Abstract: Numerical studies using ideas from statistical physics, large deviations theory and functions analysis have exhibited striking scaling invariance properties for human long-term R-R interval signals. These signals are extracted from electrocardiograms and represent the time intervals between two consecutive heartbeats. The scaling invariance measured on these empirical data are reminiscent of geometric fractal properties verified theoretically by certain mathematical objects (measures or functions), which are called (self-similar) multifractals. These numerical studies also reveal that the scaling invariance may have different forms, according to the fact that the patients have a good health or suffer from certain cardiac diseases. These observations suggest that a good understanding of multifractal properties of cardiac signals might lead to new pertinent tools for diagnosis and surveillance. However, until now, neither satisfactory physiological origin has been associated with these properties nor mathematical objects have been proposed as good models for these signals. It is fundamental for possible medical applications in the future to go beyond the previously mentioned works and achieve a deepened study of the scaling invariance structure of cardiacsignals. This requires new robust algorithms for the multifractal signals processing; specifically, it seems relevant to complete the usual statistical approach with a geometric study of the scaling invariance. In addition, it is necessary to apply these tools to a number of data arising from distinct pathologies, in order to start a classification of the different features of the observed scaling invariance, and to relate them to physiological concepts. This should contribute to develop an accurate new flexible multifractal mathematical model whose parameters could be adjusted according to the observed pathology. It is also important to strengthen the information by performing the multifractal analysis of another fundamental signal in cardiology, namely the blood pressure, as well as the simultaneous multifractal analysis/modeling of the couple (R-R,Blood Pressure). This project aims at achieving such a program. It also proposes to contribute to explain the origin of the scaling invariance properties by developing a reduced order dynamical system, which shall describe the heart's electromechanical activity and simultaneously shall generate multifractal outputs in accordance with the R-R signals models. A 1-D model of cardiac fiber would be already very satisfactory. This aspect of the project is closely related to the delicate issue of understanding the link between multifractal phenomena and PDEs, another topic that will be investigated. The project team consists in six members representing two partners: two specialists of multifractal analysis, one specialist of cardio-vascular system modeling and PDEs control, one specialist of statistical signal processing and two physiologists (among which one cardiologist) specialists of cardio-vascular signals processing. The project will benefit of a wide data's bank of long term (24h) R-R interval signals already recorded in various clinical settings including diabetes, acromegaly and sleep apnea, and a prospective data bank will be established in the field of medical intensive care unit, namely in patients presenting cardiovascular pathologies like heart failure, arterial hypertension and chock states. The data bank will include both R-R interval signals and arterial blood pressure signals.