Comparative study of OCTA algorithms with a high-sensitivity multi-contrast Jones matrix OCT system for human skin imaging

Guoqiang Chen; Wen’ai Wang; Wen’ai Wang; Yanqiu Li; Yanqiu Li

doi:10.1364/BOE.462941

1. Introduction

Optical coherence tomography (OCT) [1], working on the principle of low coherence interferometry, is a non-invasive, label-free, and depth-resolved imaging technique. Over the past 30 years, OCT has been widely used in a range of medical fields with significant commercial success in ophthalmology [2] and cardiology [3]. Exploring the visualization for fine structures at micron imaging resolution, OCT is also gaining popularity in other areas, such as oncology [4], and dermatology [5] among others. Besides the standard OCT providing only sample morphology information, various functional extensions of OCT are being developed, including OCT angiography (OCTA) [6], polarization-sensitive OCT (PS-OCT) [7], optical coherence elastography [8], and spectroscopic OCT [9], boosting the biomedical applications of OCT.

Unlike mainstream vascular imaging techniques (e.g., indocyanine green [10]), OCTA enables volumetric visualization for microvascular networks without exogenous contrast agents. It’s possible to retrieve microvascular networks through the extraction of signal fluctuation caused by the moving particles (mostly red blood cells) among the repetitively acquired OCT signals. Based on the different constituents explored, OCTA-based blood vessel visualization methods can be broadly classified into three different categories, including (1) phase-, (2) intensity-, and (3) complex-signal-based OCTA techniques. Recently, the performance of different OCTA techniques has been evaluated for ocular vascular mapping [11–15] or neuroimaging [16]. It was found that the performance of the phase-signal-based OCTA methods in visualizing the small blood vessels and capillaries is suboptimal [15]. Therefore, the amplitude- and complex-signal-based OCTA algorithms have been the most widely used. Compared to complex OCTA algorithms, amplitude-based OCTA methods have been shown to be less susceptible to bulk tissue motion and system instability [17,18]. Hence, extensive attention has been paid to the amplitude-based OCTA methods. Among them, speckle decorrelation (SD) has been applied to various human tissues due to its easy implementation and excellent vessel contrast [6,19]. In theory, more and better microvascular information can be recovered using the complex signal OCTA algorithm [13]. Unfortunately, the complex OCTA algorithms require the removal or correction of motion artifacts [17]. Especially in systems based on swept source, additional phase instability is induced by severe laser trigger jitter during cycle-to-cycle sweeping, making it challenging to implement the phase-sensitive OCTA method. Accordingly, several both software-based [20–22] and hardware-based [23–26] approaches have been proposed, resulting in removing or correcting phase artifacts but increased system costs, complexity, and computation resources. More recently, two complex-signal-based OCTA algorithms that inherently provide strong suppression of artifactual signals from bulk tissue motion or instrument instability are explored, including the split-spectrum amplitude and phase-gradient angiography (SSAPGA) algorithm [27] and complex differential variance (CDV) algorithm [26,28]. Notwithstanding, the performance for the mentioned two phase-instability-insensitive methods has not been compared in vascular imaging to guide the selection of an appropriate angiography algorithm.

Whilst it’s physiologically important to investigate tissue microvascular patterns, the evaluation of tissue birefringence primarily caused by connective tissue is generally of equal importance for biomedical applications. PS-OCT, another functional extension of OCT, allows analysis of the tissue birefringence and fiber orientation for biological tissues. On the one hand, it enables lable-free physiological process monitoring and pathological diagnosis, which has been proved essential in ophthalmology [29], cardiology [30], oncology [31], dermatology [32–34], etc. More critically, a combination of PS-OCT with OCTA has been demonstrated to improve vascular connectivity and reveal several additional vessels through the reduction of polarization fading [35,36]. Recently, synergizing the clinical benefits of both PS-OCT and OCTA, an advanced multi-contrast Jones-matrix OCT (JMT) imaging system has been first developed by the Yasuno group [37], followed by wide biomedical applications. For instance, it has been applied in ophthalmology to provide robust methods for delineation [38–40] and segmentation [41,42], and to measure the polarization properties of vessel walls [43]. Additionally, the valuable characterizations of the healthy and diseased skin [33,34,44] were also demonstrated by using the JMT system. While the comparative studies of different OCTA algorithms have been conducted for standard OCT systems, we find systematic angiographic algorithms comparison for the widely used JMT system is lacking.

In this paper, we have developed a high-sensitivity multi-contrast JMT system capable of simultaneously visualizing depth-resolved structural, birefringent, degree of polarization uniformity (DOPU), and vascular maps. The system is driven by a 200 kHz swept source with a center wavelength of 1310 nm. Using the developed system, we qualitatively and quantitatively compared the performance of the SD, SSAPGA, and CDV algorithms for human skin microvascular imaging. Particularly, no phase correction method was employed for vascular imaging. Six metrics (i.e., vascular connectivity, image contrast-to-noise ratio (CNR), image signal-to-noise ratio (SNR), vessel diameter index (VDI), blood vessel density (BVD), and processing time) are adopted for quantitative assessment. We take human skin as the sample for comparative study, not only because the skin is easily accessible, but also because angiography and polarization imaging has shown great promise to diagnose skin diseases such as scars [45], port-wine stain [46], basal cell carcinoma [47], and cutaneous wound healing [48].

2. Materials and methods

2.1 High-sensitivity multi-contrast JMT system

The schematic diagram of the high-sensitivity multi-contrast JMT is shown in Fig. 1. A MEMS-based swept-source (AXP50125-6, AXSUN Technologies) is employed as the light source with a center wavelength of 1310 nm, a sweeping range of 100 nm, and a scanning rate of 200 kHz. The light is first split by a 90/10 broadband coupler (TW1300R2A1, Thorlabs), with 90% directed to the sample arm, while 10% is directed to the reference arm.

Fig. 1. Configuration of the JMT system. C1-C4: connectors; PC1-PC4: polarization controllers; FC1-FC10: fiber collimators; PBS1-PBS4: polarizing beam splitters; BPD: balanced photodetector; M1-M3: mirrors; LP: linear polarizer; QWP1-QWP3: quarter-wave plates; PD: pupil diaphragm.

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In the sample arm, an in-house developed passive polarization delay unit (PDU) [49,50] is constructed. It enables two orthogonal polarization states to illuminate the sample simultaneously. In the PDU, the light is collimated and split into two orthogonal independent polarization states with a broadband polarization beam splitter (PBS2, CCM1-PBS254/M, Thorlabs). In either arm of the PDU, the polarization planes are rotated by 90° using the achromatic zero-order quarter-wave plated (QWP2 and QWP3, AQWP05M-1600, Thorlabs) oriented at 45°, reflected by a mirror and reverse again passed the QWP. The two orthogonal echoes are recombined at PBS2 and sent to the fiber output of the PDU. Before recombination, different delays are applied to the two polarizations. This can achieve depth-multiplexing of the two incident polarizations in the resulting OCT images. By adjusting the polarization controller (PC2, FPC020, Thorlabs) and linear polarizer (LP, LPNIR100-MP2, Thorlabs), the powers of the two output polarization states from the PDU are maximized and equal (∼ 5.4 mW). A broadband fiber circulator (circulator2, CIR-1310-50-APC, Thorlabs) is used to direct the output to the bulk probe unit and send the scattered light from the sample to the in-house developed polarization sensitive detection unit (PSDU).

In the probe unit, the beam is first collimated by a fiber-tip collimator (FC8, F280APC-C, Thorlabs, beam diameter = 3.4 mm) and focused on the sample by an objective lens (AC254-060-C-ML, Thorlabs, the effective focal length = 60 mm, working distance = 46 mm). To translate the imaging location, a two-axis galvanometer mirror scanner (GVSM002-EC/M, Thorlabs) is used. The incident power to the sample is around 10.8 mW.

In the reference arm, a broadband polarization beam splitter (PBS1, PBS254/M, Thorlabs) and an achromatic zero-order quarter-wave plate (QWP1, AQWP05M-1600, Thorlabs) are applied to compensate for the dispersion mismatch in the OCT interferometer. Any remaining dispersion mismatch is corrected numerically in post-processing. The broadband fiber circulator (circulator1, CIR-1310-50-APC, Thorlabs) is employed to direct reference light to the PSDU. The fast axis orientation of the QWP1 is set to 0° to reduce unnecessary power loss. As a result, the output of the reference arm is horizontally polarized light. However, the polarization state of the reference light arriving at the PSDU is unknown due to the birefringence effect of the single-mode fiber and the circulator. To achieve balanced detection and obtain a correct phase retardation measurement, two additional polarization controllers (PC3 and PC4, FPC020, Thorlabs) are used in the PSDU to adjust the polarization states of the reference light. First, the sample arm is blocked. Then, the powers of the two orthogonal polarization states split from PBS3 or PBS4 are measured respectively. Finally, we carefully adjust PC3 or PC4 until the powers of the two orthogonal polarization states from the identical channel are equal. In this way, the polarization state of the reference beam is modulated into 45° linearly polarized light.

In the PSDU, the scattered light from a sample interferes with the reference beam at the 50/50 broadband fiber coupler (TW1300R5A2, Thorlabs). The spectral interference signal is then split into orthogonal polarization components using two polarizing beam splitters (PBS3 and PBS4, CCM1-PBS254/M, Thorlabs). The signals with identical polarization are detected by the same balanced detector (PDB480C-AC, Thorlabs) and digitized by a dual-channel digitizer (ATS9371, AlazarTech) with 12-bit resolution and 1.0 GHz bandwidth. However, due to the imperfection of the 50/50 fiber coupler, the measured splitting ratio of the 50/50 broadband coupler is 47.5/52.5 actually, resulting in unequal power into the two ports of the balanced detector. The optimal signal sensitivity can be obtained when the system is operated under shot-noise-limited detection conditions. Particularly, the noise is mainly determined by the average optical power of the reference beam. However, to operate under shot-noise-limited detection conditions, the RF output voltage of the detector would inevitably exceed the detection limit of the digitizer (±400 mV fixed input range) due to the imperfect of the fiber coupler. What’s more, signal sensitivity is a crucial factor to consider when visualizing high-quality images [37]. To address this issue, a pupil diaphragm (SM1D12C, Thorlabs) is inserted before the PBS located at the high splitting-ratio output of the coupler. Hence, we can gradually increase the power of the reference light by adjusting PC1 on the one hand and avoid oversaturation by adjusting the aperture on the other hand. As a result, optimal sensitivity can be achieved without exceeding the digitizer threshold.

The sensitivities of the four polarization channels are measured to be 116, 108, 114, and 103 dB at close to the zero-delay location, respectively. A further increase is improved to 117 dB by coherently combining Jones matrix elements into a single OCT signal. The imaging depth range is around 2.5 mm in air, which corresponds to 1.8 mm in skin tissue assuming a refractive index of 1.38. The axial resolution and the transverse resolution are measured to be around 10 µm and 19.4 µm in air, respectively.

2.2 Measurement protocol

The homemade high-sensitivity multi-contrast JMT system is applied in the contact mode by using the optical window attached in front of the probe unit to flatten the skin surface and reduce motion artifacts. In addition, the ultrasound gel is added between the window and the skin for refractive index matching [51]. A raster scan was conducted to obtain the 3D PS-OCT angiography (PS-OCTA) dataset. The imaging range is 3.0 mm ${\times}$ 3.0 mm in lateral and 1.8 mm in depth with 512 A-lines ${\times}$ 400 B-scans ${\times}$ 4 repeats of the B-scan in 5.12 seconds.

For quantitative evaluation, 15 volunteers with informed content were recruited. The palm skin at the same position was measured once for each subject. Therefore, a total of 15 measurements were obtained. Before imaging, subjects were asked to sit in an upright position and acclimatize in the laboratory for 10 minutes. After acclimatization, the palm was first placed on a soft cushion on the table under a spacer, followed by an adjustment of the OCT probe and spacer. The adjustment set the focus to approximately just below the epidermis. This arrangement guaranteed a very similar and slight pressure was applied to the skin, even though the actual pressure was not measured.

2.3 Data process

2.3.1 Polarization imaging

For each detection channel, the collected spectral interference signals are processed using standard Fourier domain OCT routines including background subtraction, numerical dispersion compensation, zero padding, spectral shaping, and Fourier transforming to compute the complex-valued OCT signals [52]. Because two incident polarizations are multiplexed by the PDU and two detection polarization are independently detected by the PSDU, this process can provide a set of four complex OCT images. This set of OCT images forms the Jones matrix tomography, which describes the mixed effect of the polarization properties of the instrument and the tissue. A cross-correlation-based subpixel depth shift correction algorithm is employed to accurately register the elements of the Jones matrix and correct the trigger jitter for polarization imaging [44]. Since the Jones matrix at each pixel within the axial resolution has a different and unpredictable phase offset, named global phase, it deteriorates the output of birefringence measurement. Therefore, the adaptive Jones matrix averaging method is necessarily employed to improve the signal-to-noise ratio and cancel the global phase before calculating the phase retardation [37]. In the adaptive Jones matrix averaging method, the global phase between two Jones matrices is estimated as

(1)$$\Delta {\varphi ^{({0,j} )}} \equiv \textrm{Arg}\left[ {\sum\limits_{k = 1}^4 {\frac{{\exp i\left({\textrm{Arg}[{S_k^{(j )}} ]/S_k^{(0 )}} \right)}}{{{{\left|{S_k^{(0 )}} \right|}^{ - 1}} + {{\left|{S_k^{(j )}} \right|}^{ - 1}}}}} } \right], $$

where $S_k^j$ is the $k$-th entry of the $j$-th matrix under averaging.

After determining the global phase, the averaged matrix is defined as

(2)$$\overline {\mathbf S} \equiv \sum\limits_j {\exp ({ - i\Delta {\varphi^{({0,j} )}}} )} {{\mathbf S}^{(j)}}. $$

Note that ${{\mathbf S}^{(0 )}}$ is a reference matrix for the determination of the global phase. In this study, the size of the averaging window is set to $4 \times 6$ pixels.

Then, the algorithm of the Jones matrix diagonalization method is employed to calculate the local phase retardation (LPR) [53]. We assume that ${{\mathbf J}_{S,T}}({{z_i}} )$ is the round-trip Jones matrix of the sample at the depth ${z_i}$. ${{\mathbf J}_{in}}$ and ${{\mathbf J}_{out}}$ represent the Jones matrix of input and output paths in the PS-OCT system, respectively. Accordingly, the measured Jones matrix ${\mathbf S}({{z_i}} )$ at the sample depth ${z_i}$ can be written as:

(3)$${\mathbf S}({{z_i}} )= {E_{ref}}{{\mathbf J}_{out}}{{\mathbf J}_{S,T}}({{z_i}} ){{\mathbf J}_{in}}{E_{in}}, $$

where the ${E_{ref}}$ and ${E_{in}}$ are the electric fields of reference and incident light. To acquire the Jones matrix of the local tissue, the signals from the point adjacent to the depth of interest is used as the reference. We assume that ${{\mathbf J}_{S,T}}({{z_{i - n}}} )$ is the round-trip Jones matrix of the sample at the reference point ${z_{i - n}}$, where n is the local distance of index (in this study, $n = 4$ pixels). The corresponding measured Jones matrix can be expressed as:

(4)$${\mathbf S}({{z_{i - n}}} )= {E_{ref}}{{\mathbf J}_{out}}{{\mathbf J}_{S,T}}({{z_{i - n}}} ){{\mathbf J}_{in}}{E_{in}}. $$

The reference measured matrix is used to eliminate the effects of tissue above the point of interest and fiber components in the PS-OCT system on the birefringence measurement. It can be achieved by multiplying the inverse matrix of the reference matrix ${\mathbf S}{({{z_{i - n}}} )^{ - 1}}$ with all other Jones matrices ${\mathbf S}({{z_i}} )$ and we obtain the matrices ${\mathbf M}({{z_{i - n}},{z_i}} )$ as:

(5)$$\begin{aligned} {\mathbf M}({{z_{i - n}},{z_i}} )&= {\mathbf S}({{z_i}} ){\mathbf S}{({{z_{i - n}}} )^{ - 1}}\\ &= {{\mathbf J}_{out}}\left( {\prod\limits_{k = 1}^{i - n - 2} {{\mathbf J}_S^T({{z_k},{z_{k + 1}}} )} } \right){{\mathbf J}_{S,T}}({{z_{i - n}},{z_i}} ){\left( {\prod\limits_{k = 1}^{i - n - 2} {{\mathbf J}_S^T({{z_k},{z_{k + 1}}} )} } \right)^{ - 1}}{\mathbf J}_{out}^{ - 1} \end{aligned}, $$

where ${\mathbf J}_S^T$ is the transpose of the single-trip Jones matrix of the local tissue and ${{\mathbf J}_{S,T}}({{z_{i - n}},{z_i}} )$ is the round-trip local polarization properties of the tissue located at the depth from ${z_{i - n}}$ to ${z_i}$. Since Eq. (5) is a similar matrix of ${{\mathbf J}_{S,T}}({{z_{i - n}},{z_i}} )$, the eigenvalues of both matrices are identical. The eigenvalues of the Jones matrix ${{\mathbf J}_{S,T}}({{z_{i - n}},{z_i}} )$ of the local tissue can be obtained by the matrix diagonalization of ${\mathbf M}({{z_{i - n}},{z_i}} )$. Equation (5) can be rewritten in a similarity transformation with the eigenvalues, ${\lambda _{1,2}}$, as

(6)$$M({{z_{i - n - 1}},{z_i}} )= {\mathbf A}\left[ \begin{array}{l} {\lambda_1}\;\;\;0\\ \;0\;\;\;{\lambda_2} \end{array} \right]{{\mathbf A}^{ - 1}}. $$

Here, ${\lambda _{1,2}}$ and ${\mathbf A}$ are the eigenvalues and eigenvector matrix of ${\mathbf M}({{z_{i - n}},{z_i}} )$. As a result, the LPR can be derived from the eigenvalues by

(7)$$r({{z_{i - n}},{z_i}} )= \left|{{{\tan }^{ - 1}}\frac{{{\mathop{\textrm {Im}}\nolimits} [{{\lambda_1}/{\lambda_2}} ]}}{{\textrm{Re} [{{\lambda_1}/{\lambda_2}} ]}}} \right|. $$

The LPR is a functional parameter characterizing the birefringence property of samples. Additionally, DOPU is another quantity that can represent the randomness of the polarization states within a local region in an OCT tomogram [54]. Mathematically, it is derived by local averaging of the corresponding normalized Stokes vector elements within a kernel. The Stokes parameters can be obtained by

(8)$$\left[ \begin{array}{l} I\\ Q\\ U\\ V \end{array} \right] = \left[ \begin{array}{l} \;\;\;\;\;\;\;\;\;\;\;{\left|{{E_H}(x,z)} \right|^2} + {\left|{{E_V}(x,z)} \right|^2}\\ \;\;\;\;\;\;\;\;\;\;\;{\left|{{E_H}(x,z)} \right|^2} - {\left|{{E_V}(x,z)} \right|^2}\\ {E_H}({x,z} )E_V^\ast ({x,z} )+ E_H^\ast ({x,z} ){E_V}({x,z} )\\ i({{E_H}({x,z} )E_V^\ast ({x,z} )- E_H^\ast ({x,z} ){E_V}({x,z} )} )\end{array} \right], $$

where ${E_H}({x,z} )$ and ${E_V}(x,z)$ indicates the processed horizontal and vertical output data respectively. $E_{_H}^\ast ({x,z} )$ and $E_{_V}^\ast (x,z)$ are the complex conjugate data of ${E_H}({x,z} )$ and ${E_V}(x,z)$. Then the DOPU value can be calculated as

(9)$$DOPU = \sqrt {{{\left( {\sum\limits_i {\frac{{{Q_i}}}{{{I_i}}}} } \right)}^2} + {{\left( {\sum\limits_i {\frac{{{U_i}}}{{{I_i}}}} } \right)}^2} + {{\left( {\sum\limits_i {\frac{{{V_i}}}{{{I_i}}}} } \right)}^2}}, $$

where ${Q_i}$, ${U_i}$, ${V_i}$ and ${I_i}$ denote the respective normalized Stokes vector elements for the $i$-th pixel within the spatial kernel. In this study, the averaging window with $5 \times 5$ pixels is applied. DOPU values range from 0 (completely depolarized) to 1 (completely polarized).

For structural imaging, the four entries of the Jones matrix are summed coherently [37] to composite a sensitivity-enhanced scattering signal. In the coherent composition method, the depth-independent relative phase offsets (${\theta _{1,2,3}}$) relative to the first entry can be estimated as

(10)$${\mathrm{\theta }_1} \equiv Arg\left[ {\sum\limits_z {{S_2}(z ){S_1}{{(z )}^\ast }} } \right], $$

(11)$${\mathrm{\theta }_2} \equiv Arg\left[ {\sum\limits_z {{S_3}(z ){S_1}{{(z )}^\ast }} } \right], $$

(12)$${\mathrm{\theta }_3} \equiv Arg\left[ {\sum\limits_z {{S_4}(z ){S_1}{{(z )}^\ast }} } \right], $$

where ${S_k}$ was the $k$-th ($k = 1,2,3,4$) entry of the measured Jones matrix. Using ${\theta _{1,2,3}}$, the coherent composition is defined as

(13)$$C(z )= \frac{1}{4}[{{S_1}(z )+ {e^{ - i{\theta_1}}}{S_2}(z )+ {e^{ - i{\theta_2}}}{S_3}(z )+ {e^{ - i{\theta_3}}}{S_4}(z )} ]. $$

Since the composite signal is a coherent summation of four OCT signals, a sensitivity-enhanced scattering signal can be obtained and then used to generate the angiography image as shown in the following section.

2.3.2 System validation

It has been shown that polarization mode dispersion (PMD), i.e. the differential propagation time of orthogonally polarized light, can cause blurring of the OCT structural image and can lead to significant artifacts in phase retardation image [55–58]. In this system, the PMD located within the reference arm does not induce noise because a fixed polarization state of the reference beam for all wavelengths can be defined by the PC3 and PC4 in the PSDU [55]. This can ensure uniform polarization of the reference light at each receiver. Therefore, the PMD of this system is mainly induced by the fiber optical circulator within the sample arm. Moreover, the so-called second-order PMD has wavelength dependence [59]. Hence, to evaluate the PMD in the system, we monitor the evolution of the Stokes vector as a function of wavelength [56] for a sample reflector as shown in Fig. 2. The angle spanned by the trace of the Stokes vector in the Poincare sphere is around 63°. This quantity corresponding to a differential group delay (DGD) is around 0.01 ps (roundtrip), which results in a broadening of the interference peak of 1.5016 µm. This is smaller than the depth resolution of the system. Zhang and Villiger concluded that a PMD smaller than the axial resolution was not a serious issue [56,57]. Therefore, PMD correction [56] or mitigation [58] is not included.

Fig. 2. Stokes vector representation of the evolution of a reflected state from the sample arm as a function of wavelength, rendered through open access MatLab code [60]. Red trace: state1; Manganese purple trace: state2.

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Additionally, we have verified the accuracy of the JMT system by measuring 1310 nm QWP, whose theoretical round-trip phase retardation is 180°. Since its optic axis is uniform along with the depth, the front surface of the quarter-wave plate can be set as the reference point. By varying the axis orientation of QWP, the measured phase retardation can be calculated. The full range of axis orientation is covered by rotating the optic axis of QWP from 0° to 180° with a step of 10°. The comparison of measured and theoretical values of retardation is shown in Fig. 3. As shown in Fig. 3, the measured retardation (green circles) is close to but slightly lower than the theoretical value (red dashed line). The averaged measurements are 176.8° with a standard deviation of 2.1569°, which is comparable to the reported result [61]. The deviation between measured and theoretical values can be contributed by a wide spectrum of the light source, dispersion of QWP, and the incident degree of light on the sample.

Fig. 3. the result of retardation values versus QWP orientation: measured retardation values (green circles); theoretical retardation values (red dashed line).

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2.3.3 Angiographic imaging

To visualize high-quality vascular networks, a sensitivity-enhanced scattering signal which is composited by coherently combining the four entries of the Jones matrix is adopted to generate the angiograms.

In the SD angiography method, the flow signal is acquired by calculating the correlation among the repeated consecutive B-scans with the same size 2-dimensional (2D) window [19], as shown in Eq. (14):

(14)$$\begin{array}{l} {f_{SD}}({x,z} )= \\ \frac{1}{{R - 1}}\sum\limits_{r = 1}^{R - 1} {\sum\limits_{p = 0}^M {\sum\limits_{q = 0}^N {\frac{{\left[{{A_r}({x + p,z + q} )- \overline {{A_r}(x,z)} } \right]\cdot \left[{{A_{r + 1}}({x + p,z + q} )- \overline {{A_{r + 1}}(x,z)} } \right]}}{{\sqrt {{{\left[{{A_r}({x + p,z + q} )- \overline {{A_r}(x,z)} } \right]}^2} + {{\left[{{A_{r + 1}}({x + p,z + q} )- \overline {{A_{r + 1}}(x,z)} } \right]}^2}} }}} } } \end{array}, $$

where M and $N$ indicate the window size, R indicates the repetition number of B-scans at the same location, $\overline A$ is the mean intensity value within the window, and ${A_r}({x,z} )$ indicates the intensity value in $r$-th B-scans at the lateral location x and depth position z. The 2D window is then shifted across the entire B-scan and 2D cross-sectional angiogram is generated, in which the lower correlation represents the flow regions, but the areas of static tissue show the higher correlation. Although larger window size leads to a higher signal-to-noise ratio, it may also result in longer processing time, blurring effects, and loss of smaller vessels. In this study, a moving window with $5 \times 5$ pixels is applied.

The CDV algorithm is a kind of complex-signal-based angiographic technique. The flow signal is calculated by a complex correlation term between two consecutive B-scans with a depth window function [28], as shown in Eq. (15):

(15)$${f_{CDV}}({x,z} )= \sqrt {1 - \frac{{\sum\limits_{r = 1}^{R - 1} {\left|{\sum\limits_{k ={-} L}^L {w(k ){C_r}({z - k,x} )C_{r + 1}^\ast ({z - k,x} )} } \right|} }}{{\sum\limits_{r = 1}^{R - 1} {\sum\limits_{k ={-} L}^L {w(k )\frac{1}{2}\left[{{{\left|{{C_r}({z - k,x} )} \right|}^2} + {{\left|{C_{_{r + 1}}^\ast ({z - k,x} )} \right|}^2}} \right]} } }}}, $$

where $w(k )$ is the depth window function of length $2L + 1$, ${C_r}({x,z} )$ indicates the complex value in $r$-th B-scans at lateral location x and depth position z, and $C_r^\ast $ is the conjugate of ${C_r}$. In the denominator, the arithmetic mean is applied for normalization. Benefitting from the depth window, not only does the magnitude and phase random variation of the flow contribute to the angiographic signal but also the signal fluctuation from the bulk motion and laser trigger jitter has negligible effects. In this study, the size of the depth window is set to 11 pixels.

The SSAPGA, another kind of complex-signal-based angiographic technique without phase artifacts induced by the bulk motion and laser trigger jitter, is a combination of the gradient of the phase difference and split-spectrum amplitude-decorrelation algorithm [27]. In this method, the full spectrum is split firstly into several narrower bands by multiplying with Gaussian windows. After splitting the spectrum, the data in each narrower band are processed separately to generate several flow images for the same B-scan location. Finally, the flow signal is acquired by averaging the narrower-band flow images, as shown in Eq. (16):

(16)$${f_{SSAPGA}} = 1 - \frac{1}{{R - 1}}\frac{1}{M}\left|{\sum\limits_{m = 1}^M {\sum\limits_{r = 1}^{R - 1} {\frac{{2A_{_r}^m({x,z} )\cdot A_{_{r + 1}}^m({x,z} )\cdot \exp ({j \cdot \rho \cdot P{G^m}({x,z} )} )}}{{A_r^m{{({x,z} )}^2} + A_{r + 1}^m{{({x,z} )}^2}}}} } } \right|, $$

where $M$ (in this study, $M = \textrm{9}$) is the number of narrow split spectrum bands, $A_r^m({x,z} )$ indicates the intensity value in $r$-th B-scans of $m$-th split spectrum at the lateral location x and depth position z, $\rho$ is the weight parameter (in this study, $\rho = 2$) and $PG$ is the gradient of the phase difference between the consecutive B-scans.

2.3.4 quantitative metrics

Each acquired PS-OCTA dataset is processed with CDV, SD, and SSAPGA algorithms respectively. The skin images are segmented manually into three layers. For each layer, the PS-OCTA data are projected by using axial summation amplitude projection (SAP). And then the Hessian-based Frangi vesselness filter [62] is applied to reduce noise and enhance the vessels’ signal strength. The quality of the projected angiograms is compared first visually by observing how much detail of the capillary network can be resolved. To evaluate quantitatively the performance, six metrics including vascular connectivity, image CNR, image SNR, VDI, BVD, and processing time are measured. Notably, to approximately generate the true vascular networks, the vascular map indicating “ground truth” is produced by averaging the projections processed by different algorithms with equal weight [63]. In addition, the adaptive thresholding operation is employed to obtain a binary image where white corresponds to vessels, and a skeletonization method is used to preserve its morphology.

The vessel connectivity [11] is defined as the standard deviation of the intensity of the angiogram that is exactly co-registered with the skeleton diagram generated from “ground truth”, as indicated in the following Eq. (17):

(17)$$connectivity = std[{I({x,y} ){\left|_{{S_t}({x,y} )={=} 1}\right.}} ]$$

where $I({x,y} )$ denotes the intensity in the angiogram, and ${S_t}({x,y} )$ denotes the skeleton image from the “ground truth”. The lower the value, the better the mapping performance the algorithm can provide in terms of angiographic connectivity.

The image CNR is defined as the following Eq. (18):

(18)$$CN{R_{image}} = \frac{{\overline {I({x,y} ){|_{{B_t}(x,y) ={=} 1}}} - \overline {I(x,y){|_{{B_t}(x,y) ={=} 0}}} }}{{{\sigma _{I(x,y){|_{{B_t}(x,y) ={=} 0}}}}}}$$

And the image SNR of the angiogram is given in Eq. (19):

(19)$$SN{R_{image}} = \frac{{\overline {I({x,y} ){|_{{B_t}({x,y} )={=} 1}}} }}{{{\sigma _{I({x,y} ){|_{{B_t}(x,y) ={=} 0}}}}}}, $$

where $\overline {I({x,y} ){|_{{B_t}(x,y) ={=} 0}}}$ is the mean intensity of the background area, namely the non-vascular region and $\overline {I({x,y} ){|_{{B_t}({x,y} )={=} 1}}}$ is the mean intensity of the vascular region. ${B_t}({x,y} )= 0$ and ${B_t}({x,y} )= 1$ represent the pixels with values of 0 and 1, respectively, in the binary image from the “ground truth”. The $\sigma$ is the standard deviation of the background signals.

BVD is defined as the ratio of the area occupied by the vasculature to the total area in an angiogram image:

(20)$$BVD = \frac{{Pix{|_{B(x,y) ={=} 1}}}}{{Pix{|_{all}}}}, $$

where $Pix{|_{B({x,y} )= 1}}$ indicates the number of pixels with a value of 1 in the binary image $B({x,y} )$ from each corresponding angiogram and $Pix{|_{all}}$ is the number of all pixels.

VDI is defined as shown in the following formula:

(21)$$VDI = \frac{{Pix{|_{B(x,y) ={=} 1}}}}{{Pix{|_{S(x,y) ={=} 1}}}}, $$

where $Pix{|_{S(x,y) ={=} 1}}$ represents the number of white pixels in the skeletonized map from the respective different angiograms.

3. Result and discussion

3.1 Multi-contrast images

Figure 4 shows the cross-sectional images extracted from volumetric PS-OCT data for a case of human palm skin. Figure 4(a) is the scattering map that can reveal the typical skin-layered structures. For ease of analysis, the position of the basement membrane (BM) is plotted by the red dashed line in Fig. 4(a) and the black solid line in Fig. 4(b) and 4(c). The region between the stratum corneum (as shown in Fig. 4(a)) and the BM is the weakly scattering epidermis while the region below the BM represents the strongly scattering dermis, as demonstrated in Fig. 4(a). Several small hyper-scattering spots (as indicated by the red arrows) appearing on the surface are the cross-sections of ultrasound gel clusters. Additionally, Fig. 4(b) and 4(c) are the DOPU and LPR maps, respectively, which can show the distribution of biological fibrous structures. We found lower DOPU and higher LPR in parts of the epidermis, which is different from the reported results [33]. Theoretically, the epidermis should have high DOPU and low birefringence properties because of its less distributed collagen content. It is suspected the low effective signal-to-noise ratio (ESNR) in the weakly scattering epidermis is responsible for the deviation of the measured values from the true value [44]. It should be noted that regions with minimally low ESNR, such as air and deep tissue regions, have low DOPU [64] and random LPR [44], as shown in Fig. 4(c). In contrast, large amounts of collagen composition are distributed in the strongly scattering dermis [44]. As a result, many of the lower DOPU and higher LPR values appear in the dermis.

Fig. 4. The cross-sectional images of human palm skin. (a) scattering OCT, (b) DOPU, and (c) LPR; Scale bars are 400 µm.

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Figure 5(a) to 5(c), Fig. 5(d) to 5(f), and Fig. 5(g) to 5(i) show the mean projections from the epidermis (0-200 µm), superficial dermis (200-400 µm), and deep dermis (400-800 µm), respectively. Figure 5(a), 5(d), and 5(g) are the mean projections of scattering. Figure 5(b), 5(e), and 5(h) are the mean projections of DOPU. Figure 5(c), 5(f), and 5(i) are the mean projections of LPR. Due to the sweat gland pores and skin furrows, the ultrasound gel could not be applied evenly on the skin surface. This results in stronger scattering at most of the sweat gland pores (as indicated by the red arrows) and furrows (as indicated by the blue arrows), as shown in Fig. 5(a). It is noteworthy that in Fig. 5(a) there are two particular bright bands, indicated by the yellow arrows. They cross the direction of furrows and are induced by unintentional operation. As mentioned above, the weakly scattering epidermis has low ESNR. Hence, the measured DOPU and LPR deviate from the true value, manifesting as low DOPU and high LPR, as shown in Fig. 5(b) and 5(c). However, we find that several areas appear with higher DOPU and lower LPR values pointed by the black arrow in Fig. 5(b) and (c). These locations are found to be identical to those of the ultrasound gel clusters. Especially, the areas corresponding to the positions indicated by the yellow arrows in Fig. 5(a) also appear low LPR and high DOPU, but these regions cross the direction of the furrows. Therefore, it can be demonstrated that the distribution of bands in Figs. 5(b) and 5(c) are induced by noise.

Fig. 5. Mean projections of the human palm skin. Figure 5(a) to 5(c), Fig. 5(d) to 5(f), and Fig. 5(g) to 5(i) are generated from the epidermis (0-200 µm), superficial dermis (200-400 µm), and deep dermis (400-800 µm), respectively. Figure 5(a), 5(d), and 5(g) are scattering OCT. Figure 5(b), 5(e), and 5(h) are DOPU. Figure 5(a), 5(d), and 5(g) are the LPR. All scale bars are 400 µm.

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In the superficial dermis, the specular reflections caused by the ultrasound gel clusters result in reduced scattering intensity at corresponding locations, as pointed by the green arrows in Fig. 5(d). Fortunately, this has less impact on the measurement of the DOPU and LPR. Additionally, we found that lower DOPU and higher LPR values are mainly distributed in bands. This is consistent with the direction of the skin ridge [65]. According to pathological knowledge, there are a large number of fiber bundles at the ridge and these fiber bundles have a stronger characterization of scattering and birefringence [66].

In the deep dermis, the scattering intensity of the region where the ultrasonic gel clusters are located is further weakened, as indicated by the green arrows in Fig. 5(g). Since the scattered signal is weakened and the ESNR is reduced in the deep region, the measured DOPU and LPR are inevitably affected. However, in general, the low DOPU and high phase delay values still show a band distribution. Additionally, there are some vertical stripes in Fig. 5(c), 5(f), and 5(i), which are artifacts from the calculation of phase retardation.

It has been demonstrated that a reliable LPR can only be obtained when the ESNR exceeds 25 dB [67]. Unfortunately, it is not possible in some cases [67]. In the future, another more sophisticated and advanced approach may be adopted, such as the Jones matrix estimation based on the Cloude-Pottier decomposition [68], Mueller analysis [69,70], a specially designed phase-retardation estimation function [71], maximum a posteriori birefringence estimator [67,72], or Mueller matrix spatially averaging method [73]. To obtain the projections, the mean projection is used instead of the maximum projection in this section. If the maximum projection is used, the image would be dominated by a small number of intensely scattered voxels, and information on the beam coupling effect on average tissue reflectance would be obscured. Furthermore, it can be concluded that the structural information can be visualized using the scattering map, whereas polarization imaging can reveal more functional components such as fibers. Hence, the PS-OCT has attractive potential applications, at least in areas of application related to texture analysis. In the future, further studies with higher resolution and a larger field of view should be carried out as the next step to research more information about fiber orientation and distribution. Additionally, there is no doubt that the field of application is expanding when the PS-OCT technique is combined with OCTA, just as delineating [38–40] and segmenting samples [41,42]. More importantly, we believe that the distribution and status of thrombus produced during photodynamic therapy for port-wine stains can be detected in real-time by polarization and angiography imaging, which could provide potential information for further pathological diagnosis and treatment.

3.2 Qualitative comparison

Figure 6 shows the SAP of the PS-OCTA data within three different depth ranges for the palm skin processed with the SD (Fig. 6(a) to (c)), CDV (Fig. 6(d) to (f)), and SSAPGA (Fig. 6(g) to (i)) respectively. Overall, all three algorithms successfully map the vascular networks with a progressively denser vascular distribution with increasing depth, but subtle differences persist in revealing the details of the capillaries. In the superficial layer (from the skin surface to 400 µm deep), a significant number of artifacts are distributed in Fig. 6(d), followed by sporadic speckle artifacts in Fig. 6(a). Additionally, we found that the distribution of these artifacts in Fig. 6(d) is consistent with the distribution of high LPR values in Fig. 5(c). According to the color (green), these artifacts were inferred to be from the weakly scattering epidermis. As described in the previous section, the strongly scattering areas where the ultrasound gel clusters are located are mostly sweat gland pores and furrows while other regions have lower scattering intensity, as shown in Fig. 5(a). As a result, the high LPR values in Fig. 5(c) induced by noise and the artifacts in Fig. 6(d) are distributed along the ridge. Maybe it would be better to use the modified CDV algorithm [26]. But to be fairly compared, all algorithms are used with the initial formula. In contrast, although SSAPGA is also a kind of complex-signal-based angiography method, it can strongly suppress the noise with the split-spectrum method. Since the speckle pattern is spectral-dependent, the employment of the split-spectrum method can reduce this spectral speckle noise in the angiograms [11]. Therefore, by splitting the full OCT spectrum into several narrower bands, the averaged OCTA signal tends to be less affected by speckle noise and shows improved SNR. Unfortunately, after the split-spectrum method, as the axial resolution decreases, so does the sensitivity to detect signal fluctuations caused by blood cell flow [35]. Thus, Fig. 6(g) shows weaker signal strength as compared to Fig. 6(a) and 6(d). In the middle layer (from the skin 400 to 600 µm deep below the skin surface), Fig. 6(b), 6(e), and 6(h) all demonstrate good vascular connectivity. Nonetheless, the SAP of PS-OCTA data processed with the SD method shows the strongest signal strength and reveals more vessels (Fig. 6(b)). The comparison comes to be more pronounced when moving to a deeper layer (from the skin 600 to 800 µm deep below the skin surface). However, whether the SD algorithm is superior in revealing the true values still needs studies to compare with histology. The importance of the current findings, although with limited data, is that when using the JMTsystem as a tool in research or diagnostic applications, one needs to be aware of the angiography algorithm used when trying to make qualitative and quantitative comparisons. Additionally, throughout the entire imaging depth, it is found that the diameter of the blood vessels in the SAP processed by the SD method is larger than that obtained by the other two methods. It may be due to the employment of a 2D moving window in the SD algorithm, which inadvertently misjudged a small amount of static tissue adjacent to the vessel's position as vessel region. Intuitively, both complex-signal-based angiography methods successfully map the vascular network for the human skin without suffering from phase noise induced by bulk motion or the trigger jitter.

Fig. 6. Jones matrix-based PS-OCTA imaging of human palm skin processed with SD, CDV, and SSAPGA. (a), (b), and (c): SAP of the PS-OCTA data from the skin surface to 400 µm deep, from 400 µm to 600 µm deep, and from 600 µm to 800 µm deep processed with SD. (d), (e), and (f): SAP of the PS-OCTA data from the skin surface to 400um deep, from 400um to 600um deep, and from 600 µm to 800 µm deep processed with CDV. (g), (h), and (i): SAP of the PS-OCTA data from the skin surface to 400 µm deep, from 400 µm to 600 µm deep, and from 600 µm to 800 µm deep processed with SSAPGA. All scale bars are 400 µm.

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3.3 Quantitative comparison

To evaluate quantitatively the performance of CDV, SD, and SSAPGA algorithm in revealing vascular details for the human skin, the vascular connectivity, image CNR, image SNR, VDI, and BVD are calculated from SAP. It is noteworthy that the calculated BVD is not representative of the true vessel density at the deeper layer due to the existence of the tail artifacts. Typically, the calculated BVD is larger than the true vessel density in the deeper layer. However, since this comparison is relative, it does not affect the conclusion of the comparison. Although the pressure exerted on the skin is not precisely controlled in each experiment, the results of this comparison are still meaningful. As the raw dataset collected by the JMT system is just processed by three different angiographic algorithms, the difference between the results from the same raw dataset is mainly caused by the algorithms. Additionally, to avoid the negative for artifacts located in the superficial layer, the data from 400 to 800 µm below the skin surface are considered. The averaged values and the standard deviations from a total of 15 separate experimental measurements are tabulated in Table 1.

Table 1. Quantitative comparisons of image quality. The numbers are the averaged values and the standard deviations calculated from 15 separate experimental measurements.

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Consistent with the qualitative analysis, the SD algorithm indeed provides microvascular mapping with the highest VDI. The suspected reasons have been discussed in the previous section, which further may also be partly the reason for the higher mean value of BVD. In contrast, the images from the other two methods have comparable VDI values, while the SSAPGA method is easier to visualize more vessels according to the larger mean value of BVD from Table 1. In addition, the microvascular images processed by the CDV and the SSAPGA algorithm show relatively low mean values of connectivity, which indicates fewer separated blocks and better connectivity. However, it can be found that there is no perfect vessel connectivity in the images processed by the three algorithms for skin imaging. We hypothesize that this discontinuity is due to either the limited sampling density or slower blood flow in the contact mode [74]. Furthermore, the CDV and SSAPGA algorithms provide significant-high mean values of image CNR and image SNR compared to the SD algorithm, which indicates that the vasculature can be identified more clearly and the background intensities are more uniform, at least using the PS-OCTA dataset acquired in this study. Such performance can be delivered by taking full advantage of the information content available in the OCT signal, namely its amplitude and phase information, which is similar to the conclusion reported in Ref. 13. On the other hand, for the two complex-signal-based angiographic methods, whether from quantitative or qualitative analysis results, it can be found that the CDV method can provide a slightly better image CNR and SNR than the SSAPGA algorithm. But keep in mind that the CDV method is more susceptible to noise and more prone to artifacts in the weak scattering layer (as shown in Fig. 6(d)), while the SSAPGA algorithm can strongly suppress the noise with the split-spectrum method. Admittedly, the two complex-signal-based angiography methods (i.e., PGA, CDV) are not suffered from phase instability and even outperform the amplitude-signal-based algorithm (i.e., SD) in terms of vascular connectivity, image CNR, and image SNR.

Computational cost is another important factor for each algorithm to demonstrate its practicability for the dynamic monitoring of blood flow. Hence, four repeated B-scans are assessed for each of the compared algorithms coded using MATLAB processing language run on a laptop with an Intel Core i7 processor and 32 GB Memory. The processing time for three algorithms were listed in Table 2. It is indicated that the CDV method has the smallest computational cost compared to SD and SSAPGA algorithms. For SSAPGA, the longer time needed is caused by the multiple angiography calculations as a result of the split spectrum, and for SD, the pixel averaging with a 2D moving window leads to increased time. However, when more details of flow are required and the processing time is not critical, the SSAPGA algorithm can be employed for mapping vascular networks rather than the CDV according to the larger mean value of BVD from Table 2. When monitoring the dynamics of blood flow, an algorithm with a relatively faster computational speed should be applied.

Table 2. The processing time for three algorithms

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In this study, the human skin was taken as the sample to compare the performance of three angiographic algorithms in visualizing blood flow and the corresponding conclusions were also drawn. Despite the growing interest in dermatological research [35,46,75], it has to be acknowledged that the most important application of OCTA is retinal imaging [76–78]. In the future, we will redesign the JMT system and the imaging protocol for ophthalmology investigation. By imaging multiple biological tissues, a more comprehensive understanding and analysis of the blood flow imaging results processed by the angiography algorithm can be performed.

4. Conclusion

In summary, using our high-sensitivity multi-contrast JMT system based 200 kHz swept source, we analyzed the polarization characteristics of human skin and then compared the performance of SD, CDV, and SSAPGA algorithms for skin microvascular imaging qualitatively and quantitatively. The results demonstrate that high sensitivity is an essential factor in providing high-quality images. Benefiting from the polarization images, the fiber orientation and distribution can be markedly visualized. Additionally, it is shown that SSAPGA and CDV could successfully map the vascular network in different layers without suffering from phase instability induced by bulk motion and trigger jitter, and even outperform the SD algorithm in some metrics, including vascular connectivity, image CNR, and image SNR. However, in the weak scattering layer, the CDV method is more susceptible to noise and more prone to artifacts, while it can provide slightly better image CNR and image SNR with minimal computational intensity when moving to higher scattering layers compared to the SSAPGA method. This paper can provide general guidance to choose reliable information with appropriate algorithms in specific applications for JMT imaging system.

Funding

National Natural Science Foundation of China (11627808).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

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.

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metric	SD	CDV	SSAPGA
VDI	7.8085 ± 0.6074	7.0669 ± 0.5257	7.0849 ± 0.5752
BVD	0.5037 ± 0.0091	0.4268 ± 0.0064	0.4770 ± 0.0103
connectivity	0.2359 ± 0.0212	0.1838 ± 0.0106	0.1925 ± 0.0116
image CNR	2.8390 ± 0.1458	3.4122 ± 0.2345	3.2291 ± 0.4882
image SNR	3.7823 ± 0.0846	4.5554 ± 0.1423	4.2397 ± 0.3468

metric	SD	CDV	SSAPGA
VDI	7.8085 ± 0.6074	7.0669 ± 0.5257	7.0849 ± 0.5752
BVD	0.5037 ± 0.0091	0.4268 ± 0.0064	0.4770 ± 0.0103
connectivity	0.2359 ± 0.0212	0.1838 ± 0.0106	0.1925 ± 0.0116
image CNR	2.8390 ± 0.1458	3.4122 ± 0.2345	3.2291 ± 0.4882
image SNR	3.7823 ± 0.0846	4.5554 ± 0.1423	4.2397 ± 0.3468

Comparative study of OCTA algorithms with a high-sensitivity multi-contrast Jones matrix OCT system for human skin imaging

Abstract

1. Introduction

2. Materials and methods

2.1 High-sensitivity multi-contrast JMT system

2.2 Measurement protocol

2.3 Data process

2.3.1 Polarization imaging

2.3.2 System validation

2.3.3 Angiographic imaging

2.3.4 quantitative metrics

3. Result and discussion

3.1 Multi-contrast images

3.2 Qualitative comparison

3.3 Quantitative comparison

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (6)

Tables (2)

Equations (21)

Biomedical Optics Express