Multiscale elasticity mapping of biological samples in 3D at optical resolution

Introduction: The mechanical properties of tissues play a crucial role in dictating both healthy development [1] and disease progression [2,3]. As such, characterizing the degree and distribution of stiffness within biological samples provides insight into the important interplay between mechanics and biological activity. Unfortunately, most current methods for evaluating tissue stiffness (e.g., Atomic Force Microscopy (AFM), MR and optical coherence elastography) are limited to two-dimensional outputs and/or low resolutions and have inherent limitations in both accessibility and scalability. Here, we present a new µElastography platform that leverages a biocompatible, thermo-responsive hydrogel to map stiffness distributions and detect mechanical heterogeneities within biological samples [4]. Our scalable technique is compatible with a range of microscope modalities (e.g., confocal, multiphoton, optical coherence tomography) and generates highly resolved stiffness maps in units of absolute stiffness (i.e., kPa) across a range of biological length-scales, from cellular (µm) to whole murine organ (mm).

Materials and

Methods: Samples are embedded within concentric layers of agarose and thermoresponsive hydrogel (Fig. 1A). As the system is heated to 37°C, the hydrogel compacts and compresses the embedded agarose-sample complex (~10-30% linear strains). 3D image stacks are captured via fluorescent microscopy in both the relaxed and compressed states, and deformable image registration software maps the deformation between states at micron-scale resolutions. Custom-written Matlab scripts then calculate a variety of canonical strain tensors from the 3D deformation field, before a finite-element based inverse-problem solving algorithm calculates highly resolved spatial maps of sample elasticity on a user-defined plane of interest. We validate the platform using an agarose phantom (Youngs’s modulus (E) = 2.7kPa) with stiff inclusions (E = 29kPa) randomly distributed throughout. We then apply the platform to measure the elasticity of spheroids of murine breast cancer cells expressing a nuclear label (MMTV-h2B-Dendra) as well as intact murine lymph node.

Results, Conclusions, and Discussions: We first rigorously validate both the experimental and computational frameworks of the µElastography system. Using an agarose phantom (Fig. 1B), we confirm the compressive strains of 10-30% experienced by the embedded sample. We then confirm the efficacy of image registration-produced deformation fields and subsequent areal strain calculations, with the highly resolved map of areal strain (Fig. 1C) clearly depicting internal strain patterns corresponding to the location of the stiff inclusions (Fig. 1B, green spheres). The elasticity map generated by solving the inverse problem (Fig. 1D) highlights the distribution of elasticities across the plane, quantified in absolute units (kPa) and comparable to corresponding AFM measurements (Fig. 1E); the location of stiff inclusions is once again apparent in the map. Importantly, the nature of our platform allows for users to solve both a linearly elastic version of the inverse problem as well as a nonlinear, hyper-elastic Neo-Hookean version for more complex samples. Leveraging the biocompatible nature of our platform, we then quantify the internal elasticity distributions of murine cancer spheroids (Fig. 1F, 1G) and murine lymph nodes to generate internal elasticity maps. Resulting values are in agreement with AFM values for multicellular spheroids, and within the range of previously reported stiffnesses of murine lymph nodes.
Using the µElastography platform, we generate highly resolved maps that uncover the complex spatial distributions of elasticity in biological samples which give rise to higher order mechanical properties. This method represents an advance in the field of mechanical characterization, combining advantages from existing techniques in a scalable modality compatible with multiple imaging modalities, biological length scales, and mechanical measurements of interest, while preserving the native 3D structure of the tissue. Our method is both versatile and accessible, with wide-ranging applications across tissue engineering, developmental biology, and mechanobiology.

Acknowledgements (Optional): Sources cited:
1. Wozniak, M., Nat. Rev. Mol. Cell. Biol., 2009; 10: 34:43.
2. Nia, H., Science, 2020; 30:370(6516).
3. Murphy, M., Neuroimage Clin., 2016; 10: 283-290.
4. Regan, K. Acta Biomat. 2024; 176: 250-266.