Investigation on the load-displacement curves of a human healthy heel pad: In vivo compression data compared to numerical results.

The aims of the present work were to build a 3D subject-specific heel pad model based on the anatomy revealed by MR imaging of a subject's heel pad, and to compare the load-displacement responses obtained from this model with those obtained from a compression device used on the subject's heel pad. A 30 year-old European healthy female (mass=54kg, height=165cm) was enrolled in this study. Her left foot underwent both MRI and compression tests. A numerical model of the heel region was developed based on a 3D CAD solid model obtained by MR images. The calcaneal fat pad tissue was described with a visco-hyperelastic model, while a fiber-reinforced hyperelastic model was formulated for the skin. Numerical analyses were performed to interpret the mechanical response of heel tissues. Different loading conditions were assumed according to experimental tests. The heel tissues showed a non-linear visco-elastic behavior and the load-displacement curves followed a characteristic hysteresis form. The energy dissipation ratios measured by experimental tests (0.25±0.02 at low strain rate and 0.26±0.03 at high strain rate) were comparable with those evaluated by finite element analyses (0.23±0.01 at low strain rate and 0.25±0.01 at high strain rate). The validity and efficacy of the investigation performed was confirmed by the interpretation of the mechanical response of the heel tissues under different strain rates. The mean absolute percentage error between experimental data and model results was 0.39% at low strain rate and 0.28% at high strain rate.

The challenges in creating reference maps for verification of ultrasound images.

In the development of new medical imaging techniques, references to which the images can be compared are necessary if one wants to assess how precise the images are. This is especially interesting in diagnostic ultrasound where a number of artefacts influence the image. The reference can either be derived from a phantom with precisely known properties and geometry, from the specifications of a computer phantom (simulated images) or from evaluation of biological tissue. The third approach can be conducted with other medical imaging modalities (CT, MRI, etc.) or "destructive testing" involving histology. In this paper, aspects of the latter method is considered in detail. Formalin fixed tissue is moulded into an agar block containing at set of fiducial markers. The block is scanned with ultrasound. Both tissue and fiducial markers are imaged. The block is afterwards sliced at the location of the fiducial markers. The slices are then photographed and analyzed histologically. From this data, reference maps with similar geometry as the ultrasound images can be created. Ideally, for each pixel in the ultrasound image, these reference maps indicate tissue type, such as collagen poor tissue, collagen rich tissue, etc. Many of the sources of error as well as the challenges with such a method are discussed.

A method to create reference maps for evaluation of ultrasound images of carotid atherosclerotic plaque.

Ten formalin-fixed atherosclerotic carotid plaques removed by endarterectomy were molded into rectangular agar blocks containing fiducial markers on the top surface. Plaque and fiducial markers were imaged with 3-D multiangle ultrasound (US) spatial compounding as well as planar X ray. Subsequently, the blocks were decalcified, sliced, photographed and analyzed histologically. This gave a total of 123 slices. The plaque regions of the photographs were outlined and the outline adjusted to partly compensate for occasional displacement during slicing. Inside this outline, the material constitutions were found by incorporating the histologic information. From this set, slices with 1. too much tissue displacement due to cutting or 2. lack of identification of calcification as found by x ray, were removed. This resulted in 53 reference maps. The material types identified covered soft tissues, fibrous tissue, calcified tissue and unidentified tissues. The 53 reference maps can be used for direct automated quantitative comparison with US images.

Visual and quantitative evaluation of selected image combination schemes in ultrasound spatial compound scanning.

Multi-angle spatial compound images are normally generated by averaging the recorded single-angle images (SAIs). To exploit possible advantages associated with alternative combination schemes, this paper investigates both the effect of number of angles (Ntheta) as well as operator (mean, median, mean-excluding-maximum (mem), root-mean-square (rms), geometric mean and maximum) on image quality (tissue delineation and artifacts), speckle signal-to-noise ratio (SNRs) and contrast. The evaluation is based on in vitro SAI (+/-21 degrees in steps of delta theta = 7 degrees) of formalin fixed porcine tissue containing adipose, connective and muscular tissue. Image quality increased with number of angles up to +/-14 degrees after which the improvements became debatable. The mem and median operators, which try to render the images more quantitatively correct by suppressing strong echoes from specular reflectors, provide some improvement in this regard. When combining the SAI with the mean operator, the SNR, increases--in general--with Ntheta. For Ntheta = 2, the SNRs increases with delta theta as expected. When Ntheta = 7, the highest SNRs is obtained for the mem, rms, and geometric mean operators, while the lowest SNRs is obtained for the maximum operator. When comparing SNRs for adipose and fibrous tissue, the level is close to 1.91 for adipose tissue but only 1.7 for fibrous tissue which contain relatively few organized scattering structures.

A method to obtain reference images for evaluation of ultrasonic tissue characterization techniques.

A general problem when evaluating ultrasonic methods for tissue characterization is that "a golden standard" is seldom known. This paper describes a manual method to obtain a reference image, with the same geometry as the ultrasound image, indicating spatial location of the different tissue types present in the biological tissue scanned in vitro. A 30 x 10 x 2 mm3 piece of formalin fixed porcine tissue was molded into an agar block, which on the top surface, contained a set of fiducial markers, spaced 2.5 mm. The block was submerged into 20 degrees C water and a set of parallel 7.5 MHz spatial compound ultrasound images of tissue and fiducial markers were recorded each 0.5 mm. Guided by the fiducial markers, the agar block was subsequently cut into slices 2.5 mm thick, photographed and finally analyzed histologically identifying these tissues: collagen rich, collagen poor, micro vessels and muscle fibres. Due to: (1) the cutting procedure, (2) the finite size of the ultrasound beam and (3) the spatial variation in propagation velocity, the macroscopic photographs did not align completely with the ultrasound images. Likewise, the histological image is a geometrically distorted version of the macroscopic photograph, due to the histological preparation process. The histological information was "mapped back" into the format of the ultrasound images the following way: On the macroscopic images, outlines were drawn manually which defined the border of the tissue. These outlines were superimposed on the corresponding ultrasound images (identified via the fiducial markers) and modified to encompass what appeared to be tissue regions on the ultrasound images and subsequently re-applied to the macroscopic image. This modified macroscopic outline was used as guideline when drawing outlines identifying regions of the various tissue types. Specifically, the macroscopic image revealed the borders between the different tissues, while the histological image identified the four tissue types. A set of 12 reference images based on modified macroscopic outlines was created. The overlap between the ultrasound images and the macroscopic images--which are the geometrical basis for the final reference images--was between 77% and 93%. A set of 12 reference images spaced 2.5 mm, identifying spatial location of four different tissue types in porcine muscle has been created. With the reference images, it is possible to quantitatively compare different ultrasound based tissue classification techniques.

Real-time spatial compound imaging improves reproducibility in the evaluation of atherosclerotic carotid plaques.

Compound imaging has the ability of reducing speckle and clutter artifacts demonstrated in in vitro studies compared to conventional, single-angle imaging. We investigated intra- and interobserver agreement of 38 outlines of carotid artery plaque images acquired by these techniques, by measuring the overlapping area after repeated outlines. In general, both techniques showed good agreement. When considering the images with poorest overlap, compound imaging had a significant advantage over conventional imaging regarding both intra- and interobserver agreement. The interobserver variation for the overlapping area after two outlines was 20% for conventional technique and 10% for compound. The interobserver variation of the gray scale median value (GSM) for conventional technique ranged from -32 to +20 and from -6 to +6 for compound. Likewise, the coefficient of repeatability for the GSM value was 13 for conventional imaging and three for compound imaging, and interobserver variation for the GSM value for the overlapping area was 34% and 9% for conventional and compound technique. In conclusion, compound imaging improves intra- and interobserver agreement and reduces interobserver variation in the GSM value in a clinical setting.

Spiral computed tomographic imaging related to computerized ultrasonographic images of carotid plaque morphology and histology.

OBJECTIVE: Echolucency of carotid atherosclerotic plaques, as evaluated by computerized B-mode ultrasonographic images, has been associated with an increased incidence of brain infarcts on cerebral computed tomographic scans. We tested the hypotheses that characterization of carotid plaques on spiral computed tomographic images correlates with that on computerized B-mode ultrasonographic images and that spiral computed tomographic imaging predicts the histomorphometric plaque content. METHODS: The study included 38 patients with neurologic symptoms and at least 50% stenosis of the ipsilateral carotid artery. High-resolution B-mode ultrasonographic images and spiral computed tomographic images of carotid plaques were computer processed to yield a quantitative measure, the gray scale level of the plaque. RESULTS: The mean Hounsfield value for spiral computed tomographic images correlated with the gray scale median for B-mode ultrasonographic images (univariate linear regression analysis: r = 0.45; P = .01) and the histologic content of calcification in the plaque (r = 0.34; P = .04) but not with lipid, hemorrhage, or fibrous tissue in the plaque. CONCLUSIONS: Spiral computed tomographic imaging seems to correlate with B-mode ultrasonographic imaging for showing plaque characteristics. Spiral computed tomographic attenuation was also correlated with the amount of calcification noted on histologic examination but not with lipid and hemorrhage, the components thought to characterize vulnerable, rupture-prone plaques.

The influence of roughness, angle, range, and transducer type on the echo signal from planar interfaces.

The received electrical echo signal from a pulse-echo system insonifying a planar interface was measured for varying degrees of rms roughness [0 to 0.29 mm (0 to 1.7 lambda)], angles of incidence, theta, (-7 degrees to 7 degrees), and ranges to a planar or focused transducer. The effect of varying theta is quantified in terms of the energy of the received signal, E(theta), and the normalized spectrum of the received signal. E(theta) is approximately Gaussian when using a planar transducer or a focused transducer with the reflecting interface located at or beyond the focal point. For focused transducers with the interface located closer than the geometrical point of focus, two maxima can sometimes be observed when varying the incident angle. As is generally known, the width of E(theta) is strongly dependent on transducer type, e.g., for a smooth interface, the -3 dB width for a 25.4 mm diameter 5-MHz planar and focused transducer was approximately 0.5 degree and 4 degrees (at the focal point), respectively. E(0 degree) as a function of surface roughness, Rq, was nearly linear on a decibel scale, with a slope of -109 dB/(Rq/lambda) and -61 dB/(Rq/lambda) for planar and focused transducers, respectively. The characteristic nulls present in the normalized spectra of the echo signal at non-normal incidence tend to vanish with increasing Rq when using planar transducers. For focused transducers, the normalized spectra change from relatively flat to monotonically decreasing as Rq increases, and they exhibit reduced amplitude with increased incident angle.

In vitro spatial compound scanning for improved visualization of atherosclerosis.

A new off-line multiangle ultrasound (US) compound scanner has been built with the purpose of investigating possible improvements in visualization of vascular structure. Images of two formalin-fixed human atherosclerotic plaques removed by carotid endarterectomy were recorded from seven insonification angles over a range of 42 degrees and the individual images were combined (averaged) into a single image (spatial compounding). Compared to conventional B-mode imaging, this multiangle compound imaging (MACI) method features images with reduced angle-dependence, reduced random variation (speckle) and improved delineation of the plaque outline. With the MACI approach, it is, thus, easier to assess e.g., a possible residual lumen of an atherosclerotic artery as well as the level of echogenicity for the different plaque constituents.

Multi-angle compound imaging.

This paper reports on a scanning technique, denoted multi-angle compound imaging (MACI), using spatial compounding. The MACI method also contains elements of frequency compounding, as the transit frequency is lowered for the highest beam angles in order to reduce grating lobes. Compared to conventional B-mode imaging MACI offers better defined tissue boundaries and lower variance of the speckle pattern, resulting in an image with reduced random variations. Design and implementation of a compound imaging system is described, images of rubber tubes and porcine aorta are shown and effects on visualization are discussed. The speckle reduction is analyzed numerically and the results are found to be in excellent agreement with existing theory. An investigation of detectability of low-contrast lesions shows significant improvements compared to conventional imaging. Finally, possibilities for improving diagnosis of atherosclerotic diseases using MACI are discussed.

Echo-lucency of computerized ultrasound images of carotid atherosclerotic plaques are associated with increased levels of triglyceride-rich lipoproteins as well as increased plaque lipid content.

BACKGROUND: Echo-lucency of carotid atherosclerotic plaques on computerized ultrasound B-mode images has been associated with a high incidence of brain infarcts as evaluated on CT scans. We tested the hypotheses that triglyceride-rich lipoproteins in the fasting and postprandial state predict carotid plaque echo-lucency and that echo-lucency predicts a high plaque lipid content. METHODS AND RESULTS: The study included 137 patients with neurological symptoms and > or = 50% stenosis of the relevant carotid artery. High-resolution B-mode ultrasound images of carotid plaques were computer processed to yield a measure of echogenicity (gray-scale level). Lipoproteins were measured before and hourly for 4 hours after a standardized fatty meal. A subgroup of 58 patients underwent endarterectomy. On linear regression analysis, echo-lucency (low gray-scale level) was associated with elevated levels of fasting and postprandial plasma triglycerides (P=.0002 and P=.002), IDL cholesterol (P=.0009 and P=.006), and VLDL/chylomicron remnant cholesterol (P=.0003 and P=.0004) and triglycerides (P=.0003 and P=.003), the area under the plasma triglyceride curve 0 to 4 hours after a fatty meal (P=.001), and body mass index (P=.0001). On ANCOVA, body mass index, fasting IDL cholesterol, and fasting plasma triglycerides were independent predictors of echo-lucency. Echo-lucency was associated with increased relative plaque lipid content (P=.02). CONCLUSIONS: Increased plasma levels of triglyceride-rich lipoproteins predict echo-lucency of carotid plaques, which is associated with increased plaque lipid content. Because echo-lucency has been associated with a high incidence of brain infarcts on CT scans, triglyceride-rich lipoproteins may predict a plaque type particularly vulnerable to rupture.

Quantitative analysis of ultrasound B-mode images of carotid atherosclerotic plaque: correlation with visual classification and histological examination.

This paper presents a quantitative comparison of three types of information available for 52 patients scheduled for carotid endarterectomy: subjective classification of the ultrasound images obtained during scanning before operation, first-and second-order statistical features extracted from regions of the plaque in still ultrasound images from three orthogonal scan planes and finally a histological analysis of the surgically removed plaque. The quantitative comparison was made with the linear model and with separation of the available data into training and test sets. The comparison of subjective classification with features from still ultrasound images revealed an overall agreement of 60% for classification of echogenicity and 70% for classification of structure. Comparison of the histologically determined relative volume of soft materials with features from the still images revealed a correlation coefficient of r = -0.42(p = 0.002). for mean echogenicity of the plaque region. The best performing feature was of second order and denoted Contrast (r = -0.5). Though significant, the latter correlation is probably not strong enough to be useful for clinical prediction of relative volume of soft materials for individual patients. Reasons for this is discussed in the paper, together with suggestions for improvements.

The diffraction response interpolation method.

Computer modeling of the output voltage in a pulse-echo system is computationally very demanding, particularly when considering reflector surfaces of arbitrary geometry. A new, efficient computational tool, the diffraction response interpolation method (DRIM), for modeling of reflectors in a fluid medium, is presented. The DRIM is based on the velocity potential impulse response method, adapted to pulse-echo applications by the use of acoustical reciprocity. Specifically, the DRIM operates by dividing the reflector surface into planar elements, finding the diffraction response at the corners of the elements, calculating the response integrated over the surface element by time-domain convolutions with analytically determined filters, and summing the responses from the individual surface elements. As the method is based on linearity, effects such as shadowing, higher-order diffraction, nonlinear propagation, cannot be directly incorporated in the modeling. The DRIM has been compared to other modeling tools when possible. Excellent agreement between the results obtained with the DRIM and the alternative techniques have been found, and the DRIM offers reductions in computation time in the range from 30 to 400 times. Experimental results obtained using a planar circular transducer together with cylindrical reflectors were compared to DRIM results and fairly good agreement was observed.

Influence of tissue preservation methods on arterial geometry and echogenicity.

Thoracic porcine aortas from 5 pigs were investigated with 7.5-MHz ultrasound in vitro at low and high transmural pressure before and after the following tissue preservation methods were applied: 1. Storage in frozen condition (-12 degrees C) for 24 h followed by thawing; 2. fixation in formalin at zero transmural pressure for 24 h; and 3. fixation with formalin for 24 h while applying 74 mmHg of transmural pressure from within the lumen and a tensile force to longitudinally stretch the artery. Fixation in formalin at zero transmural pressure resulted in swelling of the arterial wall (25 +/- 40%, p < 0.02, at low transmural measurement pressure) and in decreased echogenicity (-23 +/- 38%, p < 0.01) of the arterial vessel wall. No changes in this respect were found after storage in a frozen condition nor after fixation in formalin at high transmural pressure which, therefore, are more appropriate procedures for fixation of arteries prior to in vitro ultrasound examination if geometry is important.

Target velocity estimation with FM and PW echo ranging Doppler systems I. Signal analysis.

The theoretical foundation is presented for velocity estimation with a pulsed wave (PW) Doppler system transmitting linear FM signals. The Doppler system possesses echo ranging capabilities and is evaluated in the context of Doppler ultrasound for blood velocity measurement. The FM excitation signal is formulated and the received signal is derived for a single moving particle. This signal is similar to the transmitted signal, but with modified parameters due to Doppler effect and range. The demodulated received signal is subsequently derived and analyzed. It is shown that, due to the Doppler effect, this is a linear sweep signal as well. The velocity and range information obtainable from one and two consecutively received signals are described. The latter case establishes the basis for an FM Doppler system for blood velocity measurements.

Target velocity estimation with FM and PW echo ranging Doppler systems. II. Systems analysis.

For part I see ibid., vol.40, no.4, pp.366-372 (1993). In Part I, the encoding of the velocity and range information into the received and demodulated signals based on transmission of coherent repetitive linear sweep signals, was discussed. In the present work, two different implementations of FM Doppler systems that can be used to obtain velocity profiles are presented. The first implementation is similar to the implementation of a conventional pulsed wave (PW) Doppler system, based on measurement of phase shift (correlation based system): the second implementation is a frequency-domain analog to the PW Doppler system, based on time shift measurements (cross correlation-based system).