Variations in the mechanical properties of the extracellular environment can alter important aspects of cell function such as proliferation, migration, differentiation and survival. However, many of the techniques available to study these effects lack the ability to characterise cell-to-cell and cell-to-environment interactions on the microscopic scale in three dimensions (3D). Quantitative micro-elastography (QME) is an extension of compression optical coherence elastography that utilizes a compliant layer with known mechanical properties to estimate the axial stress at the tissue surface, which combined with axial strain, is used to map the 3D microscale elasticity of tissue into an image. Despite being based on OCT, limitations in post-processing techniques used to determine axial strain prevented QME to quantify the elasticity of individual cells. In this study we extend the capability of QME to present, to the best of our knowledge, the first images of the elasticity of cells and their environment in 3D over millimeter field-of-views. We improve the accuracy and resolution of QME by incorporating an efficient, iterative solution to the inverse elasticity problem using adjoint elasticity equations to enable QME to visualize individual cells for the first time. We present images of human stem cells embedded in soft gelatin methacryloyl (GelMa) hydrogels and demonstrate these cells elevate the stiffness of the GelMa from 3-kPa to approximately 25-kPa. Our QME system is developed using commercially available components that can be readily made available to biologists, highlighting the potential for QME to emerge as an important tool in the field of mechanobiology.
In OCE, the link between measured displacement and elasticity is non-trivial in complex tissues and a number of simplifying assumptions regarding deformation are made to generate an elastogram. In compression OCE, for instance, elasticity is assumed to be inversely proportional to axial strain (the gradient of axial displacement with depth). However, this assumption relies on the tissue being mechanically uniform. This assumption is typically invalid and limits elastogram resolution. Despite this, few studies have explored OCE resolution in detail. Previously, OCE resolution has been reported laterally as the OCT resolution, and axially as the spatial range of displacement used to estimate axial strain. However, this describes only the ability to resolve axial strain. The ability to resolve features is also dependent on the interplay of mechanical deformation and the model with which it is analyzed. We present a framework for analyzing resolution in OCE, which combines a model of mechanical deformation, using finite-element analysis, with a model of the OCT system and signal processing, based on linear systems theory. We present simulated and experimental elastograms of tissue-mimicking phantoms, showing close correspondence, and demonstrate, for instance, that the resolution of a square 1-mm inclusion can vary, within one image, from 100 μm to 200 μm axially, and from 100 μm to 380 μm laterally. We demonstrate that axial and lateral resolution are directly related to inclusion size and mechanical contrast. Our framework may enable OCE systems to be tailored to specific applications and can be extended to other forms of OCE.
In a typical experiment in compression elastography a sample is compressed to an overall strain of about 1-5%, and then perturbed with a much smaller strain in the range of 0.05%-0.1%. The displacement field corresponding to this perturbative excitation is measured using phase-sensitive OCT. This three-dimensional perturbative displacement data carries within it a wealth of information regarding the volumetric distribution of linear elastic properties of tissue. In this talk we will describe a class of iterative algorithms that use this data input and generate volumetric maps of linear elastic properties of biological specimens. The main idea behind these algorithms is to pose this inverse problem as a constrained minimization problem and use adjoint equations, spatially adaptive resolution and domain decomposition techniques to solve this problem.
We will also consider the case when the overall compression and the perturbative excitation steps are repeated several times while increasing the overall strain. For example, a sequence wherein the overall strain varies as 2, 4, 6, 8, and 10%, and each increment is followed by a small perturbative excitation. The measured displacement field corresponding to this small excitation is sensitive to the nonlinear elastic properties of the specimen, which determine how its elastic modulus varies with increasing strain. We will extend the algorithms designed to infer the linear elastic properties of biological specimens to infer these non-linear elastic properties. We will demonstrate our ability to infer linear and nonlinear elastic properties on tissue-phantom, and ex-vivo and in-vivo tissue samples.