Authors:
M. Sc. Peter Maday | Technische Universität München | Germany
Dr. Stefanie Demirci | Technische Universität München | Germany
Dr. Markus Kowarschik | Siemens Healthcare GmbH | Germany
Prof. Dr. Nassir Navab | Technische Universität München | Germany
Cerebrovascular diseases such as aneurysms, arteriovenous malformations (AVMs), and stenoses impose significant health risks. Decreased oxygen supply and an elevated risk of hemorrhage are only a couple of potential consequences due to changes in local hemodynamics.
As the preferred treatment option minimally invasive catheterization procedures are normally considered. Here, endovascular tools such as guidewires and catheters are introduced into the vascular system. Repairing pathological alterations to the vascular morphology, healthy flow behavior is restored.
Lack of direct line of sight necessitates X-ray image guidance to monitor positioning of the surgical instruments. Further injection of a radio opaque dye (contrast agent) makes translucent vessels visible and gives insight into pathological findings in more detail. Dynamic blood flow behavior is of special interest to the operating physicians, and needs to be repeatedly assessed during the intervention. For this purpose the clinical gold standard is a specialized x-ray imaging modality, Digital Subtraction Angiography (DSA). Selective visualization of the injected contrast agent enables experienced physicians to infer characteristics of the underlying fluid motion. Dependence on the imaging configuration, and depth ambiguities however make this process highly subjective.
Automated quantitative assessment of fluid flow, providing accurate and reproducible measurements of clinically relevant variables, would thus be highly desirable. These values, such as the volumetric flow rate, depend on the instantaneous fluid velocities. DSA captures transmittance image sequences of a dye, passively transported with the underlying blood flow in three-dimensional vascular structures. Flow reconstruction therefore involves the solution of an inverse transport problem, where the fluid velocity field is to be inferred from incomplete observations of the convected contrast density. Existing techniques mostly employ reduced order modeling, and approximate flow in a 1D vessel geometry by correlating sampled intensity curves. Due to modeling simplifications, patient specific vessel geometry cannot be fully integrated into this formalism, while due to the 1D sampling of DSA images the majority of measurement data is not utilized.
In this work we propose a novel flow quantification technique, entirely conducted in three-dimensions. As a first step approximate time-resolved 3D reconstructions of the contrast density are generated from standard DSA data using the recently proposed 4D-DSA algorithm. Reconstruction of the fluid velocities is then formulated as an energy minimization problem. We employ the optical flow constraint and seek to find a vector field compatible with the observed apparent motion in consecutive three-dimensional image pairs. The optical flow problem is ill-posed, therefore various local spatial regularization techniques are normally applied. We propose an alternative approach, and posit an explicit PDE constraint on admissible solutions. This leads to a problem formulation based on optimal control of the chosen fluid model (Stokes equation). Distributed controls over the domain boundary are iteratively refined, to minimize the image based energy. The descent process relies on gradient to the energy functional computed using the adjoint method. Forward and adjoint models are discretized using finite elements (FEM).
The method is evaluated on synthetic data, using realistic computational fluid dynamics (CFD) simulations of the blood-contrast agent mixture.
Approximate reconstruction of three-dimensional contrast distributions, and consecutive physically constrained flow quantification allow the available measurement data to be fully utilized, while incorporating the known 3D vessel geometry without overly simplistic modeling assumptions.