On the dimension of Voisin sets in the moduli space of abelian varieties

We study the subsets $V_k(A)$ of a complex abelian variety $A$ consisting in the collection of points $x\in A$ such that the zero-cycle $\{x\}-\{0_A\}$ is $k$-nilpotent with respect to the Pontryagin product in the Chow group. These sets were introduced recently by Voisin and she showed that $\dim V_k(A) \leq k-1$ and $V_k(A)$ is countable for a very general abelian variety of dimension at least $2k-1$. We study in particular the locus $\mathcal V_{g,2}$ in the moduli space of abelian varieties of dimension $g$ with a fixed polarization, where $V_2(A)$ is positive dimensional. We prove that an irreducible subvariety $\mathcal Y \subset \mathcal V_{g,2}$, $g\ge 3$, such that for a very general $y \in \mathcal Y$ there is a curve in $V_2(A_y)$ generating $A$ satisfies $\dim \mathcal Y \le 2g - 1.$ The hyperelliptic locus shows that this bound is sharp.Comment: Final version to appear in Mathematische Annale

On the dimension of Voisin sets in the moduli space of abelian varieties

We study the subsets $V_k(A)$ of a complex abelian variety $A$ consisting in the collection of points $x \in A$ such that the zero-cycle $\{x\}-\left\{0_A\right\}$ is $k$-nilpotent with respect to the Pontryagin product in the Chow group. These sets were introduced recently by Voisin and she showed that $\operatorname{dim} V_k(A) \leq k-1$ and $\operatorname{dim} V_k(A)$ is countable for a very general abelian variety of dimension at least $2 k-1$. We study in particular the locus $\mathcal{V}_{g, 2}$ in the moduli space of abelian varieties of dimension $g$ with a fixed polarization, where $V_2(A)$ is positive dimensional. We prove that an irreducible subvariety $\mathcal{Y} \subset \mathcal{V}_{g, 2}$, $g \geq 3$, such that for a very general $y \in \mathcal{Y}$ there is a curve in $V_2\left(A_y\right)$ generating $A$ satisfies $\operatorname{dim} \mathcal{Y} \leq 2 g-1$. The hyperelliptic locus shows that this bound is sharp

Analysis of turbulence effects in a patient-specific aorta with aortic valve stenosis

Blood flow in the aorta is often assumed laminar, however aortic valve pathologies may induce transition to turbulence and our understanding of turbulence effects is incomplete. The aim of the study was to provide a detailed analysis of turbulence effects in aortic valve stenosis (AVS). Methods: Large-eddy simulation (LES) of flow through a patient-specific aorta with AVS was conducted. Magnetic resonance imaging (MRI) was performed and used for geometric reconstruction and patient-specific boundary conditions. Computed velocity field was compared with 4D flow MRI to check qualitative and quantitative consistency. The effect of turbulence was evaluated in terms of fluctuating kinetic energy, turbulence-related wall shear stress (WSS) and energy loss. Results: Our analysis suggested that turbulence was induced by a combination of a high velocity jet impinging on the arterial wall and a dilated ascending aorta which provided sufficient space for turbulence to develop. Turbulent WSS contributed to 40% of the total WSS in the ascending aorta and 38% in the entire aorta. Viscous and turbulent irreversible energy losses accounted for 3.9 and 2.7% of the total stroke work, respectively. Conclusions: This study demonstrates the importance of turbulence in assessing aortic haemodynamics in a patient with AVS. Neglecting the turbulent contribution to WSS could potentially result in a significant underestimation of the total WSS. Further work is warranted to extend the analysis to more AVS cases and patients with other aortic valve diseases

Evaluation of computational methodologies for accurate prediction of wall shear stress and turbulence parameters in a patient-specific aorta

Background: Recent studies suggest that blood flow in main arteries is intrinsically disturbed, even under healthy conditions. Despite this, many computational fluid dynamics (CFD) analyses of aortic haemodynamics make the assumption of laminar flow, and best practices surrounding appropriate modelling choices are lacking. This study aims to address this gap by evaluating different modelling and post-processing approaches in simulations of a patient-specific aorta. Methods: Magnetic resonance imaging (MRI) and 4D flow MRI from a patient with aortic valve stenosis were used to reconstruct the aortic geometry and derive patient-specific inlet and outlet boundary conditions. Three different computational approaches were considered based on assumed laminar or assumed disturbed flow states including low-resolution laminar (LR-laminar), high-resolution laminar (HR-Laminar) and large-eddy simulation (LES). Each simulation was ran for 30 cardiac cycles and post-processing was conducted on either the final cardiac cycle, or using a phase-averaged approach which utilised all 30 simulated cycles. Model capabilities were evaluated in terms of mean and turbulence-based parameters. Results: All simulation types, regardless of post-processing approach could correctly predict velocity values and flow patterns throughout the aorta. Lower resolution simulations could not accurately predict gradient-derived parameters including wall shear stress and viscous energy loss (largest differences up to 44.6% and 130.3%, respectively), although phase-averaging these parameters improved predictions. The HR-Laminar simulation produced more comparable results to LES with largest differences in wall shear stress and viscous energy loss parameters up to 5.1% and 11.6%, respectively. Laminar-based parameters were better estimated than turbulence-based parameters. Conclusions: Our findings suggest that well-resolved laminar simulations can accurately predict many laminar-based parameters in disturbed flows, but there is no clear benefit to running a HR-Laminar simulation over an LES simulation based on their comparable computational cost. Additionally, post-processing ‘typical’ laminar simulation results with a phase-averaged approach is a simple and cost-effective way to improve accuracy of lower-resolution simulation results

Oral liquid L-thyroxine (L-t4) may be better absorbed compared to L-T4 tablets following bariatric surgery.

Drug malabsorption is a potential concern after bariatric surgery. We present four case reports of hypothyroid patients who were well replaced with thyroxine tablets to euthyroid thyrotropin (TSH) levels prior to Roux-en-Y gastric bypass surgery. These patients developed elevated TSH levels after the surgery, the TSH responded reversibly to switching from treatment with oral tablets to a liquid formulation

Fine needle cytology of complex thyroid nodules.

OBJECTIVE: To evaluate whether a preliminary aspiration (ASP) of the cystic component and/or using spinal needles in complex thyroid nodules (CTN) could improve the adequacy of cytological sampling. METHODS: Between January 2004 and December 2006, 386 consecutive patients with CTN were enrolled in this prospective investigation. Ultrasound (US) fine needle aspiration cytology (FNAC) of the solid component of the nodule (one nodule per patient) was performed using two different 25 gauge needles, with (Yale Spinal, YS) or without (Neolus, NS) a stylet, in alternate sequence on consecutive patients. In addition, a subgroup of patients presenting larger cystic component (approximately 50%) was submitted to total aspiration of the cystic component (ASP+) or not submitted (ASP-) before US-FNAC, in alternate sequence within each needle type group. All the samplings were performed by a single endocrinologist. RESULTS: Adequate specimens were observed in 163 (84.5%) and 183 (94.8%) nodules investigated by NS and YS respectively. Sampling with the stylet needle was associated with an overall significant reduction of non-diagnostic specimens (15.5% vs 5.2% by NS and YS respectively, P < 0.001). The favourable result obtained with YS was independent from preliminary aspiration of the cystic component (ASP+: 14.8% vs 5.7% by NS and YS; ASP-: 16.2% vs 4.8%, not significant). A logistic regression analysis, taking into account nodule size and presence of intranodal vascularity at eco-colour evaluation of the solid component, confirmed that needle type was the only significant predictor of successful sampling (odds ratio 3.6 (95% confidence interval 1.7-7.6), P < 0.001). CONCLUSIONS: Our data show that adopting stylet needles to perform FNAC in CTN may significantly improve the percentage of adequate sampling. On the other hand, preliminary aspiration of CTN with large cystic component does not add any advantage