On Factors Impacting Subharmonic Aided Pressure Estimation (SHAPE)

Abstract

Subharmonic aided pressure estimation (SHAPE) estimates hydrostatic pressure using the inverse relationship with subharmonic amplitude variations of ultrasound contrast agents (UCAs). We studied the impact of varying incident acoustic outputs (IAO), UCA concentration and hematocrit on SHAPE. A Logiq 9 scanner with a 4C curvi-linear probe (GE, Milwaukee, WI) was used with Sonazoid (GE Healthcare, Oslo, Norway) transmitting at 2.5 MHz and receiving at 1.25 MHz. An improved IAO selection algorithm provided improved correlations (r from −0.85 to −0.95 vs −0.39 to −0.98). There was no significant change in SHAPE gradient as the pressure increased from 10 to 40 mmHg and hematocrit concentration was tripled from 1.8 to 4.5 ml/l (Δ0.00–0.01 dB, p=0.18) and as UCA concentration was increased from 0.2 to 1.2 ml/l (Δ 0.02–0.05 dB, p=0.75). The results for the correlation between the SHAPE gradient and hematocrit values for patients (N = 100) in an ongoing clinical trial were also calculated showing a poor correlation value of 0.14. Overall, the SHAPE gradient is independent of hematocrit and UCA concentration. An improved algorithm for IAO selection will make SHAPE more accurate.

INTRODUCTION

Subharmonic aided pressure estimation (SHAPE) uses the subharmonic frequency component from ultrasound contrast agents (UCAs) to estimate hydrostatic pressure variations by transmitting at one frequency, receiving at its subharmonic frequency and then monitoring the subharmonic amplitude variations. These UCAs have diameters less than 8 μm, having a lipid, protein or a polymer shell and can traverse the entire vasculature including the capillaries.¹ This is essential as they must cross the lung bed before reaching the target organ and provide enhancement post injection. They are designed to act as echo-enhancers. The gas within these microbubbles has high compressibility and thus, a much higher echogenicity than the surrounding tissues. Hence, the microbubbles enhance the backscattered ultrasound signal (about 10–30 dB enhancement). This aids in contrast enhanced imaging of the blood vessels carrying these UCAs and in differentiating the vessels from the surrounding tissues.² The backscattered echo intensity is proportional to the change in acoustic impedance between the blood and the gas in the microbubbles.³

At very low (< 200 kPa) incident acoustic outputs (IAO), which is the acoustic output from an ultrasound transducer incident on a region of interest, UCAs undergo oscillations which are approximately linear, i.e. the response to a sinusoidal excitation is also sinusoidal. The UCAs undergo symmetric compression and expansion with the positive and negative cycle of the incident ultrasound wave, respectively. At pressures above 200 kPa, the compression starts to retard relative to the expansion and the UCAs start to oscillate nonlinearly.⁴ The bubbles still undergo repetitive oscillations, however the periodicity is observed only for a few cycles.² This is also called stable cavitation or non-inertial cavitation. This behavior is used in diagnostic imaging as the UCA’s nonlinear oscillations occur over a wide range of frequencies from subharmonics (f₀/2) to second harmonics (2f₀) and ultraharmonics (3f₀/2) of the insonation frequency (f₀) as well as its multiples. These signals can be used to create specific contrast imaging modes, such as subharmonic imaging (SHI), harmonic imaging (HI) and superharmonic imaging, respectively.⁵

SHI is an imaging mode that transmits at double the resonance frequency and receives at half the transmit frequency i.e., f₀/2.^{5, 6} This is because subharmonic emissions occur only after a certain threshold IAO is reached. This threshold IAO is minimum for bubbles close to twice the size of those resonant with the insonating field.⁷ SHI has a much better lateral resolution and causes less cavitational bioeffects, due to its higher transmitting frequency. Also, SHI is suitable for scanning deep-lying structures owing to the much smaller attenuation for backscattered subharmonic signals.⁷ Since the surrounding tissue does not generate subharmonic response at the low power levels used, SHI has an excellent contrast-to-tissue ratio (CTR) i.e., the ratio of the mean bubble and tissue signal amplitudes.

Several techniques to estimate ambient pressures using UCAs have been proposed previously.^8–10 Measuring the ambient pressure based on the shift in resonance frequency of small bubbles (diameter 20 to 40 μm),⁹ using single bubble echo amplitudes as a measure of ambient pressure,⁸ and measuring the dissolution time of free microbubbles following the rupture of encapsulated microbubbles.¹⁰ However, all these techniques yield errors ranging from 10–50 mmHg, which is clinically unacceptable because the recommendations for using a technique for systolic and diastolic pressure assessments require the errors to be within 5 mmHg (at least for 50% of the recordings).¹¹

SHAPE uses UCAs for noninvasive, quantitative pressure estimation e.g., in cardiovascular and portal hypertension.^{5, 12} The non-linear response of microbubbles depends strongly on the incident acoustic pressure, and undergoes three stages: occurrence, growth and saturation (fig. 4).^{13, 14} In the growth stage the subharmonic component increases rapidly with acoustic power. It is in this stage that subharmonic microbubble signals (i.e., SHAPE) has the highest sensitivity to pressure changes and an inverse linear relation with the ambient pressure.^{5, 12} This inverse relationship has been validated for only lipid and protein shelled UCAs. Polymer shelled UCAs are expected to behave differently as they are bulkier and more resistant to compression and expansion. However, no polymer shelled UCAs have been tested due to lack of commercial availability.

Fig 4:

Comparison of the original and improved optimization algorithm for two patient data (shown for reference) done retrospectively. In both images, the improved method gives one single inflection point vs multiple inflection points due to noise in the original method. (a): the three stages of subharmonic signal generation namely occurrence, growth and saturation with changing incident pressures from 0 to 100% of maximum acoustic pressures, (b): y axis represents the change in subharmonic amplitude mapped from the top figure, giving the inflection point which is selected as the optimal IAO.

An in vitro study showed decreasing subharmonic amplitudes (10–14 dB) and excellent correlations were achieved with the ambient pressure variations (r = −0.98, p < 0.001) as the pressure was increased from 0 to 186 mmHg for five UCAs namely Optison (GE Healthcare, Princeton, NJ), Definity (Lantheus Imaging, N. Billerica, MA), PRC-1 (Zhifuxian, Xinqiao Hospital, the Third Military Medical University, Chongqing, China) and Sonazoid (GE Healthcare, Oslo, Norway).¹³ This technique has already been investigated for monitoring of portal hypertension,¹⁵ tracking pressure in LV,¹⁶ interstitial fluids in tumors,¹⁷and estimating portal pressures.^{18, 19} Adam et al. used Optison and observed an 8 dB reduction in subharmonic response with 40–140 mm Hg increase in ambient pressure.²⁰

Contrary to these observations, two studies have shown an opposite behavior i.e. an increase in subharmonic response with increasing ambient pressure. Frinking et al. showed a 28.9 dB increase with phospholipid coated bubbles (similar to Sonovue) and Nio et al. observed a 10 dB increase as the pressure increased from 0 to 75 mmHg for Sonovue.^{21, 22} Nio et al. also observed a plateau and a decreasing phase as the ambient pressure further increased from 75 mmHg to 200 mmHg. This reverse behavior was be attributed to a compression only phase as predicted by the Marmottant model, where there is buckling due to overpressure.²³ Katiyar et al. demonstrated that the subharmonic response from a microbubble can either increase or decrease with ambient pressure, depending on the ratio of the excitation frequency to bubble resonance frequency.²⁴ However, their analysis was based on free bubble dynamics and not encapsulated UCAs. Note that this increase has only been observed with Sonovue or Sonovue like bubbles. This can may therefore be limited to these UCAs or it may be dependent on the ratio of the insonation frequency to the resonance frequency ratio; either way it requires further investigation.

The UCA selected for this study was Sonazoid (GE Healthcare, Oslo, Norway), which contains a perfluorobutane gas encapsulated in a membrane of hydrogenated egg phosphatidyl serine, and has a volume median diameter of 2.6 ± 0.1 μm and contains about 1.2×10⁹ microbubbles per ml.²⁵ The subharmonic response of UCAs depends strongly on the incident acoustic output (IAO), and undergoes three stages: occurrence, growth and saturation with increasing IAO giving a characteristic s-curve between the two parameters²⁶ as shown in Fig. 1.

Fig 1:

Characteristic s-curve obtained from subharmonic emissions (y axis) of the microbubbles with increasing input acoustic pressures (x axis). Three distinct phases can be seen, occurrence, growth & saturation.

The subharmonic emissions from UCAs are too small in the occurrence phase and there is too much broadband noise in the saturation phase (due to inertial cavitation) to be used in SHAPE. In the growth stage the subharmonic component increases rapidly with acoustic power. It is in this stage that subharmonic microbubble signals (i.e., SHAPE) has the highest sensitivity to pressure changes and an inverse linear relation with the surrounding ambient pressure.^{5, 12} SHAPE can be used for noninvasive estimation of portal hypertension (PH), which results from obstruction of the portal blood flow.²⁶ As pressures in the portal vein cannot be directly measured, portal pressures are estimated using the hepatic venous pressure gradient (HVPG). This is defined as the difference between the wedged and free hepatic venous pressures.²⁷ The current clinical technique for measuring HVPG is invasive and requires insertion of a balloon catheter via a transjugular approach into the hepatic vasculature. Patients with an HVPG greater than 10 mmHg are at increased risk of developing varices, while patients with an HVPG above 12 mmHg are at risk of variceal bleeding. Varices, a major complication of PH, are abnormal and enlarged veins in the stomach and esophagus that develop as blood cannot flow into the liver and starts flowing backwards, which can lead to bleeding.^{18, 28} Thus, an alternative accurate, noninvasive ultrasound based procedure (i.e., SHAPE) would be a major development in the diagnosis of PH. A pilot study was conducted with 45 patients (27 men and 18 women).¹⁸ Patients at increased risk for variceal bleeding (HVPG > 12 mmHg) had a significantly higher mean subharmonic gradient than patients with lower HVPGs (1.93 ± 0.61 dB vs 21.47 ± 0.29 dB; p < 0.001), with a sensitivity of 100% and a specificity of 81%, indicating that SHAPE may be a useful tool for the diagnosis of clinically important portal hypertension.

However, it is imperative for optimal performance of SHAPE that all factors involved in the interaction of UCAs with the physiological environment of the body and the ultrasound be studied. In this study, we focused on one parameter from each of these categories namely IAO from acoustics, hematocrit from the physiological environment and microbubble concentration from UCAs.

The optimum IAO is currently selected as the highest inflection point in the s-curve (in the growth phase) using an algorithm, individually for each case to achieve maximum sensitivity by accounting for varying depth (i.e., attenuation) and acoustic parameters. This algorithm is however, user dependent and prone to artifacts, due to patient motion during breathing. This makes the IAO selection difficult and can lead to inaccurate selection. It has been demonstrated earlier that the performance of SHAPE was sub-optimal when IAO levels below- or above- the optimized levels were used.²⁹ It is therefore critical to select the correct IAO for optimal results with SHAPE. Thus, an improved algorithm was developed in vitro.

Hematocrit is the ratio of volume of red blood cells to the total volume of blood. Normal values range from 40 to 54% in men and 36 to 48% in women.³⁰ In vivo UCAs are suspended within blood vessels, in a fluid containing a varying volume fraction of red blood cells (RBCs) whose size is comparable with that of an UCA. Thus, any experiment performed with UCAs in the human body need to look at the effect of blood cells on the oscillation of UCAs under the influence of ultrasound.³¹ It has been previously established that hematocrit values do not change the scattering or attenuation of UCAs.³² However, it is not known what effect hematocrit can have on the subharmonic oscillations of UCAs, while ambient pressures vary.

The influence of UCA concentration on SHAPE was studied previously by Shi and colleagues.¹⁴ They studied the reduction in the subharmonic amplitudes at pressure increases of 100 and 200 mmHg. The subharmonic reduction increased only slightly (< 2 dB) as the UCA (Levovist; Schering AG, Berlin, Germany) concentration was more than tripled. However, Levovist was a first generation UCA, which is no longer used clinically as more stable UCAs are now available.³³

The objective of this study was to develop and validate an improved and more reliable IAO selection algorithm to minimize the effect of breathing artifacts and also study the effect of varying hematocrit and UCA concentration on SHAPE estimates for varying ambient pressures.

MATERIALS AND METHODS

Improving the IAO selection algorithm

The effect of breathing was quantified by looking at time domain noise as a tissue marker. Cine clips collected during the IAO optimization for 40 patients (as part of an ongoing IRB approved, clinical trial of SHAPE for diagnosing PH) were analyzed retrospectively. Out of these, 22 had noisy s-curves (even after optimization) with multiple inflection points and 18 had clean s-curves having a single largest inflection point. A ROI around a tissue marker was selected for all the patients on a case by case basis in their optimization cine clips. The standard deviation obtained in the time domain RF signal for the selected tissue region across all the 8 cine clips indicated the noise due to breathing motion i.e., quantified how much the patient moved ,while the optimization algorithm was running.

A modified Logiq 9 ultrasound scanner with a 4C curvi-linear probe (GE, Milwaukee, WI) was used to acquire SHAPE data transmitting at 2.5 MHz and receiving subharmonic signals at 1.25 MHz from a closed-loop flow system containing 0.8 ml of Sonazoid mixed with 800 ml isotonic diluent; a magnetic stirrer ensured uniform mixing. A Millar pressure catheter was inserted into the lumen of the vessel (as reference). In total 3 different in vitro setups were used. A 6 mm vessel with either a 3 cm standoff made of tissue mimicking material (Echo Ultrasound, Reedsville, PA, USA), or a 6 cm standoff pad or no standoff pad were used to test for varying imaging depths. A radiologist mimicked breathing by moving the probe, while scanning the flow phantom.

There is an existing IAO selection algorithm built in on the Logiq 9 scanner. A region of interest is selected in the contrast image and the automated power control algorithm is initiated to determine the optimal acoustic output power for maximum SHAPE sensitivity to account for varying depth and attenuation. Briefly, the automated program acquires data in 8 cine clips for every acoustic output level. One common Maximum Intensity Projection (MIP) is generated for all the 8 clips (fig 2a) and the extracted subharmonic amplitude from the selected ROI on the MIP, is plotted as a function of acoustic output (fig 2b). A logistic curve is fit to the data and the inflection point is selected as the optimized power(fig 2c), as this has been shown to be the point of greatest SHAPE sensitivity.¹²

Fig 2:

Existing power optimization algorithm in the flow phantom, it can be seen the common MIP has a distorted and shifted vessel because of motion created by sonographer, (a) Maximum Intensity Projection of SHI, blue square represents the region of interest selected within the vessel[dynamic range: 72dB]; (b) the three stages of subharmonic signal generation namely occurrence, growth and saturation with changing incident pressures from 0 to 100% of maximum acoustic pressures, (c) y axis represents the change in subharmonic amplitude mapped from the top figure, multiple inflection points due to high noise in the 8 cine clips.

First the existing algorithm on the scanner was run and 8 cine clips of subharmonic data with increasing acoustic powers were collected. The IAO was selected by making an ROI on the common MIP for all 8 cine clips (cf. fig 2). Next, the cine clips were optimized and processed offline using the new algorithm (cf. fig 3), which selects the IAO by creating a separate MIP for each of the 8 cine clips (cf. fig 3a) so the ROI could be repositioned each time to reduce artifacts. SHAPE results acquired in triplicate at both the IAOs from the existing and from the improved algorithms were compared for pressures ranging from 10 to 40 mmHg. This range was selected to mimic the pressures encountered in PH.^{34, 35} The pressures were measured as the peak to peak amplitude in the cyclical variations created using different flow rates in the flow phantom. Each of the 8 cine clips collected on the scanner while optimizing includes 4 IAOs and was 3 seconds long, so subharmonic data was collected for 0.75 seconds at each IAO level. This is consistent with the pressure cycles as each pressure cycle is also 0.73 seconds long therefore, data was collected at the same average pressure for all IAO levels.

Fig. 3:

Improved power optimization algorithm in the flow phantom, separate MIPs created for each of the 8 cine clips giving the freedom to adjust the ROI for each clip to reduce noise due to motion, (a) Maximum Intensity Projection of SHI, red square represents the region of interest selected within the vessel for each clip[dynamic range: 72dB]; (b) the three stages of subharmonic signal generation namely occurrence, growth and saturation with changing incident pressures from 0 to 100% of maximum acoustic pressures, (c) y axis represents the change in subharmonic amplitude mapped from the top figure, single largest inflection point.

The new algorithm was also used to reprocess a subset of the existing in vivo patient data from 22 subjects to check for robustness and verify that the algorithm can mitigate actual real life breathing artifacts.

The effect of hematocrit and UCA concentration

Contrast signals at hydrostatic pressures varying from 10 to 40 mmHg were measured using a 2.25l water tank equipped with an acoustic window and SHAPE data was collected in triplicate. The pressure inside was monitored by a pressure gauge (OMEGA Engineering Inc., Stamford, CT, model DPG1000B-05G). The scanner was used to acquire radiofrequency data at the optimized IAO following injection of Sonazoid in a 0.2 ml/l concentration into saline (Isoton II; Coulter, Miami, FL). The average frame rate was 8 fps. The average radiofrequency signal over all the frames in the 0.5 MHz bandwidth around 1.25 MHz equaled the mean subharmonic signal.^{13, 36, 37} A magnetic stirrer kept the mixture homogenous. In order to study the effect of varying UCA concentration in vitro, the Sonazoid concentration was increased from 0.2 ml/l to 1.2 ml/l using this setup. The range was selected to remain within the clinical range of contrast infusion. For a healthy human having 6 liters of blood on average, 3–6 ml of contrast is infused during the study period; hence, the clinical contrast concentration is 0.5–1.0 ml/l.

This study was performed using a blood mimicking fluid (BMF).³⁸ The BMF used for this study (Model 046 Blood Mimicking Fluid; CIRS, Virginia, USA) was formulated to simulate the acoustic and physical characteristics of blood, thus providing a stable and reliable fluid for flow studies. The composition of this BMF was Orgasol (1.82%) + fluid base (pure water + pure glycerol + dextran). The orgasol/nylon particles mimic the red blood cells in the blood and act as the scatterers. The nylon particles of the BMF are disk-shaped or spherical as compared to the biconcave red blood cells (RBCs) in the human body.³⁹ As per the International Electrotechnical Commission (IEC), that publishes international standards for all electrical, electronic and related technologies, to maintain the hematocrit similar to blood, the nylon particle concentration must be below 5% by volume. This is much lesser than the hematocrit in humans, because the nylon particles have a much higher backscatter than blood.³⁸ To vary the hematocrit, the nylon particle concentration was changed from 1.8% to 4.5% using a centrifuge (VanGuard V6500) at a speed of 1318 relative centrifugal force for 10 minutes. The sensitivity of SHAPE to hematocrit variations was investigated by calculating the gradient i.e., changes in the subharmonic signal with increasing pressure.

A one way ANOVA was used to determine if there was a significant difference in the gradient in the various cases. A p-value < 0.05 was considered significant. All statistical analysis was done using Matlab 2014b (The MathWorks, Inc, Natick, MA, USA).

Lastly, the hematocrit values from the ongoing clinical trial patient data (N = 100) were compared to their respective SHAPE gradient to determine the effect (if any) of different hematocrit levels in humans on the SHAPE estimates.

RESULTS

Improving the IAO selection algorithm

Breathing had a significant effect on the motion during optimization leading to noise in the s-curves, with a median time domain RF noise of 4.67± 1.93 dB vs 2.88±0.51 dB for cases with reduced effects due to better breath holding by the subjects (p = 0.03).

Examples of the in vitro optimization performed by the existing and the new algorithms are shown in Figs. 2 and 3. The new algorithm resulted in less noisy and, thus, clearer s-curves with one single, largest inflection point thereby reducing the noise in the IAO selection process; unlike the existing algorithm, which had multiple peaks making it difficult to select the correct one (cf., Fig 2c).

The acoustic power selected and the SHAPE results for all the three settings are shown in Table 1. The new algorithm results in better or similar correlations between the SHAPE signal and the hydrostatic pressure for all the setups (r-values ranging from −0.85 to −0.95 vs −0.39 to −0.98). The results also confirm that the performance of SHAPE is dependent on the IAO selection and that even a small deviation from the optimized power can greatly affect the correlation obtained. As can be seen for setup 3, a reduction of 4% with the original algorithm versus the improved algorithm reduced the correlation from −0.88 to −0.40. This is consistent with previous findings.²⁹

Table 1:

The acoustic power selected and the correlation obtained between the SHI signal and the ambient pressure for all the six setups using both the existing and the new improved optimization algorithm.

		Setup 1: 6 mm vessel no standoff	Setup 2: 6 mm vessel w/ 3 cm standoff	Setup 3: 6 mm vessel w/ 6 cm standoff
Acoustic Power selected	Existing algorithm	4%	11%	7%
	New algorithm	8%	15%	11%
Correlation between SHAPE and pressure	Existing algorithm	−0.98	−0.93	−0.40
	New algorithm	−0.95	−0.93	−0.88

Once, it was confirmed that the new optimization algorithm does not reduce the correlation factor and provides better s-curves mitigating the effect of breathing, it was run offline retrospectively on the optimization clips from the 22 patients with noisy s-curves. The offline optimization performed using the new algorithm gave one highest peak and suppressed the other multiple peaks arising in the original algorithm in 17 out of the 22 cases. Two examples are shown in Fig. 4, where Fig. 4A shows one tallest peak at 14% with the improved algorithm, which is not clearly observed in the original method. Again, in Fig. 4b, we see a single peak at 14% compared to multiple peaks in the original method with the tallest one being at 7%. This was a case, which was an outlier compared to the HVPG value (the SHAPE gradient was markedly below the expected value). This might be due to the erroneous selection of acoustic output at 7% instead of 14%. Hence, the improved algorithm should help to identify optimum IAO levels correctly, which in turn will make the SHAPE algorithm more accurate.

The effect of hematocrit and UCA concentration

The reduction in subharmonic amplitude as the pressure increased from 10 to 40 mmHg remained almost the same (< 1.2 dB) with no significant change (p = 0.18) as the hematocrit concentration was tripled (from 1.8 to 4.5 ml/l); Table 2. These results show that the change in hematocrit should not affect the SHAPE results indicating that the subharmonic amplitude of the UCAs depends only on the ambient pressure and not the concentration of RBCs in the blood.

Table 2:

In vitro results with BMF. Gradient is calculated by plotting the change in subharmonic amplitude vs ambient pressure.

Concentration of Nylon Particles (%wt)	Gradient (dB/mmHg)
1.8	−0.03 ± 0.02
2	−0.03 ± 0.01
3.6	−0.04 ± 0.01
4.5	−0.03 ± 0.01

The correlation between the SHAPE gradient and hematocrit values for the clinical trial patients (N = 100) were also calculated and is shown in Fig. 5. The hematocrit values for the patient population ranged from 25 to 51.4 g/dL. A poor correlation value (r = 0.14, p < 0.0001) was observed between these two parameters. Similarly, the SHAPE gradient changed only slightly (< 0.05 dB, p = 0.75) as the UCA concentration was increased from 0.2 to 1.2 ml/l. The relative change in the subharmonic signal between 10 and 40 mmHg was independent of the UCA concentration used. The results are shown in Table 3.

Fig.5:

Correlation between SHAPE gradient and hematocrit values for the clinical trial patients.

Table 3:

In vitro results for effect of UCA concentration.

Concentration of UCA (ml/l)	Gradient (dB/mmHg)
0.2	−0.04 ± 0.05
0.4	−0.06 ± 0.02
0.6	−0.06 ± 0
0.8	−0.03 ± 0.03
1.0	−0.07 ± 0.01
1.2	−0.02 ± 0

DISCUSSION AND CONCLUSION

Relative to the original IAO optimization algorithm,^{40, 41} the new algorithm gives the user the flexibility to move the ROI for each cine clip and therefore, minimize motion artifacts. Even though the algorithm was improved to provide better s–curves for easier and more accurate selection of the IAO, the end goal was to improve the correlation between the SHAPE gradient and the ambient pressure. As can be seen, the new algorithm results in smoother s curves and maintains or improves the correlation (cf., Fig 4). This makes the operation of SHAPE more robust and reliable; albeit at the cost of more user-interaction.

Previous studies have proven that the effect of blood on the scattering coefficient is small, because blood cells are filled with liquid rather than gas, and therefore, most of the scattering is caused by the UCAs.³² This behavior is valid at low insonation frequencies (within the diagnostic range; 0–20 MHz),^42–44 where the backscatter from the blood is weak and dependent on the fourth order of the insonation frequency, following Rayleigh behavior. The backscatter also does not have a linear relationship with hematocrit. It is only at higher frequencies (>20 MHz) that blood exhibits higher echogenicity and starts deviating from Rayleigh behavior.⁴⁵ In 2004, Stride and Saffari studied the interaction between the UCAs and the surrounding fluid, which was either plasma or blood.³² They demonstrated that cells surrounding the UCAs had a minimal effect on their dynamics and that the cells did not change the attenuation by any significant amount. Also, since blood cells poorly scatter ultrasound, their effect on the incident ultrasound field was negligible compared with the effect of the UCA.³² This is consistent with the relative change in subharmonic signal coming from the UCAs as well, in the diagnostic range of frequencies studied. Different concentrations of hematocrit do not change the SHAPE gradient with varying pressures. Validation of these results at higher frequencies can be a future study. However, SHAPE for pressure estimation is currently only being employed in the conventional diagnostic frequency range.

Shi et al. studied the effect of varying microbubble concentration and change in the subharmonic signal as the pressure was increased from 100 to 200 mmHg.¹⁴ They tripled the concentration of Levovist and found that the relative change in the subharmonic amplitude remained almost similar with no significant change and was almost independent of absolute values of the amplitude of the received subharmonic signals.¹⁴ This is consistent with the results of this study obtained with the newer UCA Sonazoid.

In conclusion, an improved IAO selection algorithm was developed to determine optimum acoustic pressure levels to insonate the UCAs for SHAPE applications. The approach was validated by estimating in vitro pressure gradients using SHAPE. The results demonstrated that the new algorithm is more accurate in IAO selection, which provides better SHAPE results making the technique more accurate. Also, this study concluded that SHAPE is a robust technique and the subharmonic amplitude from the nonlinear oscillations of the UCAs is only dependent on the ambient hydrostatic pressure once the IAO is optimized, while the UCA concentration and hematocrit value of the blood have very limited effect on performance.