Deformable Models: Biomedical and Clinical Applications is the first entry in the two-volume set which provides a wide cross-section of the methods and algorithms of variational and Partial-Differential Equations (PDE) methods in biomedical image analysis. The chapters of Deformable Models: Biomedical and Clinical Applications are written by the well-known researchers in this field, and the presentation style goes beyond an intricate abstraction of the theory into real application of the methods and description of the algorithms that were implemented. As such these chapters will serve the main goal of the editors of these two volumes in bringing down to earth the latest in variational and PDE methods in modeling of soft tissues. Overall, the chapters in the first volume provide an elegant cross-section of the theory and application of variational and PDE approaches in medical image analysis. This volume introduces, discusses, and provides solutions for problems ranging from structural inversion to models for cardiac segmentation, and other applications in medical image analysis. Graduate students and researchers at various levels of familiarity with these techniques will find the volume very useful for understanding the theory and algorithmic implementations. In addition, the various case studies provided demonstrate the power of these techniques in clinical applications. Researchers at various levels will find these chapters useful to understand the theory, algorithms, and implementation of many of these approaches.