Purpose Most cancers are associated with biological and structural changes that lead to tissue stiffening. Therefore, imaging tissue stiffness using quasi‐static ultrasound elastography (USE) can potentially be effective in cancer diagnosis. USE techniques developed for stiffness image reconstruction use noisy displacement data to obtain the stiffness images. In this study, we propose a technique to substantially improve the accuracy of the displacement data computed through ultrasound tissue motion tracking techniques, especially in the lateral direction. Methods The proposed technique uses mathematical constraints derived from fundamental tissue mechanics principles to regularize displacement and strain fields obtained using Global Ultrasound Elastography (GLUE) and Second‐Order Ultrasound Elastography (SOUL) methods. The principles include a novel technique to enforce (1) tissue incompressibility using 3D Boussinesq model and (2) deformation compatibility using the compatibility differential equation. The technique was validated thoroughly using metrics pertaining to Signal‐to‐Noise‐Ratio (SNR), Contrast‐to‐Noise‐Ratio (CNR) and Normalized Cross Correlation (NCC) for four tissue‐mimicking phantom models and two clinical breast ultrasound elastography cases. Results The results show substantial improvement in the displacement and strain images generated using the proposed technique. The tissue‐mimicking phantom study results indicate that the proposed method is superior in improving image quality compared to the GLUE and SOUL techniques as it shows an average axial strain SNR and CNR improvement of 44% and 63%, and lateral strain SNR and CNR improvement of 130% and 435%, respectively. The results of the phantom study also indicate higher accuracy of displacement images obtained using the proposed technique, including improvement ranges of 7–84% and 26–140% for axial and lateral displacement images, respectively. For the clinical cases, the results indicate average improvement of 48% and 64% in SNR and CNR, respectively, in the axial strain images, and average improvement of 40% and 41% in SNR and CNR, respectively, in the lateral strain images. Conclusion The proposed method is very effective in producing improved estimate of tissue displacement and strain images, especially with the lateral displacement and strain where the improvement is highly remarkable. While the method shows promise for clinical applications, further investigation is necessary for rigorous assessment of the method's performance in the clinic.

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Similar to many other types of cancer, liver cancer is associated with biological changes that lead to tissue stiffening. An effective imaging technique that can be used for liver cancer detection through visualizing tissue stiffness is ultrasound elastography. In this thesis, we show the effectiveness of an enhanced method of tissue motion tracking used in quasi-static ultrasound elastography for liver cancer assessment compared to other state of the art methods. The method

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