The CREATIS laboratory opens a Postdoctoral Research Fellowship in the context of the European H2020 project SPCCT. The core objective of this project is to develop and validate a new imaging technology combining Spectral Photon Counting Computed Tomography (SPCCT) and dedicated contrast agents to accurately detect, characterize and monitor neurovascular and cardiovascular diseases. The project is lead by Philippe Douek of the Universite Claude Bernard Lyon 1. In the context of cardiovascular diseases, blood flow velocity in the arteries is an important diagnostic parameter. Contrast agent enhanced tomography enables an rough estimate of this parameter with certain limitations. The methods previously described for the velocity estimation are not well established. One of these methods is known as time-of-flight (TOF) and is based on the difference in the arrival time of the contrast agent at two different locations. The temporal changes in the sinogram obtained in sequential scanning mode are exploited to obtain the blood velocity estimate. The TOF method is limited to the estimation of the average velocity of the flow component along the flow field propagation axis . Recently a new method to evaluate more precisely the blood velocity has been proposed combining a spiral CT scan with a contrast agent injection. Conversly to TOF, in this second method the transport equation is used as a constraint to obtain stable solutions. We have investigated an optimal control formulation of the 3D+t tomography inverse problem to reconstruct at the same time the flow velocity and the density of the contrast agent . The optimality system for the density of the constrast agent and the flow field are solved iteratively. Promising results have been obtained for very simple synthetic flow configurations and transport equations but the convergence is low .
Goal and tasks
The goal of this post-doctoral project is to improve the proposed method and to generalize it to more complex reconstruction problems. Several transport and diffusion equations and various velocity profiles should be investigated for more realistic arterial blood flow fields. In each case, based on the proposed optimal control methodology, the postdoctoral fellow will study the corresponding inverse problems, derive the optimality conditions and implement the iterative reconstruction to validate the approach. The optimality conditions involve a system of partial differential equations. Several numerical schemes may be studied for stable solutions and fast convergence. Finally, he will also study different spatio-temporal regularization schemes. Following the validation phase on synthetic data, the proposed method will then be evaluated on data acquired on the SPCCT scanner using a dedicated flow phantom.
Education: The candidate must hold a PhD in medical imaging, applied mathematics.
Experience: Inverse problems, tomographic reconstruction, partial differential equations.
Languages: English required, French optional.
Location: Lyon, France.
Salary (net): depending on experience, according to UCBL salary scale, starting at 1900 euros / month. Period: 1 years starting as soon as possible.
 S.Prevrhal, C.H.Forsythe, R.J.Harnish, M.Saeed, B.M.Yeh "CT angiographic measurement of vascular blood fowl velocity by using projection data", Radiology, vol.261, 923-929 , 2011.  A.Borzi, K.Ito and K.Kunisch "Optimal control approach to optical flow computation", International Journal for Numerical Methods in Fluids, vol.40, 231-240 , 2002.  B.Sixou, L.Boussel and M.Sigovan "Contrast enhanced computerized tomography measurement of vascular blood flow", Numerical Computational Methods for Inverse Problems, 2016.