Three-dimensional particle streak velocimetry based on optical coherence tomography for assessing preimplantation embryo movement in mouse oviduct in vivo

The mammalian oviduct (or fallopian tube) is a tubular organ hosting reproductive events leading to pregnancy. Dynamic 3D imaging of the mouse oviduct with optical coherence tomography (OCT) has recently emerged as a promising approach to study the hidden processes vital to elucidate the role of oviduct in mammalian reproduction and reproductive disorders. In particular, with an intravital window, in vivo OCT imaging is a powerful solution to studying how the oviduct transports preimplantation embryos towards the uterus for pregnancy, a long-standing question that is critical for uncovering the functional cause of tubal ectopic pregnancy. However, simultaneously tracking embryo movement and acquiring large-field-of-view images of oviduct activity in 3D has been challenging due to the generally limited volumetric imaging rate of OCT. A lack of OCT-based 3D velocimetry method for large, sparse particles acts as a technical hurdle for analyzing the mechanistic process of the embryo transport. Here, we report a new particle streak velocimetry method to address this hurdle. The method relies on the 3D streak of a moving particle formed during the acquisition of a single OCT volume, where double B-scans are acquired at each B-scan location to resolve ambiguity in assessing the movement of particle. We validated this method with the gold-standard, direct volumetric particle tracking in a flow phantom, and we demonstrated its in vivo applications for simultaneous velocimetry of embryos and imaging of oviduct. This work sets the stage for quantitative understanding of the oviduct transport function in vivo, and the method fills in a gap in OCT-based velocimetry, providing the potential to enable new applications in 3D flow imaging.


Introduction
Imaging of the female reproductive tract in the mouse model provides the opportunity to study the dynamics in female reproductive processes, which is critical for understanding fertilization, pregnancy and associated reproductive disorders [1][2][3][4][5][6][7].Optical coherence tomography (OCT) combined with in vivo experimental setups has proved to be powerful for dynamic imaging of the mouse oviduct (or fallopian tube) [8].It is label free, has a millimeter-level imaging depth that covers the entire oviduct lumen, has a micro-scale spatial resolution that provides structural details of oocytes and preimplantation embryos, and has an imaging speed that is sufficient to capture the oviduct contraction and contraction wave propagation in 3D [9,10].Functional imaging methods have also been developed with OCT that enable 3D tracking of motile sperm inside the oviduct [11], mapping of the oviductal cilia beat frequency [12], and assessment of cilia metachronal waves [13].With such imaging capabilities, OCT-based studies have revealed new insights into the reproductive process inside the oviduct, especially achieving novel 3D visualizations of oocyte/embryo dynamics that have opened a new avenue to study the transport function of the mammalian oviduct [14].
However, quantitative analysis was largely focused on the ampulla of the oviduct, where the oocyte/embryo movements are relatively slow and thus can be well captured and quantified by the regular volumetric time-lapse OCT imaging.In the isthmus of the oviduct, where embryos present fast and long-distance movement [14], measuring the embryo velocity together with the oviduct activity becomes challenging due to the generally limited volume rate of OCT.In particular, a large transverse scanning area is required to investigate potential correlations between the embryo movement and the oviduct dynamics.This demands a large number of A-scans in the volume for quality imaging that presents a trade-off with the 3D data acquisition speed.This is a significant technical hurdle in answering the fundamental question on the mechanism of embryo transport in the mammalian oviduct, and it also generalizes as a lack of OCT-based 3D velocimetry method for sparse particles [15].
The isthmus of the oviduct hosts preimplantation development and transports the embryo towards the uterus for implantation [16].While the embryo is known to experience fast, bi-directional movement within the isthmus, the mechanistic process generating this type of movement and enabling the successful transport of embryos remains unclear [17].Answering such questions is essential for understanding the functional cause of embryo retention inside the oviduct, a prerequisite of tubal ectopic pregnancy, and could contribute to the clinical management of this life-threatening reproductive disorder [18,19].
Assessing the fast embryo movement in the isthmus together with the oviduct dynamics represents a need of OCT-based velocimetry that can provide 3D velocity of sparse, large particles at the same time of 3D imaging of the surrounding tissue movement in a large field of view.Current velocimetry methods based on OCT can be summarized into four major categories, including Doppler [20][21][22], correlation [23][24][25], decorrelation [26][27][28], and tracking and streak [15,29,30], which were nicely summarized by Zhou, et al. [15].Among these, Doppler, correlation, and decorrelation methods were primarily developed for densely distributed particles, while tracking and streak methods, in contrast, are for particles in a sparse regime.In particular, streak-based OCT velocimetry can provide the total speed of particles; however, only up to 2.5 vectors of the velocity are available, and the imaging is limited to a 2D slice of the surrounding tissue environment [15].
In addressing the technical hurdle, we report a new 3D velocimetry method based on OCT for 3D imaging of preimplantation embryo movement in the mouse oviduct in vivo with a large field of view covering the major parts of the oviduct.This method builds on the basic principle of streak velocimetry, but distinct from the previous method [15], it generates the 3D streak of a moving particle during volume acquisition to obtain the velocity in 3D.The method features a single OCT volume for velocity assessment and requires double B-scans at each location to resolve ambiguity of the particle movement status in the direction of B-scan movement.We tested the method with a flow phantom for different movement statuses and validated the velocity measurement with traditional, gold-standard particle tracking across volumes.In the application of this method for in vivo imaging of the mouse oviduct, we show different statuses of embryo movement in the oviduct isthmus, the mapping of embryo velocity in 3D, the comparison of speeds between forward and backward movements, and the correlations of oviduct contraction/relaxation with the embryo dynamics, which revealed pilot insights into how the oviduct transports preimplantation embryos in the isthmus of the mammalian oviduct.

Velocimetry method
The new velocimetry method builds on the 3D streak of particle formed during the acquisition of a single OCT volume containing double B-scans at each location.Two assumptions are made: first, the particle is a sphere with a diameter measurable by OCT, and second, the particle has a constant velocity during the formation of the streak.The method is illustrated in Fig. 1.The OCT volume has three axes, where X axis is the fast-scanning axis that forms each B-scan, Y axis is the slow-scanning axis representing the movement of the B-scan, and Z axis is the depth axis.The velocity quantification is divided into two parts: a) the velocities in X and Z measured by direct particle tracking within the X-Z plane, and b) the velocity in Y measured based on the relative movement of particle with respect to the moving B-scan.While the tracking of particles for X and Z velocities is general and has been frequently used, the novelty of this method lies in the Y velocity measurement, which is the focus of our description and experimental validation.
Along the Y axis, the relationship between the particle moving velocity, V Y , and the B-scan moving velocity, V B , can be categorized into four cases: 1) In case 3 (|V Y |>2|V B |, same direction), the relative speed between particle and B-scan is larger than |V B |, which indicates that, if considering the particle as static, the B-scan movement has a relatively increased speed, producing a shorter streak length than the particle diameter, L < D. As the particle movement is faster than the B-scan movement, this process represents the particle catching and running over the B-scan, similar to case 2, and therefore, |V Y |=|V B |+D/T.
In case 4 (V Y and V B in opposite directions), because the directions of particle movement and B-scan movement are opposite, with any speed of the particle, the relative speed between particle and B-scan is larger than |V B |, resulting in L < D. Also, as the movements of particle and B-scan are against each other, the sum of the particle displacement and the B-scan displacement equals the particle diameter.Thus, Experimentally, distinguishing cases 1 and 2 from cases 3 and 4 can be through examining the streak length in Y and comparing that with the diameter of the particle, with L ≥ D representing cases 1 and 2 (background tinted red in Fig. 1), and L < D representing cases 3 and 4 (background tinted blue in Fig. 1).
Distinguishing between case 1 and case 2 requires the use of double B-scans.Specifically, the double B-scans are acquired with one repeating B-scan at the same location, and thus, the double B-scans represent two time points t 1 and t 2 , with t 2 > t 1 .In case 1, from t 1 to t 2 , and at the end of the streak, the particle is moving into this B-scan location with an increase of its cross-sectional area shown within the B-scan.While in case 2, from t 1 to t 2 , and also at the end of the streak, the particle is moving out of this B-scan location with a decrease of its cross-sectional area shown within the B-scan.Therefore, by selecting a location at the end of the streak and assessing the cross-sectional area of the particle over the double B-scans, case 1 and case 2 can be distinguished.Since case 3 and case 4 are distinct in terms of the particle moving direction, identifying the direction of particle movement provides a convenient path to distinguish between case 3 and case 4. The application context where the embryo moves inside the oviduct can be generalized as a particle moving in a tube.With this generalized context, the overall movement of the particle is only along the tube, making it possible to use the moving direction in X or Z to know the moving direction in Y based on the tube orientation in X-Y plane or Y-Z plane, respectively.This is with the assumption that the tube does not orient absolutely in parallel with Y, which is highly practical, given that the tube and Y being perfectly parallel is rare in actual applications.
With the feasibility to distinguish between all four cases, any 3D streak of particle can be assigned into one of these four cases, where the Y-direction velocity is quantified.The overall velocity of the particle, V, is then obtained based on the X, Y and Z velocity components, as For the specific application in assessing the oviductal transport of embryo, the direction of the overall velocity can be binarized into either ovary-to-uterus (forward in transport) or uterus-to-ovary (backward in transport).

OCT system
A lab-built spectral domain OCT system was used.It employed a supercontinuum laser (SuperK EXTREME EXR-9 OCT, NKT Photonics) as the light source and a spectrometer (Cobra-S 800, Wasatch Photonics) that mapped the wavelength of 852 ± 73 nm to 2048 pixels with an A-scan rate of up to 250 kHz.The system provided an axial resolution of ∼6 µm in air and a transverse resolution of ∼9 µm.A set of galvanometer-mirrors (GVS012, Thorlabs) were used for transverse scanning of the imaging beam, which was focused by a scan lens (LSM03-BB, Thorlabs).For acquiring the single-volume, double-B-scan velocimetry data, the OCT system was set with an A-scan rate of 250 kHz and had a B-scan rate of 250 Hz, and a volume took 4.8 seconds to record.The transverse field of view was ∼3.0 mm by ∼2.9 mm with a spatial sampling interval of ∼5 µm, and the B-scan moving speed, V B , was ∼0.6 mm/s.

Validation of method
Validation of the new method for V Y measurement was performed with a flow phantom, and the comparison was made with results from traditional particle tracking across volumes.The experimental setup contained a programable syringe pump, a 1 ml syringe that connected through a 23-gauge needle to a flexible tube with an inner diameter of ∼0.58 mm, and a rotational stage to which the tube was secured.Sodium chloride solution was used as the fluid, and polycaprolactone (PCL) beads were synthesized and utilized to seed the solution.A PCL bead with a diameter of ∼0.167 mm was used as the target particle for experiments.The tube was positioned at ∼45 degrees or ∼135 degrees with respect to the B-scan moving direction to have the particle moving in the same or opposite direction as the B-scan movement, respectively.For validating the velocimetry result, continuous volumetric OCT data (up to 2 Hz volume rate) was also acquired with a sufficient transverse field of view to capture the target particle over multiple volumes, and the particle positions from at least two adjacent volumes were identified in Y, which allowed for direct calculation of the particle speed in Y.The high volume rate was achieved by lowering the spatial sampling.The fluid was pumped at a volume rate ranging from 0.5 ml/h to 4.5 ml/h, providing a range of line speeds of the particle, and the velocimetry result at each line speed was validated with the direct particle tracking approach.

In vivo mouse experiment
All animal procedures have been approved by the Institutional Animal Care and Use Committee at Stevens Institute of Technology, and all experiments followed the approved guidelines and regulations.In vivo imaging experiments were performed to demonstrate the method for the in vivo application of assessing preimplantation embryo movement in the mouse oviduct.Three wild-type CD-1 adult female mice (022, Charles River) were used, and timed mating was set up and checked daily to have experiments at 1.5 days post coitum when the preimplantation embryos were located in the isthmus of the oviduct.
The in vivo experimental setup is illustrated in Fig. 2. A 3D-printed intravital window was implanted to the right dorsal side of the mouse for optical access to the female reproductive organs through an aperture of 10 mm in diameter.Detailed information about the window dimension and the window implantation can be found in [9,14].Briefly, the mouse was anesthetized by isoflurane inhalation throughout the entire surgery and imaging session, and was placed on platforms maintained at 37°C.After hair removal and skin disinfection, a circular piece of skin was removed to allow the window to be sutured to the edge of the skin.The set of reproductive organs was gently pulled out of the body cavity through a small incision on the muscle layer, and the fat pad associated with the ovary was secured onto the tissue holders of the window through surgical tissue adhesive.The oviduct was positioned to have the isthmus portion facing upward for OCT imaging.The aperture of the window was closed by a thin circular cover glass, and the window was held stable by a clamp during imaging to minimize the motion influence from the mouse breathing.This setup allows for in vivo, large-field-of-view, 3D OCT imaging of the oviduct (Fig. 2).For demonstrations of in vivo applications, velocimetry experiments were focused on assessing the embryo velocity together with high-quality imaging of the surrounding tissue environment as well as investigating the correlation between the oviduct dynamics and the embryo movement during the transport process.
up and checked daily to have experiments at 1.5 days post coitum when the preimplantation embryos were located in the isthmus of the oviduct.
The in vivo experimental setup is illustrated in Fig. 2. A 3D-printed intravital window was implanted to the right dorsal side of the mouse for optical access to the female reproductive organs through an aperture of 10 mm in diameter.Detailed information about the window dimension and the window implantation can be found in [9,14].Briefly, the mouse was anesthetized by isoflurane inhalation throughout the entire surgery and imaging session, and was placed on platforms maintained at 37°C.After hair removal and skin disinfection, a circular piece of skin was removed to allow the window to be sutured to the edge of the skin.The set of reproductive organs was gently pulled out of the body cavity through a small incision on the muscle layer, and the fat pad associated with the ovary was secured onto the tissue holders of the window through surgical tissue adhesive.The oviduct was positioned to have the isthmus portion facing upward for OCT imaging.The aperture of the window was closed by a thin circular cover glass, and the window was held stable by a clamp during imaging to minimize the motion influence from the mouse breathing.This setup allows for in vivo, large-field-ofview, 3D OCT imaging of the oviduct (Fig. 2).For demonstrations of in vivo applications, velocimetry experiments were focused on assessing the embryo velocity together with highquality imaging of the surrounding tissue environment as well as investigating the correlation between the oviduct dynamics and the embryo movement during the transport process.

Data processing
Data processing for the new velocimetry method was performed with MATLAB.From the single OCT volume containing the particle streak, the number of B-scans intersecting with the particle was first obtained, which led to the quantifications of L (streak length in Y) and T (time duration of streak).The diameter of the particle (D) was measured in the X-Z plane.The velocity in Y was measured following the design of the method (Fig. 1).By comparing L and D and by either comparing the cross-sectional areas of the particle between the double B-scans at the end of the streak or examining the particle moving directions in X or Z as appropriate, the streak was categorized into one of the four cases for Y-velocity quantification, and the speed in Y was calculated with the corresponding equation.The velocities in X and Z were then quantified by determining and tracking the centroid from the cross-sectional image of particle in the X-Z plane.The 3D velocity was thus obtained.To present the 3D velocimetry result from in vivo imaging, the forward velocity (ovary-to-uterus) was color-coded with magenta, while the backward velocity (uterus-to-ovary) was color-coded with cyan, and the brightness was linearly mapped to the speed values.

Data processing
Data processing for the new velocimetry method was performed with MATLAB.From the single OCT volume containing the particle streak, the number of B-scans intersecting with the particle was first obtained, which led to the quantifications of L (streak length in Y) and T (time duration of streak).The diameter of the particle (D) was measured in the X-Z plane.The velocity in Y was measured following the design of the method (Fig. 1).By comparing L and D and by either comparing the cross-sectional areas of the particle between the double B-scans at the end of the streak or examining the particle moving directions in X or Z as appropriate, the streak was categorized into one of the four cases for Y-velocity quantification, and the speed in Y was calculated with the corresponding equation.The velocities in X and Z were then quantified by determining and tracking the centroid from the cross-sectional image of particle in the X-Z plane.
The 3D velocity was thus obtained.To present the 3D velocimetry result from in vivo imaging, the forward velocity (ovary-to-uterus) was color-coded with magenta, while the backward velocity (uterus-to-ovary) was color-coded with cyan, and the brightness was linearly mapped to the speed values.

Results
From the flow phantom experiment, the four cases of the new velocimetry method are shown in Fig. 3. Specifically, in Fig. 3(A), with |V Y |≤|V B | and in the same direction in Y, the streak of the particle appeared to have a length in Y longer than the particle diameter, and at the end of the streak (dashed arrow), the cross-sectional area of the particle was larger in the second B-scan (t 2 ) than the first B-scan (t 1 ).In Fig. 3(B), with V B and V Y still in the same direction in Y but |V B |<|V Y |≤2|V B |, the Y-length of the particle streak also appeared to be longer than the diameter, but, distinct from Fig. 3(A), the cross-sectional area of the particle at the end of the streak (dashed arrow) was smaller in B-scan t 2 than in B-scan t 1 .In Fig. 3(C), with |V Y |>2|V B | and in the same Y-direction, the particle streak length in Y appeared to be shorter than the diameter.This was similar to the particle streak in Fig. 3(D), where the length was also shorter than the diameter.However, the particle movement direction in Y can be easily determined based on its movement direction in X, shown within the X-Z plane from the earlier and later B-scans of the streak, which clearly indicated whether the particle had the same or opposite Y-movement direction as the B-scan movement.These demonstrated that the design of the 3D velocimetry method for the streak-based measurement of the Y-direction velocity (Fig. 1) can be successfully implemented.
The results of validation are shown in Fig. 4. For the same particle moving at the same pumping rate, the measured V Y through the new velocimetry method was compared with the traditional particle tracking across volumes, and the data were plotted and analyzed with a linear regression y = ax.The results show good agreements between the two measurements for either the same or opposite V Y and V B direction, presenting high R-squared values, values of a close to 1 (the ideal value), and p < 0.001 from t statistics (Fig. 4).With V Y and V B in the same direction (Fig. 4(A)), the data points covered all three cases shown in Fig. 1, including a wide range of speeds from ∼0.1 mm/s to ∼2.0 mm/s.With V Y and V B in the opposite direction (Fig. 4(B)), the relatively higher deviation from a = 1 in comparison with the same direction was due to the fewer B-scans intersecting with the particle, especially with larger speed values, which pushed the value of T (time duration of streak) closer to the temporal sampling interval of the B-scan.Nevertheless, the validation result demonstrated that the new velocimetry method provides comparable measurements as the gold-standard volumetric particle tracking approach to assess the movement of sparse particles in flow.
From the in vivo experiments with preimplantation embryos in the mouse oviduct isthmus, representative OCT images of the four cases of the new velocimetry method are shown in Fig. 5, indicating that this method can be utilized for in vivo assessment of the embryo movement within the native, dynamic environment.In particular, in the cases of same direction, |V Y |≤|V B | (Fig. 5(A)) and |V B |<|V Y |≤2|V B | (Fig. 5(B)), comparing the cross-sectional area of the embryo from the double B-scans at the end of the streak (dashed arrows) provided a clear distinction between the two cases, with the second B-scan (t 2 ) containing relatively larger and smaller cross-sectional areas, respectively.Also, the 3D OCT image well identified the orientation of each portion of the curled mouse oviduct, making it convenient to distinguish between the two cases presenting a shorter streak length in Y than the embryo diameter.As examples, in Figs.5(C) and 5(D), although the embryo moved in the same direction in X for both cases, the distinct 3D tube orientations at the streak location clearly indicated the different Y-directions of the embryo movements, enabling the quantification of the Y-direction velocity.The results of validation are shown in Fig. 4. For the same particle moving at the same pumping rate, the measured V Y through the new velocimetry method was compared with the range of speeds from ~0.1 mm/s to ~2.0 mm/s.With V Y and V B in the opposite direction (Fig. 4B), the relatively higher deviation from a=1 in comparison with the same direction was due to the fewer B-scans intersecting with the particle, especially with larger speed values, which pushed the value of T (time duration of streak) closer to the temporal sampling interval of the B-scan.Nevertheless, the validation result demonstrated that the new velocimetry method provides comparable measurements as the gold-standard volumetric particle tracking approach to assess the movement of sparse particles in flow.From the in vivo experiments with preimplantation embryos in the mouse oviduct isthmus, representative OCT images of the four cases of the new velocimetry method are shown in Fig. 5, indicating that this method can be utilized for in vivo assessment of the embryo movement within the native, dynamic environment.In particular, in the cases of same direction, |V Y |≤|V B | (Fig. 5A) and |V B |<|V Y |≤2|V B | (Fig. 5B), comparing the cross-sectional area of the embryo from the double B-scans at the end of the streak (dashed arrows) provided a clear distinction between the two cases, with the second B-scan (t 2 ) containing relatively larger and smaller crosssectional areas, respectively.Also, the 3D OCT image well identified the orientation of each portion of the curled mouse oviduct, making it convenient to distinguish between the two cases presenting a shorter streak length in Y than the embryo diameter.As examples, in Figs.5C and  5D, although the embryo moved in the same direction in X for both cases, the distinct 3D tube orientations at the streak location clearly indicated the different Y-directions of the embryo movements, enabling the quantification of the Y-direction velocity.Using the new velocimetry method, in vivo 3D velocimetry results were generated with color-mapped velocity overlapped with the 3D OCT image of the mouse oviduct.Six examples are shown in Fig. 6(A) focusing on different regions of the isthmus, where three are with forward movement (ovary-to-uterus) and three are with backward movement (uterus-to-ovary).The movements of embryos in the isthmus appeared to be taking place at multiple sites over millimeters in distance, highlighting the need for this velocimetry method that provided a large transverse field of view.The high-quality 3D OCT image also revealed the oviductal tissue context of the embryo movement (Fig. 6(A)).The speed of embryos presented a wide range for both forward and backward movements, which is expected, as there must exist acceleration and deceleration processes for the bi-directional dynamics.Comparing between the forward and backward movements from each mouse, the backward moving speed appeared to be higher than the forward one for both average and maximum values, shown in Fig. 6(B), suggesting that, overall, the embryo movement in the uterus-to-ovary direction is faster than that in the ovary-to-uterus direction.This is in accordance with the previous speed mapping of bi-directional moving embryos through direct volumetric tracking, which, however, had a limited transverse field of view [14].
This difference in the speed suggests possibly different processes underlying the generation of the forward and backward embryo movements in the isthmus.The large field of view of the new velocimetry method covering both the ampulla and isthmus of the oviduct allowed for the investigation into such detailed dynamics.Time-lapse 3D images in Fig. 7 show the unique feasibility of this new method to perform imaging analysis of the correlation between the oviduct activity and the embryo movement, enabling the study of the transport function of the oviduct.The time-lapse images over 9.6 seconds on the left side in Fig. 7 shows the oviduct contraction propagating from the ampulla to the isthmic-ampullary junction (IAJ), which coincided with the forward movement of the embryo in the isthmus, from the isthmic region near the IAJ to the region that was further from IAJ, respectively.From the three images on the right side in Fig. 7, a relaxation of the ampulla took place at the same time as the backward movement of the embryo in the isthmus (t = 4.8 s), while a following contraction of the same ampulla region coincided with the forward embryo movement in the isthmus (t = 9.6 s).These pilot observations suggest that the forward movement of embryo in the isthmus is driven by a contraction wave propagation from the ampulla, but the backward embryo movement, in contrast, is driven by a relaxation of  movement (ovary-to-uterus) and three are with backward movement (uterus-to-ovary).The movements of embryos in the isthmus appeared to be taking place at multiple sites over millimeters in distance, highlighting the need for this velocimetry method that provided a large transverse field of view.The high-quality 3D OCT image also revealed the oviductal tissue context of the embryo movement (Fig. 6A).The speed of embryos presented a wide range for both forward and backward movements, which is expected, as there must exist acceleration and deceleration processes for the bi-directional dynamics.Comparing between the forward and backward movements from each mouse, the backward moving speed appeared to be higher than the forward one for both average and maximum values, shown in Fig. 6B, suggesting that, overall, the embryo movement in the uterus-to-ovary direction is faster than that in the ovaryto-uterus direction.This is in accordance with the previous speed mapping of bi-directional moving embryos through direct volumetric tracking, which, however, had a limited transverse field of view [14].the ampulla.This result indicates that the in vivo application of this 3D velocimetry method can potentially generate novel and important insights into the mechanistic process of the oviductal transport of preimplantation embryos.

Discussion
The velocimetry method presented here was developed for assessing fast movement of preimplantation embryos in the mouse oviduct, but it can also be generalized as a 3D velocimetry method for large, sparse particles moving in a tubular structure.Several OCT-based methods have been previously reported for velocimetry of sparsely distributed particles [15,29,30] which rely on 2D OCT imaging to provide speed information, including the total speed, but lack feasibility in resolving the velocity direction perpendicular to the imaging plane [15].In contrast, the presented method is based on 3D OCT imaging with a single volume containing the 3D particle streak.By taking advantage of the 3D imaging of surrounding structures and double B-scans within the volume, the method generates 3D velocity of the particle, filling in a gap in OCT-based velocimetry and providing a new strategy for particle velocity measurement.Traditionally, for sparse particles, repeated volumetric OCT imaging has been used to measure the particle movement in 3D [14,31].However, for fast movements in a relatively large area, direct volumetric tracking is challenging due to the generally limited volume rate of OCT.Moreover, the tradeoff between temporal and spatial sampling in typical 3D data acquisition largely prevents fast and quality imaging over a large transverse field of view.There have been technical advancements of OCT enabling ultrafast imaging that are promising in overcoming this challenge [32][33][34][35], but these are associated with a significantly higher cost or reduced imaging sensitivity.The presented method utilizes one slowly acquired OCT volume (that is widely available) to address the need of measuring fast particle movement in a large area, presenting a more accessible solution.
The method has upper and lower limits of measurable speed, which are tunable with the B-scan rate of 3D OCT imaging.For X-and Z-direction movements, 2D tracking is performed across B-scans in the volume, and thus, the highest measurable speed is set with only two B-scans from adjacent locations intersecting with the particle, and the lowest measurable speed depends on the spatial resolution in the X-Z plane for distinguishing the minimum displacement of the cross-sectional image of the particle.In Y-direction, although velocity quantification relies on the particle streak, which is different from tracking, the factors defining the upper and lower limits of measurable speed remain the same as X-and Z-directions.Specifically, the upper limit corresponds to the shortest streak that contains only two B-scan locations, while the lower limit is set by how well a streak length can be identified as being longer or shorter than the particle diameter, which is determined by the spatial resolution in Y.In comparison with the traditional, direct volumetric particle tracking, this velocimetry method turns "two volumes" capturing the particle into "two B-scans" capturing the particle for setting the upper limit of measurable speed, extending the dynamic range of measurement to orders of magnitude higher with the same OCT system.
The method builds on two assumptions on the particle and its movement.The first one requires the particle to be a sphere with a diameter measurable by OCT.This is because the diameter, or the length of particle in Y-direction, is an essential parameter for speed quantification.With the particle being a sphere, this parameter can be achieved by measurement from the largest cross-sectional area in the X-Z plane, and in this case, a faster B-scan rate, or a higher number of B-scan locations intersecting the particle, provides a better estimation.If using particles with a known size, this step of measurement is not required.The second one assumes constant-velocity movement of the particle over the duration of streak, which is a common assumption used in particle streak velocimetry.It is worth noting that the measured velocity from the presented method is the average over the duration of streak.Importantly, these two assumptions also present as the limitations of the method.
Intravital OCT imaging of the mouse oviduct is instrumental in studying the in vivo process of embryo transport towards implantation and pregnancy [8].This is an area with little knowledge largely due to the limitation in imaging, yet this is also an area that is of high significance for understanding female reproductive disorders, such as tubal ectopic pregnancy, and could provide critical insights for improving assisted reproductive technologies [36][37][38].One of the critical aspects in analyzing the transport process is to study the relationship between oviduct activity and embryo movement.As demonstrated in this study, the presented method offers a strong application in this regard, capable of revealing spatiotemporal correlations between the dynamics of oviduct and embryos.Although it has been known for a long time that preimplantation embryos have a bi-directional movement in the isthmus of the oviduct, how such forward and backward movements are generated and what the mechanism is for the oviduct to produce net displacement of embryos towards the uterus remain unclear with few investigations.The pilot data shown here in the feasibility study suggest completely different processes in generating the forward and backward movements, laying a new path to depict the native preimplantation process in mammalian reproduction.
In summary, we reported a new 3D particle streak velocimetry method based on OCT targeting the fast movement of preimplantation embryos in the mouse oviduct in vivo.The design of the method for velocity quantification was presented in both in vitro experiments under controlled conditions and in vivo mouse experiments.The method was validated by the gold-standard, direct volumetric particle tracking in a flow phantom.The in vivo data indicated the feature of the method in simultaneously providing the embryo velocity and the 3D dynamics of the oviduct over a large field of view covering the major parts of the oviduct, which revealed initial insights into the mechanistic process of in vivo embryo transport in the mammalian oviduct.

Funding. National Institutes of Health (R21EB028409).
Disclosures.The authors declare no conflicts of interest.
same direction, and 4) V Y and V B in opposite directions.In case 1 (|V Y |≤|V B |, same direction), the relative speed between particle and B-scan is smaller than |V B |, meaning that, if considering the particle as static, the B-scan speed is relatively reduced, thus producing a longer streak length in Y (L) than the diameter of particle (D), L > D.The streak length L also represents the B-scan displacement.The process can be understood as the B-scan catching the particle and running over the particle, and the B-scan displacement is the sum of the particle displacement and the particle diameter.Therefore, |V Y |=|V B |-D/T, where T is the time duration of the streak, or in other words, the time duration while the B-scan intersects with the particle.A special circumstance here is that, when |V Y |=|V B |, the streak lasts the entire B-scan movement of the volume, where T is long enough to bring D/T close to zero.In case 2 (|V B |<|V Y |≤2|V B |, same direction), the relative speed between particle and B-scan is smaller than or equal to |V B |, leading to L ≥ D, similar to case 1.The process of streak formation shows that the particle catching the B-scan and running over the B-scan, resulting in the particle displacement as the sum of the B-scan displacement and the particle diameter.As such, |V Y |=|V B |+D/T.Here, a special circumstance takes place when |V Y |=2|V B |, and in this case, L = D, making D/T=|V B |, and thus, the equation for calculating |V Y | is still valid.

Fig. 1 .
Fig.1.An illustration of OCT-based 3D velocimetry method for measuring the particle velocities in X and Z, and for determining the cases 1-4 to measure the particle velocity in Y.

Fig. 1 .
Fig. 1.An illustration of OCT-based 3D velocimetry method for measuring the particle velocities in X and Z, and for determining the cases 1-4 to measure the particle velocity in Y.

Fig. 2 .
Fig. 2.An illustration of the experimental setup for in vivo OCT imaging of the mouse oviduct through an intravital window (left) and a 3D in vivo OCT image of the mouse oviduct with parts of the ovary and the uterus (right).Scale bar is 300 µm.

Fig. 2 .
Fig. 2.An illustration of the experimental setup for in vivo OCT imaging of the mouse oviduct through an intravital window (left) and a 3D in vivo OCT image of the mouse oviduct with parts of the ovary and the uterus (right).Scale bar is 300 µm.

Fig. 3 .
Fig. 3. Representative images of the 3D particle streaks and corresponding B-scans from the new OCT-based velocimetry method for the four cases (A-D) used for particle velocity measurement in Y.For case 1 (A) and case 2 (B), the B-scan images are from the double B-scans at the end of the streak (dashed arrows), and for case 3 (C) and case 4 (D), the B-scan images are from one earlier B-scan and one later B-scan of the streak.Long, solid arrows mark the direction of particle movement, and triangles point at the cross-sections of the particle in the B-scans.Scale bars are 200 µm in 3D images (left, cross-sectional view) and 300 µm in 2D images (right).

Fig. 3 .
Fig. 3. Representative images of the 3D particle streaks and corresponding B-scans from the new OCT-based velocimetry method for the four cases (A-D) used for particle velocity measurement in Y.For case 1 (A) and case 2 (B), the B-scan images are from the double B-scans at the end of the streak (dashed arrows), and for case 3 (C) and case 4 (D), the B-scan images are from one earlier B-scan and one later B-scan of the streak.Long, solid arrows mark the direction of particle movement, and triangles point at the cross-sections of the particle in the B-scans.Scale bars are 200 µm in 3D images (left, cross-sectional view) and 300 µm in 2D images (right).

Fig. 4 .
Fig. 4. Validation of the new OCT-based velocimetry method with the traditional, gold-standard volumetric particle tracking approach.The comparison results are for (A) the same direction of V Y and V B as well as for (B) the opposite direction of V Y and V B of the same particle in the flow phantom.The p value of linear regression is from t statistics.

Fig. 4 .
Fig. 4. Validation of the new OCT-based velocimetry method with the traditional, goldstandard volumetric particle tracking approach.The comparison results are for (A) the same direction of V Y and V B as well as for (B) the opposite direction of V Y and V B of the same particle in the flow phantom.The p value of linear regression is from t statistics.

Fig. 5 .
Fig. 5. Representative images of the in vivo 3D embryo streaks and corresponding B-scans from the new OCT-based velocimetry method for the four cases (A-D) employed for measuring the Y-direction velocity of the embryo.For case 1 (A) and case 2 (B), the B-scan images are from the double B-scans at the end of the streak (dashed arrows), and for case 3 (C) and case 4 (D), the B-scan images are from one earlier B-scan and one later B-scan of the streak.Solid arrows mark the direction of embryo movement, and triangles point at the cross-sections of the embryo in the B-scans.Scale bars are 400 µm in 3D images (left, cross-sectional view) and 100 µm in 2D images (right).

Fig. 5 .
Fig. 5. Representative images of the in vivo 3D embryo streaks and corresponding Bscans from the new OCT-based velocimetry method for the four cases (A-D) employed for measuring the Y-direction velocity of the embryo.For case 1 (A) and case 2 (B), the B-scan images are from the double B-scans at the end of the streak (dashed arrows), and for case 3 (C) and case 4 (D), the B-scan images are from one earlier B-scan and one later B-scan of the streak.Solid arrows mark the direction of embryo movement, and triangles point at the cross-sections of the embryo in the B-scans.Scale bars are 400 µm in 3D images (left, cross-sectional view) and 100 µm in 2D images (right).

Fig. 6 .
Fig. 6. (A) In vivo 3D OCT imaging of the moving velocity of preimplantation embryos together with the structures of the mouse oviduct isthmus (cross-sectional view).Scale bars are 200 µm.(B) The average and maximum speeds of embryo movement with the comparison between forward (ovary-to-uterus) and backward (uterus-to-ovary) directions.Total number of measurements: 18 from Mouse #1, 8 from Mouse #2, and 56 from Mouse #3.

Fig. 6 .
Fig. 6. (A) In vivo 3D OCT imaging of the moving velocity of preimplantation embryos together with the structures of the mouse oviduct isthmus (cross-sectional view).Scale bars are 200 µm.(B) The average and maximum speeds of embryo movement with the comparison between forward (ovary-to-uterus) and backward (uterus-to-ovary) directions.Total number of measurements: 18 from Mouse #1, 8 from Mouse #2, and 56 from Mouse #3.

Fig. 7 .
Fig. 7. Time-lapse 3D OCT imaging with velocimetry of the mouse oviduct in vivo showing the temporal correlations between the oviduct dynamics in the ampulla and the forward/backward embryo movement in the isthmus (cross-sectional view).(Left) Forward movement of embryo over 9.6 s and the correlation with ampulla contractions.(Right) Backward movement followed by forward movement of embryo and the correlations with ampulla relaxation and contraction.The green dashed line illustrates the oviduct center line.Arrows indicate contraction or relaxation of the oviduct lumen, and triangles point at embryo streaks.Scale bars are 300 µm.