Nuclear Magnetic Resonance (NMR) is a very powerful analytical tool employed in a wide range of situations, such as elucidation of organic structures, biochemical studies, pharmaceutical analysis or in vivo spectroscopy. However, it suffers from major limitations due to strong overlap between peaks, and this is particularly true for complex metabolic mixtures. Therefore, 1D NMR offers a limited capacity for the precise quantification of interesting biomarkers in complex samples. Fortunately, two dimensional (2D) spectroscopy allows the unraveling of spectral complexity along a second dimension and thus presents a great potential to unambiguously and simultaneously measure a larger number of metabolite contributions. However, it is still rarely used for quantification, first because quantitative analysis by 2D NMR requires a calibration procedure due to the multi-impulsional nature of 2D NMR experiments, and above all because of the prohibitive experiment duration that is necessary to obtain such a calibration curve, due to the multi-scan nature of 2D NMR experiments. Fortunately, the past few years have witnessed the emergence of a novel and promising method that makes it possible to acquire a whole 2D spectrum in a fraction of a second. This so-called “ultrafast 2D NMR” method, proposed by Pr. Lucio Frydman, is based on a single-scan approach. Very recently, we have successfully implemented this methodology at the CEISAM laboratory. We have proposed several methodological developments to make ultrafast 2D NMR suitable for quantitative analysis of mixtures, thus enlarging the application range of this promising method. Based on this experience, the ambition of the QUANTUM project is to develop a complete methodology to set ultrafast 2D NMR as a standard tool for fast and precise quantitative analysis of complex metabolic mixtures. This project will consider original NMR developments and programming aspects, focusing on the resolution and sensitivity aspects of ultrafast methods. A complete analytical validation of these optimized methods will be carried out, in order to make them applicable to quantitative studies of real metabolic samples such as tumor cell extracts. At the end of the project, we will propose a package including the analytical strategy, the pulse sequences and the pre-acquisition and processing routines for quantitative ultrafast 2D experiments, that will be easy to implement in routine. This package will be available online on the CEISAM website, for free distribution to the academic community Our interest in ultrafast 2D NMR is an emergent research axis in our research group, which has an international expertise in isotopic analysis applied to natural product authentication and for elucidating metabolic pathways. However, even though we started working on ultrafast 2D NMR in 2007, we became in three years the second group in the world (first in Europe) regarding the number of papers on ultrafast 2D NMR. Moreover, we are the authors of the only paper published so far reporting the application of ultrafast 2D NMR to quantitative analysis. Fortified by our experience and in order to enlarge the diffusion of ultrafast methods, we wish to make ultrafast 2D NMR accessible in routine to a large number of research groups in the world, by developing adapted programs integrated to existing commercial software, and by making these available to the scientific community. Finally, the QUANTUM project will be an opportunity to develop fast quantitative 2D NMR methods applied to metabolomic studies, which really constitutes a new approach in the CEISAM laboratory. It should open new application perspectives that are currently out of the laboratory expertise.

Scientific background and objectives The project is driven by a kernel team of 3 researchers in Nantes (in mathematics), with an associated researcher in Sophia-Antipolis (in imaging). It aims at building a mathematical model for the electro-physiological behavior of the human heart in real situations, and mathematical methods for its numerical simulation. Results might be confronted to clinical data, providing a feedback on modeling and computing. Considering our work in the fields of applied mathematics or imaging for cardiac modeling during a post-doctoral, PHD, ATER or permanent position, we decided to gather our knowledges in order to better understand and model the electrical behavior of the heart inside the torso, for practical use . Cardiologists detect many pathologies from the very sparse data (mainly electrocardiogram, ECG) and simple representations (electrical dipoles) they have of the electrical behavior of the heart. Yet very complex mathematical models of the muscle tissue are now known and lead to expensive and complex computations. Additionally, at a higher level of complexity, the heart is a network of different kind of tissues (atria, ventricles, sinus node, atrioventricular node, special conduction network); and this part is not well understood, although it is essential for the activation sequence. At last, it is not clear whether realistic tissue models or realistic models of the organ (eg as a network) are the most important in ECG simulations. Several teams address the problem of simulating realistic and complex models of excitable tissues. But fast and accurate computing remains a difficult scientific computing challenge. This project intent to develop new methods to solve this problem, but also a hierarchy of simpler models and faster methods to compute the action potential (AP) propagation (monodomain, level-sets and Eikonal eqs). The second main issue of this project is the development of a model integrating the AP propagation ones to account for the whole organ in ECG simulations. Therefore, a collaborative work of mathematical modeling, scientific computing and medical imaging is necessary. The project has various issues of different nature, mainly concerning 1) nonlocal systems of reaction-diffusion equations; front propagation modeling through Hamilton-Jacobi equations; 2) numerical analysis for finite volumes schemes; fast marching and similar techniques; and at last fast multipole methods; 3) parallel computing, preconditioning and iterative solvers; 4) segmentation of moving images, registration of measure devices in images. Description, methodology The project is planned on 4 years with the help of post-doctoral researchers for the last 3 years. Starting from an original finite volumes method (PhD thesis of C. Pierre), the following problems will be considered: a) develop time-stepping methods, preconditioning and parallel computing in the current code, b) understand the limits of the available modeling levels (bidomain, monodomain, Eikonal), finding links between them, in order to adjust the numerical tools to the desired level of complexity of applications, c) use fast methods for simpler models, specifically high-order methods on 3D unstructured grids for Eikonal eqs, d) use a generic idealized model of the heart to understand the activation sequence and ECG patterns; be able to adjust it to images and measures, and therefore interact with applied scientists (clinicians, bioengineers). The discussion on modeling aspects, the choice of numerical methods to apply, the specification of useful test-cases is a common aspect to be discussed by the whole team, based on the personal work and experience of the members in analysis, approximation, scientific computing, imaging. Post-doctoral researchers will have very specific 1-year tasks: (1) parallel preconditioning and time-stepping methods, (2) integral equations, fast multipole methods and computing of the ECG and (3) front-tracking using fast-sweeping methods. Expected results Based on an analytical model of the anatomy that may be fitted to images and on an existing finite volumes code for a model of the ventricles, we plan to develop a hierarchical framework of models for the whole heart and torso and implement their numerical solutions into the current code. This ought to provide an experimental software tool usable both to understand activation sequences and ECG patterns and for practical purpose, that our collaborators from the Cardiac MR Research Group, Guy's Hospital, King's College, London are interested in. Mathematical results are expected concerning every of the issues 1) to 4) above; in the fields of analysis, numerical analysis and scientific computing.

More than 250000 Europeans are living with a graft and 80000 people are enrolled in the waiting list. Given the limited availability of donor, it is of importance to improve graft survival. The goal of our proposal is to define an appropriate methodology to assess the prognostic capacity of a composite marker to evaluate long-term graft survival. Those tools will 1. Improve the allocation of the available graft to minimize the return to dialysis and the recipient mortality; 2. Help clinicians in the care of the patients (drugs, monitoring,…); 3. Constitute a new marker to monitor the graft survival to reduce the cost, the length and the risk of clinical studies. New and innovative methodological strategies have to be design to shift from the monitoring of a single parameter (i-e graft and patient survival) to a composite marker that will fit better to the clinical reality. Preliminary studies have shown that multi-state based strategies are suitable to evaluate the clinical evolution of the patient, as such strategies take into account the evolution and distinguish two non-comparable failures (the return to dialysis and the death of the recipient). Our multi-state model will consider 4 different status: recipient without acute rejection, recipient with at least one episode of acute rejection, recipient that have return to dialysis and dead recipient with a functional graft. The primary objective is to define a composite variable that could predict the transition of the patient from one status to another. The transition from one status to another will be modelized using a semi-Markov based parametric strategy. Variables will be summarized by neuron networks, an optimal methodology to consider a great number of parameters in a flexible manner. Neuron networks have not been often used in medicine in contrast to other field, and thus strengthen the novelty of our proposal. Our multi-state model will be built based on the clinical record in order to predict the future evolution of the graft. Relative survival will be included to estimate the transition to the death with a functional graft (mortality in the general population). All the socio-demographic and clinical variables will be obtained from the DIVAT database, database which was created in 1990. This database is the only one in Europe to have a dedicated quality policy. We aim to implement this quality policy by designing automatic audit tool of the data. We think that our multi-state model will benefit from the inclusion of emerging biomarkers (identified in the biocollection that is linked with DIVAT), even if such biomarkers have not been yet validated in large prospective cohort of patients. To summarize, our project is defined by 3 specific aims: 1. To construct a complet database with clinical and biological parameters; 2. To design an innovative statistical strategy that will consider the heterogeneity of the recorded parameters to minimize the error in graft and patient evolution; 3. To built a new tool to assist physicians in their decision. The expertise in designing a complex statistical methodology and the appraisal of multiple parameters (both clinical and socio-demographic) are the strength of our proposal.