Wavy nature of collagen fibrils deduced from the dispersion of their second-order nonlinear optical anisotropy parameters ρ.

From P-SHG experiments, second-order nonlinear optical anisotropy parameters ρ = χZZZ/χZXX of collagen tissues are calculated assuming the same model of supercoiled collagen fibril characterized by a variable angle θ. Dispersion of experimental ρ values is converted into distribution of θ values based on the wavy nature of collagen fibrils deduced from EM studies. For tendon, the results show that the dispersion of experimental ρ values is mainly due to Poisson photonic shot noise assuming a slight fibrillar undulation with θ = 2.2° ± 1.8°. However for skin and vessels, the dispersion of experimental ρ values is mainly due to a stronger fibrillar undulation with θ = 16.2° ± 1.3°. The results highlight that this undulation is reduced during the development of liver fibrosis therefore, contributing to the rigidity of the tissue.

Towards a patient-specific hepatic arterial modeling for microspheres distribution optimization in SIRT protocol.

Selective internal radiation therapy (SIRT) using Yttrium-90 loaded glass microspheres injected in the hepatic artery is an emerging, minimally invasive therapy of liver cancer. A personalized intervention can lead to high concentration dose in the tumor, while sparing the surrounding parenchyma. We propose a computational model for patient-specific simulation of entire hepatic arterial tree, based on liver, tumors, and arteries segmentation on patient's tomography. Segmentation of hepatic arteries down to a diameter of 0.5 mm is semi-automatically performed on 3D cone-beam CT angiography. The liver and tumors are extracted from CT-scan at portal phase by an active surface method. Once the images are registered through an automatic multimodal registration, extracted data are used to initialize a numerical model simulating liver vascular network. The model creates successive bifurcations from given principal vessels, observing Poiseuille's and matter conservation laws. Simulations provide a coherent reconstruction of global hepatic arterial tree until vessel diameter of 0.05 mm. Microspheres distribution under simple hypotheses is also quantified, depending on injection site. The patient-specific character of this model may allow a personalized numerical approximation of microspheres final distribution, opening the way to clinical optimization of catheter placement for tumor targeting.

Determination of extracellular matrix collagen fibril architectures and pathological remodeling by polarization dependent second harmonic microscopy.

Polarization dependence second harmonic generation (P-SHG) microscopy is gaining increase popularity for in situ quantification of fibrillar protein architectures. In this report, we combine P-SHG microscopy, new linear least square (LLS) fitting and modeling to determine and convert the complex second-order non-linear optical anisotropy parameter ρ of several collagen rich tissues into a simple geometric organization of collagen fibrils. Modeling integrates a priori knowledge of polyhelical organization of collagen molecule polymers forming fibrils and bundles of fibrils as well as Poisson photonic shot noise of the detection system. The results, which accurately predict the known sub-microscopic hierarchical organization of collagen fibrils in several tissues, suggest that they can be subdivided into three classes according to their microscopic and macroscopic hierarchical organization of collagen fibrils. They also show, for the first time to our knowledge, intrahepatic spatial discrimination between genuine fibrotic and non-fibrotic vessels. CCl4-treated livers are characterized by an increase in the percentage of fibrotic vessels and their remodeling involves peri-portal compaction and alignment of collagen fibrils that should contribute to portal hypertension. This integrated P-SHG image analysis method is a powerful tool that should open new avenue for the determination of pathophysiological and chemo-mechanical cues impacting collagen fibrils organization.

Fat ViP MRI: Virtual Phantom Magnetic Resonance Imaging of water-fat systems.

OBJECT: Virtual Phantom Magnetic Resonance Imaging (ViP MRI) is a method to generate reference signals on MR images, using external radiofrequency (RF) signals. The aim of this study was to assess the feasibility of ViP MRI to generate complex-data images of phantoms mimicking water-fat systems. MATERIALS AND METHODS: Various numerical phantoms with a given fat fraction, T2* and field map were designed. The k-space of numerical phantoms was converted into RF signals to generate virtual phantoms. MRI experiments were performed at 4.7T using a multi-gradient-echo sequence on virtual and physical phantoms. The data acquisition of virtual and physical phantoms was simultaneous. Decomposition of the water and fat signals was performed using a complex-based water-fat separation algorithm. RESULTS: Overall, a good agreement was observed between the fat fraction, T2* and phase map values of the virtual and numerical phantoms. In particular, fat fractions of 10.5±0.1 (vs 10% of the numerical phantom), 20.3±0.1 (vs 20%) and 30.4±0.1 (vs 30%) were obtained in virtual phantoms. CONCLUSION: The ViP MRI method allows for generating imaging phantoms that i) mimic water-fat systems and ii) can be analyzed with water-fat separation algorithms based on complex data.

Linear least square (LLS) method for pixel-resolution analysis of polarization dependent SHG images of collagen fibrils.

A linear least square (LLS) method is proposed to process polarization dependent SHG intensity analysis at pixel-resolution level in order to provide an analytic solution of nonlinear susceptibility χ(2) coefficients and of fibril orientation. This model is applicable to fibrils with identical orientation in the excitation volume. It has been validated on type I collagen fibrils from cell-free gel, tendon and extracellular matrix of F1 biliary epithelial cells. LLS is fast (a few hundred milliseconds for a 512 × 512 pixel image) and very easy to perform for non-expert in numerical signal processing. Theoretical simulation highlights the importance of signal to noise ratio for accurate determination of nonlinear susceptibility χ(2) coefficients. The results also suggest that, in addition to the peptide group, a second molecular nonlinear optical hyperpolarizability ß contributes to the SHG signal. Finally from fibril orientation analysis, results show that F1 cells remodel extracellular matrix collagen fibrils by changing fibril orientation, which might have important physiological function in cell migration and communication.

Bias reduction in the estimation of mutual information.

This paper deals with the control of bias estimation when estimating mutual information from a nonparametric approach. We focus on continuously distributed random data and the estimators we developed are based on a nonparametric k-nearest-neighbor approach for arbitrary metrics. Using a multidimensional Taylor series expansion, a general relationship between the estimation error bias and the neighboring size for the plug-in entropy estimator is established without any assumption on the data for two different norms. The theoretical analysis based on the maximum norm developed coincides with the experimental results drawn from numerical tests made by Kraskov et al. [Phys. Rev. E 69, 066138 (2004)PLEEE81539-375510.1103/PhysRevE.69.066138]. To further validate the novel relation, a weighted linear combination of distinct mutual information estimators is proposed and, using simulated signals, the comparison of different strategies allows for corroborating the theoretical analysis.

Myofibrillar misalignment correlated to triad disappearance of mdx mouse gastrocnemius muscle probed by SHG microscopy.

We show that the canonical single frequency sarcomeric SHG intensity pattern (SHG-IP) of control muscles is converted to double frequency sarcomeric SHG-IP in preserved mdx mouse gastrocnemius muscles in the vicinity of necrotic fibers. These double frequency sarcomeric SHG-IPs are often spatially correlated to double frequency sarcomeric two-photon excitation fluorescence (TPEF) emitted from Z-line and I-bands and to one centered spot SHG angular intensity pattern (SHG-AIP) suggesting that these patterns are signature of myofibrillar misalignement. This latter is confirmed with transmission electron microscopy (TEM). Moreover, a good spatial correlation between SHG signature of myofibrillar misalignment and triad reduction is established. Theoretical simulation of sarcomeric SHG-IP is used to demonstrate the correlation between change of SHG-IP and -AIP and myofibrillar misalignment. The extreme sensitivity of SHG microscopy to reveal the submicrometric organization of A-band thick filaments is highlighted. This report is a first step toward future studies aimed at establishing live SHG signature of myofibrillar misalignment involving excitation contraction defects due to muscle damage and disease.

Analysis of the behavior of a seizure neural mass model using describing functions.

Neural mass models are computational nonlinear models that simulate the activity of a population of neurons as an average neuron, in such a way that different inhibitory post-synaptic potential and excitatory post-synaptic potential signals could be reproduced. These models have been developed either to simulate the recognized neural mechanisms or to predict some physiological facts that are not easy to realize naturally. The role of the excitatory and inhibitory activity variation in seizure genesis has been proved, but it is not evident how these activities influence appearance of seizure like signals. In this paper a population model is considered in which the physiological inter-relation of the pyramidal and inter-neurons of the hippocampus has been appropriately modeled. The average neurons of this model have been assumed to act as a linear filter followed by a nonlinear function. By changing the gain of excitatory and inhibitory activities that are modeled by the gain of the filters, seizure-like signals could be generated. In this paper through the analysis of this nonlinear model by means of the describing function concepts, it is theoretically shown that not only the gains of the excitatory and inhibitory activities, but also the time constants may play an efficient role in seizure genesis.

Study of the effect of myofibrillar misalignment on the sarcomeric SHG intensity pattern.

We present a theoretical simulation of the sarcomeric SHG intensity pattern (SHG-IP) that takes into account myofibrillar misalignment that is experimentally observed in SHG images of proteolysed muscles. The model predicts that myofibrillar displacement results in the conversion from one peak (1P) to two peaks (2P) sarcomeric SHG-IP in agreement with experimental results. This study suggests that sarcomeric SHG-IP is a powerful tool for mapping spatial myofibrillar displacement and its related excitation-contraction disruption that could occur during muscle physiological adaptation and disease.

Theoretical and experimental SHG angular intensity patterns from healthy and proteolysed muscles.

SHG angular intensity pattern (SHG-AIP) of healthy and proteolysed muscle tissues are simulated and imaged here for the first time to our knowledge. The role of the spatial distribution of second-order nonlinear emitters on SHG-AIP is highlighted. SHG-AIP with two symmetrical spots is found to be a signature of healthy muscle whereas SHG-AIP with one centered spot in pathological mdx muscle is found to be a signature of myofibrillar disorder. We also show that SHG-AIP provides information on the three-dimensional structural organization of myofibrils in physiological and proteolysed muscle. Our results open an avenue for future studies aimed at unraveling more complex physiological and pathological fibrillar tissues organization.

Computational modeling of MR flow imaging by the lattice Boltzmann method and Bloch equation.

In this work, a computational model of magnetic resonance (MR) flow imaging is proposed. The first model component provides fluid dynamics maps by applying the lattice Boltzmann method. The second one uses the flow maps and couples MR imaging (MRI) modeling with a new magnetization transport algorithm based on the Eulerian coordinate approach. MRI modeling is based on the discrete time solution of the Bloch equation by analytical local magnetization transformations (exponential scaling and rotations). Model is validated by comparison of experimental and simulated MR images in two three-dimensional geometries (straight and U-bend tubes) with steady flow under comparable conditions. Two-dimensional geometries, presented in literature, were also tested. In both cases, a good agreement is observed. Quantitative analysis shows in detail the model accuracy. Computational time is noticeably lower to prior works. These results demonstrate that the discrete time solution of Bloch equation coupled with the new magnetization transport algorithm naturally incorporates flow influence in MRI modeling. As a result, in the proposed model, no additional mechanism (unlike in prior works) is needed to consider flow artifacts, which implies its easy extensibility. In combination with its low computational complexity and efficient implementation, the model could have a potential application in study of flow disturbances (in MRI) in various conditions and in different geometries.

A new strategy for model order identification and its application to transfer entropy for EEG signals analysis.

The background objective of this study is to analyze electrenocephalographic (EEG) signals recorded with depth electrodes during seizures in patients with drug-resistant epilepsy. Usually, different phases are observed during the seizure evolution, including a fast onset activity. We aim to ascertain how cerebral structures get involved during this phase, in particular whether some structures "drive" other ones. Regarding a recent theoretical information measure, namely the transfer entropy (TE), we propose two criteria, the first one is based on Akaike's information criterion, the second on the Bayesian information criterion, to derive models' orders that constitute crucial parameters in the TE estimation. A normalized index, named partial transfer entropy (PTE), allows for quantifying the contribution or the influence of a signal to the global information flow between a pair of signals. Experiments are first conducted on linear autoregressive models, then on a physiology-based model, and finally on real intracerebral EEG epileptic signals to detect and identify directions of causal interdependence. Results support the relevance of the new measures for characterizing the information flow propagation whatever unidirectional or bidirectional interactions.

Modeling of supramolecular centrosymmetry effect on sarcomeric SHG intensity pattern of skeletal muscles.

A theoretical far-field second harmonic generation (SHG) imaging radiation pattern is calculated for muscular myosin taking into account both Gouy effect and light diffraction under high focusing excitation. Theoretical analysis, in agreement with experimental results obtained on healthy Xenopus muscles, shows that the increase on intensity at the middle of the sarcomeric SHG intensity pattern is generated by an off-axis constructive interference related to the specific antipolar distribution of myosin molecules within the sarcomere. The best fit of the experimental sarcomeric SHG intensity pattern was obtained with an estimated size of antiparallel, intrathick filaments' packing-width of 115 ± 25 nm localized at the M-band. During proteolysis, experimental sarcomeric SHG intensity pattern exhibits decrease on intensity at the center of the sarcomere. An effective intra- and interthick filaments centrosymmetry of 320 ± 25 nm, in agreement with ultrastructural disorganization observed at the electron microscopy level, was necessary to fit the experimental sarcomeric SHG intensity pattern. Our results show that sarcomeric SHG intensity pattern is very sensitive to misalignment of thick filaments and highlights the potential usefulness of SHG microscopy to diagnose proteolysis-induced muscular disorders.

Prostate segmentation in HIFU therapy.

Prostate segmentation in 3-D transrectal ultrasound images is an important step in the definition of the intra-operative planning of high intensity focused ultrasound (HIFU) therapy. This paper presents two main approaches for the semi-automatic methods based on discrete dynamic contour and optimal surface detection. They operate in 3-D and require a minimal user interaction. They are considered both alone or sequentially combined, with and without postregularization, and applied on anisotropic and isotropic volumes. Their performance, using different metrics, has been evaluated on a set of 28 3-D images by comparison with two expert delineations. For the most efficient algorithm, the symmetric average surface distance was found to be 0.77 mm.

A model-based reconstruction method for 3-D rotational coronary angiography.

This paper presents a model-based reconstruction method of the coronary tree from a few number of projections in rotational angiography imaging. The reconstruction relies on projections acquired at a same cardiac phase and an energy function minimization that aims to lead the deformation of the 3D model to fit projection data whereas preserving coherence both in time and space. Some preliminary results are provided on simulated rotational angiograms.

ECG gated tomographic reconstruction for 3-D rotational coronary angiography.

A method is proposed for 3-D reconstruction of coronary from a limited number of projections in rotational angiography. A Bayesian maximum a posteriori (MAP) estimation is applied with a Poisson distributed projection to reconstruct the 3D coronary tree at a given instant of the cardiac cycle. Several regularizers are investigated L0-norm, L1 and L2 -norm in order to take into account the sparsity of the data. Evaluations are reported on simulated data obtained from a 3D dynamic sequence acquired on a 64-slice GE LightSpeed CT scan. A performance study is conducted to evaluate the quality of the reconstruction of the structures.

Three distinct sarcomeric patterns of skeletal muscle revealed by SHG and TPEF microscopy.

We have extensively characterized the sarcomeric SHG signal as a function of animal species (rat versus xenopus), age (adult versus larval) and tissue preparation (fixed or fresh) and we found that the main feature of this signal is a single peak per mature sarcomere (about 85% of all sarcomeres). The remaining (15%) was found to be either double peak per mature sarcomere or mini sarcomeres (half of a sarcomere) using alpha-actinin immuno detection of the Z-band. The mini sarcomeres are often found in region of pitchfork-like SHG pattern. We suggest that double peak SHG pattern could indicate regions of sarcomeric proteolysis whereas pitchfork-like SHG pattern could reveal sarcomeric assembly.

Motion compensated tomography reconstruction of coronary arteries in rotational angiography.

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.

Modeling of entorhinal cortex and simulation of epileptic activity: insights into the role of inhibition-related parameters.

This paper describes a macroscopic neurophysiologically relevant model of the entorhinal cortex (EC), a brain structure largely involved in human mesio-temporal lobe epilepsy. This model is intervalidated in the experimental framework of ictogenesis animal model (isolated guinea-pig brain perfused with bicuculline). Using sensitivity and stability analysis, an investigation of model parameters related to GABA neurotransmission (recognized to be involved in epileptic activity generation) was performed. Based on spectral and statistical features, simulated signals generated from the model for multiple GABAergic inhibition-related parameter values were classified into eight classes of activity. Simulated activities showed striking agreement (in terms of realism) with typical epileptic activities identified in field potential recordings performed in the experimental model. From this combined computational/experimental approach, hypotheses are suggested about the role of different types of GABAergic neurotransmission in the generation of epileptic activities in EC.

Quantitative evaluation of linear and nonlinear methods characterizing interdependencies between brain signals.

Brain functional connectivity can be characterized by the temporal evolution of correlation between signals recorded from spatially-distributed regions. It is aimed at explaining how different brain areas interact within networks involved during normal (as in cognitive tasks) or pathological (as in epilepsy) situations. Numerous techniques were introduced for assessing this connectivity. Recently, some efforts were made to compare methods performances but mainly qualitatively and for a special application. In this paper, we go further and propose a comprehensive comparison of different classes of methods (linear and nonlinear regressions, phase synchronization, and generalized synchronization) based on various simulation models. For this purpose, quantitative criteria are used: in addition to mean square error under null hypothesis (independence between two signals) and mean variance computed over all values of coupling degree in each model, we provide a criterion for comparing performances. Results show that the performances of the compared methods are highly dependent on the hypothesis regarding the underlying model for the generation of the signals. Moreover, none of them outperforms the others in all cases and the performance hierarchy is model dependent.