODS Linearization predicts that viscoelastic shell bubbles respond very weakly to blood pressure, whereas phospholipid-coated microbubbles considerably lower their resonance frequency with increasing blood pressure because of buckling. It is unclear if this effect, as predicted by theory, occurs under more realistic experimental conditions when considering the non-linear scattering properties of microbubbles (for instance, by using acoustic pressure amplitudes higher than the perturbation model).
Fig. 2. Elasticity (a) and resonance frequency (b) versus hydrostatic pressure for a viscoelastic shell (dashed line) and a buckling phospholipid shell bubble (solid line). Drastic changes in elasticity occur when static pressure forces the microbubble to enter a transitional state. This causes a steep drop in the resonance frequency estimated using the linear model (eqn [5]).
Absolute BP measurement using microbubbles d C. TREMBLAY-DARVEAU et al.
Simulation of effect of blood pressure on bubble resonance The Rayleigh-Plesset equation is solved for the radial response, R(t), to an acoustic pressure pulse, Pac(t), using MATLAB (The MathWorks, Natick, MA, USA) for both viscoelastic (eqn [1] with microbubble parameters from der Meer et al. [2007]) and phospholipid (eqn [3]) microbubbles. The pulse sequence used is a series of 50 narrowband pulses of 17 cycles spanning the frequency range 1.0 to 5.9 MHz. The acoustic pressure, or driving pressure, Pac(t), is left as a variable ranging from 1 to 350 kPa to study the non-linear hydrostatic pressure-dependent behavior of microbubbles. To avoid the discontinuity in ceff(R) occurring in the Marmottant model (Marmottant et al. 2005) at the buckling radius, a quadratic transition zone of constant second derivative with respect to radius was used at the transition, an approach initially proposed by Sijl (2009). The scattered pressure, Pscatt, is calculated using conservation of mass/ momentum assumptions (refer to Leighton 1994): :: : r r 2 2 Pscatt r; t2 5 RðtÞ R ðtÞ12RðtÞRðtÞ (6) c r To extract the amplitude of each harmonic, Pscatt is Fourier transformed, producing a spectrum of sharp peaks at harmonic and sub-harmonic frequencies (as a result of narrowband excitation). The amplitude of each peak is extracted using bandpass filters.
In vitro measurement of effect of blood pressure on microbubble resonance The resonant pressure response of microbubbles was determined experimentally using a spectroscopic approach. The experiment was performed using a spherically focused single-element transducer centered at 3.5 MHz, with a 1.91-cm diameter, a 2.54-cm focal length and an 85% fractional bandwidth (Panametrics-NDTC381, Olympus, Quebec, QC, Canada). The microbubbles were imaged through a thin, acoustically transparent Mylar window. The pressure chamber (3.7 cm wide, 3.7 cm high and 1.3 cm long) was connected to a manometer and an adjustable pressure reservoir. The dimensions of the pressure chamber are large enough such that boundary condition effects should be negligible (Leighton 2011). A 60-mL syringe filled with water at room temperature and gas equilibrium was connected to the system and was slowly compressed or expanded to adjust the pressure (refer to Fig. 3). The frequency response was measured up to 150 mmHg static pressure, beyond which the microbubbles become unstable. The pressure was then returned to atmospheric pressure to verify if the variation in resonance frequency with respect to pressure was reversible. The static fluid pressure was
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Fig. 3. Experimental setup used for measurement of the hydrostatic pressure-dependent response of microbubble populations. A 3.5-MHz 85% bandwidth spherically focused transducer was used at low acoustic amplitude. The transducer and the acoustic cell were submerged in water.
kept fixed during each measurement. As in the simulation, a series of narrowband pulses, consisting of 50 pulses of 17 cycles covering the range 1 to 5.9 MHz, were produced using an arbitrary waveform generator (AWG520, Tektronix, Beaverton, OR, USA) and a power amplifier (RPR-4000, Ritec, Warwick, RI, USA). A low acoustic pressure (65 kPa at the center frequency) was used. The signal was time gated at the focus of the transducer. Enough measurements were compounded to minimize the effect of statistical speckle (SNR [signalto-noise ratio]z1.91Nmeasurements ). A slowly rotating magnetic stirrer ensured that each measurement was independent. In addition to the speckle effect, backscatter spectroscopy measurements are limited by the bandwidth of the transducer. Each transducer has a particular frequency response curve, or transfer function (H), which affects both the transmitted (HT 5 Ptransmitted/Vinput) and received (HR 5 Vreceived/Pinput) signals. Under the reciprocity approximation, it can be shown that HT f HR, where the proportionality constant is known as the reciprocity factor (Sijl 2009). The reciprocity approximation is ensured by keeping the applied voltage to the transducer low. To decouple the microbubble scattered spectrum from the transducer transfer function, the backscattered reflection, Vcalib(u), from a quartz plate was measured. Under linear signal propagation conditions, the transfer function of the bubble is HB(u) 5 V(u)/ Vcalib(u), where V(u) is the received bubble response. The experiment was conducted using two different types of microbubbles: Optison microbubbles and generic phospholipid microbubbles. Optison microbubbles (GE Healthcare, Burnaby, BC, Canada) are clinical octafluoropropane gas microbubbles with an albumin shell.
Ultrasound in Medicine and Biology
The generic phospholipid microbubbles were obtained as follows. A surfactant solution of 1,2-distearoyl-sn-glycero-3-phosphocholine and polyoxyethylene (40) stearate was prepared according to the recipe in Feshitan et al. (2009). The solution was then sonicated in a saturated perfluorobutane atmosphere, creating microbubbles varying between 1 and 10 mm in diameter and filled with perfluorobutane. In addition, as sonicated microbubbles typically have a wide range of radii and shell properties, a centrifuge (Legend RT, Sorvall, Newtown, CT, USA) is used to reduce the spread of the microbubble size distribution. Feshitan et al. (2009) described a method for isolating microbubbles by size using a centrifuge. The technique, similar to decantation (Goertz et al. 2007), exploits the simple idea that bubbles slowly float under the effect of gravity and that larger bubbles float faster. The slowly rising motion of bubbles in water is described by Stokes flow theory (low Reynold’s number model). The buoyancy velocity, mb, is estimated using ub 5
2ðrw 2rb Þ 2 R gc 9hw
(7)
where ru is mass density of water, hu is the dynamic viscosity of water, R is the bubble’s radius and gc is the centrifugal acceleration. To extract microbubbles of a particular size, a first slow centrifugation (1 min at 55 g) was used to remove the larger bubbles. A second faster centrifugation (1 min at 92 g) was then performed on the supernatant from the first centrifugation. The recovered precipitate contains the size-filtered microbubbles. A Coulter counter (Multisizer III, Beckman Coulter, Mississauga, ON, Canada) was used to quantify the size distribution and concentration for both the native and size-filtered microbubble populations. The radial size distributions of the populations used are illustrated in Figure 4. Linear simulation of effect of size distribution in microbubble populations In a realistic clinical setup, the echoes observed are produced by an ensemble of microbubbles of different radii and shell properties (e.g., surface tension at rest) instead of single microbubbles. This introduces further complexity because of the inherent statistics of microbubble populations. In particular, it is expected that increasing the spread in the size distribution of microbubbles (PR) should affect the resonance frequency of the echo produced by an ensemble of microbubbles. Statistical simulation is used to quantify the effect of size distribution (independent of surface tension variation). The echoes from various bubble populations were computed using the linear response equation (5). By use of central
Volume 40, Number 4, 2014 0.015 Optison Lipid shell (unfiltered) Lipid shell (centrifuge filtered)
Number [%]
780
0.01
0.005
0 0
1
2
3
4
5
6
Radius [µm]
Fig. 4. Size distributions measured with a Coulter counter for Optison (thin line), phospholipid centrifuge-filtered (dashed line) and phospholipid native sonicated (thick line) microbubbles. The coefficient of variation (CoV 5 sR/mR) achieved was 0.63, 0.72 and 0.41 for the Optison, phospholipid native and phospholipid centrifuged populations, respectively.
limit statistics, the expected scattered pressure amplitude is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pX 2 (8) jPi ðuk Þj jPðuk Þj 5 4 i where P2i ðuk Þ is the Fourier amplitude of the scattered pressure from microbubble i at frequency uk. Spatial populations of microbubbles were simulated by randomly attributing a spatial location to each bubble (affecting the phase of the scattered pressure). The radius was assigned according to a Gaussian probability distribution function with mean mR and standard deviation sR. An elastic shell model was used to study the effect of radius probability distribution, independent of surface tension effects. The coefficient of variation (CoV 5 sR/mR, dimensionless) was also introduced to normalize and quantify the spread of the microbubble size distributions.
RESULTS Simulation of effect of blood pressure on bubble resonance A viscoelastic bubble exhibits both elastic (constant elastic modulus) and viscous behavior. A simulation of a viscoelastic bubble, according to the de Jong model, is provided in Figure 5 for the pressure response to a series of narrowband pulses. The same effects as those predicted by the linear theory are observed: the resonance frequency is slowly shifted toward higher values as static pressure is increased (6 kHz per 10 mmHg, as illustrated in Fig. 7a). In addition, the resonance frequency weakly increases with increasing acoustic pressure, which causes small deviations (4% to 10%) from the linear model prediction of the resonance frequency resulting from
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Fig. 5. Simulation of the variation in echo pressure amplitude (each color scale normalized to its own maximum) with respect to static pressure of a viscoelastic bubble for both fundamental (left) and second harmonic (right) using the full equation of motion (3-mm radius, c 5 0.54 N/m). The microbubbles were driven using 17-cycle pulses with varying center frequencies (x-axis) and acoustic pressure, Pac (y-axis). The resonance frequency of the fundamental increases slowly with static fluid pressure. Acoustic pressure has only a weak effect on the resonance frequency.
non-linear effects. The second harmonic (i.e., the echo at twice the insonification frequency) scattered by the microbubbles becomes stronger as the acoustic pressure is increased. For fixed pressure, the second harmonic is maximum if the driving frequency lies between ½f0 and f0. In resemblance to the fundamental, this value also slowly increases with static fluid pressure. In contrast, phospholipid bubbles cannot be considered as purely viscoelastic at large driving pressures because they buckle and rupture at specific radius thresholds, and so the full Marmottant surface tension model must be used. Simulations of the Marmottant equation of motion with respect to frequency, acoustic pressure and static fluid pressure are provided in Figures 6 and 7b. At low acoustic pressures, simulations agree well with linear theory; the resonance frequency decreases quickly (410 kHz per 10 mmHg) as the transition regime is reached. At moderate acoustic pressures, the resonance frequency is considerably downshifted because the finite oscillations of bubbles reach the buckling radius (Figs. 6
and Fig. 7b). Such behavior is not predicted by linear theory, but a qualitative explanation is that as a bubble stays a fraction of its oscillation in the buckled state, it experiences a lower net elasticity c over a full cycle. This effect causes the microbubble to become a very poor manometer (5 kHz per 10 mmHg, refer to Fig. 7) if Pac is increased over a fixed threshold. In the studied case, a shift is observed for acoustic pressures as low as 40 kPa because the elastic regime covers a very narrow radius span. This result seems to agree with the experimental observations of Overvelde et al. (2010) that an increase in acoustic pressure also decreases the resonance frequency in microbubbles with non-linear shell properties. The linear approximation used in Figure 2 is valid only for low acoustic pressures (,40 kPa in this case), where finite oscillation effects can be safely neglected. Incidentally, the second harmonic response is maximal when the bubble is driven roughly at half of the fundamental resonance frequency of an unshelled microbubble for moderate to high acoustic pressures (Fig. 6). Finite
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Fig. 6. Simulation of the fluid static pressure-dependent response from a buckling bubble. The hydrostatic pressures used are 0 mmHg (non-buckled), 38 mmHg (transition) and 413 mmHg (buckled). R0 5 2.94 mm, Rbuck 5 2.92 mm, c0 5 2.55 N/m, z 5 5 kN/m. At low acoustic pressure, increasing the static pressure forces the bubble into a buckled state, causing a steep decrease in resonance frequency. Further increase in acoustic pressure can also cause a microbubble, initially in the elastic regime at rest, to buckle over its oscillation cycle, which also lowers the net resonance frequency (refer to P0 5 0 mmHg).
Fig. 7. Simulation of the effect of pulse pressure on the response of phospholipid microbubbles to static fluid pressure. (a) Viscoelastic model: At low acoustic pressure (Pac 5 3 kPa, solid), the resonance frequency changes by 0.008 MHz per 10 mmHg, whereas it changes by 0.006 MHz per 10 mmHg at Pac 5 350 kPa (dashed line). (b) Phospholipid microbubble: At low driving pressures, the microbubble responds well to pressure (0.41 MHz per 10 mmHg at Pac 5 3 kPa and 0.30 MHz per 10 mmHg at Pac 5 30 kPa). Finite oscillation effects cause the microbubble to become a poor manometer over a certain driving pressure (0.005 MHz per 10 mmHg at 40 kPa in this case), at which the microbubble starts to buckle within each oscillation. R0 5 2.94 mm, Rbuck 5 2.92 mm, c0 5 2.55 N/m, z 5 5 kN/m.
Absolute BP measurement using microbubbles d C. TREMBLAY-DARVEAU et al.
buckling is always dominant at these acoustic pressures, which reduces the resonance frequency close to that of an unshelled microbubble. If the hydrostatic pressure is such that the bubble rest radius is within the transitional regime, a strong second harmonic component exists at very low acoustic pressure (1–10 kPa). Because second harmonics are usually very weak at such low acoustic pressure, this emission peak can be used as a selective marker for transitional buckling. In vitro measurement of effect of blood pressure on microbubble resonance Pulse-echo spectroscopy was performed on phospholipid- and protein-shelled microbubbles (using populations of different size distributions) for different hydrostatic pressures. The resonance frequency was extracted from the resonance spectra and plotted against hydrostatic pressure (Fig. 8). The standard error on the mean resonance frequency (error bars in Fig. 8) was estimated by propagating the error of the resonance spectrum to the maximum value. The error on the resonance frequency is associated with the uncertainty in determining the resonance frequency of a low-quality-factor resonance peak from the averaged speckle noise. The resonance frequency of both size-filtered and non-size-filtered phospholipid microbubble populations was significantly reduced as static pressure was increased (p-value 5 0.02 between 16 and 77 mmHg for the centrifuged populations and p-value 5 0.005 between 3 and 103 mmHg for the native microbubble population). The mean variations
Resonance Frequency [MHz]
4.6 4.4
Native generic phospholipid Centrifuged generic phospholipid Optison
*
4.2
*
4 3.8 3.6
783
in resonance frequency were 0.24 6 0.09 and 0.11 6 0.03 MHz per 10 mmHg for the size-filtered and native populations, respectively, in the region 0 to 52 mmHg (refer to Fig. 8 and Table 1). This dependency eventually reaches a plateau for large hydrostatic pressures, which is expected because all bubbles should buckle at high enough static pressures. As a result, the sensitivity is lowered to 0.08 6 0.02 and 0.07 6 0.02 MHz per 10 mmHg for the size-filtered and native populations, respectively, if a 0 to 100 mmHg region is considered. No significant shift in the resonance frequency of protein microbubbles was detected (p 5 0.48). All pvalues (two-tailed) were estimated using an unpaired ttest. Shell effects dominated the static pressure response of phospholipid microbubbles such that the resonance frequency shifts observed were well within the target pressure range, even for polydisperse microbubbles. This confirms that phospholipid-shelled microbubbles are much more sensitive to blood pressure than proteinshelled microbubbles. Moreover, as the hydrostatic pressure was relaxed to ambient pressure, the resonance frequencies for both native and centrifuge-filtered lipid microbubbles were restored to values slightly higher than their initial values. This suggests that the effect of hydrostatic pressure on the bubble is reversible. The echo spectra from phospholipid microbubbles were measured for increasing values of acoustic pressure. As acoustic pressure was progressively increased from 111 to 225 kPa, the resonance frequency peak shifted from 4 to 2.3 MHz (see Fig. 9). This shift, also present in simulations, occurs because the microbubble experiences part of its oscillation in a buckled state if subjected to a moderate acoustic pressure. This result agrees qualitatively with the observations of Overvelde et al. (2010), and indicates that the acoustic pressure, beyond a certain insonification amplitude threshold, affects the response from phospholipid microbubbles. The measured threshold is higher (between 111 and 225 kPa) than the predicted value from simulations (40 kPa). This
3.4
Table 1. Sensitivity of resonance frequencies of different bubble populations to static pressure variations*
3.2 3
0
20
40 60 80 100 120 Additional static pressure [mmHg]
140
160
Fig. 8. Experimental pulse-echo measurement of the variation in resonance frequency as a function of static pressure for different microbubble shells. The variation in resonance frequency between 3 and 103 mmHg was statistically significant for the native microbubbles (p 5 0.005) and also significant for centrifuge-filtered microbubbles (p 5 0.02) between 16 and 77 mmHg, but not statistically significant for Optison (p 5 0.48) for the interval 0 to 107 mmHg. Error bars with asterisks were obtained after the pressure in the cell was relaxed. The trend line for each population is also a solid line. Number of replicates 5 250.
Resonance frequency shift (MHz per 10 mmHg) Microbubble type
0 to 52 mmHg region
0 to 113 mmHg region
Optison Generic phospholipid centrifuged Generic phospholipid native
0.00 6 0.02 –0.24 6 0.09 –0.11 6 0.03
–0.008 6 0.011 –0.08 6 0.02 –0.07 6 0.02
* Values were obtained from data in Figure 8. Although the proposed technique is sensitive enough for application in portal vein pressure measurements, it still suffers from some reproducibility issues related to large experimental errors.
Fundamental Response [A.u.]
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120
Pac = 65 kPa Pac = 111 kPa
100
P
ac
= 225 kPa
Pac = 335 kPa
80 60 40 20
2
3
4
5
Excitation frequency [MHz]
6
Fig. 9. Variation in backscattered response (fundamental) as a function of the driving frequency from filtered microbubbles with increasing acoustic pressure. The resonance frequency is shifted toward lower values because of the buckling of phospholipid bubbles. The peak negative acoustic pressures used were 65 kPa (solid line), 111 kPa (dashed line), 225 kPa (dotted line) and 335 kPa (dashed-dotted line). Number of replicates 5 500.
difference is reasonable considering that very little is known about the actual value of surface tension at rest within the microbubble population, which directly affects the buckling radius. Effect of size distribution in microbubble populations on blood pressure measurement The dependence of resonance frequency on static pressure is not identical for centrifuge size-filtered and native microbubbles in Figure 8, introducing the important question of reproducibility between different population measurements. At 0 mmHg, the centrifuge-filtered bubbles had a higher resonance frequency than native microbubbles, with a steeper dependence on blood pressure. As static pressure was increased between 25 and 100 mmHg, however, resonance frequency dropped faster
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for native phospholipid microbubbles than for centrifugefiltered microbubbles. It is expected that these variations were due to the statistical spread of the bubble radius and shell properties, such as surface tension. All commercially available ultrasound contrast agents contain microbubbles of different sizes (probability distribution function PDFR) and shell properties (in particular the surface tension at rest, with probability distribution PDFS). As seen in Figure 8, increasing the spread in the size distribution of microbubbles in particular (through PDFR) affects the resonance frequency of microbubbles. The resonance frequency of a microbubble is specific to its radius and will decrease with an increase in microbubble radius. This distorts the resonance peak and shifts the resonance frequency as a population becomes more polydisperse. Shifts in resonance frequency cause systematic errors in static pressure measurements. A bubble population echo spectrum is also smeared by compounding peaks of different center frequencies, which artificially decreases the quality factor (Q 5 f0/FWHMf) of the resonance peak. A less defined resonance peak causes an increase in the random error of the resonance frequency measurement, thereby reducing our accuracy in measuring pressure. It is expected that these effects should become negligible as microbubbles are made more uniform in their radii. To determine the extent of homogeneity in the radius size distribution required to minimize these statistical effects, the linear echoes from populations of 1000 microbubbles following Gaussian radius distributions (PDFR f exp [-(R – mR)2/2s2R ]) centered around mR 5 2, 4 and 6 mm were calculated for increasing values of the standard deviation. As seen in Figure 10(a, c), the quality factor, Q, was found to decrease quickly as the CoV of the bubble population increased. A CoV of 0.06 will cause the quality factor to decrease by 25%, which causes significant broadening of the resonance peak. Shifts in the resonance frequency of 1% are observed at CoVs . 0.10. On the basis of these simulation results,
Fig. 10. Effect of bubble size distribution on the scattered signal by changing the standard deviation of a Gaussian population size distribution with 4.0-mm mean radius. The shift in resonance frequency (b) and decrease in quality factor (c) were computed from the scattered pressure (a) for microbubble populations of increasing coefficient of variation (CoV) and various mean radii.
Absolute BP measurement using microbubbles d C. TREMBLAY-DARVEAU et al.
a CoV of 0.10 is required to avoid systematic error due to the shift of the resonance frequency, and a CoV of 0.06 should be targeted to minimize the statistical error associated with resonance peak broadening due to microbubble radius distribution. DISCUSSION It has been found through both simulation and experiment that buckling-type phospholipid microbubble resonance frequencies are much more dependent on hydrostatic pressure than those of simpler viscoelastic shells such as protein microbubbles. The variation in resonance frequency for phospholipid microbubbles is high enough for realistic application to portal vein hypertension diagnosis. Most of the static pressure effects on phospholipid microbubbles are attributed to the shell dynamics (radiusdependent elasticity, in particular), as opposed to the gas dynamics, of viscoelastic microbubbles. In particular, this occurs because of the non-linearity of the surface tension function, s(R), which causes large variations in the shell’s elasticity (ceff(R) 5 ½R0[ds/R]│R0 ). We may infer that other strongly non-linear shells, such as nanoparticle-coated microbubbles (Stride et al. 2008), could present an analogous sensitivity to blood pressure. Our results also indicate that changes in the resonance frequency of lipid-shelled microbubbles are reversible. Moreover, although it was previously known that the sub-harmonic amplitude of phospholipid microbubbles can be used to measure blood pressure (Forsberg et al. 2005; Frinking et al. 2009, 2010), the absolute blood pressure can be measured only by tracking changes in the resonance frequency (directly related to shell elasticity), as indicated in this work. In particular, eqn (5) can be inverted for P0 as long as the physical properties of the microbubbles (e.g., surface tension, radius) are known. At the moment, clinically available microbubble contrast agents are produced mainly by sonication, a method with poor reproducibility, which results in a highly variable size distribution (CoV .. 0.10) and, as a consequence, causes large variations in resonance frequency. Although it reduces the CoV, centrifugation of the microbubbles is not selective enough to reach the 6% threshold (a CoV of 0.41 was achieved in this study). To overcome this limitation, a three-inlet microfluidic system can instead be used to produce almost monodisperse microbubbles (Seo et al. 2010). Perfluorocarbon gas is injected at high throughput in the central channel, and the aqueous shell solution is injected through both upper and lower channels. The microfluidic microbubbles are formed in a small nozzle at the intersection of the inlets, where both immiscible phases mix. Depending on the flow rate and size of the nozzle used, the bubbles will have different diameters and coefficients of variation.
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According to Seo et al. (2010), the coefficients obtained are always smaller than 0.06. In addition, two bubbles of identical size may respond very differently to the same acoustic pulse depending on the concentration of the surfactants in their shells (Sijl 2009), which directly affects shell surface tension. It is expected that within a population, the concentration of surfactant will vary for each bubble, and therefore, we should expect each of them to have a slightly different buckling radius. The extent of the statistical fluctuations of buckling radius within a bubble population remains to be quantified experimentally. The phospholipid concentration of a single microbubble might also be affected by ultrasound exposure through mechanisms such as lipid shedding (O’Brien et al. 2011). The behavior of phospholipid-shelled microbubbles may also differ in blood compared with simpler in vitro media such as water and saline. A self-assembly process that would allow control of surface tension for bubble populations has been proposed by Marmottant et al. (2005). It has been observed that bubbles at rest, even in a saturated atmosphere, deflate quickly after being created, but become much more stable as the buckling radius is reached. Gas diffusion outward from the microbubble occurs because the gas pressure inside of the bubble is always higher than the partial gas pressure of the surrounding liquid due to surface tension (a quantitative formulation of this phenomenon was given by Epstein and Plesset [1950]). It is therefore expected that within an old population (possibly a matter of minutes), bubbles are expected to shrink very close to their buckling radius, no matter their initial radius or surface tension at rest. Bubbles close to their buckling radius are very sensitive to any additional static pressure applied, which could explain why an entire population with a polydisperse size distribution of microbubbles seems to buckle at low static pressure (Fig. 8) and potentially provides a way to control the buckling radius in microbubble populations. Even considering the current intrinsic limitations of microbubble populations of polydisperse radii and surface tension at rest, a significant shift in the resonance frequency with increasing hydrostatic pressure was observed for phospholipid-shelled microbubbles. The sensitivity of these microbubbles to hydrostatic pressure is also expected to improve as microbubble physical properties become more controlled and optimized. As long as the physical properties of the microbubbles are known, the blood pressure could then be estimated directly using eqn (5). This method could be adapted to clinical scanners and provide a non-invasive blood pressure measurement deep in the body (where conventional sphygmomanometry techniques cannot be used). In particular, the proposed method would have important value
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in the diagnosis of portal vein hyper-pressure, where the gold standard for diagnosis of portal hypertension relies solely on the symptoms (Child-Pugh score) and not directly on pressure values, making any early diagnosis of the disease very difficult. CONCLUSIONS It has been found that hydrostatic pressure affects the resonance frequencies of phospholipid-shelled microbubbles more than viscoelastic-shelled microbubbles, because of the buckling dynamics of phospholipid monolayers. This remains valid as long as the acoustic pressure is kept below a fixed threshold (between 111 and 225 kPa in this case), above which the bubble will start to undergo periodic buckling because of finite size oscillations. Experiments suggest that the method should be sensitive enough for clinical application, in particular in portal vein hypertension diagnosis, because maximal variations in the resonance frequency ranging from 0.07 6 0.02 to 0.24 6 0.09 MHz per 10 mmHg have been measured for phospholipid microbubbles, whereas no significant shift has been observed for protein microbubbles. Current measurements of the resonance frequency from bubble populations (CoVs . 0.10) suffer from poor reproducibility because the inhomogeneity of the properties within a microbubble population causes bias in the net resonance frequency measured. In particular, it has been found that reproducibility can be improved by reducing the variability in microbubble radii below a CoV of 0.06. Such a CoV could be achieved using a microfluidic-based system to produce microbubbles, instead of the sonicationbased technique currently used. Acknowledgments—This work has been supported by the Natural Sciences and Engineering Research Council of Canada, the Ontario Graduate Scholarship Program and the University of Toronto. We thank Don Plewes, Richard Cobbold, Ahthavan Sureshkumar, Brendan Lloyd, Emmanuel Cherin, David Goertz, Peter Bevan, Nikita Reznik, John Hudson, Kogee Leung and Minseok Seo for illuminating discussions as well as the support given in the completion of this project.
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