A numerical investigation on the use of the virtual element method for topology optimization on polygonal meshes

A classical formulation of topology optimization addresses the problem of finding the best distribution of an assigned amount of isotropic material that minimizes the work of the external forces at equilibrium. In general, the discretization of the volume-constrained minimum compliance problem resorts to the adoption of four node displacement-based finite elements, coupled with element-wise density unknowns. When regular meshes made of square elements are used, well-known numerical instabilities arise, see in particular the so-called checkerboarded patterns. On the other hand, when unstructured meshes are needed to cope with geometry of any shape, additional instabilities can steer the optimizer towards local minima instead of the expected global one. Unstructured meshes approximate the strain energy of the members of the arising optimal design with an accuracy that is strictly related to the geometrical features of the discretization, thus remarkably affecting the achieved layouts. In light of the above remarks, in this contribution we consider polygonal meshes and implement the virtual element method (VEM) to solve two classes of topology optimization problems. The robustness of the adopted discretization is exploited to address problems governed by (nearly incompressible and compressible) linear elasticity and problems governed by Stokes equations. Numerical results show the capabilities of the proposed polygonal VEM-based approach with respect to more conventional discretizations

Cadmium-Induced Disruption in 24-h Expression of Clock and Redox Enzyme Genes in Rat Medial Basal Hypothalamus: Prevention by Melatonin

In a previous study we reported that a low daily p.o. dose of cadmium (Cd) disrupted the circadian expression of clock and redox enzyme genes in rat medial basal hypothalamus (MBH). To assess whether melatonin could counteract Cd activity, male Wistar rats (45 days of age) received CdCl2 (5 ppm) and melatonin (3 μg/mL) or vehicle (0.015% ethanol) in drinking water. Groups of animals receiving melatonin or vehicle alone were also included. After 1 month, MBH mRNA levels were measured by real-time PCR analysis at six time intervals in a 24-h cycle. In control MBH Bmal1 expression peaked at early scotophase, Per1 expression at late afternoon, and Per2 and Cry2 expression at mid-scotophase, whereas neither Clock nor Cry1 expression showed significant 24-h variations. This pattern was significantly disrupted (Clock, Bmal1) or changed in phase (Per1, Per2, Cry2) by CdCl2 while melatonin counteracted the changes brought about by Cd on Per1 expression only. In animals receiving melatonin alone the 24-h pattern of MBH Per2 and Cry2 expression was disrupted. CdCl2 disrupted the 24-h rhythmicity of Cu/Zn- and Mn-superoxide dismutase (SOD), nitric oxide synthase (NOS)-1, NOS-2, heme oxygenase (HO)-1, and HO-2 gene expression, most of the effects being counteracted by melatonin. In particular, the co-administration of melatonin and CdCl2 increased Cu/Zn-SOD gene expression and decreased that of glutathione peroxidase (GPx), glutathione reductase (GSR), and HO-2. In animals receiving melatonin alone, significant increases in mean Cu/Zn and Mn-SOD gene expression, and decreases in that of GPx, GSR, NOS-1, NOS-2, HO-1, and HO-2, were found. The results indicate that the interfering effect of melatonin on the activity of a low dose of CdCl2 on MBH clock and redox enzyme genes is mainly exerted at the level of redox enzyme gene expression

Role of infarct scar dimensions, border zone repolarization properties and anisotropy in the origin and maintenance of cardiac reentry

Cardiac ventricular tachycardia (VT) is a life-threatening arrhythmia consisting of a well organized structure of reentrant electrical excitation pathways. Understanding the generation and maintenance of the reentrant mechanisms, which lead to the onset of VT induced by premature beats in presence of infarct scar, is one of the most important issues in current electrocardiology. We investigate, by means of numerical simulations, the role of infarct scar dimension, repolarization properties and anisotropic fiber structure of scar tissue border zone (BZ) in the genesis of VT. The simulations are based on the Bidomain model, a reaction-diffusion system of Partial Differential Equations, discretized by finite elements in space and implicit-explicit finite differences in time. The computational domain adopted is an idealized left ventricle affected by an infarct scar extending transmurally. We consider two different scenarios: i) the scar region extends along the entire transmural wall thickness, from endocardium to epicardium, with the exception of a BZ region shaped as a central sub-epicardial channel (CBZ); ii) the scar region extends transmurally along the ventricular wall, from endocardium to a sub-epicardial surface, and is surrounded by a BZ region (EBZ). In CBZ simulations, the results have shown that: i) the scar extent is a crucial element for the genesis of reentry; ii) the repolarization properties of the CBZ, in particular the reduction of IKs and IKr currents, play an important role in the genesis of reentrant VT. In EBZ simulations, since the possible reentrant pathway is not assigned a-priori, we investigate in depth where the entry and exit sites of the cycle of reentry are located and how the functional channel of reentry develops. The results have shown that: i) the interplay between the epicardial anisotropic fiber structure and the EBZ shape strongly affects the propensity that an endocardial premature stimulus generates a cycle of reentry; ii) reentrant pathways always develop along the epicardial fiber direction; iii) very thin EBZs rather than thick EBZs facilitate the onset of cycles of reentry; iv) the sustainability of cycles of reentry depends on the endocardial stimulation site and on the interplay between the epicardial breakthrough site, local fiber direction and BZ rim

AC joint osteoarthritis: the role of genetics. An MRI evaluation of asymptomatic elderly twins

Purpose: The anatomy of the articular surfaces has historically identified as major responsible for acromioclavicular joint osteoarthritis (ACJO). On the other side, the almost 100% prevalence of ACJO in subjects over 50 years old seems to suggest a multifactorial etiology. We compared ACJO between asymptomatic elderly monozygotic (MZ) and dizygotic (DZ) twins to investigate the influence of genetics and environmental factors. Materials and Methods: Thirty pairs of twins [15MZ-15DZ; mean age (SD): 63.70 (3.31); range: 53–72] were retrospectively enrolled. ACJO was evaluated on MRI through a 4-grade severity scale and ACJ configuration was assessed. Information regarding work activity were obtained. Heritability index was calculated. Results: The intraclass correlation coefficient (ICC) value of 0.868 (95% CI; 0.798 to 0.917). An ICC values of 0.889 (95% CI; 0.798 to 0.944) and 0.843 (95% CI, 0.712 to 0.920) were found in the MZ and DZ groups, respectively. The polychoric correlation was 0.857 in the MZ twins and 0.757 in the DZ twins. The calculated heritability index was 0.20 (20%), and the contribution of the shared environment (c2) and unique environment (e2) was 0.66 (66%) and 0.14 (14%), respectively. No relationship between job types and ACJO in both the total cohort (r = 0.089; p = 0.499) and in the monozygotic (r = 0.247; p = 0.187) and the dizygotic twin groups (r = −0.084; p = 0.658) was found. Conclusions: The role of genetics on ACJO accounts for only 20%; a specific anatomical configuration of the articular surfaces only partially acts on the development of joint osteoarthritis. Environmental factors have the greatest impact. Level of Evidence: IV

Obesity and bone loss at menopause: The role of sclerostin

Background. Peripheral fat tissue is known to positively influence bone health. However, evidence exists that the risk of non-vertebral fractures can be increased in postmenopausal women with obesity as compared to healthy controls. The role of sclerostin, the SOST gene protein product, and body composition in this condition is unknown. Methods. We studied 28 severely obese premenopausal (age, 44.7 \ub1 3.9 years; BMI, 46.0 \ub1 4.2 kg/m2 ) and 28 BMI-matched post-menopausal women (age, 55.5 \ub1 3.8 years; BMI, 46.1 \ub1 4.8 kg/m2 ) thorough analysis of bone density (BMD) and body composition by dual X-ray absorptiometry (DXA), bone turnover markers, sclerostin serum concentration, glucose metabolism, and a panel of hormones relating to bone health. Results. Postmenopausal women harbored increased levels of the bone turnover markers CTX and NTX, while sclerostin levels were non-significantly higher as compared to premenopausal women. There were no differences in somatotroph, thyroid and adrenal hormone across menopause. Values of lumbar spine BMD were comparable between groups. By contrast, menopause was associated with lower BMD values at the hip (p < 0.001), femoral neck (p < 0.0001), and total skeleton (p < 0.005). In multivariate regression analysis, sclerostin was the strongest predictor of lumbar spine BMD (p < 0.01), while menopausal status significantly predicted BMD at total hip (p < 0.01), femoral neck (p < 0.001) and total body (p < 0.05). Finally, lean body mass emerged as the strongest predictor of total body BMD (p < 0.01). Conclusions. Our findings suggest a protective effect of obesity on lumbar spine and total body BMD at menopause possibly through mechanisms relating to lean body mass. Given the mild difference in sclerostin levels between pre-and postmenopausal women, its potential actions in obesity require further investigation

Parallel multilevel solvers for the cardiac electro-mechanical coupling

We develop a parallel solver for the cardiac electro-mechanical coupling. The electric model consists of two non-linear parabolic partial differential equations (PDEs), the so-called Bidomain model, which describes the spread of the electric impulse in the heart muscle. The two PDEs are coupled with a non-linear elastic model, where the myocardium is considered as a nearly-incompressible transversely isotropic hyperelastic material. The discretization of the whole electro-mechanical model is performed by Q1 finite elements in space and a semi-implicit finite difference scheme in time. This approximation strategy yields at each time step the solution of a large scale ill-conditioned linear system deriving from the discretization of the Bidomain model and a non-linear system deriving from the discretization of the finite elasticity model. The parallel solver developed consists of solving the linear system with the Conjugate Gradient method, preconditioned by a Multilevel Schwarz preconditioner, and the non-linear system with a Newton\u2013Krylov-Algebraic Multigrid solver. Three-dimensional parallel numerical tests on a Linux cluster show that the parallel solver proposed is scalable and robust with respect to the domain deformations induced by the cardiac contraction

A comparison of coupled and uncoupled solvers for the cardiac Bidomain model

The aim of this work is to compare a new uncoupled solver for the cardiac Bidomain model with a usual coupled solver. The Bidomain model describes the bioelectric activity of the cardiac tissue and consists of a system of a non-linear parabolic reaction-diffusion partial differential equation (PDE) and an elliptic linear PDE. This system models at macroscopic level the evolution of the transmembrane and extracellular electric potentials of the anisotropic cardiac tissue. The evolution equation is coupled through the non-linear reaction term with a stiff system of ordinary differential equations (ODEs), the so-called membrane model, describing the ionic currents through the cellular membrane. A novel uncoupled solver for the Bidomain system is here introduced, based on solving twice the parabolic PDE and once the elliptic PDE at each time step, and it is compared with a usual coupled solver. Three-dimensional numerical tests have been performed in order to show that the proposed uncoupled method has the same accuracy of the coupled strategy. Parallel numerical tests on structured meshes have also shown that the uncoupled technique is as scalable as the coupled one. Moreover, the conjugate gradient method preconditioned by Multilevel Hybrid Schwarz preconditioners converges faster for the linear systems deriving from the uncoupled method than from the coupled one. Finally, in all parallel numerical tests considered, the uncoupled technique proposed is always about two or three times faster than the coupled approach

Levo-thyroxine Replacement in Obese Adults: the Role of Metabolic Variables and Aging on Thyroid Testing Abnormalities.

CONTEXT: General rates of over- and underreplacement in levothyroxine (LT4) users with primary hypothyroidism are variably high. No information on LT4 adequacy exists in obesity. OBJECTIVE: We explored rates and factors relating to LT4 adequacy in obese patients with primary hypothyroidism. SETTING: Tertiary care center. DESIGN: Among 4954 consecutive obese patients admitted between 2011 and 2014, 691 hypothyroid patients receiving LT4 therapy and 691 body mass index (BMI)-, age-, and sex-matched euthyroid controls underwent analysis of thyroid function, glucolipid profile, body composition, and indirect calorimetry. LT4 users were classified into low TSH (4.2 mU/L). RESULTS: LT4 users constituted 13.9% of the incident population. TSH was low in 7.5%, high in 17.2%, and normal in 75.2% of LT4 users. Overtreatment decreased with aging and more LT4 users ≥65 years of age had normal TSH than those <65 years of age (P < 0.05). Compared with the euthyroid obese group, LT4 users showed higher adiposity, similar insulin resistance, but a healthier lipid profile. In multivariable analyses, LT4 dose was predicted by fat-free mass, hypothyroidism cause, and sex (P < 0.0001 to < 0.05). Risk of LT4 overreplacement increased with younger age (OR 0.96; 95% CI 0.94 to 0.99), higher LT4 dose (OR 2.98; 95% CI 1.44 to 6.14), and lower BMI (OR 0.93; 95% CI 0.88 to 0.99). Male sex increased the likelihood of LT4 underreplacement (OR 2.37; 95% CI 1.10 to 5.11). CONCLUSIONS: Obesity is associated with milder rates of inadequate LT4 treatment compared with nonobese populations. LT4 adequacy increases with aging. Age, body composition, and sex are main determinants of LT4 requirements in obesity. Copyright © 2019 Endocrine Society

The pattern of TSH and fT4 levels across different BMI ranges in a large cohort of euthyroid patients with obesity.

Purpose: A multifold association relates the hypothalamo-pituitary-thyroid axis to body weight. The potential underlying mechanisms are incompletely understood. Further, the mild severity of obesity and the small proportion of individuals with obesity in so far published cohort studies provide little insights on metabolic correlates of thyroid function in obesity. Methods: We retrospectively enrolled 5009 adults with obesity (F/M, 3448/1561; age range, 18-87 years; BMI range, 30.0-82.7 kg/m2), without known thyroid disease in a study on TSH and fT4 levels, lipid profile, glucose homeostasis and insulin resistance, anthropometric parameters including BIA-derived fat mass (%FM) and fat-free mass (FFM). Results: The overall reference interval for TSH in our obese cohort was 0.58-5.07 mIU/L. As subgroups, females and non-smokers showed higher TSH levels as compared to their counterparts (p<0.0001 for both), while fT4 values were comparable between groups. There was a significant upward trend for TSH levels across incremental BMI classes in females, while the opposite trend was seen for fT4 levels in males (p<0.0001 for both). Expectedly, TSH was associated with %FM and FFM (p<0,0001 for both). TSH and fT4 showed correlations with several metabolic variables, and both declined with aging (TSH, p<0.0001; fT4, p<0.01). In a subgroup undergoing leptin measurement, leptin levels were positively associated with TSH levels (p<0.01). At the multivariable regression analysis, in the group as a whole, smoking habit emerged as the main independent predictor of TSH (β=-0.24, p<0.0001) and fT4 (β=-0.25, p<0.0001) levels. In non-smokers, %FM (β=0.08, p<0.0001) and age (β=-0.05, p<0.001) were the main significant predictors of TSH levels. In the subset of nonsmokers having leptin measured, leptin emerged as the strongest predictor of TSH levels (β=0.17, p<0.01). Conclusions: Our study provides evidence of a gender- and smoking-dependent regulation of TSH levels in obesity