Image-based modeling and simulation has become an important analytic and predictive tool for patient-specific medical applications, including large-scale in silico patient studies, optimized medical device design, and custom surgical guides and implants via additive manufacturing. The pipeline for patient-specific modeling and simulation is: image acquisition, image segmentation, surface generation, mesh generation, physics-based modeling and simulation, and clinical application. This research establishes a semi-automatic workflow for these steps, which includes a novel image-based meshing tool Shabaka. The toolchain is demonstrated by modeling the mechanics of a beating human heart based on magnetic resonance imaging (MRI) data. The Shabaka workflow ensures robust execution of each step of the pipeline. Medical images are processed and segmented using thresholding, region-growing, and manual techniques. Watertight surface meshes are extracted from image masks using a novel Voronoi-based algorithm. For scientific computing purposes, surface meshes are supplied either to tetrahedral meshing routines for conventional finite element approaches, or to a robust polyhedral mesh generation tool for a novel polyhedral finite element approach. A polyhedral finite element code is explored, that retains most of the favorable properties of conventional finite element methods, while reducing the system size by up to an order of magnitude compared to conventional techniques for the same input surface. In conjunction with a cardiac simulation code, the workflow is utilized to model finite-deformation cardiac mechanics. A quadratic tetrahedral mesh is generated from MRI data of the human heart ventricles. The constitutive law is comprised of an incompressible orthotropic hyperelastic stress response for the myocardium, plus an electrical activation-dependent active stress for the muscle fibers. Muscle fiber orientations are generated using a rule-based approach. Electrical activation times are read from a coupled electrophysiology code. A lumped circulatory model is used to impose time-dependent ventricular volume constraints. Simulation results are presented. The same mechanics are also implemented for the polyhedral finite element mesh, and preliminary verification results are presented. The toolchain used in performing image-based cardiac mechanics simulations makes important improvements to the speed and robustness of image-based modeling techniques. As efforts continue to mature, so too does the promise for simulation to impact and improve healthcare.