Local Birefringence Imaging by Similar Mueller Matrix Averaging Method in Catheter-Based Polarization-Sensitive Optical Coherence Tomography

Abstract

Local birefringence imaging provides the most intuitive polarization property of tissue, such as vascular plaque, in catheter-based polarization-sensitive optical coherence tomography (PS-OCT) imaging. We present a Local Birefringence Similar Mueller Matrix Averaging (LMMA) for catheter-based PS-OCT imaging. LMMA combines differential Mueller analysis, matrix decomposition, and noise compensation to address depolarization coupling and noise interference. Monte Carlo simulations show LMMA achieves 4.8% error under high noise and 4.4% under high depolarizationup to 84% improvement over the Stokes vector spectral binning (SSB) method. Polycarbonate imaging experiments yield 1.5% average error, 86% lower than the SSB. Ex-vivo porcine coronary artery imaging demonstrates significantly enhanced lipid and fibrous plaque phantom differentiation, with LMMA’s plaque recognition rate reaching 2.62 times that of SSB evaluated by spatial response of Laplacian operator (SRLO). The results show LMMA’s potential in advanced vascular imaging, particularly for monitoring and diagnosis of coronary artery disease.

1. Introduction

Catheter-based polarization-sensitive optical coherence tomography (PS-OCT) is a powerful intravascular polarimetric imaging technique. Compared with conventional intensity-based OCT, PS-OCT extends structural cross-sectional imaging to include polarization-resolved contrasts such as birefringence, diattenuation, depolarization, and optic axis orientation. − The team of Villiger first demonstrated that PS-OCT imaging reveals substantial differences in polarization properties between atherosclerotic plaques and healthy arterial wall tissues. Catheter-based PS-OCT became a more comprehensive and multidimensional assessment of vascular health. Polarization properties of a local site demodulation is a key imaging capability of catheter-based PS-OCT. The visualization of the spatial distribution of polarization parameters across the vascular cross-section enables higher sensitivity, allowing more intuitive identification of polarization contrasts in tissue. ,

Among these parameters, local birefringence holds a high clinical translational potential. Several studies have shown that pathological plaques, such as lipid-rich or fibrotic atherosclerotic plaques, exhibit characteristically reduced or enhanced birefringence compared to healthy tissues. − Therefore, high-resolution tomographic imaging of local birefringence could enable precise localization and morphological delineation of atherosclerotic plaques. A major challenge in PS-OCT imaging of local birefringence is the effect of noise. Local birefringence reconstruction relies on spatial propagation of measurements, and inaccuracies in shallow layers can lead to severe distortions in deeper regions due to error propagation and cumulative noise; hence, local birefringence imaging is very sensitive to noise. As a result, the measured birefringence values are not accurate in deeper regions. In 2010, Makita et al. first proposed a method for reconstructing local birefringence in PS-OCT using Jones matrix analysis. However, this approach models tissues as pure retarders, accounting for only phase retardation while neglecting diattenuation and depolarization effects. Thus, the proposed method is not applicable on turbid tissue with high scattering or absorbing anisotropic, namely, some typical biological tissues. In 2013, Villiger et al. conducted a systematic investigation of noise mechanisms in fiber-based PS-OCT systems for local birefringence imaging, which demonstrated that polarization mode dispersion (PMD) in the fiber system introduces spatially localized biases in the retardation image, resulting in pseudobirefringence artifacts. In the same year, Villiger et al. proposed the Stokes vector spectral binning (SSB) method within a Stokes vector-based framework to demodulate local birefringence, PMD compensation is introduced in catheter-based PS-OCT systems for the first time. The SSB method is only one local birefringence demodulation of the catheter-based PS-OCT that have been successfully used in the clinical application. However, this compensation came at the cost of reduced lateral resolution. Furthermore, Stokes-based methods inherently cannot eliminate the influence of depolarization coupling and noise. Hence methods based on Jones matrix or Stokes vector meet difficulty on birefringence decoupling from depolarization, denoising, and device complexity. Our team proposed a similar Mueller matrix method (SMM), a similar Mueller matrix averaging method (MMA) and estimation of medium depolarization index (EMDI), which can successfully eliminate the noise influence and decouple depolarization. − However, the previous SMM and MMA methods only demodulate cumulative birefringence, which hinders intuitive visualization of tissue polarization properties. Since processing in the Mueller matrix can eliminate the influence of noise and depolarization, the Mueller matrix based method has tremendous potential for high-precision local birefringence imaging in PS-OCT.

In this paper, we propose a novel local birefringence imaging method in catheter-based PS-OCT, the local Mueller Matrix average (LMMA). LMMA is based on a decomposition of similar Mueller matrix averages combined with polarization state evaluation. It enables high-precision local birefringence imaging on dual polarization states in the catheter-based PS-OCT system, with compensation for both system factors such as PMD and noise, while also suppressing depolarization interference. Among the local polarization parameters, local birefringence has a greater potential to identify fibrous plaques. We systematically evaluated the LMMA method under SNR and depolarization conditions through Monte Carlo simulations and evaluated its performance. We then conduct experimental validation using stretched polycarbonate samples in catheter-based PS-OCT to quantitatively verify the accuracy of LMMA’s local birefringence imaging. Finally, we applied LMMA in catheter-based PS-OCT imaging of collagen and cholesterol plaque phantoms prepared in ex-vivo porcine coronary arteries. We present imaging results that visually demonstrate the superiority of LMMA over the SSB method in identifying plaque phantoms from a medical imaging perspective. Furthermore, we provide performance metrics, specifically the Signal-to-Reference Level Offset (SRLO), derived from multiple experimental image sets under an automated evaluation framework. These metrics quantify the extent of improvement achieved by LMMA over SSB in interpreting plaque features according to machine-assessment standards.

2. Principle

The overall framework of the LMMA method consists of three main components: global Mueller matrix requisition, global Mueller matrix denoise, and the local birefringence computation, as illustrated in Figure .

1.

Flowchart of LMMA for PS-OCT.

The First step, we acquire global Mueller matrix M _raw . Starting from the PS-OCT output, we obtain measuring Mueller matrices S(z _n ) for all the pixels at each depth z ₁, z ₂, z ₃, ..., z _n , in the whole image. S(z _n ) is a Jones–Mueller matrix that cannot record depolarization, whereas a spatial kernel averaging to process S(z _n ), $\stackrel{\circledR }{\mathbf{S}(z_n)}$ after spatially averaging will carry depolarization information. , We select the outer line of the catheter sheath as the region of reference, and note the depth as z _ref . The reference measuring Mueller after spatially averaging is obtained as $\stackrel{\circledR }{\mathbf{S}(z_{ref})}$ . We can obtain global Mueller matrix M _raw (z _ref , z _n ) by the following:

$${\mathbf{M}}_{raw}(z_{ref},z_n)=\stackrel{\circledR }{\mathbf{S}(z_n)}{\stackrel{\circledR }{\mathbf{S}(z_{ref})}}^{-1}$$ 1

where M _raw (z _ref ,z _n ) is similar to the round-trip Mueller matrix M _ST (z _n ) at depth z _n and M _ST (z _n ) is the certain matrix directly characterizing the sample global information. Applying eq , we compute M _raw for all of the pixels at each depth in the image. Due to the high-speed rotation of the probe in the sample arm and the resultant squeezing of the optical fiber, M _raw contains serious noise-induced depolarization.

The second step is to operate denoise processing on M _raw, to reduce noise-induced depolarization. Taking advantage of EMDI, we obtain the medium depolarization matrix M _Δ. Hence, the matrix excluding the medium depolarization expressed by the pseudo-nondepolarizing Mueller matrix M _NP.raw can be obtained as follows:

$${\mathbf{M}}_{NP.raw}={{\mathbf{M}}_{\mathrm{\Delta }}}^{-1}{\mathbf{M}}_{raw}$$ 2

If noise is absent in the matrix, M _NP.raw can be considered as truly nondepolarizing. In experimental reality, M _NP.raw inevitably contains noise so that global matrix decomposition should be operated by Lu–Chipman decomposition method as follows:

$${\mathbf{M}}_{NP.raw}\Rightarrow {\mathbf{M}}_{N\mathrm{\Delta }.raw}{\mathbf{M}}_{R.raw}{\mathbf{M}}_D$$ 3

where M _NΔ.raw stands for the noise-depolarization matrix. M _R.raw is the birefringent matrix, and M _D is the diattenuation matrix. Even though M _NΔ.raw counts the majority of the noise, the predecomposition of M _NP.raw cannot ensure M _R.raw is precise enough to compute local birefringence. We operate iteratively to refine M _R.raw under the reference of the Frobenius norm judgment. First, we initialize global retardation δ₀ from M _R.raw :

$${\delta }_0=\arccos [tr({\mathbf{M}}_{R.raw}({\delta }_0))/2-1]$$ 4

M _R.raw can be considered as a function of δ₀. , We change δ₀ by a trial value Δδ to generate a test nondepolarizing matrix M _NP.test (δ₀ + Δδ) as follows:

$${\mathbf{M}}_{NP.test}({\delta }_0+\mathrm{\Delta }\delta )={\mathbf{M}}_{R.raw}({\delta }_0+\mathrm{\Delta }\delta ){\mathbf{M}}_D$$ 5

Then, a test noise matrix M _NΔ.test (δ₀ + Δδ) is generated as follows to compare the noise level with [D]:

$${\mathbf{M}}_{N\mathrm{\Delta }.test}({\delta }_0+\mathrm{\Delta }\delta )={\mathbf{M}}_{NP.raw}{{\mathbf{M}}_{NP.test}}^{-1}({\delta }_0+\mathrm{\Delta }\delta )$$ 6

To make sure δ₀ + Δδ approach the true retardation, we conduct iteration on Δδ to achieve the following conditions:

$$\begin{array}{l}{\parallel {\mathbf{M}}_{N\mathrm{\Delta }.test}({\delta }_0+\mathrm{\Delta }\delta )\parallel }_F\le {\parallel [\mathbf{D}]\parallel }_F\\ \sum _{i=1}^4|{\lambda }_i({\mathbf{M}}_{N\mathrm{\Delta }.test}({\delta }_0+\mathrm{\Delta }\delta ))|=\mathrm{MAX}({\lambda }_i({\mathbf{M}}_{N\mathrm{\Delta }.test}({\delta }_0+\mathrm{\Delta }\delta )))\end{array}$$ 7

where λ _i (M _NΔ.test (δ₀ + Δδ)) are the eigenvalues of M _NΔ.test (δ₀ + Δδ) i = 1, 2, 3, 4. MAX­(*) stands for the maximum value among *. ||*|| _F stands for the Frobenius norm operator. [D] is the standard deviation matrix of M _NP.raw within the region of reference (ROR) to mark the noise property preliminarily. We assign Δδ as the following rule until the condition of eq fits.

$$\begin{array}{l}\mathrm{\Delta }{\delta }_{i+1}=\mathrm{\Delta }{\delta }_i+{\alpha }_{i+1}\mathrm{\Delta }{\delta }_i\\ {\alpha }_{i+1}=k({\parallel {\mathbf{M}}_{N\mathrm{\Delta }.test}({\delta }_0+\mathrm{\Delta }\delta )\parallel }_F-{\parallel [\mathbf{D}]\parallel }_F)\end{array}$$ 8

where i, i + 1 stand for the iteration time, α _i+1 is the weight coefficient at i + 1 iteration, and k is a constant. Once the conditions of eq are satisfied, the noise level of the Mueller matrix at the estimation value δ₀ + Δδ matches the overall noise level in M _NP.raw , M _R.raw (δ₀ + Δδ) can be considered as the noise-free global birefringence matrix M _R . Thus, we reconstruct the denoised measured global Mueller matrix M by M _Δ M _R M _D = M.

The final step is to apply local birefringence computation. Inspired by Generalized Jones matrix method, we deduce the Mueller matrix-based framework. M can be noted as M(z _ref , z _n ) at depth z _n . The cumulative and round-trip Mueller matrix of sample M _ST (z _n ) is similar to M(z _ref , z _n ) by the following equation:

$$\mathbf{M}(z_{ref},z_n)=\mathbf{Q}{\mathbf{M}}_{out}{\mathbf{M}}_{ST}(z_n){{\mathbf{M}}_{out}}^{-1}{\mathbf{Q}}^{-1}$$ 9

where M _out is the Mueller matrix of the output path and Q is the interference matrix:

$$\mathbf{Q}=\left[\begin{array}{llll}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& \cos \psi & -\sin \psi \\ 0& 0& \sin \psi & \cos \psi \end{array}\right]$$ 10

where Ψ is the phase difference between the two input polarization states of the reference light in the H channel and the V channel. When the sample is segmented into an infinitesimal stack of thin slices along the depth axis, M _ST (z _n ) can be consider as consist of single-trip Mueller matrices of local sites as

$$M_{ST}(Z_n)=[M_S^T(Z_{ref,}{Z}_1)M_S^T(Z_1,Z_2)M_S^T(Z_2,Z_3)...M_S^T(Z_{n-1},Z_n)]$$

$$[M_S(Z_{n-1},Z_n)...M_S(Z_2,Z_3)M_S(Z_1,Z_2)M_S(Z_{ref},Z_1)]$$ 11

where z _n–1 corresponds to the depth position one pixel above z _n . M _S (z _n–1, z _n ) is a single-trip Mueller matrix of sample. z _n – z _n–1 is the thickness of the sample at a local site.

Then we applied a global-local propagating Mueller matrix transformation. We can obtain the measured local Mueller matrix M(z _n–1, z _n ) depth by depth starting from z _ref to z _n using this relation as below:

$$\mathbf{M}(z_{n-1},z_n)=\mathbf{M}(z_{ref},z_n){\mathbf{M}}^{-1}(z_{ref},z_{n-1})$$ 12

We take eq into eq as below:

$$\mathbf{M}(z_{n-1},z_n)=\mathbf{Q}{\mathbf{M}}_{out}{\mathbf{M}}_{ST}(z_n){{\mathbf{M}}_{ST}}^{-1}(z_{n-1}){{\mathbf{M}}_{out}}^{-1}{\mathbf{Q}}^{-1}$$ 13

From eq , it is clear that M(z _n–1, z _n ) is similar to M _ST (z _n ) M _ST ^–1(z _n–1). As we take eq into eq , the following relation establishes:

$$\mathbf{M}(z_{n-1},z_n)=\mathbf{Q}{\mathbf{M}}_{out}({\mathbf{M}}_S^T(z_{ref},z_1){\mathbf{M}}_S^T(z_1,z_2)...{\mathbf{M}}_S^T(z_{n-2},z_{n-1}))\times {\mathbf{M}}_{ST}(z_{n-1},z_n){({\mathbf{M}}_S^T(z_{n-2},z_{n-1})\text{...}{\mathbf{M}}_S^T(z_1,z_2){\mathbf{M}}_S^T(z_{ref},z_1))}^{-1}\times {{\mathbf{M}}_{out}}^{-1}{\mathbf{Q}}^{-1}$$ 14

According to eq , it is obvious that the local round-trip Mueller matrix of sample M _ST (z _n–1, z _n ) is similar to M(z _n–1, z _n ) . M _ST (z _n–1, z _n ) and M(z _n–1, z _n ) contain the same polarization information. Local matrix decomposition is applied to M(z _n–1, z _n ) as follows:

$$\mathbf{M}(z_{n-1},z_n)\Rightarrow {\mathbf{M}}_{\mathrm{\Delta }}(z_{n-1},z_n){\mathbf{M}}_R(z_{n-1},z_n){\mathbf{M}}_D(z_{n-1},z_n)$$ 15

where M _R (z _n–1, z _n ), M _Δ(z _n–1, z _n ), and M _D (z _n–1, z _n ) are local birefringence and depolarization and diattenuation matrices, respectively. The local birefringence retardation δ­(z _n–1, z _n ) is then computed by using the following equation:

$$\delta (z_{n-1},z_n)=\arccos [\mathrm{tr}({\mathbf{M}}_R(z_{n-1},z_n))/2-1]$$ 16

Finally, we convert local retardation into local birefringence Δn(z _n–1, z _n ) as follow:

$$\mathrm{\Delta }n(z_{n-1},z_n)=\frac{\delta (z_{n-1},z_n)\lambda }{4\pi (z_n-z_{n-1})}$$ 17

where λ is the wavelength of the light source applied in the PS-OCT device.

3. Monte Carlo Simulation

We compute the local birefringence results processed by LMMA and SSB methods based on Monte Carlo simulation. The detailed algorithm SSB method is shown in ref . The averaging kernel is a sliding window with a size of 30 × 30 pixels. For a complex field averaging in SSB and real field averaging in LMMA, we operate averaging by the same sliding window on the whole image, one pixel by one pixel. We show Monte Carlo simulation results of local birefringence images under different signal-to-noise ratio (SNR) and different depolarization levels (anisotropy index g) in Figure . The image size of Figure is 256 × 512 pixels. The length of the A-scan is 1 mm, and the length of the B-scan is 0.5 mm. To observe the tomography property of the local birefringence among different simulating materials, each simulating material is set as a two-layer structure. The simulating material is generated as a 1 mm × 1 mm × 1 mm cubic sample, where the boundary between the two layers of different birefringent materials is at 0.7 mm depth. The two-layer material birefringence distribution are all set as Δn ₁ = 4 × 10^–4 at the top layer and Δn ₂ = 8 × 10^–4 at the bottom layer. The noises are set as additive k-domain form: 4, 7, and 10 dB, noise free from the bottom line to the top. The first and second columns are set as g = 1 as a nondepolarized tissue, while the third and the fourth columns are set g = 0.9 as weak depolarizing tissue, the fifth and the sixth columns are set as high-depolarization tissue with g = 0.85, depolarization rises as g decreases. , The samples above are all simulated under differential group delay τ = 1 × 10^–11 s, a maximum rational value for typical fiber-based PS-OCT system with circulators. Each simulation is demodulated by SSB and LMMA, and all are collected in 6 columns in total. As shown in Figure (a1, b1), when g = 1 and the imaging is noise-free, the process involves only PMD, and both SSB and LMMA demonstrate comparable resolution levels, with well-defined layer structures and uniform imaging quality. When the noise level increases to SNR = 10 dB, LMMA exhibits a more effective suppression of speckle noise in the image compared to SSB, as observed in Figure (a2, b2). At a further reduced SNR of 7 dB, systematic errors begin to appear in the birefringence estimation by the SSB method, manifested as an overall overestimation in Figure (a3, b3). Specifically, in the region with a true birefringence of Δn = 4.0 × 10^–4, SSB yields an estimated value of approximately Δn = 6.2 × 10^–4, as illustrated in Figure (a3). In addition, spatial difference is observed at the image boundary, located at a depth of around 0.4 mm. The high sensitivity of SSB to noise leads to difficulty in resolving two adjacent layers with similar birefringence under high noise conditions, as seen in Figure (a4). In contrast, Figure (b3) shows that the LMMA method effectively suppresses computational errors under the same noise conditions. Moreover, the geometric distortion in the LMMA result is less pronounced than that in the SSB, with the boundary appearing at approximately 0.65 mm depth. As shown in Figure (b4), LMMA remains capable of resolving materials with closely matching birefringence even under high noise level.

2.

Local birefringence imaging results of double-layer birefringent materials by based on PS-OCT Monte Carlo simulation demodulated by SSB and LMMA methods. Columns (a), (c), and (e) are local birefringence demodulated using SSB method. Columns (b), (d), and (f) are the local birefringence demodulated using LMMA method. The imaging effect of columns (a), (b) under condition of medium depolarization (g = 1), the imaging effect of columns (c), (d) under condition of medium depolarization (g = 0.9), and the imaging effect of column (c), (d) under condition of medium depolarization (g = 0.85). Line (1) is noise free, the SNR of line (2) is set as 10 dB. SNR is set as 7 dB in line (3) and 4 dB in line (4). The birefringence distribution are all set as 4 × 10^–4 on the top layer, 8 × 10^–4 at the bottom layer for the double-layer medium. All the simulations are set with PMD at τ = 1 × 10^–11 s.

4.

Relative error of local birefringence demodulated by SSB and LMMA among various SNR based on Monte Carlo PS-OCT simulation. 1 mm × 1 mm × 1 mm cubic samples have different birefringence (Δn = 4 × 10^–4, 5 × 10^–4, 6 × 10^–4, 7 × 10^–4, 8 × 10^–4). Depolarization are fixed g = 0.95. Noise conditions are set as (a) SNR = 10 dB, (b) SNR = 7 dB, and (c) SNR = 4 dB. All the simulations are set with PMD at τ = 1 × 10^–11 s.

Since the SSB method is based on the Stokes vector space, it operates within a homogeneous computational framework and lacks the capability to systematically decouple depolarization and birefringence. As a result, when the medium exhibits depolarizing properties, the local birefringence images demodulated by SSB are adversely affected. As shown in Figure (c1) and (e1), with increasing g, the image becomes progressively distorted. In contrast, the LMMA method is built upon the Mueller matrix computational framework, which enables effective decoupling of depolarization and birefringence by matrix decomposition. As demonstrated in Figure (d1) and (f1), LMMA accurately computes local birefringence, even in the presence and amplification of depolarization. Comparing to Figure (b1), the image remains nearly unchanged, indicating that LMMA maintains imaging stability when depolarization exists or increases.

In practical experimental conditions, noise and depolarization typically both existing. Without effective denoising and decoupling strategies, these two factors jointly degrade the accuracy of local birefringence measurements. As shown in Figure (c2–c4) and 2­(e2–e4), the error of the SSB method increases, with speckle artifacts emerging in the images. Particularly under conditions of low SNR and high depolarization, the double-layer structure becomes obscured, as shown in Figure (e3). In contrast, Figure (d2–d4) and 2­(f2–f4) demonstrate that the LMMA method effectively decouples depolarization and eliminates the influence of low SNR. The image uniformity and boundary clarity remain largely unaffected by increasing depolarization or decreasing SNR, and geometric distortion is also maintained at a minimal level.

In the following simulations, we aim to focus on comparing several methods in terms of their accuracy and stability for local birefringence estimation. To enhance the statistical significance of the simulations, we employ the Monte Carlo method to compute the local birefringence at the central point on a 0.5 mm deep plane within a 1 × 1 × 1 mm cubic sample by SSB and LMMA method for comparing. The birefringence index of the cubic sample was set as Δn = 4 × 10^–4, 5 × 10^–4, 6 × 10^–4, 7 × 10^–4, 8 × 10^–4, 9 × 10^–4, 1 × 10^–3. All the simulations are set with PMD at τ = 1 × 10^–11 s, a maximum rational value for typical fiber-based PS-OCT system with circulators. Under different conditions of SNR, and g, the local birefringence is calculated using the LMMA and SSB methods. For each configuration with a certain SNR and g set, 50 independent simulations are performed, and the relative errors of mean values are plotted and relative standard deviation is extracted as an error band, as shown in Figures and . According to the simulation result, the variations are not significant. We set the confidence interval to 95% to generate error bars.

3.

Relative error of local birefringence demodulated by SSB and LMMA among various depolarization level based on Monte Carlo PS-OCT simulation. 1 mm × 1 mm × 1 mm cubic samples have different birefringence (Δn = 4 × 10^–4, 5 × 10^–4, 6 × 10^–4, 7 × 10^–4, 8 × 10^–4) among various depolarization level. SNRs are fixed at 10 dB. Depolarizations are set as (a) g = 0.95, (b) g = 0.9, and (c) g = 0.85.

As illustrated in Figure , we maintain 10 dB SNR to test SSB and LMMA among different depolarization levels as g = 0.95, g = 0.90, and g = 0.85. Among the giving depolarization set, SSB counts average relative errors 7.7%, 14.5%, and 19.8% and average standard deviation 10.9%, 16.0%, and 26.6%, when g = 0.95, g = 0.90, and g = 0.85, respectively. LMMA keeps low relative error and narrows the standard deviation; average relative errors are 4.1%, 4.5%, and 4.4%, and standard deviations are 5.0%, 5.1%, and 5.1%, when g = 0.95, g = 0.90, g = 0.85, respectively. LMMA reduces the average relative errors 47%, 69%, and 84% more than SSB as g decreases from 0.95 to 0.85, and the error level does not vary visibly as g decreases. LMMA gains stability from decoupling depolarization by Mueller matrix decomposition. While SSB has obvious errors on mean value and significant standard deviations, even varying significantly with Δn changing shown in Figure (c).

We fixed g = 0.95 to observe the comparison between SSB and LMMA among different SNR levels at 10, 7 and 4 dB in Figure . SSB shows obvious discrepancy with the true local birefringence, especially under SNR ≤ 7 dB condition, as shown in Figure (b),(c). Among the giving birefringence set, SSB counts average relative errors 7.7%, 13.9%, and 18.7% and average standard deviation 10.9%, 18.2%, and 23.9%, when SNR = 10, 7, and 4 dB, respectively. LMMA keeps low relative error and narrows the standard deviation; average relative errors are 4.1%, 5.0%, and 4.8%, and standard deviations are 5.0%, 5.4%, and 5.3%, when SNR = 10, 7, and 4 dB, respectively. LMMA reduces the average relative errors 47%, 64%, and 74% more than SSB as SNR decreases from 10 to 4 dB, and the error level does not vary visibly as SNR decreases. For above in Figures and , compared to SSB, the maximum improvement of relative error reduction of local birefringence demodulated by LMMA is up to 84%. LMMA maintains high precision and stability during repetitive simulation under high noise conditions.

4. Experimental Results

4.1. Polycarbonate Birefringence Imaging Validity Experiment

This experimental section is designed to quantitatively verify the accuracy of LMMA’s local birefringence imaging. Villiger’s team used tissue-like polycarbonate polymer films for generating local birefringence based on the photoelastic effect, providing a more effective means for local birefringence measurement validation. Our experimental setup utilizes the highly multiplexed dual-state-of-polarization, dual-channel scheme based on polarization maintaining fiber (PMF). The light source employed is a swept laser (HSL-20-100-M, Santec, Inc.) with a sweep rate of 100 kHz, a sweep range of 80 nm, and a starting wavelength of 1270 nm. In the PS-OCT system, the axial resolution, also known as the spatial resolution of an A-scan, is approximately 10 μm. The lateral resolution is 20 μm. The rotational speed of the catheter is around 2000 rotations per minute. Given the sweep rate of the swept source at 100 kHz, the system is capable of completing 100,000 A-scans per second. We rely on a strategy of highly multiplexed dual-state-of-polarization, dual-channel PS-OCT hardware basics. In our validation experiments, we also selected polycarbonate films as the imaging sample material. We prepared 11 samples of CT301326 polycarbonate (Goodfellow Inc.), each measuring 2.0 cm in length, 4 mm in width, and 0.25 mm in thickness. These samples are stretched in length-wise direction at 160 °C by 30%, 40%, 50%, 60%, 70%, 80%, 90%, 100%, 110%, and 120%, respectively, and imaged by LMMA and SSB as shown in Table. . As the stretching ratio increases, the local birefringence of the polycarbonate films increases significantly, indicating that stress-induced birefringence is activated during the stretching process. Visual inspection of the images reveals that LMMA produces images with lower speckle and higher uniformity compared to SSB, particularly at stretch ratios of 30%, 60%, 100%, and 120%. We compute the average local birefringence within the central 100 × 100 pixels of each image, with the results presented in the two rightmost columns. To determine the accuracy, we measure birefringence results of polycarbonate polymer films using an established techniqueMueller matrix polarimetry (MMP) as true values. We compare the average and standard deviation of local birefringence within the central 100 × 100 pixels from the LMMA and SSB images across the 11 samples. LMMA has an average relative error at 1.5%, while SSB is 11.1%. For the above, average relative error local birefringence measured by LMMA decreases 86% compared to results by SSB.

1. Quantitative Validation of Local Birefringence Imaging by Polycarbonate Polymer Films.

4.2. Plaque Phantom in Ex-Vivo Porcine Coronary Artery

Two ex-vivo porcine coronary arteries are selected to be injected by collagen and cholesterol, which are prepared as fibrous atherosclerosis and lipid atherosclerosis phantoms, respectively. The cholesterol is prepared by the purified mayonnaise (26% cholesterol concentration mayonnaise, Hellmann’s), while we use bone collagen gel to prepare collagen plaque (C9879 Bovine Collagen Type I-sigma Aldrich). , We operate the catheter-based PS-OCT on both of the coronary arteries, as shown in the experiment diagram on the left part of Figure . Structural OCT images are shown in the Figure (a) column, which cannot delineate locations of plaque phantom. Local birefringence images are processed by SSB and LMMA, respectively, as shown in Figure (b),(c) columns. The images of coronary artery with collagen plaque phantoms are shown in Figure (a1-a4),(b1-b4),(c1-c4), and coronary artery with cholesterol phantoms are shown in Figure (a5),(a6),(b5),(b6),(c5),(c6).

5.

Comparison of local birefringence imaging by SSB and LMMA of plaque phantom in ex-vivo porcine coronary artery in the catheter-based PS-OCT. Columns 1–4 are coronary artery with collagen plaque phantoms; columns 5 and 6 are coronary artery with cholesterol plaque phantoms. Columns a, b, c are structural images and local birefringence images by SSB and by LMMA, respectively.

The birefringence effect of collagen is relatively strong, resulting in a high local birefringence. As shown in Figure (b1),(b4), although images processed by SSB successfully identifies the presence of collagen plaque phantom, the identified region appears overly widespread and speckle-like rather than a coherent structural feature. In contrast, images processed by LMMA provide a precise delineation of the plaque phantom’s location and boundary, as seen in Figure (c1),(c4). In cases as those illustrated in Figure (b1),(b3), the injected plaque phantom has absorbed moisture over time, leading to a reduction in collagen concentration. As a result, the birefringence contrast between the plaque phantom and the surrounding vessel wall tissue shrinks. Images processed by SSB are difficult to distinguish the plaque phantom from the healthy vessel wall. Nonetheless, images processed by the LMMA method remains capable of accurately identifying the plaque region, as shown in Figure (c1),(c3). It is worth noting that early stage atherosclerotic plaques often feature a low collagen concentration, making them difficult to detect. These results highlight the potential of LMMA in identifying early stage plaques owing to its ability to resolve subtle birefringence differences.

As a contrast, the birefringence effect of cholesterol is relatively weak, and the depolarization is high, resulting in low local birefringence. Generally, depolarization PS-OCT images are used to evaluate the cholesterol plaques by certain methods like EMDI. Since the regions exhibiting strong depolarization often lead to their misidentification as irregular speckle-like structures in local birefringence maps, local birefringence images have the potential to recognize the cholesterol plaques. As the red arrows indicate in Figure (b5),(b6), these locations correspond to cholesterol plaque phantoms, which are expected to form a contiguous region of pixels with low local birefringence. Images processed by LMMA clearly and accurately delineate these low-birefringence regions, producing clear contours and plaques with uniform intensity.

We also apply the spatial response of Laplacian operator (SRLO) to evaluate the ability of plaque phantom recognition. , The higher the SRLO is, the more possible a plaque can be recognized in the image. The lower the SRLO is, the higher the uniformity of the image is. Hence we expect high SRLO for the images with plaque and as low SRLO as possible for the images with uniform tissue such as healthy artery. We calculate average SRLO for 31 groups of cholesterol phantom images, 45 groups of collagen phantom images and 70 groups of healthy artery images of our experiments to compare LMMA and SSB methods as shown in Table . For cholesterol phantom imaging evaluated by SRLO, LMMA is 1.70 times higher than SSB, while, for collagen phantom imaging, LMMA is 2.62 times higher than SSB. LMMA differentiates the plaque and the healthy tissue more obviously than the SSB method. Higher SRLO provides a higher probability to recognize the plaque than SSB based on the medical birefringence images processed by LMMA. Self-adaption characteristic recognition and Artificial Intelligence (AI) are much easier to “catch” the plaque from LMMA, in terms of machine principle. For a healthy artery, LMMA has 31% lower SRLO than SSB, suppressing the unexpected speckles caused by noise. LMMA would reduce the misrecognition based on machine principle. For the small-size phantom with a diameter at 100 μm, the SRLO of LMMA is 1.7–8 times higher than that of SSB.

2. SRLO Evaluation for Plaque Phantom Recognition by LMMA and SSB.

Method	Cholesterol phantom	Collagen phantom	Healthy artery
LMMA	1012.02	1889.62	12.89
SSB	596.70	722.37	18.55

5. Discussion

Although phantom experiments can simulate vascular imaging of various types of coronary atherosclerotic plaques, there are certain physicochemical differences between phantoms and actual plaques. For example, the arrangement of protein molecules in fibrous plaques within blood vessels may differ somewhat from that of collagen proteins in phantoms. In the future, we plan to obtain approval for human experiments to conduct extensive imaging studies on real cases of coronary atherosclerotic plaques. This will allow for a more systematic comparison of methods such as SSB, and based on LMMA, more imaging features of pathological plaques such as plaque type, developmental stage, and depth location can be obtained and fed back to clinical applications. By integrating clinical data, we aim to optimize the demodulation details of LMMA, including windowing methods, parameter tuning, and the involvement of PMD compensation, thereby advancing LMMA to genuinely assist in clinical diagnosis.

6. Conclusion

We propose a novel local birefringence PS-OCT imaging method, LMMA, which is based on differential similar Mueller matrix analysis with matrix decomposition and the Mueller matrix-based noise compensation technique. LMMA enables high-precision local birefringence imaging on a dual-polarization catheter-based PS-OCT system, with compensation for both system factors (e. g., PMD and noise), while also suppressing depolarization interference. We systematically evaluate the LMMA method under PMD, SNR, and depolarization conditions through Monte Carlo simulations and evaluate its performance against the currently proposed technique SSB. The simulation imaging results show a significant improving performance by LMMA under high depolarization and low SNR. The repetitive simulation shows LMMA has relative error at 4.8% under high noise condition and 4.4% under high depolarization condition. The maximum improvement of relative error reduction by LMMA is up to 84% compared with results by SSB. We then conduct experimental validation using PS-OCT imaging of stretching polycarbonate samples to quantitatively verify the accuracy of LMMA’s local birefringence imaging. On average 1.5% relative error counts among images of the sample with different birefringence rate in the polycarbonate validity experiments, 86% lower than that of SSB. Finally, we apply LMMA in PS-OCT imaging of collagen and cholesterol plaques phantom prepared in ex-vivo porcine coronary artery. The recognition possibility of plaque by LMMA is up to 2.62 times higher than those by the proposed SSB method evaluated by SRLO. LMMA provides clearer outlines and precise position of the plaque phantoms with less speckles; also, the misidentification is less than that by SSB.

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Ethical approval This paper does not contain animal and human studies.

The authors declare no competing financial interest.