Ultrasound B-Mode Visualization of Imperceptible Subwavelength Vibration in Magnetomotive Ultrasound Imaging

Abstract

Magnetomotive ultrasound (MMUS) is a promising imaging modality for detecting magnetic nanoparticles. In MMUS, an external oscillating magnetic field induces the motion of the injected magnetic nanoparticles within tissue, and phase-based tracking algorithms are used to detect the motion. However, the subwavelength scale of these displacements (often a few micrometers) makes direct visualization on conventional ultrasound B-mode images impossible. In this work, we adapt the Eulerian motion magnification technique to create a novel ultrasound display mode for identifying the nanoparticle locations, eliminating the need for displacement tracking algorithms. Phantom and in vivo experiments demonstrate that our technique successfully magnifies magnetomotion and the associated shear wave propagation in ultrasound B-mode imaging and pinpoints the nanoparticle vibration source, even in low-concentration scenarios.

1. Introduction

In ultrasound imaging, backscattered acoustic signals provide structural information for clinical diagnosis. Visualization methods like B-mode imaging offer an intuitive view of the imaged tissue. Recent advancements in ultrasound imaging have focused on ultrafast imaging techniques, enabling the observation of functional signals and smaller displacements [1,2]. However, displacements smaller than the wavelength of the transmitted acoustic pulse (i.e., subwavelength displacements) cannot be resolved in conventional B-mode imaging after envelope detection, leading to potential information loss.

Magnetomotive ultrasound imaging (MMUS) is an ultrasound molecular imaging modality that is used to detect the presence of magnetic nanoparticles within tissue [3,4]. MMUS systems apply an external oscillating magnetic field to induce motion of the injected magnetic nanoparticles. This induced motion is detected using various tracking algorithms, revealing the location of the nanoparticles [5,6,7,8]. Compared to other molecular imaging modalities such as magnetic resonance imaging (MRI) and nuclear imaging, MMUS is non-invasive, cost-effective, and free from ionizing radiation. It has demonstrated success in ultrasound molecular imaging, monitoring nano-drug delivery, shear wave elastography, and sentinel lymph node identification [9,10,11,12]. Moreover, recent research has established the real-time imaging capabilities of MMUS [13,14,15].

MMUS is typically visualized through a localization map that shows the location of the detected nanoparticles within the imaged tissue. The induced magnetomotion of the nanoparticles typically occurs on the order of a few microns, which is smaller than the imaging wavelength of clinical ultrasounds, making it imperceptible in B-mode images. Therefore, direct visualization of nanoparticle displacement and motion is not possible using B-mode imaging.

Motion magnification is a technique for amplifying subtle movements in natural videos [16]. Previous research introduced an Eulerian motion magnification technique that magnifies spatial motion through temporal frequency filtering [17]. Other methods utilize phase-based processing for robust motion magnification [18,19]. These techniques have shown great results in revealing previously imperceptible motion in natural videos.

Inspired by the success of motion magnification in natural videos, we believe that similar techniques can be used to amplify imperceptible sub-wavelength displacements in ultrasound imaging, specifically, amplifying the induced subwavelength motion of magnetic nanoparticles in MMUS, offering potential diagnostic benefits for clinicians [20]. Clinicians may observe the MMUS magnetomotion on B-mode imaging through the amplified vibration of the nanoparticles. For sentinel lymph node (SLN) identification, the vibration location identified from B-mode imaging with motion magnification can be used to determine whether the imaged lymph node is SLN. Motion-magnified MMUS B-mode imaging may facilitate faster and direct identification of the SLN.

In this work, we modify the Eulerian motion magnification technique for MMUS imaging. Our goal extends beyond increasing the magnitude of nanoparticle magnetomotion. We aim to introduce a novel display mode that directly distinguishes the vibration source within B-mode image sequences. This visualization would allow for immediate determination of the vibration source and nanoparticle locations, eliminating the need for displacement calculations and tracking. Moreover, this new display mode would simultaneously present both structural information and magnetomotion within the B-mode image sequences.

2. Materials and Methods

2.1. Eulerian Motion Magnification

Eulerian motion magnification is a technique that is used to extract and amplify subtle spatial motions within natural videos [17]. It implicitly maps temporal changes into spatial changes through the derivation of the first-order Taylor expansion. This allows for spatial motion magnification using simple temporal processing. Temporal filters and a Laplacian pyramid are used to extract the desired motion signal, which is then amplified by an amplification factor $\alpha$ to create the magnification effect.

We consider a one-dimensional motion signal and let $I(x,t)$ denote the signal intensity at position x and time t. We assume that at $t=0$, the initial intensity is described by a function f, such that $I(x,0)=f\left(x\right)$. The intensity change caused by the signal’s motion can be expressed by a displacement function $\delta \left(t\right)$, such that:

$$I(x,t)=f(x+\delta (t\left)\right)$$

(1)

The goal of motion magnification is to enlarge such motion. For amplification factor $\alpha$, the ideal magnified motion signal is as follows:

$$I_{ideal}(x,t)=f(x+(1+\alpha )\delta \left(t\right))$$

(2)

Assume the displacement is small enough, so that the signal $I(x,t)$ can be approximated by first-order Taylor series expansion.

$$I(x,t)=f(x+\delta \left(t\right))\approx f\left(x\right)+\delta \left(t\right)\frac{\partial f\left(x\right)}{\partial x}$$

(3)

Then, we apply a temporal bandpass filter to $I(x,t)$ at every position x and remove the static intensity (i.e., $f\left(x\right)$). The signal after filtering is as follows:

$$I_{filtered}(x,t)=\delta \left(t\right)\frac{\partial f\left(x\right)}{\partial x}$$

(4)

In Eulerian motion magnification, the bandpass signal is amplified by $\alpha$ and added back to $I(x,t)$, which creates the following:

$$I_{magnified}(x,t)=I(x,t)+\alpha I_{filtered}(x,t)$$

(5)

Combining the above equations, we can derive the following:

$$I_{magnified}(x,t)\approx f\left(x\right)+(1+\alpha )\delta \left(t\right)\frac{\partial f\left(x\right)}{\partial x}$$

(6)

Assume that the first-order Taylor expansion holds for the amplified displacement $(1+\alpha )\delta \left(t\right)$. We can see that $I_{magnified}(x,t)$ is approximately the ideal magnified motion signal $I_{ideal}(x,t)$:

$$I_{magnified}(x,t)\approx f(x+(1+\alpha )\delta \left(t\right))$$

(7)

This shows that spatial motion magnification can be performed via temporal processing. The above derivation demonstrates a case of a one-dimensional signal, which can be generalized directly to a two dimensional signal.

2.2. Motion Magnification on MMUS

A key assumption of Eulerian motion magnification is that the target signal should be narrowband. If the motion is broadband, the magnification effect will vary based on the signal’s spatial wavelength, with shorter wavelengths having greater magnification. In Eulerian motion magnification, a Laplacian pyramid decomposition is used to handle this issue to process $I(x,t)$ with different amplification factors for each scale [21]. However, the spatial frequency components of ultrasound baseband data fall within a specific frequency band that is determined by the transducer’s bandwidth and the effective imaging aperture, which is relatively narrowband compared to the natural images. Therefore, a single temporal filter is sufficient for extracting and amplifying the motion signal, and the Laplacian pyramid decomposition becomes unnecessary.

Additionally, with large amplification factors, motion magnification can lead to different intensity changes for different spatial frequencies. This intensity artifact is undesirable in natural videos, as it can create visually unpleasant patterns [20]. However, in ultrasound imaging, due to the presence of speckle patterns, the intensity artifact acts as an intensity enhancement, enabling better visualization and observation of the motion signal.

Ultrasound beamformed baseband data are the input for our motion magnification technique. This is because the sub-wavelength magnetomotion inherent to MMUS (on the order of a few microns) would be obscured after envelope detection. We perform motion magnification separately on the real and imaginary components of the complex baseband data and reconstruct the motion-magnified baseband data afterward. A temporal bandpass Butterworth filter is designed according to the magnetic pulse frequency of the MMUS system and is employed to extract the MMUS motion signal. Figure 1 illustrates the pipeline of our motion magnification method.

The motion magnification in MMUS can be expressed mathematically as follows:

$$F_{magnified}(x,z,t)=F_{original}(x,z,t)+\alpha ·F_{filtered}(x,z,t)$$

(8)

where $F_{magnified}$ is the motion-magnified MMUS data, with x representing the lateral axis, z representing the axial axis, and t representing the slow-time axis (i.e., frame by frame). $F_{original}$ is the original beamformed baseband MMUS data, $\alpha$ is the amplification factor, and $F_{filtered}$ is the original data after bandpass filtering along the slow time axis (i.e., frame-by-frame direction).

2.3. Pulsed Magneto-Motive Ultrasound (pMMUS)

In this work, we employ an ultrafast plane wave pulsed MMUS system (pMMUS) to acquire MMUS imaging data [22,23]. B-mode imaging is captured using ultrafast plane wave imaging with a frame rate of 2500 Hz. The high framerate enables us to observe the temporal changes in the induced displacement of the nanoparticles. The imaging is performed using an ultrasound research platform (Prodigy, S-Sharp, New Taipei City, Taiwan) equipped with a 7.5 MHz linear array transducer (L7.5-12840C). An external electromagnet solenoid, positioned beneath the imaged tissue and driven by a magnetic pulser, generates the magnetic field for MMUS. We utilize custom-made superparamagnetic iron oxide nanoparticles (SPIONs) as the MMUS contrast agent [24]. Figure 2 illustrates the configuration of our pMMUS system.

Each MMUS imaging sequence involves the magnetic pulser generating five 100 Hz magnetic pulse cycles, with each cycle lasting 10 ms (5 ms for active field generation and 5 ms for cooldown). The pulser produces a maximum field strength of 0.3 Tesla above the solenoid. Figure 3 depicts the magnetic pulser’s firing sequence and the corresponding measured magnetic field profile.

3. Results and Discussion

3.1. Phantom Experiment

In this section, we verify the proposed motion magnification technique using a tissue-mimicking phantom. This phantom consists of a 3 g/L gelatin base with embedded 0.5% cellulose particles to provide ultrasound scattering. Additionally, superparamagnetic iron oxide nanoparticles (SPION) with a concentration of 5 mg/mL are embedded at the center of the phantom [25]. We position this phantom directly above the electromagnet and utilize our ultrafast pMMUS system to acquire MMUS data.

We employ a temporal Butterworth bandpass filter to extract the MMUS-induced magnetomotion. For motion magnification, we apply amplification factors ($\alpha$) of 10 and 100. The motion-magnified results of the SPION inclusion phantom are shown in Figure 4. After motion magnification, the propagation of the shear wave associated with magneto motion is magnified with the intensity enhancement effect. We observe that a higher amplification factor leads to a stronger intensity enhancement effect. Therefore, both the shear wave and the location of the vibration source (i.e., SPION inclusion) can be easily observed in the B-mode image sequences. In addition to the intensity enhancement effect, we can also observe the magnified motion of the speckle patterns, which were previously invisible in the original B-mode data, as shown in Figure 5.

3.2. Phantom Experiment with Different SPION Concentrations

The intensity of the MMUS displacement signal is positively correlated to the concentration of injected magnetic nanoparticles [26,27]. Therefore, we evaluate the effectiveness of our motion magnification technique in visualizing the motion induced by varying nanoparticle concentrations, particularly for low-concentration phantoms. We made three gelatin phantoms embedded with different nanoparticle concentrations: 2 mg/mL, 3 mg/mL, and 5 mg/mL.

Figure 6 demonstrates the impact of varying nanoparticle concentrations on motion magnification with an amplification factor of 10. Compared to the 5 mg/mL phantom, the magnification effect is less obvious in the 2 mg/mL phantom, resulting in less-distinct shear wave propagation. This suggests potential limitations in visualizing very subtle magnetomotion induced by lower nanoparticle concentrations.

One potential solution for visualizing low-concentration phantoms is to increase the amplification factor for stronger motion magnification. Figure 7 illustrates this using an amplification factor of 100. While the shear wave propagation in the 2 mg/mL phantom is amplified due to the enhanced intensity effect, precisely localizing the SPION remains challenging. This suggests that even with higher amplification, there may be limitations in accurately pinpointing the vibration source within very-low-concentration scenarios.

Since the magnification is indistinguishable in B-mode image sequences in low-concentration phantoms, we track the displacement using a phase-based correlation method to localize the location of SPION [23,28]. Note that the phase-based correlation method similar to color Doppler, which only tracks the displacement in the axial direction. To track the 2D displacement, one can use speckle tracking techniques; however, tracking the MMUS subwavelength motion in the lateral direction using these techniques would be challenging [29]. Therefore, in this work, we only use the phase-based tracking method to track the axial sub-wavelength magnetomotion and to verify the performance of the proposed motion magnification technique. The tracked displacement is shown in Figure 8 and

Table 1. Root mean squared (RMS) displacement tracked using the phase-based correlation method.

Phantom Concentration	RMS Displacement
2 mg/mL	0.0615 $\mathsf{\mu }$m
3 mg/mL	0.0701 $\mathsf{\mu }$m
5 mg/mL	0.0776 $\mathsf{\mu }$m
2 mg/mL + mag.	0.1350 $\mathsf{\mu }$m
3 mg/mL + mag.	0.2262 $\mathsf{\mu }$m
5 mg/mL + mag.	0.2413 $\mathsf{\mu }$m

. The results demonstrate that motion magnification amplifies displacement, making it easier to track both the shear wave and the SPION motion.

The results suggest that the proposed motion magnification technique not only enables B-mode visualization for MMUS imaging, but it also has the potential to enhance the localization accuracy of displacement tracking algorithms, although further investigation is required. This may open up possibilities for improving localization and tracking performance within the field of MMUS imaging.

3.3. In Vivo Experiment

To further validate our motion magnification technique, we conducted an in vivo study focusing on SLN identification, which is a clinical application of MMUS imaging. SLN biopsies serve as a key indicators for cancer monitoring, and accurate SLN identification is essential for the procedure [23].

In our in vivo experiment, superparamagnetic iron oxide nanoparticles (SPION) are intradermally injected into the left hindpaw of a Sprague–Dawley rat. After 1.5 h of in vivo MMUS monitoring, methylene blue dye is injected to confirm the location of the lymph node where the nanoparticles accumulate. MMUS data are acquired using our pMMUS system.

Compared with the phantom experiments, the induced SPION displacements in in vivo experiments are typically smaller. Furthermore, physiological noise sources such as breathing and muscle tremors can interfere with motion magnification. Therefore, we employ a larger amplification factor to increase the degree of motion magnification for better visualization.

Figure 9 shows the motion magnification results of the in vivo experiment. While shear wave propagation is less pronounced than in phantom experiments (likely due to the inhomogeneity of living tissue), we successfully observe motion and brightness changes at the vibration source. This allows us to pinpoint the injected SPION and identify the sentinel lymph node.

We also calculated the displacement map using the phase-based correlation tracking method, as shown in Figure 10. As expected, motion magnification amplifies displacement, aiding in the identification of SPION and SLN. However, this technique also undesirably amplifies the displacement in surrounding tissues due to background motion noise, such as respiratory motion, heart motion, or background vibration. The noise is extracted by the temporal bandpass filter, and it adds complexity to the displacement map. This artifact may be reduced by designing more accurate temporal filters or employing more sophisticated source separation techniques such as singular value decomposition (SVD)-based filtering techniques [30]. In addition, using magnetic pulses with higher frequencies can prevent the frequency of magnetomotion from overlapping with the frequencies of noise sources, thus further reducing unwanted noise [22].

4. Conclusions

In this work, we introduce a motion magnification technique for ultrasound MMUS imaging. Our technique utilizes a bandpass temporal filter to extract the target magnetomotion, subsequently amplifying it with a designated amplification factor. The results show its ability to directly visualize previously imperceptible SPION magnetomotion within the B-mode image sequences.