Investigating active dynamics of contractile actomyosin gels with micro particle image velocimetry (micro-PIV) analysis

Abstract

Micro-particle image velocimetry (micro-PIV) is a powerful imaging method for resolving flow fields in microscopic systems, but its application to rapidly deforming gels requires key modifications. Here, we adapt micro-PIV to quantify contraction dynamics of active actomyosin gels without invasive tracer beads by tracking local myosin-generated actin inhomogeneities. We show that accurate displacement measurements depend critically on optimizing the time interval over which displacements are computed and the number of frames used in ensemble correlation, relative to the poroelastic timescale and stage of contraction. To assess reliability, we quantify four complementary metrics: displacement vector fields, displacement-magnitude maps, radial profiles of radial and tangential displacement components, and ensemble-averaged orientation with rotational measures. Incorporating the elastic response of the gel, we extract radial strain profiles under an axisymmetric approximation and demonstrate robustness for irregular geometries and off-center contractions. Across conditions, we observe common radial signatures consisting of inward radial contraction with peak displacement at intermediate radii and effective radial stretching near the boundary. These deformation fields provide a basis for inferring spatial and orientational distributions of motor-generated active stresses using appropriate constitutive models. Our approach advances quantitative analysis of active poroelastic materials and has broad applications in biomaterials design, cytoskeletal dynamics, and morphogenesis.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-54334-1.

Introduction

Cell shape changes are essential for biological processes such as cell division and cell motility during embryonic development, wound healing and immune responses¹. In animal cells, such shape changes are typically driven by the dynamic reorganization of their actomyosin cytoskeleton, a network of actin filaments, myosin molecular motors, and accessory proteins. Myosin motors consume ATP to slide actin filaments according to their polarity², leading to active contractility and self-organization of the cytoskeletal network^3–7. These active and chemo-responsive mechanical forces enable cellular functions such as shape changes and movement^8–10, and are an example of active, adaptive gels that exhibit both viscous and elastic response^11–13.

However, the complexity of the cytoskeleton, with its interconnected chemical and mechanical processes spanning diverse spatial and temporal scales, poses significant challenges for the complete understanding of its structural changes during cell motility and morphogenesis. In vitro reconstituted systems allow for controllable investigations using a minimal set of components, actin filaments, myosin II motors, ATP, and an actin crosslinker (such as fascin), which together form contractile elastic networks^5,7,14–18. These actomyosin gels, which mimic the mechanical properties of the cellular cytoskeleton^18–22, provide valuable insight into active force generation and contractility observed in processes such as shape changes, motility, and tissue mechanics^23,24. Myosin motor-induced active forces have been shown to drive complex 3D shape changes in active gel sheets^18,25, and identifying the spatiotemporal distribution of these forces requires tracking the gel dynamics. Notably, these dynamics exhibit poroelastic effects, where motor-driven contraction of the elastic actin network leads to the outflow of interstitial fluid¹⁸, consistent with observations in single cells²⁶ and multi-cellular tissues^8,27. Consequently, probing such complex two-phase dynamics requires modifications to conventional methods of tracking microscale flows.

Conventional particle image velocimetry (PIV) is a well-established, non-intrusive technique for measuring velocity fields in macroscopic flows, widely used in turbulence, aerodynamics, and engineering applications^28–30. In a typical PIV experiment, the fluid is seeded with tracer particles ranging from tens to hundreds of micrometers. A laser sheet illuminates a thin slice of the flow, and high-speed cameras record successive images. By using cross-correlation algorithms on these image pairs, the displacement of the material elements, and thus the displacement vectors, are calculated³¹. In contrast, micro-PIV extends this methodology to microscale flows using microscope-based imaging and volume illumination enabling measurements in microfluidic and biomedical systems^32–34. The need for high spatial resolution dictates that the tracing particles must be small, typically sub-micrometer length scales. For such small particles, noise due to Brownian motion can significantly hinder accurate velocity measurement, making ensemble (multi-image) correlation averaging^32,33 frequently used for extracting statistically reliable velocity fields.

Micro-PIV has been widely used to quantify velocity fields in reconstituted actomyosin and active cytoskeletal networks, enabling analysis of contractile flows, spatiotemporal patterns and organization dynamics at various length scales^{3,14,17,18,35–39}. Traction Force Microscopy (TFM) implementations also typically involve a Micro-PIV step to measure the initial material displacement field, from which the force fields can be deduced⁴⁰. This technique is also useful for measurement of velocity gradients within microchannels and complex microfluidic networks, useful for lab-on-a-chip applications^41–43. Understanding these flows is crucial not only for the development and optimization of microscale technologies for biomedical application^44,45 but also for resolving the dynamics of complex biological systems, which remain poorly understood.

In this study, Micro-PIV combined with multi-image ensemble correlation was employed to analyse the contraction dynamics of actomyosin gels of controlled composition and elastic properties. We adapt conventional micro-PIV to a system with poroelastic contractile dynamics that significantly reduces in size during the period of observation^18,25,46. Prior studies of these actomyosin gels establish that they undergo poroelastic dynamics, where contraction results from solvent efflux through the pores in the elastic actin network¹⁸. Unlike a purely viscous fluid, the characteristic timescale of contraction is therefore a stress diffusion time scale that depends on system size and network pore size. Specifically, we show how the micro-PIV analysis parameters pertaining to time interval over which material displacement is considered, and the number of image frames to be correlated need to be optimally chosen in relation to the relevant poroelastic time scale that governs the rate of gel contraction, and the stage of contraction. Instead of placing invasive beads, we track the local inhomogeneities in gel density, caused by self-organization of actin by myosin (actin foci) that appear as bright spots in network fluorescence signal which we utilize for PIV analysis^18,39. We extend our analysis of material deformation to non-axisymmetric shapes which advance upon prior work on these systems. Our analysis reveals how circular and non-circular gels share common features in their deformation profiles. Specifically, the gels exhibit an inner region with isotropic contraction and an outer, aligned region with radial stretching. Future studies involving physical modeling of the poroelastic dynamics will reveal the underlying mechanical processes that result in these deformation profiles. The methods reported here can be generally applied to study strongly deforming materials.

Methods

Preparation of contractile poroelastic actomyosin gels

We extend this methodology to explore the material and flow properties of contractile actomyosin gels of various shapes. The gels are formed by mixing 5µM actin monomers, 16.7 nM myosin motors (introduced as large aggregates of ~ 150 myosin dimers each), 280 nM of the passive crosslinker fascin, and 2mM ATP and an ATP regenerating system that maintains a constant ATP level constant¹⁸. The protein mixing time defines the experiment starting time \:t=0. A drop of solution is confined between two PEG-passivated glass coverslips. The drop volume and the spacing between the coverslips set the initial actomyosin gel radius \:R^18,25,46. Network formation begins with actin filament polymerization and bundling by fascin⁴⁷, followed by active crosslinking by myosin motors which localize to the bundles’ intersection points (bright actin foci), to create an interconnected active network that dynamically coarsens with time⁵. This initial forming phase is followed by network contraction, dominated by myosin-induced filament sliding⁴ as inferred from comparisons between bundle contour lengths and end-to-end distances^18,46. These processes can be followed by labelling the actin monomers or the myosin aggregates using fluorescent markers^5,18,46. We utilize the local inhomogeneities in gel density (i.e., actin foci) that appear as bright actin spots in network fluorescence signal^18,39 for Micro-PIV analysis. The area and mean intensity of the individual actin foci remain grossly unchanged during contraction¹⁸, unlike during the initial network forming and coarsening phases^5,18.

Image acquisition

Actomyosin gels labeled with Alexa Fluor 488 were imaged 1–2 min after protein mixing using an Olympus IX-71 inverted fluorescence microscope. Imaging was performed at low-magnification to capture the entire gel area throughout contraction while minimizing depth-of-field limitations associated with higher magnifications. Images were acquired with an Andor DV887 EMCCD camera controlled by MetaMorph software in streaming mode at 100 ms per frame. This temporal resolution was sufficient to resolve the dynamics of gel contraction while maintaining adequate signal-to-noise. The excitation intensity was kept as low as possible to prevent signal saturation at later stages of contraction. The effective pixel size at the sample plane was 6.4 μm pixel^− 1. A 512 × 512 pixels image encompassing the full gel disc (see for instance the gel shown in Fig. 1) was acquired, while preserving sufficient spatial resolution to resolve actin-density inhomogeneities (actin foci), which serve as tracers for micro-PIV analysis.

Fig. 1.

Workflow of the Micro-PIV analysis of contractile actomyosin gels. (a) Raw fluorescence image of an actomyosin gel labeled with Alexa Fluor 488, showing the initial gel radius () (white circle) and instantaneous radius . (b) Pre-processed image after background subtraction and, when required, image stabilization. (c) Time-dependent binary mask defining the gel region used for analysis. (d) Displacement vectors through ensemble-correlation PIV on the masked image sequence. (e) Map of the local strain-rate trace derived from the displacement field; negative values indicate local contraction, and positive values indicate local expansion. Scale bars, 300 μm.

Image pre-processing

Raw images were pre-processed in ImageJ/Fiji⁴⁸ prior to PIV analysis to improve data quality and reliability. Background subtraction was performed using a rolling-ball algorithm (radius = 50 pixels)⁴⁹ to remove static background signal and enhance contrast of the actin-density features. When necessary, image sequences were stabilized using image registration (StackReg, ImageJ/Fiji)⁵⁰ to correct for translational drift between frames. These steps ensured that measured displacements reflect gel deformation rather than stage motion. We also evaluated image deconvolution to enhance image sharpness, using PSFGenerator⁵¹ and DeconvolutionLab2⁵² in ImageJ/Fiji. However, in our system, deconvolution introduced artifacts in the computed velocity field. Therefore, all results presented in the main text were obtained without deconvolution. Further details are provided in Supplementary Information, Section S1.

Masking of the contracting gel

Following pre-processing, the gel region was isolated by masking in MATLAB (as shown in Fig. 1(c)) prior to PIV analysis⁵³. The mask excludes the surrounding background solution and the drop edge, preventing non-relevant regions from contributing to the correlation calculation. Importantly, the mask was updated dynamically to follow the contracting gel boundary, defined by the instantaneous gel radius . This adaptive masking ensures that the computed displacement and velocity fields correspond exclusively to the deforming gel throughout the contraction process. The procedure used to adapt the mask to the changing gel area, along with representative MATLAB code snippets, is described in Supplementary Information, Section S2. The resulting masked image sequences were then used as input for the main PIV analysis pipeline.

Workflow of micro-PIV analysis

PIV analysis was performed on the masked image sequence in MATLAB using ensemble correlation in PIVLab⁵³ to estimate local displacement vectors of actin-density features (bright actin spots) across selected image pairs. From the resulting displacement fields (Fig. 1d), velocity fields were computed over a chosen time interval , and then the local deformation field (strain rate, Fig. 1e) was derived from the Jacobian of the velocity field. Further implementation details of the PIV analysis are provided in Supplementary Information, Section S3.

Adaptive ensemble-correlation Micro-PIV for shrinking poroelastic contractile gels

To improve the accuracy of displacement estimation in the presence of noise and evolving structure, we employed ensemble correlation across multiple image pairs, enhancing signal-to-noise and stabilizing displacement estimates^32,33. The number of image pairs being correlated, \:N, the time interval between successive image pairs, and the initial frame from which correlation begins, , all play significant roles in determining the reliability of the correlation and of the resulting velocity data.

Adapting the interrogation windows size for ensemble correlation

To resolve deformation across spatial scales while maintaining robust correlation, we implemented a three-pass interrogation scheme with progressively smaller windows and 66% overlap between adjacent windows (step size equal to 1/3 the window size)⁵³, ensuring smooth spatial sampling and reducing discretization artifacts. Crucially, interrogation window sizes were defined relative to the instantaneous gel radius , determined from the automated masking procedure, allowing the analysis to adapt to the shrinking domain while maintaining a consistent spatial resolution relative to gel size. This yields a balance between spatial resolution and vector density, constrained by the need to preserve reliable correlation while resolving deformation at the scale of the gel. Further implementation details of the PIV analysis are provided in Supplementary Information, Section S4.

Displacement and strain analysis between frames

To quantify material deformation, we compute strain between consecutive frames. This is equivalent to calculating the strain rate times The actomyosin gel is a poroelastic material comprising an elastic network permeated with solvent. The timescale over which the gel displacement vectors are measured in our experiments range between (for of \:2-10)\: frames) which is much shorter than the poroelastic stress relaxation time scale given by the timescale of contraction of the gel disk which is in the order of tens of seconds. The gel deformation between two frames is thus small, and can be described by the linearized strain rate tensor, constructed from the displacements measured in PIV⁵⁴. The displacement vectors obtained from micro-PIV analysis are located at regularly spaced lattice points (Fig. 2), from which the gel strain can be calculated using finite differences.

Fig. 2.

(a) Circular annular bins are constructed around the centroid of the gel disc shown in Fig. 1. The radial and azimuthal components of the displacement vectors are averaged over all angles in each circular bin. The bin width, depends on the gel disk radius at that frame, . In other words, there are 25 circular annuli from center to the boundary. (b) The displacement vectors at the lattice points measured in cartesian coordinates, can be converted into corresponding radial and azimuthal components, and . The origin of the coordinate system is chosen to be at the geometric center of the gel (red circle).

The strain tensor is the gradient of the displacement vectors and encodes geometric information on the different deformation modes of local slices of the gel: stretching or compression, shear, and rotation⁵⁵. We note that this is more commonly computed as a strain rate in usual PIV analysis, but we here do not divide by the time interval, This gives the information of material deformation over a small-time interval. Calculation of local strain and estimation of local displacements and strains in a polar coordinate basis, along with representative MATLAB code snippets are given in the SI, Supplementary Note 5.

Obtaining radial profiles in displacement by azimuthal averaging

The gel in Fig. 1 which we analyze here appears to contract towards the centroid with all displacement vectors oriented radially. Hence, we expect the local azimuthal displacements to be very small and can approximate the gel contraction to be axisymmetric. We consider circular annuli of equal thickness, from the gel boundary to the centre (a total of 25 annular bins) (Fig. 2). The bin width is calculated at every frame and is given by In each of these annular bins, there are multiple PIV lattice points. We calculate the mean and standard deviation of the radial and azimuthal displacements in each of these annular bins. To validate our assumption of axisymmetric contraction, we consider azimuthal displacement as a function of the normalized distance from the centre of the gel (see below Figs 6, 9, 11). It fluctuates close to zero, suggesting no apparent average azimuthal displacement, consistent with axisymmetric contraction.

Fig. 6.

Radial () and tangential () displacement profiles as a function of normalized radius for each ensemble size ranging from (a-e)  image pairs. The radial and azimuthal components of the displacements from Fig. 5a-e are averaged over all angles over annular bins having a width, , where is the gel radius at the analyzed frame. For small both components exhibit large fluctuations. As \:N increases, the radial velocity profile becomes smoother, and the tangential component stabilizes. At , we see a linear profile in the inner region as expected for uniform contraction, and a slight upward curvature near the boundary. At this characteristic behavior is lost. Analysis is performed on the gel depicted in Fig. 1 for a time interval . All cases shown are for frame correlations beginning at initial frame number,

Fig. 9.

Effect of stage of contraction () on radial () and tangential () displacement profiles as a function of normalized radius . The temporal evolution of the radial profiles of both displacement components is shown for Fig. 8(a-l) for the gel shown in Fig. 1. For \:N=100 (g–l), the radial displacement exhibits an approximately linear profile in the inner region, consistent with uniform contraction, along with a slight upward curvature near the boundary. This characteristic is not observed for \:N=300 (a–e) but reappears at the highest value (f). All displacement fields are computed with 1.

Fig. 11.

Radial (\:{u}_{r}) and tangential (\:{u}_{\phi\:} ) displacement profiles for different frame intervals (). (a–h) Displacement profiles computed for and \:20 frames, respectively. For small , both \:{u}_{r} and \:{u}_{\phi\:} exhibit smooth, low-noise profiles with consistent radial decay and stable tangential components. At intermediate , the radial velocity magnitude increases approximately linearly with , as expected from larger frame separation, but begins to show elevated variability. For very large values (\:15-20), the profiles become increasingly noisy and spatially irregular, indicating correlation loss and decorrelation of tracer features. All analyses were performed on the gel shown in Fig. 1.

Results

We now present our key results from analyzing the spatio-temporal contraction dynamics of poroelastic actomyosin gels using the micro-PIV methods described above.

Gel contraction dynamics

Figure 3 depicts the characteristic time-dependent gel edge radial velocity of the actomyosin gel depicted in Fig. 1. The corresponding radial contraction velocity indicates an initial rapid contraction, characterized by a linear increase in contraction velocity up to maximal value . This initial linear phase is followed by an exponential decay phase, , where τ is the characteristic relaxation time¹⁸. This relaxation time was shown to be proportional to an effective friction constant, inversely proportional to the gel elastic modulus, and to depend on system size^18,26,56. This is consistent with poroelastic models that account for the permeation of water through the actin gel pores. At the end of gel contraction, the gel reaches a mechanically stable state where the active contractile stresses exerted by myosin motors in the gel are balanced by the elastic stresses developed due to gel deformation¹⁸.

Fig. 3.

Time-dependent evolution of actomyosin gel dynamics. Depicted is the gel edge radial contraction speed against time of the gel disc shown in Fig. 1. Gel contraction starts after protein mixing time (defined as \:t=0). First, the speed grows linearly up to a maximal value for (marked by (iii) and corresponds to Frame 550). This phase is followed by an exponential decay phase where is the poroelastic decay time. Time interval between frames is . Image acquisition starts 60 s after protein mixing (Frame 1). (i) to (vi) corresponds to specific frame numbers: \:380,\:\:500,\:550,\:\:600,\:\:800, and \:1120, respectively for which the effect of  on ensemble correlation is studied (see below).

Quantitative analysis for micro-PIV parameter selection: number of correlated image pairs and frame interval

The number of image pairs \:N is a crucial parameter as it directly impacts the statistical reliability and accuracy of velocity measurements. Specifically, for steady flows, it is expected that increasing the number of image pairs for a given frame interval will reduce random errors and enhance measurement accuracy^32,33. However, for strongly contracting gels where velocities change significantly and nonlinearly with time (Fig. 3), the choice of optimal \:N at given is not straightforward and should depend on the stage of contraction, at which velocities are being measured. Overall, the total time over which image pairs are correlated, , should be smaller than the relevant physical timescale over which the material velocities significantly change. In the following results, we use several quantitative metrics to establish the optimal choice of these parameters.

Optimizing image pre-processing for micro-PIV analysis

Before examining the effects of the values of \:N and , we first evaluated how different pre-processing steps affected the accuracy and stability of the displacement fields. We compared raw, background-corrected, and deconvolved images by examining correlation peak quality, vector yield, and the spatial consistency of the resulting displacement fields (Fig. 4a-c) and rotational flows (vorticity) (Fig. 4e-f). Raw images showed uneven illumination and residual background structures, which weakened the correlation peaks and led to noisy or missing displacement vectors. Deconvolution improved visual sharpness but also introduced artifacts, such as unusually small displacement vectors of material points within the bulk and a few large, randomly oriented displacement vectors near the boundary leading to artificially large vorticity (Fig. 4f). In contrast, background-corrected images without deconvolution generated the most spatially coherent displacement fields, which are primarily radial^14,17,18, as supported by the absence of rotational flows (Fig. 4e), and which we use in all subsequent PIV analysis.

Fig. 4.

Effect of image pre-processing on Micro-PIV displacement fields and emergence of rotational flows (vorticity) (,  frame). (a-c) Shown are displacement fields and (d-f) corresponding vorticity maps for (a, d) unprocessed, (b, e) background corrected only and (c, f) background corrected and deconvolved images. Raw images give low-quality vectors. Background-corrected images without deconvolution generated the most stable and coherent results. Background correction and deconvolution improve sharpness but introduces artifacts that degrade vector reliability and produce artificially large vorticity values, notably at the gel boundary. Blue and red correspond to clockwise and counterclockwise rotations, respectively. Analysis is performed on the gel depicted in Fig. 1. Bars are \:300μm.

Effect of number of image pairs (N) used in ensemble correlation

We examined how the ensemble size (\:N) influences the stability and reliability of the displacement fields. For ensemble sizes ranging from we systematically quantified four key metrics: (i) the displacement () vector fields and (ii) the displacement-magnitude maps as shown in Fig. 5, (iii) radial profiles of the radial and tangential components of the (Fig. 6), and (iv) ensemble-averaged orientation of displacement vectors and rotational metrics of the velocity field. Specifically, these were the mean deviation from the radial direction and the vorticity (Fig. 7). The latter two quantities are expected to be small for fully connected crosslinked networks, like in our system, because the actomyosin contractility results in primarily radial movement^14,17,18, however this property may vary with network connectivity and architecture³⁹. All these metrics consistently reveal how the correlation improves with \:N, up to a point.

Fig. 5.

Effect of ensemble size (\:N) on Micro-PIV displacement vector fields and maps. (a-e) Displacement vector fields obtained using ensemble sizes ranging from to \:(N\:=300)\: image pairs, respectively. Very small ensembles  produce noisy and artificially large vectors, while intermediate ensembles  show partial improvement. A well-defined and coherent displacement field emerges at with minimal apparent improvement beyond that\:. (f-i) Maps of the displacement field for each corresponding ensemble size. Small ensembles produce highly scattered and spatially heterogeneous displacement magnitudes, whereas ensembles of yield smooth, azimuthally symmetric profiles. Analysis is performed on the gel depicted in Fig. 1 and for . All cases shown are for frame correlations beginning at initial frame number, Interrogation window 1 size = gel disc radius, step size = radius/3, Interrogation window 2 size = radius/3, Interrogation window 3 size = (interrogation window 2 size) / 2 or radius/6.

Fig. 7.

depicts the spatially averaged orientational and rotational metrics ( and vorticity) over all displacement vectors obtained from ensemble correlation. The corresponding spatial maps of vorticity at different N are shown in the SI Fig. S1. Small ensembles ( show large fluctuations in due to large fluctuations in displacement orientations. Both the and vorticity values plateaued after , exhibiting minimal frame-to-frame variation. Increasing the ensemble size further offered no meaningful improvement and instead began to oversmooth the field, suppressing real temporal changes. Together, these analyses demonstrate that frames provide the optimal balance between noise reduction and faithful preservation of the underlying gel-contraction dynamics, at least at this stage of the contraction ( frames).

As shown in Fig. 5, very small ensembles  produced displacement fields that were highly noisy, with irregular vector orientations resulting in large spatial fluctuations in the displacement magnitude maps. In contrast, at higher N values, the displacement vectors become smaller. We expect that this is a combined effect of averaging over increasingly decorrelated displacements, and the contraction velocities getting smaller at later stages of contraction.

This instability at lower N is reflected in the radial profiles of the radial and tangential components of displacement, obtained after azimuthal averaging of the micro-PIV displacement vector map (Fig. 6). These showed strong scatter at \:N=2-10. Intermediate ensembles reduced noise and a definite physically interpretable displacement profile emerged. As expected, the tangential displacement is nearly zero in this radially contractile gel. We see a linear profile in the radial displacement in the inner region as expected for uniform contraction where displacement is proportional to the radius. We find a slight upward curvature near the boundary for . This altered behavior near the boundary of the gel is consistent with poroelastic effects and local densification of the gel near the boundary as shown in prior work¹⁸. Later in this work, we show with strain analysis that this corresponds to radial stretching and strain alignment near the boundary.

Figure 7 Mean and vorticity as a function of ensemble size (N). The main plot shows the orientation metric computed as the dot product between the local displacement vector and the radial direction, . Thus, corresponds to perfectly axisymmetric contraction, where the displacement has only radial and no azimuthal component. The error bars correspond to the standard deviation of values of for all displacement vectors within the field of view. Small ensembles ( show large fluctuations in due to fluctuations in displacement vector orientations, whereas yields stable and consistent values. The inset shows the corresponding mean vorticity, calculated using the 2D cross product which also stabilizes for . Together, these metrics indicate that  provides the optimal ensemble size for reliable Micro-PIV displacement analysis. Analysis is performed on the gel depicted in Fig. 1 for a time interval frame and Errors correspond to standard deviation of experimental data.

Effect of stage of contraction

We next show that the choice of number of image pairs correlated over (\:N) should also depend on the stage of contraction of the gel at which we measure displacements. In Figs. 8 and 9, we contrast the results of ensemble correlation over \:N=100 vs. \:N=300 frames at different stages of contraction. In each case, the reported value represents the initial frame number at which we begin correlating, i.e. the frames being correlated over range from to . We find that although the 2D PIV displacement vector fields in Fig. 8 show little apparent difference between \:N=100 and \:N=300, important qualitative differences emerge in the azimuthally averaged radial displacement profiles in Fig. 9.

Fig. 8.

Effect of stage of contraction () on micro-PIV displacement vector fields of the gel shown in Fig. 1. The temporal evolution of the gel displacement fields is shown for ensemble sizes \:N=300 (a–f) and \:N=100 (g–l), corresponding to increasing values of and \:1120, respectively. All displacement fields are computed with . At the earliest stage (), significant noise in non-radial directions is observed for \:N=100 (g), which is substantially reduced for \:N=300 (a). For all other values of , the displacement fields for \:N=300 and \:N=100 are almost visually indistinguishable.

Importantly, \:N=100 shows the characteristic upward bend in the radial component of displacement () which is not clearly present at \:N=300. This feature corresponding to radial stretching is also seen at optimal values of \:N in Fig. 6. However, at later , even \:N=300 begins to show this feature. This shows that \:N should be chosen according to the stage of contraction, represented by . Early in the contraction, e.g. at , where the velocity of contraction rapidly changes (see Fig. 3), both \:N=100 and \:N=300 lead to noisy radial profiles of displacements. At intermediate stages, \:N=100 reveals correctly the characteristic displacement profiles, while \:N=300 remains noisy. Very late in the contraction, when the gel contraction velocities are very small, even \:N=300 gives the expected displacement profile shape. Overall, we see that the number of image pairs correlated over should be chosen according to the timescale over which velocities change appreciably.

Frame interval () optimization

After optimizing for the ensemble size to , we optimized the frame interval over which displacement is calculated. We test values from 1 to 20 frames (Fig. 10). We see that small values (\:1-3\: frames) produced the most reliable measurements. For frames, the correlation time, exceeds 30s, which is the characteristic timescale of gel contraction, see Fig. 3. Thus, the displacements get uncorrelated at larger \:\varDelta\:t (\:5-20\: frames) as seen in Fig. 10(c-e) and also in corresponding, velocity maps, Figs, 10 (h-j).

Fig. 10.

Effect of  (frame interval) on Micro-PIV displacement and velocity fields. (a-e) Displacement vector fields obtained using ensemble sizes ranging from  frames \:(N=100) respectively. (f-j) Corresponding spatial maps of velocity. Analysis is performed on the gel depicted in Fig. 1. All cases shown are for frame correlations beginning at initial frame number,  Bars are 300 μm.

In addition to the displacement vectors, we also examined the corresponding velocity fields and velocity maps as shown in Fig. 10 (bottom row) for each . Because velocity is displacement divided by , reliable velocity estimation requires both (i) accurate displacement measurements and (ii) a that preserves correlation quality. Both velocity fields and maps obtained for frames show nearly identical spatial structure and magnitude, indicating that these intervals lie well within the reliable correlation regime. In all these cases, the vectors exhibit a smooth, radially inward flow toward the gel center. This is further confirmed by the corresponding vorticity maps in SI, Fig. S2, as well as the values in SI, Fig. S3. On the other hand, at larger , the velocity vectors become very small on account of averaging over decorrelated displacements. This confirms that the displacements at these values are sufficiently large to obtain reliable correlation between frames, but are small enough to avoid large changes in gel contraction dynamics.

The radial and tangential displacement profiles further demonstrate how \:\varDelta\:t influences measurement quality (Fig. 11). For frames, the profiles are nearly identical: \:{u}_{r} decreases smoothly toward the disk center, and \:{u}_{\phi\:}  remains snearly zero across the disc radius. These small \:\varDelta\:t values capture the true contraction dynamics while keeping displacements within the correlation-stable regime, resulting in minimal noise. At the large intervals (), both \:{u}_{r} and \:{u}_{\phi\:}  show strong fluctuations and irregular radial dependence, reflecting decorrelation as tracer patterns deform significantly between frames. Together, these results confirm that provides the optimal balance between signal strength and correlation reliability for quantifying actomyosin-gel contraction.

Strain analysis as measure of gel deformation in time

After optimizing the micro-PIV process, we now investigate how the displacement data can be used to obtain insights into the material deformation. The physical quantity that describes deformation is the strain or strain rate, which is obtained from spatial gradients of the displacement or velocity, respectively. It is natural to ask how the strain values are distributed in space, i.e. at different positions within the gel, and how they are oriented, i.e. along radial and azimuthal directions. The methods for calculating the components of the strain from the displacement data are detailed in SI Supplementary Note 5. Importantly, we consider small strains occurring over one frame interval ( frame) and so these values are just the strain rate times .

Bulk or area strain maps as a measure of local contraction

The representative 2D heatmap of bulk or area strain (shown in Fig. 12) is obtained by tracing filled contour plots of the trace of the strain tensor ( + ) at each lattice point. The latter are computed by taking finite differences of the PIV displacement vectors on the lattice shown. This area measures the net area deformation (contraction or expansion) at a given location in the gel. Positive (negative) values correspond to expanding (contracting) regions. In Fig. 12, we show both the strain values directly (Fig. 12c), as well as after normalizing each individual positive or negative area strain by the maximum positive and negative values in the whole field of view at that specific time. The former shows that strain values are typically much smaller than unity, justifying the linearized strain calculation. The latter emphasizes common features between strain maps at different times in the contraction. The process used to generate the 2D heatmap of bulk area strain in Fig. 12 is described in SI Supp. Note 5.

Fig. 12.

Area strain (trace of the strain matrix) of the gel shown in Fig. 1. (a) A representative PIV snapshot of the gel used to compute the strain map. (b) The cartesian components of the strain tensor are obtained by taking derivatives of the displacement using the central difference method on the square lattice. (c and d) The trace of the strain between two frames is shown as a colormap (blue: negative or contraction, yellow: positive or expansion). The red arrows show the displacements obtained from PIV over one frame (between frames \:500\: and \:501), correlated over \:N=300 frames. We show strain values, both before and after normalization by the maximum positive and maximum negative values measured in the entire gel, respectively, at that specific time. The inner region of the gel undergoes rapid contraction, as indicated by dark blue regions. Closer to the boundary, we detect patches of stretched regions shown by the yellow hotspots.

Here, the centroid of the gel is demarcated by the red circle, the PIV arrows are shown in red, and the area strain is shown as a heatmap. The contracting regions, i.e. regions with negative strain, are shown in blue, while the stretched regions with positive strain are in yellow. We see that the inner region is mostly blue corresponding to contraction, while there are patches of stretched regions (yellow) near the boundary of the gel. This indicates non-uniform or anisotropic contraction of the gel, where the boundary contracts at a different rate and direction than the interior. While a representative frame from the PIV analysis is shown here, the time course of evolution of the area strain for this gel is shown SI Fig. S4, using additional selected frames.

We may follow a similar procedure to analyze 2D heatmaps of other components of the strain. The radial strain , and azimuthal strain , reveal the stretch or compression in radial and azimuthal directions respectively. For perfectly isotropic contraction, they are equal. The difference between the radial and the azimuthal strain components reveals the extent of anisotropy in the motor-generated active stresses.

Principal strain component analysis

While the trace of the strain gives just the magnitude of expansion or contraction, an analysis of the eigenvectors of the strain tensor reveals the principal directions of the expansion or contraction. The eigenvalues of the strain tensor are given by,

1

with direction of corresponding eigenvectors:

2

As shown in the schematic in Fig. 13, the strain in general contains stretching/compression but also deviatoric or shear components that correspond to shape change. Transforming to the eigen basis removes the simple shear component and gives orthogonal directions corresponding to the maximum and minimum stretching/compression, respectively. In general, these are not necessarily the radial and azimuthal directions.

Fig. 13.

Eigenvalue and eigenvector analysis of the strain tensor gives the principal directions of contraction and stretching of the gel depicted in Fig. 1. (Left) Schematic illustrating the computational procedure and intuitive meaning of principal strain components (maximal stretch/compression directions). (Right) The color map shows the normalized difference of the two strain eigenvalues for a representative frame from PIV of a circular gel. The vector map shows the two orthogonal eigenvectors scaled by the magnitude of its corresponding eigenvalue. The plot indicates an isotropic inner region (blue) where both eigenvalues are almost equal, and an anisotropic outer region (yellow). The outer region is characterized by increased alignment of strain along the azimuthal direction, with some local instances of high radial stretching.

In Fig. 13, we show the normalized difference of the two eigenvalues, as the color map. A lower value (closer to 0) suggests a high degree of isotropy, while a bigger value (closer to 1) indicates that one eigenvalue is dominant, corresponding to significant anisotropy. We also show both orthogonal eigenvectors in the vector plot, scaled by their respective eigenvalues. We observe no apparent alignment of strain in the inner region of the gel (blue), where both eigenvalues are nearly equal. This corresponds to isotropic contraction in the inner region and is consistent with the overall negative area strain seen in Fig. 12. Close to the boundary, the alignment of eigenvectors is predominantly azimuthal, with one eigenvalue significantly higher in magnitude than the other. This suggests azimuthal alignment of actin bundles and therefore, of contractile actomyosin force dipoles, at the gel boundary. There are a few instances of radially aligned eigenvectors accompanied by large positive eigenvalue at the boundary. This suggests radial stretching of the material in response to azimuthal contraction imposed by actomyosin forces, because of the Poisson effect⁵⁴.This effect provides evidence for the elastic response of the gel to active stresses, at short timescales.

While Fig. 13 shows a representative frame from the PIV analysis, the SI Fig. S5 shows similar plots for a sequence of frames. Overall, we observe azimuthally aligned eigenvectors close to the boundary of the gel (yellow) that suggest azimuthal contraction, while the inner region (blue) acts as an isotropic core of contraction.

Analyzing gels with non-axisymmetric displacement field

Some gels exhibit rigid body motion, that is displacement of their center of mass, as they contract. The displacement of the gel is no longer axisymmetric about its center of mass which we can verify by constructing concentric annuli around this point. We see for example in Fig. 14c-d that some of the displacement vectors are not oriented radially inward. We can instead identify an apparent centre of displacement (CoD) for such gels from the displacement vectors and estimate the radial profiles of displacements and strains with respect to this special point (CoD). We note that all deformation of the gel is encoded in the strains, which are gradients of the displacement. The displacement field, by itself, does not provide any fundamental insights into gel contraction. Nonetheless, by subtracting the rigid body or center of mass (CoM) motion, and subsequent averaging, we show that we recover universal trends in the radial gel displacement profiles. In general, it is possible that a gel also undergoes some rigid body rotation, but this is not the case in our gels where the tangential displacement is negligible.

Fig. 14.

(a) When the center of mass () of the gel displaces, the displacement vectors apparently converge to a shifted center of displacement (). (b) The distribution of the shift factor α (defined in see SI Supplementary Note 6) over different lattice vectors from the PIV, with the inset focusing on the strong peak. (c) A sample PIV with gel centroid marked by a red circle while the apparent center to which the displacement vectors converge is marked by a white circle. The latter is calculated from the median intersection point of the PIV vectors (see SI Supplementary Note 6). (d) The PIV map is transformed after subtracting the displacement of the center of mass which represents the rigid body motion of the gel. The center of displacement now coincides with the centroid shown by the red circle. (e) A very noisy radial profile of the radial displacement is obtained by azimuthal averaging about the centroid of the gel, since some of the displacement vectors are oriented away from the centroid close to the center of the gel. (f) Noise is reduced when the radial displacement profile is calculated relative to the center of displacement. For this transformed coordinate system, the PIV displacement vectors point towards the CoD restoring the axisymmetry of the displacement field. This restores the characteristic radial displacement profiles observed in the more symmetrically contracting gels, suggesting the same underlying physical mechanism in gel contraction.

We now transform to polar coordinates relative to this calculated center of displacement as the new origin. The radial direction for each displacement vector in the lattice is now relative to the CoD. We calculate profiles of the radial displacement by averaging over annular bins as described before. We compare in Fig. 14e and f these radial displacement profiles centered on the CoM and CoD respectively. In Fig. 14f, we plot the displacement vectors after subtracting the CoM displacement, i.e. the rigid body motion, . As expected, the displacement profiles are less noisy, and the characteristic trends in radial displacement profile are much more clearly seen in Fig. 14f, where we used the CoD as our point of reference.

The method of locating the center of displacement is also important for irregular gels that deviate from a full circular contour. This includes for example a gel whose boundary forms part of a circular arc (Fig. 15) and for gels that do not have a well-defined centroid. Instead, we obtain the center of displacement from such gels. Through trial-and-error method we arrive at a sector which best fits a circular region of the gel centered at the CoD. Here we observed that the gel is circular within the angular bounds of to as shown in Fig. 15b. We can determine the radial profiles of displacements and strains in this circular sector enclosed by the arc (Fig. 15b, c). Further analysis of the trace of the strain and the principal components of the strain at different frames for the gel shown in Fig. 15, are provided in the SI Figs. S5 and S6, respectively. Fig. S7 shows evidence for strong anisotropy in the strain field. In almost all cases seen, the dominant strain eigenvector is azimuthal, providing strong evidence for azimuthal alignment of the force-producing actomyosin fibers near the boundary of the gel.

Fig. 15.

(a) PIV map of an irregular shaped gel with displacement vectors pointing to the center of displacement (white circle). (b) We consider a sector of the gel which forms a circular arc at the boundary between angles to with respect to the center of displacement. The radial profile is estimated for the gel within the sector enclosed by the circular arc. (c) The radial profile of radial displacement for the gel within the circular sector is shown here.

From Figs. 14f and 15c, we see that gels that have moving geometric centers as well as of non-circular shape, give rise to qualitatively similar radial displacement and therefore, strain profiles.

Conclusion

In conclusion, we establish and validate a methodology for adapting conventional micro-PIV to the dynamics of strongly contractile active poroelastic gels. A central advance is the identification of optimal analysis parameters, specifically the time interval over which displacements are computed and the number of image frames included in ensemble correlation, which must be chosen in relation to the poroelastic timescale of contraction and its stage^{18,25–27,46,56}. We further demonstrate that reliable displacement fields can be obtained without invasive tracers by tracking local myosin-generated actin inhomogeneities. The robustness of the inferred fields is assessed using multiple quantitative metrics, including displacement vector fields, displacement-magnitude maps, radial profiles of radial and tangential displacement components, and ensemble-averaged orientation and rotational measures.

Analysis of strain fields and radial profiles reveals consistent features across gels of diverse geometries, including isotropic contraction in the interior, peak inward displacement at intermediate radii, suppressed motion near boundaries, and azimuthally aligned principal strains at the edge, consistent with actin fiber alignment observed in fluorescence microscopy²⁵. Importantly, the approach remains effective even for non-axisymmetric and irregularly shaped gels. While micro-PIV is commonly used to quantify local velocity and contraction rates in cytoskeletal networks^{3,14,17,18,35–39}, many prior studies rely on correlation between single image pairs. In contrast, our use of ensemble correlation across multiple image pairs enables robust extraction of global displacement fields in rapidly contracting gels.

Several limitations should be noted. The optimization of micro-PIV parameters must be performed separately for each gel, as contraction dynamics can vary qualitatively across samples. In fast-contracting gels, the number of frames that can be correlated to reduce noise is inherently limited, whereas slower-contracting gels exhibit higher intrinsic noise levels. Furthermore, our analysis is based on two-dimensional displacement fields obtained from fluorescence imaging; however, this approximation is appropriate for our system, as significant out-of-plane buckling occurs only at later stages of contraction^18,25.

Future work will extend the analysis to multiple gels that lead to diverse three-dimensional shapes²⁵. It will leverage the strain inhomogeneities quantified here during early and intermediate stages of contraction to inform three-dimensional mechanical models that describe out-of-plane deformation driven by in-plane stress imbalances. In summary, this research highlights the necessity of modified micro-PIV approaches for studying complex fluids, specifically poroelastic active materials with large, autonomous contraction at the microscopic scale, and advances our understanding of cytoskeletal dynamics and self-organization. While this work is in vitro on a purified protein system, it shows how aligned structures may arise spontaneously through the interplay of active contractility and poroelasticity also in cytoskeletal or tissue systems. The findings have broad implications for biomaterials design, cell motility, morphogenesis, and active matter physics.

Electronic Supplementary Material

Below is the link to the electronic supplementary material.

Author contributions

SC developed analytical methods for Micro-PIV analysis, prepared figures, and wrote the first version of the manuscript. SB analyzed the Micro-PIV data, developed methods for optimizing micro-PIV parameters and strain analysis, prepared figures and movies, and contributed to writing the revised manuscript. YA and DSS developed image analytical tools for data quantification and analyzed the dynamics of gel contraction. DSS also contributed to developing methods for micro-PIV analysis and to writing the revised manuscript. GL performed experiments and analyzed the experimental results. KD designed methods for optimizing micro-PIV parameters and strain analysis and wrote the manuscript. ABG designed and developed the experimental system, developed analytical methods for data quantification, and wrote the manuscript. All authors reviewed the manuscript.

Funding

Israel Science Foundation grants 2101/20, 2804/25, and the Ministry of Science and Technology (grants 3-17491 and 1001585065) (A.B.-G). G.L. is grateful to the Israel Ministry of Science and Technology for the Jabotinsky PhD Scholarship. SB and KD were supported by the National Science Foundation CAREER award DMR-2340632. KD also acknowledges the NSF-CREST: Center for Cellular and Biomolecular Machines (CCBM) at the University of California, Merced via HRD-1547848, and the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-2210452, where part of this work was performed.

Data availability

All data are available in the manuscript or the supplementary materials. Executable codes for automated masking, batch ensemble PIV, post-processing and strain analysis are available at DOI: 10.5061/dryad.g1jwstr75.

Declarations

Competing interests

The authors declare no competing interests.