Ultrasound Perfusion Imaging: Techniques and Analytical Methods
Emilio Quaia, MD
▪ Introduction
The ability to accurately quantify tissue perfusion—blood flow equalized for the volume or weight of the perfused tissue (cm3/s/cm3 or grams)—is essential for the assessment of the physiologic functionality and viability of a tissue. Different parameters are related to tissue perfusion including blood velocity (cm/s), the speed of red blood cells in the region analyzed, blood flow (cm3/s), the volume of blood passing in a section of tissue per unit of time, the fractional vascular volume (cm3), and the proportion of tissue volume occupied by blood.
Single photon emission computed tomography (SPECT), positron emission tomography (PET), multidetector computed tomography (CT), and magnetic resonance (MR) imaging all quantify tissue perfusion accurately.
PET with (15)O-water, (13)N-ammonia, (82)RbCl, or (62)Cu-ETS and imaging techniques, MR and CT, with contrast administration represent valuable tools to assess noninvasively organ perfusion. However, the utility of PET is limited because of the short half-life of most of the radiolabeled tracers.
MR advantages include absence of ionizing radiations, high spatial resolution, and use of intravascular agents (high serum albumin binding). MR limitations include the nonlinear relation between signal intensity (SI) and gadolinium concentration at high concentrations due to concomitant reduction of T1 and T2★ (use < 0.1 mmol/kg usually 0.0125 mmol/kg), the gadolinium contrast that should be avoided when GFR is less than 30 mL/min/1.73 m2, the difficulty of measuring the arterial input function, and limited availability for perfusion studies.
CT advantages include direct and constant linearity between renal tissue attenuation and the concentration of contrast medium. Advanced scanners are available (EBCT or MDCT) allowing a high temporal resolution. CT limitations include radiation and iodinated agents and limited use in renal failure.
Unenhanced ultrasound (US) is not useful for organ perfusion quantification, while color Doppler and power Doppler are limited by the low sensitivity to low-velocity flow in smaller vessels (<2 mm in diameter). Dynamic contrast-enhanced ultrasound (CEUS) can be used to quantify microbubble enhancement and has recently been proposed as a new imaging technique for quantifying tissue perfusion.1 CEUS is an imaging modality that presents several advantages, including low financial cost, portability, availability, lack of restrictions in performing frequent serial examinations at short intervals, real-time assessment of mural enhancement after contrast injection, absence of radiation exposure, the use of blood pool contrast agents, and absence of usage of potentially nephrotoxic contrast agents.
▪ Ultrasound Technology
In the last decade, the image quality in US had important improvements due to technology advancements particularly in the new array transducers with a high number of elements, in the US systems with numerous focus lines, and in the computer processing power corresponding to a powerful beamformer with higher resolution and higher dynamic range in the images. The most important technologic advances in the US field were introduced in the signal transmission process, in the signal reception process, in compounding and equalization, in color and power Doppler, and in the 3D and elastographic imaging.2
Signal Transmission
In the signal transmission process, the transducer arrays, formed by ceramic polymer composite elements of variable shape and thickness, and the multilayered technology led to a more accurate shaping of the US pulses in terms of frequency, amplitude, phase, and length. The development of piezoelectric crystals with a lower acoustic impedance and greater electromechanical coupling coefficients, the improvement of the physical characteristics of the absorbing backing layers, and the quarter-wave impedance matching layers represent the most significant results of the US transducer research.2
Increased bandwidth of transducers allows a better spatial and contrast resolution with a consequent improvement of the axial resolution due to shorter pulse length. Shorter transmission pulses used in a broadband emission generates shorter echo pulses that can be faithfully converted into electric signals. Since short pulses are attenuated to a greater extent and are characterized by less penetration than long pulses, specific techniques have been introduced by the different manufacturers to allow a more accurate shaping of the US pulse in terms of the control of the transmission frequency, amplitude, phase, and pulse length. Phase can only be determined by the comparison with a reference waveform or with another pulse. This can be achieved by using multiple beamformers allowing the
direct integration of the phase information from the signal received from the adjacent lines.2 Another way to improve penetration is by increasing the output power, even though it is limited by safety limits, or by utilizing excitation signals much more sophisticated than the single-carrier short pulses currently used in the US scanners. These signals are usually defined coded excitation and increase the signal-to-noise ratio and the frame rate. In coded-emission mode, the scanner transmits not a single pulse but a sequence of 8 to 22 short, high-frequency transmission pulses that may have different phases and are modulated in a code sequence. Comparison between transmitted pulses and received signal shapes using matched filtering (decoding) is subsequently performed with a very high sampling rate.2 In chirp encoding, a long specially shaped pulse is transmitted with frequency and amplitude progressively varied. The matched filtering process involves comparing the echoes with a stored reference version of the transmitted chirp. When the two waveforms present identical shape but different amplitude, they are out of alignment and the output of the process is low. The filter output is a large-amplitude compressed pulse for every match between a genuine chirp echo and the reference chirp.
direct integration of the phase information from the signal received from the adjacent lines.2 Another way to improve penetration is by increasing the output power, even though it is limited by safety limits, or by utilizing excitation signals much more sophisticated than the single-carrier short pulses currently used in the US scanners. These signals are usually defined coded excitation and increase the signal-to-noise ratio and the frame rate. In coded-emission mode, the scanner transmits not a single pulse but a sequence of 8 to 22 short, high-frequency transmission pulses that may have different phases and are modulated in a code sequence. Comparison between transmitted pulses and received signal shapes using matched filtering (decoding) is subsequently performed with a very high sampling rate.2 In chirp encoding, a long specially shaped pulse is transmitted with frequency and amplitude progressively varied. The matched filtering process involves comparing the echoes with a stored reference version of the transmitted chirp. When the two waveforms present identical shape but different amplitude, they are out of alignment and the output of the process is low. The filter output is a large-amplitude compressed pulse for every match between a genuine chirp echo and the reference chirp.
Electronic focusing, obtained by activating a series of elements in the array with appropriate delay, can easily be used to regulate the focal depth. The higher the number of channels involved to activate the array elements in a combined mode and with the appropriate delays, the more accurately the US beam can be focused. In the dynamic transmit focusing modality, edge crystal elements have a longer pulse excitation than center elements, making the US beam focus at two different points in the insonated field, improving lateral resolution. As the resulting wave front has the characteristics of a short excitation pulse, the axial resolution is preserved.2 The spatial and contrast resolution of the US image had a further improvement due to matrix transducers, which allows a further reduction in the thickness of the US beam with better spatial resolution.
Signal Reception
Tissue harmonic imaging has allowed a further improvement in the signal-to-noise ratio and image quality due to the improved contrast resolution and speckle and artifact reduction even in patients with a limited explorability including obese patients. Harmonic imaging requires large transducer bandwidth and that the system is configured to receive preferentially harmonic components produced by tissues, hence at double the transmitted frequency, by a high-pass filter, and to cancel out the fundamental echo signals generated directly from the transmitted acoustic energy. Such filtering is successful in eliminating echoes from solid stationary tissues that present prevalently linear properties, even though the effect is to reduce the range of frequencies (or bandwidth) contained in the received echoes, causing a low spatial axial resolution of the resulting image. Harmonic imaging and speckle reduction techniques have improved signal-to-noise ratio and image quality also in patients who are difficult to explore by US, such as obese or largebody-habitus subjects.
Compound Imaging and Equalization
Compound imaging may be obtained by spatial (transmit compounding) or frequency compound. In spatial compound imaging, the same insonated slice is interrogated according to different insonation angles, while in frequency compound imaging, the same slice is insonated more times with different frequencies. The resulting images are managed by subtracting step by step all echoes, which appears incoherently in the different acquired images, corresponding essentially to noise. Compound imaging allows a reduction of speckles, clutter, and noise, without compromising other beneficial image characteristics such as spatial resolution, and improves contrast-to-noise ratio and better depiction of the curved surface such as the renal poles. Compounding also reduces shadowing from strongly reflecting interfaces such as organ boundaries, fascial planes, and vessel walls.
Tissue equalization is based on regional and adaptive methods to analyze, using regional speckle statistics and thermal noise identification, and applies an algorithm to perform region-by-region adjustment to lateral gain, depth gain, and overall gain.2
Color and Power Doppler
The color and power Doppler techniques have reached a high sensitivity for the renal parenchymal flows. In particular, the introduction of wideband Doppler technology, making use of short pulses, has led to some advantages in imaging subtle blood flows due to the improved frame rate and axial resolution. Differently from color Doppler, the sensitivity of power Doppler for the renal flows is not dependent from the angle of insonation. Moreover, power Doppler has a higher sensitivity than color Doppler for the renal parenchyma flow in particular at renal poles. The introduction of wideband color Doppler (e.g., advanced dynamic flow) has improved the sensitivity and contrast resolution for the flow signal of the renal parenchymal vessels up to the interlobular vessels, which can be imaged with a 2- to 5-MHz convex US transducer. 3D US (volume sonography), elastography, and microbubble contrast agents represent further advancements in US.
3D Imaging
3D US acquisition is obtained by using multidimensional matrix transducers with parallel processing of the signal. Digitally stored volume data can then be displayed in a multiplanar array that simultaneously shows three perpendicular planes throughout the volume: axial, sagittal, and reconstructed coronal views. The volume can be explored by scrolling through parallel planes in any of the three views and by rotating the volume to obtain an optimal view of the structure of interest.2 Data can also be displayed as true 3D images using various rendering algorithms, including maximum-intensity projections and surface renderings.
▪ Microbubble Contrast Agents
Microbubble contrast agents are hemodynamically inert, remain entirely intravascular, and also have the same rheology as red blood cells. Although larger microbubbles produce much greater acoustic signals, their maximum size is limited by the diameter of the capillary so that intravenously administered agents may cross the pulmonary microcirculation—which is approximately 5 µm. The limitations of a small microbubble became evident with the first commercial air-filled microbubble agent that was made by sonication of a solution of 5% human albumin. The mean microbubble size of 4.3 µm allowed it to clear the pulmonary circulation following an intravenous injection, but the air rapidly diffused out along the concentration gradient into the surrounding blood, with a resultant decrease in bubble size and backscatter signal. This inevitably meant that by the time the microbubbles had cleared the pulmonary circulation, their ability to opacify the myocardium was already substantially diminished. Therefore, the majority of studies using this agent for myocardial perfusion relied on direct intracoronary injections.
The need to improve microbubble persistence in the circulation was eventually overcome by the incorporation of high molecular weight gases with low diffusibility and solubility or by the use of gas-impermeable polymer shells into new-generation microbubbles. The gas proved to diffuse out of the microbubbles at
a much slower rate, which meant that microbubbles had the ability to maintain their size and significantly increase their half-life within the circulation. The new-generation microbubbles currently approved for clinical use in the United States share a number of similarities in that they are composed of a thin shell that enclose a core of perfluorocarbon gas. A number of other microbubbles are in various phases of development and approval.
a much slower rate, which meant that microbubbles had the ability to maintain their size and significantly increase their half-life within the circulation. The new-generation microbubbles currently approved for clinical use in the United States share a number of similarities in that they are composed of a thin shell that enclose a core of perfluorocarbon gas. A number of other microbubbles are in various phases of development and approval.
Apart from their stability, microbubble contrast agents possess a number of unique properties that distinguish them from tracers used with other noninvasive imaging technologies. The microbubbles remain entirely intravascular, unlike nuclear tracers such as thallium or 99mTc-sestamibi, which are extracted by myocytes, or radiologic contrast agents for CT or gadolinium tracers for MR imaging that diffuse into the interstitial space. Consequently, microbubble contrast agents are the ideal tracers of red blood cell kinetics and to assess organ perfusion. The microbubbles are also hemodynamically inert, so they do not affect local or systemic blood flow. By comparing the transit of microbubbles with Tc-labeled red blood cells, or by direct visualization of fluorescently labeled microbubbles and red blood cells, the in vivo myocardial kinetics and rheology of microbubbles have been shown to be very close to that of red blood cells.
Nowadays, microbubble contrast agents for ultrasound (US) (Table 10.1) have a diameter of 2 to 6 µm.3 The microbubble shell may be stiff (e.g., denatured albumin) or flexible (phospholipids) and has a thickness of 10 to 200 nm. New-generation microbubbles are filled with a high molecular weight gas (e.g., perfluorocarbon or sulfur hexafluoride) with low solubility in the bloodstream. Microbubbles have a purely intravascular distribution even though some agents present a postvascular hepato- and/or splenospecific phase beginning 5 minutes after intravenous injection and lasting from 15 minutes up to 1 hour after injection.3 The microbubble gas content is exhaled via the lungs 10 to 15 minutes after injection, while the components of the shell are metabolized by the liver or filtered by the kidney and eliminated by the liver. Adverse reactions in humans are rare, usually transient, and of mild intensity.4 Hypotensive reactions have been observed after microbubble injection, and some deaths have been reported in cardiac patients.
At resonant frequency (fo), the microbubble radial oscillation becomes efficient and exaggerated5; the scattering cross section of a microbubble is no longer simply dependent on microbubble size and can reach peak values a thousand times higher than values at off-resonance. The insonation power is usually expressed by the mechanical index (MI) defined as 
where p— is the largest peak negative pressure and f is the center frequency of the pulse. When acoustic pressures at or near the resonant frequency are sufficiently high, nonlinear microbubble oscillation develops, producing harmonic frequencies.
where p— is the largest peak negative pressure and f is the center frequency of the pulse. When acoustic pressures at or near the resonant frequency are sufficiently high, nonlinear microbubble oscillation develops, producing harmonic frequencies.Innovative US techniques, named contrast-specific modes or techniques,6 were introduced to register selectively the harmonic signal produced by the nonlinear physical behavior of microbubbles and to distinguish microbubble signal from tissue clutter. This was determined by the impossibility of traditional color and power Doppler to manage the harmonic signals produced by microbubble insonation, since they are limited by the strong presence of artifacts including the blooming and jail bar artifacts. Pulse inversion is the best-known phase modulation technique. Vascular recognition imaging combines Doppler information with phase analysis and involves the transmission of four, alternately inverted, pulses along each imaging line. Cadence contrast pulse sequencing works by interrogating each imaging line a number of times with pulses with various amplitudes and phases. Both harmonic and nonlinear fundamental signals from microbubbles are represented on a grayscale or color map suppressing the linear fundamental echoes from native tissues.
▪ Chemical Composition of Microbubble Contrast Agents
Microbubble contrast agents are now approved in most European countries and are largely employed also in Asia and Canada. The Food and Drug Administration in the United States has not yet approved microbubble contrast agents for noncardiac use. The recently introduced sulfur hexafluoride or perfluorocarbon-filled microbubbles (Table 10.1) offer both an excellent safety profile and a longer persistence in the peripheral circle than air-filled microbubbles. Microbubble contrast agents are composed by a shell of biocompatible material such as a proteins, lipids, or biopolymers. Microbubble contrast agents are injectable intravenously and can pass through the pulmonary capillary bed after a peripheral injection, since their diameter (3 to 10 µm) is below that of red blood cells.
Two principal strategies were developed to increase microbubble stability and persistence in the bloodstream: the stability in the peripheral bloodstream of the external microbubble encapsulation
and the selection of filling gases with a low diffusion coefficient. The peripheral shell presents a thickness ranging from 10 to 200 nm and may be stiff (e.g., denatured albumin or biopolymers) or more flexible (phospholipids). Low-solubility low-diffusibility gases, such as perfluorocarbons and sulfur hexafluoride gas, are employed to improve the persistence of microbubbles in the peripheral bloodstream. The physical properties of microbubble contrast agents are closely related not only to their gas content and to the peripheral shell chemical composition but also to the frequency of the US beam, to the pulse repetition frequency and, overall, to the acoustic power employed for insonation. The different microbubble contrast agents are reported in Table 10.1.
and the selection of filling gases with a low diffusion coefficient. The peripheral shell presents a thickness ranging from 10 to 200 nm and may be stiff (e.g., denatured albumin or biopolymers) or more flexible (phospholipids). Low-solubility low-diffusibility gases, such as perfluorocarbons and sulfur hexafluoride gas, are employed to improve the persistence of microbubbles in the peripheral bloodstream. The physical properties of microbubble contrast agents are closely related not only to their gas content and to the peripheral shell chemical composition but also to the frequency of the US beam, to the pulse repetition frequency and, overall, to the acoustic power employed for insonation. The different microbubble contrast agents are reported in Table 10.1.
TABLE 10.1 Microbubble Contrast Agents Classified According to the Filling Gas | ||||||
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▪ Safety of Microbubble Contrast Agents
The safety of microbubble contrast agents is somewhat complex because not only must their safety as drugs be studied, as with other contrast agents, but additionally, the effects of sonication need to be taken into account. The safety of ultrasound contrast media is the subject of a recent report by the World Federation for Ultrasound in Medicine and Biology.4 The adverse reactions in humans are rare, usually transient, and of mild intensity and include tissue irritation in the vicinity of the injection site, dyspnea, chest pain, hypo- or hypertension, nausea and vomiting, taste alterations, headache, vertigo, warm facial sensation, cutaneous eruptions, and asymptomatic premature ventricular contractions. However, serious allergic reactions have been observed at a very low incidence (estimated to be 1:10,000).
In 2004, the European Agency for the Evaluation of Medicinal Products (EMEA) temporarily withdrew the approval for SonoVue (Bracco, Milan, Italy) for cardiac applications due to three deaths reported in temporal relation with the application of SonoVue. All patients did not present any allergic reaction, but all of them had unstable ischemic heart disease. Nineteen cases of severe, nonfatal adverse events (0.002%) were reported, and most of the cases were considered to be allergic reactions. The EMEA committee recognized a favorable risk/benefit ratio for SonoVue when patients with acute coronary syndromes and unstable heart disease were excluded, and the committee otherwise restored the approval for cardiac indications. Even more recently, the FDA issued a black box warning for Definity in October 2007 due to postmarketing reports of deaths in four patients with significant underlying progressive cardiovascular disease that were temporally related to contrast agent use. On May 12, 2008, and June 6, 2008, revised labeling changes were again implemented for Definity and Optison, respectively, following mounting evidence of safety and unequivocally favorable risk-benefit profile in the acute setting. The present FDA documents state that Definity and Optison are not to be administered to patients in whom right-to-left bidirectional or transient right-to-left cardiac shunts and hypersensitivity to perflutren, blood products, or albumin are known or suspected. SonoVue is contraindicated in patients known to have right-to-left shunts, severe pulmonary hypertension (pulmonary artery pressure >90 mmHg), uncontrolled systemic hypertension, and in patients with adult respiratory distress syndrome. Both Definity and Optison may be used in acute coronary syndromes. SonoVue should be used with special caution in patients with recent acute coronary syndrome or clinically unstable ischaemic cardiac disease. The intra-arterial injection of ultrasound contrast agents also is contraindicated.
Experimental studies on small animals and cell preparation have shown that potential adverse bioeffects from microbubble contrast agents under a US field, including hemolysis, platelet aggregation, disruption of cell membrane, rupture of small vessels, and induction of ectopic heart beats, can be induced under extreme conditions (exteriorized heart preparation, no or minimal attenuation, low-frequency high acoustic pressures, and long pulse durations). The phenomenon of inertial cavitation—the rapid formation, growth, and collapse of a gas cavity in a fluid as a result of US exposure—is considered the cause of most of the microbubble side effects observed in animals in experimental studies, and no evidence of bioeffects from a clinically comparable US exposure and microbubble concentration has been reported in humans. These experimental findings cannot be extrapolated to the clinical setting where the attenuation of ultrasound significantly reduces patient exposure, even though these conditions could be reproduced also in the clinical setting during lithotripsy and focused ultrasound ablation.
▪ Microbubble Persistence in the Bloodstream: Physical Factors
To act as effective contrast agents in the peripheral circulation, microbubble contrast agents have to persist in the bloodstream. Various chemical strategies have been adopted to produce stabilized gas microbubbles in the peripheral circulation, and the different compositions have an important influence upon the performance of the resulting agent.
Diffusibility of the Filling Gas
The first factor that determines the persistence of microbubbles in the peripheral circle is the diffusibility of the filling gas throughout the peripheral shell.5 The diffusibility, expressed by the diffusion coefficient, and the solubility of the filling gas in the blood strongly affect microbubble persistence in the circle, according to the following equation:
where T is the microbubble persistence in the blood, ρ is the density of the gas, R is the initial radius of the microbubble, D is the diffusion coefficient of the gas in the substance of the shell, and Cs is the saturation coefficient of exchange of gas between aqueous and gaseous phases, which is higher in gas with increased solubility in the blood.
Surface Tension
The previous equation is an effective approximation of the microbubbles persistence in the bloodstream. Anyway, the surface tension is another important mechanism responsible for the disappearance of the filling microbubble gas in a gas-saturated liquid.5 The microbubble shell contains surface-active molecules, namely, phospholipids, which act as surfactant reducing the surface tension. The surfactant layer exerts a counterpressure against the tendency of surface tension and other forces to cause gas diffusion from a microbubble. The relation of the surface tension with microbubble dissolution is
where 
is the variation of microbubble radius (R), with time (t), which is related to microbubble disappearance from the peripheral circle; D is the diffusion coefficient of the gas; L is the Ostwald coefficient, which corresponds to the ratio of the amount of gas dissolved in the surrounding liquid and in the gas phase per unit volume; Ci/Cs is the ratio of the dissolved gas concentration to the saturation concentration; ST is the surface tension; and p0 is the ambient pressure. In Eq. (2), the surface tension is showed to strongly affect the dissolution of microbubbles, and the higher is the surface tension, the lower is the microbubble persistence.
is the variation of microbubble radius (R), with time (t), which is related to microbubble disappearance from the peripheral circle; D is the diffusion coefficient of the gas; L is the Ostwald coefficient, which corresponds to the ratio of the amount of gas dissolved in the surrounding liquid and in the gas phase per unit volume; Ci/Cs is the ratio of the dissolved gas concentration to the saturation concentration; ST is the surface tension; and p0 is the ambient pressure. In Eq. (2), the surface tension is showed to strongly affect the dissolution of microbubbles, and the higher is the surface tension, the lower is the microbubble persistence.Osmotic Pressure of the Filling Gas
The stability of a microbubble in the peripheral circle is related to the osmotic pressure of the filling gas, which counters the sum of the surface tension and blood arterial pressure5:
where CG and CA are concentrations of the filling gas (G) and air (A), K is the gas constant, T is the absolute temperature, ST is the surface tension, R is the bubbles radius, pb is the systemic blood pressure, and patm is the atmospheric pressure (101 kPa). The limited solubility in blood determines an elevated vapor concentration in the microbubble relative to the surrounding blood and establishes an osmotic gradient that opposes the gas diffusion out of the microbubble. After the initial size adjustment due to the effect of body temperature, the microbubbles will either swell or shrink depending on the partial pressure of the air in the bubble, followed by a period of slow diffusion of gas into the bloodstream.
Diffusion and Ostwald Coefficients
Also, diffusion and Ostwald coefficients strongly determine the rate of decrease of the bubble radius, which is a direct measure for the disappearance rate of the microbubble:
where CG and CA are concentrations of the filling gas (G) and air (A); R is the bubbles radius; DG, Da and LG, La are diffusion and Ostwald coefficients, respectively, for the filling gas (G) and the air (A); patm is the atmospheric pressure (101 kPa); K is the gas constant; and T is the absolute temperature. From Eqs. (4) and (5), it can be derived that the diffusion and Ostwald coefficients determine the rate of decrease of the bubble radius, which is a direct measure for the disappearance rate of the microbubble. Thus, microbubble filled with gases having lower diffusion and/or Ostwald coefficient will persist longer in the bloodstream.
Nature of the Peripheral Capsule
The nature of the encapsulating shell is the last fundamental factor, which affects microbubble persistence in the bloodstream.5 Of course, the more stable is the peripheral shell or the less is its solubility in the water, the longer is the microbubble persistence and the echo-enhancing effect. Galactose-covered microbubbles present a low persistence for the high solubility of the sugar in the water. New-generation microbubble-based agents present an albumin or lipid shell, which presents a low solubility in the water, further improving microbubble persistence in the bloodstream and the effect of scattering.
▪ Physical Basis and Principles of Action of Microbubble Contrast Agents
Resonance Frequency
Encapsulation of microbubbles affects their ability to oscillate, due to the presence of viscoelastic damping effects determined by the shell, which influence the microbubble acoustic properties. To produce effective backscattering, microbubbles have to be insonated by their characteristic resonance frequency, and the exposure to US at their resonance frequency forces microbubbles to contract and expand their diameter severalfold.5 At low acoustic power, microbubbles produce a US signal with the same frequency as the sound that excited them. By increasing the acoustic power of insonation, microbubbles exhibit nonlinear vibrations at their resonance frequency (f0) generating signals at f0, harmonics (2f0, 3f0, 4f0, etc.), and subharmonics (f0/2, f0/3, etc.). At further higher acoustic power, the expansion eventually disrupts the microbubbles’ shell generating a wideband harmonic signal similar to a burst.
The resonance—fundamental—frequency (f0) is inversely related to the microbubble diameter, and it may be expressed as
where R is the microbubble diameter, γ is the ideal adiabatic constant of gas, p0 is the ambient fluid pressure, and ρ0 is the density of the surrounding medium. To derive Eq. (6), the damping caused by the surrounding medium is assumed negligible, as no effects due to bubble surface tension or thermal conductivity.
Considering the same model employed for the backscattering of an air-filled microbubble surrounded by a thin elastic shell and taking into account the increased restoring force due to shell elasticity,
where Se is the shell elasticity parameter, which is defined as
where Ri and Ro are the inner (i) and the outer (o) diameters of the microbubble (the difference Ro — Ri is the thickness of the shell); v is the Poisson ratio, which describes the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching acoustic pressure (tensile deformation is considered positive, and compressive deformation is considered negative); and E is the modulus of Young—modulus of elasticity in tension— which describes the stiffness of a microbubble.
According to Eq. (7), the higher is the shell elasticity due to encapsulation, the higher is the resonant frequency, at equivalent microbubble radius. Moreover, the lower is the shell elasticity due to encapsulation, the lower is the generation of harmonics, due to the damping provided by the shell viscosity, which produces a notable decrease in the pulsation amplitude. So, for a stiff and thick shell, the stability in the peripheral blood is higher if compared with a flexible and thin shell, but production of harmonics is lower. In practical terms, for any given US power and frequency, less acoustic signal can be expected from microbubbles with thick, stiff shells. Since microbubble with a thick and stiff shells present an increased resistance to the US acoustic power of insonation, the produced acoustical backscattering signal may be improved simply by increasing the acoustic power of insonation.
Moreover, according to Eq. (7), the ideal resonant frequency for a microbubble is inversely related to the square of its radius. The larger the microbubble radius, the lower the resonance frequency, and the resonance frequency of microbubble with a diameter of few µm is in the low MHz frequency range, which is employed in abdominal US. Specifically, the resonance frequency for phospholipid-coated microbubbles with a diameter of 1 to 5 µm is approximately 3-4MHz.
Backscattering
According to the most accepted physical model describing microbubble backscattering properties, the microbubble is considered coated by a continuous layer of incompressible solid elastic material,
with a spherically symmetric motion, and surrounded by an incompressible liquid, which presents infinite extent and a constant viscosity according to the Newton law. A Newtonian fluid is a fluid in which the shear stress—the ratio of force up to the area subjected to the force—is proportional to viscosity and velocity gradient. The rheologic parameters (surface tension and viscosity) for microbubble-based agents may be calculated. The wavelength of the US field is assumed to be much larger than the microbubble diameter, and only the motion of the bubble surface is of interest. It is assumed that the vapor pressure remains constant during the compression and expansion phase and that there is no rectified diffusion during the short period of exposure to US. The gas in the bubble is assumed to be ideal and compressed and expanded according to the ideal gas law with the polytropic exponent (Γ) remaining constant during vibration.
with a spherically symmetric motion, and surrounded by an incompressible liquid, which presents infinite extent and a constant viscosity according to the Newton law. A Newtonian fluid is a fluid in which the shear stress—the ratio of force up to the area subjected to the force—is proportional to viscosity and velocity gradient. The rheologic parameters (surface tension and viscosity) for microbubble-based agents may be calculated. The wavelength of the US field is assumed to be much larger than the microbubble diameter, and only the motion of the bubble surface is of interest. It is assumed that the vapor pressure remains constant during the compression and expansion phase and that there is no rectified diffusion during the short period of exposure to US. The gas in the bubble is assumed to be ideal and compressed and expanded according to the ideal gas law with the polytropic exponent (Γ) remaining constant during vibration.
The first parameter to be considered in the backscattering is the motion of the microbubble wall:
where ρ is the density of the surrounding liquid medium (=998 kg/m3), R is the instantaneous microbubble radius, 
is the first-time derivative of the radius (the velocity of the microbubble wall), R is the second-time derivative of the radius (the acceleration of the microbubble wall), pL is the liquid pressure at the microbubble wall, and p∞ is the liquid pressure at infinity.
is the first-time derivative of the radius (the velocity of the microbubble wall), R is the second-time derivative of the radius (the acceleration of the microbubble wall), pL is the liquid pressure at the microbubble wall, and p∞ is the liquid pressure at infinity.The assumption is that presence of the microbubble shell completely dominates the motion of the microbubble wall. Therefore, the microbubbles are considered to be elastic particles, which have an effective bulk modulus, Keff, describing the elasticity of the shell and a friction parameter describing the viscosity of the shell.
Bulk Modulus ≈ Elasticity of the Shell
The effective bulk modulus describes the elasticity of the shell. For a spherical volume V deformed by a quasi-static pressure change, ΔP determines the volume change of the microbubble and it is uniform over the microbubble surface. The volume strain (deformation) corresponds to 
, where V is the initial volume and ΔV is the change in volume, while the volume stress (ΔP) corresponds to the ratio of the magnitude of the normal force to the area.5,6 The effective bulk modulus—Keff—is given by the ratio of the volume stress to the volume strain:
, where V is the initial volume and ΔV is the change in volume, while the volume stress (ΔP) corresponds to the ratio of the magnitude of the normal force to the area.5,6 The effective bulk modulus—Keff—is given by the ratio of the volume stress to the volume strain:
Since the volume is spherical, symmetric, and defined by the radius, the volume strain can be written as
Friction Damping ≈ Viscosity of the Shell
The friction damping parameter describes the viscosity of the shell.5,6 Since the pressure change, ΔP, determining the volume change of the microbubble, can be split into three parts: (a) the liquid pressure at the bubble wall (pL), (b) the damping pressure caused by friction damping of the system bubble—liquid (pd), and (c) the hydrostatic pressure (p0), it may be expressed as
Substitution of Eqs. (12) and (13) into Eq. (9) and using the expanded expression for p8 (p8 = p0 + P(t), where p0 is the hydrostatic pressure and P(t) is the time-varying applied acoustic pressure) yield
By equating the damping pressure, multiplied by the bubble surface, to the damping force, an expression for pd can be derived from the equation of motion of a damped forced oscillator:
where β is the mechanical resistance, R is the instantaneous microbubble radius, and 
is the first time derivative of the radius (the velocity of the microbubble wall).
is the first time derivative of the radius (the velocity of the microbubble wall).The total viscous and friction damping coefficient, 
, where ω is the insonating frequency of the applied acoustic field and m is the effective microbubble mass 
, the damping pressure can be written as
, where ω is the insonating frequency of the applied acoustic field and m is the effective microbubble mass , the damping pressure can be written as
where δtot = δrad + δvis + δth + δfr and δrad is the damping coefficient due to reradiation; δvis is the damping coefficient due to the viscosity of the surrounding medium; δth is the damping coefficient due to heat conduction; and δfr is the damping coefficient due to internal friction or viscosity of the shell.
Including friction damping, the final expression for the Rayleigh-Plesset theory is
or
or
or
where R is the instantaneous microbubble radius; 
is the first time derivative of the radius (the velocity of the microbubble wall); R is the second time derivative of the radius (the acceleration of the microbubble wall); pgo is the initial internal gas pressure in the microbubble (=[CA + CG]RT, where CA and CG are concentrations of the filling air and gas, respectively, and T is the absolute temperature); R0 is the initial microbubble radius; Γ is the polytropic exponent of the gas; pv is the vapor pressure; po is the ambient hydrostatic pressure; ST is the surface tension; δtot is the total damping constant;
ω is the angular frequency of the applied acoustic field; ρ is the density of the surrounding medium; P(t) is the time-varying applied acoustic pressure; η is the shear viscosity of liquid; ω is the driving frequency; and t is the time. These differential equations predict that the surface shell supports a strain that counters the surface tension and thereby stabilizes the microbubble against dissolution.
is the first time derivative of the radius (the velocity of the microbubble wall); R is the second time derivative of the radius (the acceleration of the microbubble wall); pgo is the initial internal gas pressure in the microbubble (=[CA + CG]RT, where CA and CG are concentrations of the filling air and gas, respectively, and T is the absolute temperature); R0 is the initial microbubble radius; Γ is the polytropic exponent of the gas; pv is the vapor pressure; po is the ambient hydrostatic pressure; ST is the surface tension; δtot is the total damping constant; ω is the angular frequency of the applied acoustic field; ρ is the density of the surrounding medium; P(t) is the time-varying applied acoustic pressure; η is the shear viscosity of liquid; ω is the driving frequency; and t is the time. These differential equations predict that the surface shell supports a strain that counters the surface tension and thereby stabilizes the microbubble against dissolution.
Scattering Cross Section—Echogenicity of Microbubbles
The scattering cross section, σ, is used as the parameter defining the acoustic behavior of the microbubble and is defined as the quotient of the acoustic power scattered in all directions per unit incident acoustic intensity.5,6 The scattered US intensity (Is) is a function of the incident intensity I0, the distance between the receiving transducer and the scatterer z, and the scattering cross section of the scatterer σ according to
The scattering cross section is directly related to the scattered acoustic power and to microbubble radius and inversely related to the applied pressure.
The general expression for the scattering cross section in the frequency domain including higher harmonics is
where R is the microbubble radius, R0 is the initial microbubble radius, ω is the insonating frequency, 
with f0 is the resonance frequency, and δ is the damping constant.
with f0 is the resonance frequency, and δ is the damping constant.Equation (22) may be further developed as
where δ is the damping constant, ρ is the density respectively of the scatterer (subscript s, microbubble) and the surrounding medium (tissue or plasma), and k is the adiabatic compressibility. The k and ρ are also related to the speed of sound 
. Consequently, the scattering cross section is strongly dependent from frequency both for free air and encapsulated microbubbles and from the difference in density between the microbubble and the surrounding medium.
. Consequently, the scattering cross section is strongly dependent from frequency both for free air and encapsulated microbubbles and from the difference in density between the microbubble and the surrounding medium.At the resonant frequency, the scattering cross section of a microbubble is no longer simply dependent on their size and can reach peak values a thousand times higher compared to values at off-resonance frequencies. Since the scattering cross section is strongly dependent between the ratio between the insonating frequency and the resonant frequency (Eq. (23)), at frequency below resonance most of the scattering occurs at 180 degrees relative to the incident wave, with an angular distribution pattern depending on the scatterer shape and the contrast in the acoustic properties between the particle and the surrounding medium.
The compressibility (k value, see Eq. (24)) of air is 7.65 × 10-6 m2/N, and the compressibility of water is 4.5 × 10-11 m2/N, similarly to tissue and plasma, while the compressibility of a coated microbubble-based agents falls within this range (5 × 10-7 m2/N in the case of Albunex). This high difference in compressibility, and so in impedance, results in a very high echogenicity, which increases the sensitivity of the US equipments to microbubble.
Scattering cross-sectional equations may be simplified to
known as Born approximation, where R0 is the initial microbubble radius, f0 is the resonance frequency, and Z is the difference in acoustic impedance (ratio of acoustic pressure to sound flow) between the surrounding medium and the microbubble. Encapsulation drastically reduces the influence of resonance frequency on scattering cross section since the lower is the shell elasticity due to encapsulation, the higher is the resonant frequency. Moreover, since Eq. (22) shows that the scattering cross section is inversely related to the damping constant, the encapsulation of microbubbles with a thick and stiff shell produces a lower scattering cross section also for the viscoelastic properties of the surrounding shell.
US Beam Attenuation and Microbubble Size Distribution
The US weakening results from scattering and absorption.5,6 The combined effect of scattering and attenuation depends on microbubbles concentration. Scattering is the prevalent phenomenon with low microbubble concentrations while the attenuation, caused by multiple scattering, dominates when the microbubble concentration increases.
where a(f) is the US frequency-dependent attenuation coefficient expressed in nepers[Np]/length and neper is a dimensionless quantity, Rmax and Rmin are minimum and maximum microbubble radii, n(r) is the microbubble concentration, and σ is the scattering cross section.
Equation (26) may be employed to calculate the microbubble size distribution, which is in agreement with values measured with optical methods. Microbubble-size distribution is normal shaped, and the standard deviation is larger for first-generation agents and lower for new-generation agents, which present a more uniform microbubble diameter.
Scattering to Attenuation Ratio
In a suspension of microbubbles, each microbubble has to be considered as an element, which absorbs and scatters US at the same time.5,6 The total energy loss or attenuation for an acoustical beam traveling through a screen of microbubbles is called the extinction coefficient, µe(ω), and is given by
where µa(ω) is the absorption coefficient and µs(ω) is the scattering coefficient.
The scattering to attenuation ratio (STAR) is a measure of the acoustical effectiveness of the contrast agent. The STAR is defined as
where µs(ω) represents the part of the energy that is scattered away omnidirectionally by the microbubbles, while µa(ω) represents the part of the energy that is absorbed by the microbubbles.
Therefore, the lower the absorption of the incoming plane US wave, the higher the STAR. A maximum value of STAR = 1 is obtained when there is no absorption. However, this index is only valid for low acoustic pressures, and at high acoustic pressures, nonlinear transient effect appears.
The attenuation of the acoustical beam traveling through a screen of microbubbles can cause shadowing of underlying biologic structures and is not considered to be a useful parameter. An effective contrast agent, therefore, is defined by good scattering properties and low attenuation. For these reasons, the higher is the STAR, the more effective is the contrast agent. There is a nonlinear relation between the increase in microbubble acoustic pressure of insonation and the produced backscattering and attenuation.
▪ Acoustic Power of Insonation
The probability for a single US pulse to destroy a microbubble increases for high acoustic power amplitudes, long US pulse lengths, and low frequencies according to the following equation:
where Eacoustic is the acoustic power of insonation (W0), P0 is the acoustic pressure amplitude, f is the frequency, t is the time, and K is the number of cycles per burst, which determines the US pulse length.
To obtain a useful harmonic signal for imaging, the microbubbles have to be insonated at their specific fundamental frequency, defined also resonance frequency, which corresponds to the frequency range usually employed for the abdominal US examination from 3 to 3.7 MHz. The acoustic power employed to insonate the microbubbles is usually expressed by the MI, which measures the potential for mechanical damage to tissues exposed to intense US pulses.
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