Acoustomotive diffuse correlation spectroscopy for sensing mechanical stiffness in tissue-mimicking phantoms

Many diseases, such as inflammation, dropsy, or tumors, often cause alterations in the mechanical stiffness of human tissues. Ultrasound-based techniques are commonly adopted in clinics for stiffness assessment, whereas optical methodologies hold promise for sensing strain changes and providing optical information pertaining to the microcirculatory network, thereby facilitating comprehensive measurements of tissue physiopathology. Diffuse correlation spectroscopy (DCS), an emerging dynamic light scattering technique, has been used to capture the enhanced motion of light scatterers induced by acoustic radiation force (ARF). Theoretically, the amplitude of this enhanced scatterers motion is related to the medium stiffness. Based on this relationship, we report a light coherent technique that combines ARF and DCS to qualitatively evaluate changes in the stiffness of medium. We experimentally demonstrate the accuracy and feasibility of this technique for probing stiffness in homogeneous phantom by comparing it with independent ultrasound methods. Additionally, we explore a potential application of this technique in distinguishing between fluid filled lesion and homogeneous tissue through heterogeneous phantom experiments. This unique combination of ARF and DCS, namely, acoustomotive DCS (AM-DCS), would provide an alternative way to measure particle-motion related stiffness, thereby assisting in the diagnosis and treatment of diseases.


Introduction
Tissue diseased conditions, such as inflammation, dropsy or tumors, are often accompanied by alterations in mechanical properties, such as stiffness and viscosity [1,2,3].In the past, the physicians often manually judge the pathological state of the tissue or organ by palpation, when the tissue mechanical properties differ significantly from those healthy tissue.As a diagnostic modality, however, palpation outcomes would be deviated by the sensing from different physicians, resulting in misjudgment when dealing with small or deeply located lesions [4].As such, many technologies have been developed for non-invasive assessment of the mechanical properties in various tissues or organs, including kidney [5], skeletal muscle [6], arterial wall [7], breast [2], and liver [8].The main principle of these techniques is to impose an internally [9] or externally [10] generated stress to the tissue and measure its strain response, from which viscoelastic information about the tissue can be extracted.Among these techniques, magnetic resonance elastography (MRE) and ultrasound elastography (UE) have been widely utilized [11].MRE is a time-consuming and expensive technique that requires unmovable heavy equipment [12].UE offers a cost-effective approach for stiffness assessment, but it does not provide information on tissue function at the microcirculatory level [13,14].Alternatively, optical methods could offer an approach to measure the stiffness of tissues, meanwhile providing additional optical information about the tissue, such as light absorption and scattering, which is associated with microcirculatory network [15][16][17].Over a decade of development, optical coherence elastography (OCE) has emerged as the most advanced and extensively employed method for detecting stiffness of biological tissues within optical-based techniques [18][19][20][21][22][23][24].OCE is developed from optical coherence tomography (OCT), which has the limited penetration depth (1∼2 mm in highly scattering media) [18,25,26,19], thereby constraining its clinical applications.For example, the breast cyst or tumor is commonly located approximately 10 mm below the breast skin [27,28], which is beyond the accessible depth by OCE.
Diffuse correlation spectroscopy (DCS) is a method with optical modality for microvascular blood flow measurements [29][30][31][32] that gains rapid development in recent years.DCS utilizes the long coherent light (> 5 m) in the near-infrared range (typically 650-950 nm) to illuminate the biological tissue [30,33].The light, when undergoing numerous absorption or scattering events, forms interference speckles on the surface of the tissue, are detected about 1∼3 cm away from the light source [30,32].The motion of the scatterers within tissue causes the interference speckle to fluctuate rapidly [31,32].Through calculating temporal-autocorrelation function of the single fluctuating speckle, the scatterer motion can be quantified as a blood flow index (BFI), which is denoted by αD B [31].There are typically two types of DCS measurements: reflective and transmissive modes.Reflective mode involves placement of the emitting source and detector fibers on the same side of the tissue surface [Fig.1(a)], which is suitable for most bulk tissues and can achieve a depth of detection of approximately 1.5 cm [30,31,32,33].By contrast, transmissive mode requires placement of the emitting source and detector fibers on opposite sides [Fig.1(b)], which is only suitable for thin tissues such as human finger.DCS is a portable, non-invasive modality with relative low-cost, making it ideal for longitudinal monitoring of patients in the clinic [30,34,35].The accuracy and feasibility of DCS for real-time measurement of tissue blood flow has been validated against other flow standards including 15 O-water PET [36], transcranial Doppler ultrasound [37], and perfusion MRI [38].Ultrasound is a mechanical wave that also has the advantage of non-ionizing and noninvasiveness.When ultrasound wave is launched into an elastic medium whose acoustic impedance is mismatches, ultrasound intensity will be attenuated.This phenomenon is caused by the momentum transfer between the acoustic wave and the medium, inducing resonance at a low frequency within the medium and thereby the acoustic radiation force (ARF) [39,40].As for the focused ultrasound, a few studies have demonstrated that the medium motion caused by the ARF is primarily concentrated near the focal spot, at dimensions ranging from nanometers to micrometers [41].On the other hand, our previous study has demonstrated the capability of DCS for probing the low-frequency strain [42].Theoretically, the local strain displacement occurring at the ultrasound focal spot should be highly associated with the stiffness of the medium [Fig.1(c)].Therefore, the combination of DCS and ARF holds promise for detecting tissue stiffness.However, the feasibility and efficiency of integrating DCS and ultrasound has not been fully explored.As one of the few examples, Robinson et al. [43] investigated the acousto-optic effect induced by high-frequency compression oscillations of ultrasound through combination with DCS.They proposed a comprehensive theoretical model to quantitatively extract flow index in the presence of ultrasound modulation.In our previous study [42], we compared the influences from different ultrasound parameters on the flow index when DCS was used to detect the flow enhancement by ARF.No report has been found on the use of DCS for sensing of tissue mechanical stiffness.
In this study, we present an optical technique for discriminating stiffness through combination of ARF and DCS, namely, acoustomotive DCS (AM-DCS).This combination enables the identification of accelerated optical speckle decorrelation resulting from scatterers motion induced by ARF in turbid medium.The stiffness-related scatterers motion within the turbid medium could be quantified through noninvasive DCS measurements, providing an indication of the medium stiffness.Through ultrasound field finite element (FE) simulation, we demonstrate a direct relationship between the amplitude of scatterers motion induced by ARF and the stiffness of medium.From the outcomes of the homogeneous phantom experiments, we confirm that DCS can effectively quantify the scatterers motion caused by ARF, with capability to discriminate different stiffness levels among phantoms.Moreover, we explore the potential application of this technique in differentiating between fluid-filled lesion and the homogeneous tissue through heterogeneous phantom experiments.

Ultrasound field FE simulation
Among the available numerical modeling tools for ultrasound physics, COMSOL Multiphysics performs excellently through constructing finite element (FE) model and solving the partial differential equations (PDEs) that depicts physical phenomenon (e.g., acoustic propagation and mechanical vibration) [44].The software also has the advantage that integrates different physical modules into a whole model, which permits to simulate ultrasonic system that also features elastic mechanical effects.Therefore, we used COMSOL Multiphysics (version 6.1) to simulate ultrasound field and amplitude of strain induced by ARF.The FE simulation was performed to demonstrate that the ARF-induced magnitude of strain correlates with medium stiffness, assisting in understand the principle of phantom experiments.
The FE model of ultrasound field was composed of acoustic emission system and the propagation medium, which are required for the coupling of multiple physical fields.An ultrasound array was created by setting 60 piezoelectric elements, at 0.3 mm apart between adjacent elements.By manipulating the acoustic emission time of each piezoelectric material (i.e., phase control), the ultrasonic waves could be focused at a target position.Specifically, the piezoelectric elements located on both sides were controlled to be initially excited, followed by the activation of the central piezoelectric elements, ultimately resulting in simultaneous arrival of ultrasonic waves from all emitting piezoelectric elements at the setting position and thereby achieving a focal effect.These focused ultrasonic waves were then propagated through a medium with the varied stiffness.In this study, three different modules were selected to simulate these physical effects in the COMSOL Multiphysics software: (1) a total of 60 piezoelectric materials module for the acoustic emission; (2) the elastic medium module with different stiffness; and (3) a low reflection boundary module for absorbing ultrasound at the boundary, with aim to minimize reflective effects.Figure 2 shows the geometric model of ultrasound field FE simulation.The elastic medium properties of the ultrasound field FE simulation are shown in Table .1.In the medium properties, we kept the speed of sound and the density constant, and defined Young's modulus of medium through manipulating the speed of shear wave, according to the following relationship [45].
Where E represents the Young's modulus, c T is the speed of shear wave.c L is the speed of longitudinal wave (i.e., the speed of sound).ρ is the density of medium.As shown in Table 1, for E = 7.08 kPa, 15.11 kPa, and 25.87 kPa, the speeds of shear wave are set to be 1.49m/s, 2.17 m/s, and 2.84 m/s, respectively.These values of Young's modulus were chosen to match the expected Young's modulus of the agar phantoms (i.e., phantom A, B, and C) used in phantom experiments (see section 2.4).According to the literature, the Young's modulus of normal human liver tissue is approximately 1.2 kPa, and the Young's modulus of cholangiocarcinoma is approximately 12.1 kPa [46].The Young's modulus of the medium in the ultrasonic field FE simulation falls within a comparable range to that of human tissue.Based on the uniform speed of sound and the density of the elastic medium in FE simulation, it is safe to conduct that the pressure and location of focal region of ARF is similar for all models, and therefore the magnitude of ARF should remain consistent.

DCS principle
The DCS has exhibited high sensitivity to the coherent light intensity fluctuations induced by moving scatterers and demonstrated the capability in detecting low-frequency strains within the medium caused by ARF [42].In this article, DCS was used as the monitoring modality to investigate the relationship between the magnitude of the motion induced by ARF and the medium stiffness.When the incident light at long coherent length is emitted into the turbid medium and experienced multiple events of absorption and scattering, the movement of scatterers within the medium will cause speckle fluctuations from the detected light on the medium surface.The intensity fluctuation caused by scatterers motion can be quantified by DCS through calculation of the normalized light electric field temporal autocorrelation function g 1 (τ), thereby enabling the extraction of the information about scatterers motion.The g 1 (τ) can be expressed as [30]: where E(t) represents the field of light electric at time t, ⟨ • ⟩ represents the time average, P(s) is the normalized distribution of the photon path length s, k is the number of light waves in the scattering medium, µ ′ s is the reduced scattering coefficient, ⟨∆r 2 (τ)⟩ is the unknown to be solved, which denotes the mean square displacement of the moving scattering particles, and τ is the delay time of the normalized electric field temporal autocorrelation function.For most cases, ⟨∆r 2 (τ)⟩ = 6D B τ, where D B denotes the diffusion coefficient of Brownian motion.Since the scatterers in the medium that do not move, do not contribute to the decay of the correlation function, a fraction α is defined to denote the percentage of moving scatterers to the total scatterers in the photon scattering event, i.e., ⟨∆r 2 (τ)⟩ = 6αD B τ.The αD B is referred to as the amplitude of motion of the optical scatterers.
In fact, the normalized light intensity temporal autocorrelation function, g 2 (τ), is feasible to obtain, rather than g 1 (τ).By measuring the light intensity, g 2 (τ) can be obtained by Eq. (3) through autocorrelation computation, and then the Siegert relationship equation [30] [i.e., Eq. ( 4)] is used to obtain g 1 (τ).In Eq. ( 4), β is a parameter which is depends on the laser stability, coherence length, and the number of speckles detected [30].The analytical solution of Eq. ( 2) allows for the extraction of αD B under a specific geometry.However, this analytical solution method is limited by the regular boundary and is proven to have errors in tissue geometries with large curvature [47].Previously, we proposed an Nth-order linear (NL) algorithm that utilizes Nth-order Taylor polynomial expansion [i.e., Eq. ( 2)] to overcome the limitations of irregular tissue boundary and extract αD B by using an iterative linear computational strategy.In this study, the NL algorithm was adopted to extract αD B [48,49].In addition, the Verasonics Vantage research system (Vantage 64 LE, Verasonics Inc., USA), a commercial ultrasonic research platform, was adopted as the ARF generator.In recent years, the Vantage system has been widely used in ARF experiments [50,51], demonstrating its capability to produce ARF at sufficient magnitude.An ultrasound transducer (UST) was connected to the Vantage system via a 260 pin universal transducer adapter (Model L11-5 v, with 128-element piezoelectric linear array).The Vantage system was connected to a customized host computer via PCIe express cable.The L11-5 v was controlled to send or receive ultrasound signals by using MATLAB program.The specifications of L11-5 v UST are listed in Table 2.

Module (Unit) L11-5v
Bandwidth [Min, Max] (MHz) [5,11] Elevation focus (mm) 18 All of hardware components mentioned above were placed on the optical table to avoid ambient vibrations.The MMF (source fiber) and SMF (detector fiber) were placed on the both side of UST.When MMF emitted NIR laser beam to illuminate the phantom, the DCS will output the αD B that was associated with the fluctuations of the moving scatterers in the phantom.With this configuration, a background αD B was obtained in the absence of the ARF, which was defined as αD BG B .When an elastic medium was subjected to ARF, the ultrasound will strengthen the movement of optical scatterers inside the medium, and elevating the decay of light electric field autocorrelation function simultaneously.With the ultrasound modulation, there was an increase in αD B , defined as αD M B .Finally, we calculated the term of interest, ∆αD B [see Eq. ( 5)], representing the enhancement of scatterers motion solely induced by ARF.The motion of the scatterer induced by the ARF was proportional to the magnitude of ∆αD B .Theoretically, within the low stiffness medium, the ARF leads to larger scatterers motion, indicating a higher value of ∆αD B .On the contrary, the high stiffness medium leads to lower value of ∆αD B .

Phantoms
In this study, a total of four phantoms were designed: three homogeneous semi-solid phantoms; and one heterogeneous phantom composing of both semi-solid and liquid components.Three homogeneous (50×80×50 mm 3 ) phantoms was made with different agar powder concentrations (0.5%, 0.75% and 1%, mass concentration) and 0.4% Intralipid (volumetric concentration).The agar was chosen due to fact that different concentrations of agar powder provide different levels of stiffness for the phantom, e.g., the higher concentration of agar yields higher stiffness of phantom, meanwhile keeping the acoustic impedance constant [16,17].Moreover, agar exhibits minimal light scattering, allowing the optical scattering coefficient of phantom to be well controlled using Intralipid.A concentration of 0.4% Intralipid was used to provide similar optical scattering coefficient (the reduced scattering coefficient is set to be around 5 cm −1 [16]).The optical scattering coefficient of all agar phantoms was expected to be identical, as they all contained the same concentration of Intralipid (0.4%).These homogeneous phantoms were employed to investigate the capability of AM-DCS in detecting variations in mechanical stiffness.We labeled these semi-solid homogeneous phantoms as phantom A, phantom B, and phantom C, according to the agar concentration from lowest to highest (stiffness from low to high).
A heterogeneous phantom (50×80×50 mm 3 ) was made for the purpose of mimicking cystic tissue.The heterogeneous phantom is composed of two components: a semi-solid phantom made with 0.5% agar (same with phantom A) and 0.4% Intralipid, to mimic the tissue surrounding pus, and a cylindrical liquid phantom inclusion, to mimic the pus.The cylindrical liquid phantom (with 6 mm in diameter and 30 mm in height) was made through mixing the distilled water, Intralipid and glycerol.The distilled water was utilized as the baseline solution, and the Intralipid is used to provide the same optical scattering coefficient as homogeneous phantoms.The glycerol was adopted to lower the viscosity of the liquid inclusion, and the lower viscosity will cause a decline in αD BG B of the heterogeneous phantom.As such, the αD BG B measured on heterogeneous phantom was identical to the αD BG B measured on homogeneous phantom A. The viscosity of the liquid phantom was measured for 10 times by a viscometer (NDJ-9S, Lichen Inc., China), and was set to be 0.92 ± 0.06 mPa•s (mean ± standard deviation) at a temperature of 18.6 °C.We labeled the heterogeneous phantom as phantom D. Figure 4 shows the schematic geometry of three homogeneous [Fig.4(a)] and one heterogeneous phantom [Fig.4(b)].In summary, all these phantoms had similar optical scattering coefficient.However, the three homogeneous phantoms had different mechanical stiffness (phantom A < phantom B < phantom C); the semi-solid components in phantom A and phantom D were expected to have the same stiffness; phantom A and D had the same αD BG B measured in AM-DCS at reflective mode (i.e., the direction of light incidence and ultrasound propagation are both parallel to the Z-axis shown in Fig. 4(a)).

Experimental setup
There were two different optical configurations for the phantom experimental setup: reflective mode [Figs.light source fiber and detector fiber are positioned at opposite side, with a kernel-shaped light energy distribution.In all phantom experiments, including both homogeneous and heterogeneous phantoms, the ARF excitation function was implemented using a long sinusoidal pulse (length of the pulse was set to be 2 × 10 −4 s) with an amplitude of 65 V and a frequency of 5 MHz to ensure consistent intensity of the generated ARF within the phantom for facilitating subsequent result comparison.The ultrasound power after transducer lens and coupling attenuation is around 16 mW/cm 2 , which is within safety limit of clinical ultrasound [52].
In addition, the water content in agar-based phantoms gradually diminishes over time, potentially affecting their stiffness.Therefore, all phantom experiments were conducted within 12 to 24 hours after phantom fabrication (allowing for a solidification period of 0 to 12 hours) in order to minimize the effects and ensure experimental reproducibility.

Measurements on homogeneous phantoms
In order to investigate the relationship between phantoms mechanical stiffness and ∆αD B defined in Section 2.3, three homogeneous phantoms at the varied agar concentrations were measured in both reflective and transmissive modes.This approach was used to demonstrate that AM-DCS was able to capture mechanical stiffness information from different modalities.Figures 3(c) and 3(d) show the measurement set-up of the homogeneous phantom experiment in reflective mode and transmissive mode, respectively.In both modes of optical measurement, the phantom was positioned within 3D printed container of appropriate dimensions and filled with degassed water.The line-array UST (L11-5 v) was situated 2 mm above the phantom, while the focal depth of UST was set to be 12 mm.The differences between the reflective mode and transmission mode were: (1) In the reflective mode [Fig.3(c)], the light source fiber and the detector fiber, composed of metal, were positioned parallel to each other and in direct contact with the surface of the homogeneous phantom.In order to avoid possible deformation of phantom, the source-detector (S-D) separation was set at 26.4 mm, while the ultrasound transducer was centrally located between them.(2) In the transmissive mode [Fig.3(d)], the light source and detector fibers were aligned in opposition to each other and positioned within homogeneous phantom, precisely 12 mm below the UST (10 mm beneath the surface of the phantom), and S-D separation was set to be 25 mm.

Differentiating between tissue with a fluid filled lesion and homogeneous tissue
To demonstrate the potential of AM-DCS in clinical practice, we adopted phantom D as a model for mimicking cystic tissue, as described in Section 2.3.Subsequently, AM-DCS was utilized to differentiate between the tissue containing a fluid-filled lesion (phantom D) and the homogeneous tissue (phantom A).In the heterogeneous phantom experimental setup, the reflective mode of optical measurement was adopted, because it is more commonly used in clinical practice [35,53,54].This choice stem from the fact that the transmissive mode of measurement is only applicable to thinner tissues where light can penetrate, whereas cysts are typically located within thicker tissues.Figure 3(e) illustrates the measurement configuration of the heterogeneous phantom experiment.The phantom D was placed within a suitably-sized container fabricated via 3D printing.The liquid on the surface of phantom D is same as the cylindrical liquid inclusion which is filled above the phantom D. Similar to the water, its role is to serve as a coupling medium for ultrasound propagation.The UST was positioned 2 mm directly above the cylindrical liquid inclusion of phantom D, with a focal depth of 12 mm.The light source and detector fibers were configured at reflective mode, with a S-D separation of 26.4 mm.And the optical fibers were set to be exactly in contact with the surface of phantom D. The relative spatial arrangement of the UST and the optical fibers for heterogeneous phantom experiment was consistent with that in the reflective mode for the homogeneous phantom experiment.

Comparison to ultrasound shear wave elastography
To independently test the relative magnitude of mechanical stiffness of homogeneous phantoms, we used the Vantage 64 LE system for shear wave propagation imaging of phantom A, B, and C, respectively.Theoretically, the mechanical stiffness of the medium is directly proportional to the shear wave velocity [9].Specifically, a faster shear wave velocity indicates a larger Young's modulus of the medium.
The software for the Vantage 64 LE system includes an official MATLAB script called "SetUpL7_4ShearWaveImaging", which is specifically designed for the L7-4 UST model.This script enables users to emit focused ultrasound waves with user-defined parameters in order to generate ARF within medium and subsequently produce shear waves for imaging their propagation.We adapted this script to accommodate the L11-5 v transducer, allowing us to image shear wave propagation in phantom A, B, and C for comparative analysis of their relative stiffness.In this study, the script was utilized for visualizing shear wave propagation in homogeneous phantoms and qualitatively comparing the velocities of shear wave in phantom A, B, and C.
The ultrasound shear wave propagation experiments were just for independently validate the relative stiffness of three homogeneous phantoms by using the conventional US methods rather than AM-DCS.The ultrasound shear wave propagation experiments were conducted immediately after the AM-DCS phantom experiments, permitting us to qualitatively compare the relative stiffnesses of phantom A, B, and C.This comparison aimed to independently estimate the relative stiffness of the homogeneous phantoms through the well-established US methods, thereby assessing the reliability of the AM-DCS experimental results.
The semi-solid component of phantom D has the same concentration of agar as phantom A, and it is therefore expected to have the same stiffness as phantom A. Furthermore, the inclusion of phantom D is a liquid inclusion, the determination of the liquid stiffness is usually not taken into account.Moreover, the liquid inclusion occupies only 0.4% of the volume of the phantom D [see Fig. 4(b)].Therefore, it can be inferred that the presence of the liquid inclusion has negligible impact on the stiffness of the phantom D.More importantly, the heterogeneous phantom experiments [Fig.3(e)] were designed to demonstrate the capability of AM-DCS to distinguish between phantom D (mimic tissue with a fluid filled lesion) and phantom A (mimic homogeneous tissue), rather than quantifying the absolute value of stiffness for phantom D or phantom A. Hence no needs to evaluate the stiffness of the phantom D.

Results of ultrasound field FE simulation
The ultrasound field FE simulation was conducted to demonstrate that mediums with different Young's modulus exhibit varying magnitudes of strain response under the same intensity of ARF excitation, which is the basic assumption that the AM-DCS system is capable for sensing the mechanical stiffness of medium.In the FE simulation, three simulations were conducted at different values of Young's modulus (E = 7.08 kPa, E = 15.11kPa, and E = 25.87 kPa, according to the literature [55], these values of Young's modulus are the same as the expected Young's modulus of agar phantoms) for the ultrasonic propagation medium.To ensure uniformity of the ARF at the focal spot in all three simulations, a consistent excitation of 60 piezoelectric elements was employed in each simulation.The excitation was achieved with an identical sinusoidal long-pulse function, lasting for a total of 10 cycles, at an amplitude and frequency set at 65 V and 5 MHz respectively.
The ultrasound focusing area in the FE simulation was represented by a circle centered at coordinates (0, -10) with a diameter of 0.1 mm (see Fig. 2 for the specific location).Figure 5 demonstrates a comparison of the strain displacement response at the ultrasound focusing area for three mediums with different stiffness after being excited by the same intensity of ARF.Through sequentially exciting the piezoelectric materials located at the two sides and finally exciting the piezoelectric materials positioned in the middle, we achieved a focusing effect as described in Section 2.1.After the central piezoelectric material was excited, making an acoustic wave reach the focal point (indicating completion of the focusing effect) at approximate 13.46 µs.Therefore, in Fig. 5, we select the displacement data at times 15 µs, 16 µs, and 17 µs as representative outcomes.As shown in Fig. 5, the displacement response consistently exhibits a smaller magnitude in ultrasonic propagation media with higher Young's modulus under the same intensity of ARF excitation.

Characterization of phantom stiffness by US
The speed of shear wave propagation is directly proportional to the stiffness of the medium.i.e., the faster shear wave propagation indicates the harder medium.Figure 6 shows the typical images of the visualized shear wave propagation at different frame counts, which were obtained from experimental measurements through the Vantage ultrasound research platform on phantom A, B, and C. It should be noted that an increase in frame number displayed in the shear wave visualization image corresponds to a longer time duration.Evidently, the time-course increase in shear wave velocity sequentially from phantom A to B and C indicates a gradual elevation in stiffness across the phantoms.This section was designed to independently validate the relative hardness of the homogeneous phantoms by using the conventional methods rather than AM-DCS, in other words, the higher agar concentration indeed leads to the increased hardness.Because the unavailability of inter-frame times for ultrasound shear wave images, the shear wave propagation images do not include functions for quantitative calculation of shear wave velocity (Young's modulus).The adoption of agar concentration as a way to adjust phantom stiffness has been reports in relevant studies [16,17,56], further demonstrating the feasibility of the methodologies proposed in this study.

Results for homogeneous phantom with AM-DCS
Figure 7 and Fig. 8 exhibit the graphs of the measurement results obtained from the three homogeneous phantoms by using AM-DCS in both reflective mode and the transmission mode, respectively.Figure 7(a) (or Fig. 8(a)) illustrates the 20 data points (αD BG B ) measured in the absence of ARF, as well as the subsequent measurements of another set of 20 data points (αD M B ) obtained in the presence of ARF by using the AM-DCS in reflective mode (or transmission mode).As expected, in the absence of ARF, the αD BG B exhibits a sequential decline with the increasing stiffness from phantom A to phantom C.This is because the αD B directly reflects the amplitude of light intensity fluctuations caused by the motion of the optical scatterers.Through this physical relationship, the DCS provide an effective tool to observe the microscopic origin of the viscoelastic properties of soft materials [57].At microscopic level, a larger stiffness is associated with a stronger attractive tension between the scatterers, subsequently reducing their random motions (i.e., smaller αD BG B ).In the presence of ARF, a sequential decrease in αD M B is observed as stiffness was increased from phantom A to phantom C. To investigate the data fluctuation, the coefficient of variation (CV, defined as CV = Standard deviation / mean) over the 40 data points (20 for αD BG B and 20 for αD M B ) were calculated.The outcomes show an elevating trend with the increase of phantom stiffness in both αD BG B and αD M B , as illustrated in Fig. 7(c) and Fig. 8(c).Moreover, the data variations observed throughout the measurement period are minimal (CV < 10%), indicating a high stability for both αD BG B and αD M B .To demonstrate the capability of AM-DCS in differentiating the medium with the varied mechanical stiffnesses at depth of centimeter, we extracted the ∆αD B from phantom A, B, and C, as shown in Fig. 7(b) [reflective mode] and Fig. 8(b) [transmissive mode], respectively.As is clearly seen, ∆αD B decreases significantly as the stiffness of phantoms elevates (from phantom A to C).Specifically, from phantom A to C, the AM-DCS measurements yielded ∆αD B : 1.50 × 10 −9 cm 2 /s, 0.48 × 10 −9 cm 2 /s, 0.27 × 10 −9 cm 2 /s (in reflective mode); 1.94 × 10 −9 cm 2 /s, 1.04 × 10 −9 cm 2 /s, 0.57 × 10 −9 cm 2 /s (in transmissive mode).Moreover, when measured on the softest phantom A, ∆αD B reaches 49.6% (in reflective mode) and 59.3% (in transmissive mode) of the αD BG B ; when measured on the phantom B, ∆αD B reaches 26.7% (in reflective mode) and 63.1% (in transmissive mode) of the αD BG B ; when measured on the hardest phantom C, ∆αD B reaches 33.2% (in reflective mode) and 78.3% (in transmissive mode) of the αD BG B .

Results for cyst-like heterogeneous phantom with AM-DCS
The AM-DCS can effectively discriminate between liquid and semi-solid regions through observing the phenomenon of acoustic streaming.Specifically, the ARF induces a bulk steady motion in liquids which is termed as acoustic streaming, whereas in solids, no such streaming is generated.To demonstrate the potential of AM-DCS for clinical applications, we conducted the reflective measurements in the cyst-like heterogeneous phantom D, as well as in the homogeneous phantom A. The obtained results and their corresponding analyses are presented in Fig. 9.The 20 data points (αD BG B ) measured before the activation of the ARF and the 20 data points (αD M B ) measured after its activation by using the AM-DCS on the phantom D and phantom A are illustrated in Fig. 9(a).It is evident that in the absence of ARF, the background motion of scatterers exhibited similar sizes between phantom D and phantom A, i.e., similar sizes of αD BG B .In the presence of ARF, phantom D exhibits a significantly higher αD M B than phantom A. Specifically, the average αD M B in phantom D and phantom A are 7.76 × 10 −9 cm 2 /s (phantom D), and 4.58 × 10 −9 cm 2 /s (phantom A), respectively.The CV over the 40 data points (20 for αD BG B and 20 for αD M B ) obtained from both phantom D and phantom A were calculated.Figure 9(c) illustrates the CV for αD BG B and αD M B , indicating that both phantom A and phantom D exhibit stability of αD BG B and αD M B (CV less than 5%). Figure 9(b) shows the ∆αD B measured by AM-DCS when ARF is applied on the liquid inclusion of the cyst-like phantom D, as a comparison with phantom A (semi-solid homogeneous phantom).As expected, the ∆αD B measured on the phantom D exhibits a significantly larger magnitude when compared with that measured on the phantom A, in the case of similar αD BG B .
The reason for this phenomenon is probably that, in liquids, the ARF induces a bulk steady motion which called acoustic streaming, whereas in solids, no such streaming is generated.The appearance of acoustic streaming in AM-DCS measurements is evidenced by a significantly larger ∆αD B , as observed in this experiment where the ∆αD B for phantom D and phantom A are 4.73 × 10 −9 cm 2 /s (phantom D) and 1.57 × 10 −9 cm 2 /s (phantom A), respectively.Notably, the ∆αD B of phantom D is 301% of the phantom A. The results of cyst-like heterogeneous phantom experiments demonstrate that AM-DCS exhibits significantly higher sensitivity in detecting ∆αD B in liquid area (fluid filled lesion) compared to semi-solid area (homogeneous tissue).

Discussion
To the best of our knowledge, the study is the first attempt to use DCS for stiffness measurement, and presents a potential for clinical applications through cyst-like phantom experiments.The AM-DCS utilizes the well-established dynamic light scattering technique, DCS, which enables quantitatively and continuously measurement of stiffness-related scatterers motion induced by ARF.This unique capability holds promise for facilitating stiffness measurements in vivo and in vitro, offering a valuable tool for scientific research.
Compared with the ultrasound elastography (e.g., ultrasound shear wave elastography), AM-DCS offers the extra blood flow information at a microvasculature level which is directly relevant to the functional information of human tissues.Furthermore, the utilization of the optical fiber in AM-DCS also facilitates integration with diffuse optical spectroscopy (DOS, a well-established optical technique for blood oxygen information).The integration of blood flow and blood oxygenation information can provide insights into the neoangiogenesis which is associated with autonomic growth and spread of tumors [58,59].This approach provides multiple dimensions of information, and our future work will focus on developing this technique and investigating the role of ARF in the proposed AM-DCS technology.
As a well-established technique, the ultrasound elastography focuses primarily on the macroscale property of tissue stiffness, but less related to microvasculature level of tissue such as cell metabolism.In this study, we propose AM-DCS as a pilot combination of ARF and DCS for tissue stiffness measurement.Although the accuracy and stability of AM-DCS measurements may not be comparable to the ultrasound elastography, the functional information of tissue provided by AM-DCS would be more directly linked to physiological pathology, thus serving as a foundation for future in-depth research on diseased-related tissue malfunctions.The aim of this study is not to replace the ultrasound elastography, but rather to establish a correlation between the microscopic tissue environment (i.e., the motion of red blood cells, RBCs) and macroscopic tissue stiffness, thereby serving as an alternative to the existing ultrasound techniques.The combination of US techniques and AM-DCS holds promise for identifying new disease-related biomarkers in the future.
Previously, Li et al. [17,56] and Cheng et al. [16] proposed a static optical technique (solely measuring light intensity, primarily focusing on light absorption effects) with a conventional CCD camera serving as the detector, with aim to assess the local velocity of shear waves induced by ARF as well as determine the stiffness at depths of centimeters in the phantom.In their measurements, the scatterer displacement caused by ARF in the optical signal was considered as noise.The fluctuation of the optical signal resulting from scatterer displacement was mitigated by adjusting CCD exposure time.Additionally, these results were exclusively presented under the transmissive mode.The transmissive mode is only able to assess thin tissue that allows light to pass through it, while the reflective mode enables the measurement of thicker tissue that is more realistic in clinical setup.Compared to this approach, the AM-DCS differs fundamentally in principle as we primarily assess the motion of optical scatterers induced by ARF.Additionally, we present results obtained from both transmissive and reflective optical measurement modes, both of which exhibit a satisfied signal-to-noise ratio.
The resolution of AM-DCS is constrained by the size of the ARF focal spot region, which is inherently linked to the frequency of ultrasound.Specifically, at a fixed focal length, a higher ultrasound frequency corresponds to a smaller size of focal spot region.Therefore, the resolution of AM-DCS can be enhanced by employing high-frequency ultrasound.
Theoretically, the maximal detection depth of the AM-DCS is determined by the detection depth of the DCS.The detection depth of the DCS is up to ∼1.5 centimeters [33], thereby permitting the AM-DCS to effectively sense the stiffness variations within this range.Spatial sensitivity maps are commonly adopted for investigating the detection depth in field of diffuse optical methods, where the regions with larger spatial sensitivity contribute more to the global signal [60].Specifically, at a fixed source-detector separation, when the ARF acts on a larger spatial sensitivity region, the AM-DCS produces a larger ∆αD B .The spatial sensitivity map of the DCS, which could be estimated through Monte Carlo simulation, is illustrated in Fig. 10.The reflective and transmissive modes corresponding to the phantom experimental configuration are depicted in Figs.10(a) and 10(b), respectively.Monte Carlo simulations were performed by using MCVM software [61] and the optical property parameters used for the simulations were consistent with the agar phantoms (absorption coefficient µ a = 0.1 cm −1 , reduced scattering coefficient µ ′ s = 5 cm −1 , refractive index n = 1.37, anisotropy factor g = 0.9) [15].For reflective mode [Fig.10(a)], an increase in the penetration depth leads to a reduction in optical spatial sensitivity as well as a decreased signal-to-noise ratio of the AM-DCS signal.For transmissive mode [Fig.10(b)], the AM-DCS signal exhibits a high signal-to-noise ratio (i.e., high spatial sensitivity) across the entire detection area, with the maximal signal-to-noise ratio observed in area of the proximity to both the light source and detector.How to explore the DCS capability for depth discrimination has emerged as a critical challenge for researchers in the field of diffuse optics, and several studies have made efforts towards this goal [62,63].The combination of these techniques and AM-DCS would be an efficient way to achieve the depth discrimination measurements.On the other hand, however, the spatial sensitivity of DCS varies at different depths (see Fig. 10), even ARF at the same magnitude may not equally enhance the diffusion coefficient at the different depth locations in the medium.Therefore, a significant challenge exists for effectively manipulating the DCS spatial sensitivity as well as diffusion coefficient contrast between different depths within the medium (e.g., malignant tumors and surrounding healthy tissues), thereby facilitating accurate diagnosis of various diseases.
ARF is a form of volume force generated from ultrasound waves within medium, and the medium displacement induced by the focused ultrasound has been demonstrated to primarily localize around the focal spot.The ARF can induce tissue compression oscillations at the micron level and generate shear waves perpendicular to the direction of ultrasound propagation.Both effects can be used to measure the stiffness of medium.The amplitude of tissue displacement exhibits a negative correlation with Young's modulus, which has been validated by ultrasound field FE simulation (see Fig. 5), and the velocity of shear wave propagation demonstrates a positive correlation with Young's modulus (see Fig. 6).The AM-DCS measures tissue stiffness through the enhanced motion of optical scatterers by ARF and an increased decay of the light autocorrelation function, indicated by a higher αD B .The term of interest ∆αD B , which is defined through subtraction, was used to indicate the degree of enhancement in scatterers motion.A larger ∆αD B represents a more pronounced enhancement in the motion of scatterers, implying a smaller stiffness (or Young's modulus).Additionally, the subtraction helps reduce the system fluctuations from ambient noise and drift in light intensity.
For AM-DCS experiments, we used static semi-solid medium as the experimental phantom, without the influence from blood flow and tissue pulsation.According to the physical principle of dynamic light scattering [31,34,54], what the DCS measures is the averaging movement of red blood cells (RBCs) over a bulk of microvasculature network, rather than the blood flow velocity in a large vessel (e.g., the major cerebral artery).The Brownian motion, instead of directional flowing along the vessels, is the dominant manner of RBC movement within the relative static capillary system.Therefore, in the absence of stimulating physiological activity such as muscle contraction, the motion of RBCs within the static capillary system typically remains relatively stable during the time required for AM-DCS to measure a single ∆αD B data.For future in vivo measurements, the defined term of interest, ∆αD B , is capable of minimizing the influence of blood flow and tissue pulsation through subtraction [see Eq. ( 5)].Further studies will be conducted to assess the influence of RBC movement on estimating the tissue stiffness.
With the aim to explore the capability of AM-DCS in discriminating the stiffness changes of the medium, we fabricated three homogeneous phantoms at varying stiffnesses and presented the measurement outcomes of AM-DCS in both transmissive and reflective modes.According to the literature [55], the estimated Young's modulus of agar phantoms (phantom A, B, and C) was reported as 7.08 kPa, 15.11 kPa, and 25.87 kPa.Therefore, the estimated change in Young's modulus for agar phantoms were ranged from 8.07 kPa to 10.76 kPa.The results of the phantom experiments (Fig. 7 and Fig. 8) demonstrate that the ARF has a significant impact on improving αD B in both transmissive and reflective modes.Moreover, the correlation analysis between Young's modulus and ∆αD B of agar phantoms (phantom A, B, and C) was performed.We observed a negative correlation between Young's modulus and ∆αD B of agar phantoms at both reflective mode (r = -0.9)and transmissive mode (r = -0.97).These promising findings highlight the robust discriminatory capability of AM-DCS in detecting variations in medium stiffness.
In Fig. 7(b) and Fig. 8(b), the ∆αD B at reflective mode is consistently slightly lower than that at transmissive mode within the same phantom.This discrepancy can be attributed to the reduced optical spatial sensitivity of photons in reflective mode at the ultrasonic focal spot, when compared with that at transmissive mode (see Fig. 10).Consequently, the scatterers displacement induced by ARF at same magnitude would result in a smaller increase in ∆αD B at reflective mode when compared with those at the transmissive mode.
In both reflective (Fig. 7) and transmissive (Fig. 8) homogeneous phantom experiments, the phantoms utilized had an identical composition and were fabricated following the same standardized procedures.Theoretically, the αD BG B measured by AM-DCS should be the same in reflective [Fig.7(a)] and transmissive [Fig.8(a)] homogeneous phantom experiments.However, there is a constant increase in the αD BG B for the phantoms in the reflective mode, but not in the transmissive mode.The distinct source-detector fiber arrangements in the reflective [Fig.1(a)] and transmissive [Fig.1(b)] modes contribute to this phenomenon.In this study, we employ the NL algorithm for extraction of αD B .Although the NL algorithm has demonstrated its versatility in accommodating various source-detector placements [48,49], it is inevitable to encounter deviations when dealing with two distinct source-detector configurations.
To demonstrate the potential clinical applicability of AM-DCS, we fabricated a heterogeneous phantom to simulate fluid filled cyst.The aim is to utilize AM-DCS for distinguishing between fluid filled lesion (which exhibits no stiffness) and homogeneous tissue (which exhibits stiffness) in the case of similar background moving scatterers (i.e., similar αD BG B ).The results of heterogeneous phantom experiments (Fig. 9) demonstrated that the ∆αD B measured by AM-DCS on the phantom for mimicking fluid filled lesion was 301% of the measured on the phantom for mimicking homogeneous tissue.These discoveries suggest that AM-DCS demonstrate potential in discriminating between fluid filled lesion and homogeneous tissue.As the pilot study to experimentally estimate the stiffness of medium, we have not placed another layer of the phantom on the top of the current heterogeneous phantom [Fig.4(b)], with aim to avoid complicated manufacture of phantom.Adding a layered phantom on top of heterogeneous phantom (phantom D) will inevitably create a small gap between the two, consequently resulting in ultrasonic distortion.The current manufacturing processes generates significant challenges in achieving a fluid-filled phantom without any internal gaps, making it difficult to fully replicate the structure of a real cyst by using such phantoms.Moreover, it has been demonstrated that ARF can generate an acoustic streaming within human breast tissue, which remains detectable even when the pus is covered by a layer of tissue [64].Therefore, AM-DCS has the potential to accurately identify cysts within human tissues.In future studies, we will further validate the feasibility of employing AM-DCS for cyst identification in both human and animal tissue samples.
The viscosity of cylindrical liquid phantom inclusion [see Fig. 4(b)] was set to be 0.92 ± 0.06 mPa•s (mean ± standard deviation) at a temperature of 18.6 °C.The cylindrical liquid phantom inclusion with such low viscosity cannot account for the propagation of shear waves.The ∆αD B reflects the amount of motion generated by ARF, consisting of the initial displacement at focus followed by the propagation of shear waves.Therefore, the absence of shear wave propagation results in a decrease in the ∆αD B that was observed in phantom D, when compared with that in semi-solid phantom A, wherein the propagating shear waves is possible.Figure 9(b) shows the ∆αD B of phantom D is 301% of the phantom A. Hence, if the liquid inclusions within phantom D were capable of propagating shear waves, the disparity of ∆αD B between phantom D and phantom A would exceed 301%.The present outcomes [Fig.9(b)] demonstrate that, even without the ∆αD B contribution from shear wave propagation, the 301% disparity remains large enough for AM-DCS to discriminate between phantom D (representing the cyst) and phantom A (representing homogeneous tissue).Therefore, the propagation of shear wave has minimal impact on the application of AM-DCS in differentiating between cyst and homogeneous solid tissue.
The presence of cyst lesion is typically determined by B-mode ultrasound imaging in clinical practice.Given the shared utilization of ultrasound transducers in both AM-DCS and B-mode ultrasound, these two technologies can be seamlessly integrated.The development of AM-DCS is not intended to replace B-mode ultrasound; rather, our aim is to enhance the identification of cysts and homogeneous tissue through providing an additional dimension of information.The AM-DCS and B-mode ultrasound imaging differ fundamentally in identifying cysts, and therefore AM-DCS can provide useful supplements for B-mode ultrasound.For instance, although most of normal cystic tissue can be identified by B-mode ultrasound imaging, a few small condensed breast cysts may exhibit as the pattern of internal hypoechoic areas which are similar with the solid lesions shown in B-mode ultrasound imaging, due to the reflection of ultrasound by cholesterol crystals, fat globules, and protein particles within the cysts [65,66,67].Therefore, the identification of small condensed cysts with solid lesions requires an experienced physician.Theoretically, ARF could produce acoustic streaming even in small condensed cysts.Hence, AM-DCS can reduce the burden of expertise physicians that uses B-mode ultrasound to detect small condensed cysts.Furthermore, AM-DCS offers valuable information of microvascular blood flow, an in vivo tissue functional information that is unavailable through B-mode ultrasound imaging.Therefore, the combination of B-mode ultrasound and AM-DCS allows physicians to comprehensively assess the physiopathology.

Conclusion
To conclude, we show a novel dynamic light scattering technique for stiffness measurement that combines DCS and ARF.This technique enables the discrimination of stiffness variations in turbid medium at centimeter depth, providing an alternate approach to detect strain displacements that could be a valuable complement to the existing ultrasound techniques.The feasibility and accuracy of this technique are verified through homogeneous phantom experiments, and the results are compared with ultrasound shear wave propagation imaging experiments.The outcomes derived from heterogeneous phantom experiments demonstrate the capability of AM-DCS to differentiate between fluid filled lesion and homogeneous tissue.Furthermore, both DCS and ARF are non-ionizing and non-invasive, thereby making AM-DCS suitable for future in vivo or in vitro applications.Future studies include development of a robust theoretical framework for the quantitative assessment of stiffness and application of this combined technique for clinical settings.

Fig. 1 .
Fig. 1.(a) Principle of reflective optical measurement mode.(b) Principle of transmissive optical measurement mode.(c) The radiation force induced by ultrasound causes a long displacement of the scatterers in soft medium, whereas it results in a short displacement of the scatterers in hard medium.

Fig. 2 .
Fig. 2. Geometrical model of ultrasound field FE simulation and the physical fields of each area.

2. 3 .Figure 3 (
Figure 3(a)  shows the hardware components of AM-DCS, including both optical and ultrasonic hardware.The custom-built DCS equipment is responsible for detecting the tiny particle vibrations induced by ARF and the ultrasonic equipment for generating ARF.As illustrated in Fig.3(a), a NIR laser (DL-785-120-SO, Crystallaser Inc., USA, 785 nm, 120 mW) at long

Fig. 3 .
Fig. 3. (a) The overview of AM-DCS system and phantom experiment.NIR: near infrared; MMF: multimode fiber for emitting photons; SMF: single mode fiber for receiving photons; UST: ultrasound transducer.(b) DCS measurement principle.(c) The side view of homogeneous phantom experiments set-up under reflective mode.(d) The side view of homogeneous phantom experiments set-up under transmissive mode.(e) The side view of heterogeneous phantom experiments set-up under reflective mode.

Fig. 4 .
Fig. 4. Schematic geometry of the phantoms.(a) Three homogeneous simi-solid phantoms (50 × 80 ×50 mm 3 ) with same optical scattering property and different mechanical stiffness (the greater darkness color indicates the higher level of stiffness, phantom A < phantom B < phantom C).(b) One heterogeneous phantom (50 × 80 ×50 mm 3 ) with a liquid cylindrical inclusion (with 6 mm diameter and 30 mm height) for mimicking cyst, wherein the semi-solid component of phantom D (with same stiffness of phantom A) was used to mimic the tissue surrounding pus and the liquid inclusion was used to mimic the pus.The phantom D had the same optical scattering property and αD BG B as phantom A.
3(c) and 3(e)] and transmissive mode [Fig.3(d)].The two configurations correspond to distinct spatial arrangements of the light source fiber and detector fiber.Under the reflective mode [Fig.1(a)], light source fiber and detector fiber are positioned in parallel, resulting in a banana-shaped distribution of light energy.By contrast, under the transmission mode [Fig.1(b)],

Fig. 5 .
Fig. 5. Comparison of the strain displacement response at the ultrasound focusing area for three mediums with different stiffness after being excited by the same intensity of ARF.The displacement exhibits a decrease with the increment of the Young's modulus of the medium.

Fig. 6 .
Fig. 6.Representative graphs of shear waves propagation in three homogeneous phantoms with varying stiffnesses, when being subjected to the same size of ARF excitation.(a)-(d) images are for phantom A; (e)-(h) images are for phantom B; (i)-(l) images are for phantom C. For each phantom type, images at the 3rd, 7th, 11th, and 15th frames are displayed to illustrate the increasing propagation time of shear waves.

Fig. 7 .
Fig. 7. Measurement outcomes from the homogeneous phantoms by using AM-DCS in the reflective mode and their corresponding analytical plots.(a) in the reflective mode, αD B values obtained from AM-DCS measurements on phantom A, B and C before (αD BG B ) and after (αD M B ) ARF action.(b) Comparison of ∆αD B obtained from AM-DCS measurements on phantom A, B and C in reflective mode.Error bars: standard deviations.The * indicates a statistically significant difference among the ∆αD B of phantom A, B, and C (Tukey comparison of ANOVA at α=0.05, * p < 0.05).(c) The coefficient of variation (CV) of αD BG B (at ARF absent stage) and αD M B (at ARF present stage).

Fig. 8 .
Fig. 8. Measurement outcomes from the homogeneous phantoms using AM-DCS in the transmissive mode and their corresponding analytical plots.(a) in the transmissive mode, αD B values obtained from AM-DCS measurements on phantom A, B and C before (αD BG B ) and after (αD M B ) ARF action.(b) Comparison of ∆αD B obtained from AM-DCS measurements on phantom A, B and C in transmissive mode.Error bars: standard deviations.The * indicates a statistically significant difference among the ∆αD B of phantom A, B, and C (Tukey comparison of ANOVA at α=0.05, * p < 0.05).(c) The coefficient of variation (CV) of αD BG B (at ARF absent stage) and αD M B (at ARF present stage) in transmissive mode.

Fig. 9 .
Fig. 9. Measurement outcomes from the cyst-like heterogeneous phantom D and homogeneous phantom A by using AM-DCS in the reflective mode and their corresponding analytical plots.(a) in the reflective mode, αD B values obtained from AM-DCS measurements on phantom A and phantom D before (αD BG B ) and after (αD M B ) ARF action.(b) Comparison of ∆αD B obtained from AM-DCS measurements on phantom A and phantom D in reflective mode.Error bars: standard deviations.The * indicates a statistically significant difference between the ∆αD B of phantom A and that of phantom D (Tukey comparison of ANOVA at α=0.05, * p < 0.05).(c) The coefficient of variation (CV) of αD BG B (at ARF absent stage) and αD M B (at ARF present stage).

Fig. 10 .
Fig. 10.Spatial sensitivity maps of DCS.(a) Spatial sensitivity map corresponding to the reflective mode used in phantom experiments.(b) Spatial sensitivity map corresponding to the transmissive mode used in phantom experiments.

Funding.
National Key Research and Development Program of China (2023YFE0202800); Natural Science Foun- dation of Shanxi Province (202203021211100, 202203021221097); Graduate Innovation Program in Shanxi Province (2023KY583); Graduate Technology Program of North University of China (20231929).