All animal care and research were conducted in compliance with the Guide for the Care and Use of Laboratory Animals of the National Research Council under protocols that were approved by the Institutional Animal Care and Use Committee of the Missouri State University.

Studies were carried out on male C57BL/6 mice. The mice were purchased from the Jackson Laboratory and then bred in the animal facility at Missouri State University. Male mice with 8 - 12 weeks old and 21 - 30 g body weight were used for the study. Mice were anesthetized via an intrapleural injection of 150 mg/kg ketamine and 11.25 mg/kg xylazine (Med-Vet International) in a mixed solution.

The cremaster muscle preparation was modified from a previous method [ 27 ]. Briefly, the animal was placed supine on a custom Plexiglass tray with a water circulator (Fisher Scientific™, Model 9005) to maintain a body temperature of 37˚C. After fur removal and skin disinfection, an incision was made from the scrotal apex to the inguinal fold, and the sac was carefully opened. The epididymis, testes, and spermatic cord were separated from connective tissue and repositioned into the abdomen via the inguinal canal. The main vasculature of the cremaster muscle was centered on a quartz pillar.

During tissue preparation, the muscle was continuously superfused with Krebs solution at 37 ± 1˚C, followed by a 30-minute equilibration on the microscope stage. To label leukocytes, Rhodamine 6G (0.67 mg/kg, Fisher Scientific™) was administered intravenously via the lateral tail vein.

Venules were identified by their converging blood flow pattern, in contrast to the divergent flow pattern in arterioles. The venule selection criteria were based on standards from Ley K, [ 13 , 14 , 28 , 29 ], Granger DN, [ 6 , 7 , 30 ] and Gavins [ 31 ]. Briefly, a selected venule had to be unbranched within the region of interest (ROI), 20 - 40 µm in diameter, >100 µm in length, maintain intact blood flow during recording, and exhibit high-velocity, free-flowing leukocytes.

Images were captured by a side-mounted CCD EXi Blue camera (QImaging, British Columbia, Canada) attached to an IX81 Olympus microscope, operated by Micro-manager [ 32 ] (open source; https://micro-manager.org/ ). A 10X objective lens (UPlanFL N 10x, NA 0.3, WD 10MM, Fluorite UPLFLN10X2) and a Semrock Brightline CY3 filter set (Ex531/40, 562DM, Em593/40) were used for Rhodamine 6G to detect leukocytes, illuminated by a Xenon Burner (UXL-75XB 75W Short Gap). Time-lapse images were captured at 14 bit; 30 Mhz.

The centerline blood velocity was assessed by measuring the centerline velocity of red blood cells (V_rbc) in the lumen center of the venule, using bright-field imaging captured at 30 - 40 fps for 100 - 120 frames. Fluorescent time-lapse images were captured at consecutive time point intervals (0 min, 5 min, 10 min, 15 min, 30 min, 45 min, 60 min) for each indexed venule for 60 sec at 12.5 fps ( Figure 1 ).

Off-line image analysis was conducted using ImageJ 1.51. Time-lapse images (100 frames) were acquired at 30 - 45 fps. To determine venule diameter, we converted pixels to distance by applying a correction factor of 1.54 pixels/μm, which was obtained through measurement with an Objective Micrometer (Olympus). Given that motion artifacts from tissue movement, respiration, and hemodynamic flow can significantly distort image data, we implemented a rigorous image registration and stabilization protocol based on the method described by Goobic [ 33 ]. Briefly, stable background regions, identified as areas free of motion artifacts and consistent across frames, were selected. These stable regions were then used to construct a background template, which served as a reference for aligning subsequent frames. This template correction minimized background fluctuations, intensity variation, and motion distortions. The full methodology is outlined in Abbreviations.

After background registration, an imageJ macro, Stack CLAHE (Contrast Limited Adaptive Histogram Equalization) ( https://imagej.net/Enhance_Local_Contrast_(CLAHE) ) was used to ensure consistent pixel intensity scaling across the image stack by enhancing local contrast. For precise alignment, the ImageJ StackReg plugin, using a normalized cross-correlation algorithm for sub-pixel registration, was applied with a maximum displacement threshold of 10 pixels.

After stabilization, microvascular structures were enhanced using the unsharp mask filter with a radius of 1.5 pixels and a mask weight of 0.6 to improve edge definition for vessel segmentation. This enhancement step was critical for optimizing vessel segmentation.

Following template matching and stabilization, a background subtraction macro (see Abbreviations) was used to normalize each image frame to a background ROI (5 × 5 pixels) selected by the user to represent an area corresponding the image intensity minima. Additional compensatory steps, adapted from Goobic et al. (2005) [ 33 ], were implemented to address background motion artifacts (see Abbreviations).

To improve signal-noise ratio (SNR) and eliminate image artifacts, image enhancement and processing were conducted ( Table 1 ). Key artifacts included background noise, stochastic noise, motion artifacts [ 34 ]. First, images were enhanced using an edge detection and morphological intensity filter. The macro applied a local contrast enhancement filter (“blocksize = 2, histogram = 256, maximum = 2, mask = *inverted*”), followed by a median intensity filter (0.5-pixel diameter) and Gaussian blur (0.5-pixel diameter) to refine image quality [ 35 ]. Image segmentation was then performed to selectively enhance the leukocyte pixels.

Table 1. Summarized techniques used in image pre-processing, enhancement, and processing.

^aBF (bright field) or F (fluorescence) images, ^bEach image was matched to a template image, removing intensity and motion artifacts (background noise, motion artifacts), ^cLAP (linear assignment problem). ^dSee Abbreviations for additional information.

Optical flow, a method that tracks the movement of pixels between consecutive frames in an image stack, was used to assess blood flow in a vessel. This computational imaging technique estimates the apparent motion of intensity patterns between consecutive frames, making it widely applicable in blood cell tracking and fluid motion studies. Optical flow assumes that the intensity (brightness) of a moving pixel remains constant between consecutive frames, the motion of pixels is small enough to be approximated linearly, and that neighboring pixels typically exhibit similar motion. Mathematically, optical flow is represented as,

$I_x{V}_x+I_y{V}_y+I_t=0$ (1)

In this equation, I_x and I_y represent the spatial intensity gradients (changes in brightness along the x and y axes), I_t is the temporal intensity gradient (intensity change over time), and V_x and V_y are the velocity components of motion in the x and y directions. Since this equation contains two unknowns (Vₓ and V_y), additional constraints are needed for a unique solution. There are typically provided by methods such as the Lucas-Kanade method, which estimates motion locally using small pixel windows, or the Horn-Schunck method, which enforces a global smoothness constraint across the image.

Optical flow was performed in ImageJ using the Particle Image Velocimetry (PIV) plugin ( https://sites.google.com/site/qingzongtseng/piv ) to create velocity vector fields with the ImageJ FlowJ plugin to ultimately compute the optical flow analysis and derive the V_rbc.

Following brightfield image registration, linear flow “streak” profiles were created using the PIV plugin to produce velocity and direction vectors profiles. The PIV method implements a cross-correlation algorithm based on the Horn-Schnuck method and is applied globally. To ensure accurate flow modeling, vessel centerlines were extracted and the local flow vector at any given pixel (x, y) was computed by identifying the 10 nearest centerline pixels, denoted as NCLP (x, y) (see Abbreviations). The directional angle of the centerline segment was determined by averaging the angles between adjacent pixels, providing a smooth estimate of local flow direction.

Since vessel topology alone cannot distinguish between opposing flow directions, an initialization step was required. This involved tracking flowing RBCs over five consecutive frames and calculating their median motion direction. The final virtual flow direction VF (x, y) was assigned the angle closest to the median motion vector, resolving ambiguities within ±π/2.

Following PIV analysis, the V_rbc 5.1 macro (see Abbreviations) was ran on the images produced, and the optic flow velocity profiles were then used to derive the centerline velocity at a given point, computed for each frame pair (T₂-T₁) and analyzed in FlowJ utilizing the Lucas-Kanade algorithm using parameters σ_s = 0.5, σ_t = 1.0, σ_w = 1.0, τ = 1.0. The resulting horizontal (V_x) and vertical (V_y) displacements were used to determine instantaneous velocity ( ${\stackrel{\rightharpoonup }{V}}_{xy}$).

${\stackrel{\rightharpoonup }{V}}_{xy}=\sqrt{{\left(V_x\right)}^2+{\left(V_y\right)}^2}$ (2)

These vectors were then used to estimate the V_rbc, in pixels per frame ( Figure 2 ). The velocity profiles were cross-checked against known velocities, conducted by manual V_rbc estimation, and that of the velocity profiles yielded by the PIV plugin. Subsequently, the instantaneous velocity magnitude between two frames computed from FlowJ was measured over 3 - 5 sequential frames in a fixed region, in triplicate. If no deviation was observed for the three independent measures, the optical flow was computed for the entire experimental time frame (100 frames), yielding the mean centerline red blood cell velocity (V_rbc).

Once the V_rbc for an image was obtained from optical flow, the average blood flow velocity (V_avg) was determined by dividing V_rbc by an empirical factor of 1.6 using Equation (3) and the venular wall shear rate ( ${\gamma }_w$) [ 41 - 43 ] was computed using Equation (4)

$V_{avg}=V_{rbc}/1.6$ (3)

${\gamma }_w=2.12\cdot 8\cdot V_{avg}/D_v$ (4)

where V_avg represents the average blood flow velocity and the white blood cell velocity, V_wbc, approximates V_avg [ 7 , 13 , 44 ] and D_v was the venular diameter previously measured using the image caliper as described in the Methods section 2.3. The critical velocity (V_crit) was defined as the lowest or threshold velocity at which leukocytes are assumed to minimally interact with the vascular wall, calculated as

$V_{crit}=V_{avg}\cdot \epsilon \left(2-\epsilon \right)$ (5)

where ε was the ratio of leukocyte diameter to the venular diameter. In addition, all hemodynamic parameter symbols are listed in ( Table 2 ).

Table 2. Hemodynamic parameters for leukocyte rolling by intravital microscopy.

Experimental (Exp.).

Image segmentation was performed on 8-bit or 16-bit images using intensity thresholding, binarizing them into two intensity values (0 or 1). Following image pre-processing and optical flow analysis, image segmentation in ImageJ improved cell tracking efficiency by reducing computational runtime and false positives [ 47 ]. The auto-threshold plugin applied global thresholding methods, including Huang, Intermodes, Otsu, IsoData, MaxEntropy, Percentile, and RenyiEntropy based on histogram intensity.

RenyiEntropy threshold filter was selected [ 37 , 48 ] due to its effectiveness in high-entropy image sequences. It has been shown to differentiate leukocyte nuclei in peripheral blood smears and selectively isolates fluorescent leukocytes [ 37 ]. Studies, including Ghosh et al. (2011) have demonstrated its efficacy in segmenting leukocytes in images of intravital microscopy. Additionally, RenyiEntropy thresholding has been shown to efficiently separate leukocytes from the background in microvascular environments, even under low-contrast conditions. It outperformed standard methods, such as Otsu’s, particularly in images with non-uniform lighting or when leukocytes were partially obscured by other cells or tissue structures [ 48 ].

Additionally, RenyiEntropy thresholding effectively handles noisy images. Wu et al. (2019) found it more robust than traditional methods, providing accurate segmentation in IVM images. This robustness is crucial for tracking leukocyte behavior in vivo, where subtle intensity differences might otherwise be misclassified [ 49 ].

To enhance thresholding accuracy, users first defined a manual ROI representing each frame’s intensity maxima and minima, then applied the auto-contrast feature in ImageJ to adjust thresholding based on the image’s intensity histogram. Once an ROI including a representative cell, vessel wall, and background was selected, the RenyiEntropy algorithm analyzed the histogram, calculated total entropy for all possible thresholds, and determined an optimal threshold.

The algorithm generated an output video with threshold values, where pixel intensities >120 were classified as foreground and ≤120 as background. Running the algorithm independently on each frame—an adjustable parameter—ensured optimal threshold selection for diverse images. The segmentation process converted grayscale pixels (0 - 255) into binary (0 or 1), simplifying data for computer vision analysis [ 50 ]. Pixels below the threshold were set to black (“0”), while those above were set to white (“1”), facilitating accurate cell detection and tracking using the SALT module ( Figure 3 ).

Following fluorescence image enhancement and binarization, leukocyte detection was performed using ImageJ’s TrackMate plugin with the Laplacian-of-Gaussian (LoG) filter, further described in previous studies [ 19 , 51 - 53 ]. Parameters for LoG-based spot detection were customized for intravital conditions: a spot diameter of 10 µm and intensity threshold of 5 ± 2.5, based on the filtered image’s local maxima. These settings accounted for contrast and resolution changes introduced during pre-processing ( Figure 4 ).

After leukocyte indexing, we introduced a semi-automated framework to track cell trajectories across sequential frames. A modified Linear Assignment Problem (LAP) tracker was implemented in TrackMate, utilizing a Kalman filter for predictive modeling.

Whereas the Kalman filter operated in a two-step process: (1) prediction, estimating a leukocyte’s next position based on motion history, and (2) correction, refining that estimate using new, potentially noisy observations. In contrast, the TrackMate LAP tracker included features well-suited for biological imaging, accommodating occlusions, signal fluctuations, and frame-to-frame variability. However, it struggled to accurately track cells transitioning between free-flowing, rolling, adhered states. Free-flowing cells moved at approximately the average blood flow velocity (V_avg), rolling cells at velocities between 0 and critical velocity (V_crit), where 0 < V_crit, and adhered cells at velocities approaching 0 µm/sec.

Leukocyte-endothelial interactions, including rolling and adhesion to the venular wall, were assessed following leukocyte flux measurements in the selected venule. Operational definitions of leukocyte flux, rolling, and adherent were are as follows ( Table 3 ).

(A) Total leukocyte flux: The total number of leukocytes observed within the observational window including free-flowing, rolling and adhered cells.

(B) Rolling leukocytes: Defined by V_avg > 1.0 μm/sec, but also V_avg < V_crit, persisting for more than 3 frames.

(C) Adherent leukocytes: Characterized by V_avg < 1.0 μm/sec for ≥ 15 frames (~30 sec).

Table 3. Leukocyte classification criteria.

The original LAP tracker was designed for tracking particles moving at a constant velocity but struggled with leukocytes circulating in venules of living animals, where motion conditions are more variable, but also with cells that could drastically shift their velocity between frames ( Figure 5 ). To enhance the accuracy and reliability of leukocyte trajectory prediction, the original TrackMate LAP tracker was modified to utilize a Kalman filter-based multiple-hypothesis tracking model [ 14 , 16 , 23 ] to handle the dynamic leukocyte behavior observed in vivo. The Kalman filters model state transitions over time, predicting future positions and refining them using incoming observations and modifying the predictive algorithm real-time based on the cost-penalty-gap functions. As such, with each frame, the algorithm utilized a multi-hypothesis model that was processed in parallel so that for each frame pair $t\to t_{n+1}$, the algorithm would consider (three) possibilities: (A) rolling, (B) adhesion, and or (C) free-flowing (see Table 3 above). The algorithm exemplifies a hybrid AI approach, blending Boolean/Bayesian mathmatics with neural-network-inspired strategies for efficient biomedical image analysis.

After cells were indexed, SALT utilized Kalman filtering integrated with LAP-based optimization to track leukocyte trajectories, utilizing temporal smoothing and prediction mechanisms found in recurrent neural networks (RNNs) or transformers’ attention models. While not a traditional deep neural network machine learning framework, SALT utilized unsupervised and semi-supervised functionality to mimic modern deep learning neural network principles in a pseudo-neural network (pseudo-labeling) framework implemented by relatively simplistic tools like ImageJ macros, OpenCV-style plugins, and Excel.

SALT utilized convolutional neural network (CNN) principles in leukocyte detection, recurrent neural network (RNN) principles in leukocyte spatiotemporal movement motion modeling with Kalman filters and sequence prediction, and finally classification logic that parallels how MLP (multilayer perceptron) layers map features to labels. Modification of the SALT parameters and tracking algorithm were adjusted by comparing predicted trajectories to known leukocyte trajectories obtained from manual frame-by-frame tracking data. The SALT model framework incorporated ( Table 4 ).

Table 4. Neural networks frameworks adopted by SALT.

1. Prediction of Cell Position (Forward Pass):

Similar to the forward propagation in neural networks, the SALT tracker generated predictions of leukocyte positions based on a priori data (previous frames and leukocyte trajectories). The leukocyte’s predicted position was computed using leukocyte free-flowing velocity ( $V_{avg}$) and the threshold for leukocyte rolling, the critical velocity ( $V_{crit}$ This mimics the weighted summation step in neural networks.

2. Cost Function and Penalty System (Loss Function):

The SALT method incorporates a cost function, $f\left(c\right)$, similar to the loss function in neural networks, where it computed the penalty based on MSD difference between predicted leukocyte positions and their actual measured positions, represented as,

$f\left(c\right)={\displaystyle \sum {\left(x_i-x^{*}\right)}^2\left(t_n\right)+\cdots +{\left(x_i-x^{*}\right)}^2\left(t_{n+1}\right)}$ (6)

where, $x_i$ was the predicted displacement, and $x^{*}$ was the actual displacement, quantifying prediction errors, and calculating the loss or error term in a neural network.

3. Adaptive Decision-making (Backpropagation Analogy):

Additionally backpropagation involved adjusting the weights based on errors. In SALT, instead of weight adjustment, the framework updated the leukocyte trajectory prediction dynamically, where each linkage. It employs a Bayesian tracking approach (through MATLAB’s µtrack gap function) to refine predictions when leukocytes temporarily disappear from view, effectively adapting future predictions based on past inaccuracies.

4. Multiple-Hypothesis Tracking (Ensemble-like Predictions):

The SALT method uses multiple hypotheses simultaneously to track leukocytes—free-flowing or rolling leukocytes—similar to neural networks utilizing ensemble methods (multiple models and weighted predictions)

SALT dynamically classifies leukocytes into rolling, adherent, or free-flowing categories based on the blood flow velocity calculations computed for each venule analyzed and the derived threshold velocity (V_crit), at which cells start to slow down (rolling) through leukocyte-endothelial interactions, real-time velocity of each , historical data, and the penalty-cost matrices. It combines velocity history with condition-specific predictions (free-flow vs. rolling) to assign the most probable leukocyte trajectory, further resembling how neural networks use historical context and multiple inputs to refine outputs. We adopted a semi-supervised training framework utilizing the blood flow velocity to predict leukocyte free-flowing velocity (V_avg) and rolling velocity (0 < V_rolling < V_crit), using the initial search radius ( $x_i$), assuming the cell was free-flowing and the maximal search radius ( $x_f$) to increase the search area to modify the input parameters and fine tune the SALT algorithm. The initial search radius, $x_i$, was calculated as,

$f\left(x_i\right)=x_0+V_{avg}\cdot t_n$ (7)

where $x_0$ represents the leukocyte’s starting position, V_avg is the average leukocyte velocity, and $t_n$ is time. The maximal search radius, $x_f$, the cell displacement from a predicted position, was calculated as:

$f\left(x_f\right)=V_{crit}\cdot t_n$ (8)

thus, the most probable leukocyte location, $f\left(x_{i+f}\right)$, combined both radii:

$f\left(x_{i+f}\right)=f\left(x_i\right)\pm f\left(x_f\right)$ (9)

Tracking was initiated with a minimum of three frames, including two consecutive ones. To enhance decision-making, a penalty cost was incorporated into the model by assigning quantitative penalties to suboptimal choices or constraint violations. To ensure accurate linkage between predicted and observed positions, the neural network employed a penalty cost matrix. This cost function was computed based on squared displacement errors between predicted ( $x_i$) and observed positions ( $x^{*}$):

$f\left(c\right)={\displaystyle {\sum }_n^{n+1}{\left(x_i-x^{*}\right)}^2\left(t_n\right)}$ (10)

where $x_i$ represents the predicted displacement and $x^{*}$ is the true displacement. The greater the magnitude of the penalty cost, the higher the cost, making the decision less desirable.

To address leukocytes disappearing out of frame or due to image artifacts, we weighted the cost matrix with the gap interval penalty function until the SALT tracking data aligned with the manual ground truth data. For a leukocyte track initiated at frame t_n−1 and detected through t_n but missing at t_n+1, the gap penalty function used estimated the position at t_n+2 independently of t_n+1. The tracking algorithm then retrospectively estimated the missing position at t_n+1 based on V_avg, the LAP algorithm, as:

$t_{n-1}\to t_n\to \cdots \to t_{n+2}$ (11)

The dots (…) represents the missing gap. If a leukocyte was undetected across successive frames, the penalty cost for the missing gap was estimated based on subsequent linkages; with weights applied according to the gap(s). With each frame-frame link, a cost function determined the most probable trajectory, and was the summation of (penalty cost matrix, gap closing penalty, and probability for the cell to be predicted to be free flowing (Equation (12)) or rolling (Equation (13)). For a predicted track (P), the cost function (C) was conditionally determined by,

$C_{\left(x_i\right)}=P_{\left(C_{x_i}\right)|\left(C_{x_f}\right)}{f}_{\left(x_i\right)}$ (12)

$C_{\left(x_f\right)}=P_{\left(C_{x_f}\right)|\left(C_{x_i}\right)}{f}_{\left(x_f\right)}$ (13)

where $x_i$ is the predicted position based on initial velocity (assuming leukocyte is free-flowing), $x_f$ is the

predicted position based on rolling velocity (slower, transient leukocyte-endothelial interaction, $f_{\left(x_i\right)}$ and $f_{\left(x_f\right)}$ are the penalty cost functions, and $P\left(C_{x_i}|C_{x_f}\right)$ and $P\left(C_{x_f}|C_{x_i}\right)$ is the reverse probability that

the true cell behavior was governed by the free-flowing trajectory model, $x_i$, given the evidence from the alternative rolling trajectory model, $x_f$, and vice versa.

The penalty cost and predicted trajectory was also confined to,

$C\left(x_i\right)\ne C\left(x_f\right)$ over the frames $t_{\left(n-1\right)}\leftrightarrow t_{\left(n\right)}\leftrightarrow t_{\left(n+1\right)}$ (15)

indicating that a cell could only be classified as either rolling or free-flowing for a given frame. The penalty function penalized larger deviations, guiding the algorithm to prefer linkages with minimal spatial displacement error fine-tuned by matching the SALT predicted trajectories while comparing it to the ground truth method. If a leukocyte was undetected across consecutive frames, a cost penalty was applied, terminating the track if it exceeded the predefined threshold (p < 0.05) and could not be assigned positions based on predicted trajectories. After fine-tuning the SALT module, the probable trajectories of leukocytes was observed to clean up the noisy detections and yielded greater consistency in the tracking the same cell across frames ( Figure 6 ).

After obtaining V_crit, V_avg, and the number of points, the SALT Tracker computed additional parameters for leukocyte analysis in Excel. The number of adherent and rolling leukocytes were determined off-line from Trackmate data ( Table 3 ). The exported variables from the SALT output included Vxy (apparent Vavg), frames, Vmin, Vmax and total track duration. These parameters were then input into Excel, where conditional logic formulas quantified the total leukocyte flux, rolling flux, and number of adherent cells for each image set. To validate the SALT method, the image was analyzed in parallel using both SALT and the traditional manual frame-by-frame analysis methods for comparison.

All statistical analyses were performed using GraphPad Prism 8 (GraphPad Software) and R v4.4.2.

Data from multiple experiments (videos) were compiled in Excel spreadsheets and imported into Prism/R for analysis. We first evaluated the relationship between automated SALT measurements and manual measurements using Pearson correlation coefficients (r). High Pearson r values (close to 1.0) indicate strong linear agreement between the two methods. Next, we used paired two-tailed t-tests to determine if there were any systematic differences between SALT and manual measurements (e.g., in average rolling velocity). A significance level of α = 0.05 was used throughout; p-values < 0.05 were considered statistically significant. Statistical results are reported in the Results section with exact p-values where relevant. In cases of comparing two groups with potentially unequal variances, Welch’s corrected t-test was used instead of the standard t-test. All data are reported as mean ± standard error of the mean (SEM) unless noted otherwise. Normality of distributions was assessed informally.

To validate SALT, an expert (Rater 1) and two novices (Raters 2 and 3) independently analyzed images using both SALT and manual tracking methods. Leukocyte rolling velocity was assessed as described below in Table 5 .

Table 5. SALT validation methodology.

^arepresents the # of cells analyzed. ^bindicates rater designations: Rater 1 (expert), Rater 2 (novice 1), Rater 3 (novice 2).

To determine cell-to-cell precision in tracking, individual leukocytes rolling velocity was cross-analyzed on image sets, comparing data obtained from the SALT method (n = 5, 283 cells) against the ground truth (n = 5, 318 cells). RMSE values, expressed as either standard error in microns or percentages, with lower values reflecting higher precision and centroid trackers having RMSE values upwards of 66.8% [ 58 ]. Cui (2006) created a Monte Carlo approach to rolling leukocyte tracking in vivo and assessed a centroid tracker, correlation tracker, GVF snake tracker, and Monte Carlo tracker, for rolling leukocyte analysis, yielding RMSE values of 1.04 μm, 0.97 μm, 0.52 μm, and 0.47 μm, respectively [ 59 ].

For intra-rater validity assessment, a single rater (Rater 1) analyzed leukocyte rolling velocity (n = 5) using both SALT (283 cells) and manual (318 cells) tracking methods. Minimal deviation was observed (RMSE = 0.11 μm/sec, 1.92%) between SALT (7.95 ± 2.1 μm/sec, n = 5) and manual tracking (7.8 ± 5.1 μm/sec, n = 5), further exhibiting a very high correlation between SALT and manual tracking measure (r = 0.97, p < 0.001) ( Figure 8 , left).

For inter-rater validity evaluation, leukocyte rolling velocity data (n = 8) was analyzed in parallel by 3 raters: Rater 1 (322 cells), and 2 novice raters, Rater 2 (303 cells) and Rater 3 (235 cells) ( Figure 8 , right). Comparing leukocyte rolling RMSE of 1.13 μm/sec (9.88%) between novice raters (8.1 ± 3.4 μm/sec; n = 8) and the expert rater (6.50 ± 1.20 μm/sec; n = 8) was observed. The correlation was r = 0.89 (p = 0.055). Although the correlation was strong, it was near statistical significance likely due to individual cell tracking differences between raters. Welch’s t-test (t = 0.0083, p = 0.993) indicated no significant difference in leukocyte rolling velocity between these two approaches when accounting for heterogenic populations (see Abbreviations).

In addition to leukocyte rolling velocity to define local tracking accuracy as described in Section 3.1, the quantification of leukocyte-endothelium interactions-such as leukocyte displacement, total leukocyte flux, rolling flux, and adherent cells was assessed to further validate the accuracy of the SALT module (n = 8) vs ground truth, manual frame-by-frame tracking (n = 8), and were measured at 0, 5, 10, 15, 30, 45, 60 minutes in mice under resting conditions, shown in Figure 9 .

The Pearson correlation coefficient (r) was calculated to assess the relationship between data obtained from SALT and manual (ground truth) analyses [ 58 ] shown in Figure 9 , insets and summarized in Table 5 . For each variable measured at each time point, denoted as X_n and Y_n, respectively, the correlation was computed:

$\text{Predicted}\left(X_n,Y_n\right)=\text{Manual}\left(X_n,Y_n\right)$ (14)

If SALT accurately predicted leukocyte movement, each measured variable would have a perfectly linear relationship (r = 1), as assessed by Pearson’s correlation coefficient

Comparisons of leukocyte flux, rolling, and adherence using SALT versus manual ground truth analysis across multiple experiments yielded consistently strong correlations ( Table 5 ). Total leukocyte flux, rolling

flux, and adherent leukocyte counts demonstrated significant correlation coefficients, r = 0.81, 0.89, and 0.97, respectively (p < 0.05). Hemodynamic-dependent parameters including leukocyte rolling velocity and leukocyte displacement, the mean squared displacement (MSD), and wall shear rate (γ_W), exhibited strong relationships with blood flow velocity highlighting SALT’s reliability in dynamic vascular environments, r = 0.97, 0.96, and 0.98, respectively (p < 0.001) ( Table 6 ).

Table 6. Correlation of SALT and with respective manual ground truth parameters.

Pearson correlation coefficient (r), mean squared displacement (MSD), Standard error (SEr), *p < 0.05, **p < 0.001.

Although, total leukocyte flux and rolling flux showed a slightly weaker association, with r values of 0.81 and 0.89, respectively, both were statistically significant (p < 0.05). No significant changes were observed in leukocyte displacement, total leukocyte flux, rolling flux, and adherent cell counts over the 60-minute analysis period ( Figure 9 ). To confirm that hemodynamics were not influencing any observed differences or variance, both hemodynamic-dependent and hemodynamic-independent parameters associated with leukocyte-endothelial interaction were included in the analysis ( Table 6 ) [ 6 , 8 , 13 , 40 , 42 , 45 , 60 - 62 ].

The computational cost in cell tracking, primarily refers to the time, resources, and complexity involved in processing and analyzing image data for leukocyte tracking. The SALT method, developed for semi-automatic leukocyte tracking in vivo, explicitly aimed to address the computational costs associated with manual frame-by-frame analysis, which is typically time-consuming and labor-intensive, and to maximize computational efficiency ( Table 7 ).

Table 7. Computational cost comparison between SALT and other tracking methods.