Perfusion refers to the passage of fluid through the circulatory system to tissue and is defined as delivery of blood to the capillary bed in tissue. Perfusion as well as other vascular properties, including vessel permeability, vascular space volume, and extravascular space volume, directly reflect whether the organ is under normal physical condition. Direct estimation of perfusion parameters is not feasible in most situations, as capillaries are deeply buried in human body, and invasive operations will disrupt blood flow and affect organ function. Under this circumstance, contrast enhanced medical imaging techniques were developed, where contrast agents are injected into human body (alternatively, spin labeled water molecule can also work as contrast agent), and then images are acquired while contrast agent travels through the region of interest. By analyzing images before and after contrast agent injection, contrast agent propagation and underlying blood perfusion parameters can be estimated.This thesis developed a fast and accurate tracer propagation simulation method based on underlying fluid mechanics, as well as an inversion method that can recover perfusion parameters from contrast enhanced medical images (Quantitative Transport Mapping, QTM). The tracer propagation simulation method provides a rigorous way to simulate the traveling of contrast agent in organs. QTM overcame the disadvantages of traditional perfusion parameter estimation method (kinetic modeling method), and makes perfusion parameter estimation from medical images accurate, fast and automatic.