Cardinal Points Symmetry Landmarks Distribution Model for Segmentation of Region of Interest in Simulated B-Mode Ultrasound Carotid Artery Images

DOI: http://dx.doi.org/10.24018/ejers.2019.4.5.1243 26  Abstract—Measurement accuracy and understanding of geometry of Common Carotid Artery (CCA) play an important role in carotid atherosclerosis assessment and management. In order to device techniques that can accurately analyze the effects of plaques on the carotid artery, a model that can sufficiently segment the Region of Interest (ROI) in the B-mode ultrasound image of carotid artery is needed. In this paper, a new Cardinal Points Symmetry Landmarks Distribution Model (CPS-LDM) to sufficiently segment the ROI in the carotid artery B-mode ultrasound imaged in the transverse plane is developed. The developed model employs a combination of fixed landmarks (FLs) and movable landmarks (MLs) to obtain the total landmarks (TLs) that can sufficiently segment the shape of the ROI of the carotid artery. Simulated ultrasound images are used. Four FLs are fixed on each of the four ROIs of the simulated carotid artery determined by the cardinal points North (N), South (S), East (E) and West (W) drawn on the ROIs of the carotid artery. The MLs are determined by the inter-cardinal directions such as North-East (NE), North-West (NW) and so on. The CPS-LDM equation developed allows us to visualize graphically the optimum number of points that can sufficiently segment the ROIs. ImageJ2 software was used to generate the Cartesian coordinates for each landmark which were then used to generate the Shape Space Pattern (SSP) of the carotid artery ready for further statistical analysis. The results showed that the CPS-LD model is sufficiently generic and adaptable to a variety of carotid artery B-mode ultrasound image simulated under different scenarios.


I. INTRODUCTION
One area in which ultrasonography has found very useful application in the medical field is in the area of cardiovascular image diagnosis.Recently, the increase in the number of patients suffering from cardiovascular diseases has become a serious social problem [1].The most wellknown risk factor for the development of cardiovascular events is internal carotid artery stenosis also known as internal carotid artery disease [2].Carotid stenosis is the constriction of the lumen of the carotid artery as a result of Carotid Atherosclerosis [3].Carotid atherosclerosis is a condition in which the carotid artery wall thickens as a result of plaque formation.Plaques are made up of cholesterol and fatty acids, calcium, and sometimes fibrous connective tissue [4].Stroke is one of the leading causes of long-term disability and death throughout the world.It is caused by the disruption of brain function due to ischemia, and carotid atherosclerosis is one of the major causes of ischemia [5], [6], [7].Most strokes are caused by a blood clot, plaque buildup, or a combination of the two which and are known as ischemic strokes.Around 87% of all strokes are ischemic strokes [8].Internal carotid artery stenosis has been found to be responsible for 30% of ischemic strokes [9] and it has also been shown to be a strong predictor of death in the general population [10], [11].
Measurement accuracy and understanding of geometry of Common Carotid Artery (CCA) play an important role in carotid atherosclerosis assessment and management [12].The typical arterial wall consists of three layers: an innermost layer, "the intima", a middle layer, "the media", and an outer layer, "the adventita" [13].This is illustrated in Fig. 1.Fig. 1.A schematic cross section of an artery.From within, the arterial wall consists of three layers: intima, media and adventitia [13].
Important factors in diagnosis of atherosclerotic disease of the carotid arteries are the intima-media thickness (IMT), plaque morphology, criteria for grading stenosis, limiting factors such as the presence of dissection or cardiac abnormalities, distinction between near occlusion and total occlusion, and the presence of a subclavian steal [14].The IMT measurement is indicative of the thickness of the arterial wall, and is precisely imaged using ultrasound technology [15].This imaging can be in two planes: the longitudinal plane (long axis plane) and the transverse plane (short axis plane).
In this paper, we developed a novel Cardinal Point Symmetry Landmark Distribution Model (CPS-LDM) for the complete geometric shape characterization of simulated carotid artery B-mode ultrasound images in the transverse plane (short axis plane).The model consists of the following components.
1) Cardinal point and inter-cardinal point symmetry description of the simulated carotid artery.
2) Fixed landmarks (FLs)  The remainder of this paper is organized as follows.Section II describes the Cardinal Point Symmetry (CPS) of the simulated carotid artery geometry used in deriving the CPS-LDM model.Section III derives the fixed, movable and total landmarks on the CPS carotid artery.Section IV shows the results obtained from the developed equations and conclusions are finally drawn in Section V.

II. DEVELOPMENT OF CARDINAL POINT SYMMETRY (CPS) MODEL FOR SIMULATED CAROTID ARTERY IMAGE
A. Data Acquisition Images were obtained from [16] which were simulated images using Field II ( [17], [18]) a MATLAB based program that can simulate all kinds of ultrasound transducers and other associated ultrasound images.Figure 2 shows a sample of a simulated B-mode ultrasound carotid artery obtained using Field II software.Each landmark coordinate was registered and digitized using ImageJ2 software [19].

B. CPS Model Description
The four cardinal points also known as cardinal directions are the North, East, South, and West, commonly denoted by their initials N, E, S, and W. The inter-cardinal points or directions are North-East (NE), South-East (SE), South-West (SW), and North-West (NW). Figure 3 shows the cardinal and inter-cardinal points used to develop the CPS-LDM.The cardinal points concept was then used to describe and label strategic points on the carotid artery image which subsequently led to the full description of the carotid artery image.This is shown in Fig. 4 and Fig. 5.   1 shows a detailed description of each label used in Fig. 4.
The VS-VS line also divides the ROIs into two equal halves which are the Eastern (Rightward) half and the Western (leftward) half.The leftmost tip of ROI 1 is marked West1 i.e.W1 and the rightmost tip of ROI 1 is marked East1 i.e.E1.The same designation goes for the other ROIs so that we have W2 and E2 for ROI 2, W3 and E3 for ROI 3 and W4 and E4 for ROI 4. This designation led to the full description of the imaged carotid arterial wall in the transverse plane shown in Fig. 5. Table 2 shows a detailed description of each notation used in Fig. 5.The first two ROIs (ROI [1] and ROI [2]) occupy the AR while the last two ROIs (ROI [3] and ROI [4]) occupy the PR.

III. DEVELOPING THE CPS-LDM EQUATIONS
The CPS model describes the geometric shape of the carotid arteries by two set of landmarks; The Fixed Landmarks (FLs) and the Movable Landmarks (MLs).The Total Landmarks (TLs) which completely describe the shape of the carotid arteries is given by equation (1).

MLs FLs TLs   (1)
A. Fixed landmarks (FLs) equation Fig. 6 shows the FLs on the artery, there carotid are four FLs for each ROI which are the North (N), the South (S), the East (E) and the West (W).For example, ROI 1 has points on N1 , S1 , E1 , and W1.These FLs are the red points marked on the ROIs of Fig. 6.Let the number of ROI(s) desired to be described be represented by U, and then position of the described ROI(s) be represented by index M, then the number of FLs on any desired ROI is given by equation (2).
Equation ( 2) governs the annotating of fixed landmarks on the carotid artery image.

B. Rules followed in selecting the index M
1) When the positions of the ROIs to be described follow each other in sequence, then a hyphen (-) is used in between the numbers to separate them e.g.For M = 1-2; this means that ROI 1 and ROI 2 are described.
For M = 1-3; this means that ROI 1, ROI 2 and ROI 3 are described.For M = 1-4; this means that ROI 1, ROI 2, ROI 3 and ROI 4 are described.For M = 2-4; this means that ROI 2, ROI 3 and ROI 4 are described.For M = 3-4; this means that ROI 3 and ROI 4 are described 2) When the positions of the ROIs to be described do not follow each other sequentially, then a comma (,) is used in between the numbers to separate them e.g.For M = 1, 3; this means that ROI 1 and ROI 3 are described.
For M = 1, 4; this means that ROI 1 and ROI 4 are described.
For M = 2, 4; this means that ROI 2 and ROI 4 are described.3) A combination of the above two rules can also be used.e.g.For M = 1-2, 4; this means that ROI 1, ROI 2 and ROI 4 are described.
The fixed landmarks (FLs) are not sufficient to fully capture the geometry of the carotid artery, hence the need for the movable landmarks (MLs).

C. Movable landmarks (MLs) equation
In developing the MLs equation, the symmetry of the The MLs equation is then given as; Applying the symmetry equations (3 to 18) into equation (19) yield equation ( 20)

D. ROI "mirror-image" condition
Looking carefully at Fig. 6, it can be observed that the horizontal line of symmetry HS-HS divides the image such that ROI 4 is like a mirror image of ROI 1 and ROI 3 is a mirror image of ROI 2. This leads to the postulation of the "mirror-image" condition for simulated ultrasound carotid artery imaged in the transverse cross-sectional plane which is stated below.

If an ultrasound carotid artery is properly and carefully simulated in the transverse cross-sectional plane such that all the ROIs are captured, the horizontal line of symmetry HS-HS divides the image such that then the posterior region is like the mirror image of the anterior region. i.e. ROI 4 is like a mirror image of ROI 1 and ROI 3 is like a mirror image of ROI 2.
Applying the "mirror-image" condition, equation ( 20) is further simplified into equation ( 21)

E. Total landmarks (TLs) equation
The total number of landmarks that can be annotated on the transverse section of any simulated carotid artery image to govern its complete shape characterization is given in equation ( 1) which is repeated below.

B. Calculations, Results and Discussion
Comparing the given equation ( 24) with the CPS-LDM equation in (23), it is observed that the first term in the right hand side of equation ( 24  The landmark coordinates which is obtained from imageJ2 software and the SSP generated from these coordinates for the FLs is shown in Table 3 and Fig. 8 respectively.= 10 implies that ROIs 1 and 4 is divided equally into NW and NE respectively.The integer 10 is chosen by the user and it can be changed at the user's discretion.The underlying principle in the MLs equation is that the integer 10 is divided also into two equal integers.These equal integers in this case will be landmarked on the NW and NE of ROIs considered at that point, in this case, ROIs 1 and 4.This procedure applies to all other terms and integers in the MLs equation.This operation is captured mathematically in equations ( 28) and (29).Figure 9 shows the landmark distribution of both the FLs and MLs on the simulated carotid artery image.The MLs is distributed on the carotid artery image using equation (26).Figure 10 shows the complete SSP of the carotid artery.The coordinates used to generate the SSP is obtained from imageJ2 in the same way it was done for the FLs.

C. Spacing constraints when annotating the FLs and MLs together on the carotid artery image
According to our model, the carotid artery image is completely characterized by its number of FLs and MLs.Though the spacing between these points are intuitively determined by the user, the following spacing constraints are followed when annotating these landmarks on the carotid artery image.
1) The distance between any consecutive ML annotated along the path of the cardinal point of any chosen ROI should be equally spaced.For example from figure 9  The spacing of the MLs in ROI 1, 4: along the SW cardinal point is constrained by the condition |ML 1 -ML 2| = |ML 2 -ML 3| = |ML 3 -ML 4| = …….= h2 , where h1 and h2 are any real number and h1 and h2 may be equal or not.
2) The distance between a FL and a consecutive ML either in the forward or backward direction along the path of the cardinal point of any chosen ROI should be equal to the distance between the consecutive MLs along that same ROI path.For example from figure 9  3) Based on the above two conditions, all consecutive landmarks (either FLs and MLs) along the path of the cardinal point of any chosen ROI should be equally spaced so that consistency of annotation can be maintained on any set of numbers of images.
There are situations when the number chosen by the user for the MLs are not even integers, this poses a problem for equal integer divisibility.Example 2 in appendix B addressed how such challenge was overcome.

E. Calculations and Results
Comparing the given equation ( 31  K n = 9, symmetry equation demands that NE = 4.5, and NW = 4.5.But the number of points must be an integer, hence the symmetry equations will be modified to make one side greater than the other side by one integer.For our example above, the following choices can be made Figure 11 shows the landmark distribution of both the FLs and MLs on the simulated carotid artery image.Figure 12 shows the complete SSP of the carotid artery.


Abstract-Measurement accuracy and understanding of geometry of Common Carotid Artery (CCA) play an important role in carotid atherosclerosis assessment and management.In order to device techniques that can accurately analyze the effects of plaques on the carotid artery, a model that can sufficiently segment the Region of Interest (ROI) in the B-mode ultrasound image of carotid artery is needed.In this paper, a new Cardinal Points Symmetry Landmarks Distribution Model (CPS-LDM) to sufficiently segment the ROI in the carotid artery B-mode ultrasound imaged in the transverse plane is developed.The developed model employs a combination of fixed landmarks (FLs) and movable landmarks (MLs) to obtain the total landmarks (TLs) that can sufficiently segment the shape of the ROI of the carotid artery.Simulated ultrasound images are used.Four FLs are fixed on each of the four ROIs of the simulated carotid artery determined by the cardinal points North (N), South (S), East (E) and West (W) drawn on the ROIs of the carotid artery.The MLs are determined by the inter-cardinal directions such as North-East (NE), North-West (NW) and so on.The CPS-LDM equation developed allows us to visualize graphically the optimum number of points that can sufficiently segment the ROIs.ImageJ2 software was used to generate the Cartesian coordinates for each landmark which were then used to generate the Shape Space Pattern (SSP) of the carotid artery ready for further statistical analysis.The results showed that the CPS-LD model is sufficiently generic and adaptable to a variety of carotid artery B-mode ultrasound image simulated under different scenarios.Index Terms-Cardinal Points, Carotid Artery, Landmarks, Region of Interest, Ultrasound.

(
MLs) equation, and the total landmarks (TLs) equation to yield the CPS-LDM equation.3)Shape Space Pattern (SSP) of the carotid artery based on the CPS-LDM equation developed.

Fig. 2 .
Fig. 2. Simulated B-mode ultrasound image of carotid artery in the transverse plane obtained from [16] using Field II software.

Fig 3 :
Fig 3: The cardinal and inter-cardinal points used to develop the CPS-LD Model.

Fig. 6 .
Fig. 6.Positions of the FLs on the carotid artery carotid artery shape shown in Fig.6is utilized.Symmetry equations for each ROI given in equation (3number of integer points that can be annotated on the ROI boundaries of the carotid artery where n(K) is the number of integer points on the ROIs, ROI (superscript) is the position of the ROI under consideration (ROI = 1, 2, 3, 4) and CP (subscript) is the cardinal point under consideration (CP = NW, NE, etc.) can be written in a matrix-like form as shown in (22). ) governs the landmarking of movable points on the simulated carotid artery image.

(
called equation (23) the Cardinal Point Symmetry Landmark Distribution Model (CPS-LDM) Equation and this equation completely characterize the geometric shape of any simulated B-mode ultrasound carotid artery imaged in the transverse cross-sectional plane.IV.CONCLUSION In this paper, a new Cardinal Point Symmetry Landmark Distribution Model (CPS-LDM) was developed.This model was shown to be able to segment sufficiently the ROIs of Bmode ultrasound carotid artery simulated in the transverse plane.This model was also shown to be generic enough and adaptable to varieties of B-mode ultrasound carotid arteries simulated under various scenarios.APPENDIX In appendix A and B, examples are shown on how to use CPS-LD Model to landmark and segment simulated carotid artery B-mode ultrasound images in the transverse plane.4 and M = 1-4.Calculate the TLs required to fully annotate the carotid artery and show its Shape Space Pattern (SSP).

4 ;
) determines the FLs while the second term of the equation determines the MLs.The numbers imputed into the matrix of the MLs equation is user dependent.To determine the FLs, equation (2) given as equation (25) here is used.ROIs 1, 2, 3 and 4 are required to be described).Each ROIs will contain 4 FLs.Fig.7shows how the FLs are annotated on the carotid artery.

Fig. 7 .
Fig. 7. Annotation of FLs on a simulated carotid artery image in transverse plane

Fig. 9 .Fig. 10 .
Fig. 9. Landmark distribution for both the FLs and MLs on the simulated carotid artery image
4 and M = 1-4.Calculate the TLs required to fully annotate the carotid artery and show its Shape Space Pattern (SSP).

Fig. 11 .Fig. 12 .
Fig. 11.Landmark distribution for both the FLs and MLs on the carotid artery image

TABLE I :
DESCRIPTIONS OF LABELS IN FIG. 4 HS -HSHorizontal Symmetry Line.This line divides the ROIs into two regions which are the Anterior Region (AR) and the Posterior Region (PR).

TABLE II :
Full Description of Labeling of Fig.5

TABLE III :
LANDMARK COORDINATES FOR THE FLS Each ROIs will contain 4 FLs.Also comparing the given equation (31) with the CPS-LDM equation given in (23), the MLs equation given as equation (33) here is;