A rapid and universal method for depth estimation of lesions in heterogeneous tissues via photosafe ratiometric transmission Raman spectroscopy

Noninvasive detection of deep lesions remains a long‐standing goal for clinical applications, with depth estimation of a single lesion in heterogeneous tissues being a key challenge. Currently, optical techniques are widely applied for lesion detection, but they face difficulties in achieving rapid and precise lesion depth estimation, particularly when the lesions are buried in thick heterogeneous tissues and the applied irradiance is below clinically maximum permissible exposure. Herein, we theoretically and experimentally demonstrate a universal method for depth prediction of phantom lesions labeled with surface‐enhanced Raman scattering nanotags in thick biological tissues using ratiometric transmission Raman spectroscopy (TRS). We begin by highlighting the linear relationship between the natural logarithm of Raman peak‐to‐peak ratio and the lesion depth and establishing a home‐built TRS system with the clinically safe irradiance. We achieve an accurate depth prediction for phantom lesions hidden in 6‐cm‐thick ex vivo homogeneous tissue with a root mean squared error (RMSE) as low as 2.42%. Additionally, we predict the depth of phantom lesions buried in 5‐cm‐thick ex vivo heterogeneous tissues with an RMSE of down to 8.35%. We also demonstrate the applicability of this method theoretically for highly heterogeneous tissues such as complex in vivo environments. This work provides a rapid, robust, and universal method to estimate the depth of lesions in complex biological samples, demonstrating the potential of ratiometric Raman spectroscopy for lesion localization in clinical applications.


INTRODUCTION
Most lesions are deeply seated inside the human body with depths ranging from a few to tens of centimeters beneath the body surface. To determine the location of lesions, current clinical procedures begin with preoperative or intraoperative medical imaging. This information is highly significant for clinical theranostic applications, informing the design of therapeutic strategies, surgical planning, and surgery guidance. For example, estimates of lesion depth before photodynamic therapy can help determine a suitable drug type, dose, and laser parameters. 1 Also, accurate depth estimation of lymph nodes during sentinel lymph node (SLN) biopsy is conducive to the identification of lesions, shortening the surgical identification process, and reducing bleeding risk during the surgery. 2 Similarly, for tumor therapies, tumor depth information can be used to determine the stage of colorectal cancer and then help devise therapeutic strategies. 3 Noninvasive optical three-dimensional (3D) imaging of deep lesions remains a long-standing goal for clinical applications, with depth estimation of a single lesion in heterogeneous tissues a key challenge. To date, optical techniques have garnered much attention for their real-time acquisition capability, nonionizing radiation, low cost, and numerous nanoprobe candidates. 4 Some reported optical lesion depth estimation methods use timeresolved measurements or fluorescence diffuse tomography, which typically requires complex equipment and is sensitive to small instrument misalignment. 5 Others, such as fluorescence spectral distortion, take advantage of varying tissue attenuations of light at different wavelengths to predict the depth of fluorophore-tagged lesions. 6 However, this strongly relies on the calibration model in homogeneous biological tissues, which limits the application in real complex in vivo scenarios. Moreover, fluorescence is intrinsically restricted by its broad spectrum. This brings additional complications since fluorescence-based depth estimation methods using multiple fluorophores have to be equipped with multiple excitations. Fluorescence imaging is also relatively shallow (a few millimeters) and only applicable for shallow lesions such as brain tumor surgery post-craniotomy. 7 Lastly, the autofluorescence background of biological tissues may lead to unexpected spectral distortion, reducing the accuracy of depth prediction. Depth prediction of lesions deep-seated in complex heterogeneous tissues remains a significant challenge.
Surface-enhanced Raman spectroscopy (SERS) has a number of promising advantages for this application, such as unique spectral fingerprints with narrow linewidth, allowing clear discrimination between the target spectrum and tissue background. 8 The spectral signatures of different SERS nanotags can all be excited by a single laser and detected with a single sensor, making SERS the perfect candidate for multiplexing applications. 9 Recently, the capability of SERS for deep detection has been significantly enhanced by the development of transmission Raman spectroscopy (TRS), which separates laser illumination and collection on opposite sides of the sample. 10 TRS suppresses the background noise from surface layers and increases the signal-to-noise ratio (SNR) from deep layers, greatly increasing the detection depth to a few centimeters, a significant improvement over the backscattering mode (millimeters). 11 TRS detection has been explored for the diagnosis of lesions such as breast cancers. 10a,11b,12 Very recently, we have achieved deep TRS detection of SERS nanotags through up to 14-cm ex vivo biological tissue, which is close to the thickness of an adult human body. 13 Several TRS-based approaches have been recently explored to estimate the depth of phantom lesions in turbid media. For example, depth information was obtained with prior knowledge of computed tomography images. 14 Also, the depth of a single, chemically distinct layer has been determined by recording two TRS measurements: with and without a photon diode; however, this relies on a medium with low optical absorption which limits application in bio-tissue samples. 15 In addition, the lesion depth has been determined by taking advantage of the differences in attenuation of light at different wavelengths from the components with absorption properties 16 or by ratiometric analysis of the Raman intensities of nanotags and the tissue barrier with foreknowledge of SERS nanotag intensity. 17 However, these methods strongly rely on the pre-calibration of predictive models in the same homogeneous tissue, which is challenging to obtain in real complex in vivo scenarios. As a result, even state-of-the-art methods work only for homogeneous tissue models, failing for real complex media such as thick heterogeneous tissues.
Another downside of current SERS studies is that they typically apply high laser power density, well over the clinical maximum permissible exposure (MPE)-the highest light irradiance or radiant exposure with negligible risk of causing damage to an exposed surface of the body. 18 This greatly limits their feasibility for clinical applications due to the potential damage of the irradiated tissues. 16 Therefore, it is of great importance and value to develop a photosafe method suitable for clinical practice that can enable the rapid determination of lesion depth in turbid media in either homogeneous or heterogeneous tissues. F I G U R E 1 Schematic of surface-enhanced Raman spectroscopy (SERS) "phantom" lesion depth estimation in biological samples using ratiometric transmission Raman spectroscopy.
Here, we propose a rapid and robust method for depth estimation of "phantom" lesions labeled by SERS nanotags in bio-tissues using ratiometric TRS ( Figure 1). The method is based on the different attenuations of Raman photons at different wavelengths when passing through the bio-tissue. We first theoretically investigate the photon attenuation and discover a linear relationship between the natural logarithm of Raman peak-to-peak ratio (RPR) and propagation depth. The slope of the linear relationship can be calculated in advance based on the effective attenuation coefficients of Raman photons at two wavelengths, and an intercept can be obtained as the natural logarithm of the RPR of pure SERS nanotags. This enables the prediction of lesion depth in tissues without prior knowledge of tissue thickness, the concentration of nanotags, or Raman measurement parameters. We experimentally confirm this linear relationship using a home-built TRS system with clinically safe laser irradiance. Our as-synthesized ultrabright SERS nanotags with multiple characteristic Raman peaks are used as phantom lesions and buried in ex vivo porcine fat and muscle tissues. We achieve an accurate depth estimation with a root mean square error (RMSE) as low as 2.42%. We also demonstrate the effectiveness of this linear prediction model in ex vivo heterogeneous tissue using multiple pairs of Raman spectral peaks, achieving lesion depth estimation in a 5-cm heterogeneous tissue stack with an RMSE of 8.35%. Finally, we theoretically demonstrate the depth prediction model in highly heterogeneous tissues (as in practical in vivo situations). This work provides a rapid, robust, and universal method to analyze the depth information of lesions in complex biological samples, demonstrating the potential of ratiometric Raman spectroscopy-guided lesion localization for practical clinical applications.

Linear relationship between RPR and depth of SERS phantom in homogeneous tissue
Our work began with theoretical calculations to investigate how the Raman peak ratio changed with Raman photon propagation distance in tissue ( Figure 2A). As in our previous work, 13 we apply the steady-state radiative transport equations (RTE) to model the field inside a homogeneous medium for incident light (see Section 4 for more details). Since continuous wave (CW) illumination and transmissive detection were applied in TRS, the excitation on the surface of SERS nanotags and Raman photon propagation through the tissue can also be modeled using a diffusion approximation within an RTE framework. Based on this, we established an analytic solution for the semi-infinite homogeneous bio-tissue geometry in a standard TRS setup. As shown in Figure 2A, a lesion labeled by SERS nanotags (the SERS phantom) is buried at a depth d in the tissue with thickness T. The tissue absorption coefficient is µ a , and the reduced scattering coefficient is ′ s at a given wavelength. An excitation beam with a wavelength of λ 0 , power of P 0 , and a spot radius of a is incident on the tissue from the illumination side (bottom) and then propagates through the tissue. At the position of the lesion, incident photons (λ 0 ) interact with the SERS nanotags. The Raman photons (λ i ) are generated and then continue to propagate through the tissue until exiting from the collection side (top). We apply the RTE and the diffusion approximation to describe photon propagation in the homogeneous tissue, and find the analytic solution for the Raman intensity (I det ) of a lesion buried at a depth (d) as follows: and is a function related to the incident light propagation in the tissue before interaction with the SERS nanotags; σ (wavelength dependent) and C are the SERS cross-section and concentration of SERS tags, respectively; D and µ eff , both related to µ a and ′ s , are the photon diffusion coefficient and effective attenuation coefficient (see Section 4 for details), respectively.
The detected TRS signal intensity is dependent on tissue optical properties and d of the SERS nanotag-labeled lesion (Equation 1). Different Raman peaks experience different intensity attenuation rates with increasing depth, and differences in total attenuation between different Raman peaks become more pronounced with increasing lesion depth (Figures 2B and S1a). If we choose two Raman peaks with wavelengths λ 1 and λ 2 (λ 2 > λ 1 ) and define Δµ = µ eff (λ 2 ) -µ eff (λ 1 ), then we can obtain a linear form as follows: where = ln ( 1 2   2 1 ).
In Equation (2), the natural logarithm of RPR depends linearly on the depth (d) of the SERS phantom in a homogeneous medium. The slope of the linear function corresponds to the difference in the effective attenuation coefficients of Raman photons propagating in the tissue at the two wavelengths (i.e., Δµ). Assuming µ eff (λ 2 ) is higher than µ eff (λ 1 ), that is, Δµ > 0, then Equation (2) can be plotted as shown in Figure 2C; otherwise, we plot it as shown in Figure S1b. The intercepts (b) of both lines correspond to the values of ln(I 1 /I 2 ) when d = 0. This is equivalent to the natural logarithm RPR of pure SERS nanotags, depending only on the Raman peak pair chosen. When Δµ of the tissue is known, d is the only unknown in this equation. The optical parameters (mainly absorption or reduced scattering coefficients) of some tissues and measurement methods have been reported, 19 which allows us to calculate Δµ. Once Δµ is known, the depth of the SERS phantom can be easily calculated using this linear function. Conversely, the linear model of Equation (2) can also be used to calculate Δµ if the phantom is buried at a known depth. Compared with the method based on timedomain diffuse spectroscopy reported in the literature, 19 using Equation (2) to determine Δµ could be much simpler. This relationship is independent of medium type, tissue thickness, excitation wavelength, and beam size.
Following this theoretical analysis, we carried out an experimental study to verify the relationship between the natural logarithm of the RPR and depth of the SERS phantom in homogeneous tissue. For this, we used ultrabright SERS nanotags known as "gap-enhanced resonance Raman tags" (GERRTs), as reported in our previous work. 20 Figure 2D shows the structure of the GERRTs which were obtained from spiky Au cores absorbed with IR-780 iodide molecules and then coated with a Ag layer. The transmission electron microscopy (TEM) image shows the morphology of the smooth surface of the GERRTs, and two resonant peaks at 424 and 541 nm in the ultraviolet (UV)-vis spectrum of GERRT colloids correspond well with the expected localized surface plasmonic resonance (LSPR) positions of Ag and Au nanostructures, respectively ( Figure S2). As shown in Figure 2E, the GER-RTs exhibit characteristic Raman modes at 520, 556, 931, 1203, 1369, 1523, and 1580 cm −1 . These modes can be distinguished clearly from background in biological tissues such as porcine muscle and fat tissues. The multiple, easily dis-tinguishable Raman peaks of GERRTs are critical for our method using Raman peak pairs for depth prediction.
To mimic lesions in TRS, a quartz tube of 1 mm in inner diameter filled with 60 µL of GERRTs (3.6 × 10 11 particles/mL) was used as a "phantom" lesion labeled by SERS nanotags (which we call the "SERS phantom," with a schematic shown in Figure 2D). The phantom was embedded in the porcine tissue stack ( Figure 2F) at different depths (d). The homogeneous tissue was obtained by assembling porcine tissue sections with a controlled thickness in a stack, and the total thickness (T) of the tissue stack could be precisely adjusted by subtracting or adding tissue sections. The whole tissue stack was placed on a sample stage with a hole of 2 × 2 cm 2 in the middle. On top of the tissue stack, a fiber bundle probe coupled to the Raman spectrometer was fixed to collect the Raman signals. The applied laser beam was incident from the bottom. The laser spot and fiber probe were vertically aligned with the SERS phantom to minimize the intensity variation caused by scattering and maximize the accuracy of the predicted depth. To make the TRS technique photosafe for clinical use, we were careful to maintain power density below the MPE limit (i.e., 1.627 W/cm 2 for 1 s exposure time and 0.296 W/cm 2 for over 10 s exposure time under 785 nm excitation). Therefore, we chose a diffuse beam with a radius of 0.85 cm on the surface of the sample.
The diffuse beam has been demonstrated to have a negligible effect on the TRS signal intensity compared with a conventional focused beam for illumination. 13 All TRS measurements with diffuse beam illumination were performed using a 785 nm laser, 1 or 10 s integration time, and 100, 200, 400, or 600 mW of laser power corresponding to a power density of 0.044, 0.088, 0.176, or 0.264 W/cm 2 , respectively, which were all below the MPE threshold.
We collected Raman spectra from the phantom at different depths (d) in the range of 0-3 cm (0.5 cm/step) in a homogeneous porcine fat tissue stack (T = 3 cm). As shown in Figure S3a, the intensity of the Raman peak at 520 cm −1 shows significantly different attenuations with depth compared to that at 1580 cm −1 , although the whole Raman signal shows a U shape, which has been previously reported by us. 13 The spectra were then normalized to the intensity of the Raman peak at 1580 cm −1 to better visualize their attenuation trends. As shown in Figure 2G, we find that the normalized intensity of the Raman peak at 520 cm −1 increases continuously with increasing depth. This is explained by the fact that the effective attenuation coefficient at 520 cm −1 (818 nm) is smaller than that at 1580 cm −1 (896 nm). 19 Further plotting of the natural logarithm of the RPR (I 520 /I 1580 ) versus the depth indicates a linear relationship between the two with R 2 ≥ 99.7% and a best-fit slope of 0.685 ( Figure 2H), which is almost the same as Δµ (0.692) obtained from the literature (see Section 4 for more details). 19 Meanwhile, the fitting intercept (0.855) is also close to the ln(I 520 /I 1580 ) of the pure SERS nanotags (1.059). These results agree well with our theoretical predictions ( Figure 2B,C).
We further investigated whether the linear relationship persists in the other types of tissue and when measurement parameters (e.g., tissue thickness, integration time, laser power, etc.) change. As shown in Figure 2J, the case when the SERS phantom was buried in porcine muscle tissue was investigated. The results in Figures 2J,K and S3b show that the different attenuations of intensity of the Raman peaks at 520 and 1580 cm −1 (Figures 2J and S3b) and that the natural logarithm of RPR again depends linearly on the depth ( Figure 2K) in the porcine muscle. The fitting slope (0.168) and intercept (0.743) are also close to the Δµ (0.145) of the two Raman photons propagating in porcine muscle obtained from literature and ln(I 520 /I 1580 ) of the pure SERS nanotags (1.059), respectively. These results indicate that the prediction model (Equation 2) is also effective for other laser sources, such as a typical Gaussian beam. Notably, the data error bars in repeated measurements in muscle tissue appear larger than those in fat tissues. This is because the errors caused by repeated measurements in both fat and muscle tissues are at the same level ( Figure S3c). However, due to the greater slope (i.e., Δµ), the value of ln(I 520 /I 1580 ) increased more significantly in fat tissues when the Raman photons passed through the bio-tissues. Therefore, as shown in Figure 2H,K, after traveling a certain depth, the variation range of ln(I 520 /I 1580 ) in fat tissues is significantly larger than that in muscle tissues, resulting in the error bars in fat tissues looking much smaller. In addition, this linear relationship is not affected by changes in total tissue thickness, incident laser power, or integration time ( Figure S4). These results demonstrate the universality and robustness of the linear relationship between the natural logarithm of the RPR and the depth of buried SERS phantoms.

Experimental depth prediction in homogeneous tissues
To investigate the capability of our linear model (Equation 2) to predict the depth of SERS phantoms, we experimentally performed TRS measurements on ex vivo homogeneous tissues. Equation (2) was used to predict the depth of the SERS phantom based on the natural logarithm of the RPR. We chose the peak pair of 520/1580 cm −1 , corresponding to Δµ of 0.692 and 0.145 cm −1 for fat and muscle tissues (see Section 4 for more details), respectively, and the intercept as 1.059 (obtained from ln(I 520 /I 1580 ) of pure SERS nanotags). The predicted d in fat tissue can thus be calculated as (ln(I 520 /I 1580 ) − 1.059)/0.692 and in muscle tissue, (ln(I 520 /I 1580 ) − 1.059)/0.145. The predicted d was then plotted against the experimental one. Also, the RMSE, which represents the difference between model predictions and observations as well as the correlation R-value which represents the degree of linear correlation between the two sets of data and measures the spread of points relative to the standard deviation, were calculated. The prediction results indicate an RMSE of 0.07 cm or 2.42% in the 3 cm predicted range in the porcine fat tissue ( Figure 3A). This result demonstrates high accuracy with lower error and no requirement for prior calibration when compared with previously reported techniques using a backscattering Raman or TRS system for depth prediction in bio-tissues. 16c The correlation R-value is 0.987, indicating the high correlation between the predicted and experimental depth and indicating the good stability between the repeated measurements (n = 5). Moreover, it is worth noting that our experiments were all conducted within the clinical safety illumination, that is, MPE limit, avoiding possible tissue damage caused by the laser. The depth predictions of SERS phantoms in the porcine muscle tissue are also found to be highly accurate with a RMSE of 0.29 cm or 5.83% in 5 cm depth ranges and a correlation R-value of 0.954 ( Figure 3B). The errors in repeated measurements in muscle are notably larger than those measured in the porcine fat. This could be owing to the much lower value of Δµ in porcine muscle tissues: fluctuations of ln(I 520 /I 1580 ) caused by systematic error are at the same level, so the larger Δµ (i.e., slope) results in clearer changes in ln(I 520 /I 1580 ) for small changes in depth. Overall, both results with ex vivo porcine fat and muscle tissues allowed the depth of the buried SERS phantom to be accurately predicted, validating the use of the proposed approach without prior calibration.

Linear relationship between RPR and the depth of SERS phantom for multiple Raman peak pairs in homogeneous tissue
Considering that the Raman spectrum presents multiple peaks with narrow bandwidths, we proceeded to explore the possibility of using peak pairs other than the pair used so far. However, if we look at the Raman spectra in Figure 4A, which were measured when the SERS phantom was placed in homogeneous fat tissue (as shown in Figure 2F), many characteristic Raman peaks of GERRTs can be found. Some of these Raman peaks overlap with those of fat tissue ( Figure S5). To avoid confusion with tissue background, the Raman peaks at 520, 931, 1203, 1369, 1523, and 1580 cm −1 were selected for calculations ( Figure 4A). We then plotted the relationship between ln(RPR) and d for a variety of Raman peak pairs. As shown in Figure 4B, ln(RPR) versus d for each pair of Raman peaks can be satisfactorily fitted with a linear function. Four Raman peak pairs were randomly selected for an example of depth prediction of a SERS phantom buried in ex vivo homogeneous fat tissue ( Figure S6), and the Δµ (obtained from literature) and b (the ln(RPR) of pure SERS nanotags) of different Raman peak pairs used for depth prediction are shown in Table S1. We find that the predictions are highly accurate ( Figure S6), demonstrating that different Raman peak pairs have utility for depth prediction. Slight differences in the RMSE between different peak pairs were found, which will be elaborated on later.
As shown in Figure 4C,D, a linear relationship between ln(RPR) and d was also found in porcine muscle. This indicates that different Raman peak pairs may be used to predict depth in various tissue types. The fitting slopes and intercepts of these linear models of fat tissue and muscle tissues are all obviously different. This agrees well with our theoretical prediction (Equation 2) that the slope of the linear model corresponds to the difference between the effective attenuation coefficients (Δµ) between two Raman peaks for a specific tissue. Additionally, the fitting intercepts of the same pairs of Raman peaks in porcine muscle and fat tissue are almost the same ( Figure 4B,D), indicating that intercept values are independent of the tissue types, as expected.
We extracted the slopes from our fitting lines and compared them with the Δµ obtained from literature (see Section 4 and Table S1 for more details) to further demonstrate the accuracy of the linear model (Equation 2). In Figure 4E, the Δµ from our fit is plotted against the Δµ from literature. The black points represent Δµ from the linear fit for porcine muscle, and the red points for porcine fat. It is noteworthy that some results where Δµ between the two Raman peaks is too small are not shown here because they are easily affected by the noise. Almost all points fall on the line y = x or very close to it, the RMSE is 0.026 cm −1 (3.863% of 0.675 cm −1 of Δµ range) and the correlation R-value is 0.997. This indicates close agreement between the data obtained by two different methods, demonstrating the accuracy of the theoretical linear model (Equation 2). Furthermore, we compare the intercepts of our fitting lines to the natural logarithm of the corresponding RPR of the pure SERS nanotags ( Figure S7); the two values are also similar. This suggests that when the contrast agent and the Raman peak pair are determined, the intercept of the specific Raman peak pair can be directly calculated from the RPR of pure SERS nanotags. This agrees well with our theoretical calculations (i.e., b = ln(RPR) when d = 0) and may be convenient for practical applications. Similar results were found when we reduced the radius of the laser beam to 0.01 cm using focused beam illumination as shown in Figures S8 and S9. Table  S1 lists all values of Δµ and b. These values demonstrate good consistency between experimental and theoretical calculations (Equation 2), indicating that the linear relationship between ln(RPR) and d is universal and robust and determined only by the Δµ and intensity ratio of the two Raman peaks. We therefore expect this method to also be feasible to predict the depth of lesions in other biotissues or using other SERS contrast agents, opening up many new possibilities for the use of Raman spectroscopy for depth prediction of SERS nanotags buried in various kinds of turbid media. In addition, the multiple peaks of the characteristic Raman spectra offer more choices for depth prediction. For example, suitable Raman peak pairs can be selected to avoid interference from background tissues. Furthermore, the combination of multiple Raman peaks may allow prediction of lesion depth in complex tissues.

F I G U R E 4
The relationship between Raman peak-to-peak ratio (RPR) and buried depth of a surface-enhanced Raman spectroscopy (SERS) phantom in homogeneous tissue for multiple Raman peaks. (A) The measured Raman spectra and (B) the ln(RPR) versus depths of SERS phantom buried in fat tissue from different peak pairs. (C) The measured Raman spectra and (D) the ln(RPR) versus depths of the SERS phantom buried in muscle tissue from different peak pairs. Raman peaks in gray in panels (A) and (C) were used for plotting. (E) Comparison of Δµ from fitting curves (i.e., the slopes of the fitting curves) with Δµ from literature. 19 The black and red points correspond to the data obtained in the muscle and fat tissue, respectively. The dashed line is the line y = x.
We should note that light scattering contributes to the photons in different directions besides those in the optical path. However, this does not influence our results. Our depth prediction method only relies on the intensity ratio between the Raman peak pairs rather than the intensity of the Raman peaks. Therefore, as long as the Raman peak SNR is sufficient, it can be used to predict depth directly. The Raman spectra obtained in this work all have SNRs of over 3.

Depth prediction model in heterogeneous tissues
After a successful demonstration of depth prediction in homogeneous tissues, we investigated the effectiveness of this method in heterogeneous tissues. In these samples, the process of light propagation becomes complicated and may be affected by multiple changes in Δµ. Therefore, further study of the relationship between lesion depth and ln(RPR) in heterogeneous tissues is necessary. As shown in Figure 5A, it is assumed that the heterogeneous tissue sample consists of two types of tissue stacked in sequence with thicknesses of T 1 and T 2 . Theoretically, we expect that the linear relationship between ln(RPR) and depth depends only on the travel thickness in each tissue layer (X 1 and X 2 ) of Raman photons before they reach the collection surface and detector. In the first tissue (d ≤ T 1 ), we can predict the depth of the SERS phantom through the linear relationship between ln(RPR) and depth since the tissue which Raman photons pass through up to this point is a homogeneous medium. However, when d > T 1 , Raman photons need to pass through a second kind of tissue to reach the collection surface, and d is the sum of X 1 and X 2 . In this case, the heterogeneity of the tissue has to be considered. We can infer that the curve of ln(I 1 /I 3 ) versus d is simply the superposition of linear models for each homogeneous tissue, as shown in Figure 5B. There is a sharp turning point at the interface of the two homogeneous tissues since Δµ is different in each tissue type. With two unknown variables: X 1 and X 2 , it becomes difficult to obtain a unique solution for the depth when relying only on a pair of Raman peaks. Benefiting from the multiple peaks in the Raman spectrum, we can select another pair of Raman peaks (I 2 /I 3 ) and establish the linear relation model, as shown in Figure 5C. By combining the two linear models of the two Raman peak pairs, we can obtain a determined system of equations shown in Figure 5D, which can be used to solve for X 1 and X 2 , and the unknown total depth (d) of the SERS phantom in heterogeneous tissues.
For a more complex situation, assuming that heterogeneous tissue consists of two different types of tissue layers staggered and stacked on top of each other as shown in Figure 5E, there will be multiple tissue interfaces. Similarly, the curves of the natural logarithm of RPR versus depth in Figure 5F,G change at each tissue interface, but the slopes of the linear models are consistent for the same type of homogeneous tissues in different layers. This indicates that the depth prediction model depends only on the total thickness of each of the different kinds of tissues that Raman photons pass through, no matter how those tissues stack up. Therefore, a determined system of equations ( Figure 5D) equivalent to the case with one layer of each unique tissue can be used for depth prediction. In this case, d is still the sum of the travel thicknesses of Raman photons in the tissues, that is, d = X 1 + X 2 for two tissues.
We continued to experimentally verify the effectiveness of the above prediction method using multiple Raman peak pairs. Here, we used an ex vivo heterogeneous tissue model of two kinds of tissues interleaved and stacked. Figure 5H shows the TRS system for detection of a SERS phantom buried in a heterogeneous tissue stack consisting of five interleaved 1-cm-thick blocks of porcine muscle or fat tissues. Two porcine fat tissue blocks were placed in the first and fourth layers, and the other three were porcine muscle layers. We collected Raman spectra at different depths, and two Raman peak pairs (I 520 /I 1369 and I 931 /I 1369 ) were used to plot the relationship between natural logarithm of RPRs and depth. As shown in Figure 5J, two different curves were obtained, and the slopes of all the curves changed significantly at each interface between different tissue types. These results are consistent with the curves calculated by Equation (2) (dashed lines in Figure 5J), where the values of b were obtained from the ln(I 520 /I 1369 ) and ln(I 931 /I 1369 ) of the pure SERS nanotags and Δµ were obtained from the literature (see Table  S1 for detailed data), 19 implying the possibility of depth prediction in heterogeneous tissue samples.

Experimental depth prediction in heterogeneous tissues
We continued to investigate the capability of our model for SERS phantom depth prediction in heterogeneous tissues. Here, we performed TRS measurements and applied a determined system of equations to predict the depth of the SERS phantom. Figure 6A shows a schematic of the experimental heterogeneous tissue block consisting of five interleaved porcine muscle and fat layers (1 cm in thickness each). Two pieces of fat tissue were placed as the second and fifth layers, and the other three were muscle layers. The determined system of equations was established using the two Raman peak pairs: I 520 /I 1369 and I 931 /I 1369 . The Δµ from literature and b from the ln(RPR) of pure SERS nanotags (Table S1) were then used to predict the depths. As shown in Figure 6B, the predicted d was plotted against the experimental d, RMSE was calculated as 0.19 cm (3.81% with a 5 cm depth range) and correlation R-value was calculated as 0.801. There is some deviation between the repeated measurements (n = 5) at each depth, which is due to the relatively small value of Δµ of the two Raman peak pairs, that is, 0.083 for the 520/1369 cm −1 pair and 0.042 for the 931/1369 cm −1 pair, for muscle tissues. Their averages maintained high accuracy, demonstrating the capability for depth prediction in heterogeneous tissues. In addition, we can also choose other combinations of Raman peak pairs, recombining their equations and solving again for depth. Figure 6C shows the predicted depths when combining the two Raman peak pairs: I 931 /I 1369 and I 1203 /I 1369 . Compared with the result in Figure 6B, this shows obvious deviation, with RMSE reaching 60.41% (correlation R-value of 0.602). To further determine whether there are significant differences in predicted depth between different combinations of Raman peak pairs, we considered all possible combinations of Raman peak pairs to obtain F I G U R E 5 Surface-enhanced Raman spectroscopy (SERS) phantom depth prediction model in heterogeneous tissue. (A) Schematic of a SERS phantom seated in a heterogeneous tissue block composed of two types of tissue. T 1 and T 2 are the total thickness of tissue 1 and tissue 2, respectively. X 1 and X 2 represent the thickness of each tissue traversed by Raman photons before being collected. The theoretical natural logarithm plot of Raman peak-to-peak ratio (RPR) versus depths: (B) I 1 /I 3 and (C) I 2 /I 3 , and (D) the corresponding determined system of equations for depth prediction. (E) Schematic of a SERS phantom seated in a heterogeneous tissue block formed by interleaved stacking of two types of tissue. ′ 1 and ′′ 1 are the thicknesses of tissue 1 in different layers, and ′ 2 and ′′ 2 are the thicknesses of tissue 2 in different layers. 1 = ′ 1 + ′′ 1 and 2 = ′ 2 + ′′ 2 . ′ 1 , ′′ 1 , ′ 2 , and ′′ 2 represent the thickness of each tissue traversed by Raman photons before being collected. The theoretical natural logarithm plot of RPR versus depths: (F) I 1 /I 3 and (G) I 2 /I 3 . (H) Photograph of transmission setup for detection of SERS phantom in heterogeneous tissue block formed by interleaved stacking of porcine fat and muscle tissues. The total tissue thickness is 5 cm. (I) Measured Raman spectra and (J) the measured natural logarithm of RPRs versus depth (solid lines). The dashed lines were calculated from Equation (2), the values of b were obtained from the ln(RPR) of the pure SERS nanotags and Δµ were obtained from the literature. 19 The black curves correspond to the results from the peak pair of 520/1369 cm −1 , and red curves correspond to the results from the peak pair of 931/1369 cm −1 .

F I G U R E 6
Experimental surface-enhanced Raman spectroscopy (SERS) phantom depth prediction in heterogeneous tissues. (A) Schematic of the experimental heterogeneous tissue block. ′ m , ′′ m , ′′′ , ′ f , and ′′ represent the thickness traveled through each tissue layer by Raman photons before being collected. Predicted depths obtained by solving a determined system of depth prediction equations for two different Raman peak pairs: (B) I 520 /I 1369 and I 931 /I 1369 and (C) I 931 /I 1369 and I 1203 /I 1369 . (D) Comparison of root mean squared error (RMSE) (5 cm predicted range). The green bars represent the RMSE of the depths predicted using the determined system of equations formed from the depth prediction models of two Raman peak pairs. The orange bar represents the RMSE of the depths predicted by solving the overdetermined system of equations formed from the depth prediction models of nine Raman peak pairs. (E) Overdetermined system of equations formed from the depth prediction models of nine Raman peak pairs. (F) Predicted depths obtained by solving the overdetermined system of equations. For each measured depth, we collected five spectra and calculated the averaged prediction with standard errors. different depth prediction equations, and then solved for the unknown SERS phantom depth, d, in the heterogeneous tissue. For nine pairs of Raman peaks, a total of 36 sets of depth prediction results can be obtained, take the RMSE for comparison and their RMSE values are shown in Figure 6D (green bars). There are clear differences in accuracy when different Raman peak pairs are selected. For example, when the Raman peak at 520 cm −1 was combined with other Raman peaks (931,1203,1369,1523, and 1580 cm −1 ), the RMSE values were much smaller than when the Raman peak at 931 or 1203 cm −1 was combined with other Raman peaks (931, 1203, 1369, 1523, and 1580 cm −1 ). This may be due to the Δµ of the latter being smaller than that of the former (see Table S1 for details), leading to decreased signal discrimination between two depths.
Therefore, to avoid uncertainty in depth prediction caused by the random selection of different Raman peaks in practical applications, we considered nine pairs of Raman peaks. The overdetermined system of equations (the number of equations in this system is more than unknowns) for depth prediction is shown in Figure 6E. Overdetermined equations are generally contradictory equations with no analytic solution because the given conditions are too strict. Here, the overdetermined system of equations was solved using the ordinary least squares method to obtain the optimal solution. The optimal solutions (i.e., predicted d) were plotted against the experimental d as shown in Figure 6F, and RMSE was calculated as 0.42 cm or 8.35% with a 5 cm depth range. Compared with the RMSEs of the predicted depths based on only two pairs of Raman peak pairs, the RMSE of the predicted depths obtained after considering nine pairs of Raman peak pairs is almost the smallest (orange bar in Figure 6D). These results indicate that the robustness of the predicted depth can be greatly improved by comprehensively considering more Raman peak pairs. It also implies that the numerous characteristic Raman peaks of the SERS nanotags are an advantage that can be exploited to improve the accuracy of depth predictions. Overall, these results demonstrate the capability of the proposed approach for noninvasive and rapid depth prediction of a SERS phantom buried inside heterogeneous tissues, at which almost all other state-of-the-art methods based on full optical modalities still fail (see Table S2 for the summary). 6a,6b,6d,7,16,17

Depth prediction model in highly heterogeneous tissue
We further attempt to theoretically discuss lesion depth prediction in highly heterogeneous tissues, such as in real in vivo situations. Highly heterogeneous tissue is very complex in composition, and its geometric structure is represented by the schematic in Figure 7A, consisting of staggered stacks of many different types of tissues. According to the above study, the curve of ln(RPR) versus depth will change at each tissue interface, owing to the difference in attenuation coefficients of Raman photon propagation in the different tissues. Therefore, when detecting lesions in such highly heterogeneous tissue ( Figure 7A), we obtain the ln(RPR) versus depth curve shown in Figure 7B. The number of unknowns in this curve is determined by the number of homogeneous tissue species that the Raman photons have traveled through before being collected. Therefore, as shown in Figure 7C, prediction of the SERS phantom depth in the tissue can still be carried out by combining the linear relationships between the natural logarithm of the intensity ratio of different Raman peaks and the depth.
Typically, there are many kinds of tissues in the body. The basic tissues are skin, fat, muscle, and bone. Limbs and breasts are mainly made up of these four types of tissues. While in other parts of the body, such as the cranial, thoracic, and abdominal cavities, there are other tissue types besides these four. For example, the brain, brainstem, cerebellum, and diencephalon are included in the cranial cavity, while the heart and lungs are included in the thoracic cavity. The abdominal cavity is the most complex one, which can be divided into the upper abdomen and lower abdomen. The former includes the liver, gallbladder, stomach, pancreas, spleen, kidney, etc., while the latter consists of the kidney, intestine, cecum, appendix, bladder, ovary, uterus, etc. Once the site under consideration is determined, the tissue composition can be derived. Then, through measurement and analysis, the distance from the lesion to the collection surface (i.e., d), as well as the travel thickness in each type of tissue (X 1 , X 2 , X 3 , . . . , X n ) can be obtained. If X i ≠ 0 (i = 1, 2, 3, . . . , n), it indicates that this kind of tissue structure exists between the lesion and the collection surface; otherwise, it does not.
Noteworthy is that, as stated earlier, the prerequisite for the system to have a unique solution is that the number of equations must be greater than or equal to the number of unknowns. This determines the required number of equations and Raman peak pairs. If the number of Raman peaks from SERS nanotags is over eight, 21 which corresponds to 28 or more pairs of Raman peaks, then this is typically sufficient for the prediction of lesion depth in the body. If some of those Raman peaks are disturbed by the tissue background, other approaches can be applied to construct more equations. For example, measurements with 180 • rotation can be performed, or more characteristic Raman peaks can be introduced by using different Raman reporters or adding more different types of SERS F I G U R E 7 Model for depth prediction of a surface-enhanced Raman spectroscopy (SERS) phantom in highly heterogeneous tissue. (A) Schematic of highly heterogeneous tissue, (B) theoretical natural logarithm plot of the Raman peak ratio and the depth of the SERS phantom, and (C) the corresponding system of equations for depth prediction using different Raman peak pairs. X 1 , X 2 , X 3 , . . . , and X n represent the thickness traveled by Raman photons in each tissue layer before being collected.
tags. 22 This highlights the many possibilities for simple and real-time depth prediction of deep-seated lesions in highly complex tissue samples (such as in vivo tumors), which are difficult to achieve by fluorescence detection techniques. It may also greatly accelerate the application of TRS in clinical noninvasive disease diagnosis with a depth prediction capability. Depth predictions of in vivo lesions are not shown in this work since reported Δµ for different tissues are incomplete and significant further work is still needed to collect tissue samples and measurements of Δµ.

CONCLUSION
We have predicted the depth of a SERS nanotag-labeled phantom inside various kinds of homogeneous or heterogeneous biological tissues based on the natural logarithm of RPR obtained from TRS measurements. Our work started with the theoretical study of photon propagation process in TRS, which revealed (1) a linear relationship between the natural logarithm of RPR and the depth, (2) the equivalence of the slope of the linear model to Δµ of two Raman photons and the equivalence of the intercept of linear model and the natural logarithm of the RPR of pure SERS nanotags, and (3) the negligible effect of tissue thickness, laser beam size, integration time, laser power, etc., on the linear relationship. These theoretical predictions were then validated through experiments using a home-built TRS setup and ultrabright SERS nanotags. High-accuracy depth predictions of SERS phantoms buried in different homogeneous tissues were achieved (2.42% RMSE in fat tissue, 5.83% RMSE in muscle tissue) under clinically safe laser irradiance. Moreover, the depth prediction of SERS phantoms in heterogeneous tissue was also achieved with an RMSE of 8.35% by combining multiple peak pairs from the Raman spectrum to form overdetermined equations. In addition, methods for depth prediction of SERS phantoms in highly heterogeneous tissues (such as real in vivo situations) without any prior knowledge, were also theoretically demonstrated. The proposed approach provides new insights into the use of Raman spectroscopy for depth prediction of lesions buried in kinds of turbid samples, and highlights the clinical potential of transmission Raman-guided noninvasive and rapid tumor depth estimation. This work provides a universal and reliable model for rapid and noninvasive depth estimation of imaging agentdecorated lesions for practical studies. We can predict the depth of lesions deeply seated up to several centimeters within different kinds of bio-tissues. If combined with our previous work, 13 this depth could possibly be further increased to more than 10 cm, using only simple Raman detection without any prior calibration technology. This would be very convenient and suitable for practical applications. In addition, further improvement of depth limit of our technique will largely advance the clinical theragnostic applications ranging from the design of therapeutic strategies to surgical planning and surgery guidance. For example, wavefront shaping can be used to achieve optical focusing deep inside scattering media for biomedical sensing, imaging, stimulation, and treatment, opening up new ways for noninvasive or minimally invasive optical interactions and arbitrary control inside deep tissues. 23 The integration of this technique with our TRS method is expected to further improve the depth limit on biological tissues. The applicable wavelength range of the proposed approach includes but is not limited to the visible and near-infrared (NIR) windows (including NIR-I and NIR-II) as long as Δµ ≠ 0. In addition, the power density of the incident laser used in the experiments is lower than MPE to the skin, which is essential for techniques proposed for clinical practice. This approach is promising for the noninvasive percutaneous detection and depth estimation of SLNs in patients, especially in obese patients where the SLNs are covered by thick fats. The application of the approach to SERS imaging to test samples and investigate the prediction of their position within 3D space is of great significance for the intraoperative noninvasive and accurate localization of SLNs in real time. Taking breast cancer SLN biopsy surgery as an example, this type of SLN is usually distributed several centimeters below the skin surface and cannot be directly observed by the naked eye even when the contrast agents (e.g., blue dyes) are applied. With the TRS technique, which possesses the deep layer detection and depth estimation capability, the location and depth of lymph nodes can be obtained percutaneous preoperatively, helping to make the surgical planning and greatly shorten the surgical procedure. Besides, the preknowledge of lymph node depth allows the surgeons to determine the incision location, protect the blood vessels near the chest and back, and avoid excessive movement of surrounding tissues. Furthermore, 3D tomographic imaging based on TRS could potentially be realized by using multiple pairs of laser-detector or rotating the laser-detector pair. Worthy to note is that, in this study, we focused on the establishment of depth prediction methods and the feasibility study of lesion depth prediction in thick heterogeneous tissues. In the future, in-depth studies based on this prediction model, such as accuracy, will be further explored. Overall, the capability of this method for detection and depth prediction of SERS nanotags in homogeneous and heterogeneous bio-tissues without any prior calibration technology promises future applications for noninvasive and real-time preoperative and intraoperative navigation.

Analytic expression of TRS in biological tissue
The photon propagation in the homogeneous tissue can be described using the RTE: where v represents the speed of light in the tissue, ( ,̂, ) represents the energy radiance at position r and the direc-tion̂at time t, µ a and µ s are the absorption and scattering coefficients, respectively, (̂,̂′) is the scattering phase function that describes the probability of scattering from tô′, and ( ,̂, ) is the light source term. For the TRS study, the steady-state solution of Equation (3) is established by setting ( ,̂, )∕ t = 0. The diffusion approximation can also be applied when photons propagate longer than the transport mean free path * = 1∕( a + ′ s ). In practice, the fluence ( , ) = ∫ 4 ( ,̂′, )̂′, that is, specific intensity, represents the local energy term for the next Raman excitation and final photon detection. Therefore, for > * , the steady-state diffusion approximation model for TRS is obtained in a 3D Cartesian coordinate system: where CW illumination is applied, the radius of illumination beam on the sample is a with the beam center at origin (0, 0, 0), I 0 represents the light source intensity, I is the intensity at (x, y, z), and = √ 2 + 2 + 2 is the distance between the beam center of the incident light and the SERS nanotag-labeled lesion. ′ s = s (1 − ) represents the effective scattering coefficient, where g is the anisotropy parameter, defined as the mean cosine of the scattering phase function (̂,̂′), = 1∕[3( a + ′ s )] represents the photon diffusion coefficient, and ef f = √ 3 a ( a + ′ s ) is the effective attenuation coefficient.
The steady-state light field of incident light excites the SERS nanotags, and then Raman photons are emitted. The emission of Raman photons is determined by both I(x 0 , y 0 , z 0 ) at the position of SERS nanotag-labeled lesion, the SERS cross-section (σ), and concentration (C) of SERS nanotags. A single SERS nanotag acts as the point source inside the tissue and produces Raman photons. Raman photons propagate through the tissue and again can be modeled using the steady-state diffusion approximation: wherẽe f f and̃represent the effective attenuation coefficient and photon diffusion coefficient of a Raman photon, respectively, and the distance between (x, y, z) and the SERS nanotag-labeled lesion is The TRS signals are detected at the transmitted surface ( , , d ) ∈ Ω + with Robin boundary condition. For depth prediction measurements, the intensity of Raman signal collected by a probe can be described by combining Equations (4) and (5): where T is the tissue thickness, d represents the depth of lesion, 0 = 2 0 is the power of light source, and λ 0 and λ i are the wavelengths of incident light and Raman light, respectively.

Chemicals
All chemicals were received commercially and used as received without any further purification.

Preparation and characterization of GERRTs
GERRTs were synthesized according to our previous work. 20 Firstly, petal-like gold (Au) nanoparticles were synthesized and served as core templates. 24 Then, 1.2 mL of IR-780 iodide (0.16 mM in DMF) was added slowly into 6 mL of Au core colloids (0.25 nM) under vigorous sonication and then incubated at 32 • C water bath for 1 h. Next, 7.2 mL of IR-780 iodide-modified Au core solution was added to a mixture of 15 mL of CTAC (25 mM), 2.4 mL of AgNO 3 (14.58 mM), and 11.25 mL of AA (40 mM) under vigorous sonication and then incubated in a 70 • C water bath for 3 h. Finally, the products were washed twice with CTAC (50 mM) to remove excess reagents, and the precipitates were redispersed in 2.5 mL of CTAC (10 mM).
The absorbance spectrum was obtained with a UV1900 UV-Vis Spectrometer (Aucybest, China). Raman spectrum of the GERRT colloids was measured using a portable Raman spectrometer (Cora 5700, Anton Paar, Austria) with 785 nm laser wavelength, 10 mW laser power, and 0.01 s integration time. TEM image was acquired with a JME-2100F transmission electron microscope (JEOL, Japan) operating at 200 kV.

Experimental setup of TRS
The transmission Raman setup used in these measurements was described in detail in our previous work. 13 For the transmission Raman setup with focused beam illumination, a portable Raman spectrometer equipped with a hand-held laser probe and a focusing lens was used as the laser device to produce a 785 nm laser beam, and the resulting focused laser beam was a typical Gaussian beam. The laser beam was incident on the tissue surface with a focal spot of ∼0.01 cm radius and 400 mW laser power, corresponding to 1.27 × 10 3 W/cm 2 power density. For a transmission Raman setup with diffuse beam illumination, we remove the focusing lens at the laser exit of the handheld probe. The diffuse beam emits from the laser probe first and is then reflected by a plane mirror to illuminate the bottom surface of the tissue stack. By adjusting the distance between the laser probe and the sample, the laser spot size at the sample surface could be adjusted. We controlled the laser spot size at the sample surface to ∼0.85 cm in radius, and laser powers of 100, 200, 400, or 600 mW was applied to produce a power density of 0.044, 0.088, 0.176, or 0.264 W/cm 2 . All these are lower than the MPE (1.627 W/cm 2 for 1 s exposure time and 0.296 W/cm 2 for over 10 s exposure time under 785 nm excitation). And 1 or 10 s integration time was applied in all TRS measurements. A fiber bundle probe that consists of six fibers arranged in a ∼0.2 cm diameter circle with a 300 µm diameter of each fiber and 500 µm working distance was connected to a Raman spectrometer (Andor back-illuminated deepdepletion CCD, EMvision HT-SPEC-785-01-IVAC spectrograph, EMvision HT-PROB-ENDO-785 Raman probe, −60 • C working temperature) and used to collect the Raman signals. The laser incident area and signal collection area are on the opposite sides of the tissues to form a transmission Raman geometry. An automatic XYtranslational stage was used to fix the fiber bundle and adjust the light path.

Ex vivo TRS signal measurements
All ex vivo porcine tissues (from part of the shoulder blade) were obtained fresh from a local market, frozen before use, and dissected into slices by an electric meat slicer (SL-518, Chigo, China) with an adjustable thickness (0.5−1.5 cm). The length and width of slices were both more than 5 cm to meet the experimental requirements. Considering the softness of tissue samples, a 10%−15% deviation in thickness is acceptable. For the ex vivo TRS signal measurements, a quartz tube (1 mm internal diameter, 2 mm external diameter, and approximately 10 cm length) filled with GERRT colloids (60 µL, 3.6 × 10 11 particles/mL) was embedded in the tissue stacks with different layers surrounded on each side. Therefore, the total thickness of the tissue can be tailored by decreasing or increasing the number of tissue sections. Meanwhile, the depth of GERRTs can be varied by simply changing the position of the quartz tube along the optical axis (z-axis) within the tissue slabs.

Data analysis
Fluorescence background of the raw spectra collected in the TRS measurements was first removed using adaptive iteratively reweighted penalized least squares (airPLS) method. The Raman intensity (̂) of one Raman peak was calculated as its maximum value, while the noise was calculated as the mean value (I noise ) in the region of 1650-1710 cm −1 , without specific Raman signals. Therefore, the final intensity of one Raman band in the spectrum was calculated as follows: =̂− noise . The Δµ of different Raman peak pairs obtained from the literature were calculated as follows. 19 The values of µ a and ′ s , obtained using time-domain diffuse spectroscopy from the literature, were first linearly interpolated. And then they were used to calculate the value of Δµ, that is, Δµ = µ eff (λ j ) -µ eff (λ i ), where ef f = √ 3 a ( a + ′ s ). Some values of µ a and ′ s obtained from literature are shown in Table S3. and the values of Δµ of different Raman peak pairs in porcine fat and muscle tissues are shown in Table S1.

A U T H O R C O N T R I B U T I O N S
Methodology, formal analysis, investigation, data curation, writing-original draft, and visualization: Yumin Zhang. Supervision, visualization, funding acquisition, and writing-review and editing: Li Lin. Project administration, validation, resources, funding acquisition, and writingreview and editing: Jian Ye. All authors have read and agreed to the published version of the manuscript.

A C K N O W L E D G M E N T S
We gratefully acknowledge the National Natural Science Foundation of China (No. 82272054), the Science and Technology Commission of Shanghai Municipality (No. 21511102100), Shanghai Jiao Tong University (Nos. YG2019QNA28 and YG2022QN006), and the Shanghai Key Laboratory of Gynecologic Oncology. We are also grateful for the support from the "Chenguang Program" supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission (21CGA09).

C O N F L I C T O F I N T E R E S T S TAT E M E N T
The authors declare no conflict of interest.

D ATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.