IN
DEGREE PROJECT MEDICAL ENGINEERING, SECOND CYCLE, 30 CREDITS
STOCKHOLM SWEDEN 2020,
Acoustic Characterization of the Frequency-Dependent Attenuation Profile of Cellulose Stabilized
Perfluorocarbon Droplets
Akustisk Karakterisering av Frekvensberoende Attenuering hos Cellulosastabiliserade Droppar fyllda med Perfluorokarbon
LISA SALJÉN
Acoustic Characterization of the Frequency-Dependent Attenuation
Profile of Cellulose Stabilized Perfluorocarbon Droplets
L i s a S a l j é n
Degree Project
Advanced Level (Second Cycle), 30 credits Supervisor: Dmitry Grishenkov
Reviewer: Martin Wiklund Examiner: Matilda Larsson
School of Engineering Sciences in Chemistry, Biotechnology and Health
Royal Institute of Technology KTH CBH
SE-141 86 Flemingsberg, Sweden http://www.kth.se/cbh
2020
Abstract
The use of ultrasound contrast agents increases the information available for reconstruction during ultrasound imaging. Previously studied microbubbles, consisting of a gas core, are subject to limitations such as a short lifetime and a large size. Droplets with a liquid perfluorocarbon core that is stabilized by cellulose nanofibers eliminate these drawbacks, but require further investigation. By studying the frequency-dependent attenuation profile of the cellulose nanofiber coated perfluorocarbon droplets within an ultrasound field, information about the droplets as oscillators can be retrieved, enabling characterization of their physical properties.
In this study, the frequency-dependent attenuation profile was experimentally acquired and compared between two concentrations, using flat transducers covering the frequency range of 1-15 MHz. The data collected in the time domain was processed and transformed into the frequency domain and the attenuation was calculated across the entire frequency range.
Among the frequencies studied, the attenuation increases with frequency and covers the range of approximately 0.25-8.3 dB/cm and 0.01-3.3 dB/cm at the concentrations of 50 ∙ 106 droplets/ml and 10 ∙ 106 droplets/ml respectively. The attenuation reaches a minimum at 3 MHz within the highest concentration, compared to 4.43 MHz within the lowest. The increase of the attenuation with frequency is explained by the droplets not exhibiting large oscillations within the range covered. It is probable that the droplets do exhibit oscillations, due to a viscosity lower than that of water, but a resonance frequency is not found within the spectrum studied. This could be explained by a shell elasticity or a small droplet radius placing the resonance frequency outside of the spectrum studied, or high levels of damping broadening the resonance peak. Localizing the resonance frequency would enable characterization of these physical properties of the cellulose nanofiber shell as well as the perfluorocarbon liquid core of the droplets. The increase of the attenuation with frequency demonstrates that the droplets do not produce a maximized amount of scattering at a specific frequency within the range studied, which is observed among other oscillating particles implemented as ultrasound contrast agents. The attenuation is, however, larger than that of blood across all frequencies except for those among which the attenuation reaches its minimum.
Potential errors that are affecting the results include droplet vaporization, the formation of flocs after the mechanical agitation has ceased, the experimental setup, the settings on the pulse generator, the sensitivity of the transducers and the processing code.
Table of content
1. Introduction
1.1 Aim of study 1
2. Methods
2.1 Fabrication of droplets 2
2.2 Size distribution and concentration 2
2.2.1 Materials 2
2.2.2 Procedure 3
2.3 Experimental work 4
2.3.1 Materials 4
2.3.2 Procedure 4
2.3.3 Transducer range and sensitivity 5
2.4 Data processing and attenuation calculations 6
2.4.1 Data processing 6
2.4.2 Attenuation calculations 7
3. Results
3.1 Data results and attenuation profile 8
3.1.1 Data results 8
3.1.2 Frequency-dependent attenuation profile 8
4. Discussion
4.1 Frequency-dependent attenuation profile 10
4.1.1 Frequency-dependent attenuation profile 10
4.1.2 Evaluation of the attenuation profile 10
4.2 Experimental setup and sources of error 11
4.3 Future studies 12
5. Conclusions References Appendix A
A.3.4 Ultrasound interaction with a droplet 4
A.4 Attenuation 5
A.4.1 Extinction cross section 5
A.4.2 Concentration 5
A.4.3 Droplet flocculation 6
A.5 Acoustic characterization of attenuation 7
A.6 Review of experimental setups 7
A.6.1 Number of transducers 7
A.6.2 Axis of measurement 8
A.6.3 Type of transducer 8
A.6.4 Acoustic reverberations 8
A.6.5 Summary 9
A.7 Summary 10
1 Introduction
Ultrasound images are built of sound echoes [1]. The echoes consist of backscattered signals and reflections from inhomogeneities, reducing further propagation of the ultrasound wave. Introducing contrast agents into a medium to be imaged increases the intensity of the scattered signals and the information available for reconstruction [1]. The propagation of an ultrasound wave is further described in Appendix A section A.2.
Microbubbles are previously studied contrast agents that consist of a gas core. Besides contrast enhancement due to oscillations, these bubbles can be used in other purposes such as drug delivery [2]. The limitations appearing when using bubbles include a short lifetime and a relatively large size, thus inhibiting their penetration ability. Liquid filled droplets eliminate these drawbacks when used in the vascular system [3]. The droplets have a smaller size than the bubbles, enabling them to enter narrower vasculature or interstitial space of tumors, and their lifetime can be extended to days or months if consisting of low solubility liquid cores [3].
Acoustic droplet vaporization, ADV, is the process in which liquid filled droplets are phase-transitioned into gas-filled microbubbles due to pressure variations in the propagating ultrasound wave [4]. Phase transitioning the droplets into gas-bubbles while inside the body combines the stable transportation of the droplets and the medical applications of the bubbles. The vaporization takes place when the peak negative pressure amplitude of the propagating ultrasound wave increases above a certain threshold [4].
The behavior of the resulting gas-filled microbubbles has been previously determined, described in Appendix A section A.3.1, while the droplets are far less investigated. Depending on the shell material and the liquid core, the physical properties of the droplets vary. In this thesis, the droplets consist of a perfluoropentane (PFC5) liquid core, stabilized by cellulose nanofibers (CNF). Perfluorocarbon droplets are further described in Appendix A section A.1. Knowing the physical properties of the droplets to be used in investigations is of importance in order to predict the response of the applied ultrasound. The physical properties and the droplet behavior within an ultrasound field can be determined based on attenuation measurements. Attenuation describes the loss of signal amplitude of the traveling ultrasound wave, which includes both scattering and absorption for an inhomogeneous medium containing droplets. An attenuation spectrum gives information about the droplets as oscillators, providing knowledge about the resonance frequency and the damping, further described in Appendix A section A.3.1. Knowledge of the resonance frequency is important for optimization of the imaging and for calculations of the droplet properties.
Depending on the droplet behavior within the ultrasound field, the attenuation differs with frequency and concentration. The behavior as well as the physical properties of the droplets can therefore be categorized by experimentally identifying the frequency dependence of the attenuation profile.
1.1 Aim of the study
The aim of the study is to characterize the attenuation of the CNF-stabilized PFC5 droplets. To achieve
2 Methods
The procedure of assessing the frequency-dependent attenuation profile consisted of multiple steps.
Initially, the droplets were fabricated. Then, the size distribution and the concentration among them were determined and the physical experiments for assessing the attenuation profile were performed. Lastly, the experimentally acquired data was processed in order to be transformed from the time domain into the frequency domain and the attenuation was calculated.
2.1 Fabrication of droplets
The droplets were fabricated using mechanical agitation. A mixture was created by combining 0.89 grams of PFC5 (Apollo Scientific Ltd, U.K.) and 32 grams of CNF (0.38 wt%) (Department of Fiber and Polymer Technology, KTH, Stockholm). The mixture was shaken by hand. When two immiscible liquids are mixed in the presence of a stabilizing agent, one liquid becomes dispersed as droplets in the continuous phase of the other liquid during agitation [5]. The manual shaking initiated the creation of droplets, locking the PFC5 inside the CNF keeping it from coalescing [6]. The probe of the sonicator (Vibracell W750, Sonics, USA) was kept cold with a bucket of ice and water, as shown in Figure 1, before being positioned within the mixture of CNF and PFC5. The mixture was sonicated for 60 seconds at an amplitude of 80%.
The vibrations when sonicating the mixture were faster than the manual shaking, enabling the creation of droplets in the range of micrometers. Four solutions of droplets were fabricated.
Figure 1: Fabrication of droplets. The mixture of the PFC5 and the CNF being created (left) and the probe of the sonicator under ice-cooling (right).
2.2 Size distribution and concentration
2.2.1 Materials
The materials used during the study of the droplet size distribution and concentration are listed below.
- Microscope (ECLIPSE Ci-S, Nikon, Japan) - Neubauer Counting Chamber
- ImageJ Analysis Software (National institutes of health, USA)
2.2.2 Procedure
A transmission optical microscope was used to study the size distribution and the concentration of the droplets. The sample of droplets was diluted with a 1:20 dilution ratio and loaded into the counting chamber using a pipette, as shown in Figure 2. The dilution factor is important as to avoid overlapping during the study with higher concentrations and statistical errors with lower concentrations. A 40x objective was used during the image acquisition of the droplets in the counting chamber.
Figure 2: Determination of the droplet size distribution and concentration. The optical microscope (left), the droplets being loaded into the Neubauer Counting Chamber (middle) and the Neubauer Counting Chamber up close (right).
The counting chamber consists of patterns with known distances, used for calibration in ImageJ. The calculation of the size distribution was conducted from measurements of the particle areas with the aid of the ImageJ software, according to equation 1, and the concentration was conducted from the shear number of particles, according to equation 2.
𝑑 = 2 ∙ 𝑟 = 2√𝑎
𝜋 (1)
𝑐 =average number of droplets in sample area
𝑉 ∙ 𝐷𝐹 (2)
In equation 1, d equals the droplet diameter, r equals the droplet radius and a is the area measured with the aid of the ImageJ software. In equation 2, c is the concentration, V is the volume of the sample area and DF equals the dilution factor. The size distribution was plotted with mean value and standard deviation recovered from the experimentally collected data, presented in Figure 3. The most frequently occurring droplet size was 2.67 ± 0.6 μm and the droplet concentration was 500 ∙ 106 droplets/ml. The size is a measure of the droplet diameter. These results are averages among the droplet solutions fabricated.
Figure 3: The size distribution of the droplets. The distribution followed a Gaussian function and the most frequently occurring droplet size was 2.67 ± 0.6 μm.
2.3 Experimental work
2.3.1 Materials
The materials used during the experimental work are listed below.
- Single Element Flat-faced Transducers (Panametrics V311, OLYMPUS, NDT, Waltham, MA, USA)
- Digital Phosphor Oscilloscope (Tektronix, TDS 5052)
- Pulse Generator (OLYMPUS, Panametrics-NDT, Model 5072PR) - Universal Motion Controller/Driver (Newport, Model ESP300) - Plastic Sample Holder
- Aluminum Reflector 2.3.2 Procedure
The experimental setup was designed based on the review presented in Appendix A section A.6. Single element flat-faced transducers were mounted on the motion controller along a vertical axis facing down towards a water bath. The front faces of the transducers were lowered below the water surface. The solution of droplets was diluted with a 1:10 dilution ratio using MilliQ water, resulting in a concentration of 50 ∙ 106 droplets/ml, as well as a 1:50 dilution ratio resulting in a concentration of 10 ∙ 106 droplets/ml. One at a time, the diluted solutions were loaded into a sample cell within the plastic sample holder. A reference sample consisting of only water was loaded into the other sample cell. The walls of the plastic sample holder are thin compared to the wavelength of the ultrasound wave, hence acting as acoustic windows with transmission coefficients of 1. The plastic sample holder was placed on top of an aluminum reflector, positioned at a distance of 40 mm from the transducer within the water bath, illustrated in Figure 4.
Figure 4: The experimental setup. A transducer mounted on the motion controller, the plastic sample holder with two sample cells and the reflector within the water tank (left) and the pulse generator and the water tank (right).
The ultrasound was applied with the aid of the pulse generator and the oscilloscope was presenting the amplitude of the reflected ultrasound signals from the reflector in real time. The signal was averaged 16 times in order to improve the signal-to-noise ratio. The transducer alignments were optimized by maximizing the amplitude of the reflected signal on the oscilloscope. The settings on the pulse generator included a pulse repetition frequency of 500 Hz, an energy of 20 kPa, a gain of 0 dB and a damping of 50 Ω. The data presented on the oscilloscope was saved in order to be processed. The temperature of the experimental setup was 24 °C. In total, 12 measurements were obtained for each transducer and concentration, eight for the droplet sample and four for the water reference. The transducers were moved across each sample in between acquisitions. Furthermore, the samples were either gently flipped or emptied and reloaded into the sample holder in between measurements. As described in Appendix A section A.1, the droplets have a density higher than that of water, potentially making them sink to the bottom of the sample holder. The flip of the sample holder positioned the droplets at the top of the sample cell, avoiding accumulation at the bottom. The samples were emptied and reloaded into the sample holder in order to eliminate gas-bubbles.
2.3.3 Transducer range and sensitivity
The bandwidths of the transducers were previously studied by Löffler, presented in Table 1 [7]. The actual center frequencies, peak frequencies and bandwidths differ from the theoretical values given in the data sheet [7]. The bandwidths were determined relative to the maximum value and presented in a -12 dB profile.
Table 1: The -12 dB profile including the verified frequency values and ranges of the transducers used.
Theoretical center frequency [MHz]
Actual center frequency [MHz]
Peak frequency [MHz]
Low cut-off frequency [MHz]
High cut-off frequency [MHz]
Bandwidth [MHz]
1 1.01 0.99 0.72 1.30 0.58
2.25 2.30 2.21 1.59 3.00 1.41
3.5 3.34 3.25 2.28 4.40 2.12
5 4.75 4.59 3.43 6.07 2.64
10 8.13 8.54 5.09 11.17 6.07
15 11.4 11.08 8.69 14.11 5.42
As can be seen in Table 1, the bandwidths of the 1 MHz and 2.25 MHz transducers do not overlap, resulting in a small frequency spectrum not being covered during the measurements. Furthermore, for the 3.5 to 15 MHz transducers, the actual center frequencies lie below the expected ones. This is due to the manufacturing process [7]. The sensitivity of the transducers reaches a maximum at their peak frequency, presented in Table 1, and is considered only within the range of the cut-off frequencies [7]. The actual frequency range covered is therefore 0.72-14.11 MHz, compared to the theoretical values of 1-15 MHz.
The sensitivity reaching its maximum equals the reliability of the signal measured reaching its maximum.
2.4 Data processing and calculations
2.4.1 Data Processing
The processing of the data was performed by extracting attenuation information from the data collected using the software MATLAB (version R2016b, MathWorks Inc., Natick, MA, USA). Firstly, the experimentally acquired measurements were averaged for each transducer and each concentration. The averaged signals were used during all executions of the processing code developed. In order to downsample the signals, a sampling frequency, 𝑓𝑠, fulfilling the Shannon-Nyquist theorem was chosen. The Shannon- Nyquist theorem requires 𝑓𝑠 > 2𝑓𝑚𝑎𝑥 for signals containing sinusoidal components, in which 𝑓𝑚𝑎𝑥 equals the highest significant frequency present in the signal being processed [8]. The sampling frequency was set to 20 times the highest frequency, 𝑓𝑠 = 20𝑓𝑚𝑎𝑥, fulfilling the Shannon-Nyquist theorem for all transducers.
𝑓𝑚𝑎𝑥 is equal to the highest cut-off frequency for each transducer respectively.
The signals were transformed into the frequency domain using Fast Fourier transform, FFT, as was done by Löffler [7]. The execution time of the FFT in MATLAB depends on the length of the transform and is fastest for powers of two or lengths that have only small prime factors [9]. The execution time was sped up by computing the FFT for the power of two that was either greater or equal to the number of samples in the signals, through the use of zero padding. Additionally, zero padding helps improve the accuracy of the amplitude estimates [10]. If disregarding the mathematics behind the FFT, the process can be simplified by the illustration in Figure 4 below.
Figure 4: Illustration of the Fast Fourier transform. The original signal in the time domain, s(t), is Fourier transformed, resulting in signal ŝ(w) in the frequency domain.
2.4.2 Attenuation calculations
The frequency domain carries information about the magnitude and the phase of the experimentally acquired signal at each frequency. The signal in the frequency domain can be simplified using equation 3, in which |ŝ(w)| equals the magnitude of ŝ(w) and φ(w) equals the phase. The magnitude of the complex output was calculated in MATLAB using the formula presented in equation 4 for the droplet sample and the water reference, providing the intensity of the signals in the frequency domain.
𝑠̂(𝑤) = |𝑠̂(𝑤)| ∙ 𝑒𝑖𝜑(𝑤) (3)
|𝑠̂(𝑤)| = √𝑠𝑟2+ 𝑠𝑖2 (4)
Following Hoff [1] and Grishenkov et al. [11], the attenuation profiles were determined from equation 5, further explained in Appendix A section A.4. According to this equation, the attenuation is presented as the logarithm of the fractional decrease of intensity in decibels per unit length. The attenuation was calculated for the frequencies within the bandwidth of each transducer, that is within the range of the cut- off frequencies.
∝ (𝑤) = −20
2𝐿log( |𝑠̂(𝑤)|
|𝑠̂𝑟𝑒𝑓(𝑤)|) (5)
In equation 5, 𝐿 equals the thickness of the plastic sample holder illustrated in Figure 4 and 𝑠̂ and 𝑠̂𝑟𝑒𝑓 equals the Fourier transformed intensity signals from the droplet sample and the water reference. w is the angular frequency of the wave. The results in the time and frequency domains were plotted for each transducer and a code for merging the attenuation plots together was developed in order to cover the entire frequency range at each concentration.
3 Results
The results presented below include the experimentally acquired and processed data as well as the frequency-dependent attenuation profile at each concentration.
3.1 Data results and attenuation profile
3.1.1 Data results
The amplitude of the signal passing through the droplet sample is lower than the signal passing through the water reference in the time domain across the entire frequency range. This is illustrated in Figure 5 for the 10 MHz transducer at both concentrations and suggests an increased attenuation of the signal passing through the droplet sample compared to the water reference across all frequencies.
According to the formula presented in equation 5, an intensity of the signal passing through the droplet sample being lower than that of the water reference in the frequency domain should result in a positive attenuation coefficient. This is expected by looking at the data presented in the bottom row in Figure 5.
Figure 5: The time- and frequency domain signals of the 10 MHz transducer at both concentrations. The plots on the left represent a droplet concentration of 50 ∙ 106 droplets/ml and the plots on the right represent a droplet concentration of 10 ∙ 106 droplets/ml.
3.1.2 Frequency-dependent attenuation profile
The frequency-dependent attenuation profile is presented in Figure 6. The attenuation decreases among the lowest frequencies and reaches a minimum before increasing to the end of the spectrum. The attenuation is positive for all frequencies within the range studied, implying an increased attenuation when the signal is passing through the droplet sample compared to when its passing through the water reference across all frequencies. This result is in agreement with the data presented in Figure 5.
Figure 6: The frequency-dependent attenuation profile at both concentrations. The attenuation profile on the left represents a droplet concentration of 50 ∙ 106 droplets/ml and the attenuation profile on the right represents a droplet concentration of 10 ∙ 106 droplets/ml.
According to Figure 6, the attenuation does not reach a maximum within the range studied. The highest value of the attenuation included in the bandwidth of the 15 MHz transducer is approaching 8.3 dB/cm at the concentration of 50 ∙ 106 droplets/ml, compared to 3.3 dB/cm at the concentration of 10 ∙ 106 droplets/ml. The values of the attenuation at the peak frequencies of all transducers are presented in Table 2, showing higher values at all peak frequencies covered for the sample diluted 10 times compared to the sample diluted 50 times. The total ranges covered are approximately 0.25-8.3 dB/cm and 0.01-3.3 dB/cm at the concentrations of 50 ∙ 106 droplets/ml and 10 ∙ 106 droplets/ml respectively. The attenuation reaches its minimum at 3 MHz within the highest concentration, compared to 4.43 MHz within the lowest.
Table 2: The attenuation at the peak frequency of each transducer at each concentration.
Theoretical center frequency [MHz]
Peak frequency, 𝑓𝑝, [MHz]
Attenuation [dB/cm] at 𝑓𝑝, 50 ∙ 106 droplets/ml
Attenuation [dB/cm] at 𝑓𝑝, 10 ∙ 106 droplets/ml
1 0.99 1.122 0.578
2.25 2.21 0.467 0.399
3.5 3.25 0.634 0.207
5 4.59 0.940 0.560
10 8.54 2.555 1.461
15 11.08 5.022 2.204
Since the bandwidths of all transducers do not overlap, it is not known what values the attenuation reaches at the areas not covered by any of the transducers. Contrarily, at some of the areas where the bandwidths of the transducers are overlapping, the values of the attenuation differ.
4 Discussion
The discussion below covers the experimental setup, the attenuation profile at each concentration and conclusions on the droplet properties and behaviors within an ultrasound field based on the information presented in Appendix A. Furthermore, sources of error that might have influenced the results are presented and discussed and future studies of interest are introduced.
4.1 Frequency-dependent attenuation profile
4.1.1 Frequency-dependent attenuation profile
The results show an increased attenuation for increasing frequencies and concentrations. The attenuation covers the range of approximately 0.25-8.3 dB/cm and 0.01-3.3 dB/cm at the concentrations of 50 ∙ 106 droplets/ml and 10 ∙ 106 droplets/ml respectively. According to Amin, the attenuation coefficient at 1 MHz for blood is 0.087 dB/cm, 0.61 dB/cm for fat and 0.7-1.4 dB/cm for muscle tissue [12]. At the concentrations used in this study, the attenuation coefficient at 1 MHz is approximately 1.12 dB/cm and 0.57 dB/cm respectively, as presented in Table 2. The attenuation for the CNF-stabilized PFC5 droplets is therefore close to the values of fat and muscle tissue at 1 MHz, depending on the concentration used, but higher than that of blood.
According to Hoskins et al., the attenuation increases linearly with frequency for blood and muscle tissue [13]. Blood attenuates 0.15 dB/cm per MHz and muscle tissue 0.57 dB/cm per MHz [13]. Based on these coefficients, blood and muscle tissue attenuates 2.25 dB/cm and 8.55 dB/cm at 15 MHz respectively.
These values are close to the maximum values measured in the attenuation profiles. The lowest concentration measured a maximum attenuation of 3.3 dB/cm and the highest measured a maximum attenuation of 8.3 dB/cm at 14.11 MHz. This confirms that the droplets attenuate more than blood at the higher frequencies studied across both concentrations, but not more than muscle tissue. Around the frequencies among which the attenuation reaches its minimum, that is 3 MHz within the highest concentration and 4.43 MHz within the lowest, the attenuation coefficient for blood is not exceeded by any of the concentrations studied.
4.1.2 Evaluation of the attenuation profile
The increase of the attenuation with frequency is explained by the droplets not exhibiting large oscillations within the range covered, which has its explanation in the physical properties of the CNF-shell and the PFC5 liquid core. A high viscosity results in an increased damping, explained by Appendix A section A.3. Higher values of damping lower the attenuation and broaden the resonance peak. This result is in agreement with the results produced by Dayton et al., who state that lipid coated perfluorocarbon nanoparticles do not exhibit the large oscillations produced by gas-filled microbubbles and therefore are difficult to detect within the clinical frequencies [14]. The attenuation increases with frequency for both concentrations studied, but reaches higher values for the solution of higher concentration. This is explained by Appendix A section A.4.2.
According to Ghorbani et al., the viscosity of the CNF-coated PFC5 droplets is lower than that of water, which according to Appendix A section A.3 should result in oscillations within the field [15]. If exhibiting large oscillations, a clear resonance frequency should be found at which the attenuation reaches a maximum. As described in Appendix A section A.3.2, the shell elasticity can cause an increase of the resonance frequency, possibly placing it outside of the frequency spectrum studied. Furthermore, the PVA shelled gas-filled microbubbles studied by Löffler were bigger than the CNF-coated PFC5 droplets and a resonance frequency was found at 11.6 MHz [7]. As described in Appendix A section A.3.2, the size of a
with a higher resonance frequency. Since the droplets have an average size of 2.67 μm, while the gas-filled microbubbles had an average size of 3 μm, the resonance frequency of the droplets should exceed the one of the bubbles if assuming a similar oscillating behavior within the field. Based on this, the droplets could be oscillating within the ultrasound field, but with a resonance frequency high enough not to be detected in the spectrum studied. This agrees with Hoff, who mentions that the scattering increases with frequency far below the resonance frequency [1]. Since the mean particle distance is larger than the droplet size, the droplets do not interact during oscillations. This is true unless they form clusters, which is further discussed below.
Since it cannot be guaranteed that the solutions are homogeneously distributed at all times, flocculation could occur at the particle densities used in this study. The risk of flocculation is greater within the solution of higher concentration, since the mean particle distance is smaller while the collision frequency is higher, as described in Appendix A section A.4.3. If clusters are formed, the mean size of the particles within the field increases, resulting in a lowered resonance frequency and an increased damping if passing the dilute limit of interaction. Since no resonance frequency is found within any of the attenuation profiles, the characteristics of an attenuation spectrum based solely on droplet flocculation, described in Appendix A section A.4.3, have to be identified. These characteristics include a decrease of the attenuation among the low frequencies. Both attenuation profiles exhibit this characteristic, which is in agreement with the plots presented by McClements et al. when investigating the influence of droplet flocculation on the ultrasonic attenuation [16]. Contrarily, both attenuation profiles following the same shape suggests that the same behaviors are observed at both concentrations, which minimizes the risk of clusters being included within any of them. This lowered risk is due to the high particle distance and low collision frequency within the lowest concentration studied, which should induce a low number of encounters leading to flocculation.
Potentially, clusters have been avoided due to the flipping and emptying of the sample cells, as well as the transducer being moved across the samples in between acquisitions. The droplet samples could be investigated using a microscope in order to verify the absence of clusters. Based on this, the decrease of the attenuation among the lowest frequencies should be further investigated, taking into account the additional sources of error presented below.
4.2 Experimental setup and sources of error
The experimental work involved multiple sources of error. However, additional errors when using two transducers or a horizontal setup have been eliminated, making this setup a good choice. The sources of error appearing mostly have to do with factors that would not have been eliminated if using other setups evaluated in Appendix A section A.6. Potentially, however, other setups could verify the results obtained.
Due to many sources of error, a substantial amount of time was spent optimizing the results. Nevertheless, the signals obtained varied in between acquisitions. These variations could potentially have been avoided with additional time spent obtaining data.
During the experimental procedure, there was dirt in the water tank potentially covering the ultrasound field during acquisition. It cannot be guaranteed that the field was fully cleared during all measurements.
bubbles have been destroyed. In order to lower the probability of vaporization occurring, other values could be chosen for the energy or the pulse repetition frequency included among the settings on the pulse generator.
Regarding the study of the size distribution and the concentration of the droplet solutions, the values presented in section 3.1, as stated, averages among the solutions fabricated. Since different solutions were used among the measurements, the exact size distributions and concentrations are not known. This in turn has an effect on the dilution of the droplet sample and the conclusions drawn based on the average size among the droplets.
Since the results from the raw data in the time- and frequency domains point to an attenuation in agreement with the one presented in the frequency-dependent attenuation profile, the processing code seems to accurately process the data. Small errors could have been introduced during the downsampling or the Fourier transforming of the data into the frequency domain, which could be further investigated by using another sampling frequency, 𝑓𝑠, or another code for transforming.
A final source of error is the sensitivities among the transducers varying. A transducer of 7.5 MHz was removed due to an obvious sensitivity error, but small differences in between the transducers included cannot be detected and would therefore affect the resulting attenuation in the spectrums presented.
4.3 Future studies
In future studies, the acoustic experiments should be conducted using other settings, temperatures and concentrations. Since the concentration has an obvious effect on the attenuation, further studies would be of interest. Enabling further comparisons, either the temperature or the energy of the pulse generator could be modified. Furthermore, if knowing the circumstances under which the droplets are vaporized, the creation of gas-bubbles could be avoided in order to eliminate errors. Similarly, if knowing the exact circumstances under which the droplets form clusters, the absence of flocculation could be guaranteed.
Additionally, the viscosities and elasticities of the CNF-shell and the PCF5 liquid core could be determined in order to theoretically predict the behavior of the droplets within an ultrasound field. In order to measure the efficiency of the droplets as contrast agents, the acoustic backscatter could be investigated across the entire frequency range studied.
5 Conclusions
The frequency-dependent attenuation profile was obtained using an experimental setup containing flat transducers in a vertical setup. Among the frequencies studied, the attenuation covers the range of approximately 0.25-8.3 dB/cm and 0.01-3.3 dB/cm at the concentrations of 50 ∙ 106 droplets/ml and 10 ∙ 106 droplets/ml respectively. The increase of the attenuation with frequency is explained by the droplets not exhibiting large oscillations within the range studied. It is probable that the droplets do exhibit oscillations, due to a viscosity lower than that of water, but a resonance frequency is not found within the spectrum covered. This could be explained by a shell elasticity or a small droplet radius placing the resonance frequency outside of the spectrum studied, or high levels of damping broadening the resonance peak. Localizing the resonance frequency would enable characterization of the CNF-shell as well as the PFC5 liquid core of the droplets. The increase of the attenuation with frequency demonstrates that the droplets do not produce a maximized amount of scattering at a specific frequency within the range studied, which is observed among other oscillating particles implemented as ultrasound contrast agents. The attenuation is, however, larger than that of blood across all frequencies except for those among which the attenuation reaches its minimum.
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Appendix A
A.1 Perfluorocarbon droplets 2
A.2 Plane harmonic wave propagation 2
A.3 Droplets in an ultrasound field 3
A.3.1 Linear oscillations 3
A.3.2 Droplets as linear oscillators 4
A.3.3 Droplets as small and highly viscous particles 4
A.3.4 Ultrasound interaction with a droplet 4
A.4 Attenuation 5
A.4.1 Extinction cross section 5
A.4.2 Concentration 5
A.4.3 Droplet flocculation 6
A.5 Acoustic characterization of attenuation 7
A.6 Review of experimental setups 7
A.6.1 Number of transducers 7
A.6.2 Axis of measurement 8
A.6.3 Type of transducer 8
A.6.4 Acoustic reverberations 8
A.6.5 Summary 9
A.7 Summary 10
State of the art
This appendix consists of background information as well as a review of previous experimental setups.
The information presented includes facts about perfluorocarbon droplets, ultrasound wave propagation, droplets in an ultrasound field and attenuation. To conclude, the acoustic procedure of assessing the attenuation is presented, including the review of previous experimental setups.
A.1 Perfluorocarbon droplets
The core of the droplets used in this thesis consists of perfluorocarbon, PFC, in a liquid state. PFC is commonly used within medicine due to its high biocompatibility and inertness [17]. Freire et al. state that the viscosity of PFCs increases with the carbon number and decreases with increasing temperatures [18].
The viscosity is a measure of the resistance of a fluid to deformation. Perfluoropentane, a volatile and commonly used type of PFC, has a boiling point of 29 °C [19]. According to the Royal Society of Chemistry, perfluoropentane has a density of around 1,62 kg/L [20].
Coating helps prevent dissolution while increasing the stiffness and the viscous damping of the droplet [19]. The increased stiffness results from the shell elasticity, while the increased damping results from the viscosity of the shell [1]. Cellulose is a naturally occurring material that has been used within medical applications due to qualities such as biocompatibility, nontoxicity and biodegradability [21]. Covering the PFC droplet with a shell of cellulose nanofibers helps stabilizing and preventing vaporization due to the low boiling point of PFC.
The acoustic properties of the droplets, including the shell, can be characterized using the ultrasound nondestructive evaluation, NDE, technique, further described in section A.5. The behavior of the droplets when positioned in an ultrasound field are determined by the physical properties of the core and the shell.
A.2 Plane harmonic wave propagation
Ultrasound waves are of the longitudinal type. Longitudinal waves travel in directions perpendicular to the wavefront, thus causing particles to move back and forth producing pressure disturbances in the medium [22]. Plane harmonic waves are longitudinal waves propagating only in one direction perpendicular to the wavefront. These waves can be described by the complex wavenumber presented in equation 1, resulting in the pressure varying according to equation 2 [1].
𝑘𝑐= 𝑘𝑟+ 𝑖𝑘𝑖 (1)
𝑝(𝑧, 𝑡) = 𝑝0𝑒𝑖(𝑤𝑡−𝑘𝑐𝑧)= 𝑝0𝑒𝑘𝑖𝑧𝑒𝑖(𝜔𝑡−𝑘𝑟𝑧) (2) In equation 2, 𝑝 equals the resulting pressure and 𝑝0 equals the incident pressure. z is the distance traveled, t is the time and w is the angular frequency of the wave [1].
The complex wavenumber possesses one real and one imaginary part. As can be seen in equation 2, the imaginary part contributes to the amplitude of the wave, while the real part contributes to the phase. The amplitude of the wave is reduced when passing through a medium. This reduction of the amplitude of the wave, the attenuation, mainly depends on absorption in a homogenous medium [13]. Attenuation is further described in section A.4.
A.3 Droplets in an ultrasound field
Placing the droplets in an ultrasound field affects the droplets and the continued propagation of the wave. Since the droplet behavior is dependent upon its properties, multiple potential scenarios have to be considered.
A.3.1 Linear oscillations
The acoustic pressure presented in equation 2 travels in the form of a sinusoidal wave, depending on the pressure amplitude and the angular frequency [19]. Microbubbles are previously studied contrast agents with a gas core that start oscillating when positioned in an ultrasound field [7]. These oscillations can be either linear or non-linear depending on the amplitude of the changing pressure field. During low acoustic pressures a linear response is assumed [23]. Oscillations consist of volume changes due to the change in pressure produced by the wave, with compressions during positive pressures and expansions during negative pressures, illustrated in Figure 1 [24].
Figure 1: Linear oscillations at low acoustic pressures, including expansions during negative pressures, rarefactions, and compressions during positive pressures, compressions.
The oscillations illustrated in Figure 1 result in a radial displacement as well as energy being transformed to heat [1]. Energy being transformed to heat results in energy absorption and damping of the oscillations. The conversion takes place if the pressure resulting from temperature variations is out of phase with the acoustic pressure of the traveling wave [1]. The radial displacement caused by the oscillations
A.3.2 Droplets as linear oscillators
The properties of the droplets and the surrounding medium determine if the droplets behave like microbubbles when positioned in an ultrasound field. Miller et al., who studied fluid droplets immersed in other fluids, state that small oscillations of droplets are possible depending on the core, the shell and the surrounding medium [25]. The results are said to be applicable to droplets of viscous fluids positioned in other viscous fluids, where the interface possesses viscous and elastic properties of its own. The oscillating motion of microbubbles can therefore be applied to the droplets used in this thesis [25].
Both the resonance frequency and the rate of the damping of the oscillations are dependent upon the droplet size, the shell properties and the physical characteristics of the fluids involved [25]. Shpak et al.
mention how a smaller particle radius results in a higher resonance frequency [19]. The shell properties cause an increase of the stiffness and the damping of the droplets, mentioned in section A.1 [24]. The shell elasticity increases the stiffness, which produces an increase of the resonance frequency, while the shell viscosity increases the damping and thereby lowers the attenuation and broadens the resonance peak [1].
What differs from the previously studied microbubbles is the liquid core of the droplets. The viscosities of the droplet core and the surrounding liquid have an effect on the damping of the oscillations, in a similar way to the surrounding shell [26]. An increased rate of damping counteracts oscillating motions, meaning that a highly viscous liquid or shell could be a reason for the droplets not to oscillate. This is further described below.
A.3.3 Droplets as small and highly viscous particles
The increased damping in the case of a highly viscous shell is explained by expansions or compressions of small amplitudes producing large restoring forces, counteracting any further motion of the droplet [25].
Furthermore, in the case of the viscosity of the droplet being much higher than the surrounding liquid, the droplet viscosity completely dominates the damping which becomes aperiodic. Aperiodic damping results in the droplet interface returning to its equilibrium position without oscillations after being hit by an ultrasound wave [26].
When droplet oscillation does not occur, the scattering and the absorption of energy are still present.
The size of a particle positioned in an ultrasound field is enough to produce scatter, given that it is smaller than the wavelength of the incoming wave and possesses a difference in acoustic impedance from the surrounding medium [13]. For particles much smaller than the wavelength, the scattered power is proportional to the fourth power of the frequency and the sixth power of the size, described by equation 3 [13].
𝑊𝑠 = 𝑑6
𝜆4= 𝑑6𝑓4 (3)
In equation 3, 𝑊𝑠 equals the scattered power, d is the size of the droplet and f is the frequency of the ultrasound wave [13]. As can be seen in equation 3, the maximized amount of scattering differs from an oscillating particle, where a peak is reached at the resonance frequency.
The absorption of energy is related to the frequency of the incoming ultrasound wave and the viscosity of the material through which it travels. An increase of absorption is a result of a highly viscous material or an ultrasound wave of high frequency [27].
A.3.4 Ultrasound interaction with a droplet
If not scattered or absorbed, the ultrasound wave hitting a droplet can be either reflected or further transmitted. This gives rise to two new ultrasound waves, one reflected outside the droplet and one
both the pressure and the radial particle velocity are assumed to be continuous. These assumptions represent boundary conditions and give rise to one reflection coefficient and one transmission coefficient, both dependent upon the acoustic impedance of the medium inside as well as outside of the droplet [19].
In the case of the ultrasound wave consisting of multiple frequency components, a broadband ultrasound signal, the components travel independently of each other [28]. A change of phase velocity between frequencies can then occur when traveling through an inhomogeneous medium, called dispersion [22]. The phase describes the position of the wave during a cycle of oscillation [13]. This change of phase velocity results in a changed pulse shape during propagation [13].
A.4 Attenuation
Attenuation describes the reduced intensity of a propagating ultrasound wave, when passing through a medium [1]. The rate of attenuation is proportional to the logarithm of the fractional decrease of intensity, according to equation 4 [13].
∝ (𝑤) = −20
2𝐿log( |𝑠̂(𝑤)|
|𝑠̂𝑟𝑒𝑓(𝑤)|) (4)
In equation 4, 𝐿 equals the thickness of the specimen to be measured and 𝑠̂ and 𝑠̂𝑟𝑒𝑓 equals the Fourier transformed intensity signals. w is the angular frequency of the wave [7].
The attenuation of an ultrasound wave passing through a solution containing droplets is affected by the interaction of the wave with the droplets, described in section A.3. The effect of scattering and absorption on attenuation when encountering a solution of particles is further described below.
A.4.1 Extinction cross section
The amount of scattering and absorption of a specific frequency of the incoming wave is dependent upon the behavior of the droplet, as described previously. The total loss of energy of an ultrasound wave encountering a particle can be expressed as the extinction cross section, including both the scattering and the absorption of energy [1]. This cross section is defined as the sum of the power scattered and absorbed divided by the unit incident acoustic intensity.
According to Chatterjee et al., the attenuation of a specific frequency within a sample of particles is built off of the extinction cross sections according to equation 5 [28].
∝ (𝑤) = 10 (log 𝑒) 𝑁 ∫ 𝜎𝑒(𝑎; 𝑤)𝑓(𝑎)𝑑𝑎
𝑎𝑚𝑎𝑥
𝑎𝑚𝑖𝑛
(5)
In equation 5, 𝜎𝑒(𝑎; 𝑤) equals the extinction cross section and 𝑓(𝑎) equals the normalized number of particles per unit radius 𝑎. w is the angular frequency of the wave and 𝑁 is the number of particles per unit volume [28]. From this equation, it is seen that the attenuation also varies with particle density and
are added and that interactions are negligible [29]. The attenuation expressed in equation 5 is derived within this limit of particle interaction for a bubbly medium [28].
Outside of this limit, Ando et al. describe how different sized oscillating particles result in phase cancellations, acting as damping of the wave propagation [30]. Keeping the concentration below the limit of interaction, all particles oscillate with the same phase regardless of their size, eliminating phase cancellations [30]. The dilute limit of interaction occurs when the mean particle distance equals the particle size.
A.4.3 Droplet flocculation
There is a possibility of the droplets flocculating, i.e. forming clusters. Clusters are formed due to attractions between negative and positive edge charges that result in flocs of droplets after the mechanical agitation has ceased. During flocculation, two or more droplets form an aggregate in which each droplet retains its original size [31]. The droplets merging together forming one single drop is called coalescing.
According to McClements, the rate at which droplets flocculate is dependent upon the collision frequency [31]. The collision frequency describes how many droplet encounters happen per unit time and volume. For dilute solutions containing spherical particles, the collision frequency is described by equation 6.
𝑁 =4𝑘𝑇𝑛02
3𝜂 𝐸 (6)
In equation 6, kT equals the thermal energy, n is the initial number of particles per unit volume and 𝜂 is the viscosity. E is the collision efficiency, which is the fraction of encounters that lead to aggregation [31]. According to this equation, the collision frequency, and therefore the flocculation, is dependent upon the temperature and the concentration of droplets in an experimental setting.
According to Povey, the separation of oil droplets in a solution has to be smaller than 10 nm for flocculation to occur within a homogeneously distributed solution [32]. Assuming this distance is applicable to the droplets at hand, the mean particle distance can be calculated using equation 7 [30].
𝑑 = 1 𝑛13
(7)
In equation 7, d is equal to the mean particle distance and n is equal to the particle number density [30].
According to Chanamai et al., the attenuation coefficient decreases at low frequencies due to overlapping of thermal waves generated by the droplets during flocculation [33]. Contrarily, the attenuation coefficient increases at high frequencies due to an increased scattering with flocculation. A theory developed by McClements et al. states that the influence of flocculation on the attenuation spectrum of emulsions is dependent upon the size of the droplets, the size of the clusters, the packing of the droplets within the clusters and the fraction of flocculated droplets [16]. The clusters have properties determined by the size and the volume fraction of the individual droplets within the clusters [16]. The attenuation spectrum is therefore not valid for individual droplets, but for the bigger sized clusters during flocculation.
A.5 Acoustic characterization of droplet attenuation
Characterization of the PFC droplets and their behavior can be done through the use of the ultrasound nondestructive evaluation, NDE, technique. This is a technique in which material characteristics can be determined based on its interactions with an ultrasound wave. According to Hoff et al., acoustic measurements of the attenuation as a function of frequency is the basic method used in order to characterize contrast agents [1]. The attenuation spectrum gives information about the droplets as oscillators, providing knowledge about the resonance frequency and the damping. In order to measure the efficiency of the droplets as contrast agents, the acoustic backscatter has to be investigated [1].
Acoustic measurements are based on ultrasound being sent into the medium and recorded by a receiving transducer in the time domain. In order to eliminate the attenuation of experimental equipment, a sample containing only water is used as a reference. The droplet sample and the reference sample are positioned in a water bath during acquisition [7]. The experimental setup can be designed in multiple ways, presented and evaluated in section A.6. Calculating the attenuation according to equation 4 requires the acquired intensity signals in the frequency domain. According to Löffler, fast Fourier transform, FFT, can be used to attain the magnitude of the signal in the frequency domain [7].
A.6 Review of previous experimental setups
Varying setups are presented and evaluated below in order to design a setup for the acoustic characterization of droplet attenuation. The factors varying among the potential setups are the number of transducers used, the axis of the setup and the transducer type. All potential differences and combinations are summarized in Table 1 and illustrated in Figure 2. The reports presented do not represent all published reports for characterizing contrast agents.
A.6.1 Number of transducers
The number of transducers varies among previous experimental setups for acoustic attenuation measurements. Emmer et al. used separate transducers transmitting and receiving the ultrasound signal when measuring the pressure dependent attenuation of phospholipid-coated microbubbles [34]. Contrarily, one single transducer was used transmitting and receiving the signal reflected off of a reflector when verifying the frequency dependence of the attenuation profile [34].
According to Gros, the technique using one single probe transmitting and receiving the signal is called the pulse echo technique, while the usage of two different probes on opposite sides of the specimen is called through transmission [35]. The through transmission technique requires access to the sample from multiple sides when placing the probes on opposite sides of the specimen as in the case of Emmer et al. Placing a sample at the bottom of a bigger container would make it difficult to position a probe on both sides if measuring along the vertical axis. The receiving probe would have to be mounted on the outside of the container.
Martinez et al. compared the through transmission and pulse echo techniques for attenuation measurements in pure water. According to their results, the overall behavior between the two techniques
the wave further transmitted through the medium. Oppositely, one single probe, both transmitting and receiving, would detect the intensity of the reflected wave, which according to Ahmad et al. is suitable for characterization [37].
A.6.2 Axis of measurement
Both Emmer et al. and Perez-Sabroid et al. evaluated lipid-coated microbubbles [34] [38]. Protein- coated microbubbles were studied by Frinking et al. [39]. Similar to these, many previously published reports have designed their setups in order to examine bubbles with a gas core. The usage of a liquid, PFC, instead of a gas changes the density of the droplet. The density of PFC, mentioned in section A.1, is higher than that of water, resulting in the droplets most likely falling to the bottom of the solution in the sample container. Keeping this in mind, a horizontal setup might not result in a homogeneous distribution of droplets across the cross section of the ultrasound beam. This would affect the amount of attenuation measured by the transducers and therefore compromise the accuracy of the results.
Sarkar et al. measured the attenuation of ultrasound in a solution of microbubbles in a horizontal setup.
The bubbles in the solution were kept in circulation by a magnetic stirrer [29]. Another report using magnetic stirrers is that by Sun et al., characterizing three phospholipid contrast agents [40]. Not having access to a stirrer, as opposed to Sarkar et al. and Sun et al., a vertical setup would keep the droplets spread all over the sample container even when falling to the bottom, resulting in them being homogeneously distributed perpendicular to the ultrasound beam.
A.6.3 Type of transducer
Emmer et al. used unfocused transducers in order to measure the pressure dependence of the attenuation, while focused transducers were used to verify the frequency dependence. Perez-Sabroid et al. and Frinking et al. used focused transducers when acoustically characterizing lipid and protein coated microbubbles [38]
[39]. It is not mentioned by Emmer et al. why focused transducers were used for the frequency measurements, while unfocused transducers were used when determining the pressure dependence. Neither Perez-Sabroid et al. or Frinking et al. discussed their choices. According to Ahmad et al., advantages of focused transducers are said to be a higher sensitivity and resolving power, while a lowered effect of surface roughness and noise [37]. Furthermore, focused transducers receive more energy from defects near the focus than unfocused ones. The natural focus of unfocused transducers is defined as the end of the near- field zone [37]. A limitation of a focused transducer is the small region of the focusing that can be interrogated, i.e. the small useful depth range [37].
Flat, unfocused, transducers were used by Sarkar et al. and Lavisse et al., who both implemented the pulse echo technique. Sarkar et al. used a horizontal setup while Lavisse et al. used a vertical one [29] [41].
According to Ahmad et al., a flat-faced transducer can result in a distorted pattern of reflections due to multiple back reflections [37]. These back reflections result from the difference in length traveled across the beam due to the wide front surface echo [37].
A.6.4 Acoustic reverberations
It is mentioned by both Frinking et al. and Emmer et al. that the samples were positioned at an angle with respect to the ultrasound beam in order to avoid multiple reflections. Another technique that can be used to characterize mediums is that by Achdjian et al., in which acoustic reverberations are measured [42].
The aim of this report is not to characterize contrast agents but to provide reliable information about the properties of mediums overall. It is mentioned how reverberations of the ultrasound wave contain both quantitative and qualitative information about the properties to be determined. The advantage is the possibility of studying the medium as its whole structure, compared to the classical technique for characterization of contrast agents in which the studying is limited to the propagation path of the first wave
mediums, even though it is not mentioned by many reports characterizing contrast agents [42]. The reasons for avoiding multiple reflections are not stated in any of the reports studied, but the fact that none of them used reverberations for characterizing contrast agents might be a reason good enough to avoid it.
Reverberations are not included in Figure 2 or Table 1, due to the lack of reports using it.
A.6.5 Summary
The pulse echo technique was recommended by Ahmad et al. for characterization, making it a promising setup for the experiment at hand. Furthermore, the vertical setup is a logical choice due to the density of the droplets. Regarding the transducer type, both the focused and the flat-faced transducers possess advantages and drawbacks. Without knowledge of how they work for the droplets at hand, the choice will be based on what transducer type is available. Based on this evaluation, the use of a pulse echo technique in a vertical setup, with either flat or focused transducers, seems to optimize the characterization. The discussion is summarized in Table 1 and all possible combinations are presented in Figure 2 below.
Figure 2: The setups from the evaluation. a) the pulse echo technique in a horizontal setup. b) the through transmission technique in a vertical setup. c) the through transmission technique in a horizontal setup. d) the pulse echo technique in a vertical setup. The transducers are either flat or focused.
