Brain

Cerebrovascular accidents (CVA) are caused by a perturbation in the blood supply of the brain leading to a quick loss of cerebral functions, that is very often lethal. There are two categories of CVA: ischemic CVA (80% cases) resulting from the occlusion of a cerebral artery and haemorrhagic CVA (20% cases) provoked by a bleeding vessel.

It is nowadays a major challenge in terms of public health-care. In Western countries, one of 600 people suffers from a CVA each year and 120,000 cases are counted yearly in France.

From a medical point of view, the detection and a fast characterisation of a CVA (ischemic or haemorrhagic, each having a specific and antinomian treatment) is crucial for patient survival. The faster the treatment is, the more brain damages are reversible and the chances of cure are high. If it is important to act promptly, it is just as crucial, once the urgent phase ended, to closely monitor the evolution of the CVA for adapting, if necessary, the treatment of the patient. But a continuous monitoring needs, theoretically, an image of the brain every fifteen minutes.

Yet, today, physicians can use two imaging systems of the brain: Magnetic resonance imaging (MRI) and CT (cerebral tomogram) scan. Even if these techniques are very precise - particularly MRI with a spatial resolution around a millimetre - and of high quality, their use is expensive, not well adapted to a prompt medical care as they need to be embedded in inside an ambulance, and indeed harmful in the case of a continuous monitoring with CT scan that measure the absorption of tissues by X rays.

This fully justifies the great interest of the project led by Frédéric Nataf, senior researcher at CNRS and INRIA, and his team. For the first time in the world, they have demonstrated on synthetic data the feasibility of a new imaging technique based on microwaves, allowing both the characterization of the CVA from the very first patient care in an ambulance and throughout his continuous monitoring during his hospitalisation. Winner of the 1st Bull Fourier 2015 award, the research team, gathering specialists of in Applied Mathematics (from the Universities of Paris 6, Toulouse and Nice) and of in Electronics (from Sophia Antipolis), has carried out its work in the context of an ANR (Agence Nationale de la Recherche) project in collaboration with an Austrian innovative SME, dedicated to biomedical imaging, EMTensor.

Promises of microwaves imaging

The electric properties of biological tissues are a great indicator of their functional and pathological conditions. Able to fully distinguish tissues, microwaves can image them, on the basis of differences in their dielectric properties. The principle of such a system is the following: The patient’s head is equipped with a helmet consisting of electromagnetic antennas, that transmit data to a high performance computing centre for processing them and then sending the resulting images to doctors at the hospital where the patient will be treated. This type of imaging asks requires only a very reduced data acquisition phase - few milliseconds - with a satisfying spatial resolution and also with a level of harm lowest than that of a mobile phone. These characteristics make microwaves imaging very competitive even if a product for medicinal use doesn’t exist yet. 

It leverages several new technologies that are getting more and more common: Miniaturized antennas, mobile broadband technologies (4G, 5G, ...) and large-scale parallel computers with tens or hundreds of thousands of cores. From a computational point of view, it demands the fast solving of Maxwell equations with high contrasts in the coefficients in order to image the brain via the solving of an inverse problem. 

Principle of microwaves imaging by courtesy of EMTensor 

For demonstrating the feasibility of such a technique, Frédéric Nataf and his team have developed a High Performance Computing approach which generates brain images before sending them back to the physician, all in less than 15 minutes.

Work of the team

In order to develop a numerically robust and precise methodology for microwaves imaging, three distinct research fields, must be controlled: optimisation, inverse problems and the simulation of the direct problem modeled using the Maxwell equations system. This last aspect implies mastering approximation and resolution methods (parallel solvers by domain decomposition, parallel computing). The precise simulation of a direct problem for a complex and highly heterogeneous medium in a frequency domain is a challenge in itself: EMTensor was led to develop its own simulation code for modelling the propagation of the electromagnetic field in a brain circled in a measurement chamber, not feasible with the existing commercial software.

The French team has capitalised on the tools developed by the researchers: The HPDDM library for domain decomposition and its interface with the FreeFem++ software (finite elements), that lead to a gain of several orders of magnitude in terms of development and execution time of the imaging algorithm. The core hours, firstly allocated by the computing centre of the Université Pierre et Marie Curie (UPMC) and then by Genci and PRACE on the massively parallel supercomputers, Turing at Idris (1,2 million hours in 2014) and Curie at TGCC (500,000 hours awarded by GENCI in 2015 and 3 million hours globally given through two PRACE allocations between 2012 and 2014), have been decisive to achieve the project.

Feasibility of the experimental system

EMTensor’s experimental system consists in an electromagnetic reverberating chamber surrounded by five layers of 32 antennas each, able to work alternately as an emitter or a receptor.

The object to be reconstructed is introduced in the chamber. Alternately, each of the 160 antennas emits a signal at a fix frequency, typically 1 GHz. The electromagnetic field is propagated within the chamber and the object to be imaged regarding its properties. The other 159 antennas record the total field in the form of complex transmission coefficients traducing the amplitude and phase in each antenna. The electronic systems thus acquire the 160 measures in only around one millisecond. Each series of measures is represented in the form of a matrix of complex coefficients of 160x159 size. The inversion algorithm is aimed at reconstructing a brain image on the basis of these data.

For assessing the capacity of such a system to characterise a CVA and to monitor its evolution, a first step was to successfully compare the measure of data acquisition made with EMTensor’s system with those numerically performed by the resolution of Maxwell equations on a 3D mesh (5 million degrees of freedom). 

Measurement chamber and corresponding mesh for numerical simulation (diameter: 28.5 cm)

Need for speed with parallelism

For the second step, researchers created synthetic data on a brain model coming from scan sections (362x434x362 voxels) and then simulated a haemorrhagic CVA. At last, they designed and tested an inversion algorithm for monitoring the evolution of the CVA, reconstructed by successive slices. Here, a slice corresponds to one layer of 32 antennas on the five equipping the experimental system.

Thanks to the use of parallelism, the reconstruction of each layer can be independently generated. Each reconstruction of a layer needs about thirty iterations.

An iteration asks several calculations, each one corresponding to the resolution of 32 3D Maxwell problems, that is one by emitting antenna. For each iteration, these 32 problems differ only by their right hand side. We can see here a second level of trivial parallelism, each resolution being independent.

Each Maxwell problem is solved by a domain decomposition method through the HPDDM library coupled to FreeFem++. We have thus a third level of coarse grains parallelism well fitted to modern HPC architectures.

The different levels of parallelism and of arithmetic complexity involved in the inversion process make it a suitable candidate for generating images. The inversion algorithm helps reconstruct an image in 320 seconds on 2,048 computing cores of Curie. This restitution time, that can be further refined, already fits the physicians’ objective to get an image every fifteen minutes for an efficient monitoring of the patient. It is only the case by using a massively parallel resource. 

Reconstruction time of an image regarding the number of computing cores

Outlook

Frédéric Nataf and his team intend now to confirm their results with experimental data taken from twenty patients at the Département de neurologie of the University of Vienna (Austria) between 2013 and 2014. They also want to improve the performance of their numerical methods for saving computing time: by accessing to very big decompositions (more than 10,000 subdomains), recycling information obtained during the convergence of the optimisation algorithm and exploring iterative methods by blocks in order to reduce the number of iterations.

The medical and industrial challenge of this work is very important. It is the first time that such a realistic study demonstrates the feasibility of microwaves imaging. Although it is less precise than RMI or CT scan, its low price, its reduced size and its lack of harm even in a continuous use could make microwaves imaging of the brain the equivalent of what echography (ultrasound imaging) brings to the exploration of other parts of the human body.

“This outstanding result is a new illustration, in one hand of the necessary complementarity of local, national and European resources and in the other, in a more general point of view, of the impact of numerical simulation and high performance computing on highly societal challenges such as health”, Stéphane Requena, Chief Innovation Officer of Genci, concluded. 

Related Open Source Software
HPDDM: P. Jolivet, F. Hecht, F. Nataf, C. Prud'homme. Scalable Domain Decomposition Preconditioners For Heterogeneous Elliptic Problems. Best Paper Finalist at SC13.  https://github.com/hpddm/hpddm
FreeFem++:  Hecht, F. New development in FreeFem++. J. Numer. Math. 20 (2012).

“Imaging CVAs with high performance computing”, Frédéric NATAF (CNRS), Victorita DOLEAN (Université de Nice Sophia Antipolis et University of Strathclyde, Grande-Bretagne), Frédéric HECHT (Université Pierre et Marie Curie), Pierre JOLIVET (CNRS) et Pierre-Henri TOURNIER (Inria)

The five winners of the 1st Bull Fourier 2015 award (from left to right): Victorita Dolean, Frédéric Nataf, Frédéric Hecht, Pierre-Henri Tournier et Pierre Jolivet, on 12 April 2016 in Paris © Atos