Traditional black-box deep learning models often require large annotated datasets, which are not available for image reconstruction problems for estimating parametric maps in tissues. Model-based deep learning offers a promising solution by integrating known imaging physics and models into the learning process, enabling learning from limited data and/or simulations while still maintaining generalizability to actual data despite potential domain gap. In my PhD project, we are exploring model-based deep learning solutions for computed tomography problems in medical imaging, including X-ray and ultrasound. We will develop and assess frameworks such as Model-based Deep Learning (MoDL) and Variational Networks (VN), with a primary focus on tomographic reconstruction of speed-of-sound (SoS) maps in tissue using ultrasound waves. SoS is an emerging quantitative tissue biomarker that can provide additional and/or independent information on tissue composition compared to current imaging modalities such as B-Mode and elastography, particularly in applications such as breast imaging. Our research group has several earlier publications laying the ground-work and understanding in such novel ultrasound imaging technique, which will be extended to deep-learned solutions herein.