Pierre Bouillot

Thermodynamics of the Spin Luttinger Liquid in a Model Ladder Material

The phase diagram in temperature and magnetic field of the metal-organic, two-leg, spin-ladder compound (C5H12N)2CuBr4 is studied by measurements of the specific heat and the magnetocaloric effect. We demonstrate the presence of an extended spin Luttinger-liquid phase between two field-induced quantum critical points and over a broad range of temperature. Based on an ideal spin-ladder Hamiltonian, comprehensive numerical modeling of the ladder specific heat yields excellent quantitative agreement with the experimental data across the entire phase diagram.

Controlling Luttinger liquid physics in spin ladders under a magnetic field.

We present a 14N nuclear magnetic resonance study of a single crystal of CuBr4(C5H12N)2 (BPCB) consisting of weakly coupled spin-1/2 Heisenberg antiferromagnetic ladders. Treating ladders in the gapless phase as Luttinger liquids, we are able to fully account for (i) the magnetic field dependence of the nuclear spin-lattice relaxation rate T1(-1) at 250 mK and for (ii) the phase transition to a 3D ordered phase occurring below 110 mK due to weak interladder exchange coupling. BPCB is thus an excellent model system where the possibility to control Luttinger liquid parameters in a continuous manner is demonstrated and the Luttinger liquid model tested in detail over the whole fermion band.

Particle Imaging Velocimetry Evaluation of Intracranial Stents in Sidewall Aneurysm: Hemodynamic Transition Related to the Stent Design

We investigated the flow modifications induced by a large panel of commercial-off-the-shelf (COTS) intracranial stents in an idealized sidewall intracranial aneurysm (IA). Flow velocities in IA silicone model were assessed with and without stent implantation using particle imaging velocimetry (PIV). The use of the recently developed multi-time-lag method has allowed for uniform and precise measurements of both high and low velocities at IA neck and dome, respectively. Flow modification analysis of both regular (RSs) and flow diverter stents (FDSs) was subsequently correlated with relevant geometrical stent parameters. Flow reduction was found to be highly sensitive to stent porosity variations for regular stents RSs and moderately sensitive for FDSs. Consequently, two distinct IA flow change trends, with velocity reductions up to 50% and 90%, were identified for high-porosity RS and low-porosity FDS, respectively. The intermediate porosity (88%) regular braided stent provided the limit at which the transition in flow change trend occurred with a flow reduction of 84%. This transition occurred with decreasing stent porosity, as the driving force in IA neck changed from shear stress to differential pressure. Therefore, these results suggest that stents with intermediate porosities could possibly provide similar flow change patterns to FDS, favourable to curative thrombogenesis in IAs.

Field{Controlled Magnetic Order in the Quantum Spin{Ladder System (Hpip)2CuBr4

Neutron diffraction is used to investigate the field-induced, antiferromagnetically ordered state in the two-leg spin-ladder material (Hpip)2CuBr4. This “classical” phase, a consequence of weak interladder coupling, is nevertheless highly unconventional: its properties are influenced strongly by the spin Luttinger-liquid state of the ladder subunits. We determine directly the order parameter (transverse magnetization), the ordering temperature, the spin structure, and the critical exponents around the transition. We introduce a minimal microscopic model for the interladder coupling and calculate the quantum fluctuation corrections to the mean-field interaction.

Statics and dynamics of weakly coupled antiferromagnetic spin-1/2 ladders in a magnetic field

We investigate weakly coupled spin-1/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound (CH12N)CuBr4 (BPCB). We use a combination of numerical and analytical methods, in particular, the density-matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic-field dependence of the nuclear-magnetic-resonance relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean-field or quantum Monte Carlo approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore, we compute, using time-dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to describe directly the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid or onto a t-J model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high-energy part of the spectrum that are potentially testable in future experiments.

Wall Shear Stress Distribution of Small Aneurysms Prone to Rupture A Case–Control Study

Background and Purpose— Subarachnoid hemorrhage after intracranial aneurysm rupture remains a serious condition. We performed a case–control study to evaluate the use of computed hemodynamics to detect cerebral aneurysms prone to rupture. Methods— Four patients with incidental aneurysms that ultimately ruptured (cases) were studied after initially being included in a prospective database including their 3-dimensional imaging before rupture. Ruptures were located in different arterial segments: M1 segment of the middle cerebral artery; basilar tip; posterior inferior cerebellar artery; and anterior communicating artery. For each case, 5 controls matched by location and size were randomly selected. An empirical cumulative distribution function of aneurysm wall shear stress percentiles was evaluated for every case and used to define a critical prone-to-rupture range. Univariate logistic regression analysis was then used to assess the individual risk of rupture. Results— A cumulative wall shear stress distribution characterizing a hemodynamic prone-to-rupture range for small-sized aneurysms was identified and fitted independent of the location. Sensitivity and specificity of the preliminary tests were 90% and 93%, respectively. Conclusions— The wall shear stress cumulative probability function may be a potential predictor of small-sized aneurysm rupture.

Assessment of intra-aneurysmal flow modification after flow diverter stent placement with four-dimensional flow MRI: a feasibility study

Background Flow diverter stents (FDS) have been effectively used for the endovascular treatment of sidewall intracranial aneurysms (IAs). Unlike standard endovascular treatments used to exclude directly the aneurysm bulge from the parent vessel, FDS induce reduction in the intra-aneurysmal flow and promote progressive and stable thrombosis therein. The advent of FDS has therefore increased the need for understanding of IA hemodynamics. Methods We proposed the use of the most recently evolved four-dimensional (4D) flow MRI technique to evaluate qualitatively and quantitatively post-FDS flow modification in 10 patients. We report intra-aneurysmal velocity measurements and the influence of metal artifacts induced by the stent. Results An index was defined to quantitatively measure flow changes—namely, the proportional velocity reduction ratio (PVRR)—with ranges from 34.6% to 71.1%. Furthermore, we could compare streamlines characterizing the post-stent flow patterns in five patients in whom the intra-aneurysmal velocity was beyond the visualization threshold of 7.69 cm/s. Conclusions Despite metal artifacts and the low velocities involved, 4D flow MRI could be of interest to measure qualitatively and quantitatively flow changes in stented aneurysms. However, further enhancements are required together with further validation work before it can be considered for clinical use.

Spectral and thermodynamic properties of a strong-leg quantum spin ladder

The strong-leg S=1/2 Heisenberg spin ladder system (C(7)H(10)N)(2)CuBr(4) is investigated using density matrix renormalization group calculations, inelastic neutron scattering, and bulk magnetothermodynamic measurements. Measurements showed qualitative differences compared to the strong-rung case. A long-lived two-triplon bound state is confirmed to persist across most of the Brillouin zone in a zero field. In applied fields, in the Tomonaga-Luttinger spin-liquid phase, elementary excitations are attractive, rather than repulsive. In the presence of weak interladder interactions, the strong-leg system is considerably more prone to three-dimensional ordering.

Computational fluid dynamics with stents: quantitative comparison with particle image velocimetry for three commercial off the shelf intracranial stents

Background and purpose Validation of computational fluid dynamics (CFD) in stented intracranial aneurysms (IAs) is still lacking, to reliably predict prone to occlusion hemodynamics, probing, in particular, velocity reduction, and flow pattern changes. This study compares CFD outcome with particle imaging velocimetry (PIV) for three commercial off the shelf (COTS) stents of different material densities. Material and methods The recently developed uniform and high precision multi-time lag PIV method was applied to a sidewall aneurysm before and after implantation of three COTS stents with high, intermediate, and low material densities. The measured laser sheet flow patterns and velocity reductions were compared with CFD results and correlated with stent material density. Results Velocity reduction was in good agreement for unstented high and low porosity stented IA, while flow pattern change was fully matched for unstented and high porosity stented IA. Poor CFD–PIV matching in IA was found for intermediate porosity stents. Conclusions CFD reproduced fully PIV measurements in unstented and high porosity stented IAs. With low porosity stents, CFD reproduced velocity reduction and high velocities close to the neck, while a marked mismatch on sluggish flow was found at the dome. CFD was unable to match PIV with intermediate porosity stents for which hemodynamic transition occurred.

Computational fluid dynamics analysis of flow reduction induced by flow-diverting stents in intracranial aneurysms: a patient-unspecific hemodynamics change perspective.

Background and purpose Flow-diverter stents (FDSs) have been used effectively to treat large neck and complex saccular aneurysms on the anterior carotid circulation. Intra-aneurysmal flow reduction induces progressive aneurysm thrombosis in most patients. Understanding the degree of flow modification necessary to induce complete aneurysm occlusion among patients with considerable hemodynamics variability may be important for treatment planning. Materials and methods Patients with incidental intracranial saccular aneurysms who underwent FDS endovascular procedures were included and studied for a 12 months’ follow-up period. We used computational fluid dynamics on patient-specific geometries from 3D rotational angiography without and with virtual stent placement and thus compared intra-aneurysmal hemodynamic problems. Receiver operating characteristic analysis was used to estimate the stent:no-stent minimum hemodynamic ratio thresholds that significantly (p≤0.05) determined the condition necessary for long-term (12 months) aneurysm occlusion. Results We included 12 consecutive patients with sidewall aneurysms located in the internal carotid or vertebral artery. The measured porosity of the 12 deployed virtual FDSs was 83±3% (mean±SD). Nine aneurysms were occluded during the 12 months’ follow-up, whereas three were not. A significant (p=0.05) area under the curve (AUC) was found for spatiotemporal mean velocity reduction in the aneurysms: AUC=0.889±0.113 (mean±SD) corresponding to a minimum velocity reduction threshold of 0.353 for occlusion to occur. The 95% CI of the AUC was 0.66 to 1.00. The sensitivity and specificity of the method were ∼99% and ∼67%, respectively. For both wall shear stress and pressure reductions in aneurysms no thresholds could be determined: AUC=0.63±0.16 (p=0.518) and 0.67±0.165 (p=0.405), respectively. Conclusions For successful FDS treatment the post-stent average velocity in sidewall intracranial aneurysms must be reduced by at least one-third from the initial pre-stent conditions.