Mathematical Methods in Medical Imaging: Analysis of Vascular Structures for Liver Surgery Planning

Mathematics and medicine do not have a long history of close and fruitful cooperation. The application of mathematical methods in medical applications has become viable due to the increasing performance of computers and since more and more digital image data is acquired. While in former times conventional X-ray images – recorded at an analog film – have been used for diagnosis and treatment planning, more and more (digital) 3D datasets, such as Computed Tomography (CT-images) and Magnetic Resonance Imaging (MRI) are acquired for patients with severe diseases. With mathematical methods these 3D datasets may be quantitatively analyzed and visualized such that medical diagnosis and the assessment of therapeutic strategies becomes more reliable and reproducible.