As a modality to measure tissue mechanical properties, optical coherence elastography (OCE) [1] has been rapidly developed to support biomedical and clinical investigations [2,3]. Among several approaches, compression-based OCE is promising as an optical biopsy method because of its non-invasive, rapid, and relatively high-resolution imaging properties.

In the early stages of OCE development, tissue mechanical properties were qualitatively observed by local displacement and strain measurements [4,5]. However, to quantitatively analyze the mechanical properties of tissues, i.e., to measure the elastic modulus, the stress on a tissue should be measured, in addition to the strain. Therefore, a compliant layer has recently been employed to estimate the local stress on a tissue, and en face mapping of the tangential modulus was demonstrated [6,7].

Despite its success, compression OCE relies on several assumptions. Among them, the major assumptions are constant axial stress, isotropic tissue mechanical properties, and the absence of lateral tissue displacement [6–9]. However, these assumptions are not always valid.

The artifacts (or errors) caused by violation of the first two assumptions can be eliminated using the approach of iteratively solving the inverse elasticity problem [10]. This method is successful in resolving the inaccuracy problem of uniform axial stress and assumptions of isotropic mechanical properties. This method could be more robust if the lateral displacement information was available. However, compression OCE with a lateral displacement measurement capability has not yet been demonstrated.

To overcome these limitations of compression OCE, it is necessary to perform a lateral displacement measurement.

In this Letter, we demonstrate a new method of axial and in-plane lateral displacement measurements and its application to compression OCE. This method uses optical coherence tomography (OCT) images of a tissue under two different compressive conditions. Using complex correlation maps computed from these two OCT images, depth-resolved axial and lateral displacement maps of the tissue are obtained.

In addition, a depth-resolved microstructural decorrelation (MSD) map is obtained. When a tissue is compressed, microscopic deformation of the tissue ultrastructure, which is smaller than the OCT resolution, occurs in addition to the relatively macroscopic displacement of in and out of the cross-sectional plane in OCT. The MSD map qualitatively visualizes the combined effect of the microstructural deformation and out-of-plane displacement, whereas current compression OCE only measures tissue displacement and strain.

The OCT system used in this Letter is a swept-source Jones matrix OCT (SS-JM-OCT) with a 1.3 μm probe. The A-line acquisition trigger was generated by a fiber Bragg grating (FBG, FBG-SMF-1354-80-0.2-A-(2)60F/E, $\ge 80\%$ reflectivity at 1354 nm; Tatsuta Electric Wire and Cable Co., Ltd., Osaka, Japan). The sample arm consists of an encased passive polarization delay module (DE-G043-13; Optohub Co., Ltd., Saitama, Japan) that multiplexes two incident polarization states into two different depths in the OCT image. It should be noted that this delay module was installed only for future extension toward polarization-sensitive measurement. The detection is performed by an encased polarization diversity detection module (DE-G036-13, Optohub).

This system is nearly identical to that in Ref. [11], but with some modifications. First, a light source with a longer coherence length (40 mm coherence length, AXP50124-8; Axsun Technologies, MA) was used. A frequency multiplier (MK-3, 0.1–300 MHz output; Mini-Circuits) was applied to double the $k$-clock frequency. In addition, the long passive polarization delay of the probe beam corresponding to a 2.8-mm depth range in tissue was used. The sensitivity was measured to be 104 dB for each polarization channel. The stability of the phase shift measurement was evaluated as 44.1 mrad with a static scattering sample, where the signal-to-noise ratio (SNR) of the OCT signal was 33.6 dB. The theoretical SNR-limited phase stability is 20.9 mrad.

To achieve mechanical compression of the sample, a ring piezoelectric transducer (PZT, HPSt 150/20-15/12 VS35 SG; Piezomechanik GmbH, Germany) was installed in front of the objective (effective focal length = 54 mm, working distance = 42.3 mm, LSM04; Thorlabs). A glass coverslip (0.4 mm in thickness) was attached to the front end of the PZT, which was used to compress the measured tissue. This configuration is similar to that in Ref. [8]; the OCT probing beam passes through the ring PZT and glass window. The lateral resolution ($1/e^2$-width) and axial resolution (full width at half-maximum) were 19 and 14 μm in the tissue, respectively. The imaging range was $2.0\times 2.8\mathrm{mm}$ (width × depth).

For the measurements, 512 B-scans covering 2.0 mm were sequentially acquired at the same location. One B-scan contained 512 A-lines. During the consecutive B-scan acquisition, the PZT continuously compressed the tissue by 12 μm. Therefore, two adjacent B-scans were obtained with a 0.023 μm compression difference. Displacement and MSD images were computed using the two OCT images with an $n$-B-scan interval corresponding to the $0.023n\mathrm{\mu m}$ compression difference. In this Letter, the interval of two selected B-scans is 40. Thus, the compression difference of the two B-scans is about 0.9 μm.

OCE was computed by the digital shifting complex correlation method [12]. First, the noise-corrected complex correlation (NCC) map [13] between two B-scans was computed. The NCC is a correlation in which the reduction of the correlation induced by noise is canceled based on a theoretical model of the OCT signal correlation and measured noise power. Then four additional correlation maps were computed between the target B-scan and four differently directionally shifted reference B-scans. The five correlation values at each point in the B-scan are explained by five simultaneous equations that are parametrized by five unknowns: in-plane lateral and axial displacements, lateral and axial resolutions, and an out-of-plane displacement. Here all unknowns vary in the B-scan. Therefore, the simultaneous equation system is defined at each point in the B-scan. Finally, by solving the simultaneous equations, in-plane axial and lateral displacement, axial and lateral OCT resolution, and out-of-plane displacement maps were computed. Intuitively, this algorithm can be understood as splitting a decorrelation into in-plane lateral and axial displacements, and an unexplained decorrelation. Because the correlation used in this method is the above mentioned NCC, the variation in the OCT signal intensity or SNR does not affect the result. However, if the SNR is too weak to provide the available information of the tissue structure, it would be hard to calculate the displacements and deformation maps of this part of the tissue.

This method was originally developed for in situ monitoring of tissue dynamics during retinal laser coagulation [12]. In the original method, residual decorrelation was interpreted as out-of-plane displacement. However, this component also reflects microscopic tissue alterations and deformation [12,14]. Thus, in this Letter, it is denoted as MSD.

Because the OCT system used in this Letter employed JM-OCT, it had two incident and two detected polarizations, which can generate four OCT images. Therefore, four maps were obtained for each axial and in-plane lateral displacement. The final maps were obtained by weighted averaging of four maps corresponding to the polarization channel where the weight was the OCT intensity of each channel. The OCT intensity images shown in figures [Figs. 1(b) and 2(b)] are polarization-insensitive OCTs, each of which is the average of four polarization diversity OCT intensity signals. Because the number of sequentially acquired B-scans is 512 and the interval of the B-scan pair for OCE computation is 40, 472 in-plane lateral and axial displacement image sets are obtained. A part of these images is averaged to reduce noise and artifacts.

 

Fig. 1. (a) Photo, (b) intensity OCT, (c) in-plane lateral displacement map, (d) axial displacement map, and (e) MSD map of a piece of dissected porcine carotid artery on a metal wire. The metal wire imitated a hard tissue. The yellow round dashed lines in (b)–(e) indicate the position of the metal wire. The wire has a round cross section of 0.78 mm in diameter. The thickness of the tissue over the wire is around 230 μm.

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Fig. 2. (a) Photo, (b) OCT, (c) in-plane lateral displacement map, (d) axial displacement map, and (e) MSD map of the porcine esophagus tissue.

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Using this method, we measured the displacement and deformation of a porcine carotid artery and esophagus tissues. To reduce the friction at the interface between the sample and glass coverslip, a moderate amount of silicon oil (Wacker AK 35) was applied evenly on the surface of the sample. The sample size is larger than the compression plate in at least on one direction to avoid bulk motion of the whole sample upon compression.

The first measurement was performed on a part of the dissected porcine carotid artery tissue close to the heart. As shown in the photo [Fig. 1 (a)], a part of the carotid artery was opened along the longitudinal direction, and the inside was placed upwards to the probe. To drive lateral displacement, a metal wire was fixed on the working stage at the center of the compression plate, and the center of the sample was also set on the metal wire. This wire can be considered as a phantom of a hard tissue such as bone. The yellow line indicates the position of the B-scans, i.e., the B-scan is along the longitudinal direction of the carotid artery. Figure 1(b) is an OCT B-scan. The strong scattering at the bottom is the surface of the metal wire. Almost no remarkable structures were observed in the B-scan, except for some low contrast lamellar structures. They could be considered as elastic fiber layers of the tunica media by referring to a previous study of porcine carotid artery histology [15]. The bottom area contacting the top surface of the metal wire shows a slightly lower scattering intensity than the other parts of the tissue, which should be the tunica externa. The bright line at the center of the wire in Fig. 1(b) may be a coherence revival signal. Figure 1(c) shows an in-plane lateral displacement image of the tissue under compression, which is the average of 30 displacement images. To determine the compression range of averaging, we computed phase-sensitive high-accuracy axial displacement maps which are similar to those in Ref. [6]. The averaging range was selected, as it has nearly constant displacement over compression. It demonstrates significant lateral displacement, as the outer left part of the tissue moved to the left (yellow), and the outer right part moved to the right (blue). The middle and bottom parts around the metal wire of the tissue show a complicated pattern, appearing as the left bottom part moves to the right, and the right bottom part moves to the left. A similar appearance was also found in other measurements of the porcine artery and some other tissues. Therefore, it is surmised that it is an actual effect. However, its interpretation may require detailed numerical analysis of tissue mechanics. The upper middle part of the tissue shows much less displacement than both end parts of the tissue, but the pattern appeared similar to the lamellar structures of the tunica media. In the corresponding axial displacement image [Fig. 1(d)], most tissue moves down, except the mid-bottom part of the tissue, which contacts the metal wire surface (green arrow). This part has almost no displacement. The MSD images show that the lower part of the tissue, except the mid-bottom part, has a larger decorrelation, i.e., microstructural deformation or out-of-plane displacement, than the upper tissue. Because the metal wire is placed along the out-of-plane direction and has no structure along the out-of-plane direction, the out-of-plane displacement induced by the metal wire is not expected to be as large as the in-plane lateral displacement. Therefore, we interpret this result [Fig. 1(e)] as the tunica externa having larger microstructural deformation than the elastic lamina tissue, i.e., the tunica externa is softer than the tunica media.

We also applied this method to measure another animal organ tissue, dissected porcine esophagus. The esophagus was opened along the longitudinal direction, and the inside was set towards to the probe. The yellow short line overlaid on the sample photo [Fig. 2(a)] indicates the measured position (B-scans). The B-scan is along the circumferential direction. The total thickness of the compressed tissue was around 2 mm. However, the deep region, such as the tissue located under 0.8 mm from the surface, was not observed because of the limited penetration of OCT. The surface of the tissue was lubricated by a moderate amount of silicon oil. In the OCT [Fig. 2(b)], a layer with low scattering and a lamellar appearance (indicated by a red arrow) is shown. In the corresponding MSD images [Fig. 2(e)], we found that the top part of the tissue shows the smallest decorrelation, the low scattering layer shows the highest decorrelation, and the tissue beneath this layer shows relatively low decorrelation. The in-plane lateral displacement map shows that the tissue was expanded laterally [Fig. 2(c)]. In this measurement, although there was no wire, the lateral displacement was still observed because, when a material is compressed (or stretched), it tends to expand (or contract) in directions perpendicular to the direction of the external force. This phenomenon is called the Poisson effect. Moreover, Poisson’s ratio represents the compressibility of a material. Biological material can be considered as an incompressible, i.e. volume-preserving, material. Therefore, its maximal Poisson’s ratio would be close to 0.5 [16]. In this case, to preserve its volume, the tissue expands laterally to accommodate the axial displacement.

According to the image appearances, the MSD map is more similar to in-plane axial displacement than in-plane lateral displacement. However, it does not suggest a real connection between axial displacement and MSD. The MSD map can visualize only the absolute value of displacement. Therefore, it has no directionality information, whereas the in-plane lateral displacement map visualizes bidirectional displacement. However, the axial displacement induced by the compression is monodirectional in practice, although the method itself can measure bidirectional axial displacement. These directionality properties of the map would be the reason for the resemblance.

The spatial resolutions of the displacement and deformation measurements were defined by three independent factors, including OCT imaging resolution, the kernel size of the correlation computation, and digital shifts of the reference B-scan. The OCT imaging resolution was defined by both the optical resolution and pixel separation. In this case, the optical resolutions were 19 (lateral) and 14 μm (axial in tissue), while the pixel separations were 3.9 and 7.0 μm, respectively. Thus, the lateral and axial OCT image resolutions were dominated by the optical resolution, which were $\mathrm{\Delta }{x}_{\mathrm{oct}}=19\mathrm{\mu m}$ (lateral) and $\mathrm{\Delta }{z}_{\mathrm{oct}}=14\mathrm{\mu m}$ (axial). The second factor, the correlation kernel size, was $7\times 7$ pixels. By multiplying the pixel separations, the kernel occupied $\mathrm{\Delta }{x}_{ck}=27.3\mathrm{\mu m}$ (lateral) and $\mathrm{\Delta }{z}_{ck}=49\mathrm{\mu m}$ (axial in tissue). The third factor, the digital image shift, was $\pm 1$ pixel. It corresponded to $\mathrm{\Delta }{x}_{ds}=7.8\mathrm{\mu m}$ (lateral) and $\mathrm{\Delta }{z}_{ds}=14\mathrm{\mu m}$ (axial in tissue). The overall resolution of the displacement and deformation measurements was defined by the convolution of these factors. Therefore, it was roughly estimated as $\mathrm{\Delta }x=\mathrm{\Delta }{x}_{\mathrm{oct}}+\mathrm{\Delta }{x}_{ck}+\mathrm{\Delta }{x}_{ds}=54\mathrm{\mu m}$ (lateral) and $\mathrm{\Delta }z=\mathrm{\Delta }{z}_{\mathrm{oct}}+\mathrm{\Delta }{z}_{ck}+\mathrm{\Delta }{z}_{ds}=77\mathrm{\mu m}$ (axial in tissue). This relatively low resolution may account for the broadening of the wire surface signal in the displacement and deformation images [Figs. 1(c)–1(e)].

The performance of the displacement measurement was quantitatively evaluated with a static polyvinyl chloride sample (plastic eraser) on a three-axis piezoelectric translation stage. Displacement measurement was continuously performed as the stage was continuously translated. Subsequently, 10 displacement maps with 10 different equally spaced set displacements were computed. For each displacement map, 12, i.e., $4\times 3$, points were selected for analysis. This evaluation was performed for both in-plane lateral and axial displacements. As ground truths, the position-sensor readout of the stage was used for lateral translation, while the phase-sensitive displacement measurement was used for axial displacement. The translation ranges are [0.1, 1.1] μm for lateral and [0.1, 1.2] μm for axial. The root-mean-square error (RMSE) was computed among the 12 points, and the average of the RMSEs was computed among the 10 displacements. The average RMSEs for lateral and axial displacements were 0.25 and 0.38 μm, respectively. It should be noted that the lateral RMSE was found to be mainly restricted by the accuracy of the translation stage.

The digital shifting complex correlation method [12] used in this Letter was originally designed for quasi-three-dimensional displacement (quasi-3-D) measurement. However, the out-of-plane displacement component is coupled with microstructural deformation, especially in the compression OCE measurement. Here the microstructural deformation denotes an alteration of the physical structure of the sample smaller than the OCT resolution or correlation-computation kernel. This coupling prevents the 3-D displacement measurement and pure microstructural deformation measurement. In a future study, we can modify the digital shifting complex correlation method to be compatible with the 3-D displacement measurement and pure microstructural deformation measurement by using two 3-D OCT volumes with two different compression states. In this case, the out-of-plane displacement and microstructural deformation are decoupled. Therefore, it is safe to interpret the residual decorrelation as microstructural deformation.

In conclusion, we developed a new method to visualize two-dimensional in-plane displacement and the coupled effect of out-of-plane displacement and microstructural deformation induced by micrometer-scale tissue compression. The method provides depth-resolved maps of these quantities. Although it is still qualitative, it can be used for a detailed analysis of the mechanical properties of tissues. In addition, because the system is based on Jones matrix OCT, it enables simultaneous polarization and OCE imaging in the future. It may also facilitate investigations of collagenous tissues.