CHAPTER 2 CLINICAL DIAGNOSIS OF LIVER DISEASES BASED ON
2.3 Correlation between Tissue and Echotexture
2.3.2 Echotexture of the liver
In a typical ultrasound image of the liver are examples of all the four scattering types (Figure 5). As liver parenchyma is a collection of molecules, Class 0 scatterers are present. The speckle indicates Class 1 scatterers. Small vessels (including the terminal branches of bile duct, hepatic artery, and portal vein in a portal triad, the central vein in
Figure 5: Ultrasound image of a normal liver. This image exemplifies several acoustic scattering types.
Class 3
Class 2
a liver lobule) correspond to Class 2 scatterers. Eventually, the liver boundaries are Class 3 scatterers. Comparing Figure 5 with those of sponge (Figure 1 and 4), the main difference between the textures is there are some “white spots” with higher local contrast in the echotexture of the liver, and these white spots represent scattering of Class 2. Therefore, the assumption that only fully developed speckle present in the echotexture of normal liver should be corrected.
The tissue structure of liver parenchyma is assumed isotropic. As mentioned above, however, digital scan conversion and the comparatively lower lateral sampling rate make the echotexture anisotropic. With the unification of sampling format and sampling rate, the echotexture of the liver parenchyma should be more isotropic, like that of the
Figure 6: Ultrasound image with the unification of sampling rate.
Class 2
sponge. Figure 6 is the one in Figure 5 with the unification of the sampling format and sampling rate. Even if the region of interest surrounded by a rectangle is somewhat
“heterogeneous”, there is no obvious tissue structure information for rough endoplasmic reticulum. For this reason, this echotexture may be categorized as one which does not have morphological structural change.
Connective tissue which supports the structure of the liver may be Class 1, 2 or 3, depending on the ka number and the incident angle, where k denotes the mean wavenumber and a is the radius. Low density extracellular matrix (ECM) complex present in the space of Disse may be considered as Class 1 scatterers. When the liver is in injury, ECM complexes become cross-linked, and thus most of them are associated with Class 2 scatterers. If the dimension scale of cross-linked ECM complex confronting the wavefront is large enough (i.e. ka>>1), this ECM complex is referred to Class 3. According to the striking increase on the amount of Class 2 (and 3) scatterers, forming a cross-linked reticulum, the echotexture of liver fibrosis (and liver cirrhosis) looks “coarser” or “rougher” and its contrast is higher than that of normal liver (or the region of tissue without obvious reticulum). Figure 7 is a typical ultrasound image of liver cirrhosis. There is prominent reticulum, denoted as Reticulum A, which is
“superposed” on speckles. While in the subregion denoted as Reticulum B, it is not easy to distinguish the reticulum from the speckles. With the unification of sampling format
Figure 8: Ultrasound image of liver cirrhosis with the unification of sampling rate.
Reticulum A
Boundary
Reticulum B
Reticulum A Reticulum B
Boundary
Figure 7: Ultrasound image of liver cirrhosis. Connective tissue caused by liver injury is apparent.
and sampling format, the corresponding to Reticulum B becomes apparent (Figure 8).
This implies that the unification of sampling rate and sampling format may help separate cross-linked reticulum from speckles based on the scale.
Chapter 3
Feature Extraction for B-mode Ultrasound Echotexture of the Liver
Computer-aided diagnosis based on the ultrasonic image must meet what is seen by the physicians. In this chapter, the useful perceptual features for ultrasound liver echotexture are provided, and then a measure model is introduced. The textural features are vulnerable to the non-uniform sampling rate caused by digital scan conversion (DSC), thus we propose a “back-scan conversion” method with consideration to the sampling rate unification as a preprocessing before quantifying the visual features.
3.1
Perceptual Features for Ultrasound Liver EchotextureTissue characterization attempts to provide quantitative information about the state of health of the liver interrogated by ultrasound beams. Arrangement of these beams forms a 2-dimensional image, representing geometrically structural information of the tissue. Nevertheless, ultrasound echotexture suffers from the low signal to noise ratio and other physical limitation, such as the diffraction and DSC. It is hard to analyze ultrasonic echotexture quantitatively with a reliable and reusable method. Thus perceptual properties are widely used to measure the characteristics of an image texture, because it is very fast to diagnose the liver disease by the human vision of well-trained experts.
Clinically and usually, physicians use the terms of “coarseness” [2, 3], “roughness”
[4-6], and “heterogeneity” [13] to describe the ultrasound echotexture. As mentioned in Chapter 2, these visual properties are indicative of cross-linked reticulum consisting of collagens, and this cross-linked reticulum is the result of secretion caused by liver injury.
However, it is very difficult to define these terms consistently; they are individually relative properties. Besides, the echotexture of severe liver fibrosis is inferred as more
“coarser” than that of mild liver fibrosis, or the contrast of echotexture of liver cirrhosis is more than that of mild fibrosis. The quantities of these perceptual properties are directly relative to the distribution of cross-linked reticulum and the structure change of the liver, which are important to indicate the stage of liver injury. Thus, we try to quantify the echotexture based on the perceptual properties.
3.2
Textural Features for Ultrasound Liver EchotextureUltrasound tissue characterization (UTC) could be defined as the assessment by ultrasound of quantitative information about the characteristics of biological tissues, and pathological changes [24]. UTC which might use B-mode echotexture to characterize the liver of a health man was first developed by Nicholas et al. [25]. After that, many literatures tried to detect diffuse liver diseases [4, 14-16, 20, 26-31]. Even several of them [15, 16] used perceptual properties, like coarseness, to analyze ultrasound echotexture, however, there is no evident relationship between the used features and
perceptual properties. Rosenfeld and Thurston [32] suggested that coarseness of image texture is inversely related to the number of edges per unit area. Weszka et al. [33] used
“gray level difference statistics” to measure the degree of coarseness. Amadasun and King [34] extended the methods proposed by Rosenfeld et al. and Haralick [35], and provided several textural features based on the concept of “patch” to evaluate the textural properties. Those textural features were demonstrated corresponding to parts of the ability of human vision, in which the “coarseness” feature was used to estimate the coarseness of echotexture of liver [36]. Very few literatures try to analyze ultrasound image textures based on tissue texture standpoint. The frequent textural features based on co-occurrence matrix proposed by Haralick [35] are not clinically suitable for ultrasound echotexture of the liver. It is because that one co-occurrence matrix needs a priori distance and orientation, but for liver tissue needs several distinct distances and orientations. It is necessary to develop a complex algorithm to compute the correlations between the co-occurrence matrices with distinct distances and orientations, resulting to an incredible consumption of computation complex.
Amadasun and King [34] proposed several textural features which relate highly to visual properties, and some literatures [37-39] used these features to estimate the characteristics of several categories of image textures. These features benefit from local and global texture information, and the computation complexity and effort of
Amadasun’s measure is very low. The basic interrelationships of Amadasun and King in the gray level texture concept are as the following. The spatial organization may be random, may have a pair-wise dependence of one pixel on a neighborhood, or may have a dependence of n primitives at a time. The dependence may be structural and/or probabilistic. When a small-area “patch” of an image has little variation of gray level, the dominant property of that area is just “tone”. When a small-area “patch” has wide variation of gray level, the dominant property of that area is “texture.” In other words, the characteristics of textural properties are associated with the spatial interrelationships between them. This implies that gray level texture is really a two-layered structure. The first layer is to specify the local properties which manifest themselves in tonal primitives, and the second layer having to do with is specifying the organization among the tonal primitives.
Amadasun’s measure [34], based on a vector s(i) called neighborhood gray-tone
difference matrix (NGTDM, see in Appendix), is chosen for texture analysis here, and it relates highly to visual properties. The original definition of NGTDM from Amadasun is ROI-size dependent; to make feature of ROI with different size comparable and rational, the definition of NGTDM for an M×N ROI must be modified as follows:
⎪⎪
The denominator is a normalization factor for different size of ROI. s(i) is a summation of the intensity difference of all the neighborhoods, whose central pixels are with gray level i. Suppose Di is the mean Laplacian pertaining to gray level i, then eqn (1) may
be modified as
i
where p(i) is the probability of occurrence of intensity i. We adopt four of the textural features proposed by Amadasun and describe their relationships to the echotexture of liver.
3.2.1 Coarseness
The first feature proposed by Amadasun is used to evaluate the degree of coarseness of ultrasound image texture, which is defined as
,
where p(i) is the probability of occurrence of gray level i , excluding those in the peripheral regions of the ROI, G is the highest image gray level, and h ε is a very small number to prevent fcos being infinite.
In an ultrasound image, speckle is inevitable and texture patterns with high spatial frequency are usually treated as speckle; on the other hand, low frequency texture patterns are considered coarser and have primitives with larger areas. In a coarse texture,
as a high degree of local uniformity in intensity, there would be small differences between )fi(k,l and Aikl , leading to the value of i−Aikl in eqn ( A2) small.
Hence the summation of NGTDM over all image pixels would give an index of coarseness. From eqn (2), a small value of fcos implies large value of s(i), which
means a significant change in intensity, and it captures the characteristics of fully developed speckles; while a large value of fcos corresponds other coarser texture
patterns, including speckles and structural information of the tissue. In other words,
fcos might be treated as representing the characteristics of texture on a scale. i−Aikl in eqn ( A2) may be regarded as the response of the eight-neighbor Laplacian filter, used to find local contrast (or edge) around an image pixel, and fcos in eqn (2)
corresponds to the suggestion of Rosenfeld et al. [32, 33].
Amadasun’s measure was demonstrated useful for ranking the coarseness of natural images; however, it has not been demonstrated useful for ranking ultrasound images. The efficacy of measuring coarseness of ultrasound image texture by Amadasun’s feature is to be shown by measuring the coarseness of ROIs at different sampling rates. Theoretically, the discrete Laplacian of a texture increases as the sampling rate decreases unless the sampling rate is so low to make the texture loses all information. If the sampling rate is kept to maintain texture information properly, the shape of gray level distribution would not change much. Therefore, the change of
coarseness will due primarily to the sampling spacing (i.e. distance between adjacent pixels), which makes the magnitude of Laplacian increases as sampling spacing increases. Let the coarseness at sampling rate ω be fcos(ω) (eqn (A3) in Appendix).
Aikl
i− in eqn (2) may be regarded as the response of the eight-neighbor Laplacian
filter. If the sampling rate decreases, the numerator in eqn (2) increases, making the output of eqn (A3) decreases; that is, the coarseness ratio, fcos(ω1) fcos(ω2), must be a
monotonic function of ω1 ω2 with positive correlation. Thus, if ω1 >ω2, then )
( )
( 1 cos 2
cos ω f ω
f >1 for the efficacy of Amadasun’s measure, and vise versa.
3.2.2 Contrast
Human visual system is more sensitive to contrast than absolute luminance. We can perceive the world similarly regardless of the huge changes in illumination. An image is said to have a high level of contrast if the gray level difference between two objects in the image is large. The human contrast sensitivity function shows the spatial intensity variation of image texture also affects the contrast of an image [40]. For example, a small checkbox seems perceptually to have a higher contrast than a coarse checkbox with the same dynamic range of gray level. Taking these two factors into consideration, Amadasun et al. proposed a textural feature to express the contrast of an image:
⎥⎦
where Ng is the total number of different gray levels present in the image,
⎩⎨
This feature is composed by two components. The first term is the average weighted squared difference between the different gray levels taken in pairs, reflecting the dynamic range of gray level. It may be expanded as follows:
[
( )]
, term is proportional to the variation in intensity. The second term is the average difference between pixel gray level and the average gray level of their neighborhoods;this quantity increases with the amount of local variation in gray level.
Texture of an ultrasound image is composed by speckles and the structural scattering of the tissue. It is supposed that the spatial intensity variation of fully developed speckles is higher than that of the structural scattering of the tissue, and the
threshold leads to the discriminability of this object in ultrasound image. According to the supposition and the definition of contrast proposed by Amadasun, an image texture with fully developed speckles or obviously structural scattering has a higher value of fcon
than that composed by unclear structure and speckles.
If a point P’ between two adjacent pixels (P1 and P2) is sampled, the mean contrast between P’ and P1, with P’ and P2 is lower than that between P1 and P2. Therefore, the ratio of contrast with higher sampling rate over that with lower sampling rate is less than one.
3.2.3 Busyness
Busyness represents the texture of cluttering of the space. A fine image texture with busyness is one in which there are rapid changes of gray level from one pixel to its neighbor; that is the spatial intensity variation of the image texture is very high. Thus, a fine image texture has a low level of local uniformity in gray level. On the other hand, if the spatial intensity variation is very low, the image texture has a high degree of local uniformity too, even if the contrast is large. Therefore, the degree of busyness was proposed by Amadasun et al. as the following equation:
0
The numerator is to measure the spatial intensity variation of the image texture; while
and each value is weighted by its probability of occurrence. The denominator results in the suppression of the effect of contrast variations, leading to the emphasis of the spatial intensity variation of image texture. However, there exist some problems in the denominator proposed by Amadasun. For example, let the distribution of gray level shift by t upward, i.e.
keep the same degree of busyness with only a shift of gray level. Therefore, this equation for measuring busyness is modified using the first term of fcon as:
[
2 2]
It is generally assumed that homogeneous soft parenchyma has an ultrasound image texture with fully developed speckles; nevertheless, tissue structure affects ultrasound image textures as well. That is, it is necessary to consider the structural scattering in analyzing ultrasound image texture. The numerator of ffin is related to the number of edges of a texture, implying the number of patches, but susceptible to the
contrast of the texture; while the denominator stands for the contrast of texture caused mainly by the tissue structure. Therefore, ffin may be used to express the spatial frequency of an ultrasound image texture without the dependence on the texture contrast.
For higher sampling rate, the spatial change of an echotexture becomes lower, and then the ratio of busyness with higher sampling rate over that with lower sampling rate is less than one.
3.2.4 Complexity
A texture is considered complex if it contains rich information. This occurs when there are many patches or primitives present in the texture and the primitives have different average gray levels. Also, a texture with a large number of sharp edges may be considered as complex. All these depend on the spatial period of pattern repetition and on the dynamic range of gray scale, which means complexity is partly correlated with fineness and contrast.
Generally, ultrasound image textures in which the spatial intensity variation is low tend to have few patches with different average gray levels, and the patches would be large. Consequently, the resulting high level of local uniformity in intensity will produce few edges. A texture in which there are rapid gray level changes is comparatively more complex than a texture that has a high degree of local uniformity in
intensity. However rapid gray level changes would generally result in a large number of different gray levels, leading to a low probability of each individual value occurring.
Therefore the sizes of primitives and/or occurrence of gray level values tend to are inverse with complexity. A proposed measure for complexity is as follows:
{ }
The fcom is a sum of differences between intensity values taken in pairs, and these differences are weighted by the sum of the probability-weighted s(i) and s( j). The
normalizing factor, Ar( pi + pj), is used to represent the inverse relationship between complexity and the sizes of primitives and/or the probabilities of gray levels. Ar( pi + pj) would be high for coarse textures and small for fine textures. The absolute differences convey the influence of contrast variations on complexity. High values of fcom indicates a high degree of richness of information content.
For higher sampling rate, the spatial contrast of an echotexture becomes lower, leading to a lower degree of complexity, and then the ratio of busyness with higher sampling rate over that with lower sampling rate is less than one.
3.3
Unifying the Sampling RateIn order to obtain a large field of view, a curved-linear (convex-) array transducer
the scan lines of the presented sector image are displayed in Cartesian coordinate grid (raster format) on a monitor, which is accomplished by a procedure called “digital scan conversion (DSC)”. Since DSC induces various sampling rates [20, 41] according to the depth and orientation, it is necessary to unify the sampling rate before analyze the ultrasound images. The preprocessing contains two aspects: back-scan conversion (sampling format unification) and sampling rate unification.
3.3.1 Sampling Format Unification
In B-mode ultrasonic imaging, the transducer transmits each ultrasonic wave in one direction according to the prior settings, and then receives and places the echo information with respect to the direction and transmitting period in a 2-dimensional matrix. This matrix pertains to a polar coordinate (Figure 9). In order to make a television or PC-style rectangular image, this information has to be spatially remapped by a digital scan converter, which converts the acquired polar coordinate ultrasound data to the Cartesian format used by digital monitors (Figure 10). Data in Cartesian raster format are created by interpolation from real scan lines, and data at deeper depth require more interpolations than that at shallow depth, leading to a coarser image texture.
The speckle size also determines the spatial bandwidth of the images. For imaging distance smaller than the focal distance, the speckle size is proportional with the imaging distance, which means the speckle size in radians is constant. For imaging
Figure 10: DSC converts the polar matrix which stores the echo information on the left side into the raster format on the right side, where k and l are the Cartesian
coordinates.
Figure 9: The left depicts the scan lines (F1 to F9) of ultrasonic wave, where O is the
Figure 9: The left depicts the scan lines (F1 to F9) of ultrasonic wave, where O is the