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International audience; Today the coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2), has become a global health problem. After more than a year with the pandemic, although our knowledge has progressed on COVID-19, there are still many unknowns in virological, pathophysiological and immunological aspects. It is obvious that the most efficient solution to end this pandemic are safe and efficient vaccines. This manuscript summarizes the pathophysiological and thrombotic features of COVID-19 and the safety and efficacy of currently approved COVID-19 vaccines with an aim to clarify the recent concerns of thromboembolic events after COVID-19 vaccination. The influx of newer information is rapid, requiring periodic updates and objective assessment of the data on the pathogenesis of COVID-19 variants and the safety and efficacy of currently available vaccines.

International audience; Insights into the mechanisms of development of the mammalian four-chambered heart are based on biological observations at organ, tissue, cell, and molecular levels, but the full integration of these experimental data awaits a systems biology approach. Such an approach can be employed to formulate and test conceptual models in a computational simulation. To illustrate how this can be applied to heart development, we used the process of trabeculation, which is the formation of muscular strands during chamber development. We selected this process because it is localized, involves a restricted number of cell types, and a range of experimental data is available. Trabeculation of the ventricles is based on the interplay between endocardial and myocardial cells and involves molecular pathways underlying cell-cell interactions and tissue-specific cell behavior. A cellular Potts model was used for the simulation of these multi-scale processes. With fairly simple inputs, of which the relative contributions are unknown, an iterative exploration achieved an outcome that resembles the trabeculation process and allows further investigation of contributing factors. The systems biology pipeline from biological observations and conceptual modeling to a mathematical model and computational algorithms is described and discussed. The multi-level biological observations provide the components and their connections of the conceptual model. However, the true strength of systems biology must be found in the biological test of the predictions that result from an experimental change in the computational model. These validated predictions will ultimately elucidate the functional role of a component or interaction in the process of heart development.

To test the hypothesis that cycling exercise modulates heart rate variability (HRV), we applied a short-time Fourier transform on the electrocardiogram of subjects performing a maximal graded cycling test. A pedaling frequency component (PFC) in HRV was continuously observed over the time course of the exercise test and extracted from R-R interval series obtained from 15 healthy subjects with a heterogeneous physical fitness, exercising at three different pedaling frequency ( n = 5): 70, 80, and 90 rpm. From 30 to 50% of the maximal power output (Pmax), in the 90 rpm group, spectral aliasing caused PFC to overlap with the respiratory sinus arrhythmia (RSA) band, significantly overestimating the PFC amplitude ( APFC). In the meantime, APFC did not increase significantly from its minimal values in the 70 rpm (∼1.26 ms) and 80 rpm (∼1.20 ms) groups. Then, from 60 to 100% maximal power output (Pmax), workload increase caused a significant ∼2.8-, ∼3.3-, and ∼3.4-fold increase in APFC in the 70, 80, and 90 rpm groups, respectively, with no significant difference between groups. At peak exercise, APFC accounted for ∼43, ∼39, and ∼49% of the total HRV in the 70, 80, and 90 rpm groups, respectively. Our findings indicate that cycling continuously modulates the cardiac chronotropic response to exercise, inducing a new component in HRV, and that workload increase during intense exercise further accentuates this cardiolocomotor coupling. Moreover, because PFC and RSA overlapped at low workloads, methodological care should be taken in future studies aiming to quantify RSA as an index of parasympathetic activity.

Fibrous cap thickness is often considered as diagnostic of the degree of plaque instability. Necrotic core area (Corearea) and the arterial remodeling index (Remodindex), on the other hand, are difficult to use as clinical morphological indexes: literature data show a wide dispersion of Corearea thresholds above which plaque becomes unstable. Although histopathology shows a strong correlation between Corearea and Remodindex, it remains unclear how these interact and affect peak cap stress (Capstress), a known predictor of rupture. The aim of this study was to investigate the change in plaque vulnerability as a function of necrotic core size and plaque morphology. Capstress value was calculated on 5,500 idealized atherosclerotic vessel models that had the original feature of mimicking the positive arterial remodeling process described by Glagov. Twenty-four nonruptured plaques acquired by intravascular ultrasound on patients were used to test the performance of the associated idealized morphological models. Taking advantage of the extensive simulations, we investigated the effects of anatomical plaque features on Capstress. It was found that: 1) at the early stages of positive remodeling, lesions were more prone to rupture, which could explain the progression and growth of clinically silent plaques and 2) in addition to cap thickness, necrotic core thickness, rather than area, was critical in determining plaque stability. This study demonstrates that plaque instability is to be viewed not as a consequence of fibrous cap thickness alone but rather as a combination of cap thickness, necrotic core thickness, and the arterial remodeling index.

In magnetic resonance imaging (MRI), cerebral blood volume (CBV) quantification is dependent on the MRI sequence and on the properties of the contrast agents (CAs). By using the rapid steady-state T1 method, we show the potential of gadolinium per (3,6-anhydro) α-cyclodextrin (Gd-ACX), a new MRI paramagnetic CA (inclusion complex of Gd3+ with per (3,6-anhydro)-α-cyclodextrin), for the CBV quantification in the presence of blood—brain barrier lesions. After biocompatibility and relaxivity experiments, in vivo experiments on rats were performed on a C6 tumor model with 0.05 mmol Gd-ACX/kg (1-weighted images, a signal enhancement of 170% appeared in vessels after injection, but not in the tumor (during the 1 h of observation), in contrast to the 90% signal enhancement obtained with Gd-DOTA (a clinical MRI CA) injected at a T1 isoefficient dose. This result shows the absence of Gd-ACX extravasation into the tumor tissue and its confinement to the vascular space. Fractional CBV values were found similar to Gd-ACX and Gd-DOTA in healthy brain tissue and in the contralateral hemisphere of tumor-bearing rats, whereas only Gd-ACX was appropriate for CBV quantification in tumor regions.

Heterogeneity of ADP diffusion and regulation of respiration were studied in permeabilized cardiomyocytes and cardiac fibers in situ and in silico. Regular arrangement of mitochondria in cells was altered by short-time treatment with trypsin and visualized by confocal microscopy. Manipulation of matrix volumes by changing K+ and sucrose concentrations did not affect the affinity for ADP either in isolated heart mitochondria or in skinned fibers. Pyruvate kinase (PK)-phosphoenolpyruvate (PEP) were used to trap ADP generated in Ca,MgATPase reactions. Inhibition of respiration by PK-PEP increased 2–3 times after disorganization of regular mitochondrial arrangement in cells. ADP produced locally in the mitochondrial creatine kinase reaction was not accessible to PK-PEP in intact permeabilized fibers, but some part of it was released from mitochondria after short proteolysis due to increased permeability of outer mitochondrial membrane. In in silico studies we show by mathematical modeling that these results can be explained by heterogeneity of ADP diffusion due to its restrictions at the outer mitochondrial membrane and in close areas, which is changed after proteolysis. Localized restrictions and heterogeneity of ADP diffusion demonstrate the importance of mitochondrial functional complexes with sarcoplasmic reticulum and myofibrillar structures and creatine kinase in regulation of oxidative phosphorylation.

In this second of two articles on signal processing, we explore the coupling between modeling and signal processing and the critical importance of well-posed clinical questions or hypotheses, as well as a deep knowledge of the underlying mechanisms of such coupling. Our approach consists of building models either as open-loop simulators allowing us to analyze the influence of one or several internal variables on the observations, or as dynamic systems that can enhance our understanding of these underlying mechanisms to be identified in order to lead to an explanative interpretation. These explorations are illustrated by epileptic network and cardiac models, both derived at the macroscopic level.

International audience; The structure of mouse atherosclerotic lesions may differ from that of humans, and mouse atherosclerotic plaques do not rupture except in some specific locations such as the brachiocephalic artery. Recently, our group was the first to observe that the amplitudes of in vivo stresses in ApoE-/- mouse aortic atherosclerotic lesions were much lower and differed from those found in a previous work performed on human lesions. In this previous preliminary work, we hypothesized that the plaque mechanical properties (MP) may in turn be responsible for such species differences. However, the limited number of human samples used in our previous comparative study was relevant but not sufficient to broadly validate such hypothesis. Therefore, in this study, we propose an original finite element strategy that reconstructs the in vivo stress/strain (IVS/S) distributions in ApoE-/- artherosclerotic vessels based on cross substitution of ApoE-/- mouse and human plaque components stiffnesses and including residual stress/strain (RS/S). Our results: (1) showed that including RS/S decreases by a factor 2 the amplitude of maximal IVS/S, and more importantly, (2) demonstrated that the MP of the ApoE-/- plaque constituents are mainly responsible for the low level-compared with human-of intraplaque stress in ApoE-/- mouse aortic atherosclerotic lesions (8.36 ± 2.63 kPa vs. 182.25 ± 55.88 kPa for human). Our study highlights that such differences in the distribution and amplitude of vessel wall stress might be one key feature for explaining for the difference in lesion stability between human coronary and mouse aortic lesions.

International audience; Several MR methods have been proposed over the last decade to obtain quantitative estimates of the tissue blood oxygen saturation (StO2) using a quantification of the blood oxygen level dependent effect. These approaches are all based on mathematical models describing the time evolution of the MR signal in biological tissues in the presence of magnetic field inhomogeneities. Although the experimental results are very encouraging, possible biases induced by the model assumptions have not been extensively studied. In this study, a numerical approach was used to examine the influence on T(2)*, blood volume fraction, and StO2 estimates of possible confounding factors such as water diffusion, intravascular signal, and presence of arterial blood in the voxel. To evaluate the impact of the vessel geometry, straight cylinders and realistic data from two-photon microscopy for microvascular geometry were compared. Our results indicate that the models are sufficiently realistic, based on a good correlation between ground truth and MR estimates of StO2.

International audience; A computational model is potentially a powerful tool to apprehend complex phenomena like solid tumour growth and to predict the outcome of therapies. To that end, the confrontation of the model with experiments is essential to validate this tool. In this study, we develop a computational model specifically dedicated to the interpretation of tumour growth as observed in a mouse model with a dorsal skinfold chamber. Observation of the skin vasculature at the dorsal window scale shows a sparse network of a few main vessels of several hundreds micrometers in diameter. However observation at a smaller scale reveals the presence of a dense and regular interconnected network of capillaries about ten times smaller. We conveniently designate this structure as the submicrovascular network (SMVN).(1) The question that we wish to answer concerns the necessity of explicitly taking into account the SMVN in the computational model to describe the tumour evolution observed in the dorsal chamber. For that, simulations of tumour growth realised with and without the SMVN are compared and lead to two distinct scenarios. Parameters that are known to strongly influence the tumour evolution are then tested in the two cases to determine to which extent those parameters can be used to compensate the observed differences between these scenarios. Explicit modelling of the smallest vessels appears mandatory although not necessarily under the form of a regular grid. A compromise between the two investigated cases can thus be reached.

Coronary bifurcations represent specific regions of the arterial tree that are susceptible to atherosclerotic lesions. While the effects of vessel compliance, curvature, pulsatile blood flow, and cardiac motion on coronary endothelial shear stress have been widely explored, the effects of myocardial contraction on arterial wall stress/strain (WS/S) and vessel stiffness distributions remain unclear. Local increase of vessel stiffness resulting from wall-strain stiffening phenomenon (a local process due to the nonlinear mechanical properties of the arterial wall) may be critical in the development of atherosclerotic lesions. Therefore, the aim of this study was to quantify WS/S and stiffness in coronary bifurcations and to investigate correlations with plaque sites. Anatomic coronary geometry and cardiac motion were generated based on both computed tomography and MRI examinations of eight patients with minimal coronary disease. Computational structural analyses using the finite element method were subsequently performed, and spatial luminal arterial wall stretch (LWStretch) and stiffness (LWStiff) distributions in the left main coronary bifurcations were calculated. Our results show that all plaque sites were concomitantly subject to high LWStretch and high LWStiff, with mean amplitudes of 34.7 ± 1.6% and 442.4 ± 113.0 kPa, respectively. The mean LWStiff amplitude was found slightly greater at the plaque sites on the left main coronary artery (mean value: 482.2 ± 88.1 kPa) compared with those computed on the left anterior descending and left circumflex coronary arteries (416.3 ± 61.5 and 428.7 ± 181.8 kPa, respectively). These findings suggest that local wall stiffness plays a role in the initiation of atherosclerotic lesions.

International audience; This paper presents two approaches in parallel modeling of vascular system development in internal organs. In the first approach, new parts of tissue are distributed among processors and each processor is responsible for perfusing its assigned parts of tissue to all vascular trees. Communication between processors is accomplished by passing messages, and therefore, this algorithm is perfectly suited for distributed memory architectures. The second approach is designed for shared memory machines. It parallelizes the perfusion process during which individual processing units perform calculations concerning different vascular trees. The experimental results, performed on a computing cluster and multicore machines, show that both algorithms provide a significant speedup.

International audience; In this paper, an approach for heart rate variability analysis during exercise stress testing is proposed based on the integral pulse frequency modulation (IPFM) model, where a time-varying threshold is included to account for the nonstationary mean heart rate. The proposed technique allows the estimation of the autonomic nervous system (ANS) modulating signal using the methods derived for the IPFM model with constant threshold plus a correction, which is shown to be needed to take into account the time-varying mean heart rate. On simulations, this technique allows the estimation of the ANS modulation on the heart from the beat occurrence time series with lower errors than the IPFM model with constant threshold (1.1% ± 1.3% versus 15.0% ± 14.9%). On an exercise stress testing database, the ANS modulation estimated by the proposed technique is closer to physiology than that obtained from the IPFM model with constant threshold, which tends to overestimate the ANS modulation during the recovery and underestimate it during the initial rest.

Background Arterial stiffness is considered as an independent predictor of cardiovascular mortality, and is increasingly used in clinical practice. This study aimed at evaluating the consistency of the automated estimation of regional and local aortic stiffness indices from cardiovascular magnetic resonance (CMR) data. Results Forty-six healthy subjects underwent carotid-femoral pulse wave velocity measurements (CF_PWV) by applanation tonometry and CMR with steady-state free-precession and phase contrast acquisitions at the level of the aortic arch. These data were used for the automated evaluation of the aortic arch pulse wave velocity (Arch_PWV), and the ascending aorta distensibility (AA_Distc, AA_Distb), which were estimated from ascending aorta strain (AA_Strain) combined with either carotid or brachial pulse pressure. The local ascending aorta pulse wave velocity AA_PWVc and AA_PWVb were estimated respectively from these carotid and brachial derived distensibility indices according to the Bramwell-Hill theoretical model, and were compared with the Arch_PWV. In addition, a reproducibility analysis of AA_PWV measurement and its comparison with the standard CF_PWV was performed. Characterization according to the Bramwell-Hill equation resulted in good correlations between Arch_PWV and both local distensibility indices AA_Distc (r = 0.71, p < 0.001) and AA_Distb (r = 0.60, p < 0.001); and between Arch_PWV and both theoretical local indices AA_PWVc (r = 0.78, p < 0.001) and AA_PWVb (r = 0.78, p < 0.001). Furthermore, the Arch_PWV was well related to CF_PWV (r = 0.69, p < 0.001) and its estimation was highly reproducible (inter-operator variability: 7.1%). Conclusions The present work confirmed the consistency and robustness of the regional index Arch_PWV and the local indices AA_Distc and AA_Distb according to the theoretical model, as well as to the well established measurement of CF_PWV, demonstrating the relevance of the regional and local CMR indices.

The renin-angiotensin system (RAS) is critical in sodium and blood pressure (BP) regulation, and in cardiovascular-renal (CVR) diseases and therapeutics. As a contribution to SAPHIR project, we present a realistic computer model of renin production and circulating RAS, integrated into Guyton’s circulatory model (GCM). Juxtaglomerular apparatus, JGA, and Plasma modules were implemented in C ++/M2SL (Multi-formalism Multi-resolution Simulation Library) for fusion with GCM. Matlab© optimization toolboxes were used for parameter identification. In JGA, renin production and granular cells recruitment (GCR) are controlled by perfusion pressure (PP), macula densa (MD), angiotensin II (Ang II), and renal sympathetic activity (RSNA). In Plasma, renin and ACE (angiotensin-converting enzyme) activities are integrated to yield Ang I and II. Model vs. data deviation is given as normalized root mean squared error (nRMSE; n points). Identification: JGA and Plasma parameters were identified against selected experimental data. After fusion with GCM: (1) GCR parameters were identified against Laragh’s PRA-natriuresis nomogram; (2) Renin production parameters were identified against two sets of data ([renin] transients vs. ACE or renin inhibition). Finally, GCR parameters were re-identified vs. Laragh’s nomogram (nRMSE 8%, n = 9). Validation: (1) model BP, PRA and [Ang II] are within reported ranges, and respond physiologically to sodium intake; (2) short-term Ang II infusion induces reported rise in BP and PRA. The modeled circulating RAS, in interaction with an integrated CVR, exhibits a realistic response to BP control maneuvers. This construction will allow for modelling hypertensive and CVR patients, including salt-sensitivity, polymorphisms, and pharmacotherapeutics.

This paper describes an acquisition and reconstruction strategy for cardiac cine MRI that does not require the use of electrocardiogram or breath holding. The method has similarities with self-gated techniques as information about cardiac and respiratory motion is derived from the imaging sequence itself; here, by acquiring the center k-space line at the beginning of each segment of a balanced steady-state free precession sequence. However, the reconstruction step is fundamentally different: a generalized reconstruction by inversion of coupled systems is used instead of conventional gating. By correcting for nonrigid cardiac and respiratory motion, generalized reconstruction by inversion of coupled systems (GRICS) uses all acquired data, whereas gating rejects data acquired in certain motion states. The method relies on the processing and analysis of the k-space central line data: local information from a 32-channel cardiac coil is used in order to automatically extract eigenmodes of both cardiac and respiratory motion. In the GRICS framework, these eigenmodes are used as driving signals of a motion model. The motion model is defined piecewise, so that each cardiac phase is reconstructed independently. Results from six healthy volunteers, with various slice orientations, show improved image quality compared to combined respiratory and cardiac gating. Magn Reson Med 63:1247-1257, 2010. (C) 2010 Wiley-Liss, Inc.

International audience; Isolated cardiac myocytes exhibit spontaneous patterns of rhythmic contraction, driven by intracellular calcium waves. In order to study the coupling between spatio-temporal calcium dynamics and cell contraction in large deformation regimes, a new strain-energy function, describing the influence of sarcomere length on the calcium-dependent generation of active intracellular stresses, is proposed. This strain-energy function includes anisotropic passive and active contributions that were first validated separately from experimental stress-strain curves and stress-sarcomere length curves, respectively. An extended validation of this formulation was then conducted by considering this strain-energy function as the core of an integrated mechano-chemical three-dimensional model of cardiac myocyte contraction, where autocatalytic intracellular calcium dynamics were described by a representative two-variable model able to generate realistic intracellular calcium waves similar to those observed experimentally. Finite-element simulations of the three-dimensional cell model, conducted for different intracellular locations of triggering calcium sparks, explained very satisfactorily, both qualitatively and quantitatively, the contraction patterns of cardiac myocytes observed by time-lapse videomicroscopy. This integrative approach of the mechano-chemical couplings driving cardiac myocyte contraction provides a comprehensive framework for analysing active stress regulation and associated mechano-transduction processes that contribute to the efficiency of cardiac cell contractility in both physiological and pathological contexts.

International audience; This paper deals with the 3-D reconstruction of the coronary tree from a rotational X-ray projection sequence. It describes the following three stages: the reconstruction of the 3-D coronary tree at different phases of the cardiac cycle, the motion estimation, and the motion-compensated tomographic reconstruction of the 3-D coronary tree at one given phase using all the available projections. Our method is tested on a series of simulated images computed from the projection of a segmented dynamic volume sequence acquired in multislice computed tomography imaging. Performances are comparable to those obtained by reconstruction of a statical coronary tree using an algebraic reconstruction technique algorithm.

International audience; It is now recognized that prediction of the vulnerable coronary plaque rupture requires not only an accurate quantification of fibrous cap thickness and necrotic core morphology but also a precise knowledge of the mechanical properties of plaque components. Indeed, such knowledge would allow a precise evaluation of the peak cap-stress amplitude, which is known to be a good biomechanical predictor of plaque rupture. Several studies have been performed to reconstruct a Young's modulus map from strain elastograms. It seems that the main issue for improving such methods does not rely on the optimization algorithm itself, but rather on preconditioning requiring the best estimation of the plaque components' contours. The present theoretical study was therefore designed to develop: 1) a preconditioning model to extract the plaque morphology in order to initiate the optimization process, and 2) an approach combining a dynamic segmentation method with an optimization procedure to highlight the modulogram of the atherosclerotic plaque. This methodology, based on the continuum mechanics theory prescribing the strain field, was successfully applied to seven intravascular ultrasound coronary lesion morphologies. The reconstructed cap thickness, necrotic core area, calcium area, and the Young's moduli of the calcium, necrotic core, and fibrosis were obtained with mean relative errors of 12%, 4% and 1%, 43%, 32%, and 2%, respectively.

International audience; PURPOSE: To analyze the relationship between late contrast enhancement (LCE) and the interstitial distribution volume (V(In)) of gadolinium (Gd) tracers in the myocardial infarction (MI) areas supplied by chronically occluded arteries from patients. In animal experimental models, LCE has already been shown to correspond to an enhanced V(In) of Gd tracers and thus, to a decrease in the amount of intact cells. MATERIALS AND METHODS: A multicompartmental analysis was applied to serial MRI images encompassing both infarct and remote areas and recorded with a conventional two-dimensional (2D) segmented inversion-recovery gradient-echo (IR-GRE) sequence during a 15-minute period following Gd-diethylenetriamine pentaacetic acid (Gd-DTPA) injection in 12 patients with Q-wave MI supplied by chronically occluded coronary arteries. RESULTS: V(In) from infarct tissue was: 1) higher than V(In) from remote areas (in % of myocardial volume: 74 +/- 16% vs. 20 +/- 7%, P < 0.001); and 2) correlated with the quantification of LCE between infarct and noninfarct areas at the 15th minute (R(2) = 0.63, P = 0.002). However, the difference in V(In) between infarct and remote myocardium was a much better correlate of this quantified LCE (R(2) = 0.85, P < 0.001). CONCLUSION: Detection of LCE in the MI territories supplied by chronically occluded arteries relates to the difference in the V(In) of tracers between the infarct and the noninfarct areas.

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International audience; The cold pressor test (CPT) triggers in healthy subjects a vascular sympathetic activation and an increase in blood pressure. The heart rate (HR) response to this test is less well defined, with a high inter-individual variability. We used traditional spectral analysis together with the non-linear detrended fluctuation analysis to study the autonomic control of HR during a 3-min CPT. 39 healthy young subjects (23.7+/-3.2 years, height 180.4+/-4.7 cm and weight 73.3+/-6.4 kg) were divided into two groups according to their HR responses to CPT. Twenty subjects have a sustained increase in HR throughout the test with reciprocal autonomic interaction, i.e. increase in sympathetic activity and decrease vagal outflow. In the 19 remainders, HR decreased after an initial increase, with indication of involvement of both sympathetic and vagal outflow. Baseline evaluation of the subjects revealed no difference between the two groups. Nevertheless, a higher sympathetic activity at the skin level during CPT was present in the group with decreased HR. Further studies are needed to explain why healthy subjects react differently to the CPT and if this has potential clinical implications.

We present the current state of the development of the SAPHIR project (a Systems Approach for PHysiological Integration of Renal, cardiac and respiratory function). The aim is to provide an open-source multi-resolution modelling environment that will permit, at a practical level, a plug-and-play construction of integrated systems models using lumped-parameter components at the organ/tissue level while also allowing focus on cellular- or molecular-level detailed sub-models embedded in the larger core model. Thus, an in silico exploration of gene-to-organ-to-organism scenarios will be possible, while keeping computation time manageable. As a first prototype implementation in this environment, we describe a core model of human physiology targeting the short- and long-term regulation of blood pressure, body fluids and homeostasis of the major solutes. In tandem with the development of the core models, the project involves database implementation and ontology development.

International audience; This paper presents a new method to analyse cardiac electrophysiological dynamics. It aims to classify or to cluster (i.e. to find natural groups) patients according to the dynamics of features extracted from their ECG. In this work, the dynamics of the features are modelled with Continuous Density Hidden Semi-Markovian Models (CDHSMM) which are interesting for the characterization of continuous multivariate time series without a priori information. These models can be easily used for classification and clustering. In this last case, a specific method, based on a fuzzy Expectation Maximisation (EM) algorithm, is proposed. Both tasks are applied to the analysis of ischemic episodes with encouraging results and a classification accuracy of 71%.

International audience; During exercise, analysis of the spectral components of the heart rate variability (i.e. R-R interval series variability; HRV) points out a new high frequency component related to the pedalling frequency. This component is independent of the classical low and high frequency bands related to the autonomic nervous system modulation of the heart period. It is not related to ECG distortion or artifacts, and could be linked to the mechanical influence of the muscle pump on venous return. To assess this new component, we develop and propose a method based on a time-varying filter, designed in the time-frequency plane, as well as a new model to link the potential input of the modulation (the muscle pump) to the pedalling frequency component of HRV.

International audience; The transverse-axial tubular system (TATS) of cardiac ventricular myocytes is a complex network of tubules that arises as invaginations of the surface membrane; it appears to form a specialised region of cell membrane that is particularly important for excitation-contraction coupling. However, much remains unknown about the structure and role of the TATS. In this brief review we use experimental data and computer modelling to address the following key questions: (i) What fraction of the cell membrane is within the TATS? (ii) Is the composition of the TATS membrane the same as the surface membrane? (iii) How good is electrical coupling between the surface and TATS membranes? (iv) What fraction of each current is within the TATS? (v) How important is the complex structure of the TATS network? (vi) What is the effect of current inhomogeneity on lumenal ion concentrations? (vii) Does the TATS contribute to the functional changes observed in heart failure? Although there are many areas in which experimental evidence is lacking, computer models provide a method to assess and predict the possible function of the TATS; such models suggest that although the surface and TATS membranes are electrically well coupled, concentration of ion flux pathways within the TATS, coupled to restricted diffusion, may result in the ionic composition in the TATS lumen being different from that in the bulk extracellular space, and varying with activity and in pathological conditions.

International audience; Vulnerable plaque morphology has been described by gross pathology and intravascular ultrasound, but morphological criteria cannot fully explain vulnerability, which involves four distinct factors: 1) inflammatory and biological processes; 2) geometry; 3) composition; and 4) hemodynamic stress. These last three aspects underlie the biomechanical study of vulnerable plaque. By virtue of the nature of their evolution, atherosclerotic plaques tend to be excentric, and this is a crucial morphological feature, causing circumferential stress to peak in very specific juxta-luminal locations, where it can exceed the rupture threshold of collagen, the basic constituent of arterial architecture. The lipido-necrotic core covered by a fibrous cap, formed in young plaques, is another morphological feature, which, can also increase and concentrate circumference stress in the juxta-luminal fibrous cap. The larger the lipid core, the thinner the fibrous cap and the greater is the stress. There are also inflammatory processes in such areas, which tend to reduce cap thickness. Ruptures occur when this thickness falls below 65 microns. Heart rate, blood pressure and pulse pressure are all biomechanical factors affecting vulnerable arterial walls, increasing circumferential stress and material fatigue. Vulnerable plaques are almost always associated with positive arterial remodeling. Numerical simulation has shown such so-called compensatory remodeling to be exclusively due to the healthy arc stretching in vulnerable plaques. Positive remodeling is optimal when the healthy arc is around 170 degrees, which keeps the lumen area relatively stable as long as the plaque does not exceed 40% to 50%. This mechanism does not apply to concentric plaques. In conclusion, the mechanism of vulnerable plaque rupture is highly complex and multifactorial. This complexity more or less precludes prediction in individual cases: we are in the realms of chaos theory and acute sensitivity to initial conditions. The greatest caution is therefore required in any attempt to predict rupture from diagnostic imagery, which provides only morphological data on plaque's nature.

International audience; This paper reports on a method for left ventricle three-dimensional (3-D) reconstruction from two orthogonal ventriculograms. The proposed algorithm is voxel-based and takes into account the conical projection geometry associated with the biplane image acquisition equipment. The reconstruction process starts with an initial ellipsoidal approximation derived from the input ventriculograms. This model is subsequently deformed in such a way as to match the input projections. To this end, the object is modeled as a 3-D Markov-Gibbs random field, and an energy function is defined so that it includes one term that models the projections compatibility and another one that includes the space-time regularity constraints. The performance of this reconstruction method is evaluated by considering the reconstruction of mathematically synthesized phantoms and two 3-D binary databases from two orthogonal synthesized projections. The method is also tested using real biplane ventriculograms. In this case, the performance of the reconstruction is expressed in terms of the projection error, which attains values between 9.50% and 11.78 % for two biplane sequences including a total of 55 images.

International audience; Echography is a useful tool to diagnose a thrombosis; however, since it is difficult to learn to perform this procedure, the objective of this work is to create a simulation to allow students to practice in a virtual environment. Firstly, a physical model of the thigh was constructed based on experimental data obtained using a force sensor mounted on a robotic arm. We present a spring damper model consisting of both linear and non-linear elements. The parameters of each of these elements are then fitted to the experimental data using an optimization technique. By employing an implicit integration to solve the dynamics of the system we obtain a stable physical simulation at over 100 Hz. Secondly, a haptic interface was added to interact with the simulation. Using a PHANToM force-feedback device may touch and deform the thigh in real-time. In order to allow a realistic sensation of the contact we employ a local modeling technique allowing to approximate the forces at much higher frequency using a multi-threaded architecture. Finally, we present the basis for a fast echographic image generation depending on the position and orientation of the virtual probe as well as the force applied to it.

International audience; The purpose of this study, was to asses whether LF/(LF+HF) obtained from ventricular repolarization variability (VRV) reflects the state of sympathovagal balance. The VRV time series and heart rate variability (HRV) time series from seventy two electrocardiogram (ECG) records in four different autonomic nervous system (ANS) profiles (athletes, cardiac transplant patient, heart failure patients and normal subjects) were extracted. A dynamic linear parametric model was applied to separate the VRV in two parts, VRV correlated with HRV (VRV(r)) and VRV uncorrelated with HRV (VRV(u)). Spectral indices were obtained from HRV, VRV, VRV(u) and VRV(u) time series. Changes of these indicators from rest to tilt position were analyzed. Results showed that: i) only LF/(LF+HF) from HRV time series increases significantly from rest to tilt in all ANS profiles, this information could not be retrieved in the other three series (VRV, VRV (u) and VRV(u)) ii) LF/(LF+HF) index in HRV series are significantly different between normal subjects and heart failure patients, while cardiac transplant patients show a low coherence between HRV and VRV power spectra and iii) HF rhythm in VRV series seem to be related to the mechanical effect of respiration.

Persistence of respiratory sinus arrhythmia (RSA) has been described in humans during intense exercise and attributed to an increase in ventilation. However, the direct influence of ventilation on RSA has never been assessed. The dynamic evolution of RSA and its links to ventilation were investigated during exercise in 14 healthy men using an original modeling approach. An evolutive model was estimated from the detrended and high-pass-filtered heart period series. The instantaneous RSA frequency ( FRSA, in Hz) and amplitude ( ARSA, in ms) were then extracted from all recordings. ARSA was calculated with short-time Fourier transform. First, measurements of FRSA and ARSA were performed from data obtained during a graded and maximal exercise test. Influences of different ventilation regimens [changes in tidal volume (VT) and respiratory frequency ( FR)] on ARSA were then tested during submaximal [70% peak O2 consumption (V̇o2peak)] rectangular exercise bouts. Under graded and maximal exercise conditions, ARSA decreased from the beginning of exercise to 61.9 ± 3.8% V̇o2peak and then increased up to peak exercise. During the paced breathing protocol, normoventilation (69.4 ± 8.8 l/min), hyperventilation (81.8 ± 8.3 l/min), and hypoventilation (56.4 ± 6.2 l/min) led to significantly ( P < 0.01) different ARSA values (3.8 ± 0.5, 4.6 ± 0.8, and 2.9 ± 0.5 ms, respectively). In addition, no statistical difference was found in ARSA when ventilation was kept constant, whatever the FR-VT combinations. Those results indicate that RSA persists for all exercise intensities and increases during the highest intensities. Its persistence and increase are strongly linked to both the frequency and degree of lung inflation, suggesting a mechanical influence of breathing on RSA.

International audience; A convenient way to analyze blood-oxygen-level-dependent functional magnetic resonance imaging data consists of modeling the whole brain as a stationary, linear system characterized by its transfer function: the hemodynamic response function (HRF). HRF estimation, though of the greatest interest, is still under investigation, for the problem is ill-conditioned. In this paper, we recall the most general Bayesian model for HRF estimation and show how it can beneficially be translated in terms of Bayesian graphical models, leading to 1) a clear and efficient representation of all structural and functional relationships entailed by the model, and 2) a straightforward numerical scheme to approximate the joint posterior distribution, allowing for estimation of the HRF, as well as all other model parameters. We finally apply this novel technique on both simulations and real data.

International audience; In vitro angiogenesis assays have shown that tubulogenesis of endothelial cells within biogels, like collagen or fibrin gels, only appears for a critical range of experimental parameter values. These experiments have enabled us to develop and validate a theoretical model in which mechanical interactions of endothelial cells with extracellular matrix influence both active cell migration--haptotaxis--and cellular traction forces. Depending on the number of cells, cell motility and biogel rheological properties, various 2D endothelial patterns can be generated, from non-connected stripe patterns to fully connected networks, which mimic the spatial organization of capillary structures. The model quantitatively and qualitatively reproduces the range of critical values of cell densities and fibrin concentrations for which these cell networks are experimentally observed. We illustrate how cell motility is associated to the self-enhancement of the local traction fields exerted within the biogel in order to produce a pre-patterning of this matrix and subsequent formation of tubular structures, above critical thresholds corresponding to bifurcation points of the mathematical model. The dynamics of this morphogenetic process is discussed in the light of videomicroscopy time lapse sequences of endothelial cells (EAhy926 line) in fibrin gels. Our modeling approach also explains how the progressive appearance and morphology of the cellular networks are modified by gradients of extracellular matrix thickness.

International audience; Changes in vessel wall elasticity may be indicative of vessel pathologies. It is known, for example, that the presence of plaque stiffens the vascular wall, and that the heterogeneity of its composition may lead to plaque rupture and thrombosis. Another domain of application where ultrasound elastography may be of interest is the study of vascular wall elasticity to predict the risk of aneurysmal tissue rupture. In this paper, this technology is introduced as an approach to noninvasively characterize superficial arteries. In such a case, a linear array ultrasound transducer is applied on the skin over the region of interest, and the arterial tissue is dilated by the normal cardiac pulsation. The elastograms, the equivalent elasticity images, are computed from the assessment of the vascular tissue motion. Investigating the forward problem, it is shown that motion parameters might be difficult to interpret; that is because tissue motion occurs radially within the vessel wall while the ultrasound beam propagates axially. As a consequence of that, the elastograms are subjected to hardening and softening artefacts, which are to be counteracted. In this paper, the Von Mises (VM) coefficient is proposed as a new parameter to circumvent such mechanical artefacts and to appropriately characterize the vessel wall. Regarding the motion assessment, the Lagrangian estimator was used; that is because it provides the full two-dimensional strain tensor necessary to compute the VM coefficient. The theoretical model was validated with biomechanical simulations of the vascular wall properties. The results allow believing in the potential of the method to differentiate hard plaques and lipid pools from normal vascular tissue. Potential in vivo implementation of noninvasive vascular elastography to characterize abdominal aneurysms and superficial arteries such as the femoral and the carotid is discussed.

International audience; BACKGROUND: A 'thin' fibrous cap atheroma is the typical morphological characteristic of vulnerable plaque. Yet the very pathological studies that have provided these descriptions have also shown the actual prediction of plaque rupture to be rather less exact. Other relevant characteristics must be involved in the mechanisms of plaque rupture--blood pressure loading (P) and the material properties of the soft atheromatous core--as predictors of the distribution of the peak circumferential stress (PCS) locations. METHODS AND RESULTS: We used a computational structural analysis based on three typical in-vivo intravascular ultrasound images of fibrous cap atheroma in which we decreased the cap thickness (CTh). With different soft atheromatous core Young's moduli (Ecore), 414 simulations were performed under eight different physiological loading blood pressures. The transition from plaque stability to plaque instability was defined by a threshold of 300 kPa and is a feature of vulnerability. It was found that (1) irrespective of plaque geometry and composition, CTh < 60 microm exposed the plaque to PCSs in excess of 300 kPa; (2) the exponential variations in PCS with change in CTh and Ecore values show that very slight structural changes are enough to tilt a vulnerable plaque from stability to instability or vice versa; and (3) the relationship between P and PCS is proportional with P acting as trigger or as protector. CONCLUSION: The present study shows why, in clinical practice, mere morphological detection by imaging techniques of thin-cap fibro-atheroma is not in itself enough for the prediction of future rupture.

International audience; This paper deals with the estimation of the blood oxygen level-dependent response to a stimulus, as measured in functional magnetic resonance imaging (fMRI) data. A precise estimation is essential for a better understanding of cerebral activations. The most recent works have used a nonparametric framework for this estimation, considering each brain region as a system characterized by its impulse response, the so-called hemodynamic response function (HRF). However, the use of these techniques has remained limited since they are not well-adapted to real fMRI data. Here, we develop a threefold extension to previous works. We consider asynchronous event-related paradigms, account for different trial types and integrate several fMRI sessions into the estimation. These generalizations are simultaneously addressed through a badly conditioned observation model. Bayesian formalism is used to model temporal prior information of the underlying physiological process of the brain hemodynamic response. By this way, the HRF estimate results from a tradeoff between information brought by the data and by our prior knowledge. This tradeoff is modeled with hyperparameters that are set to the maximum-likelihood estimate using an expectation conditional maximization algorithm. The proposed unsupervised approach is validated on both synthetic and real fMRI data, the latter originating from a speech perception experiment.

International audience; A convenient way to analyze BOLD fMRI data consists of modeling the whole brain as a stationary, linear system characterized by its transfer function: the Hemodynamic Response Function (HRF). HRF estimation, though of the greatest interest, is still under investigation, for the problem is ill-conditioned. In this paper, we recall the most general Bayesian model for HRF estimation and show how it can beneficially be translated in terms of graphical models, leading to (i) a clear and efficient representation of all structural and functional relationships entailed by the model, and (ii) a straightforward numerical scheme to approximate the joint posterior distribution, allowing for estimation of the HRF, as well as all other model parameters. We finally apply this novel technique on both simulations and real data.

The purpose of this research is to study the growth of the normal human left ventricle (LV) during the fetal period from 14 to 40 weeks of gestation. A new constitutive law for the active myocardium describing the mechanical properties of the active muscle during the whole cardiac cycle has been proposed. The LV model is a thick-walled, incompressible, hyperelastic cylinder, with families of helicoidal fibers running on cylindrical surfaces [1]. Based on the works of Lin and Taber [2] done on the embryonic chick heart, we use for the human fetal heart a growth law in which the growth rate depends on the wall stresses. The parameters of the growth law are adapted to agree with sizes and volumes inferred from two dimensional ultrasound measurements performed on 18 human fetuses.Then calculations are performed to extrapolate the cardiac performance during normal growth of the fetal LV. The results presented support the idea that a growth law in which the growth rate depends linearly on the mean wall stresses averaged through the space and during whole cardiac cycle, is adapted to the normal human fetal LV development.

International audience; The aim of this study was to investigate mitochondrial alterations in an animal model of chronic myocardial ischemia in rats obtained by surgical constriction of the left coronary artery. Resting coronary blood flow was measured using the fluorescent microsphere technique. Contractile function, defined by rate-pressure product, and myocardial oxygen consumption were measured in a Langendorff preparation. The mitochondrial function was evaluated on permeabilized skinned fibers. Three weeks after surgery, ischemic hearts showed a significant decrease in coronary blood flow compared with sham. Hemodynamic measurements showed a significant systolic and diastolic dysfunction. Alterations in mitochondrial function in ischemic hearts were mainly characterized by a significant decrease in the maximal velocity and apparent half-saturation constant for ADP, loss of the stimulatory effect of creatine, and a stimulatory effect of exogenous cytochrome c. These functional alterations were supported by structural alterations characterized by mitochondrial clustering and swelling associated with membrane rupture. We conclude that the alterations in systolic function after chronic ischemia are supported by severe modifications of mitochondrial structure and function.

International audience; The aim of this thesis is to investigate the link between biochemical intracellular processes and mechanical contraction of the cardiac muscle. First, the regulation of intracellular energy fluxes between mitochondria and myofibrils is studied. It is shown, that the experimentally observed metabolic stability of the cardiac muscle is reproducible by a simple feedback regulation mechanism, i.e., ATP consumption in myofibrils and ATP production in mitochondria are balanced by the changes of the high energy phosphate concentrations. Second, an important property of energy transformation from biochemical form to mechanical work in the cardiac muscle, the linear relationship between the oxygen consumption and the stress-strain area, is replicated by a cross-bridge model. Third, by using the developed cross-bridge model, the correlation between ejection fraction of the left ventricle and heterogeneity of sarcomere strain, developed stress and ATP consumption in the left ventricular wall is established. Fourth, an experimentally observed linear relationship between oxygen consumption and the pressure-volume area can be predicted theoretically from a linear relationship between the oxygen consumption and the stress-strain area. Summing up, it is shown how the macrovariables of a cardiac muscle are interwoven with intracellular physiological processes into a whole.

International audience; An improved and very fast algorithm dealing with the extraction of vessels in three-dimensional imaging is described. The approach is based on geometrical moments and a local cylindrical approximation. A robust estimation of vessel and background intensity levels, position, orientation, and diameter of the vessels with adaptive control of key parameters, is provided during vessel tracking. Experimental results are presented for lower limb arteries in multidetector computed tomography scanner.

The purpose of this study is to investigate theoretically which intracellular factors may be important for regulation of mitochondrial respiration in working heart cells in vivo. We have developed a model that describes quantitatively the published experimental data on dependence of the rate of oxygen consumption and metabolic state of working isolated perfused rat heart on workload over its physiological range (Williamson JR, Ford G, Illingworth J, Safer B. Circ Res 38, Suppl I, I39–I51, 1976). Analysis of this model shows that for phosphocreatine, creatine, and ATP the equilibrium assumption is an acceptable approximation with respect to their diffusion in the intracellular bulk water phase. However, the ADP concentration changes in the contraction cycle in a nonequilibrium workload-dependent manner, showing the existence of the intracellular concentration gradients. The model shows that workload-dependent alteration of ADP concentration in the compartmentalized creatine kinase system may be taken, together with the changes in Piconcentration, to be among the major components of the metabolic feedback signal for regulation of respiration in muscle cells.

Different approaches have been proposed in order to achieve knowledge integration for coronary care monitoring applications, usually in the form of expert systems. The clinical impact of these expert systems, which are based only on "shallow" knowledge, has not been remarkable due to the difficulties associated with the construction and maintenance of a complete knowledge base. Model-based systems represent an alternative to these problems because they allow efficient integration of the "deep" knowledge on the underlying physiological phenomena being monitored. In this work, a brief review of existing model-based systems for cardiac rhythm interpretation is presented, followed by the description of a new system for Cardiac Arrhythmia Recognition by Model-Based ECG Matching (CARMEM). Fundamental characteristics of CARMEM are presented; in particular, its ability to provide online parameter adaptation to simulate complex rhythms and to match observed ECG signals. The proposed model can be useful for the explanation of the origin of cardiac arrhythmias and contribute towards their robust characterization in the context of coronary care units.

International audience; A time-frequency scaling transformation based on the matching pursuit (MP) method is developed for the phonocardiogram (PCG). The MP method decomposes a signal into a series of time-frequency atoms by using an iterative process. The modification of the time scale of the PCG can be performed without perceptible change in its spectral characteristics. It is also possible to modify the frequency scale without changing the temporal properties. The technique has been tested on 11 PCG's containing heart sounds and different murmurs. A scaling/inverse-scaling procedure was used for quantitative evaluation of the scaling performance. Both the spectrogram and a MP-based Wigner distribution were used for visual comparison in the time-frequency domain. The results showed that the technique is suitable and effective for the time-frequency scale transformation of both the transient property of the heart sounds and the more complex random property of the murmurs. It is also shown that the effectiveness of the method is strongly related to the optimization of the parameters used for the decomposition of the signals.

International audience; The mathematical model of the compartmentalised energy transfer system in cardiac myocytes, which includes mitochondrial synthesis of ATP by ATP-synthase, phosphocreatine production in the coupled mitochondrial creatine kinase reaction, the myofibrillar and cytoplasmic creatine kinase reactions, ATP utilisation by actomyosin ATPase during contraction cycle, and diffusional exchange of metabolites between different compartments, was used to calculate creatine kinase reaction rates (fluxes) in different cellular compartments at a workload corresponding to the rate of oxygen consumption of 46 micrograms-atom O2 *min-1 * (g wet mass)-1. The results of calculations showed that at this high workload all creatine kinase isoenzymes function most of their time in the cardiac cycle in the steady state far from equilibrium. This mathematical modelling shows that the validity of assumption of creatine kinase equilibrium is limited only to the diastolic phase of the contraction cycle in the working cardiac cells and only to the cytoplasmic compartment. In the systolic phase, due to rapid release of ADP at increased workloads, all creatine kinase isoenzymes are rapidly shifted out of the equilibrium. Cytoplasmic ADP concentration may increase up to 9 times in the systolic phase of the cardiac cycle, correspondingly changing all ADP-dependent parameters. Mitochondrial creatine kinase functions permanently in "metastable" steady state (Jurgen Daut, Biochim. Biophys. Acta 895, 41-62, 1987). It may be proposed that a more precise, in comparison to the equilibrium concept, way of calculating steady state cytoplasmic ADP concentrations at increased workloads is to use kinetic equations and mathematical models of energy metabolism.

International audience; The current problems of regulation of myocardial energy metabolism and oxidative phosphorylation in vivo are considered. With this purpose, retarded diffusion of ADP in cardiomyocytes was studied by analysis of elevated apparent Km for this substrate in regulation of respiration of saponin-skinned cardiac fibers, as compared to isolated mitochondria. Recently published data showing the importance of the outer mitochondrial membrane were compared with new experimental results on the proteolysis of skinned fibers and tissue homogenates. In both cases 10 min incubation and 0.125 mg/ml of trypsin resulted in a decrease of apparent Km for ADP from 297 +/- 35 and 228 +/- 16 to 109 +/- 2 and 36 +/- 16, respectively. Thus, the permeability of the outer mitochondrial membrane for ADP may be controlled by some unknown cytoplasmic protein(s), probably related to the cytoskeleton, which are separated from mitochondria during their isolation. The extent of expression of this protein(s) depends on the energy state and type of muscle. Activation of mitochondrial creatine kinase reaction coupled to oxidative phosphorylation overcomes the diffusion difficulties of ADP by amplifying the stimulatory effect of ADP on respiration. It is concluded that both cytoplasmic and mitochondrial creatine kinases, adenylate kinase and cytoplasmic factor controlling outer membrane permeability may participate in metabolic feedback regulation of respiration in muscle cells.

International audience; The main transforms of Cohen's class allow signal representation simultaneously in time and frequency domains. Wavelet transforms make it possible to link the temporal window width to the analyzing frequency and leads to a "modified wavelet transform" which improves resolution both in time and frequency. A simulation study illustrates the artifacts of every time-frequency representation (TFR) on pure sinusoids and gives performance evaluation of the different methods when searching a sinusoid embedded in a QRS complex. Analyses of real signals from healthy and pathological subjects confirm the simulation results and complete the characterization of ventricular late potentials (VLP) yet detected by signal averaging.

International audience; The purpose of this paper is to review the basic principles of diffusion measurement with spin echoes. These principles can be combined with those of MR imaging to generate maps of diffusion coefficients. Diffusion imaging can be extended to imaging of other intravoxel incoherent motions (IVIM), such as blood microcirculation. Some of the technical problems encountered when implementing IVIM imaging are presented.

International audience; Preliminary assumption of this model is that interactions between actin and myosin presupposes an exact three-dimensional geometrical correspondence between sites, due to the very short time constants present under physiological conditions. Only small and controlled torsions of the actin filaments are accepted. The model uses geometrical information concerning orientations and dimensions of myosin crossbridges and actin monomeres to modelize the distribution of their inter-actions. An orientation map of actin sites in the cross-section perpendicular to the filament axis is proposed, adapted to the specific filament array of vertebrate muscle. Orientation of myosin crossbridges follows Luther's rules. According to the model, any interaction between actin and myosin implies the superimposition of their respective cross-sectional planes. The axial length of actin monomere is 55 A; the distance between two crossbridges along the myosin filament axis is 143 A. The following properties are derived: 1) The shortening step of the sliding actin filament must be a multiple of 11 A (highest common factor). Taking into account the staggered disposition of the two actin strands and the presence of two heads for each cross-bridge, the most probable value for this shortening step is equal to 99 A. A specific scheme is proposed to describe the shortening process. The behavior of the modelized crossbridge does not need any elastic structure--2) Planes situated at 715 A (lowest common multiple) of actin and myosin coinciding planes are also in coincidence. In a hemi-sarcomere the maximal number of these planes, referred to as simultaneously activable planes, is 10 (20 if both myosin heads are considered). The proportion of interactions authorized by the site orientations is 1/12. In the model, the concept of randomly recruited crossbridges is replaced by a discretized recruitment, based on geometrical properties at an ultrastructural level. The proposed distribution is homogeneous: it can be extended radially in the sarcomere and authorizes the actin filament sliding in the whole physiological range under the control of a dual activation function, reproducing Ca++ temporal and spatial distribution.

International audience; Different rheological concepts and theoretical studies have been recently presented using models of myocardial mechanics. Complex analysis of the mechanical behavior of the left ventricular wall have been developed in order to estimate the local stresses and deformations that occur during the heart cycle as well as the ventricular stroke volume and pressure. Theoretical models have taken into account non-linear and viscoelastic passive properties of the myocardium tissue, when subjected to large deformations, through given strain energy functions or stress-strain relations. Different prolate spheroid geometries have been considered for such thick shell cardiac structure. During the active state of the contraction, the rheological behavior of the fibers has been described using different muscle models and relationships between fiber tension and strain, and activation degree. A forthcoming approach for bridging the gap between the knowledge of the muscle fiber microrheological properties and the study of the mechanical behavior of the entire ventricle, consists in including anisotropic and inhomogeneous effects through fiber direction field.