Ultrasound Measurement of Vascular Distensibility Based on Edge Detection and Speckle Tracking Using Ultrasound DICOM Data

Abstract

This study presents an edge detection and speckle tracking (EDST) based algorithm to calculate distensibility as percentage of change of vessel diameter during cardiac cycles. Canny edge detector, Vandermonde matrix representation, Kanade Lucas Tomasi algorithm with pyramidal segmentation, and penalized least squares technique identifies the vessel lumen edge, track the vessel diameter, detrend the signal and find peaks and valleys when the vessel is fully distended or contracted. An upper extremity artery from 10 patients underwent an ultrasound examination as part of preoperative evaluation before arteriovenous fistula surgery. Three studies were performed to evaluate EDST with automatic peak and valley selection versus manual speckle selection of expert users using manual peak and valley selection. Results demonstrate the effectiveness of the proposed methodology, to obtain comparable results as those obtained by expert-users, and considerably reducing the variability associated with external factors such as excessive motion, fluctuations in stroke volume, beat-to-beat blood pressure changes, breathing cycles, and arm-transducer pressure.

Distensibility can be defined as the difference between the maximum and minimum diameter of blood vessel normalized to the baseline vessel diameter within multiple cardiac cycles.^1,2 Distensibility is related to dilatation of the vessel and may play an important role in arteriovenous fistula (AVF) maturation³ in addition to vessel diameter.^4,5 Vascular distensibility can be assessed with ultrasound, venography, or manually with a caliper.^5–8 Arteriovenous fistula maturation failure rate is high, from 20% to 60%,^9–11 according to Allon et al.,⁹ the minimum criteria for AVF surgery are 2 mm in arterial diameter and 2.5 mm in veins and no evidence of stenosis or thrombosis. While there are accepted criteria for prognosticating fistula maturation using the vein diameter measurement,^12–14 and we have used speckle tracking to estimate vein distensibility,¹⁵ the role of the artery in maturation is increasingly explored.^16–19

Arterial biomechanical measurements can be obtained from noninvasive ultrasound measurements, detecting the elastic modulus differences between patients with chronic kidney disease.¹⁷ Our group has developed an open-source speckle tracking application using digital imaging and communications in medicine (DICOM) ultrasound data, Kanade Lucas Tomasi (KLT) algorithm, and pyramidal segmentation to detect changes during fistula maturation using B-mode imaging.¹⁸

Conventional ultrasound devices use transducers (compound by piezoelectric plate and other elements), to convert electrical transmission pulses into ultrasonic (acoustic) pulses, and conversely, ultrasonic echo pulses into electrical echo signals. The electrical signals from multiple-element array transducers are numerically combined into imaging beams perpendicular to the probe face. The electrical echo signals are then processed during the beam formation process and contain the original transmit frequency, also referred to as the radiofrequency (RF) signal.²⁰ Considerable early work in this field has been performed using the RF data, obtained either under nondisclosure agreements with ultrasound manufacturers or by using expensive ultrasound research platforms.^21,22 All ultrasound machines use RF signals to reconstruct lower resolution (the envelope of the RF data) brightness-mode or “B-mode” images that are routinely used. B-mode is available in DICOM format in almost every commercial device²³ and available to all clinicians. Recent work has suggested that comparatively low-resolution B-mode data that is used clinically is sufficient for high-resolution vascular distensibility measurements.^18,19,23 In this study, we continued work with open source B-mode DICOM data to advance our automation aims toward making more widely accessible and useable tools for research into vascular distensibility. Automation with open-source data will reduce barriers to more widespread testing with conventional clinical ultrasound machines.^18,22,24

Previous methods¹⁸ rely on a manual user selection of points on the intimal layer of the vessel and manual peak and valley selection (MPVS). In this study, we implement and test an automatic edge detection and automatic peak and valley selection (APVS) application to reduce the inter-user variability during the manual selection of the edge and calculate distensibility automatically.

Materials and Methods

The four-step procedure using an open-source graphic user interface implemented in Matlab 2020a to calculate distensibility is presented as follows:

Step 1: Region of Interest identification

The identification of the region of interest (ROI) reduces DICOM data required for speckle tracking by enclosing the area that conforms to the vessel of interest. The input parameters associated with the manipulation of DICOM files are frame rate and frame interval. The frame rate is an input parameter associated with a specific number of frames (n) displayed per second using DICOM data. The frame interval I, is the clipped interval range of frames from the original DICOM file as a set of matrices defined as $I=\left(I_1,\dots ,I_k\right)$, where $I_1$ and $I_k$ are two matrices that define the beginning and end of all the frames to be analyzed from the DICOM file. Every frame representation from $I_1$ to $I_k$ corresponds to an independent matrix in grayscale that can be manipulated to discard the initial frames that contain undesired movement due to initial probe alignment in the vessel detection stage.

Two ROIs are manually selected in $I_1$ and I_k, and represented by $S{q}_1\in M_{2x2}$ and $S{q}_2\in M_{2x2}$, see Equation 1. Every matrix of Sq₁ and Sq₂ are conformed by two coordinates $\left[x_1^{},x_2^{}\right]$, and $\left[x_3^{},x_4^{}\right]$ representing the corresponding extremes of each ROI (Figure 1). By using Sq₁ and Sq₂ is possible to define a new ROI, $S{q}_3\in M_{2x2}$, that contain the first and second column of the matrix, where $\delta$ is compound by Sq₁ and Sq₂ (see Equation 1). The ROI Sq₃ encloses the vessel in the complete frame interval I by including the displacement of the vessel from I₁ to I_k. A new frame interval defined as $I^{\text{'}}$ is created utilizing the ROI Sq₃ that delimitates to the area of I to reduce processing time during the speckle tracking procedure. Speckle tracking allows the measurement of internal displacement and strain fields of tissue motion comparing the similarity of ROIs defined as kernels through a sequence of frames.²⁵

Figure 1.: General scheme to reduce overload and facilitate edge detection based on ROI selection. ROI, region of interest.

$$S{q}_1=\left[\begin{array}{cc}{x}_1^1& x_2^1\\ x_3^1& x_4^1\end{array}\right]\cdot S{q}_2=\left[\begin{array}{cc}{x}_1^2& x_2^2\\ x_3^2& x_4^2\end{array}\right]\cdot \delta =\left[\begin{array}{c}S{q}_1\\ S{q}_2\end{array}\right]$$

$$S{q}_3=\left[\begin{array}{cc}\text{min}({\delta }_1)& min({\delta }_2)\\ \max \left({\delta }_1\right)& \max \left({\delta }_2\right)\end{array}\right]$$

Step 2: Semi-Automated Assisted Edge Detection

Edge detection is a technique that allows the identification of the inner contour of the vessel by analyzing the changes of grayscale intensity, where the resolution of the DICOM data affects directly to edge detection. The edge detection is implemented utilizing an improved version of the frame representation $I_1^{\text{'}}$ defined as $I_1^{\text{'}\text{'}}$. The matrix $I_1^{\text{'}\text{'}}$ has a wider grayscale in comparison to $I_1^{\text{'}}$ in cases where it is possible spanning the initial and final grayscale mapping intervals and $G_{out}=\left[l_{out},h_{out}\right]$, where every element of G_in and G_out defined as l and h are scalars and correspond to the lowest and highest limits manually selected by the operator using grayscale histogram.²⁶ The frame representation $I_1^{\text{'}}$ is a matrix defined as $I_1^{\text{'}}\in M_{mxn}$, where $mxn$ corresponds to the rows and columns of $I_1^{\text{'}}$ (see Equation 2). The matrix $J$ is an all-ones matrix defined as $J\in M_{mxn}$ that has the same number of rows and columns as $I_1^{\text{'}}$ (see Equation 2).

$$I_1^{\text{'}\text{'}}=J{l}_{out}+\frac{(I_1^{\text{'}}-J{l}_{in})(h_{out}-l_{out})}{(h_{in}-l_{in})}$$

The frame representation $I_1^{\text{'}\text{'}}$ requires passing through an optical character recognition starting by a binarization process from into $B_1^{\text{'}\text{'}}$ by thresholding. The matrix contains multiple pixel portions in black and white (Figure 2A). The number of pixels from every portion is counted and stored in a database where portions with a higher number of pixels are considered part of the ROI and tinier pixel portions are discarded from (Figure 2B). The resultant matrix $B_1^{\text{'}\text{'}}$ passes through a process of smoothing, nonmaximal suppression, and hysteresis²⁷ to identify changes of grayscale intensity in the portions that generate contrast on $B_1^{\text{'}\text{'}}$. Canny edge detector (CED) was implemented using MATLAB image processing toolbox²⁷ (Figure 2C) presenting a good detection of edges to discard noise, a good localization of the detected edge as the true edge, and finally, a minimal response when only one edge is accepted for each position.^28,29

Figure 2.: Image processing scheme for edge detection.

The result of CED on $B_1^{\text{'}\text{'}}$ is a binary matrix defined as $E_1^{\text{'}\text{'}}$ that represents the edge of the vessel (Figure 2C). The frame representation $E_1^{\text{'}\text{'}}$ is overlapped with $I_1^{\text{'}}$ to create the matrix $U_1^{\text{'}}$. Figure 3A shows $U_1^{\text{'}}$ as a visual frame representation used to manually select a speckle $S{p}_0$ above the edge of the vessel to create automatically a line that traces a vertical intersection across the vessel edge utilizing $E_1^{\text{'}\text{'}}$as mask of $U_1^{\text{'}}$ to identify two speckles defined as $S{p}_1$ and $S{p}_2$. The distance between these two speckles represents the diameter of the vessel to be tracked along a set of matrices $H=[H_1,\dots ,H_k]$using the KLT speckle tracker, where $H=I^{\text{'}}$ (Figure 3B).

Figure 3.: A: Speckle selection that intersects a vertical line with the vessel from the manual user selection. The user selects a speckle above the vessel and the program search through the vertical line to find all the borders. B: Sequential displacements from consecutive frames using KLT. KLT, Kanade Lucas Tomasi.

During the vessel diameter identification, two speckles are tracked using KLT and pyramidal segmentation. In the first tracking $u_{}^{L_o}$takes the value of $S{p}_1$ while in the second tracking $u_{}^{L_o}$ takes the value of $S{p}_2$, where $u_{}^{L_o}$ is defined as $u_{}^{L_o}={[u_x^{L_o},u_y^{L_o}]}^T$ (Figure 3B). Vessel distension tracking for multiple cardiac cycles requires the identification of large motion displacements frame to frame that can be achieved using pyramidal segmentation.¹⁸ Pyramidal segmentation subsamples consecutive frames by levels, reducing their resolution, increasing the spatial information in each pixel to track large motion tracking frame-to-frame and applying feedback displacement from low- to high-resolution frame-to-frame.¹⁸ Every level is defined as $L_o$ and serves as feedback to the following level below where $o$ determines the level of L. When $L_o=L_0$, (the level zero), this means that the process reached its maximum level where every frame has its original resolution.

The KLT algorithm is implemented for every $L_o$, obtaining a vector displacement approximation $d^{L_o}={[d_x^{L_o},d_y^{L_o}]}^T$ and a vector displacement estimation $g^{L_o}={[g_x^{L_o},g_y^{L_o}]}^T$where every $g^{L_{o-1}}$ depends on $g^{L_o}$  and $d^{L_o}$. Equation 3 evaluates the pixel intensity inside of windows centered at $u_{}^{L_o}$ for consecutive frames. The window size is defined as $w={[w_x^{},w_y^{}]}^T$ using $H_j^{L_o}$ and $H_{j+1}^{L_o}$ for $1\ge j\ge (k-1)$, where $H_j^{L_o}\left(x,y\right)$ is a pixel intensity value of $H_j$ in the coordinate ${[x,y]}^T$ with an specified level $L_o$.

The combination between KLT and pyramidal segmentation searches for the similarity between the two speckles from consecutive frames minimizing the residual error function $\epsilon {\text{}}^{Lo}\left(d^{L_o}\right)$, to find a $d^{L_o}$ that minimizes the matching function $\epsilon {\text{}}^{L_o}$ defined as a sum of squared pixel intensity differences¹⁸ (see Equation 3).

$$\begin{array}{l}{\epsilon }^{L_o}\left(d^{L_o}\right)={\displaystyle \sum }_{x=u_x^{L_o}-w_x}^{u_x^{L_o}+w_x}{\displaystyle \sum }_{y=u_y^{L_o}-w_y}^{u_y^{L_o}+w_y}\\ {\left[H_j^{L_o}\left(x,y\right)-H_{j+1}^{L_o}\left(x+d_x^{L_o}+g_x^{L_o},y+d_y^{L_o}+g_y^{L_o}\right)\right]}^2\end{array}$$

Step 3: Signal Detrending

The distance in vertical position between Sq₁ and Sq₂ represents the vessel diameter. When Sq₁ and Sq₂ are tracked by the KLT algorithm along H, then it is possible the calculation of vascular distensibility for multiple cardiac cycles (Figure 4A). Least squares method is implicit in Equation 4 and minimizes the sum of the squares of the residuals produced by the difference between the original displacement of the vessel f obtained by KLT tracker and the fitted values obtained by a low order polynomial y. To eliminate the trend caused by external factors, it is possible to fit y and later subtract such signal from f such that the detrended signal $\tau$ is equal to $\tau =f-y$ (Figure 4B).

Figure 4.: A: Vessel displacement from patient No 1 before detrending. B: displacement after detrending.

The low order polynomial y can be obtained by using Equation 4, where P is a vector that contains the coefficients of a polynomial defined by the order predefined on y, and V is the Vandermonde matrix to complement y, such as: $V=QR$, where Q is an orthogonal matrix that satisfies:$Q^{T}Q=\mathbb{I}$, and R is an upper triangular matrix. Q and R can be found by QR decomposition.³⁰

$$y=VP$$

where $P=R^{-1}{Q}^{T}f$.

Step 4: Automated Peak and Valley Selection

The result of detrending the vessel displacement of Figure 4A is a normalized signal to zero defined as $\tau$ (Figure 4B). Automatic peak and valley selection employs an approximant function based on penalized least squares method³¹ that provides a smoother approximation of the vessel displacement to search for only one local maxima and minima approximant for every distention or contraction. The distance from peak to peak or valley to valley from the smoothed approximation, $\gamma ={\left[{\gamma }_1,\dots ,{\gamma }_h\right]}^T$or $\rho ={\left[{\rho }_1,\dots ,{\rho }_h\right]}^T$ (Figure 5A), is the initial search interval to find local maxima or minima of peaks $p={\left[p_1,\dots ,p_h\right]}^T$ and valleys$\upsilon ={\left[{\upsilon }_1,\dots ,{\upsilon }_h\right]}^T$ from $\tau$ by applying brute force (Figure 5B), where every interval to find peaks and valleys is defined as two-thirds of $\gamma$ or $\rho$. Every Peak and Valley found by APVS is stored to calculate distensibility. The distance between Sq₁ and Sq₂ on $U_1^{\text{'}}$ represents the initial vessel diameter, see Figure 3A, and it is added to the normalized signal $\tau$ from Figure 4B to adjust the detrended signal as well as p and $\upsilon$ found by APVS (Figure 5B).

Figure 5.: A: Smoothed function obtained from multiple cardiac cycles, for APVS and closed interval detection. B: Detrended function taking as a reference the initial vessel diameter from l ₁. APVS, automatic peak and valley selection.

The peaks and valleys (p and 

$\upsilon )$

found from the APVS, can be utilized to calculate distensibility $\phi$ defined as maximum average of distention (MAD) over the mean contracted vessel diameter, where MAD is defined as the difference between the mean distended and contracted vessel diameter (see Equation 5).²⁴

$$\phi =\frac{{{\displaystyle \sum }}_{s=1}^h{p}_s-{{\displaystyle \sum }}_{s=1}^h{\upsilon }_s}{{{\displaystyle \sum }}_{s=1}^h\text{}\text{}{\upsilon }_s}$$

Clinical Evaluation

After informed consent and under a research protocol approved by our local Institutional Review Board, 10 patients were enrolled. Standard DICOM files were used for 10 different arteries (one artery per patient, brachial or radial) as part of the preoperative evaluation in preparation for AVF surgery. Three case studies were performed testing the cardiac cycle variability captured using the new approach with DICOM data of every clinical study in Table 1.

Table 1. - Characteristics of 10 Different Clinical Studies

Study	Artery	Arm	Frame used in analysis	Interval frames	Frame rate (Hz)
1	Brachial	Left		1–282	33
2	Radial	Left	Excessive motion	21–261	33
3	Brachial	Left		1–128	17
4	Brachial	Left		1–322	33
5	Brachial	Right		1–373	33
6	Brachial	Left		1–247	33
7	Brachial	Left	Excessive motion	21–375	33
8	Brachial	Left		1–373	33
9	Brachial	Left		1–319	33
10	Brachial	Left		1–337	33

The patients were examined resting with their arms at the level of the heart. The ultrasound data were recorded with a frame rate of 17 or 33 Hz depending on the capabilities of the ultrasound device and transducer (Table 1). Ten specialists evaluated every artery from Table 1 for the three different case studies. The ultrasound movies were recorded using the ultrasound device GE LOGIQ E9 equipped with two linear transducers (9L-D and L8-18i-D), with a bandwidth of 2–8 MHz and 4–15 MHz, respectively (Figure 6).

Figure 6.: A: Ultrasound device GE LOGIQ E9. B: Example of transducer 9L-D positioned to capture brachial artery imaging. C: Transducer L8-18i-D positioned to capture brachial artery imaging.

Results

Three studies were carried out to evaluate the quality of the edge detection and speckle tracking (EDST) with APVS versus MPVS. The coefficient of variation (CV) with respect to the peaks and valleys from the vessel displacement were measured when the vessel was completely contracted or distended for multiple cardiac cycles.

In study 1 (Table 1), 10 patients were evaluated by 10 different specialists. Every specialist selected two speckles manually from the intima layer of every vessel of Table 1 (without comparing point selection from other specialists). The 10 different specialists centered the speckles with respect to the origin of the vessel diameter (Figure 3). Every pair of speckles were tracked making use of KLT algorithm and pyramidal segmentation implemented by Belmont et al.^18,19 The signal result from the speckle tracking represents the displacement in cm of the arteries extracted from the DICOM file (Figure 4A). Ten arteries were analyzed by 10 specialists, selecting six peaks and six valleys for every specialist per artery. Peak average and SD were performed using the peaks manually selected by 10 specialists. The CV was obtained from the peak average and peak SD. The process was repeated for valleys in the same manner (see Table 2 for study 1). The results for study 1 show a CV average for the 10 vessels analyzed of 6.14% ± 0.03% when the vessel is completely distended and 6.45% ± 0.03% when it is contracted (Table 2).

Table 2. - Comparative for the Three Different Studies Using MPVS and APVS

Study	CV (%) for Study 1				CV (%) for Study 2				CV (%) for Study 3
	Peaks		Valleys		Peaks		Valleys		Peaks		Valleys
1	6.36	±0.03	7.05	±0.03	0.35742	±0.00181	0.3002	±0.0014	0.34761	±0.00174	0.33018	±0.00161
2	5.19	±0.01	5.35	±0.01	0.13152	±0.00036	0.2967	±0.0008	0.37741	±0.00105	0.27474	±0.00075
3	4.68	±0.02	4.81	±0.02	0.64858	±0.00259	0.5104	±0.0019	0.64607	±0.00258	0.51438	±0.00198
4	6.12	±0.03	6.31	±0.03	0.3996	±0.00158	0.2684	±0.0010	0.40676	±0.00161	0.34724	±0.00134
5	7.02	±0.03	7.20	±0.03	0.68507	±0.00431	0.2040	±0.0012	0.51580	±0.00370	0.36010	±0.00251
6	3.11	±0.01	3.15	±0.01	0.13974	±0.00063	0.1691	±0.0007	0.14916	±0.00069	0.14595	±0.00065
7	7.67	±0.03	8.10	±0.03	0.63050	±0.00271	0.8327	±0.0033	0.53690	±0.00231	0.80532	±0.00326
8	9.83	±0.04	10.49	±0.04	0.83837	±0.00226	0.7547	±0.0019	0.83973	±0.00227	0.82562	±0.00208
9	6.91	±0.03	7.12	±0.03	0.09399	±0.00036	0.1388	±0.0005	0.15453	±0.00059	0.13802	±0.00051
10	4.54	±0.02	4.88	±0.02	0.62359	±0.00275	0.6524	±0.0026	0.71285	±0.00325	0.77850	±0.00330
Total	6.14	±0.03	6.45	±0.03	0.45485	±0.00194	0.4127	±0.0015	0.46868	±0.00198	0.45200	±0.00180

APVS, automatic peak and valley selection; CV, coefficient of variation; MPVS, manual peak and valley selection.

In study 2, the x-coordinate was used for every speckle manually selected from study 1 to obtain a median value as first approximant of the two speckles that defines the initial diameter of the vessel to be tracked (Figure 3). Every vessel from Table 1 had an independent median value that was used in combination with a random y-coordinate above the intima layer of the vessel. This y-coordinate was selected above the vessel and it was modified by the edge detector to find the two centered speckles Sq₁ and Sq₂, located in the intima layer of the vessel in an automated way. The EDST, signal detrending, and APVS methodologies explained in sequence in the previous chapter were implemented to obtain six peaks and six valleys automatically. The average and SD of these six peaks and valleys were calculated to obtain the CV from Table 2 for study 2. The average CV for the 10 vessels analyzed was 0.454% ± 0.004% when the vessel was completely distended and 0.412% ± 0.003% when it was contracted.

In study 3, the x-coordinate was used for every speckle manually selected from the most experienced specialist of the study 1 as first approximant of the two speckles that define the initial diameter of the vessel (Figure 3). Every vessel from Table 1, had an independent x-coordinate utilized in combination with a random y-coordinate above the intima layer of the vessel. This last y-coordinate was selected differently from the original position of the specialist and placed above the vessel. This last y-coordinate was also modified by the edge detector to find the two centered speckles of the intima layer of the vessel in an automated way. The EDST, signal detrending, and APVS methodologies explained in the previous chapter were implemented to obtain six peaks and six valleys automatically. The average and SD of these six peaks and valleys were used to obtain the CV from Table 2 for study 3. The CV average for 10 arteries analyzed when the vessel was completely distended was 0.468% ± 0.001%, and 0.452%±0.001% when the vessel was contracted.

Linear regression was carried out between distensibility and MAD comparing the fitness from study 1 with respect to studies 2 and 3 (Figure 7).

Figure 7.: A: Regression line from study 1 vs. study 2 comparing distensibility. B: Regression line from study 1 vs. study 3 comparing distensibility. C: Regression line from study 1 vs. study 2 comparing MAD. D: Regression line from study 1 vs. study 3 comparing MAD. MAD, maximum average of distention.

Bland & Altman's (B&A) plot was also implemented to evaluate the bias between the mean differences.³²Figure 8, A and B show the B&A plots comparing distensibility measurements in study 1 with those of studies 2 and 3. The overall bias for both is negative, with values of −0.43 and −0.31, respectively. The negative sign indicates that studies 2 and 3 have an average increase of 0.43% and 0.31% in comparison with the first study.

Figure 8.: A: B&A plot from study 1 vs. study 2 comparing distensibility. B: B&A plot from study 1 vs. study 3 comparing distensibility. C: B&A plot from study 1 vs. study 2 comparing MAD. D: B&A plot from study 1 vs. study 3 comparing MAD. B&A, Bland & Altman; MAD, maximum average of distention.

Figure 8, C and D present the B&A plots for studies 2 and 3 in comparison with study 1, for the difference of the MAD in cm. The average difference between studies 1 and 2 was 0.0017 cm, while the average difference between studies 1 and 3 was 0.0021 cm. The MAD from each of the studies 1, 2, and 3 was 0.018, 0.016, and 0.016 cm, respectively. There is a 10% difference in study 1 with respect to those in studies 2 and 3.

Discussions

Studies 2 and 3 show a noticeable improvement using signal detrending in comparison with study 1. From a CV average for 10 arteries analyzed in study 1 of 6.14% and 6.45% for peaks and valleys to 0.4% for peaks and valleys in studies 2 and 3 (Table 2). The coefficient of determination (r²) in Figure 7, between distensibility in study 1 relative to studies 2 and 3 was 0.97 and 0.92, indicating relatively good linear match in between the observed distensibility data. The regression coefficients for distensibility in Figures 7, A and B show a matching slope of 1.06 and 1.08 from studies 2 and 3 with respect to study 1. Analyzing the regression analysis in terms of MAD in Figure 7, C and D, the r² for study 1 relative to studies 2 and 3 are 0.79 and 0.90.

Results indicate an increase of distensibility of 0.43% and 0.31% from studies 2 and 3 in comparison with that in study 1, while MAD showed a difference of only 10% from study 1 with respect to studies 2 and 3.

Conclusions

The new methodology using EDST, signal detrending, and APVS successfully identified the intima of the vessel to calculate distensibility in an automated way for the 10 case studies presented. Results comparing study 1 with respect to studies 2 and 3 demonstrated the capability of this new approach to make use of relatively low-resolution ultrasound B-mode data and reduce the variability in measurement. This methodology can measure small changes of vascular diameter induced by the patient’s pulse pressure and reduces the time required by eliminating manual selection of peaks and valleys. While our study uses the patient’s artery, the same method can be applied to dialysis fistula, artery, anastomosis, and vein, either in a normal area or in an area of stenosis. This tracking method can also be applied to measure vein compliance when external occlusion is applied using methods that others have implemented.⁶

In clinical setting, noninvasive measurements of morphologic and functional parameters, including diameter and volumetric flow^16,33–36via ultrasound, assist in evaluating fistula maturation, and the physiologic and mechanical factors regulating fistula maturation and patency are currently being evaluated.^{15,16,21,22,35,37,38} The biomechanical behavior of the vessels in fistulas is gaining increased attention as key players in fistula maturation, remodeling, and stenosis.^37,39,40 It is becoming clear that both artery and vein may be predictors of fistula maturation. Obtaining distensibility in a reproducible matter will allow future users to use this variable to more reliably calculate vascular elastic modulus measurements. In the current study, the blood pressure information from patients was not available at the time of the ultrasound so we were not able to calculate the modulus. In future work, we plan to measure blood pressure and the presented distensibility methods to determine elastic modulus.

This work represents the continuation of previous work performing speckle tracking with MPVS and B-mode data.^18,19,23 In the present work, we have found that it is possible to incorporate automatic point selection, edge detection, speckle tracking, and detrending to reduce the potential for operator-induced variation and to obtain more reliable and reproducible distensibility measurements.

Acknowledgment

The authors acknowledge The University of Michigan and the VA Ann Arbor Healthcare System in Michigan for the facilities provided.

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Keywords:

speckle tracking; Kanade Lucas Tomasi algorithm; edge detection; distensibility; fistula

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