Corrigendum to “Cavitation emissions nucleated by Definity infused through an Ekosonic catheter in a flow phantom” [Ultrasound Med. Biol, 47:693–709, 2021]

In equation (1), a set of brackets were inadvertently omitted. The original equation written as:

$$E_{BF}[n,\vec{r}]=\frac{1}{\rho c_0{f}_s^2{S}_a}{\left|\sum _{l=1}^{128}{S}_l{X}_l[n]e^{-i2\pi n\text{Δ}f\left|\frac{{\vec{r}}_l-\vec{r}}{c_0}\right|}\right|}^2-\sum _{l=1}^{128}{\left|S_l{X}_l[n]\right|}^2$$ (1)

should read:

$$E_{BF}[n,\vec{r}]=\frac{1}{\rho c_0{f}_s^2{S}_a}\left\{{\left|\sum _{l=1}^{128}{S}_l{X}_l[n]e^{-i2\pi n\text{Δ}f\left|\frac{{\vec{r}}_l-\vec{r}}{c_0}\right|}\right|}^2-\sum _{l=1}^{128}{\left|S_l{X}_l[n]\right|}^2\right\}$$ (1)

The beamformed energy has units of mJ µV² MPa⁻².

The custom MATLAB code used to produce the results of this paper had the following errors:

1. The parameter, $S_l$, in the left term of Eq. 1 was omitted in the computation.

2. Immediately after $E_{BF}\left[n,\vec{r}\right]$ was computed using Eq. 1, negative values were forced to zero. To take advantage of frequency compounding (Szabo 2014), this step should have been performed after Eq. 2 for passive cavitation images and after Eq. 8 for total cavitation energy calculations. The total cavitation energy also has units of mJ µV² MPa⁻².

3. When determining the ultraharmonics that were 3 dB higher than the average energy in the surrounding inharmonic bands, the conversion from volts to dB was missing a factor of 2.

These errors have been corrected. Though the overall results and discussion presented in this paper are not impacted, Table 1 and Figures 5, 6, 7, and 8 are rendered below to correct the quantitative energy values:

Table 1.

Four-parameter logistic fitting parameters for the ultraharmonic and inharmonic acoustic emissions as a function of Definity concentration

	$x_1$	$x_2$	$x_3$	$x_4$
Ultraharmonic ($R^2$ = 0.98)	−0.42 ± 0.59	−3.22 ± 3.0	−1.88 ± 2.02	6.92 ± 0.79
Inharmonic ($R^2$ = 0.97)	0.44 ± 1.11	−3.48 ± 4.63	1.30 ± 1.83	6.92 ± 1.23

Fig. 5.

Effect of infused Definity concentration on the (a) ultraharmonic and (b) inharmonic total cavitation energy, indicative of stable and inertial cavitation, respectively. Results are presented as the total energy in a single 14.4-ms pulse obtained in three experimental runs, calculated using eqn (9). Error bars are the standard deviations across seven pulses and three runs (n = 21). The black lines are four-parameter sigmoid fits of the data, weighted by the inverse of the coefficient of variation. B-Mode image inserts were acquired at the end of a 3-min infusion with infused Definity concentrations of $4.0\times {10}^7$ and $8.0\times {10}^8\text{microbubbles/mL}$.

Fig. 6.

(a) Ultraharmonic and inharmonic acoustic emissions within seven 15-ms pulses at a pulse repetition frequency of 10 Hz. The concentration of Definity infused through the catheter was $4.0\times {10}^7\text{microbubbles/mL}$. Data are represented as the mean ± standard deviation (n = 7). Time points 0.6, 1.7 and 11.5 ms are marked with gray dashed lines. The 0-ms time point corresponds to the start of the ultrasound pulse. (b) Cross-sectional multiplex images of cavitation emissions obtained by passive cavitation imaging for processing windows starting at 0.6 ms (left column), 1.7 ms (middle column) and 11.5 ms (right column). B-Mode ultrasound in gray scale and passive cavitation image overlays: signal from the transducers (harmonics) in blue, stable cavitation (ultraharmonics) in green and inertial cavitation (inharmonics) in red. The color maps represent values in decibels relative to $1{\text{μJ mV}}^2/{\text{MPa}}^2$. The bottom row illustrates the merged inharmonic and ultraharmonic layers, highlighting the spatiotemporal dynamics of stable and inertial cavitation.

Fig. 7.

(a) Stable and (b) inertial cavitation activity measured throughout Definity infusions at 2.0 mL/min through the EkoSonic catheter. The concentration of Definity infused through the catheter was $4.0\times {10}^7\text{microbubbles/mL}$. Cavitation activity measured in phosphate-buffered saline (PBS) only (noise) is plotted as a dashed black line. Data are expressed as the mean ± standard deviation (n = 3). (c) Passive cavitation images of the average stable (left) and inertial (right) energy acquired over the course of one 3-min infusion of Definity.

Fig. 8.

(a) Stable and inertial cavitation activity at a single axial image location in the flow phantom during a single 3-min infusion at 2.0 mL/min with a catheter pullback rate of 0.5 mm/s. The concentration of Definity infused through the catheter was $4.0\times {10}^7\text{microbubbles/mL}$. Data time points were aligned in post-processing to set the first peak at 0 s to compensate for positioning variability between experimental runs (n = 3). (b) Composite passive cavitation images acquired at time points when the array was above the first (T1) and fourth (T4) pairs of transducers.

The authors would like to apologize for any inconvenience caused.