Section 7—Discussion of the Mechanical Index and Other Exposure Parameters

There have been long-term efforts to identify a threshold pressure for the onset of inertial cavitation under conditions relevant to ultrasound in medicine. Before the introduction of the Output Display Standard [AIUM/NEMA, 1992a], quantities such as the spatial peak pulse average intensity (I_SPPA), and, earlier, I_m, the spatial peak intensity averaged over the largest half-cycle, were used to give a measure of the potential of a cavitation-based bioeffect due to an acoustic field. Relatively early in the Output Display Standard development effort, the Food and Drug Administration indicated a need for a superior indicator for the potential for cavitation-related bioeffects, initiating a search for such an index. The following paragraphs give an outline of the steps used to develop the Mechanical Index, its relevance as a potential bioeffects indicator, and some information on other exposure parameters involved in bioeffects research.

7.1 On The Origins of The Mechanical Index

One important determinant of the likelihood for cavitation is the operating frequency of the system being used. It has been shown that the growth of the gas-filled cavitation nuclei during the rarefactional portion of the pressure wave is retarded by fluid inertia, viscosity, and surface tension (Apfel, 1981, 1986; Flynn, 1982; Flynn and Church, 1988). As we consider the dynamics of bubble formation, it becomes apparent that the time period of the negative half-cycle of the pressure waveform becomes a critical determinant of the extent of growth. The shorter this interval is, the less likely it is that there will be extensive bubble growth and, hence, cavitation. We can therefore conclude that cavitation is less likely to occur with higher transducer frequencies.

Holland and Apfel (1989) have shown that the minimum acoustic negative pressure amplitude (also termed peak rarefactional pressure) required to cause significant bubble growth and subsequent collapse is strongly influenced by the initial size of the cavitation nucleus. With smaller nuclei, higher negative pressures are required to overcome the effect of stronger surface tension. Alternatively, with larger cavitation nuclei and bubbles, the inertial and viscous effects begin to dominate and, once again, higher negative pressure amplitudes are needed. Thus, for any given frequency, there is an optimal size for a nucleus for cavitation to occur. This dependency is displayed in Figure 7-1 in which the Holland-Apfel model has been used to calculate the negative threshold pressures at which cavitation will occur given various initial radii for the cavitation nuclei. In this context, cavitation was defined to occur if, after growth, the bubble collapses and reaches a collapse temperature of 5,000 K.

Figure 7-1.

Calculated variation of the negative pressure threshold for cavitation with radius of cavitation nuclei and with the frequency of applied ultrasound (Holland and Apfel, 1989). The range of sizes for the nuclei that may cavitate increases with decreasing frequency. Similarly, the minimum negative pressure threshold decreases with decreasing frequency. At zero frequency, the curve decreases to that associated with the Blake threshold pressure. (Figure adapted from and reprinted with permission from Apfel RE, Holland CK: Gauging the likelihood of cavitation from short pulse, low duty cycle diagnostic ultrasound. Ultrasound Med Biol 17:179, 1991).

An interesting way to look at the information in Figure 7-1 is to consider the range of bubble radii that might cavitate at the various transducer frequencies. For example, if a 2 MHz transducer generates a mean rarefactional pressure exceeding 1 MPa, then the range of bubble radii likely to cavitate would go from about 0.1 μm to about 3 μm. Increasing the frequency to 4 MHz would reduce this range to 0.1 to 1.5 μm, and so forth. It is easy to see that the higher frequencies require a very specific and small bubble radius for cavitation.

We can also take the results of Figure 7-1 and determine the minimum negative threshold pressure at a given frequency assuming that all bubble radii are available. This involves determining the threshold pressure minima, let us call them p_opt, for all of the curves in Figure 7-1 and plotting them with respect to frequency. Performing a least squares data fit to such a data set, Apfel and Holland (1991) have shown that the peak negative pressure threshold (in MPa) is given by the following relation:

$$\frac{{({\text{p}}_{\text{opt}})}^{\text{a}}}{\text{f}}=\text{K}$$ (7-1)

where f is the frequency in MHz, a is roughly equal to 1.67 for blood and 2.10 for water, and K is equal to 0.1 for blood and 0.06 for water.

They proposed the use of a Mechanical Index (MI), I, of the form

$$\text{I}\equiv \frac{{\text{P}}^{\text{a}}}{\text{f}}$$ (7-2)

where p is the derated peak rarefactional pressure in MPa, and f is the center frequency in MHz. Because a, the exponent of p, ranges between 1.67 and 2.1 for physiologically relevant host fluids, a value of 2 was chosen for a. Apfel and Holland (1991) proposed the value of 0.5 for the index I as the level below which physical conditions to promote bubble growth do not exist. However, for values higher by factors of two to three above this index, cavitation clearly exists. They also noted that there is a strong need for additional in vivo experimentation to further determine the best index value.

Upon Nyborg’s recommendation, the square root of the index I was adopted as the MI in the Output Display Standard (ODS), and the pressure, p, was taken to be the derated pressure p_r.3 (Apfel and Holland, 1991; Kremkau, 1991).

$$\text{MI}=\frac{{\text{p}}_{\text{r}.3}}{\sqrt{\text{f}}}$$ (7-3)

where p_r.3 is the peak rarefactional pressure (in MPa) that has been derated by 0.3 dB/MHz-cm and f is the center frequency (in MHz). The predicted MI value below which cavitation theoretically will not occur is thus the square root of 0.5, or 0.7. It is important to recognize that these modeling efforts assume the existence of stabilized pockets of gas or free bubbles and that the endpoint under investigation was inertial cavitation. Other than for contrast agents, whether these gas pockets or free bubbles exist in an in vivo setting is not clear.

7.2 Relevance of the Mechanical Index

In assessing the relevance of the MI as an indicator for cavitation-related bioeffects, it is useful to review the conditions under which they may occur. Recently, the likelihood of occurrence of cavitational bioeffects in an in vitro setting has been reviewed (Miller MW et al, 1996). It was noted that these effects required specific exposure conditions with the following important (although somewhat obvious) characteristics:

• Bubbles or cavitation nuclei must be present and in close proximity to cells.

• Physical or chemical interaction between bubbles and cells is required for a bioeffect to occur.

These conditions are certainly met during the use of microbubble contrast agents or other gas-containing bodies.

The investigators (Miller MW et al 1996) questioned whether it is an inertial event that is the prime mechanism by which cell lysis occurs; shear forces due to bubble translation may play a role. Other important possibilities (summarized by Miller MW et al, 1996) include the following mechanisms of lysis that were believed to occur in in vitro experiments:

• near-boundary streaming,

• shear forces near moving bubbles,

• cell-bubble collisions,

• bubble implosions and jets, and

• inertial cavitation-produced chemicals and free radicals.

The multiple physical mechanisms from this list (as well as others that have been proposed) do not yield easily to being modeled by a single expression. The streaming effects are related to the radiation force, as are the shear forces near bubbles moving in response to radiation forces. The latter two mechanisms are more directly related to inertial cavitation and the severity of the bubble implosion. In assessing the relevance of the MI, it will be useful to identify which of these mechanisms is dominant, which can be ignored, and which additional mechanisms may play a role. In some cases, the research has proceeded from the observation of bioeffects in experimental animal studies followed by attempts to identify the underlying physical mechanism, and an assessment of the utility of the MI to function as a predictor of the threshold for such bioeffects. Some of these issues have been addressed in Section 4; they will also be briefly discussed later this section.

Figure 7-2 gives an example of how the MI might be employed by clinical ultrasound users or those providing information to them. Although the Thermal Index (TI) is not addressed in this paper, some previously proposed thresholds are given for completeness of this type of decision tree.

Figure 7-2.

Example of how the MI and the corresponding TI (not addressed in this report) might be used as a clinical guide.

7.3 Other Possibly Relevant Exposure Quantities

7.3.1 Alternative Amplitude, Time, and Frequency Dependencies

It is important to understand some of the limitations of the MI and areas for potential improvement. The MI concept was based only on the threshold for inertial cavitation, not on the severity of effects. Consideration of severity is also important, but will require extensive additional discussion and research. To produce severe or even significant bioeffects in most tissues may require not only high pressures, as addressed by the MI, but also long dwell times or pulse durations. The amount of ultrasonically visible bubbles generated in canine arterial blood increased with duration of the bubble generating burst, and arterial wall microthrombi were observed only for burst durations greater than 125 ms (Ivey et al, 1995).

Other dependencies possibly affecting thresholds or severity of effects include shape of the waveform. For several types of cavitational effects, the pulse polarity, or other aspects of the waveform shape, have been shown to affect thresholds or magnitude of the effect (Umemura and Kawabata, 1993). Ayme and Carstensen (1989) studied relative effects of positive and negative lithotripter pulses and found a surprisingly small difference. Bailey et al (1996) found no difference in effects on Drosophila larvae and murine lung between positive and negative pulses. Umemura et al (1997) reported enhancement of effects with superposition of second harmonic at the correct phase relative to the fundamental, and Chapelon et al (1996) showed reduction of cavitation in ultrasound therapy using pseudo-random CW rather than single frequency CW insonification.

Over the last few years, there has been considerable discussion regarding the frequency dependence in the MI expression. While the thresholds for inertial cavitation appear to be dependent on frequency, some authorities have encouraged an alternative MI without a frequency dependence. This is based loosely on homogeneous nucleation theory (Herbertz, 1988) or, more relevantly, on an argument that for intestinal hemorrhage in mice, the frequency dependence of the threshold of damage may be slightly stronger than f^0.5 (Dalecki et al, 1995b). Carstensen et al (1998) have argued that for this reason, only the pressure amplitude should be reported, along with the frequency used. Nonetheless, it is considered convincing that with respect to a specific bioeffect (lung damage in mouse, rat, and pig; see Section 4, especially Fig. 4–7), a data fit over these different species based on data from different investigators gives the exponent of the frequency term as 0.54. It would seem that a scientifically compelling justification should be given for changing a broad feature of an existing standard, which has just been implemented in most “high end” ultrasound systems at great cost. Also, with a regulatory MI limit, removal of the frequency dependence in the MI would also limit the performance of ultrasound systems at high frequencies or would allow significant increases in peak pressure at lower frequencies where an increase is in general not needed.

7.3.2 Alternative Tissue Models

The attenuation and absorption models for tissues in the computation of the MI are considered to be generally conservative, but they do not represent the worst case anatomical situations and are highly conservative for some examinations and anatomical types. There is a trade-off between simplicity and stability of applications. This trade-off was considered during development of the standard, but it is an area in which changes can be made that are relatively transparent to the user but that can increase the confidence in the displayed quantities such as the MI. Computation with several more specific models for tissues between the transducer and exposure point of interest was considered in development of the MI, and several have since been proposed. Foremost among these probably is the case of propagation through a long low-loss fluid path, such as urine or amniotic fluid. The experimental data on thickness of tissues overlying the fetus in the first trimester (Ramnarine et al, 1993; AIUM, 1993) and of insertion loss from the skin to the vaginal cervix (Siddiqi et al, 1991) suggest that in a majority of first-trimester cases, the attenuation by overlying tissues is lower than that of the homogeneous attenuation model assumed by the ODS. A convenient adjustment to the ODS biophysical indices, namely their recalculation by using a derating factor of 1 dB/MHz rather than the 0.3 dB/cm/MHz, overestimates the expected attenuation in only 10% of those cases. Table 7-1 lists maximum correction factors that might reasonably be applied to the current MI to obtain a better estimate of in situ pressure p for propagation through the inflated bladder in obstetrical ultrasound. The correction factor C_MI would be applied as

Table 7-1.

Maximum Correction Factors for MI Transbladder Imaging.

Frequency (MHz)	CMI
3.5	1.5
5	2
7.5	2

$${\text{MI}}_{\text{corr}}=\frac{{\text{C}}_{\text{MI}}{\text{p}}_{\text{r}.3}}{\sqrt{\text{f}}}={\text{C}}_{\text{MI}}·\text{MI}$$ (7-4)

For cavitation effects, the table may be even more relevant for procedures involving transbladder imaging of the ovaries, intestines, and other tissues likely to contain microbubble contrast agents or natural gas bodies.

Less than with obstetrical ultrasound, but still frequently, echocardiography is mentioned as an extensive application of ultrasound worth investigating for special exposure considerations. Echocardiography is the most frequent source of lung exposures, and it is lung that is subject to bioeffects at the lowest pressure amplitudes. The lung lies alongside and behind the heart and in many echocardiographic views can overlie the heart momentarily. Duck and Martin (1991) noted that amplitude focal gains (peak pressure at the focus over peak pressure at the transducer face) were about as great or greater for beams of short focal length, 1 cm–1.5 cm, as for deeper focal lengths, e.g., 4 cm. In the case of a moderate focal length, such as 4 cm, and a moderate amplitude focal gain of 5, the pressure at the lung immediately under a 1 cm thick chest wall would be about as high as the calculated pressure at the 4 cm focus using the standard derating of 0.3 dB cm⁻¹ MHz⁻¹. That result is based on assuming a specific attenuation coefficient in the chest wall of 1 dB cm⁻¹ MHz⁻¹. This suggests that the MI is a conservative but reasonably accurate representation of the peak ratio of pressure to the square root of frequency on the lung surface. Stronger focal gains are employed in some of the “high-end” systems introduced commercially in the last 6 years and with large numbers of channels. Two 3.5 MHz scanheads employed for echocardiography (GE Model LOGIQ 700, scanhead 326S and Siemens Elegra, scanhead 3.5PL28, respectively) have approximate amplitude focal gains of 13 and 10, for foci at 4.8 and 3.2 cm, respectively. With those scanheads, the MI, quoted at a deep focal point, may significantly overestimate the exposure at the lung surface lying just below the chest wall. This is a problem only if it prevents use of higher pressures when needed for a diagnosis. It is not evident that a specific modification or correction to the MI is needed to minimize the risk of damage from the acoustic fields. However, as echocardiographic use of contrast agents and other enhancement techniques, such as nonlinear imaging, grows along with demand for improved diagnosis, more rigorous modeling of echocardiographic anatomy and acoustic fields therein for safety evaluation is warranted.

7.3.3 Effects of Nonlinear Propagation on the MI’s Estimate of In Situ Pressure and Frequency

It is important to discuss this topic because the achievable peak negative pressure tends to saturate in the water measurement fluid at the highest diagnostic outputs. When measurements are made in water and then derated at 0.3 dB cm⁻¹ MHz⁻¹ to estimate pressures in tissue, the pressures in tissue can be underestimated. In addition, increased particle acceleration and other related phenomena are produced at the shock wavefront. Implications of the latter effects are not well understood.

A recent workshop (Edmonds, 1998) addressed the effects of nonlinear ultrasound propagation in the measurement medium (water) on the reported output display indices, MI and TI. Examples were given in which measurements in water with subsequent derating by 0.3 dB cm⁻¹ MHz⁻¹ contributed to underestimates of the in situ peak rarefactional pressure p by a factor of two compared with measurements in tofu samples with specific attenuation coefficient matching that of the derating of the MI and TI (Szabo et al, 1998). This result was consistent with the 6 dB underestimate of negative pressures from measurements in water compared with those in liver, presented by Carstensen et al (1998) as adapted from Christopher (1998) for a 3 MHz, 2 cm diameter, 8 cm focal length circular transducer. Christopher used a nonlinear propagation model for calculations simulating the fields of a commercial, 2 MHz phased array with 10 cm focus (ATL HDI-3000 P3-2 scanhead). He estimated a similar error from the ODS computations compared with those in an idealized (0.3 dB cm⁻¹ MHz⁻¹) tissue-mimicking (TM) material. He addressed the overestimate of pressure resulting from simulating measurements performed at low outputs and then linearly extrapolated the results to the higher source pressures modeled. In TM material at a value of $\text{p}/\sqrt{\text{f}}$ of 1.37 (an ODS MI of perhaps 0.7 to 0.9), the linear extrapolation was 18% too high. The error may be greater at the maximum MI of 1.9 originally reported by the manufacturer for this scanhead. (Subsequently, the maximum MI for this scanhead was reduced to 1.3.) Sandstrom (1998) showed an analysis based on Christopher (1998) and Carstensen et al (1998) of a factor of two overestimate by linear extrapolation from low amplitudes and a factor of two underestimate of pressure amplitude by the current ODS method.

Immediately following this AIUM Mechanical Bioeffects Conference in Aspen, Colorado, Christopher reported revised calculations that contradicted the old ones and, apparently, some of the experimental data (Christopher, personal communication). For a maximum MI value of 1.88 (predicted in a tissue path), the largest error predicted by the ODS protocol computations was 8% (underestimate). The earlier simulations had considered the potential effects of derating from one fixed focal position. Those earlier simulations incorrectly did not consider the axial shifts in the location of the MI value (as given by the peak in the derated pulse intensity integral curve). The new computations did suggest a possible improvement in the ODS protocol. If the MI were taken from the (spatial) peak value of the derated (temporal) peak rarefactional axial curve, more accurate MI estimates might result. That would require separate measurement positions for MI and TI.

What are practical approaches to correction for the effects of nonlinear propagation in water if, indeed, corrections are deemed warranted? The above methods (Christopher, 1998) for calculating the nonlinear effects may be time-consuming for implementation in ultrasound systems in the next 5 to 10 years. Averkiou (1998) reported on calculations with the KZK equation, which he extended to rectangular apertures and obtained good agreement with experiment. While the broadband field from a rectangular aperture is still prohibitive for real-time calculation, that may not be the case in several years.

MacDonald and Madsen (1998), as well as Szabo et al (1998), have considered alternatives to performance of the measurements in water. The former’s emulsion of evaporated milk and n-propanol in water simulates quite adequately the acoustic properties of idealized tissue. There are concerns, however, about its effect on hydrophones and the ability to standardize its constituents and maintain its stability in large, open measurement tanks.

The apparent dominant approach to addressing the effects of nonlinear ultrasound propagation in water is performance of measurements at low amplitudes. Because reasonably high amplitudes are required for effective measurements, Duck (1998) has addressed how low the amplitudes must be to be in an acceptable quasilinear amplitude range. One method of quantifying the degree of nonlinear distortion employs the shock parameter, σ_s, given by

$${\sigma }_s=\left(1+\frac{B}{2A}\right)\epsilon kx$$ (7-5)

where B/A is the adiabatic nonlinear parameter (ratio of the linear and quadratic terms of the pressure-density relation for a lossless medium), ε is the Mach number, k = 2 π/λ where λ = wavelength, and x is the distance along the direction of propagation. The value of σ_s increases linearly with frequency and with the pressure amplitude of the wave. When σ_s is less than 1.0, the wave has not reached shock conditions and no significant loss of energy is associated with its propagation through a medium such as water. Formation of a fully developed shock wave occurs for σ_s > 3 and implies substantial loss of energy due to the absorption of the higher frequency harmonics produced. Measurements of σ_s have been reported by Starritt and Duck (1992) for 37 pulsed diagnostic beams generated in water by commercial scanning equipment. The range of σ_s reported for Doppler and pulse-echo systems was 0.1 to 6.9. In 30% of the beams, the value of σ_s exceeded 3.0.

7.4 Summary

This section has reviewed the development of the MI that identifies an inertial cavitation pressure threshold. Because of this, it is strictly a cavitation index; however, as its name implies, it was always desired for it to be applicable to a broader set of mechanisms than just cavitation. Should new noncavitational mechanical bioeffects be discovered, the utility of the MI, or some simple correction to it, in predicting those effects will have to be evaluated.

In the evaluation of the MI, it is of interest to consider alternative amplitude, time, and frequency dependencies for this index. The MI does not address the severity of the effects whose threshold it predicts. To effectively do this would require considerable additional research. Issues of dwell time or pulse duration are not included as factors contributing to the value of the MI. The MI is related to the rarefactional pressure; yet, as noted above, it is known that the compressional pressure is associated with certain bioeffects. The frequency dependence is a topic of some controversy, although the most recent results do suggest that the f^−0.5 dependence appears to hold for same in vitro and in vivo situations. Embedded in the MI definition is a tissue model, the derating model used by the Food and Drug Administration (FDA) in 510(k) measurements of acoustic power parameters (FDA, 1993). Cases of obstetrical imaging may involve considerably less attenuation in the path, which might result in a considerably higher MI. Finally, the measurement conventions used to estimate the MI are subject to errors due to the use of water as the medium in which the measurements are made. These measurement methodologies are still under investigation by researchers.