On stability of discretizations of the Helmholtz equation (extended version)

We review the stability properties of several discretizations of the Helmholtz equation at large wavenumbers. For a model problem in a polygon, a complete $k$-explicit stability (including $k$-explicit stability of the continuous problem) and convergence theory for high order finite element methods is developed. In particular, quasi-optimality is shown for a fixed number of degrees of freedom per wavelength if the mesh size $h$ and the approximation order $p$ are selected such that $kh/p$ is sufficiently small and $p = O(\log k)$, and, additionally, appropriate mesh refinement is used near the vertices. We also review the stability properties of two classes of numerical schemes that use piecewise solutions of the homogeneous Helmholtz equation, namely, Least Squares methods and Discontinuous Galerkin (DG) methods. The latter includes the Ultra Weak Variational Formulation

Frail older adults are more likely to have autonomic dysfunction : a systematic review and meta-analysis

Autonomic dysfunction and frailty are two common and complex geriatric syndromes. Their prevalence increases with age and they have similar negative health outcomes. In PubMed and Web of Science we screened studies identifying a relationship between autonomic function (AF) and frailty in adults aged ≥65 years. Twenty-two studies of which two prospective and 20 cross-sectional were included (n=8375). We performed a meta-analysis for the articles addressing orthostatic hypotension (OH). Frailty was associated with 1.6 higher odds of suffering from consensus OH (COH) {OR=1.607 95%CI [1.15–2.24]; 7 studies; n=3488}. When measured for each type of OH the largest trend was seen between initial OH (IOH) and frailty {OR=3.08; 95%CI [1.50–6.36]; 2 studies; n=497}. Fourteen studies reported other autonomic function alterations in frail older adults with 4-22% reduction in orthostatic heart rate increase, 6% reduction in systolic blood pressure recovery, 9-75% reduction in most common used heart rate variability (HRV) parameters. Frail older adults were more likely to have impaired AF. Diagnosis of frailty should promptly lead to orthostatic testing as OH implicates specific treatment modalities, which differ from frailty management. As IOH is most strongly correlated with frailty, continuous beat to beat blood pressure measurements should be performed when present at least until cut-off values for heart rate variability testing are defined

The influence of hypertension management on frailty prevention among older persons aged 65 and over : a systematic review

Background: Frailty and hypertension are interrelated, but it remains unclear whether this relationship is modifed by antihypertensive drugs. Methods and results: A systematic review of PubMed and Web of Science databases was performed to review the infuence of hypertension management on preventing the occurrence or progression of frailty in older people aged 65 and over. Studies providing information on this association regardless of the study setting, or defnition of hypertension and frailty were included. Among the initial 2298 articles identifed, 7 were included in the review. Three observational studies assessed the association between frailty and hypertension. Two of them reported no relationship between Aldosterone Antagonists use and frailty prevention. No relationship between BP and incidence frailty after adjustment for hypertension treatment was observed in two other articles. An indirect relationship was reported in the RCTs included. Higher AT11RaAb levels (control group), can lead to a generalized weakness/frailty risk shown by a decrease in grip strength (r=–0.57, p<0.005) and walking speed (r=– 0.47, p<0.005). No signifcant diferences between int-hypertensive intervention and control were observed in frailty status after a 12-weeks follow-up after applying three diferent frailty measurement tools in the other RCT. Conclusions: Based on the results of this systematic review we conclude that BP and frailty occur together but whether the treatment with anti-hypertensive drugs modifes this relationship remains unclear and needs to be further investigated

The interrelationship between grip work, self-perceived fatigue and pre-frailty in community-dwelling octogenarians

Introduction: Low Grip Work and high feelings of self-perceived fatigue could be an early characteristic of decline in reserve capacity, which comes to full expression as physical frailty in a later stage. When Grip Work and self-perceived fatigue can be identified as characteristics differentiating between robustness and pre-frailty it might allow to identify pre-frailty earlier. Therefore, this study aimed to investigate whether the combination of Grip Work and self-perceived fatigue is related to pre-frailty in well-functioning older adults aged 80 and over. Methods: Four-hundred and five community-dwelling older adults aged 80 and over (214 robust and 191 pre-frail) were assessed for muscle endurance (Grip Work corrected for body weight (GW_bw)), self-perceived fatigue (MFI-20) and frailty state (Fried Frailty Index, FFI). A Capacity to Perceived Vitality ratio (CPV) was calculated by dividing GW_bw by the MFI-20 scores. ANCOVA analysis (corrected for age and gender) was used to compare robust and pre-frail older adults, and binary logistic regressions were applied to analyze the relationship between CPV and pre-frailty status. Results: Pre-frail older adults who scored negative on the exhaustion item of the FFI still showed significantly lower GW (p<0.001), CPV ratios (p<0.001) and higher self-perceived fatigue (p<0.05) compared to the robust ones. The likelihood for pre-frailty related significantly to higher age, being men and lower CPV ratios. In women, every unit increase in CPV ratio decreased the likelihood for pre-frailty by 78% (OR 0.22; 95% CI: 0.11-0.44), for men this effect was less strong (34%, OR 0.66; 95% CI: 0.47-0.93). Conclusions: Pre-frail community-dwelling persons aged 80 years and over without clinical signs of exhaustion on the FFI still experience significantly higher fatigue levels (lower Grip Work, higher self-perceived fatigue and lower CPV levels) compared to robust ones. CPV ratio could therefore be a good tool to identify subclinical fatigue in the context of physical (pre-)frailty

Transitions in robust and prefrail octogenarians after 1 year : the influence of activities of daily living, social participation, and psychological resilience on the frailty state

Background: Knowledge opportunities lie ahead as everyday activities, social participation, and psychological resilience might be important predictors for frailty state transitioning in the oldest old. Therefore, this article aims to examine whether changes in basic-, instrumental-, advanced- activities of daily living (b-, i-, a-ADLs), social participation, and psychological resilience predict both a transition from robustness to prefrailty or frailty and vice versa among community-dwelling octogenarians over a follow-up period of one year. Methods: To evaluate worsened and improved frailty transitions after one year in 322 octogenarians (Mage=83.04±2.78), the variables sex, ADLs (b-ADL-DI, i-ADL-DI, a-ADL-DI as baseline and as difference after 6 months values), the CD-RISC (Connor-Davidson Resilience Scale, as baseline and as difference after 6 months), the social participation variables (total participation score, being a member, total number of memberships, level of social participation, being a board member, volunteering, and formal participation as baseline and as difference after 6 months values), were included in a logistic regression analysis. Results: Limitations in a-ADLs at baseline (OR: 1.048, 95% confidence interval, 1.010–1.090) and an increment of limitations in a-ADLs after 6 months (OR: 1.044, 95% confidence interval, 1.007–1.085) were predictors to shift from robust to a worsened frailty state after one year follow-up. Additionally, being a woman (OR: 3.682, 95% confidence interval, 1.379–10.139) and social participation, specifically becoming a board member in 6 months (OR: 4.343, 95% confidence interval, 1.082–16.347), were protectors of robustness and thus related to an improved frailty transition after one year. Conclusions: Encouraging healthy lifestyle behaviors to help the maintenance of ADLs, possibly leading to more social participation, could be promising in the prevention of frailty