28Structural heterogeneity is a hallmark of living cells and nuclei that drives local mechanical 29 properties and dynamic cellular responses, including adhesion, gene expression, and 30 differentiation. However, robust quantification of intracellular or intranuclear mechanics are 31 lacking from conventional methods. Here, we describe new development of deformation 32 microscopy that leverages conventional imaging and an automated hyperelastic warping 33 algorithm to investigate strain history, deformation dynamics, and changes in structural 34 heterogeneity within the interior of cells and nuclei. Using deformation microscopy, we found 35 that tensile loading modes dominated intranuclear architectural dynamics in cardiomyocytes in 36 vitro or myocytes in vivo, which was compromised by disruption of LINC complex molecule 37 nesprin-3 or Lamin A/C, respectively. We also found that cells cultured on stiff substrates or in 38 hyperosmotic conditions displayed abnormal strain burden and asymmetries compared to controls 39 at interchromatin regions where active translation was expected. Deformation microscopy 40 represents a foundational approach toward intracellular elastography, with potential utility to 41 provide new mechanistic and quantitative insights in diverse mechanobiological applications. 42 43 44 45 46 47 48 49 50 Science Advances Manuscript Template Page 2 of 34 MAIN TEXT 51 52 93 registration (21). Over the course of the analysis, a penalty factor (21) is used to enforce the 94 registration. Additionally, regularization can be achieved using a hyperelastic material model. If 95 known, the associated material properties can be assigned to improve the strain estimates in 96 regions where image intensity differences may be lacking. Spatial averaging in the form of 97 normal or Gaussian blurring are used in the image analysis to avoid local minima which would 98 stop the global image registration prematurely resulting in false, unreliable deformation data (22). 99 Consequently, defining a suitable method to map deformation, or a correct set of parameters to 100 Science Advances Manuscript Template Page 3 of 34 obtain an optimal deformation map in a manageable time frame, is challenging and largely 101 lacking. 102 103 We introduce a technique, deformation microscopy, which utilizes an automated sweep over a 104 wide range of registration parameters, to quantify precise, high-resolution, and reliable spatial 105 patterns of intracellular displacements and strain. We demonstrated and validated the efficacy of 106 the technique across several biological scales, including examples of extracellular matrix, cell, 107 and nucleus deformation in vitro and in vivo. Next, we focused on applying the technique to 108 understand the spatiotemporal mechanics of nucleus in several normal and pathological 109 conditions. We altered the integrity of nuclear envelope by modulating the KASH domain, 110 nesprin-3, and Lamin A/C to understand their structural role in nuclear mechanics both in vitro 111 (cultured cells) and ...