James P. K.
Armstrong
a,
Stephanie A.
Maynard‡
a,
Isaac J.
Pence
a,
Amanda C.
Franklin
b,
Bruce W.
Drinkwater
b and
Molly M.
Stevens
*a
aDepartment of Materials, Department of Bioengineering, and Institute for Biomedical Engineering, Imperial College London, London, SW7 2AZ, UK. E-mail: m.stevens@imperial.ac.uk
bDepartment of Mechanical Engineering, University of Bristol, Bristol, BS8 1TR, UK
First published on 22nd January 2019
Acoustic patterning using ultrasound standing waves has recently emerged as a potent biotechnology enabling the remote generation of ordered cell systems. This capability has opened up exciting opportunities, for example, in guiding the development of organoid cultures or the organization of complex tissues. The success of these studies is often contingent on the formation of tightly-packed and uniform cell arrays; however, a number of factors can act to disrupt or prevent acoustic patterning. Yet, to the best of our knowledge, there has been no comprehensive assessment of the quality of acoustically-patterned cell populations. In this report we use a mathematical approach, known as Voronoï tessellation, to generate a series of metrics that can be used to measure the effect of cell concentration, pressure amplitude, ultrasound frequency and biomaterial viscosity upon the quality of acoustically-patterned cell systems. Moreover, we extend this approach towards the characterization of spatiotemporal processes, namely, the acoustic patterning of cell suspensions and the migration of patterned, adherent cell clusters. This strategy is simple, unbiased and highly informative, and we anticipate that the methods described here will provide a systematic framework for all stages of acoustic patterning, including the robust quality control of devices, statistical comparison of patterning conditions, the quantitative exploration of parameter limits and the ability to track patterned tissue formation over time.
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The magnitude of the acquired energy potential is dependent upon several factors: the mean squared pressure 〈|p0|2〉, the mean squared particle velocity 〈|0|2〉, the cell volume (Vc), density (ρc) and compressibility (κc), and the host medium density (ρm) and compressibility (κm):28
![]() | (2) |
![]() | (3) |
![]() | (4) |
These equations can be used to compute the acoustic radiation force for different acoustic fields. For instance, a single standing wave of the form p0(x) = P0 cos(kx) sin(ωt) and unit vector in the x-direction (x) will produce a one-dimensional field with an acoustic radiation force that is dependent upon the wavelength (λ) and speed of sound (cm) in the host medium:
![]() | (5) |
![]() | (6) |
The superposition of a second standing wave in an orthogonal direction (y) will create a two-dimensional field, which can be described by an extension of eqn (5) and (6). Here, the acoustic radiation force is proportional to the sum of the squared pressures from each standing wave, where the subscripts x and y denote the orthogonal directionality for the amplitude and wavelength components of the force distribution:
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In practice, however, an acoustic radiation force does not always result in translation of cells to the nodes. The extent of patterning is dependent on the balance between the supplied acoustic radiation force and the forces that act to oppose cell translation. For instance, acoustic patterning can be inhibited by attractive cell-material interactions (e.g. with an adherent surface), mechanical agitation, thermal currents or acoustic streaming.29 In addition, gravity can oppose the acoustic levitation of cells, while viscous drag becomes an increasingly important consideration as the field moves from solution-based manipulation towards patterning cells in gels.11,16–20,30 Overall, the characteristics of the cell, material and field all contribute to the balance of forces experienced by the cell and the final pattern quality. A well-defined patterned array offers: (1) a low proportion of “untrapped” cells, which is essential when attempting to measure bulk functional effects of cell patterning; (2) dense structures with a high degree of cell–cell contact, a critical feature for adhesion and membrane spreading studies; (3) uniformity in structure dimension and geometry, which is vitally important for achieving consistent development and functional properties of cell spheroids and organoid microtissues.11–13
Given the evident importance of pattern structure and consistency upon the design and outcome of acoustic cell patterning studies, there is a surprising dearth of feature characterization and quality control of the generated cell arrays. The recent, major reports of acoustically patterned cell assemblies have reported only a binary, visual assessment of micrographs to ascertain whether or not a population is patterned.11–14,16–22,24–27,30–34 Only three of these studies provided characterization beyond basic sizing: Christakou et al. indirectly evaluated the cluster “compactness” based on the penetration depth of a fluorescent dye,26 Comeau et al. used peak-to-peak and peak-to-trough measurements of patterned lines to estimate band spacing and density, respectively,21 while Olofsson et al. counted both the number of clusters and the number of single cells patterned in each well of a microwell plate.13 In our recent report of acoustically-patterned muscle engineering, we used a Fast Fourier Transform algorithm to identify major frequencies in micrographs of acoustically-patterned myoblasts and define a unidirectional patterning index.15 However, such analysis provides a relatively limited assessment of the overall pattern quality, averaged over the entire image, and no quantification of the individual cell structures formed at the acoustic pressure nodes. In principle, it is actually relatively straightforward to characterize well patterned arrays, as these typically have tightly packed structures that can be identified using pixel intensity thresholding. However, this direct approach cannot be readily applied to the analysis of loosely packed structures that do not exhibit a clearly identifiable perimeter. Thus, a more sophisticated form of image analysis is required to make fair comparisons across different patterning conditions.
Here, we demonstrate the quantification of acoustically-patterned cell systems using Voronoï tessellation, an image analysis tool that has previously been used to compute atomic packing,35 simulate the cosmic evolution of galaxies36 and analyze the clustering of cell membrane proteins.37 This algorithm uses localized points in space known as “seeds” to generate a set of tessellated polygons, which each contain a single seed and encompass the points in space closer to its own seed than any other seed.37 In this case, the seeds corresponded to high intensity pixels arising from the fluorescence of cells that had been acoustically patterned into clusters under different experimental conditions (pressure amplitude, ultrasound frequency, cell concentration and biomaterial viscosity). We used Voronoï tessellation maps to evaluate patterning using a series of metrics (e.g. cluster density, ratio, area, number, barycenter), which allowed us to compare pattern quality and consistency in an impartial, quantitative and statistical manner. Moreover, we extended this algorithm to the analysis of spatiotemporal processes: the translation of cells exposed to an ultrasound field as well as the migration and proliferation of cells acoustically patterned on an adherent surface. The studies detailed in this report highlight some of the most relevant and practical applications of Voronoï tessellation for acoustic cell patterning. However, the versatile nature of this approach should enable application across different patterning systems and experimental conditions, from quantitative characterization and tracking of cell arrays to monitoring device performance or predicting the characteristics of untested cell systems.
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Fig. 1 Demonstration of acoustic cell patterning and Voronoï tessellation analysis. (a) A custom-built acoustic patterning device was assembled with four orthogonal transducers surrounding a central cavity enclosing a 35 mm tissue culture dish holding a cell suspension. The piezotransducers were driven at resonance frequency to generate ultrasound standing waves capable of producing clustered arrays of cells (blue, inset). (b) Confocal fluorescence microscopy was used to capture micrographs of clusters of cells (green) after 5 min of acoustic patterning. Scale bar = 200 μm. (c) High intensity pixels were used to determine seeds (red markers), (d) which were used to construct a Voronoï tessellation map. (e) A threshold of the seed density was then used to identify cell clusters (blue). (f) This approach enabled quantitative assessment under different experimental conditions, for example, the measurement of cluster area at different cell concentrations. This information can then be used, if necessary, to inform the parameters of any future acoustic patterning. The data shown was collected from four separate images per group and plotted as median ± interquartile range. For a full analysis of the effect of cell concentration, refer to Fig. S5.† |
As a proof-of-concept demonstration, we used Voronoï tessellation analysis to quantify the clusters formed using different concentrations of myoblasts (1.25 × 105–2 × 106 cells per mL). We observed that using a higher concentration of cells resulted in negligible change in cluster number but rather the formation of larger sized clusters (Fig. 1f and S5A and B†). These profiles were expected, given the conserved total area and number of pressure nodes in the system. Indeed, the capacity to generate uniform and well-defined clusters is a valuable characteristic of acoustic cell patterning and one that has been used to exert control over spheroid culture and organoid tissue engineering.11–13 In this context, accurate measurement of cluster size could be used to determine size thresholds for the formation of nutrient gradients or the developmental fate of stem cells. However, it should be noted that this analysis provides a measure of cluster area not volume. This is not an issue for many systems: for instance, the clusters we formed using a low concentration of cells predominantly occupied a single layer. On the other hand, when cells are patterned at high concentration, they can occupy multiple layers within an acoustic node and may not contribute to the cluster size measurements made using Voronoï tessellation analysis. Indeed, this effect was evident in the non-linear relationship that we observed between cell concentration and cluster area (Fig. S5C†).
We were able to generate Voronoï diagrams from a range of cell structures, including low-frequency clusters (2.1 × 2.1 MHz), high-frequency clusters (6.7 × 6.7 MHz) and linear arrays (2.1 MHz) (Fig. S6†). In these examples, we employed frequencies close to the known primary resonance and first harmonic of the piezotransducer in order to produce steep pressure gradients and well patterned clusters. Indeed, the piezotransducer resonance often dominates the chamber resonance of the device and can be viewed as one of the most critical factors for acoustic cell patterning. To investigate this effect, we captured confocal fluorescence micrographs of myoblasts patterned in cell medium using transducers driven at 15 Vpp (corresponding to a mean squared pressure amplitude of 0.0051 (MPa)2 for this device) across a range of ultrasound frequencies (1.75–2.45 MHz) (Fig. 2a). This range was selected as it centered on the primary resonance of the piezotransducers (2.12 MHz), which was identified using impedance spectroscopy (Fig. 2b). We then used Voronoï tessellation analysis to quantify the cell cluster area, which revealed a strong association between the ultrasound frequency and the final pattern quality (Fig. 2c). As expected, the frequencies close to the piezotransducer resonance (2.05, 2.15, 2.25 MHz) produced a tight distribution of large clusters, due to effective acoustic patterning. The more distant frequencies (1.75, 2.45 MHz) generated clusters with statistically-significant differences in area distribution to the resonance condition (2.15 MHz) and much more similar to the control with no applied field. Moreover, the frequencies on the shoulder of the piezotransducer resonance (1.85, 1.95, 2.35 MHz) produced clusters of intermediate size distribution, and interestingly, the highest median cluster area of the tested range. This result was attributed to the fact that off-resonance patterning produces loosely aggregated cell clusters with a greater size than the tightly-packed clusters formed at resonance. Indeed, we used Voronoï tessellation to calculate the number of clusters per image and the density of the largest 16 clusters across the patterned range (Fig. 2d). This analysis revealed a strong association between the cluster number minimum and the cluster density maximum, which were both centered around 2.15 MHz.
We next investigated how Voronoï tessellation could be used to characterize myoblasts patterned in solution across a range of pressure amplitudes. First, we used a hydrophone mounted on a motorized stage to map the pressure field generated by a 2.1 × 2.1 MHz ultrasound field at different load voltages (0–15 Vpp). Unsurprisingly, the devices driven with higher load voltage produced standing waves with higher mean squared pressure amplitude (Fig. 3a and S7†). Importantly, the steeper pressure gradients produced by the higher load voltages appeared to produce more defined cell clusters (Fig. 3b). For this analysis, we identified the barycenter of the clusters detected from the Voronoï tessellation maps and mapped their x and y coordinates individually, in order to assess the performance of each piezotransducer pair (Fig. 3c). This analysis, which we also performed in two dimensions (Fig. S8†), showed that driving the patterning device at higher load voltage generated a more periodic distribution of barycenter coordinates. Indeed, when the higher load voltage systems were fitted to a tetramodal curve, we were able to measure peak-to-peak separation distances of 0.36 ± 0.02 and 0.36 ± 0.03 mm that were consistent with the theoretical half wavelength separation of the acoustic pressure nodes (0.35 mm, using an ultrasound frequency of 2.1 MHz and a speed of sound in water of 1482 m s−1) (Fig. S9†).41 This geometric evaluation was consistent with numerical and dimensional analysis. Each micrograph encompassed a 4 × 4 array of pressure nodes, so in theory, a perfectly patterned system would comprise 16 uniformly-sized clusters. Voronoï tessellation analysis revealed the 15 Vpp/0.0051 (MPa)2 system to have a small number of clusters (N = 17 ± 1) with a relatively large median cluster size (Ã = 4.6 ± 0.3 × 103 μm2). When we reduced the load voltage, we observed a large increase in cluster number and a concomitant decrease in cluster area (Fig. 3d and e). These observations are consistent with theory; the acoustic radiation force experienced by a cell is proportional to the mean squared pressure (F α〈|p0|2〉). Although a radiation force will be exerted in all field-exposed systems, this analysis showed that the load voltage must exceed a certain threshold limit (6 Vpp/0.0017 (MPa)2) in order to produce pressure gradients capable of generating detectable cell clusters.
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Fig. 3 Voronoï tessellation analysis of clusters formed in different pressure amplitude fields. (a) A hydrophone was scanned across the center of an acoustic patterning device to map the mean squared pressure amplitude at different load voltages. Scale bars = 200 μm. For low magnification maps, refer to Fig. S7.† (b) Representative confocal fluorescence micrographs of myoblasts (green) imaged after a 5 min exposure to an acoustic field across the same voltage range. Scale bars = 200 μm. (c) The cluster barycenter coordinates, output from the Voronoï tessellation analysis, were plotted for each ultrasound standing wave pair (x = red, y = blue). The higher amplitude fields produced clusters with barycenters localized at periodic intervals corresponding to the acoustic nodes of the standing wave. Data was collected from three separate images per group. For a full analysis, refer to Fig. S8 and 9.† (d) Voronoï tessellation was also used to quantify the number of clusters per image. In higher amplitude fields, this value tended towards 16 (red line), which was equivalent to the number of acoustic nodes in each field of view. Data was collected from three separate images per group, and plotted as the mean, interquartile range and 95% confidence intervals. (e) Raising the pressure amplitude also produced an increasingly tight distribution of large cell clusters. Data was collected from three separate images per group, plotted as median ± interquartile range and statistically treated using a Kruskal–Wallis test with Dunn's correction for multiple comparisons (n.s. is nonsignificant, *** is p < 0.001). |
Recently there has been interest in moving away from solution-based arrays towards approaches that use biomaterial systems to encapsulate and preserve acoustically-patterned cell arrays (e.g. hydrogels of poly(ethylene glycol) norbornene,15 Matrigel,15 fibrin,16,17 alginate,30 agar/agarose,15,30 collagen,15,19,20,42 gelatin methacryloyl15,18). In these examples, cells are acoustically patterned in a liquid hydrogel precursor before or during a triggered crosslinking process (e.g. enzymatic, thermal, pH, ultraviolet irradiation). The chemical and physical properties of the biomaterial components, the total weight percentage and any pre-gelation crosslinking will dictate the rheological properties of the liquid precursor, and thus the degree of constraint placed upon the acoustic patterning process. Accordingly, we used Voronoï tessellation to assess the relationship between viscosity and cluster formation (Fig. 4a). For this study, we used a two-component hydrogel system, namely a photocrosslinkable 8-arm PEG norbornene hydrogel precursor that was systematically doped with high molecular weight PEG (0–3% w/v). We used rheological creep tests to measure a respective viscosity of 16.7 ± 0.1, 20.7 ± 0.2, 26.2 ± 0.2 and 38.8 ± 0.2 mPa s for the systems containing 0, 1, 2 and 3% (w/v) PEG dopant (Fig. 4b). We used a 2.1 × 2.1 MHz field to acoustically pattern myoblasts within these four hydrogel precursors, followed by a 2 min exposure to ultraviolet light, in order to immobilize the arrays in a self-supporting hydrogel (see Experimental for more details). The center of the hydrogel contained a uniform array of clusters (Fig. S10†), which we imaged and analyzed using Voronoï tessellation analysis. As expected, the cluster size distribution was impacted by increasing the viscosity, with 3% dopant producing a cluster area profile with statistically-significant difference to the undoped system (Fig. 4c). Moreover, the proportion of clustered seeds (Z) was markedly decreased in the 2% (Z = 42 ± 3%) and 3% (Z = 19 ± 3%) systems compared to the undoped hydrogel (Z = 54 ± 3%) (Fig. 4d). These results highlight the implications for acoustic patterning applications that require high viscosity hydrogels. More generally, this route offers a means to quantifiably determine the viscosity limits for acoustic patterning in different biomaterial systems.
The results described thus far demonstrate the capacity of Voronoï tessellation for quantifying cluster formation at single timepoints during the acoustic cell patterning process. In practice, however, the cluster definition improves over time as the acquired potential energy of the cells is converted into kinetic energy and the cells are translated towards the acoustic pressure nodes. Here, we used time-lapse microscopy and Voronoï tessellation to investigate the dynamics of the acoustic patterning process. Specifically, we employed in situ confocal fluorescence microscopy to capture the patterning of myoblast clusters formed using a 2.1 × 2.1 MHz ultrasound field (Fig. 5a and video S1†). We tracked the x and y barycenter coordinates of the clusters, both prior to field exposure (−5 to 0 s) and during patterning (0 to 30 s) (Fig. 5b and S11†). This revealed a transition from a broadly uniform distribution to a periodic profile comprising four distinct peaks. In order to quantify this system, the profiles were fitted to a tetramodal Gaussian distribution mixture based on the expectation maximization algorithm43 and the variance of the peaks expressed as a function of time (Fig. 5c and S12 and 13†). This revealed a rapid decrease in variance, as the cell patterning transitioned the system from relatively uniform distributions into periodic arrays fitted with narrow Gaussian distribution curves. In addition to this coordinate analysis, the cluster area and proportion of clustered seeds proved to be particularly insightful metrics for characterizing the patterning process (Fig. 5d). For the five seconds prior to field exposure, the system was predominantly composed of small clusters (Ã < 5 × 102 μm2) and a low proportion of clustered seeds (Z < 20%). Initiating the patterning process produced rapid increases in both cluster area and proportion of clustered seeds to produce a final system that exhibited a stable and consistent profile after 20 s of patterning (Ã > 6 × 102 μm2, Z > 35%). This analysis clearly demonstrates how Voronoï tessellation can be used for spatiotemporal quantification and kinetic evaluation of acoustic cell patterning.
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Fig. 5 Spatiotemporal Voronoï tessellation analysis of the acoustic cell patterning process. (a) Time-lapse confocal fluorescence micrographs of myoblasts (green) in culture medium, imaged at intervals during acoustic cell patterning. Scale bars = 200 μm. (b) The x and y coordinates of the cluster barycenters were plotted as a function of time. Data was collected from four separate videos of patterning, here, one representative x coordinate dataset is shown. For the full coordinate analysis, refer to Fig. S11.† (c) The cluster barycenter analysis was used to define histogram profiles at 1 s intervals, which were fitted to a tetramodal Gaussian distribution mixture based on the expectation maximization algorithm. The variance on the four identified peaks was relatively high in the initial unpatterned system but decreased as the acoustic patterning generated periodic cell arrays. Data plotted as mean ± standard deviation from tetramodal fits of four separate videos of patterning, with only the x coordinate data shown. For all data fitting and the y coordinate variance analysis, refer to Fig. S12 and 13.† (d) This process could also be visualized by describing the proportion of clustered seeds as a function of median cluster area. A clear transition could be observed between two distinct regions: the unpatterned cell suspension with small clusters and a low proportion of clustered seeds (t < 3 s) and the patterned arrays with large clusters and a high proportion of clustered seeds (t > 13 s). |
We next applied Voronoï tessellation to characterize spatiotemporal changes that occur after acoustic cell patterning. For this study, we used a common experimental approach of patterning cells onto a substrate and then removing the acoustic field once the cells have adhered.24,25,27,33 Without the field, there are no external forces acting to constrain the cells to their patterned configuration.25 As a result, there is almost always some degree of pattern loss over time, due to normal cell processes such as membrane spreading, migration and proliferation.24,25,27 Generally, this effect is greater than for cells grown on surfaces engineered with topographic, mechanical or chemical cues, which are able to exert long-term effects during culture.44–46 In some cases, pattern loss is slow and does not hinder the final application: for instance, Gesellchen et al. showed that Schwann cells largely retained their patterned configuration on glass for at least 24 h, and could be used to guide neurite outgrowth from a dorsal root ganglion for a further four days.27 However, pattern loss will depend on factors such as the cell type and environment: for instance, Li et al. showed that linear arrays of HeLa cells were reasonably well preserved after 24 h in monoculture, but over the same time period, cocultured HeLa cells and endothelial cells each lost their patterned configuration.24 To the best of our knowledge, the only reported analysis of acoustically-patterned cultures involved the tracking of individual cells24 and individual clusters.25 Accordingly, we sought to characterize the population-wide pattern loss using live-cell microscopy of C2C12 myoblasts expressing cytosolic GFP. Specifically, we generated uniform clusters of adherent myoblasts on the surface of laminin-coated glass, and then imaged the cells over 18 h of culture using time-lapse wide field microscopy (Fig. 6a).
As before, we used Voronoï tessellation to measure the distribution in the cluster barycenter coordinates over time. This provided an effective means of visualizing the loss of pattern fidelity, with the clusters spreading out from the acoustic nodes to fully occupy the coordinate space (Fig. 6b). We also used Voronoï tessellation to monitor the median area of the nine largest clusters (Ã) and the total number of clusters over time (N), which provided interesting insights into the dynamic changes occurring over the culture period (Fig. 6c). During the first hour of culture, in the early stages of cell-substrate adhesion, the initial patterning profile was well maintained (Ã < 1.0 × 103 μm2, N < 15 at t < 1 h). After this initial lag period, the clusters remained largely intact but underwent membrane spreading; this was characterized by an unchanged cluster number but an increase in cluster size (Ã = 2.2 × 103 μm2, N = 13 at t = 3.5 h). The next transition saw a steady increase in cluster number, due to the outward migration of myoblasts from the patterned clusters (Ã = 2.5 × 103 μm2, N = 60 at t = 18 h). This rapid deterioration in pattern quality affords an exceptionally small window of opportunity to study biological processes, a factor that has limited acoustically-patterned culture systems to a small number of studies with short term outcomes.24,27 We hypothesized that we could extend this time frame by restricting migration with a constraining matrix. Indeed, by layering Matrigel on the surface of the adherent myoblasts we were able to slow cell migration and retain the acoustically-formed clusters over a greater period of time (Fig. 6d and e). Interestingly, the eventual loss of definition in the Matrigel system appeared to be dominated by cell proliferation, as opposed to the outward migration seen in the uncoated clusters. This was reflected in the Voronoï tessellation metrics; the coated system produced appreciably larger clusters during the intermediate stages (Ã = 8.3 × 103 μm2 at t = 10 h) than in the uncoated system (Ã = 2.8 × 103 μm2 at t = 10 h) (Fig. 6f). This migration analysis provides a further demonstration of how Voronoï tessellation can be applied to quantitatively characterize spatiotemporal processes in acoustically-patterned cell cultures.
Finally, we sought to demonstrate that Voronoï tessellation analysis can be applied to acoustically-patterned cells that were not labelled with any fluorescent marker. We generated 5% (w/v) PEG norbornene hydrogels patterned with unlabelled myoblasts using a 2.1 × 2.1 MHz ultrasound field, as described previously. We removed the hydrogel from the device and imaged the clusters using bright field, differential interference contrast and phase contrast microscopy (Fig. S14†). We were able to analyze these images using Voronoï tessellation, with little difference observed between the identified clusters.
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c8lc01108g |
‡ Current address: Institut de Biologie de l'École Normale Supérieure, 46 rue d'Ulm, 75007, Paris, France. |
This journal is © The Royal Society of Chemistry 2019 |