Principal Component Analysis of the Longitudinal Carotid Wall Motion in Association with Vascular Stiffness: A Pilot Study

Ultrasound in Med. & Biol., Vol. -, No. -, pp. 1–14, 2016 Copyright
2016 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/$ - see front matter

http://dx.doi.org/10.1016/j.ultrasmedbio.2016.07.020

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Original Contribution PRINCIPAL COMPONENT ANALYSIS OF THE LONGITUDINAL CAROTID WALL MOTION IN ASSOCIATION WITH VASCULAR STIFFNESS: A PILOT STUDY HEIKKI YLI-OLLILA,*yz MIKA P. TARVAINEN,*y TOMI P. LAITINEN,*x and TIINA M. LAITINEN* * Department of Clinical Physiology and Nuclear Medicine, Kuopio University Hospital, Kuopio, Finland; y Department of Applied Physics, University of Eastern Finland, Kuopio, Finland; z Department of Clinical Physiology and Nuclear Medicine, Kanta-H€ame Central Hospital, H€ameenlinna, Finland; and x Department of Clinical Physiology and Nuclear Medicine, University of Eastern Finland, Kuopio, Finland (Received 17 January 2016; revised 29 June 2016; in final form 25 July 2016)

Abstract—The longitudinal motion of the carotid wall during a heart cycle has a multiphasic waveform. Recent studies have examined the amplitude of this motion. Instead of amplitude measurements, we focus on making a detailed characterization of the motion waveform. Two-minute carotid ultrasound videos were obtained for 19 healthy volunteers, and a speckle tracking algorithm was used to measure the motion of the carotid wall. Principal component analysis revealed the characteristic features of wall motion and their relation to known arterial stiffness indices. By estimating two principal components, we could account for more than 92% of the variation in the motion graphs. The first principal component derived from the longitudinal motion curves was significantly correlated to pulse pressure, indicating that the main dominant base waveform of the longitudinal motion was related to blood pressure. The second principal component derived from the longitudinal motion curves had multiple significant correlations to known stiffness indices, indicating that the stronger biphasic structure of the motion curve, especially on the adventitia layer, was associated with higher distensibility and compliance, as well as reduced carotid artery stiffness. According to this study, the second principal component of the longitudinal motion may be a useful parameter reflecting vascular health. (E-mail: [email protected])
2016 World Federation for Ultrasound in Medicine & Biology. Key Words: Arterial stiffness, Carotid artery, Eigenvalue, Eigenvector, Ultrasound imaging.

INTRODUCTION

2012; Persson et al. 2003; Svedlund and Gan 2011a; Yli-Ollila et al. 2013; Zahnd et al. 2011b, 2013, 2014, 2015b). Our group has also developed a motion tracking method that uses contrast optimization to reduce the noise in the ultrasound images; this can be used with clinical ultrasound devices without requiring access to the raw radio frequency ultrasound signal (Yli-Ollila et al. 2013). In preliminary clinical studies, carotid longitudinal wall motion has been linked to arterial stiffness (Bukac and Canic 2013; Taivainen et al. 2015; Yli-Ollila et al. 2014, 2016), ageing (Zahnd et al. 2012), plaque burden (Svedlund and Gan 2011b), diabetes (Zahnd et al. 2011a) and cardiac well-being (Svedlund et al. 2011), reflecting the reduction in amplitude and rapidity of longitudinal wall motion in unhealthy/stiffer arteries. Despite the multiple studies on the subject, the actual force initiating longitudinal motion is still unclear, as is the manner in which the motion is affected by pathophysiology. In addition, the temporal characteristics of longitudinal motion are still far from clear. It has been reported that

The prodromal phase of cardiovascular disease, which is often long lasting and symptomless, may later develop into life-threatening symptomatic disease. Arterial stiffening has often started during childhood and young adulthood (Juonala et al. 2005; Veijalainen et al. 2013), but at present there are no quick, inexpensive and non-invasive screening methods that accurately detect this early stage. The need for new methods to study early arterial stiffness has been emphasized (Naghavi et al. 2003). One novel line of study is focused on the longitudinal (i.e., in the direction of the blood flow) wall motion of the inner wall of the blood vessel. Multiple techniques to measure the small, aberrant longitudinal motion of the carotid wall have been reported (Albinsson et al. 2014; Cinthio et al. 2005; Gastounioti et al. 2011; Golemati et al. 2003,

Address correspondence to: Heikki Yli-Ollila, Kanta-H€ame Central Hospital, Ahvenistontie 20, H€ameenlinna FI-13530, Finland. E-mail: [email protected] 1

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longitudinal motion displays a multiphasic waveform and, furthermore, that the main direction of the motion can vary from subject to subject (Ahlgren et al. 2012; Cinthio et al. 2006; Yli-Ollila et al. 2013). It also has been reported that there is decay in longitudinal amplitude moving along the vessel length further from the heart (Zahnd et al. 2015a). More research is needed to understand the biomechanics of longitudinal motion so that it can serve as an independent arterial stiffness index. There are only a few publications focusing on mathematical approaches to the study of longitudinal artery wall motion. Finite-element and fluid–structure interaction models have been used to represent the anatomy and the physiology of an artery and to estimate the kinetics of the arterial wall (Bukac and Canic 2013; Warriner et al. 2008). Bukac and Canic (2013) used an atherosclerotic artery model and revealed that unlike radial motion, longitudinal motion is highly dependent on atherosclerotic lesion geometry. Warriner et al. (2008) created a working carotid artery fluid–structure model and concluded that the presence of longitudinal wall motion should always be considered when studying the effect of arterial wall motion on fluid velocity. Mathematical modeling has also been used to create an ultrasound imaging phantom, including the longitudinal motion component (Stoitsis et al. 2008). In addition to the modeling-based studies, a different mathematical approach linking artery wall motion and the stage of atherosclerosis has been reported (Gastounioti et al. 2014). In the study, hidden Markov models were used to build a computer-aided diagnosis scheme for potential clinical use. The scheme used the motion characteristics of the measured carotid arteries, including the longitudinal motion component, and was able to discriminate atherosclerotic high-risk patients from low-risk patients with good accuracy. In addition, a mathematical Fourier series-based approximation has been successfully adapted to the longitudinal motion signal to assess arterial stress from the measured in vivo data (Soleimani et al. 2016). In healthy common carotid arteries, the maximum stress in the longitudinal direction was measured as 1.7 kPa (60.6 kPa). In this study, we applied mathematical principal component analysis (PCA) to characterize the longitudinal carotid wall motion waveform in detail in a study population of 20 healthy volunteers. The PCA compresses the common features of the arterial motion waveform into a few parameters. For comparison, the PCA was also performed for the radial motion of the carotid wall. Previous studies on longitudinal motion have focused on its amplitude, but to better understand longitudinal motion and its relation to arterial stiffness, the characteristics of the motion waveform need to be clarified in

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detail. Multiple referential arterial stiffness measurements were performed in this study to investigate how early arterial stiffening affects longitudinal waveforms (principal component [PC] values). This kind of PCA approach to clarifying the wall motion waveform has not been conducted previously. METHODS Patients and study protocol Twenty healthy, non-smoking patients of normal weight were recruited, but one volunteer was omitted from the final analysis because left bundle branch block was detected. After at least 10 min of rest in the supine position, a 2-min ultrasound imaging video of the longitudinal section of the left common carotid artery was recorded with a Philips EPIQ 7 equipped with an 18-MHz linear transducer (Philips, L18-5, Best, Netherlands) and electrocardiography (ECG) electrodes. The ultrasound video frame (1.25 3 1.5 cm, width 3 height) was positioned so that the carotid bifurcation was merely visible on the right side of the image and the focus of the ultrasound was positioned on the far wall of the artery. The imaging rate achieved with the setup was 85 Hz. The 2-min video was cut into two 1-min signals for principal component analysis and repeatability analysis. Ultrasound imaging was performed by an experienced physician. The large amount of video data allowed the removal from the analysis of such artifacts subject swallowing; the variation in longitudinal motion amplitude caused by breathing was averaged out by collecting data over multiple breathing cycles. After ultrasound imaging, both applanation tonometry and pulse wave velocity measurements were conducted with the SphygmoCor system (Version 9, AtCor Medical, Itasca, IL, USA) on the radial and carotid arteries to obtain referential stiffness indices. The systolic and diastolic brachial blood pressures (SBP and DBP) were measured in the left arm with an automatic blood pressure monitor (Omron, M4-I, Matsusaka, Kyoto, Japan) before and after ultrasound imaging and before the tonometry measurements. The carotid applanation tonometry measurement was used convert the brachial blood pressure values into carotid pressures that were used in the computation of stiffness indices. All of measurements described here are pain-free, non-invasive and non-harmful to the volunteers. Written informed consent was obtained from every participant, and the ethics committee of Kuopio University Hospital approved the study protocol. Carotid wall motion tracking Longitudinal motion tracking was performed for the far arterial wall, using our in-house MATLAB code

PCA of carotid wall motion with vascular stiffness d H. YLI-OLLILA et al.

(R2014b, The MathWorks, Natick, MA, USA). The motion tracking algorithm is based on 2-D cross-correlation; the algorithm was described in our previous study (YliOllila et al. 2013). Briefly, the user selects five region of interest (ROIs) from the first frame of the ultrasound video, approximately 1 cm upstream from the carotid bifurcation: one larger ROI from the near wall and one larger ROI from the far wall, both covering the intima, media and adventitia layers; one smaller ROI from the far wall intima–media layer; one smaller ROI from the far wall adventitia layer; and one larger referential ROI from the surrounding tissues to permit longitudinal motion tracking. The first two ROIs are used for radial motion (diameter change) tracking, and the last three ROIs are used for longitudinal (perpendicular to the radial direction) motion tracking. The average sizes of the ROIs (width 3 height) were 2.58 3 0.97, 2.58 3 1.83, 2.58 3 0.33, 2.58 3 0.30 and 2.58 3 1.15 mm, respec-

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tively. The width of the ROIs was kept constant subjectwise, but the height of the ROI was allowed to vary because of physical size differences in the different arterial wall layers. After ROI selection, the algorithm tracks the 2-D motion of the ROIs for one heart cycle (from one automatically detected R-spike to the next). A fixed-size template is used as a search area, adding 0.58 mm to the top, bottom and sides of the ROI’s current position. This motion tracking procedure allows accurate measurement, with the maximum detectable longitudinal motion velocity being 48 mm/s. After the heart-cycle-long motion tracking procedure is complete, the user can inspect the gathered motion signals and accept the data, redo the tracking or skip over some measured part of the ultrasound video. Once the motion trace is accepted, the procedure starts again by checking the ROI positions and by motion tracking the next heart cycle. To form a continuous signal of the subsequent motion traces, our

Fig. 1. Averaging procedure used to form a robust longitudinal motion signal from the 1-min recordings. (a) A motion trace and an electrocardiogram are collected in synchrony. (b) An average heart-cycle-long graph of the longitudinal motion is formed from the 1-min original signal, using automatic detection of the R-spikes of the electrocardiogram signal. Thin gray lines represent all measured heart cycles of the subject, and the thick blue line is the average. (c) For principal component analysis, the average graphs from every individual are put into the same matrix and cut to the same length according to the shortest average signal. The cut has been highlighted with a vertical red dashed line. All signals start at the peak of the R-spike in the electrocardiogram.

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algorithm uses linear detrending to parse the heart-cyclelong traces together. We used repeated 1-min data recordings per subject to be sure that the quality of the average graphs used in this study would be good. The average graphs for every individual were reconstructed by detecting the shortest cardiac cycle in the whole study population and cutting all individual cardiac cycles to the same length (Fig. 1). With this procedure, it was possible to obtain all of the average graphs in the same length and in sync without any time shifts for the PCA. Free breathing was allowed and its effect on arterial wall motion was assumed to average out in the 1-min recordings. Swallows were omitted from the averaging. The following accumulated radial and longitudinal motion waveforms were used in this study: radial motion of the artery (radial motion between ROI 1 vs. ROI 2) (Fig. 2a), longitudinal motion between intima–media and adventitia (IA) (ROI 3 vs. ROI 4) (Fig. 2b), longitudinal motion between intima–media and reference point (origin) selected from the surrounding tissues (IO) (ROI 3 vs. ROI 5) (Fig. 2b) and longitudinal motion adventitia and reference point (AO) (ROI 4 vs. ROI 5) (Fig. 2b). The use of a reference point was necessary to remove all possible motion artifacts caused by the physician’s handling of the probe. Principal component analysis Principal component analysis can be used to study and summarize the variance in a large group of data sets (Hotelling 1933). Here, PCA was used to

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examine the waveforms of longitudinal carotid wall motion because PCA compresses the common features of longitudinal motion waveforms into a few parameters. Computation of the eigenvectors and their subjectspecific PC values was conducted in five steps: 1. The average motion waveforms of every subject were stacked into a data matrix X, and the matrix was cut according to the shortest average motion curve (the subject who had the highest heart rate during ultrasound imaging), and hence the size of data matrix X was N 3 M, where M is the length of the shortest waveform, and N is the number of patients in this study. 2. The size M 3 M correlation matrix R was computed as

R 5

1 T X X N

where T designates the matrix transposition. 3. Eigenvalues l and eigenvectors (loadings) v of correlation matrix R were solved using eigendecomposition. The eigenvalues of R reveal how a large portion of the data variance is represented by each eigenvector, and they are the roots of the characteristic polynomial:

pðlÞ 5 detðR2lIÞ

Fig. 2. Common carotid artery imaged at the start of the carotid bifurcation is merely cut from the right side. (a) For radial motion tracking, region of interest (ROI0 1 is placed on the near carotid wall, and ROI 2 on the far carotid wall. (b) For longitudinal motion tracking, ROI 3 is placed on the intima–media complex (innermost white layer and darker thin slice under it), ROI 4 on the adventitia layer (thicker white layer under media layer) and ROI 5 on the surrounding tissues.

PCA of carotid wall motion with vascular stiffness d H. YLI-OLLILA et al.

where det refers to the determinant, and I is the M 3 M identity matrix. For each eigenvalue, a corresponding eigenvector can be defined by solving the linear equation

Referential stiffness measures To test how well the PCs are associated with arterial stiffness, referential stiffness measures were performed. The test individuals’ radial arteries were subjected to applanation tonometry, and from these measurements we obtained the following parameters: aortic augmentation (AA), augmentation index (Aix), augmentation index adjusted for a heart rate of 75 bpm (Aix@75) and average pulse wave velocity (PWV) between the carotid and radial arteries. From the ultrasound-devised radial motion curve, combined with carotid pressure information, we computed the following multiple stiffness indices: distensibility coefficient (DC), compliance coefficient (CC), carotid artery compliance (CAC), Young’s elastic modulus (EY), Persson’s elastic modulus (EP) and characteristic impedance of the carotid (Z). The calculations involved in obtaining these parameters are presented in Table 1. The lumen areas needed in some computations were evaluated assuming circular geometry of the artery; that is, cross-sectional areas were calculated from the artery diameters. Intima–media thickness was measured from a single frame (time of R-spike on the electrocardiogram) of the ultrasound videos by drawing two lines, one on top of the lumen–intima border and the other one on top of the media–adventitia border.

ðR2lIÞH 5 0 where H 5 (v1,v2,.,vK)˛RM3K. 4. The eigenvectors were sorted in descending order of eigenvalues; thus, the eigenvector that explains the majority of the variance in the motion curve data is defined as the first eigenvector (v1). The second eigenvector (v2) explains the second largest portion of the variance in the data, and so on. 5. Principal components were ultimately computed as

PC 5 H T X T The PCs were computed for every motion curve type (three different longitudinal curves and one radial curve) separately for every subject and are the multipliers for the common eigenvectors to form the original motion graphs of individual patients. In other words, the original motion graphs can be computed by summing each product vector of the corresponding PC and eigenvector, LM 5

K X

5

Statistical methods Spearman’s rank correlation coefficient was used to assess the correlations between PC values and referential stiffness indices. In addition, Spearman’s rank correlation coefficient (r) was used to test the correlations between

PCi vi

i 5 1

where LM is the original longitudinal (or radial) motion graph of the subject.

Table 1. Referential stiffness indices measured from the radial motion curve of the carotid artery and from the pressure curve of the aorta (estimated after applanation tonometry from the radial artery) Stiffness index Applanation tonometry AA (mm Hg) Aix (%) Aix@75 (%) PWV (m/s) Radial distension of carotid DC (kPa21* 1023) 23

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Explanation/formula

Mean 6 SD

Aortic augmentation Augmentation index: ratio of the pressure peak height of the forward propagating pressure wave to that of the reflecting pressure wave in aorta Augmentation index adjusted for a heart rate of 75 bpm Pulse wave velocity measured between carotid and radial arteries

3.53 6 3.49 10.89 6 11.09

DA Distensibility coefficient: DC 5 Asystole PP (Laurent et al. 2006)

32.59 6 8.58

CC 5 DA PP

CC (m /kPa * 10 )

Compliance coefficient:

CAC (kPa21* 1023)

DA Carotid artery compliance: CAC 5 Adiastole PP (Juonala et al. 2005)  

EY (kPa * 103)

Young’s elastic modulus: EY 5

(Laurent et al. 2006)

3.05 6 11.39 6.81 6 1.02

1.00 6 0.31 19.80 6 5.69

A

EP (kPa) 2

Persson’s elastic modulus: 3

Z (kg/m s * 10 )

avg 3 11WCSA

DC A PP EP 5 avgDA

(Laurent et al. 2006)

(Laurent et al. 2006) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi EY IMTr Characteristic impedance: Z 5 (O’Rourke 1990) Davg

0.39 6 0.10 29.01 6 6.55 5.80 6 0.64

SD 5 standard deviation; PP 5 carotid pulse pressure; IMT 5 intima-media thickness; WCSA 5wall cross-sectional area; DA 5 maximum change in lumen area; Aavg 5 average lumen area; Adiastole 5 diastolic lumen area; Asystole 5 systolic lumen area; Davg 5 average diameter of the lumen area; r 5 blood density (1060 kg/m3).

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the PC values and the original motion graph time points. A rank correlation test was used because it was not possible to assume that there would be a linear relationship between the PC values and the stiffness indices. p values of the two-tailed significance tests , 0.05 were considered to indicate statistical significance. In Spearman’s correlation analysis with 19 patients, p , 0.05 is achieved with absolute r values .0.46. Cronbach’s a was used to study the repeatability of the PCA. Cronbach’s a values .0.8 are considered to be a sign of good repeatability, and parameters achieving this criterion are suitable for individual diagnostics (Cronbach 1951). All correlations and p-values were calculated in SPSS (Version 22.0, IBM, Armonk, NY, USA).

analysis. An average number of 53 heart cycles (range: 30–69) were successfully motion tracked per 1-min clip and used to form the average longitudinal and radial motion curves for every volunteer. The final study population was young, including 9 men and 10 women. Average age was 28.5 y (standard deviation: 7.5 y, range: 19–49 y). The average heart rate among the study population was 56 bpm (range: 44–80 bpm). The average brachial blood pressure was 115/68 mm Hg (systolic range: 96– 135 mmHg, diastolic range: 60–84 mmHg). For PCA, the motion signals were cut to the same length according to the shortest heart cycle within the population, and the length of the cycle was 0.67 s. The first two eigenvectors from every longitudinal motion curve and from the radial curve can be seen in Figure 3. The waveforms of the eigenvectors defined from the IO and AO curves are rather similar, but the amplitude, of the eigenvectors as well as the original longitudinal motion signals are higher in the IO curves, indicating that longitudinal motion is greater in the intima–media complex than in the adventitia layer. In addition to the presentation of the whole study population in Figure 3, the

RESULTS Motion tracking for the 2-min data sets imaged from every volunteer was successful. The first minute of the recording was used for all analyses described here, and the second minute was used only for the repeatability

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Fig. 3. First two eigenvectors of the longitudinal motion data: The first eigenvector is represented by the blue solid line, and the second eigenvector, by the orange dashed line. Eigenvectors are presented in arbitrary units (scale on right side). The light gray motion graphs of the study population are presented in millimeters (scale on left side). (a) Eigenvectors derived from the longitudinal motion between intima-media and adventitia (IA). (b) Eigenvectors derived from the longitudinal motion of intima–media (IO). (c) Eigenvectors derived from the longitudinal motion of adventitia (AO). (d) Eigenvectors derived from the radial motion. All signals start at the peak of the R-spike in electrocardiogram.

PCA of carotid wall motion with vascular stiffness d H. YLI-OLLILA et al.

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Table 2. Repeatability analysis and correlations between the two first principal components, longitudinal motion amplitudes and known arterial stiffness indices, as well as with gender, age and blood pressure Longitudinal PC

Radial PC

Variable

IA first PC

IA second PC

IO first PC

IO second PC

AO first PC

AO second PC

Radial first PC

Radial second PC

Cronbach’s alpha DC CC CAC EY EP Z AA Aix Aix@75 PWV Gender Age SBP DBP PP IAampl IOampl AOamlp

0.95 20.28 20.16 20.14 0.09 0.17 0.33 20.06 20.11 20.09 20.29 0.08 0.00 0.29 20.32 0.47* 0.58y 0.55* 0.10

0.85 0.21 0.08 0.16 20.50* 20.17 20.18 0.15 0.22 0.16 0.31 0.17 0.16 20.46* 0.13 20.54* 0.01 20.01 0.05

0.97 20.29 20.11 20.15 0.09 0.18 0.34 0.05 20.02 20.05 20.32 20.02 0.02 0.35 20.30 0.52* 0.59y 0.76z 0.40

0.94 0.43 0.35 0.42 20.55* 20.44 20.38 0.04 0.11 0.01 20.04 20.08 20.02 20.27 20.04 20.29 20.15 20.05 0.22

0.91 20.12 0.04 20.04 0.08 0.06 0.15 0.05 20.02 20.03 20.19 0.00 20.05 0.27 20.09 0.41 0.16 0.71z 0.81z

0.96 0.63y 0.53* 0.64y 20.58y 20.66y 20.59y 20.19 20.12 20.18 20.31 20.02 20.20 20.32 20.28 20.25 20.09 20.15 0.01

0.99 0.58y 0.81z 0.69y 20.49* 20.68y 20.52y 20.04 20.02 20.26 20.53* 0.10 20.37 0.04 20.56* 0.25 0.32 0.44 0.30

0.99 0.07 0.00 0.08 0.04 20.10 20.01 0.03 0.02 0.28 0.00 20.29 0.18 0.28 0.25 0.23 20.32 0.14 0.54*

Longitudinal amplitude IAampl

IOampl

AOampl

0.86 20.17 0.01 20.04 20.36 0.06 0.22 0.22 0.18 0.00 20.48* 0.04 20.11 0.13 20.36 0.24

0.94 20.02 0.17 0.01 20.28 20.08 0.10 0.20 0.14 0.04 20.49* 0.06 20.12 0.18 20.38 0.38 0.70z

0.94 0.18 0.26 0.21 20.11 20.21 20.13 0.04 0.02 0.03 20.33 20.06 20.11 0.09 20.20 0.28 0.01 0.70z

DC 5 distensibility coefficient; CC 5 compliance coefficient; CAC 5 carotid artery compliance; EY 5 Young’s elastic modulus; EP 5 Persson’s elastic modulus; Z 5 characteristic impedance; AA 5 aortic augmentation; Aix 5 augmentation index; Aix@75 5 augmentation index adjusted for a heart rate of 75 bpm; PWV 5 pulse wave velocity; SBP 5 systolic blood pressure; DBP 5 diastolic blood pressure; PP 5 pulse pressure; IA 5 longitudinal motion between the intima-media complex and the adventitia layer; IO 5 longitudinal motion between the intima-media complex and the surrounding tissues; AO 5 longitudinal motion between the adventitia layer and the surrounding tissues; ampl 5 peak-to-peak amplitude. Significant values are in boldface type. * p , 0.05. y p , 0.01. z p , 0.001.

motion graphs and eigenvectors of two representative cases with different degrees of arterial stiffness are provided in Figure 4. Repeatability of the PC values is good as all Cronbach’s a values are clearly .0.8 (Table 2). The first eigenvectors greatly resemble the average longitudinal/radial motion graph of the specific arterial layer and can explain 87.2%, 83.1% and 80.8% of the variance in the longitudinal motion of IA, IO and AO, respectively, as well as 97.9% of the variance in radial motion. The second eigenvector adds some detail related to the systolic and diastolic phases of arterial wall motion. By combining the first and second eigenvectors, it is possible to explain approximately 94.4%, 93.5% and 92.3% of the variance for longitudinal IA, IO and AO motion, respectively. Correspondingly, by using the two most significant eigenvectors, one can explain 99.5% of

=

the variance observable in the radial motion graphs of the whole study population. Because more than 92% of the longitudinal arterial wall motion can be expressed with the two most significant PCs, there is no need to observe the less significant PCs. The variability in the first five PC values is illustrated in Figure 5, which reveals a clear decline in values after the two most significant PCs and the dominance of the positive values in the two first PCs. The referential stiffness values are listed in Table 1, and the correlations between the first PCs and arterial stiffness indices, as well as age, gender and blood pressure, are listed in Table 2. The second PC of longitudinal motion of the adventitia layer had a good correlation with known stiffness indices derived from the radial motion curve. In addition, the second PC of longitudinal motion of the intima–media complex had the similar tendency to

Fig. 4. Two representative cases of the recorded motion graphs and the two first eigenvectors multiplied by their corresponding principal component (PC) values. (a, c, e, g) Longitudinal and radial motion graphs of a 30-y-old woman with a more elastic carotid artery. (b, d, f, h) Longitudinal and radial motion graphs of a 33-y-old woman with stiffer carotid artery (based on the Young’s elastic modulus). The purple solid line represents the measured average motion graph, the thin dashed blue line the first eigenvector, the thin dashed orange line the second eigenvector and the thicker yellow dashed line the sum of the two first eigenvectors. EY 5 Young’s elastic modulus; IO 5 longitudinal motion of intima– media; AO 5 longitudinal motion of adventitia. All signals start at the peak of the R-spike in the electrocardiogram.

PCA of carotid wall motion with vascular stiffness d H. YLI-OLLILA et al.

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Fig. 5. Variation in the values of the first five principal components. Whiskers represent the minimum and maximum, values, the blue box the inner quartile, the plus sign the average and the orange horizontal line the median. (a) Principal components derived from the longitudinal motion graphs between intima–media and adventitia (IA). (b) Principal components derived from the longitudinal motion graphs of intima–media (IO). (c) Principal components derived from the longitudinal motion graphs of adventitia (AO). (d) Principal components derived from the radial motion graphs.

reflect arterial stiffness, but the p values merely exceeded the 0.05 limit. The exact correlations with the second PCs in longitudinal motion of the intima–media complex and the adventitia layer were as follows: DC (r 5 0.432, p 5 0.065, and r 5 0.633, p 5 0.004); CC (r 5 0.349, p 5 0.143, and r 5 0.530, p 5 0.020); CAC (r 5 0.418, p 5 0.075, and r 5 0.644, p 5 0.003); EY (r 5 20.547, p 5 0.015, and r 5 20.581, p 5 0.009); EP (r 5 20.435, p 5 0.063, and r 5 20.656, p 5 0.002); and Z (r 5 20.382, p 5 0.106, and r 5 20.586, p 5 0.008), respectively. The first PC values of longitudinal motion were associated with pulse pressure: the first PC of longitudinal motion between the intima–media complex and the adventitia layer had a correlation value of 0.466 (p 5 0.044), and the first PC of longitudinal motion of the intima–media complex had a correlation value of 0.523 (p 5 0.022). The first PC of longitudinal motion of the adventitia layer merely

missed the criterion for statistical significance (r 5 0.407, p 5 0.084). In addition, the first PCs of longitudinal motion were associated with the corresponding longitudinal motion amplitudes: the correlation between the first PCs of IA and IAampl was 0.582 (p 5 0.009), the correlation between the first PCs of IO and IOampl was 0.761 (p 5 0.000) and the correlation between the first PCs of AO and AOampl was 0.814 (p 5 0.000). The second PCs were independent of longitudinal motion amplitudes. In comparison to the longitudinal waveform, the first PC of the radial waveform had a good correlation with DC (r 5 0.584, p 5 0.009), CC (r 5 0.809, p 5 0.000), CAC (r 5 0.686, p 5 0.001), EY (r 5 20.491, p 5 0.033), EP (r 5 20.677, p 5 0.001), Z (r 5 20.519, p 5 0.023), PWV (r 5 20.526, p 5 0.021) and DBP (r 5 20.548, p 5 0.015), whereas for the second PC, no statistically significant correlations with any of the correlates studied were observed.

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Applanation tonometry parameters did not have statistically significant correlations with any of the PC values. The correlations of the two first PCs with every time point of the original motion graphs are illustrated in Figure 6. In the case of longitudinal motion, the first PC has the highest inverse correlation with the original motion graphs from 0.1 s after the R-spike to the end of the motion signals. The second PC had a high direct correlation at the same time points, except a small notch on the correlation curve 0.4 s after the R-spike. The graphs in Figure 6 reveal the good statistical significance of both PCs as ways of describing the original waveform. DISCUSSION In this study, we successfully analyzed the variation in longitudinal carotid wall motion waveforms in 19

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healthy patients. In addition, variation of the radial motion of the carotid wall was analyzed for comparison. Characteristic features of the motion waveforms were extracted with PCA, and by using the first two eigenvectors and corresponding PC values, we were able to account for more than 92% of the original variance of the data in the longitudinal direction. A correlation was found between conventional arterial stiffness indices and the second PC of the longitudinal motion curves, but not with the first PC or with the amplitudes of longitudinal motions. The good repeatability of the PC values emphasizes the usability of the method. This application of mathematical PCA to investigation of arterial motion waveforms is a novel feature of this study. The first and second PC values express the variation within the measured longitudinal waveforms well: More than 92% of the variance is presented only by these two

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Fig. 6. Correlations of the first and second principal component (PC) values of every time point against the motion curve values of the same time point. The blue solid line represents the correlations of the first PC, and the orange dashed line represents the correlations of the second PC. Thin gray dashed lines represent the limits of statistical significance (jrj . 0.46). (a) Correlations from the longitudinal motion curve between intima–media and adventitia. (b) Correlations from the longitudinal motion curve of intima–media. (c) Correlations from the longitudinal motion curve of adventitia. (d) Correlations from the radial motion curve.

PCA of carotid wall motion with vascular stiffness d H. YLI-OLLILA et al.

parameters. The PCs represent well the waveforms from approximately 0.05 s after the R-spike of the electrocardiogram to the end of the measured longitudinal signal (0.67 s after the R-spike). The correlation is slightly higher between the first PC values and the original waveforms than between the second PC values and the original waveforms. However, this is expected because the first PC values alone account for more than 80% of the variance within the longitudinal motion waveforms. The first PC values of the radial motion waveforms account for more than 97% of the data variance, making the second radial PC unnecessary when describing the radial waveforms. The second radial PC values represent mainly the variance in the waveforms between 0.08 and 0.14 s after the R-spike, whereas the first radial PC values represent the variance in the waveforms from 0.11 s after the R-spike to the end of the measured radial signal. Overall, based on the ability of PCs to summarize motion data, longitudinal motion waveforms are more complex than radial waveforms. The first PC of longitudinal motion of the carotid intima–media complex had a significant direct correlation with carotid pulse pressure. The first eigenvector of longitudinal motion follows to some extent the average motion graph that would be obtained by estimating the mean from all of the patients in this study. The first eigenvectors from all carotid wall layers are one-phasic and smooth, reflecting retrograde motion (against the main direction of blood flow) when multiplied by a positive PC value. In this study population, a positive first PC value was more common than a negative one. It has previously been described that there is a correlation between the longitudinal amplitude of intima–media motion and blood pressure (Yli-Ollila et al. 2016; Zahnd et al. 2012); a plausible preliminary link between the main direction of the longitudinal waveform and arterial stiffness has also been reported (Yli-Ollila et al. 2014). In this study, the correlation coefficients between the first PC values derived from the longitudinal motion curves and the conventional stiffness indices did not achieve statistical significance, although there was a slight tendency for the first PC to increase as arteries were deemed to be stiffer (inverse correlation with DC, CC and CAC and direct correlation with EP and Z). The lack of significant correlation between the first PC values, which are strongly associated with the corresponding longitudinal amplitudes, and arterial stiffness indices might be due to the small number of patients in this study. The other possible reason is that the first PCs add too little extra information to the peak-to-peak amplitude of the longitudinal motion and thus might not be the best indicators of early stiffness. More interestingly, the second PCs of the longitudinal motion graph of the adventitia layer exhibited a statis-

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tically significant relationship with the measured arterial stiffness parameters. In addition, the second PC of the longitudinal motion graph of the intima–media complex exhibited a marked correlation with stiffness parameters, but because of the limited statistical power in our study setting, the correlations did not reach statistical significance. The second PC values derived from the longitudinal motion of the intima–media complex and the adventitia layer both displayed a tendency to be elevated in the more elastic arteries. The modulation of longitudinal wall motion in both intima–media and adventitia by arterial stiffening was reported earlier in a larger clinical study from our laboratory (Taivainen et al. 2015). That study measured the amplitudes of longitudinal motion and connected them with arterial stiffness parameters, whereas here we have focused on the finer details of the motion waveform. The second PC values derived from longitudinal motion of the intima–media complex and the adventitia both displayed higher correlations with arterial stiffness measures DC, CC, CAC, EY, EP and Z than the corresponding longitudinal amplitudes. In addition, the second PC values of longitudinal motion were all independent of the longitudinal amplitudes. This emphasizes the added value of PCA over plain amplitude measurement in detecting early arterial stiffening. Nevertheless, our results go hand-in-hand with Taivainen et al. (2015), illustrating the association between arterial stiffness and longitudinal motion of the carotid wall. The second eigenvector of longitudinal motion exhibits a biphasic form; that is, it has a positive spike in early systole (0.15 s) and a negative spike in early diastole (0.4 s). When multiplied by a positive PC value, the second eigenvector has the capacity to reveal the antegrade (direction of main blood flow) component of the longitudinal waveform during early systole, as well as the longitudinal motion in the retrograde direction during early diastole. These are the time points when the blood flow velocity reaches its positive and negative peak values. According to our results, the reduction of this extra fluctuation on top of the first eigenvector seems to be associated with the presence of stiffer arteries, especially on the adventitia layer. Physical motion of the heart and blood pressure, as well as flow characteristics inside the carotid artery, have been proposed as the force initiating longitudinal wall motion (Cinthio et al. 2006). Our study does not rule out any of these possibilities because the waveform characteristics of longitudinal wall motion studied here are in good agreement with the known time characteristics of actual heart motion and blood pressure/flow waveform in the carotid artery (the radial motion of the artery has the same temporal characteristics as the blood pressure waveform [Giannattasio et al. 2008]).

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The good correlations between the first radial PC and DC, CC, CAC, EY, EP and Z are to be expected because radial diameter is used to calculate the stiffness indices and the first PC reflects extensively the amplitude of radial motion. In contrast, the poor correlation between pulse pressure and the radial first PC is somewhat surprising because the amplitude of radial motion and pulse pressure are related to one another (Yli-Ollila et al. 2016). But it is logical that there is a significant inverse correlation between the first radial PC and DBP because diastolic blood pressure sets the starting tonus of the vessel wall, and the higher the pressure in diastole, the larger is the diameter of the artery and, thus, the lower is the capacity for stretch in the vessel wall. No statistically significant correlations were found between any of the applanation tonometry parameters and any of the PC values. The applanation tonometry parameters had higher standard deviations than the stiffness indices measured from the radial motion of the carotid artery. The high variability of applanation tonometry measurements within a small presumably healthy population has been reported previously (Wilkinson et al. 1998). This means, for instance, that augmentation index may not be best indicator of early arterial stiffness, at least not in individual diagnostics or in studies with small populations. Although augmentation index and aortic augmentation are well-known parameters widely used to study arterial well-being, they are not direct arterial stiffness measures. Aix and AA measure the stretch of the aorta, but do not take into account the driving force (pulse pressure) and, thus, cannot be considered direct measures of stiffness. In addition, Aix and AA are mathematically computed from the pulse pressure of the radial artery, and this can contribute to discrepancies in the results. Furthermore, Aix and AA are measured in the radial artery and are believed to reflect the stiffness properties of the aorta, not the carotid artery, as do all of the stiffness indices used in this study. Thus, stiffness changes in the aorta do not necessarily represent the stiffness changes in the carotid, especially in subclinical cases in which the stiffening process is at an early stage. The repeatability analysis revealed that all measured PC values are repeatable and not influenced by large random noise or large variability from one minute to another. The highest repeatability was achieved with the PC values defined from the radial motion curves. This was expected because measurement of longitudinal motion is more challenging, and thus, the repeatability of radial motion measurements in general has been better (Yli-Ollila et al. 2013). Nevertheless, by use of a high imaging frequency (85 Hz) and a large amount of averaging (1-min signals), the measured Cronbach a values were all

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.0.8, which is a criterion used to judge a variable suitable for individual diagnostics. The pitfall of the presented repeatability analysis is that the measurements were not performed by different individuals or on different days. Therefore, extensive conclusions cannot be made from the repeatability analysis, and inter- or intra-observer variability needs to be measured in the future studies. Nevertheless, the extremely high minute-to-minute repeatability is still promising and proves that the measured PC signals are not random. A previous repeatability analysis of longitudinal motion signals over 4 mo also adds credibility to the usability of this method (Ahlgren et al. 2012). Further studies are necessary to clarify the force driving longitudinal motion, although pulse pressure seems to exhibit some relationship with longitudinal wall motion. In addition, the decay of longitudinal motion amplitude along the vessel length indicates that aortic traction is one force driving longitudinal motion (Zahnd et al. 2015a). The average referential stiffness index values in this study clearly indicate that the study population was healthy (Benetos et al. 1993; Janner et al. 2010). In the future, the applicability of the proposed framework will need to be tested in a larger clinical material. However, the results presented here are promising, and the main purpose of this study was to devise a new method to study the waveform of longitudinal motion and to identify novel measures that would be capable of detecting early arterial stiffening. CONCLUSIONS In this study, we used PCA to study the characteristics of carotid wall motion waveforms and their relationship to arterial stiffness. It was found that the first PC values of longitudinal wall motion, describing much of the main orientation and amplitude of the motion, were associated with pulse pressure, whereas the second PC values were more strongly related to arterial stiffness. The waveform of the second eigenvectors indicates that arterial stiffening initially starts to reduce the retrograde amplitude during early diastole and lowers the antegrade spike on systole. The effects of arterial stiffening are most distinct on longitudinal motion of the adventitia layer. The results of the PCA described here highlight the possibility of detecting early arterial stiffening by characterizing the waveform of longitudinal artery wall motion, as the association between the second PC of the adventitia layer and arterial stiffness was evident even in this rather young and homogeneous study population. Further studies are needed to clarify the mechanism underlying the early stiffness changes reported in this study and to

PCA of carotid wall motion with vascular stiffness d H. YLI-OLLILA et al.

observe the progression of arterial stiffening in patients already diagnosed with atherosclerosis or arteriosclerosis. Acknowledgments—We acknowledge the financial support of the Kuopio University Hospital (EVO 5031320, 5031316 and VTR 5031356) and the University of Eastern Finland. In addition, we express our gratitude for financial support from the Science Foundation of Kuopio University Hospital, the Aarne and Aili Turunen Foundation, the Foundation for the Promotion of Technological Advances, the Aleksanteri Mikkonen Foundation, the Finnish Foundation for Cardiovascular Research and the Antti and Tyyne Soininen Foundation.

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