Mapping Collective Forces of Lung Cancer Spheroids Using Traction Force Microscopy.

1
Introduction
Epithelial tissues and multicellular aggregates have been reported to mechanically deform their surrounding extracellular matrix (ECM) during various critical biological processes (DuFort et al. 2011; Gutierrez et al. 2021; Leggett et al. 2020; Mohagheghian et al. 2023; Raghuraman et al. 2022; Trepat et al. 2009; Yamaguchi et al. 2022). These collective mechanical interactions play a pivotal role in orchestrating tissue architecture and function, influencing cell behavior, and driving morphogenetic events (DuFort et al. 2011; Gómez‐González et al. 2020; Gutierrez et al. 2021; Mohagheghian et al. 2023; Raghuraman et al. 2022; Trepat et al. 2009; Yamaguchi et al. 2022). Dysregulation of these mechanical forces can lead to tissue disorganization and contribute to pathogenic phenotypes, especially cancer development (Boghdady et al. 2021; DuFort et al. 2011; Gómez‐González et al. 2020; Leggett et al. 2020; Raghuraman et al. 2022; Trepat et al. 2009; Yamaguchi et al. 2022). Cancer cells live in a physiological environment characterized by densely packed cell‐cell interactions, in which multicellular spatio‐temporal dynamics and collective effects cannot be ignored. Hence, it is necessary to quantify such multicellular forces by taking the cancer cell group as an integrated research object (Mark et al. 2020). Understanding the nature and magnitude of these forces provides a unique window into elucidating the underlying mechanisms of cancer progression, and presents innovative phenotypic readout into identifying potential therapeutic targets.
Traction force represents the active force generated by cells to sense and interact with the ECM (Parsons et al. 2010; Saraswathibhatla et al. 2023), which is an instinctive cellular behavior (Roca‐Cusachs et al. 2017; Saraswathibhatla et al. 2023). At present, single‐cell based measurements have confirmed the essential role of traction force in cancer development (Clark and Vignjevic 2015; Isomursu et al. 2022; Saraswathibhatla et al. 2023). In essence, traction force constitutes a fundamental mechanotransduction mechanism underlying cancer metastasis. For example, breast cancer cell can effectively translate physical ECM‐information (curvature and stiffness) to changes in cell traction force, which further regulated cell migration (C. Wang et al. 2024; H. Zhang et al. 2020). And the traction force influence the metastasis of endometrial cancer cell through Wnt‐β‐catenin pathway (X. Li et al. 2024). Besides, the magnitude of single‐cell traction force has been suggested to be a biophysical marker for distinguish different degrees of cancer cell invasiveness (Cambria et al. 2024; Chen et al. 2023). For instance, metastatic breast, lung, and prostate cancer cells have been shown to exert significantly higher traction forces compared to their non‐metastatic counterparts (Koch et al. 2012; Laird et al. 2012; Z. Li et al. 2017; Liew et al. 2024; Tavares et al. 2017; Zancla et al. 2022). Meanwhile, the dynamics and outliers of the single‐cell traction stresses can also serve as an effective indicator to the invasiveness of cancer cell (Koch et al. 2012; Peschetola et al. 2013; Zancla et al. 2022). Moreover, traction forces of individual cells have been assessed to be a potential metric for antimetastatic drug screening (Liew et al. 2024). However, despite single‐cell‐scale measurements have confirmed the pivotal role of traction force in cancer progression, the traction force of cancer cell collective remains largely unexplored.
Traction forces at the collective scale can be different from single‐cell scale traction forces. Recently, some studies have employed monolayers of cancer cells to investigate the collective traction forces of cancer cells in crowded multicellular environments, with results deviating from single‐cell measurements. For instance, at the single‐cell scale, highly metastatic prostate cancer cells exhibit significantly higher traction forces than lowly metastatic prostate cancer cells in a stiffness‐dependent manner (Laird et al. 2012; Molter and Ehrlicher 2021; Molter et al. 2022); whereas the traction forces of prostate cancer cell sheets are not universally proportional to the stiffness and metastatic potential (Molter et al. 2022). Meanwhile, cancer cell monolayers move cooperatively with internal tension and intercellular mechanical interactions, with cells in different regions exhibiting varying traction forces (Bazellières et al. 2015; Ollech et al. 2020; Tambe et al. 2011; H. Zhang et al. 2023). Additionally, traction force exerted by patterned cancer cell monolayer also exhibit significant spatial heterogeneity, with distinct variations depending on the specific position of the cells within the pattern (Lin et al. 2022; S. Liu et al. 2020). These findings indicate that collective traction force is an independent parameter with distinct physiological significance compared to single‐cell traction force, underscoring the necessity to study cancer traction force at collective scale. Despite this, with a historical focus on traction forces at the single‐cell and subcellular levels, collective traction force of cancer cells remains largely unexplored. Cancer spheroids enable precise quantification of collective traction forces, which balanced the physiological relevance and experimental operability (Pei et al. 2020; H. Wang et al. 2023; Yao et al. 2024). Compared to two‐dimensional (2D) monolayers, cancer spheroids recapitulate three‐dimensional (3D) cell‐cell contacts and hypoxic cores of solid cancers in vitro. This intricate 3D architecture confers cancer spheroids with multi‐faceted physiological relevance, including ECM deposition, gene expression profiles, growth kinetics, and dispersion mode (Alert and Casademunt 2019; Costa et al. 2016; Zimmermann et al. 2013). Therefore, the cancer spheroids have become ideal cell sources for migration research to better simulate the process by which cancer cells leave from the primary cancer site and escape outward. Regrettably, at present, the traction forces of cancer spheroids are mainly evaluated indirectly via matrix displacement (Cheung et al. 2024). By embedding cancer spheroids into collagen‐based hydrogels, these studies have focused on the precise and efficient acquisition of 3D displacement fields induced by cancer spheroids (Blauth et al. 2024; Kopanska et al. 2016; Leggett et al. 2024; Leggett et al. 2020; Mulligan et al. 2021). However, the degradation and remodeling of the nonlinear‐elastic matrix, combined with the inherent computational burden associated with larger imaging volumes (Mark et al. 2020), inevitably limits the translation of spheroid‐induced deformation into mechanical force.
To date, rather than using displacement as a surrogate, only a few pioneering studies have truly calculated the traction force of multicellular spheroids. These approaches can be categorized into two types: “3D spheroid traction force (3D‐STF)” and “intra‐spheroid traction force (intra‐STF).” Among them, the 3D‐STF, which is measured by embedding cancer spheroid in an ECM‐based‐hydrogel matrix, focuses on the force between the spheroid surface and the surrounding ECM (Gjorevski and Nelson 2012; Mark et al. 2020). However, due to the degradation and remodeling of the matrix induced by multicellular spheroids, as well as the inherent nonlinear elastic properties of the ECM‐based matrix, the accuracy of this class of algorithms remains limited and requires further improvement. Additionally, the 3D‐STF methods cannot detect traction forces within the cancer spheroid, even though the ECM deposited inside the spheroid has been shown to exert critical physiological effects (Bai et al. 2015; Ferreira et al. 2021). Therefore, the intra‐STF has attracted increasing attention, which was quantified by embedding hyper‐compliant microparticles (HCMPs), such as collagen‐functionalized PAAm microgels or RGD‐modified PEG microgel, in the multicellular spheroids (Gutierrez et al. 2021; Mohagheghian et al. 2023). However, the intra‐STF technique involves complex HCMP fabrication, imaging, and computation, cannot map traction forces on the spheroid surface, and fails to decouple “internal tissue stress” from the traction force within the spheroid.
In this study, by extending traditional traction force microscopy (TFM) to cancer spheroid measurement, we established a precise and efficient platform for quantifying collective‐scale forces of cancer cells in 3D aggregate states. Different from above‐mentioned “3D‐STF” and “intra‐STF” methods, our work avoids inherent spatiotemporal complexity of 3D imaging and nonlinear elasticity of the ECM‐based matrices, and enables the quantification of spheroid traction forces across a spheroid‐substrate contact plane, including contributions from both the periphery and the interior regions of the plane. Using this system, we systematically quantified the magnitude and distribution of traction forces exerted by cancer spheroids, elucidating the relationship between these forces and spheroid dispersion, and investigating their response to anticancer drugs. Our results show that cancer spheroid traction force is a novel mechanobiological indicator closely associated with dispersion, providing an innovative perspective for elucidating the underlying mechanisms of cancer progression and identifying potential therapeutic targets.

2
Results
2.1
Spatial Distribution of NSCLC Spheroid Traction Force
We advanced the conventional TFM technique to measure the traction force of cancer spheroids. Cancer spheroids of A549 cells have been validated as a clinically relevant model for non‐small cell lung cancer (NSCLC) (Friedrich et al. 2009; Honeder et al. 2021; Lopez‐Pardo et al. 2024; Pei 2020; Pei et al. 2020; Yao et al. 2024). Using the hanging‐drop method, we prepared NSCLC spheroids of various sizes by adjusting the initial number of A549 cells (Figure 1A,B). To characterize the size of cancer spheroid, we defined the “equivalent diameter” of the spheroid as “the diameter of a circle that corresponds to the maximum cross‐sectional area of the cancer spheroid.” Notably, our experiments shown that the diameter of the spheroids did not indefinitely increase with the number of initial cells (Figure 1B and Supporting Information S1: Figure S1). An excessive number of initial cells led to a significant decrease in the efficiency of spheroid formation. As shown in Figure 1B, the maximum diameter of the cancer spheroid formed by the A549 cells was about 367.15 μm. Therefore, we selected 30, 150, 900 and 2400 cells/spheroid as the initial number of A549 to form NSCLC spheroids, resulting on average equivalent diameters of 179, 221, 317, and 367 μm, respectively. And there were significant statistical differences in equivalent diameter of spheroids in different groups, as shown in Figure 1B. For descriptive purposes, in this article, spheroids prepared with 30, 150, 900, and 2400 initial cells/spheroid were designated as small, medium, large, and ultra‐large spheroids, respectively. As presented in Figure 1C, there is no difference in spheroid roundness of the four groups, and all of them are above 0.8. Consistently, from the typical bright‐field images across four different sizes (Figure 1D), it can be directly seen that all groups of cancer spheroids exhibit compact round morphology with well‐defined peripheral boundary, a structural feature previously attributed to robust intercellular adhesion (Lopez‐Pardo et al. 2024).
To provide a near‐physiological stiffness for NSCLC spheroids, polyacrylamide (PAAm) hydrogels with an elastic modulus of 5 kPa—matching that of lung tissue (Asmani et al. 2018; Balestrini et al. 2012; Levental et al. 2007; F. Liu et al. 2010)—were selected as the substrate. And the surface of the PAAm hydrogel was covalently modified with collagen. As shown in Figures 1A and 2A, in the case of relatively low surface collagen density, cancer cells scarcely migrated out of spheroids, which can be used to simulate the interactions between cancer and stromal matrix in early tumor progression. As shown in Figure 2B, the maximum gel displacement induced by cancer spheroids did not exceed 2.9 μm, which falls within the range of PAAm deformations caused by individual cells (Ma et al. 2024; Ng et al. 2011; Zancla et al. 2022), indicating the technical feasibility of quantifying spheroid‐traction using conventional TFM. Essentially, similar to 2D single‐cell traction force, cancer spheroids exert traction forces on the ECM via integrin‐based adhesions. Therefore, when analyzing traction forces at the level of cancer spheroid using conventional TFM, we aim to objectively describe the in‐plane distribution of traction forces across the PAAm surface where cell‐ECM interactions occur.
Interestingly, at the spheroid‐substrate contact interface, the traction force of cancer spheroid exhibits a well‐defined spatial distribution. The traction force exerted by the spheroid on the substrate caused a radial displacement toward the center of the planar interface (Figure 2A,B), suggesting that the spheroid pulled the substrate inward. In addition, the spheroids did not induce deformation of the substrate directly beneath its center. Meanwhile, at the spheroid–substrate interface, the traction force fields of the cancer spheroids exhibited a characteristic annular distribution, with the peak traction forces concentrated along the periphery of the contact plane, independent of spheroid size (Figure 2C). Consistently, this spatial force configuration maintained temporal stability throughout the observation period, as illustrated in Figure 3A,B. To sum up, the traction force of cancer spheroids demonstrated a clear spatial distribution pattern. The spheroids exerted inward traction forces on the substrate, with the maximum force concentrated at the periphery of the spheroid‐substrate interface. That is to say, during the early stage of cancer spheroid dispersion, while cancer cells have not yet substantially migrated outward, cancer cells located at the edge of the spheroid have accumulated the initial impetus to leave by pulling the substrate, and the mechanical interaction between the spheroid and the substrate is mainly concentrated on the periphery where cancer cells were more likely to migrate out.

2.2
Traction Force Is Regulated by the Size of the NSCLC Spheroids
Living tissues, as well as in vitro cell aggregates, undergo wetting transitions (Alert and Casademunt 2019; Esteve Pallares et al. 2023; Yousafzai et al. 2022). Specifically, upon encountering a surface, the cell aggregate can either maintain its spherical morphology or undergo dispersion by extending a cell monolayer (Alert and Casademunt 2019; Esteve Pallares et al. 2023; Yousafzai et al. 2022). Wetting transition is an essential physiologically relevant model for collective cell migration. Herein, we found that increasing the collagen concentration on the surface of polyacrylamide hydrogel can induce the wetting transition of NSCLC spheroids (Figure 1A).
For NSCLC spheroids yet to undergone wetting transition, we discovered that the traction force exhibited an inverse correlation with spheroid size. Taking spheroids cultured on low collagen density surface as examples, from Figure 3A,B which respectively show the traction forces of small and large spheroids at different time points, it can be directly seen that the traction forces of small‐sized spheroids were significantly greater than those of large‐sized spheroids. Corresponding statistical results further demonstrated that the cancer spheroid traction force decreased significantly with increasing spheroid size over a 24‐h monitoring period (Figure 3C). Specifically, after 24 h of culture on relatively low collagen density surfaces, the traction force generated by small‐sized spheroids reached 97.3 Pa, exceeding twice the value observed in large‐sized counterparts (44.0 Pa). Consistently, as long as cancer spheroids have not entered the dispersion stage, even under high collagen density conditions, the spheroid traction force was similarly correlated with spheroid size. Using the traction forces of spheroids cultured on high‐density collagen substrates at 4 h post‐seeding (a timepoint before single‐cell layer protrusion) as a representative case, the spheroid traction force significantly decreased with increasing spheroid size, with the average value of spheroid traction declining from 90.04 to 26.4 Pa (Figure 3D).
Besides, for NSCLC spheroids yet to undergone wetting transition, spheroid size also regulated the mode of traction force dynamics. The smaller of the NSCLC spheroids, the more rapidly their traction force increases and the earlier they reach a plateau. As shown in Figure 3C, the traction force of large and ultra‐large spheroids kept increasing until close to 24 h, while small and medium spheroids displayed similar pattern of traction force versus time curves, characterized by an initial rapid increase followed by a gradual leveling off into a plateau period. Moreover, considering the varying force field areas generated by spheroids of different sizes, we also calculated the total traction force for each sphere size. As shown in Figure 3E, the total traction force of NSCLC spheroids undergoes a size‐dependent resting period following an initial rapid increase, followed by a secondary increase. Specifically, the total traction force exhibited a progressive delay in the onset of resting phase as the size of the cancer spheroids increases, commencing approximately at 10, 14, 18, and 21 h, respectively; while the plateau duration displayed an inverse relationship with spheroid size, maintaining for approximately 7, 4, 3, and 1 h for small, medium, large, and ultra‐large spheroids, respectively (Figure 3E).
Overall, the size of cancer spheroid regulates the magnitude and dynamics of their traction force. During the non‐dispersion stage, the traction force of cancer spheroid increases with the decrease of spheroid size. Meanwhile, the smaller the size of the spheroids, the faster the increase in traction force, and the shorter the time required to reach the plateau period. The total traction force is also regulated by spheroid size, and the smaller cancer spheroid enters this quiescent phase earlier and exhibit a longer resting duration. These data illustrate that traction forces of cancer spheroids encompass information across size and temporal scales, which are distinct from traction forces of individual cells.

2.3
Traction Dynamics of NSCLC Spheroids Reflect Their Dispersion Process
To investigate the relationship between cancer spheroid dispersion and traction, we induced the dispersion of cancer spheroids on PAAm hydrogel by increasing the surface collagen density. As seen from Figure 4A,B, under high collagen density, cancer cells escaped from the spheroid via collective migration, forming a monolayer around the spheroid. Figure 4B showed the dispersion of spheroids of various sizes after 24 h of cultivation on hydrogel surface with 5 kPa physiological stiffness. It was evident from Figure 4B that cancer spheroids of varying sizes exhibit significantly distinct dispersion capacities. At 24 h, the small spheroids had nearly completely spread into a cell monolayer, whereas the ultra‐large spheroids had not yet initiated dispersion. However, despite extent of dispersion significantly varied between spheroids of different sizes, statistics based on the absolute dispersion area (i.e., substrate coverage by both spheroids and their corresponding monolayers) entirely failed to reflect such variations. As shown in Figure 4C, no statistically significant differences were observed among the absolute dispersion area of differently sized NSCLC spheroids after 24 h of cultivation. Therefore, the absolute dispersion area is not a reliable indicator of cancer spheroid dispersion. To better characterize the dispersion of cancer spheroids, we defined the normalized dispersion area (NDA): NDA = (S
1 − S
2)/S
2, where S
1 is the total area occupied by the spheroid and the cell monolayer resulting from dispersion on the substrate, and S
2 is the area occupied by the spherical portion of the spheroid (Figure 4A). Statistical analysis showed that, unlike the absolute dispersion area but aligned with the diffusion tendency, the NDA significantly decreased with increasing initial spheroid diameter (Figure 4D). That is to say, the diffusion capacity of cancer spheroid increased as the size of the spheroid decrease, and this trend can be quantitatively described using NDA.
We found that the dynamics of cancer spheroid traction force can temporally indicate the initiation of spheroid wetting transition. As shown in Figure 4E, for small spheroids, the traction force increased rapidly and was maximized within 5 h, followed by a slight decrease and then a plateau; while the NDA of small spheroids remained near 0 for the first 5 h before increasing rapidly. The bright field image also showed no migration of cells from the small spheroid within the first 5 h after inoculation, but a large number of cells began to migrate after 5 h of culture (Figure 4F). That is to say, with the initiation of spheroid dispersion, the increase in traction force of small‐sized cancer spheroid is terminated. Consistently, the medium‐sized cancer spheroid exhibited a same relationship between traction force and dispersion dynamics, with the initiation of dispersion delayed from 5 to 8 h (Figure 4G,H). For the large spheroid, the traction force increased almost linearly during the first 9 h, followed by a significant reduction in the rate of increase (Figure 4I). Correspondingly, based on the NDA and bright‐field imagines, the large spheroids did not exhibit cell migration during the first 9 h after inoculation (Figure 4I,J). With the similar trend, ultra‐large spheroids did not initiate dispersion within the first 10 h and showed slight dispersion and a slightly inhibited rate of increase in traction force after 10 h (Figure 4K,L). To sum up, the onset of dispersion abruptly downregulated the increase rate of spheroid traction force, creating a distinct inflection point on the traction force–time curve.
Notably, spheroids with higher dispersal capacity initiate the wetting transition earlier, and exhibit a more pronounced inhibitory effect on the traction force increase. Specifically, as the size of cancer spheroids increased, the inflection points of both NDA and traction force curves were progressively delayed, occurring at approximately 5, 8, 9, and 10 h, respectively. Hence, the superior dispersal capacity of smaller cancer spheroids was characterized by both a greater extent of spatial diffusion and an earlier initiation of wetting transition. Furthermore, stronger dispersion capability correlated with a more pronounced suppression of the traction force growth rate. For small and medium spheroids, the initiation of wetting transition completely inhibited the further increase in traction force and resulted in a plateau period (Figure 4E,G). In contrast, for large‐sized spheroids, the onset of dispersion slowed the rate of increase in the traction force without fully suppressing it (Figure 4I,K). To quantify this suppression, we employed linear regression to calculate the slopes of the traction force–time curves of cancer spheroid before and after dispersion, which were defined as k1 and k2 respectively. As shown in Figure I, for large cancer spheroid, the slope of the traction force curve decreased abruptly from 9.50 (R² = 0.9855) to 2.28 (R² = 0.9918) upon the onset of wetting transition, representing a 4.17‐fold reduction. As for ultra‐large spheroid, the slope of the traction force curve decreased abruptly from 5.64 (R² = 0.9855) to 2.30 (R² = 0.9789) after the initiation of dispersion, corresponding to a 2.45‐fold reduction (Figure 4K). Thus, NSCLC spheroids with greater diffusive capacity exhibiting higher traction forces before dispersion initiation, and they also experience more substantial suppression of traction force increments post dispersion initiation. Besides, spheroid with high dispersion potential exhibited significantly greater traction forces during the stage that cancer spheroid had not yet disseminated, as the value of k1 rose from 5.64 to 22.53 with the increased spheroid dispersion capacity (Figure 4E, G, I, K).
To sum up, there is an intrinsic correlation between cancer spheroid dispersion process and traction dynamics. The onset of spheroid dispersion was accompanied by a significantly downregulation in the growth rate of traction force, with a higher dispersion potential corresponding to greater inhibition of the traction force increase rate. Besides, the spheroid traction force during the non‐wetting transition stage holds the potential to indicate the spheroid dispersion capacity.

2.4
Effects of Anticancer Drugs on NSCLC Spheroid Traction Force
Deadly malignant cancer is not merely a disorder of cell proliferation, but also a condition marked by uncontrollable cellular migration (Clark and Vignjevic 2015; Shi et al. 2024). From a therapeutic perspective, inhibiting the force and dissemination of cancer cells is essential for preventing metastasis(Chaffer and Weinberg 2011), which offers promising targets for the development of anticancer drugs.
Cancer spheroid traction force represents an innovative metric for assessing the anticancer drugs targeting cell force and dispersion. To validate the potential of cancer spheroid traction force as an indicator for antitumor drug screening, we defined the drug concentration required to reduce the traction force of cancer spheroids by 50% as the “50% inhibitory concentration of cancer spheroid traction force (ICF50).” Similarly, to quantitatively assess the inhibitory effect of anticancer drugs on spheroid dispersion, we defined the 50% inhibitory concentration of NDA (ICD50) as the drug concentration required to reduce the dispersion of cancer spheroids by half. As described in the “Traction dynamics of NSCLC spheroids reflect their dispersion process “section, before cancer spheroid initiate dispersion, higher traction force reflected stronger spheroid diffusion ability; whereas the relative magnitude of traction force no longer directly correlated with the spheroid diffusion ability once the diffusion process had commenced, emphasizing the significance of dispersion state selection for cancer spheroid traction measurement. Therefore, we firstly explored the feasibility of employing the traction forces of cancer spheroids that have not undergone dispersion as a phenotypic indicator for anticancer drug screening. By culturing the cancer spheroid on low‐collagen substrates to inhibit wetting transition, we measured the spheroid traction forces under varying concentrations of docetaxel. As shown in Figure 5A, the inhibition of traction force by docetaxel at various concentrations was well‐fitted to a standard dose–response curve, yielding an ICF50 of 1.835 nM. Meanwhile, the cancer spheroids exhibited no signs of dispersion, with their normalized dispersion area (NDA) consistently maintained at approximately 1 (Figure 5B). That is to say, despite the established connection between spheroid traction force and dispersion, traction force can be used as an indicator for anticancer drug evaluation even in the absence of spheroid dispersion.
Furthermore, by inducing cancer spheroid dispersion with high‐collagen substrates, we compared the inhibitory effects of cisplatin on both spheroid traction force and dispersion. Similar to the docetaxel experiment, the inhibitory effects of cisplatin on cancer spheroid traction force at different concentrations also followed a standard dose–response relationship, with an ICF50 value of 35.76 mΜ (Figure 5C). Interestingly, under identical conditions (Figure 5D), the dispersion (represented by NDA) of cancer spheroid shared a similar concentration‐dependent trend, with a comparable ICD50 (17.73 μM) to ICF50. These results further confirmed the intrinsic connection between the traction force and dispersion of cancer spheroids, and suggested that the traction force of cancer spheroid can serve as a quantitative phenotypic readout for anticancer drug testing. In contrast to the prevalent biochemical assessments of cancer cells, the quantification of cancer spheroid traction provided an innovative phenotypic readout for directly identifying anticancer drugs targeting the collective force and migration potential of cancer cells at the tissue level.

3
Discussion and Conclusions
Traction forces serve as a crucial mechanism for cells to sense and alter their microenvironment (Gardel et al. 2010; Parsons et al. 2010), which are deeply involved in cancer progression, invasion, and metastasis (Rao et al. 2021). To date, single‐cell TFM has predominantly been applied to cellular force research. However, cancer is characterized by densely packed cell‐cell interactions, where intercellular spatiotemporal orchestration and collective effects play a vital role in cancer evolution. At present, physical properties of cancers have been increasingly recognized to be equally significant as their biological characteristics (Massey et al. 2024; Nia et al. 2020). However, while the traction forces of individual cancer cells have been extensively studied, the forces collectively exerted by cancer cells within a physiologically relevant three‐dimensional model remains to be elucidated.
Distinguished from previous spheroid traction force measurement—specifically, “3D spheroid traction force (3D‐STF)” and “intra‐spheroid traction force (intra‐STF)”—we advanced the conventional traction force microscopy technique to measure the traction force of cancer spheroids. For 3D‐STF analysis, despite a wealth of elegant work dedicated to rapidly and accurately mapping the matrix deformation elicited by 3D‐cultured cancer spheroids (Leggett et al. 2020), translating these displacements into reliable force fields remains rare (Cheung et al. 2024). This limitation primarily arises from the reorganization and degradation of the nonlinear matrix, coupled with the substantial computational burden caused by large‐volume imaging (Mark et al. 2020). Besides, current 3D‐STF measurement technology is unable to decouple “spheroid growth force (Alessandri et al. 2013; Aoun et al. 2019)” from “spheroid traction force” when proliferation‐driven volumetric expansion compresses the 3D matrix (Gjorevski and Nelson 2012), and remains blind to the traction force within the spheroid. However, it is worth noting that, ECM deposition also occurs internally within cancer spheroid. Indeed, the capacity to recapitulate the extensive deposition of ECM within solid tumors represents a key advantage of cancer spheroid as in‐vitro tumor models (Alessandri et al. 2013; Bjerkvig et al. 1989; Costa et al. 2018; Costa et al. 2016; Longati et al. 2013), which has been demonstrated to regulate spheroid drug resistance (Bai et al. 2015; Ferreira et al. 2021). Therefore, some recent studies have focused on the intra‐STF, which was quantified by embedding integrin ligand‐functionalized HCMPs in the multicellular spheroids (Gutierrez et al. 2021; Mohagheghian et al. 2023). However, intra‐STF was developed on the basis of measuring “internal tissue stress” within the cancer spheroid. Specifically, in earlier studies where integrin ligands were not immobilized on the surface of HCMPs, this approach was employed to assess “internal tissue stress” of cancer spheroid (Dolega et al. 2017; Lee et al. 2019); whereas after the HCMP surface was coated with integrin ligands, the measured output was termed intra‐STF. Nevertheless, by definition, traction force refers specifically to the active forces exerted by the cytoskeleton onto the ECM via focal adhesions (FAs). Therefore, current methodologies for measuring so‐called “intra‐STF” do not fully exclude the contribution of “internal tissue stress.” Differentiating from the existing technologies, our methodology avoided elaborate 3D imaging, complex nonlinear elastic algorithms and HCMPs preparation, thereby balancing experimental convenience with measurement accuracy. Moreover, our methodology emphasized the actively‐exerted force on ECM generated by cancer spheroid, effectively excluding the confounding effects of “spheroid growth force” on 3D‐STF and “ internal tissue stress” on intra‐STF.
Moreover, our work provided a unique perspective for observing the spatial distribution of cancer spheroid traction forces. For the intra‐STF, which is measured by embedding HCMPs in the multicellular spheroids, the spatial distribution pattern has not yet been revealed, as the position where HCMPs integrate into the spheroid body is uncontrollable (Gutierrez et al. 2021; Mohagheghian et al. 2023). Notably, for the 3D‐STF, the traction spatial distribution has been reported to exhibit symmetry, which has been exploited to simplify the corresponding force reconstruction (Cheung et al. 2024; Mark et al. 2020). But this symmetry‐based simplification restricts the spheroid‐traction calculation on an equatorial plane, and neglects the impact of tissue morphology on spheroid traction forces (Mark et al. 2020). However, the geometry of epithelial micro‐tissues has been reported to dictate the distribution of traction forces. Larger traction forces are predominantly concentrated at the short ends of cylindrical tissues or angular regions of the epithelium (Gjorevski and Nelson 2012). Therefore, the spatial distribution of cancer spheroid traction force cannot be ignored, particularly as the spheroid loses its spherical symmetry during invasion and dispersion. In this study, as illustrated in Figure 1A and Figure S2 in the Supporting Information, upon inoculation onto the surface of collagen‐modified PAAm hydrogels, cancer spheroids progressively adhered to the substrate. During this process, the initial cancer spheroid gradually deformed into the hemispherical shape, with all cells located on the basal surface of the hemisphere can establish integrin‐based adhesion to the underlying collagen‐modified substrate. This configuration is analogous to the PAAm‐hydrogel surface sectioning the cancer spheroid along its equatorial plane, thereby enabling the quantification of traction forces exerted by the spheroid across this cross‐sectional interface, including contributions from both the periphery and the interior regions. It is worth noting that, traction forces of cancer spheroids exhibited a well‐defined annular distribution at the cell‐substrate contact plane, with peaks at the contact periphery and negligible values in the interface center, implying that the cell‐ECM mechanical interactions were primarily concentrated at the spheroid periphery where cancer cells were preparing to migrate outward. Similar spatial distribution pattern of traction force has recently been observed in traction force of individual cancer cells applied to the hydrogel microspheres, which was reported to reflect that the tendency and effect of cancer cell metastasis depended on the cell's periphery (Ma et al. 2024). Distinct from the traction of individual cells, we found that the traction force of cancer spheroid was regulated by the size of the spheroid. Smaller spheroids exhibited a faster initial increase in traction force and reached a plateau in a shorter period. That is, the traction of cancer spheroid was not necessarily related to the traction force of single cells, especially over a longer time scale. Therefore, the traction force exerted by cancer spheroids represents a novel biophysical parameter distinct from single‐cell traction, and the variations in cancer spheroid traction force with spatial distribution, spheroid size and time provide more comprehensive parameters for understanding of cancer progression and metastasis.
Our work also established the preliminary relationship between cancer spheroid traction force and dispersion. Currently, while the matrix deformation caused by cancer spheroid has been confirmed and quantified (Agrawal et al. 2023; Amaral et al. 2017; Kopanska et al. 2016), quantitative analysis of the relationship between spheroid force and dispersion remains lacking, as existing studies did not effectively translate the spheroid‐induced deformation into spheroid force. In contrast to previous studies, this work quantitatively calculated the force actively exerted on matrix by cancer spheroid. In fact, by assessing the matrix deformation as a reflection of spheroid forces, some studies have preliminarily explored the relationship between spheroid traction and invasion. For example, collagen displacement generated by breast cancer spheroids traction has recently been reported to reflect their aggressiveness (Blauth et al. 2024). And ECM deformation induced by A549 spheroids has recently been demonstrated to be mediated by stromal cells (such as cancer‐associated fibroblasts and endothelial cells), which in turn further influences the spheroid invasive capacity (Agrawal et al. 2023). In alignment with these prior research, our data quantitatively shown that early traction force of cancer spheroids was positively correlated with their dispersal capability, irrespective of whether the spheroids were actually undergoing dispersion. Moreover, we revealed a temporal correlation between the dynamics of spheroid dispersion and traction force.
Force generation and cell‐matrix interactions have been increasingly recognized as potential targets for antimetastasis therapy (Chaudhuri et al. 2018; Holle et al. 2018). Cancer spheroid traction force represents a novel promising indicator for evaluating anticancer drugs that target the collective cellular forces associated with dispersion. Currently, anticancer treatments primarily focus on inhibiting uncontrolled cell proliferation through radiotherapy and systemic cytotoxic chemotherapy, both of which aim to kill rapidly dividing cells but inevitably damage the normal self‐renewal of tissues such as bone marrow and intestines. With the advancement of cancer research, people have increasingly recognized that the most lethal malignant tumors are not merely a disease of unrestrained proliferation, but also one of uncontrolled cell migration (Clark and Vignjevic 2015; H. Wang et al. 2023), which presents novel targets for anticancer drug development. At present, traction force of single cancer cell has been shown to hold the potential as a readout for antimetastasis drug screening (Liew et al. 2024), whereas the forces collectively exerted by cancer cells under physiologically relevant conditions have not been utilized for drug detection. In fact, the matrix deformation induced by cancer spheroid has been proposed to guide personalized therapies (Leggett et al. 2020). Besides, collagen gel contraction assay, which is a qualitative assessment of the ability of cells to mechanically pull the ECM, has been proposed for force‐informed anticancer‐drug screening (Q. Zhang et al. 2022; Zhao et al. 2015). Compared with the aforementioned methods, we presented quantitative force outcomes of in‐vitro cancer microtissue models, and conceptually verified the ability of cancer spheroid traction force as the read‐out for antitumor drug detection regardless of whether the cancer spheroid have undergone diffusion.
In summary, we proposed the concept of cancer spheroid traction force, systematically quantified the active force of cancer cells collectively applied to ECM under physiologically relevant conditions. We revealed the distribution pattern of the cancer spheroid traction, elucidated the regulatory role of the spheroid size on the traction force, uncover the temporal relationship between cancer spheroid traction force and dispersion, and explored the feasibility of using cancer spheroid traction force as an evaluation index for anticancer drugs. Future research endeavors should aim to elucidate the physiological significance of the spatial distribution of spheroid traction force, identify the specific role of traction force in spheroid dispersion and explore the mechanisms by which dispersion inhibits the increase rate of traction force. Moreover, future work should also integrate state‐of‐the‐art algorithms to further enhance the accuracy, spatial resolution, and computational efficiency of the cancer spheroid traction‐force calculations. For instance, inverse methods can be employed to improve accuracy by iteratively converging the displacement field toward a state of mechanical equilibrium (Apolinar‐Fernández et al. 2023; Apolinar‐Fernandez et al. 2025a, 2025b; J. Barrasa‐Fano et al. 2021; Jorge Barrasa‐Fano et al. 2021; Sanz‐Herrera et al. 2021; Shapeti et al. 2024; Van Oosterwyck 2022; Vargas et al. 2020). In addition, optimized noise processing and regularization parameter selection techniques should also be taken into consideration (Apolinar‐Fernández et al. 2024; A. Jorge‐Peñas et al. 2017; Alvaro Jorge‐Penas et al. 2015; Sune‐Aunon et al. 2017). On the whole, this work investigated the distribution, magnitude, and dynamics of spheroid traction force, its relationship with spheroid dispersion, and its response to anticancer drugs; presented a novel mechanobiological metric for cancer research, providing new insights and methods for understanding the mechanisms of cancer invasion and developing anticancer drugs that target cellular forces.

4
Materials and Methods
4.1
Cell Culture
The human non‐small‐cell lung cancer cell line A549 was purchased from ATCC. The cells were cultured in an incubator at 37°C under 5% CO2. The RPMI‐1640 complete medium was prepared by supplement with 10% fetal bovine serum, 100 U mL−1 penicillin, and 100 U mL−1 streptomycin. Cells at 80%–90% confluence were detached with 0.25% trypsin for 1 min, and the enzymatic reaction was terminated by adding RPMI‐1640 complete medium. The detached cells were pipetted into a cell suspension and centrifuged at 1200 rpm for 3 min. The cell pellets were resuspended in complete medium and subcultured at a 1:6 ratio every 3 days.

4.2
Generation of 3D Cancer Spheroids
Cancer spheroids were prepared using an optimized hanging drop method. Specifically, Methylcellulose was dissolved in complete medium to prepare a 2.4 mg/mL stock solution, which was filter‐sterilized through a 0.22‐μm membrane. A549 cells at 80%–90% confluence were detached, centrifuged, and resuspended in 1640 complete medium supplemented with 5 μg/mL collagen and 0.24 mg/mL methylcellulose. The A549 density was adjusted to 3 × 103, 15 × 103, 30 × 103, 60 × 103, 90 × 103, and 240 × 103 cells/mL. The cell suspension containing collagen and methylcellulose was dropped on a 10‐cm diameter Petri dish lid at 10 μL/drop. Subsequently, 12 mL of Dulbecco's phosphate‐buffered saline (DPBS) was added to the Petri dish, and the lid containing the drops of cell suspension was inverted and placed on the dish overnight (Figure 1A).

4.3
Characterization of 3D Cancer Spheroid Morphology
To characterize the size and roundness of the 3D cancer spheroids, the spheroids were imaged in bright field using a 10 × phase‐contrast lens. ImageJ software was used to manually outline spherical boundaries to determine spheroid diameter and roundness. The spheroid diameter was defined as the equivalent diameter calculated using the cross‐sectional area of the spheroid. Spheroid roundness was measured using the shape index (SI), which was calculated as follows: SI=2π×spheroid_area/spheroid_perimeter.

4.4
Characterization of Cancer Spheroid Dispersion Dynamics
During 2D culture on high‐collagen surface, cancer spheroids gradually adhered to the substrate surface and dispersed, forming a cell monolayer that surrounded the spheroid (Figure 4A and Figure S2). To investigate the dispersion dynamics of spheroids, a confocal microscope equipped with a live‐cell chamber was used to record their growth after inoculation on the polyacrylamide hydrogel with physiological stiffness. Images were captured every 5 min for the first 3 h and every 15 min for the next 21 h. To quantify the dispersion of spheroids and to compare the dispersion of spheroids of different sizes, we defined the NDA, which was calculated by dividing the area of the cell monolayer from the spheroid by the area occupied by the spherical part of the spheroid on the substrate.

4.5
Preparation of Artificial Speckle‐Elastic Substrates
First, the glass bottom of the laser confocal dish was activated using the following steps: (1) Add 2 mL of 0.5 M NaOH solution into a 35‐mm‐diameter laser scanning confocal dish (with a 20‐mm‐diameter glass bottom). After incubation for 3 h, the dish was thoroughly rinsed with deionized water and air‐dried. Subsequently, the glass bottom was washed with anhydrous ethanol and methanol three times each, followed by air‐drying. (2) An APTES (3‐aminopropyltriethoxysilane) acetone solution was prepared at a working concentration of 12% (v/v). Then, the glass bottom was incubated with 300 µL of the APTES acetone solution per dish and reacted in a fume hood for 6 h. Unreacted APTES was removed by thorough rinsing with deionized water, and the dish was dried using a vacuum pump. (3) Phosphate buffered saline (PBS) (300 μL) containing 0.5% glutaraldehyde was added to the dish and allowed to react for 30 min at room temperature. Finally, the solution was discarded, and the dish was rinsed three times with deionized water and air‐dried for subsequent use.
Next, polyacrylamide (PAAm) hydrogel film containing fluorescent beads was prepared as follows: (1) Prepare the pre‐polymerized solution of PAAm hydrogel: In a 600‐μL centrifuge tube, add 160 μL of deionized water, 25 μL of 40% acrylamide solution, 15 μL of 2% N,N’‐methylenebisacrylamide solution, and 0.2 μL of N,N,N’,N’‐methylethylenediamine successively (Tse and Engler 2010). To the above solution, 4 μL of polystyrene fluorescent beads and 2 μL of 10% ammonium persulfate solution were added, followed by immediate vortex mixing. The PAAm hydrogel employed in this study exhibits a Young's modulus of 5 kPa and a Poisson's ratio of 0.48, which were characterized by a mechanical testing system (MTS Systems Corporation, USA) integrated with a noncontact full‐field strain measurement system (VIC‐3D, Correlated Solutions Inc., USA). Detailed experimental procedures are provided in Section S1 of the Supporting Information. (2) Pipette 30 μL of the above‐mentioned pre‐polymerized solution onto the activated glass bottom of the laser scanning confocal dish, and cover it with a clean 18‐mm‐diameter coverslip, taking care to avoid air bubbles. (3) Immediately invert the laser scanning confocal dish to promote the deposition of fluorescent beads onto the gel surface. (4) Allow the gel to polymerize at room temperature in the dark for 40 min. (5) Remove the coverslip and add PBS to the dish for later use.
Finally, the hydrogel surface was modified with ECM proteins as follows: (1) Prepare the crosslinker working solution. Use sulfo‐SANPAH as the crosslinker and dissolve it in 50 mM HEPES solution (pH = 8.5) at a sulfo‐SANPAH concentration of 1.5 mg/mL. (2) Incubate 300 μL of the crosslinker working solution on the surface of the PAAm hydrogel film and irradiate it with UV light for 30 min at a distance of 10 cm from the UV lamp. (3) Discard the excess reaction solution and wash the gel surface twice with HEPES buffer (50 mM, pH = 8.5) for 5 min each time. (4) Add 300 μL of collagen solution to the gel surface and incubate it at 4°C overnight.

4.6
Calculation of Cancer Spheroid Traction Force
Essentially, the traction forces of cancer spheroids represent the collective forces exerted by the cancer cells within the spheroid on the substrate, and their calculation method is consistent with that of single‐cell traction forces. Cancer spheroid inoculation was performed at a density of six spheroids per square centimeter on the elastic PAAm hydrogel embedded with fluorescent microbeads (0.5 μm, F8812, Invitrogen). Using a spinning disk inverted laser confocal system (UltraView VOX, PerkinElmer, USA) with a 10x lens, images were captured in both bright field and fluorescence channels to document the dispersion of spheroids and the displacement of the fluorescent beads. The spatial resolution of the fluorescent images is 0.714 µm/pixel. Images of fluorescent beads before spheroid attachment were used as the reference for displacement field calculation. For displacement field calculation, a digital image correlation (DIC) method was used to determine the substrate deformation caused by spheroid dispersion. Specifically, the motion of the fluorescent beads were tracked between reference and deformed states using a DIC approach available in the u‐track software package (available at: https://github.com/DanuserLab/u‐track), which enabled reconstruction of the full displacement field via stage drift correction, sub‐pixel localization and trajectory linking (Han et al. 2015; Welf et al. 2020; Zancla et al. 2022). Based on the displacement field, the traction force of cancer spheroid was reconstructed by the Fourier transform traction cytometry (FTTC) method with a self‐adaptive filtering scheme to suppress the amplification effect of high‐frequency noise (Han et al. 2015; Huang et al. 2012; Welf et al. 2020; Zancla et al. 2022) (see details in Section S2 in the supporting information). The root mean square traction force (T

RMS
) was adopted to quantify the magnitude of cancer spheroid traction force, which was calculated by the formula as follows:
where Ti represented the surface traction vector at every ith of N samples above the noise floor inside the manually selected spheroid boundary at the cell‐substrate contact plane (corresponding error analysis is presented in Section S3 of the supporting information).

4.7
Treatment With Anticancer Drugs
Cisplatin was dissolved in N,N‐Dimethylformamide (DMF) to prepare a 0.5 M stock solution, which was diluted with complete medium to target final concentrations of 0.5, 1, 5, 10, 20, 50, 100, 250, 350, and 500 μM before use. A complete medium containing DMF (1:1,000 dilution) was used as the control.
Docetaxel was dissolved in dimethyl sulfoxide (DMSO) to prepare a 35‐mM stock solution, which was diluted in complete medium to target final concentrations of 0.1, 0.5, 1, 3, 5, 10, 20, 50, 100, and 350 nM before use. A complete medium containing DMSO at a 1:100 dilution was used as the control.

4.8
Statistical Analysis
For all assays presented as bar chart, data are expressed as mean ± standard deviation (SD). For all assays presented as line chart, data are expressed as mean ± standard error of the mean (SEM). Statistical analyses were performed using ordinary one‐way analysis of variance (ANOVA) or Student's t‐test using GraphPad Prism software as indicated. Statistical significance was accepted at a P value less than 0.05.

Author Contributions
Qing Zhang conceived and designed the project. Qing Zhang, Jiaqi Chen, Zhaoxu Zhang and Weili Liu completed the experiment and data collection. Qing Zhang contributed to the data analysis and manuscript writing. All authors reviewed the manuscript.

Conflicts of Interest
The authors declare no conflicts of interest.

Supporting information

Figure S1: Equivalent diameter and roundness of cancer spheroid versus initial A549 cell number. Figure S2: Schematic diagram showing the cancer spheroid traction force. Figure S3: Mechanical Testing System for PAAm Hydrogels. Figure S4: Preparation of a rectangular PAAm hydrogel featuring a single speckled surface for mechanical testing. Figure S5: Calculating displacement from pre‐set traction force field. Figure S6: Digital speckle images generated from the undeformed and deformed displacement fields. Figure S7: Traction force field reconstructed via the TFM approach used in this work.