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Quantification of Morphological Features in Non-Contrast Ultrasound Microvasculature Imaging

Morphological features of small vessels provide invaluable information regarding underlying tissue, especially in cancerous tumors. This paper introduces methods for obtaining quantitative morphological features from microvasculature images obtained by non-contrast ultrasound imaging. Those images suffer from the artifact that limit quantitative analysis of the vessel morphological features. In this paper we introduce processing steps to increase accuracy of the morphological assessment for quantitative vessel analysis in presence of these artifact. Specifically, artificats are reduced by additional filtering and vessel segments obtained by skeletonization of the regularized microvasculature images are further analyzed to satisfy additional constraints, such as diameter, and length of the vessel segments. Measurement of some morphological metrics, such as tortuosity, depends on preserving large vessel trunks that may be broken down into multiple branches. We propose two methods to address this problem. In the first method, small vessel segments are suppressed in the vessel filtering process via adjusting the size scale of the regularization. Hence, tortuosity of the large trunks can be more accurately estimated by preserving longer vessel segments. In the second approach, small connected vessel segments are removed by a combination of morphological erosion and dilation operations on the segmented vasculature images. These methods are tested on representative in vivo images of breast lesion microvasculature, and the outcomes are discussed. This paper provides a tool for quantification of microvasculature image from non-contrast ultrasound imaging may result in potential biomarkers for diagnosis of some diseases.


INTRODUCTION
Microvasculature architecture is known to be associated with tissue state and pathology. Different conditions and diseases can alter vasculature at different size scales. Several studies have shown that malignant tumor growth coincides with changes in the vascularity of normal tissue [1][2][3]. Malignant tumors are known to present different mechanical features leading to the growth of more permeable and tortuous vessels [4,5]. Vessel tortuosity has been found to reveal information about some diseases [6,7]. Moreover, it has been shown that microvascular parameters such as vessel size and branching correlate very well with tumor aggressiveness and angiogenesis [8].
Several preclinical and clinical studies are available to derive quantitative information from microvasculature images obtained by contrast agent ultrasound for diagnostic purposes [9][10][11][12][13]. Additional examples include perfusion imaging [14,15] and molecular imaging [16,17]. Conventionally, these techniques endeavor to screen either the measure of blood flow inside a tissue volume by testing the increase in ultrasound signal from the blood pool contrast agents, or the presence of molecular markers of an ailment through imaging of the targeted contrast agent held in the blood flow. While a few researches have recently shown the capacity to quantify the architecture of the blood vessels in thyroid nodules and breast lesions, the use of contrast agents remains a barrier for extensive investigations [18][19][20]. On the other hand, analyzing vascular networks using ultrasound imaging devoid of contrast agent is a new framework made possible only recently, thanks to new clutter removal processing methods [21][22][23]. For example, Cohen et al. [24] demonstrated that vascular structures provide useful information for neuronavigation in brain imaging. This framework exploits the coherence of the tissue data provided by fast plane wave imaging of a large field of views to enable detailed imaging of the micro-vasculature structure by integrating longer data ensembles.
Blood vessel segmentation and analysis techniques have been studied exhaustively in other imaging modalities, such as optical imaging of the retina [25]. Retinal vessel segmentation algorithms are a principal component of automatic retinal infection screening frameworks. Different vessel analysis methods used in retinal images acquired by a fundus camera and have been summarized in detail in the literature [25]. Application of the brain vessel segmentation has also been described in magnetic resonance imaging (MRI) [26]. A vessel analysis tool was reported for morphometric measurement and representation of the vessels in computed tomography (CT) and MRI data sets [27]. Methods of blood vessel segmentation algorithms have been reviewed widely in the literature [28]. An isotropic minimal path-based framework has been proposed for segmentation and quantification of the vascular networks [29].
In this paper, we focus on challenges of vessel quantification for 2-dimensional (D) label-free ultrasound Doppler imaging and propose solutions to overcome such challenges. We evaluate performance of proposed solutions on the quantification of in vivo breast data. As noted, vessel quantification has been widely used in a broad range of imaging modalities; however, adaptation for the analysis of the microvasculature images obtained by non-contrast ultrasound requires careful treatment. This imaging modality, while enabling a versatile mechanism for acquiring small vessel images, introduces some challenges. The main problem stems from the 2-D interpretation of 3-D vascular structures. The work in retinal vessel analysis, while performed in 2-D, only considers surface vascularity for which a 2-D model is well-justified. When considering vessels distributed in a volume, 2-D cross-sectional ultrasound imaging may provide erroneous branching and vessel crossings that can lead to incorrect interpretation of vessel segments. While quantitative evaluation of parameters such as vessel density and diameter are not significantly affected by this phenomenon, measures of tortuosity, branching points, and number of vessel segments may become inaccurate. Another difficulty arises from imaging vessels in the cross-sectional orientation. Vessels may appear as small segments with incorrect information regarding vascular tree segments. The main contribution of this paper is to address these issues using either vessel filtering or morphological operations such that the most dominant vascular features can be obtained from 2-D noncontrast ultrasound imaging.
The remainder of this paper is organized such that Section II contains methods which include a background on image formation, Hessian-based filtering, vessel segmentation, morphological filtering, vessel quantification, and patient studies. Results are presented and discussed in section III. Finally, in section IV offers our main conclusions and future directions.

II. MATERIALS AND METHODS
Before quantitative information of vessels can be extracted from ultrasound microvasculature images, one must perform multiple preprocessing steps. The first step is image formation, which reconstructs the microvasculature image from a sequence of plane wave ultrasound images [22]. Second, vessel filtering is used to enhance the structure of vessels and provide adequate background separation for segmentation.
Morphological filtering, vessel segmentation, and skeletonization occurs last. The main contribution of this paper is in the last two modules, i.e. vessel segmentation and filtering and vessel quantification. First, though, we provide background on image formation and Hessian-based filtering.

A. Background on image formation
6 In this paper threshold n is selected based on setting a threshold on the slope of the second order derivative of eigenvalues decay, as described by Bayat, et al. in [22]. The filtered signal where T is the sampling time between two successive ultrafast ultrasound frames. To further enhance clutter removal performance, an additional step can be introduced before forming the intensity image in Finally, a top hat filter (THF) is applied on   , I x z to remove the background noise. A THF is comprised of a background estimation, followed by a background subtraction, operation [35]. Details about application of this filter for background removal of non-contrast ultrasound microvasculature images has been previously described [22]. The output image of THF is denoted by  

B. Hessian-based filtering
To enhance the visibility of the microvasculature image in the presence of strong background signals, morphological filtering based on a THF was used. Due to background noise, though, random patterns will also be present at the output of a THF. Hence, vessel enhancement filters are used to penalize background noise and further enhance vessel structure. Enhancement filters based on the analysis of eigenvalues of the Hessian matrix applied on a 2 -D image selectively amplify a specific local intensity profile or structure in an image. Hessian-based filters [36] distinguish between different local structures by analyzing the second order intensity derivatives at each point in the image. To enhance the local structures of various sizes, the analysis is typically performed on a Gaussian scale space of the image as previously described [22].   For 2-D images the following vessel likeliness measure has been proposed [36] and used [22] for vessel filtering of the ultrasound microvasculature images: where, 21 B R   is the blobness measure in 2-D image and accounts for the eccentricity of the second order ellipse;  and  are filter parameters. For consistency in notation, output image of Hessian filter is denoted by

C. Morphological filtering, vessel segmentation and skeletonization
Morphological filtering and subsequent vessel segmentation is performed on the output of the Hessian filter. Morphology analysis is a broad set of image processing operations that process images based on shapes (see Figure 2 and Table 1). Morphological operations apply a structuring element to an input image, creating an output image of the same size. In a morphological operation, the value of each pixel in the output image is based on a comparison to the corresponding pixel in the input image with its neighbors. By choosing the size and shape of the neighborhood, we can construct a morphological operation that is sensitive to the specific shapes in the input image. Morphological filtering and vessel segmentation include the following steps: converting the microvasculature image (output of Hessian filter) to a binary image, removing small noise-like objects through an erosion and dilation operation, removing small holes, filling small holes with a dilation and erosion operation, finding image skeleton, cleaning skeleton image, removing spur pixels, labeling connected components, finding branch points, dilating branch points, removing branch points, and removing small objects. In the remainder of this section, each step will be briefly described. After these steps, the output image includes the vessel segments. Those segments are analyzed in the vessel quantification module to estimate desired quantitative parameters of the vessels.

2) Erosion followed by dilation: One of the basic morphological operations is dilation and erosion.
Dilation adds pixels to the boundaries of objects in an image, while erosion removes pixels on object boundaries. The number of pixels added or removed from the objects in an image depends on the size and shape of the structuring element used to process the image. In the morphological dilation and erosion operations, the value of any given pixel in the output image is determined by applying a rule to the corresponding pixel and its neighbors in the input image. The rule used to process the pixels defines the operation as dilation or erosion [37]. We use erosion followed by dilation to remove some noise-like small objects in the image after amplitude thresholding.
3) Removing small holes: The spectral subtraction in equation 7, while providing additional clutter suppression, may induce erroneous intensity nulling in the image, at isolated points along the vessels with horizontal orientation. This intensity nulling is the effect of spectral nulling due to the ultrasound beam being perpendicular to the blood flow, resulting in symmetric spectrum in the frequency domain. Thus, the two components in spectral subtraction of equation 7 cancel each other. To avoid erroneous splitting of the vessels at these points, a morphological "hole-filling' step is added. This step sets a pixel to 1 if five or more pixels in its 3-by-3 neighborhood are 1s; otherwise, it sets the pixel to 0. After this operation, some small holes may still remain. To remove the remaining small holes in the vessels, we use the operation of dilation followed by erosion 4) Finding the skeleton image: The next step in the morphological operations on binary images is removing pixels so that an object without holes shrinks to a line, and an object with holes shrinks to a connected ring halfway between each hole and the outer boundary. Finding the skeleton image is based on a thinning algorithm [38].
Vessel segments (overlaid on the binary vessel image in Figure 4) are used for vessel quantification. Figure 4 shows the block diagram of the vessel quantification algorithm. We use three types of vessel analysis: structure analysis, diameter analysis, and tortuosity analysis. Therefore, the quantification parameters considered here include the number of vessel segments, vessel density, the number of branch points, the diameter of vessels, and vessel tortuosity. Two different tortuosity metrics are considered: the distance metric (DM) and the sum of angle metric (SOAM). We use Moore-Neighbor tracing algorithm modified by Jacob's criteria [39] to track vessels. The location vector of vessel j is

1) Distance Metric" (DM):
The DM of vessel j is the most common approach used to evaluate vascular tortuosity in 2-D [25] . It provides a ratio between the actual path length of a meandering curve and the linear distance between endpoints as depicted by : cos The torsional angle at point , , which is defined as , 1 : cos Since we are performing 2D imaging, 2 components of internal product are parallel and kj T is derived zero or 180. For all analyses in this paper, all torsional angles are considered 0 when they are 180.
Therefore, the total angle The SOAM calculates the total tortuosity of vessel j and is defined as 3) Estimating diameter: To acquire localized vessel diameter, we first invert the binary image. Therefore, pixels corresponding to vessel are 0 and pixels corresponding to background are 1. Next we obtain the Euclidean distance in the inverted image between zero pixels (corresponding to vessel segments) and the nearest non-zero pixel (corresponding to background) of the image. For all pixels corresponding to vessels (zero pixels), the distance to the nearest non vessel pixel (one pixel) is dedicated to that pixel.
For each vessel segment, the average diameter of the vessel segment over points related to that vessel is obtained as follows: We define the erosion/dilation (ED) factor as follows

4) Quantification of vessel trunks:
to remove small objects and analyze trunks inside the lesion. Using this method, vessel structures with a size less than r are removed from the image. In dilation, only structures larger than r that remain in the image are dilated and converted to their original size. Therefore, we expect only vessel trunks to appear in the final image. In the tortuosity analysis, our goal is to analyze the vessels that are fully located in the imaging plane. Therefore, by removing small vessel segments connected to main vessel trunks, it is possible to analyze the main vessel trunk.

E. Patient demographics and histopathological outcomes
This study was done to demonstrate the process and potential application of microvasculature quantification in vivo. Under an institutional review board-approved protocol, 4 patients with breast lesions participated in this study; they gave written, informed consent beforehand. To assess the performance of the proposed methods for morphological analysis of the microvasculature images obtained by contrast-agent-free ultrasound, an Alpinion Ecube12-R ultrasound machine (ALPINION Medical Systems, Seoul, Korea) and a linear array transducer L3-12H (ALPINION Medical Systems, Seoul, Korea) were used. For each patient, 3 seconds of high frame rate, 5-angle compounded plane wave imaging data were acquired at 680 frames per second. The lesions from the 4 patients were manually segmented using the B-mode image obtained from the first frame in the imaging sequence. All patients underwent biopsy following the ultrasound examination and pathology results were used as the final diagnosis. Vasculature images were obtained using SVD clutter removal filtering, followed by THF background removal and Hessian-based vessel filtering as described previously in the literature [22]. The THF was employed using a disk structuring element of size 577.5 µm. Vessel filtering was applied using size scales in the range of 115.5 µm to 346.5 µm. Values outside this range are explicitly noted in the results section. The vessel's filter parameters and were set to 1 and 0.6, respectively. Vessel images were further analyzed to acquire morphological parameters using the proposed method. The minimum length for a vessel segment was considered 385 µm; the minimum diameter for a vessel segment was considered to be 181.2 µm. To convert the gray scale images to binary, a THR of 0.15 was used, which is obtained empirically for noise fluctuations removal.

III. RESULTS
We applied the vessel quantification algorithm on the microvasculature images obtained from vascularized breast lesions. Four different lesions: 2 malignant [invasive/infiltrating ductal carcinoma (IDC) grade III], and 2 benign (fibroadenomas) were studied. For clarity, we refer to them as IDC grade III (1) and (2) and fibroadenoma (3) and (4). We derived quantitative parameters of the microvasculature images for these 4 lesions to study and address challenges of vessel quantification using contrast-agentfree ultrasound imaging.   The B-mode image of IDC grade III lesion (2) is seen in Figure 7(a). A number of representative vessels are seen in Figure 7(b), in which the DM has been applied to highlight the accuracy of measuring tortuosity by DM. As can be observed, the estimated tortuosity well-corroborates with the visual appearance of the vessel segments, such that larger deviations from the straight line indicate increased tortuosity.
To examine the effect of small vessel branches connected to the main vessel trunk on vessel quantification, we studied IDC grade III lesion (2). Figure 8(a) and (b) show the output of the Hessianbased filtering for this lesion with different minimum size scale. As Figure 8(a) shows, there are some branches connected to the main vessel trunk, and these branches cause the main trunk to break down into small vessel segments at branching points. By increasing the minimum size scale of the vessel filter to 462 µm, though, these branching vessels are not visible in Figure 8(b). Hence, the multiple scale size processing capability of the vessel filter enables removing the smaller vessel branches so that large trunks can be more accurately analyzed for tortuosity. The obvious disadvantage of increasing the minimum size scale is losing fine vessel segments with diameters smaller than the minimum allowed.      (1) seen in Figure 8(a) as a function of the erosion-dilation (ED) factor in µm. The mean(τ) is shown to be an increasing function of the ED factor. Figure 11(b) demonstrates the mean diameter of vessel segments [mean(diameter)] as a function of the ED factor. As expected, the mean diameter of vessel segments is an increasing function of the ED. Figure 11(c) shows the mean length of vessel segments [mean(length)] as a function of the ED factor . As expected, by removing small vessel segments, the mean length of vessel segments is an increasing function of the ED factor. Figure 11(d) shows the number of vessel segments as a function of the ED. It is evident that the number of vessel segments is a decreasing function of the ED, mainly due to removal of the small vessel segments. By comparison, the results seen in Figure 9(a) and Figure 11(a) demonstrate that using erosion-dilation for removing small vessel segments provides a smoother increment in the DM than changing the minimum size scale of the Hessian filter; however, large 23 ED values (≥ 6 pixels, equivalent to 231 µm) should be avoided to prevent adding unwanted distortion to the image.
As discussed previously, spectral subtraction may result in a small number of holes in parts of the vessel images where the Doppler shift is perfectly symmetric (i.e., flow perpendicular to the ultrasound beam).
These areas need to be filled before further analysis. To assess the performance of our solution for removing these holes with spectral subtraction, we consider two cases. Figure 12      The last case is a highly vascularized fibroadenoma breast lesion (4) shown in Figure 16.
Here, we study the effect of different threshold values on minimum acceptable vessel length. This threshold can remove isolated vessel segments but cannot keep vessel trunks. By removing isolated vessel segments, we found it possible to increase the average tortuosity in the image. Figure 18 shows the number of vessel segments, mean of vessel segment length, mean of vessel segment diameter, and mean of DM in terms of threshold, defining the minimum vessel length for our four examined lesions. As expected, by increasing the threshold for minimum vessel length, the number of vessel segments is reduced and the mean of vessel segment length is increased, since by increasing the minimum threshold of vessel length, more small vessel segments are removed and longer vessels remain for analysis. Vessel segment diameter remains almost constant in terms of the threshold of minimum vessel length. Also, DM exhibits an increasing behavior in terms of the threshold of minimum vessel length, since small vessel segments normally are straight; therefore mean (τ) increases by removing small vessel segments.   Quantitative assessment of these four lesions is summarized in

IV. CONCLUSIONS
A set of methods for quantification of the tissue microvasculature obtained by non-contrast ultrasonic microvasculature imaging was presented. The micro-vasculature map comprises vessel segments resulting from blood activity. We introduced procedures to acquire morphometric parameters with additional morphological constrains to reduce erroneous data. Vascular structures were accepted as vessel segments when multiple constraints on amplitude of the vessel segment, diameter of the vessel segment, and length of the vessel segment were satisfied. We addressed challenges in acquiring segmentation-ready microvasculature images and showed that a combination of background removal and vessel enhancement filtering allows vessel segmentation and skeletonization, in turn allowing morphological analysis. The quantitative parameters may include tortuosity measures, (DM and SOAM), diameter of vessel segments, length of vessel segments, number of vessel segments, number of branching points, and vessel density.
Given the 2-D nature of B-mode ultrasound imaging, accurate interpretation of some vascular features can be difficult. 2-D cross sectional imaging may provide erroneous branching and vessel crossings that may lead to incorrect interpretation of the vessel segments. While quantitative evaluation of parameters, such as vessel density and diameter, are not significantly affected by this phenomenon, measures of the tortuosity, number of branching points, and number of vessel segments may become inaccurate. In this paper, we introduced a number of strategies to enable extraction of several morphological features by adding additional constrains. The most important contribution was to devise methods to preserve large vessel trunks that may be broken into small pieces due to intersection with out-of-plane vessel segments, namely by removing small size-scales from the vessel filtering and small vessel segments connected to large trunks via morphological operations. Another limitation in ultrasonic microvasculature images is related to small vessel segments which may result from cross sectional imaging of vessels. These may appear as small vessel segments with incorrect information regarding the vascular tree segments. We addressed this issue by enforcing vessel segment length and diameter constraints. The methods presented in this paper provide a set of tools for quantitative assessment of microvasculature morphological features. These features may be associated with certain diseases or different health conditions. In cancer, for example, malignant tumors have been shown to give rise to tortuous vessels. The initial results in this paper suggest the quantitative morphological parameters may allow differentiation of certain lesions, such as benign and malignant breast lesions. Therefore, the methods presented in this paper for quantitative assessment of microvasculature morphological features obtained from non-contrast ultrasound images may result in potential biomarkers for the diagnosis of some diseases.

ACKNOWLEDGMENT
This work was supported by the NIH Grants R01EB017213, R01CA148994, R01CA168575, R01CA195527, and Ro1CA174723. The authors wish to thanks Desiree J. Lanzino, PT, PhD, for her help in editing the paper.
V. REFERENCES