Use of Nonlinear Frequency Modulated Signals for the Enhancement of Subharmonic Response from Contrast Microbubbles

Ultrasound imaging with the subharmonic component from contrast microbubbles provide improved CTR (Contrast-to-Tissue Ratio), however it is susceptible to the low amplitude of the subharmonic component. In this simulation study, NLFM (Nonlinear Frequency Modulated) signals are proposed in order to enhance the subharmonic response from microbubbles. NLFM signals having fractional bandwidths of 10, 20, and 40% with up and down sweeps were used as excitation. The performance of NLFM signals were compared with the reference tone-burst and LFM (Linear Frequency Modulated) signals. The results show that the ultrasound contrast microbubbles can produce subharmonic response which is dependent on the applied signal pressure and bandwidth. It is observed that the subharmonic component of the scattered NLFM signal is 3.2dB higher than the LFM signal, whereas it is 9dB higher compared to the sinusoidal tone-burst signal. The results are also presented which show that the up and down sweeps NLFM signals performed better than the LFM signals at the same acoustic pressure and bandwidth.


INTRODUCTION
can be degraded by the nonlinear second harmonic component produced by the tissue [3,4].
On the other hand, ultrasound imaging with the subharmonic component can provide improved CTR as it is exclusively produced by the contrast microbubbles at low applied pressures [5]. The ultrasound subharmonic imaging is susceptible to the reduce axial resolution because the subharmonic component has a bandwidth which is one-half of the fundamental frequency. However, the subharmonic component will face less attenuation due U ltrasound imaging using contrast microbubbles has been widely used in diagnostic ultrasound [1]. When microbubbles are insonated at low acoustic pressure, they can produce the fundamental frequency as well as second harmonic, ultra-harmonic and subharmonic frequencies. In ultrasound contrast imaging, these harmonic frequencies are used to improve the image contrast for blood detection from tissues [2].
Modern ultrasound scanners offer imaging with the second harmonic in order to enhance the image contrast with better axial resolution. However, the image quality to the lower frequency and will improve the penetration depth [6,7].
In the past decade, research works mainly focused to enhance the nonlinear response of contrast microbubbles.
It was proved that the subharmonic response has a threshold value which depends on the applied acoustic pressure. This threshold has a minimum value if the applied signal frequency is double the bubble resonance frequency [8]. It has been observed that the subharmonic response is altered by the variations due to the ambient pressure [9]. It has been verified that the nonlinear subharmonic component is changed according to the applied frequency and signal shape [10]. It has been demonstrated that the nonlinear subharmonic component is produced due to the compression-only nature of the contrast microbubbles [11]. The applied low acoustic pressure on microbubbles will produce nonlinear harmonics with less microbubbles destruction. Moreover, it has the potential to use in many clinical applications such as real time estimation of non-invasive blood pressure [12], intravascular ultrasound subharmonic contrast imaging [13], contrast enhanced subharmonic imaging [14], and in-vivo perfusion estimation in kidneys using contrast microbubbles [15].
Many multiple excitation techniques are proposed in the past to increase the nonlinear response of contrast microbubbles at low acoustic pressure. Some of these famous techniques are the pulse inversion [16], pulse amplitude modulation [17], pulse inversion with amplitude modulation [18], microbubble radial modulation [19], and ultrasound CRCI (Chirp Reversal Contrast Imaging) [20].
All these techniques can provide improved SNR (Signalto-Noise Ratio) with better CTR and microbubble detection, however they can reduce the frame-rate of the system and susceptible to motion artifacts.
LFM chirp signals are long in duration and provide improved SNR without reducing the system frame-rate.
However, pulse compression is required at the receiver to recover signal axial resolution. The power spectrum of an unweighted LFM chirp is approximately rectangular in shape and therefore produce higher sidelobes level after pulse compression. These higher sidelobes in the compressed signal can be reduce by applying a windowing function which can reduce the SNR [21]. NLFM are widely used in RADAR and SONAR communications to provide improved SNR [22]. NLFM signals are also suitable for ultrasound imaging [22] and ultrasonic non-destructive testing [23]. The NLFM chirps provide an alternative way to modify the chirp power spectrum into a desirable shape so that it can produce higher SNR and reduced sidelobes level after pulse compression [24,25].
The main aim of the present study is to use the NLFM signals in order to enhance the nonlinear response from contrast microbubbles. It is also to investigate the signal bandwidth effect on the subharmonic frequency component of the microbubble. The performance of the proposed NLFM signal is also compared to the toneburst and LFM (Linear Frequency Modulated) signals.

Frequency Modulated Chirp Signals
Frequency modulated signals have been used extensively in medical ultrasound scanners to get an improved image quality and better penetration depth [21].
The frequency modulated signal is defined as: where v(t) is the signal envelop, T is the chirps weeping time, and f i (t) is the instantaneous frequency of the chirp signal.
For LFM signal, the instantaneous frequency is defined as [21]: where B is the signal bandwidth, and f c is the signal center frequency.
However, in the case of NLFM signal, the instantaneous frequency is defined as [25]: The α and γ values can be set to get the desired shape of the nonlinear instantaneous frequency curve.

Excitation Signals
The NLFM, LFM and tone-burst signals were used as an excitation in all simulations. The design parameters of the excitation signals and their values are shown in Table 1.
The α and γ parameters of the NLFM signal can control the nonlinear curve of the instantaneous frequency function which can change the rectangular shape of the power spectrum and the -3dB bandwidth of the signal.
Therefore, α and γ parameters of the NLFM signal were carefully tuned to get the smooth NLFM power spectrum with equal -3dB bandwidth compared to the LFM signal.
For NLFM signal, a customized window function was used for amplitude tapering as designed in [25]. A Hann window was applied on both reference signals to get the smooth power spectra. In order to see the signal bandwidth effect to the subharmonic response, three fractional bandwidths 10, 20 and 40% were used for NLFM and LFM signals. Fig. 1 is showing the NLFM, LFM, and tone burst excitation signals. The NLFM and LFM signals with a fractional bandwidth of 40% are shown in Fig. 1.

SIMULATIONS
The microbubble model of Marmottant et. al. [26] was tension is expressed as: The simulations were performed for SonoVue® (Sulphur Hexafluoride, Braco Research SA, Milan, Italy) which is a commercially available contrast agent. The bubble size distribution of SonoVue® is ranging from 0.7-10 μm [27], therefore, a bubble radius of 1.7 μm was selected in the simulation. The parameters of the equation with simulation values for SonoVue® are shown in Table- The buckling radius of the microbubble is defined as: Whereas the radius of rupture microbubble is: The pressure waveform scattered from the microbubble can be computed as [28]: Where d is the distance of waveform measurement from the microbubble. The value of d is normally set according to the focal length of the measuring transducer so that maximum scattered pressure from microbubble will be induced in the transducer. In this simulation study the measuring distance from microbubble was taken to d=10 mm. The symbols description and the values used in the simulation are shown in Table 2. The coated microbubble shell viscosity μ S and shell elasticity χ parameters values were taken from [29,30].

RESULTS AND DISCUSSION
The power spectra of the scattered signals from a contrast microbubble are shown in Fig. 2  The comparison of the power spectra of NLFM and LFM signals scattered from the contrast microbubble are shown in Fig. 5. The NLFM and LFM with bandwidths of 10, 20, and 40% were used as excitation signals. It is observed for the same bandwidth signals that the subharmonic response from contrast microbubbles is always higher for NLFM signals compared to the LFM signals.

CONCLUSION
The subharmonic response from contrast microbubbles can be enhance by using NLFM signals. Ultrasound subharmonic imaging with NLFM signals potentially improve the CTR, SNR and microbubbles detection present in the blood without increasing the peak excitation pressure. The subharmonic frequency component has always higher magnitude for the NLFM signal when compared with the reference tone-burst and LFM signals. It is also observed that increasing the signal bandwidth will reduce the magnitude of the subharmonic component. However, increase bandwidth will improve the axial resolution and hence suitable for subharmonic imaging.