First published online June 22, 2006
British Journal of Radiology (2006) 79, 707-711
© 2006 British Institute of Radiology
doi: 10.1259/bjr/22522280
Quantitative optical coherence tomographic elastography: method for assessing arterial mechanical properties
J Rogowska, PhD
1,2
N Patel, BS
1
S Plummer, BS
1 and
M E Brezinski, MD, PhD
1,2
1 Brigham and Women's Hospital, 75 Francis Street, Boston, MA 02115, 2 Harvard Medical School, Boston, Massachusetts, USA
Correspondence: Mark E Brezinski, Brigham and Women's Hospital, MRB 106, 75 Francis Street, Boston, MA 02115, USA.
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Abstract
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Optical coherence tomography elastography represents a potentially attractive new technique for measuring elastic properties of tissues on a micron scale. In this study, the feasibility of optical coherence tomography (OCT) to study the mechanical properties of phantoms and atherosclerotic arterial samples is reported. The elastic modulus of tissue-mimicking phantoms was measured using OCT and correlated with mechanical measurements. The results indicate that elastography based on OCT represents an attractive technique for evaluating the mechanical properties of tissues.
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Introduction
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Knowledge of the mechanical properties of vascular tissue could provide diagnostic information about a range of vascular diseases, from pulmonary hypertension to coronary atherosclerosis. Therefore, it is important to develop and evaluate new quantitative methods for measuring the elastic modulus of normal and abnormal arterial tissue.
The term ultrasound elastography was introduced for the first time by Ophir and colleagues in 1991 [1]. The elastography technique was based on applying a pressure on the examined tissue and in estimating the induced strain distribution by tracking the tissue motion [1–3]. An ultrasound elastography is limited by a resolution between 80 µm and 100 µm, which is likely insufficient for vascular assessments. A technology that has shown considerable promise as a method of high resolution intravascular imaging and elastography is optical coherence tomography (OCT) [4–9]. OCT is a micrometre scale imaging technology analogous to ultrasound, measuring the back-reflection of near-infrared light rather than sound. Current OCT systems that can be used in vivo have a resolution between 10 µm and 20 µm. Recently, several semi-quantitative approaches to OCT elastography have been demonstrated using speckle tracking [10–12]. However, in order for the technique to be used clinically, the quantitative accuracy of tissue elasticity measurements must be established, which is the focus of this paper.
In this paper, we first describe and implement an OCT elastography technique on tissue phantoms, measuring deformation of samples to obtain stress-strain curves that characterize the linear elastic properties. Second, these results of OCT elasticity measurements are validated and quantitated with non-imaging mechanical measurements of the same phantoms. Finally, this validated OCT elastography approach was applied to atherosclerotic arterial samples.
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Materials and methods
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Experimental elastography system
OCT is analogous to ultrasound, measuring the intensity of back-reflected infrared light [4, 5]. Ultrashort light pulses or low coherent light is generated at the sample. The time for the light to be reflected back or echo delay time is used to measure distances. The intensity of back-reflection is plotted as a function of depth. The beam is then scanned across the sample to produce two- and three-dimensional data sets.
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Phantom and aorta images
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Phantoms were made by mixing different amounts of agar, gelatin and water. Using a fixed amount of gelatin (8 g), phantoms with different hardness were made by varying the amount of agar: 0.5 g for 1% phantom, 1.0 g for 2% phantom, 3 g for 3% phantom. Gelatin and agar were mixed together and dissolved in 50 ml of boiling water. The 0.25 g of activated charcoal particles were added as scatterers. After refrigeration, the gelatin phantoms were cut into 2.5 cmx2.5 cmx1 cm thick block shaped samples, covered with a cover slip, and scanned. The elastic properties of the phantoms were confirmed by applying weights of 49.81 g, 102.88 g and 133.03 g. The changes in tissue width were measured both with callipers and OCT imaging. All measurements were repeated three times for each of the phantoms, thus producing three sets of data. The OCT measurements were corrected for refractive index.
The human atherosclerotic aorta samples were obtained post-mortem and stored at 0°C with 0.1% sodium azide. The samples were placed under the OCT system and scanned before and after compression, using a procedure similar to phantom scanning. The weights applied to the aorta samples were 2.29 g, 5.60 g and 8.21 g. The OCT scanning was performed in the axial cross-sections of the samples, covering 2 mmx2 mm areas in the centre, far away from the sample edges. The OCT image resolution was 400 by 400 pixels, where each pixel was 0.005 mmx0.005 mm.
Calculation of elastic modulus of phantoms
Our goal was to calculate the local values of elastic modulus in the phantoms. If we assume that the phantoms are elastic, isotropic and incompressible, and the stress is applied uniformly in axial direction, then the Young's modulus (or elastic modulus) E is defined by [13]:
where 
is the axial (or normal) stress (defined as the force F perpendicular to the cross sectional area, divided by the cross sectional area A):
and 
is the axial strain (defined as the fractional change in sample thickness L):
By applying weights, samples were compressed, and their thicknesses before and after compression were measured using callipers and OCT displacement vectors. The image data were processed pixel-by-pixel and the total axial displacement vectors were calculated using cross-correlation [10, 11]. For strains up to 5%, the relationship between force and displacement is usually linear [14]. Based on Equation (2), the equivalent stress applied to phantoms was computed by dividing the force by the surface dimensions of the samples, which yielded stress values of 0.77 kPa, 1.60 kPa and 2.06 kPa for three compressions. The optical coherence tomographic elastography (OCTE) displacement values in pixels were converted to millimetres and corrected using refraction index. By measuring the strain (Equation (3)) for three different applied stresses, the stress-strain relationship was calculated using a linear regression. The Young's modulus was estimated from the slope of the strain-stress linear function. All measurements were repeated three times for three sets of samples, and then averaged.
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Estimation of the elastic modulus of aorta
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Once the stress-strain measurements are obtained on the phantoms, the slopes of these stress-strain curves are used to determine the elastic modulus values. Since the Young's moduli (E) of the phantoms are known, and the slope values (S) of the stress-displacement curves for the phantoms can be measured, the conversion factor C relating the stress-displacement slope values to the Young's modulus could be determined by:
where E1%, E2%, and E3% are elastic moduli for 1%, 2% and 3% phantoms, respectively, and S1%, S2%, and S3% are slope values from the corresponding stress-displacement curves.
In order to calculate the estimated elastic modulus of the aorta (rEAorta), the slope value of the OCTE stress-displacement curve for the aorta (SAorta) was transformed to Young's modulus using a conversion factor C [13, 15]:
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Results
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The phantoms underwent compression with weights and the changes in phantom's thickness were measured both with callipers and OCT imaging. The image data were processed pixel-by-pixel and the total axial displacement vectors were calculated. An example of the 2% phantom is shown on Figure 1
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Figure 1. A typical optical coherence tomography(OCT) 2% phantom images after applying stress of (b) 0.772 kPa, (c) 1.595 kPa and (d) 2.062 kPa to original phantom (a). The displacement vectors are shown in red.
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For all phantoms, stress-strain relationships using calliper and OCT measurements were calculated and Young's modulus was estimated (Figure 2). The differences between calliper and OCT measurements were found to be non-significant (paired t-test; p = 0.6 for 1% phantom, p = 0.25 for 2% phantom and p = 0.38 for 3% phantom). The relationship between two Young's modulus estimators (using callipers and OCTE) was found to be highly correlated, R2 = 0.92.
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Figure 2. Young's modulus for 1%, 2%, and 3% phantoms estimated using two techniques: callipers' measurements and OCT elastography. The bars indicate standard deviation. The differences between calliper and OCTE measurements were found to be non-significant (p = 0.6, p = 0.25 and p = 0.38 for 1%, 2% and 3% phantoms, respectively).
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Aorta samples also underwent compression with weights (Figure 3). The changes in tissue thickness were measured using OCT. The image data were processed pixel-by-pixel and the axial displacement vectors (Figure 3b–d) and displacement maps (Figure 4) were calculated. In order to calculate the relative elastic modulus of the aorta, we used the conversion factor C = 12.14, which was derived from stress-displacement phantom curves. The average estimated Young's modulus for the aorta sample shown on Figure 4 was equal to 6.11 kPa.
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Figure 3. Aorta images after applying stress of(b) 0.0355 kPa, (c) 0.0868 kPa and (d) 0.1273 kPa to original image (a). Figure 3a indicates location of intima (I), media (M) and glass compression plate (G). The displacement vectors are shown in red.
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Discussion
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This paper attempts to quantify OCT elastography as a method for assessing Young's modulus, and therefore evaluating tissue mechanical properties. The OCT elastography system was calibrated with tissue-mimicking phantoms and the elastic modulus of the atherosclerotic arterial samples was estimated. A strong correlation existed between the mechanical measurements and those performed with OCT elastography, with no significant difference existing between the two techniques. OCT elastography was then used to estimate Young's modulus through the use of the conversion factor. According to other reports [15], our estimated elastic modulus of 6.11 kPa for the aorta was within the range of Young's modulus values calculated for smooth muscle (0–100 kPa) and soft tissue (0–200 kPa).
Several obstacles need to be overcome for OCT elastography application in human arteries in vivo. First, controlled transmural pressures need to be applied to make OCT measurements in vivo. This can potentially be achieved with an intravascular pressure balloon or saline flushes with measured pressures. Second, it is assumed that the tissue under investigation is elastic, uniform and nearly incompressible. Based on work with ultrasound, the approximation of vascular tissue being elastic and incompressible is reasonable. However, with atherosclerotic or severely hypertensive arteries, the tensile properties will not necessarily be completely uniform. The importance of this has to be examined with future studies. Third, for correct conversion of stress-displacement data to an elastic modulus, it is essential that the calibration sample and tissue sample have similar shape [13]. This needs to be taken into account when calibrating the technique for imaging in vivo arteries. Sample height and sample compressibility are non-critical factors for system accuracy. However, the size of the area where the stress is applied to the sample is a very critical parameter and needs to be well controlled to obtain accurate results.
In summary, OCT elastography represents an attractive technique for evaluating the mechanical properties of tissue due to its micrometre scale resolution. Other OCT elastography studies have essentially focused on qualitative analysis, not on the accuracy of measured mechanical parameters. The focus of this work was to establish quantification of OCT elastography. The study reported here was also the first attempt to calculate the elastic modulus of atherosclerotic tissue using OCT.
This research is sponsored in part by the National Institutes of Health, Contracts NIH-RO1-AR44812 (MEB), NIH R01 AR46996 (MEB), NIH R01- HL63953 (MEB), NIH-1-R01-HL55686 (MEB), NIH R01 EB000419 (MEB) and NIH-1-R29-HL55686 (MEB).
Received for publication November 23, 2005.
Revision received March 9, 2006.
Accepted for publication April 12, 2006.
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Abstract
Introduction
