Axial Full Width At Half Maximum Research Articles

Enhancing Image-Guided Radiation Therapy for Pancreatic Cancer: Utilizing Aligned Peak Response Beamforming in Flexible Array Transducers.

To develop ultrasound-guided radiotherapy, we proposed an assistant structure with embedded markers along with a novel alternative method, the Aligned Peak Response (APR) method, to alter the conventional delay-and-sum (DAS) beamformer for reconstructing ultrasound images obtained from a flexible array. We simulated imaging targets in Field-II using point target phantoms with point targets at different locations. In the experimental phantom ultrasound images, image RF data were acquired with a flexible transducer with in-house assistant structures embedded with needle targets for testing the accuracy of the APR method. The lateral full width at half maximum (FWHM) values of the objective point target (OPT) in ground truth ultrasound images, APR-delayed ultrasound images with a flat shape, and images acquired with curved transducer radii of 500 mm and 700 mm were 3.96 mm, 4.95 mm, 4.96 mm, and 4.95 mm. The corresponding axial FWHM values were 1.52 mm, 4.08 mm, 5.84 mm, and 5.92 mm, respectively. These results demonstrate that the proposed assistant structure and the APR method have the potential to construct accurate delay curves without external shape sensing, thereby enabling a flexible ultrasound array for tracking pancreatic tumor targets in real time for radiotherapy.

Assessment of the axial resolution of a compact gamma camera with coded aperture collimator

PurposeHandheld gamma cameras with coded aperture collimators are under investigation for intraoperative imaging in nuclear medicine. Coded apertures are a promising collimation technique for applications such as lymph node localization due to their high sensitivity and the possibility of 3D imaging. We evaluated the axial resolution and computational performance of two reconstruction methods.MethodsAn experimental gamma camera was set up consisting of the pixelated semiconductor detector Timepix3 and MURA mask of rank 31 with round holes of 0.08 mm in diameter in a 0.11 mm thick Tungsten sheet. A set of measurements was taken where a point-like gamma source was placed centrally at 21 different positions within the range of 12–100 mm. For each source position, the detector image was reconstructed in 0.5 mm steps around the true source position, resulting in an image stack. The axial resolution was assessed by the full width at half maximum (FWHM) of the contrast-to-noise ratio (CNR) profile along the z-axis of the stack. Two reconstruction methods were compared: MURA Decoding and a 3D maximum likelihood expectation maximization algorithm (3D-MLEM).ResultsWhile taking 4400 times longer in computation, 3D-MLEM yielded a smaller axial FWHM and a higher CNR. The axial resolution degraded from 5.3 mm and 1.8 mm at 12 mm to 42.2 mm and 13.5 mm at 100 mm for MURA Decoding and 3D-MLEM respectively.ConclusionOur results show that the coded aperture enables the depth estimation of single point-like sources in the near field. Here, 3D-MLEM offered a better axial resolution but was computationally much slower than MURA Decoding, whose reconstruction time is compatible with real-time imaging.

Monte Carlo simulation of the system performance of a long axial field-of-view PET based on monolithic LYSO detectors

BackgroundIn light of the milestones achieved in PET design so far, further sensitivity improvements aim to optimise factors such as the dose, throughput, and detection of small lesions. While several longer axial field-of-view (aFOV) PET systems based on pixelated detectors have been installed, continuous monolithic scintillation detectors recently gained increased attention due to their depth of interaction capability and superior intrinsic resolution. As a result, the aim of this work is to present and evaluate the performance of two long aFOV, monolithic LYSO-based PET scanner designs.MethodsGeant4 Application for Tomographic Emission (GATE) v9.1 was used to perform the simulations. Scanner designs A and B have an aFOV of 36.2 cm (7 rings) and 72.6 cm (14 rings), respectively, with 40 detector modules per ring each and a bore diameter of 70 cm. Each module is a 50 × 50 × 16 mm3 monolithic LYSO crystal. Sensitivity, noise equivalent count rate (NECR), scatter fraction, spatial resolution, and image quality tests were performed based on NEMA NU-2018 standards.ResultsThe sensitivity of design A was calculated to be 29.2 kcps/MBq at the centre and 27 kcps/MBq at 10 cm radial offset; similarly, the sensitivity of design B was found to be 106.8 kcps/MBq and 98.3 kcps/MBq at 10 cm radial offset. NECR peaks were reached at activity concentrations beyond the range of activities used for clinical studies. In terms of spatial resolution, the values for the point sources were below 2 mm for the radial, tangential, and axial full width half maximum. The contrast recovery coefficient ranged from 53% for design B and 4:1 contrast ratio to 90% for design A and 8:1 ratio, with a reasonably low background variability.ConclusionsLonger aFOV PET designs using monolithic LYSO have superior spatial resolution compared to current pixelated total-body PET (TB-PET) scanners. These systems combine high sensitivity with improved contrast recovery.

Optimization of the Algorithm for the Implementation of Point Spread Function in the 3D-OSEM Reconstruction Algorithm Based on the List-Mode Micro PET Data

Positron emission tomography (PET) is a popular research topic. People are becoming more interested in PET images as they become more widely available. However, the partial volume effect (PVE) in PET images remains one of the most influential factors causing the resolution of PET images to degrade. It is possible to reduce this PVE and achieve better image quality by measuring and modeling the point spread function (PSF) and then accounting for it inside the reconstruction algorithm. In this work, we examined the response characteristics of the MetisTM PET/CT system by acquiring 22Na point source at different locations in the field of view (FOV) of the scanner and reconstructing with small pixel size for images to obtain their radial, tangential, and axial full-width half maximum (FWHM). An image-based model of the PSF model was then obtained by fitting asymmetric two-dimensional Gaussians on the 22Na images. This PSF model determined by FWHM in three directions was integrated into a three-dimensional ordered subsets expectation maximization (3D-OSEM) algorithm based on a list-mode format to form a new PSF-OSEM algorithm. We used both algorithms to reconstruct point source, Derenzo phantom, and mouse PET images and performed qualitative and quantitative analyses. In the point source study, the PSF-OSEM algorithm reduced the FWHM of the point source PET image in three directions to about 0.67 mm, and in the phantom study, the PET image reconstructed by the PSF-OSEM algorithm had better visual effects. At the same time, the quantitative analysis results of the Derenzo phantom were better than the original 3D-OSEM algorithm. In the mouse experiment, the results of qualitative and quantitative analyses showed that the imaging quality of PSF-OSEM algorithm was better than that of 3D-OSEM algorithm. Our results show that adding the PSF model to the 3D-OSEM algorithm in the MetisTM PET/CT system helps to improve the resolution of the image and satisfy the qualitative and quantitative analysis criteria.

Technical Note: Performance evaluation of a small‐animal PET/CT system based on NEMA NU 4–2008 standards

The MetisTM PET/CT is a self-developed, silicon photomultiplier (SiPM) detector-based, rodent PET/CT system. The objective of this study was to evaluate the performance of the system using the National Electrical Manufacturers Association (NEMA) NU 4-2008 standard protocol. Energy resolution, spatial resolution, sensitivity, scatter fraction (SF), noise-equivalent count rate (NECR), and image quality (IQ) characteristics were measured. A micro Derenzo phantom experiment was performed to evaluate the spatial resolution using three-dimensional ordered-subsets expectation maximization (3D-OSEM) and maximum likelihood expectation maximization (MLEM) reconstructed images. In addition, the CT imaging agent Ioverol 350 was mixed with fluorine-18 (18 F)-fluorodeoxyglucose (FDG) and then injected into the micro Derenzo phantom to evaluate the PET/CT imaging. In vivo PET/CT imaging studies were also conducted in a healthy mouse and rat using 18 F-FDG. The mean energy resolution of the system was 15.3%. The tangential resolution was 0.82mm full-width half-maximum (FWHM) at the center of the field of the view (FOV), and the radial and axial resolution were generally lower than 2.0mm FWHM. The spatial resolution was significantly improved when using 3D-OSEM, especially the axial FWHM could be improved by up to about 57%. The system absolute sensitivity was 7.7% and 6.8% for an energy window of 200-750 and 350-750keV respectively. The scatter fraction was 8.2% and 12.1% for the mouse- and rat-like phantom respectively. The peak NECR was 1343.72kcps at 69MBq and 640.32kcps at 53MBq for the mouse- and rat-like phantom respectively. The 1-mm fillable rod in the IQ phantom can be clearly observed. We can identify the 0.6-mm aperture of the micro Derenzo phantom image clearly using 3D-OSEM (10 subsets, 5 iterations). We also performed the fusion of the PET and CT images of the mouse and the brain imaging of the rat. The results show that the system has the characteristics of high-resolution, high-sensitivity, and excellent IQ and is suitable for rodent imaging-based research.

3D synthetic aperture imaging with a therapeutic spherical random phased array for transcostal applications

Experimental validation of a synthetic aperture imaging technique using a therapeutic random phased array is described, demonstrating the dual nature of imaging and therapy of such an array. The transducer is capable of generating both continuous wave high intensity beams for ablating the tumor and low intensity ultrasound pulses to image the target area. Pulse-echo data is collected from the elements of the phased array to obtain B-mode images of the targets. Since therapeutic arrays are optimized for therapy only with concave apertures having low f-number and large directive elements often coarsely sampled, imaging can not be performed using conventional beamforming. We show that synthetic aperture imaging is capable of processing the acquired RF data to obtain images of the field of interest. Simulations were performed to compare different synthetic aperture imaging techniques to identify the best algorithm in terms of spatial resolution. Experimental validation was performed using a 1 MHz, 256-elements, spherical random phased array with 130 mm radius of curvature. The array was integrated with a research ultrasound scanner via custom connectors to acquire raw RF data for variety of targets. Imaging was implemented using synthetic aperture beamforming to produce images of a rib phantom and ex vivo ribs. The array was shown to resolve spherical targets within ±15 mm of either side of the axis in the focal plane and obtain 3D images of the rib phantom up to ±40 mm of either side of the central axis and at a depth of 3–9 cm from the array surface. The lateral and axial full width half maximum was 1.15 mm and 2.75 mm, respectively. This study was undertaken to emphasize that both therapy and image guidance with a therapeutic random phased array is possible and such a system has the potential to address some major limitations in the existing high intensity focused ultrasound (HIFU) systems. The 3D images obtained with a therapeutic array can be used to identify and locate strong scattering objects aiding to image guidance and treatment planning of the HIFU procedure.

PEO-CYTOP Fluoropolymer Nanosheets as a Novel Open-Skull Window for Imaging of the Living Mouse Brain.

SummaryIn vivo two-photon deep imaging with a broad field of view has revealed functional connectivity among brain regions. Here, we developed a novel observation method that utilizes a polyethylene-oxide-coated CYTOP (PEO-CYTOP) nanosheet with a thickness of ∼130 nm that exhibited a water retention effect and a hydrophilized adhesive surface. PEO-CYTOP nanosheets firmly adhered to brain surfaces, which suppressed bleeding from superficial veins. By taking advantage of the excellent optical properties of PEO-CYTOP nanosheets, we performed in vivo deep imaging in mouse brains at high resolution. Moreover, PEO-CYTOP nanosheets enabled to prepare large cranial windows, achieving in vivo imaging of neural structure and Ca2+ elevation in a large field of view. Furthermore, the PEO-CYTOP nanosheets functioned as a sealing material, even after the removal of the dura. These results indicate that this method would be suitable for the investigation of neural functions that are composed of interactions among multiple regions.

Design and simulation of a helmet brain PET system

The desire to obtain a reconstruction image with high resolution using a short scanning duration motivates us to design a new brain positron emission tomography (PET) system. We design and simulate a wearable helmet brain PET system. This helmet PET scanner has a radius of 185 mm and comprises five parts (bottom, face, forehead, head, and top). The entire helmet PET system has 512 Lu1.8Y0.2SiO5: Ce (LYSO) PET detector blocks. Each PET detector is made of 12 × 12 LYSO crystals with 1.5 × 1.5 × 10 mm3elements. The proposed scanner has a global absolute sensitivity of 3.08% and a global scatter fraction of 0.56. Maximum likelihood expectation maximization (MLEM) reconstruction of the simulated data shows that full width at half maximum (FWHM) is 1.97 mm and full width at tenth maximum (FWTM) is 2.80 mm at the center of the field of view. In the radial direction, the FWHM increases from 1.97 mm to 3.82 mm, and the FWTM increases from 2.80 mm to 5.64 mm. In the axial direction, FWHM and FWTM are 1.98 mm and 2.80 mm, respectively. We use simulated line sources, a Derenzo phantom, and an MRI image to test the imaging ability of the simulated brain helmet PET. The scanner achieves higher resolution and higher sensitivity than a clinical PET scanner and will be of practical use in the diagnosis of brain illness.

Imaging Performance for Two Row-Column Arrays.

This study evaluates the volumetric imaging performance of two prototyped 62 + 62 row-column-addressed (RCA) 2-D array transducer probes using three synthetic aperture imaging (SAI) emission sequences and two different beamformers. The probes are fabricated using capacitive micromachined ultrasonic transducer (CMUT) and piezoelectric transducer (PZT) technology. Both have integrated apodization to reduce ghost echoes and are designed with similar acoustical features, i.e., 3-MHz center frequency, λ /2 pitch, and [Formula: see text] active footprint. Raw RF data are obtained using an experimental research ultrasound scanner, SARUS. The SAI sequences are designed for imaging down to 14 cm at a volume rate of 88 Hz. Two beamforming methods, spatial matched filtering and row-column adapted delay-and-sum, are used for beamforming the RF data. The imaging quality is investigated through simulations and phantom measurements. Both probes on average have similar lateral full-width at half-maximum (FWHM) values, but the PZT probe has 20% smaller cystic resolution values and 70% larger contrast-to-noise ratio (CNR) compared to the capacitive micromachined ultrasonic transducer (CMUT) probe. The CMUT probe can penetrate down to 15 cm, and the PZT probe down to 30 cm. The CMUT probe has 17% smaller axial FWHM values. The matched filter focusing shows an improved B-mode image for measurements on a cyst phantom with an improved speckle pattern and better visualization of deeper lying cysts. The results of this study demonstrate the potentials of RCA 2-D arrays against fully addressed 2-D arrays, which are low channel count (e.g., 124 instead of 3844), low acoustic intensity mechanical index (MI ≤ 0.88 and spatial-peak-temporal-average intensity [Formula: see text]), and high penetration depth (down to 30 cm), which makes 3-D imaging at high volume rates possible with equipment in the price range of conventional 2-D imaging.

Effects of MRTI sampling characteristics on estimation of HIFU SAR and tissue thermal diffusivity

While the non-invasive and three-dimensional nature of magnetic-resonance temperature imaging (MRTI) makes it a valuable tool for high-intensity focused ultrasound (HIFU) treatments, random and systematic errors in MRTI measurements may propagate into temperature-based parameter estimates used for pretreatment planning. This study assesses the MRTI effects of zero-mean Gaussian noise (SD = 0.0–2.0 °C), temporal sampling (tacq = 1.0–8.0 s), and spatial averaging (Res = 0.5–2.0 mm isotropic) on HIFU temperature measurements and temperature-based estimates of the amplitude and full width half maximum (FWHM) of the HIFU specific absorption rate and of tissue thermal diffusivity. The ultrasound beam used in simulations and ex vivo pork loin experiments has lateral and axial FWHM dimensions of 1.4 mm and 7.9 mm respectively. For spatial averaging simulations, beams with lateral FWHM varying from 1.2–2.2 mm are also assessed. Under noisy conditions, parameter estimates are improved by fitting to data from larger voxel regions. Varying the temporal sampling results in minimal changes in measured temperatures (<2% change) and parameter estimates (<5% change). For the HIFU beams studied, a spatial resolution of 1 × 1 × 3 mm3 or smaller is required to keep errors in temperature and all estimated parameters less than 10%. By quantifying the errors associated with these sampling characteristics, this work provides researchers with appropriate MRTI conditions for obtaining estimates of parameters essential to pretreatment modeling of HIFU thermal therapies.

Temporally focused wide-field two-photon microscopy: Paraxial to vectorial

Temporal focusing allows for optically sectioned wide-field microscopy. The optical sectioning arises because this method takes a pulsed input beam, stretches the pulses by diffracting off a grating, and focuses the stretched pulses such that only at the focal plane are the pulses re-compressed. This approach generates nonlinear optical processes at the focal plane and results in depth discrimination. Prior theoretical models of temporal focusing processes approximate the contributions of the different spectral components by their mean. This is valid for longer pulses that have narrower spectral bandwidth but results in a systematic deviation when broad spectrum, femtosecond pulses are used. Further, prior model takes the paraxial approximation but since these pulses are focused with high numerical aperture (NA) objectives, the effects of the vectorial nature of light should be considered. In this paper we present a paraxial and a vector theory of temporal focusing that takes into account the finite spread of the spectrum. Using paraxial theory we arrive at an analytical solution to the electric field at the focus for temporally focused wide-field two-photon (TF2p) microscopy as well as in the case of a spectrally chirped input beam. We find that using paraxial theory while accounting for the broad spectral spread gives results almost twice vector theory. Experiment results agree with predictions of the vector theory giving an axial full-width half maximum (FWHM) of 2.1 μmand1.8 μmrespectively as long as spectral spread is taken into account. Using our system parameters, the optical sectioning of the TF2p microscope is found to be 8 μm. The optical transfer function (OTF) of a TF2p microscope is also derived and is found to pass a significantly more limited band of axial frequencies than a point scanning two-photon (2p) microscope or a single photon (1p) confocal microscope.

Spatial Resolution and Sensitivity of the Inveon Small-Animal PET Scanner

The Inveon small-animal PET scanner is characterized by a large, 127-mm axial length and a 161-mm crystal ring diameter. The associated high sensitivity is obtained by using all lines of response (LORs) up to the maximum ring difference (MRD) of 79, for which the most oblique LORs form acceptance angles of 38.3 degrees with transaxial planes. The result is 2 phenomena that are normally not encountered in PET scanners: a parallax or depth-of-interaction effect in the axial direction and the breakdown of Fourier rebinning (FORE). Both effects cause a deterioration of axial spatial resolution. Limiting the MRD to smaller values reduces this axial blurring at the cost of sensitivity. Alternatively, 3-dimensional (3D) reconstruction techniques can be used in which the rebinning step is absent. The aim of this study was to experimentally determine the spatial resolution and sensitivity of the Inveon for its whole field of view (FOV). Spatial resolution and sensitivity were measured using filtered backprojection (FBP) with FORE, FBP with LOR angle-weighted adapted FORE (AFORE), and 3D ordered-subset expectation maximization followed by maximum a posteriori reconstruction (OSEM3D/MAP). Tangential and radial full width at half maximum (FWHM) showed almost no dependence on the MRD using FORE and FBP. Tangential FWHMs were 1.5 mm in the center of the FOV (CFOV) and 1.8 mm at the edge of the FOV (EFOV). Radial FWHMs were 1.5 and 3.0 mm in the CFOV and EFOV, respectively. In contrast, axial FWHMs increased with the MRD and ranged between 1.1 and 2.0 mm in the CFOV and between 1.5 and 2.7 mm in the EFOV for a MRD between 1 and 79. AFORE improved the axial resolution for a large part of the FOV, but image noise increased. OSEM3D/MAP yielded uniform spatial resolution in all directions, with an average FWHM of 1.65+/-0.06 mm. Sensitivity in the CFOV for the default energy and coincidence time window was 0.068; peak sensitivity was 0.111. The Inveon showed high spatial resolution and high sensitivity, both of which can be maintained using OSEM3D/MAP reconstruction instead of rebinning and 2D algorithms.

Single-pinhole confocal imaging of sub-resolution sparse objects using experimental point spread function and image restoration.

Sparse fluorescent pointlike subresolution objects have been imaged using a diffraction limited single-pinhole confocal fluorescence microscope. A Maximum likelihood image restoration algorithm has been used in conjunction with a measure of the experimental point spread function for improving the three-dimensional imaging of subresolution sparse objects. The experimental point-spread-function profiles have been improved by a factor of 1.95 in lateral direction and 3.75 in axial direction resulting in full-width half maximum (FWHM) values of 91 +/- 11 nm and 160 +/- 26 nm. This amounts to 1. 43 and 2.15 in optical units, respectively. The lateral and axial FWHM of the sparse pointlike subresolution objects is about 5 and 3 times smaller than the wavelength. This result points to the attractive possibility of utilising a compact confocal architecture for localising punctuate fluorescent objects having subresolution dimensions. The key resides in the utilisation of the measured point spread function coupled to an appropriate image restoration approach, and, of course, in the stability of the confocal system being used.

Statistical moments of backscattered ultrasound in porous fiber reinforced composites

Statistical moments are important tools for understanding wave propagation in random media and are applied here to backscatter measurements in porous, fiber-reinforced polyimide composites. High temperature resins, such as PMR-15, used in load critical components are much more prone to void production than traditional epoxies. Porosity was induced in thin laminates by cure cycle perturbations and quantified destructively as to void content (0.3 to 8.1%) and radius distribution (10 to 250 mum). Measurements of the statistical moments of the scattered field were made using a single, large aperture transducer. Backscatter signals were acquired and used to calculate the rectified ensemble average, and the point signal-to-noise ratio. The lateral and axial full-width half-maximum (FWHM) were extracted from a two-dimensional auto-covariance of the field and compared to the limiting values set by the diffraction pattern and bandwidth of the measurement transducer. Results confirm that the statistical behavior of the echo amplitudes from porous fabric laminates follow predictions based on circular Gaussian statistics for void contents in the range 2 to 5%. Deviations from these predictions occur for void contents outside this range primarily due to changes in the void distribution. These results are important to the development of better void content measurement techniques and are particularly crucial when imaging specularly reflecting defects embedded in a porous volume because spatial and contrast resolution are limited by speckle and the image signal-to-noise.

Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy

In a theta microscope the axis of illumination and the axis of observation are tilted by an angle ϑ. One lens is used to illuminate the sample and one lens is used to observe the light emitted by the sample. In a confocal theta arrangement the axial discrimination is substantially improved over a linear confocal arrangement and the observation volume becomes spherical. Using a numerical aperture of 0.94 in water the axial resolution is improved by a factor 3.5 and the volume of the point spread function is decreased by a factor of 2.2. This means that the point spread function of a confocal theta two-photon microscope operating at a wavelength of 780 nm has an axial full width half maximum of 230 nm. In a 4Pi(A)-confocal theta microscope the axial side lobes are removed.

A new approach to the measurement of resolution and sampling on a positron emission tomograph

Two technical difficulties underlie the accurate determination of spatial resolution in positron emission tomography (PET): (1) measuring the full-width half-maximum (FWHM) and full-width tenth-maximum (FWTM) from undersampled profiles; (2) measuring axial resolution from multiple reconstructed data sets. To address the first problem, a technique that involves a quadratic estimation of the peak of the profile distribution was developed. This method was compared with the standard technique of Gaussian fitting and was found to be as accurate for constant background distributions. For axial resolution, a second method involving a single scan and imaging of line sources oriented 45 degrees to the axis of the scanner was proposed. Axial FWHM estimations were achieved by deconvolving the values obtained with line spread functions from sources placed parallel to the axis of the scanner. This technique was validated by comparing the results with those obtained by others using a multiple-scan technique on a similar machine.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Effects of axial spatial resolution and sampling on object detectability and contrast for multiplanar position emission tomography.

A multiplanar positron emission tomography (PET) system is simulated using Gaussian curves to model the axial point spread functions (PSFs) of the planes to study the effects of resolution and sampling. Poor spatial resolution or insufficient sampling may cause deleterious data losses or artifacts in the reconstructed image. For a multiplanar PET system with an axial full width at half-maximum (FWHM) of 6 mm and a 12 to 13 mm ring separation, a ripple in sensitivity of 9% is observed. A 1 mm object placed at the central direct plane results in detection of 59% of the signal in that plane. The theoretical observed contrast of a 3 mm object positioned at the center plane is 25% of the true contrast and decreases to 24% when the object is positioned between the central direct and cross planes. A PET system with an axial FWHM of 12 mm and a ring separation of 5-6 mm has a uniform sensitivity. A 1 mm object placed at the central direct plane detects 14% of the object signal in that plane. The theoretical observed contrast for a 3 mm object is 13% of true contrast when the object is positioned between the central direct and cross planes. It should be noted that all dimensions refer to the z direction through the center of the gantry in the simulated multiplanar system. The uniform sensitivity due to wider axial FWHMs decreases the amount of data loss for inter-ring gaps; however, the blurring associated with wider FWHMs decreases observed contrast.(ABSTRACT TRUNCATED AT 250 WORDS)

Phase-derivative imaging. II: Effects of beam diffraction and scatterer density.

The potential of using the phase derivative (PD) of the radio-frequency echograms for producing 2-dimensional grey scale images was further investigated. The PD images were produced by five different algorithms, which according to the results described in the companion paper yield PD images dominated by the amplitude (envelope, ENV), mixed PD-AM images and pure PD images. These images are termed according to their algorithms: ZCS, zero crossing counter with squelch; ASS, analytic signal with squelch; ASW, analytic signal with Wiener kernel; UNP, unwrapped phase; and SAS, smoothed analytic signal. The rf data were obtained from simulations and from experiments with a tissue mimicking phantom. PD images were analysed by calculation of the first and second order grey level statistics: mean level, signal-to-noise ratio (SNR) and the full width at half maximum (FWHM) of the autocovariance functions (ACVF). These parameters were systematically investigated for a range of depths with respect to the transducer and a range of scatterer densities of the insonated medium. The UNP and SAS images do not suffer much from the diffraction effect but do not display much information about the scatterer density either. The ASW and ASS images qualitatively display beam diffraction effects similar to those of the AM images, with the exception of the mean value which is at the minimum in the focus, where the AM yields a sharp maximum at that depth. The mean and the SNR of the ASW and ASS images increase with increasing scatterer density and saturate at a density of 5000 cm-3. The mean value of the envelope, however, displays a square root dependency over the whole range. The axial and lateral FWHM of the ACVF of the UNP and SAS methods are not significantly dependent on the scatterer density and decrease with increasing density for the ASW and ASS images, as was observed in the envelope images. It may be concluded that ASW and ASS methods produce PD grey scale images which are equally well suited for the diagnosis of diffuse diseases of parenchymal tissues as conventional AM images. The smaller "speckle" size of the ASW images might be advantageous, for the detection of focal lesions, but the lesion contrast is found to be much lower than for the ENV.

Phase-derivative imaging II: Effects of beam diffraction and scatterer density

The potential of using the phase derivative (PD) of the radio-frequency echograms for producing 2-dimensional grey scale images was further investigated. The PD images were produced by five different algorithms, which according to the results described in the companion paper yield PD images dominated by the amplitude (envelope, ENV), mixed PD-AM images and pure PD images. These images are termed according to their algorithms: ZCS, zero crossing counter with squelch; ASS, analytic signal with squelch; ASW, analytic signal with Wiener kernel; UNP, unwrapped phase; and SAS, smoothed analytic signal. The rf data were obtained from simulations and from experiments with a tissue mimicking phantom. PD images were analysed by calculation of the first and second order grey level statistics: mean level, signal-to-noise ratio (SNR) and the full width at half maximum (FWHM) of the autocovariance functions (ACVF). These parameters were systematically investigated for a range of depths with respect to the transducer and a range of scatterer densities of the insonated medium. The UNP and SAS images do not suffer much from the diffraction effect but do not display much information about the scatterer density either. The ASW and ASS images qualitatively display beam diffraction effects similar to those of the AM images, with the exception of the mean value which is at the minimum in the focus, where the AM yields a sharp maximum at that depth. The mean and the SNR of the ASW and ASS images increase with increasing scatterer density and saturate at a density of 5000 cm −3. The mean value of the envelope, however, displays a square root dependency over the whole range. The axial and lateral FWHM of the ACVF of the UNP and SAS methods are not significantly dependent on the scatterer density and decrease with increasing density for the ASW and ASS images, as was observed in the envelope images. It may be concluded that ASW and ASS methods produce PD grey scale images which are equally well suited for the diagnosis of diffuse diseases of parenchymal tissues as conventional AM images. The smaller “speckle” size of the ASW images might be advantageous, for the detection of focal lesions, but the lesion contrast is found to be much lower than for the ENV.

Texture of B-mode echograms: 3-D simulations and experiments of the effects of diffraction and scatterer density.

B-mode echograms were simulated by employing the impulse response method in transmission and reception using a discrete scatterer tissue model, with and without attenuation. The analytic signal approach was used for demodulation of the RF A-mode lines. The simulations were performed in 3-D space and compared to B-mode echograms obtained from experiments with scattering tissue phantoms. The average echo amplitude appeared to increase towards the focus and to decrease beyond it. In the focal zone, the average amplitude increased proportionally to the square root of the scatterer density. The signal to noise ratio (SNR) was found to be independent of depth, i.e., 1.91 as predicted for a Rayleigh distribution of gray levels, although a minimum was found in the focal zone at relatively low scatterer densities. The SNR continuously increased with increasing scatterer density and reached the limit of 1.91 at relatively high densities (greater than 10(4) cm-3). The lateral full width at half maximum (FWHM) of the two dimensional autocovariance function of the speckle increased continuously from the transducer face to far beyond the focus and decreased thereafter due to the diffraction effect. The lateral FWHM decreased proportionally to the logarithm of the scatterer density at low densities and reached a limit at high densities. Introduction of attenuation in the simulated tissue resulted in a much more pronounced depth dependence of the texture. The axial FWHM was independent of the distance to the transducer to a first approximation and decreased slightly with increasing scatterer density until a limit was reached at densities larger than 10(3) cm-3. This limit was in agreement with theory. The experiments confirmed the simulations and it can be concluded that the presented results are of great importance to the understanding of B-mode echograms and to the potential use of the analysis of B-mode texture for tissue characterization.