Extremal functions for the anisotropic Sobolev inequalities

The existence of multiple nonnegative solutions to the anisotropic critical problem - \sum_{i=1}^{N} \frac{\partial}{\partial x_i} (| \frac{\partial u}{\partial x_i} |^{p_i-2} \frac{\partial u}{\partial x_i}) = |u|^{p^*-2} u {in} \mathbb{R}^N is proved in suitable anisotropic Sobolev spaces. The solutions correspond to extremal functions of a certain best Sobolev constant. The main tool in our study is an adaptation of the well-known concentration-compactness lemma of P.-L. Lions to anisotropic operators. Futhermore, we show that the set of nontrival solutions \calS is included in $L^\infty(\R^N)$ and is located outside of a ball of radius $\tau >0$ in $L^{p^*}(\R^N)$

Cutpoints for Low Appendicular Lean Mass That Identify Older Adults With Clinically Significant Weakness

Background. Low lean mass is potentially clinically important in older persons, but criteria have not been empirically validated. As part of the FNIH (Foundation for the National Institutes of Health) Sarcopenia Project, this analysis sought to identify cutpoints in lean mass by dual-energy x-ray absorptiometry that discriminate the presence or absence of weakness (defined in a previous report in the series as grip strength <26kg in men and <16kg in women). Methods. In pooled cross-sectional data stratified by sex (7,582 men and 3,688 women), classification and regression tree (CART) analysis was used to derive cutpoints for appendicular lean body mass (ALM) that best discriminated the presence or absence of weakness. Mixed-effects logistic regression was used to quantify the strength of the association between lean mass category and weakness. Results. In primary analyses, CART models identified cutpoints for low lean mass (ALM <19.75kg in men and <15.02kg in women). Sensitivity analyses using ALM divided by body mass index (BMI: ALMBMI) identified a secondary definition (ALMBMI <0.789 in men and ALMBMI <0.512 in women). As expected, after accounting for study and age, low lean mass (compared with higher lean mass) was associated with weakness by both the primary (men, odds ratio [OR]: 6.9 [95% CI: 5.4, 8.9]; women, OR: 3.6 [95% CI: 2.9, 4.3]) and secondary definitions (men, OR: 4.3 [95% CI: 3.4, 5.5]; women, OR: 2.2 [95% CI: 1.8, 2.8]). Conclusions. ALM cutpoints derived from a large, diverse sample of older adults identified lean mass thresholds below which older adults had a higher likelihood of weakness

Criteria for Clinically Relevant Weakness and Low Lean Mass and Their Longitudinal Association With Incident Mobility Impairment and Mortality: The Foundation for the National Institutes of Health (FNIH) Sarcopenia Project

Background. This analysis sought to determine the associations of the Foundation for the National Institutes of Health Sarcopenia Project criteria for weakness and low lean mass with likelihood for mobility impairment (gait speed ≤ 0.8 m/s) and mortality. Providing validity for these criteria is essential for research and clinical evaluation. Methods. Among 4,411 men and 1,869 women pooled from 6 cohort studies, 3-year likelihood for incident mobility impairment and mortality over 10 years were determined for individuals with weakness, low lean mass, and for those having both. Weakness was defined as low grip strength (<26kg men and <16kg women) and low grip strength-to-body mass index (BMI; kg/m2) ratio (<1.00 men and <0.56 women). Low lean mass (dual-energy x-ray absorptiometry) was categorized as low appendicular lean mass (ALM; <19.75kg men and <15.02kg women) and low ALM-to-BMI ratio (<0.789 men and <0.512 women). Results. Low grip strength (men: odds ratio [OR] = 2.31, 95% confidence interval [CI] = 1.34–3.99; women: OR = 1.99, 95% CI 1.23–3.21), low grip strength-to-BMI ratio (men: OR = 3.28, 95% CI 1.92–5.59; women: OR = 2.54, 95% CI 1.10–5.83) and low ALM-to-BMI ratio (men: OR = 1.58, 95% CI 1.12–2.25; women: OR = 1.81, 95% CI 1.14–2.87), but not low ALM, were associated with increased likelihood for incident mobility impairment. Weakness increased likelihood of mobility impairment regardless of low lean mass. Mortality risk patterns were inconsistent. Conclusions. These findings support our cut-points for low grip strength and low ALM-to-BMI ratio as candidate criteria for clinically relevant weakness and low lean mass. Further validation in other populations and for alternate relevant outcomes is needed

The FNIH Sarcopenia Project: Rationale, Study Description, Conference Recommendations, and Final Estimates

Background. Low muscle mass and weakness are common and potentially disabling in older adults, but in order to become recognized as a clinical condition, criteria for diagnosis should be based on clinically relevant thresholds and independently validated. The Foundation for the National Institutes of Health Biomarkers Consortium Sarcopenia Project used an evidence-based approach to develop these criteria. Initial findings were presented at a conference in May 2012, which generated recommendations that guided additional analyses to determine final recommended criteria. Details of the Project and its findings are presented in four accompanying manuscripts. Methods. The Foundation for the National Institutes of Health Sarcopenia Project used data from nine sources of community-dwelling older persons: Age, Gene/Environment Susceptibility-Reykjavik Study, Boston Puerto Rican Health Study, a series of six clinical trials, Framingham Heart Study, Health, Aging, and Body Composition, Invecchiare in Chianti, Osteoporotic Fractures in Men Study, Rancho Bernardo Study, and Study of Osteoporotic Fractures. Feedback from conference attendees was obtained via surveys and breakout groups. Results. The pooled sample included 26,625 participants (57% women, mean age in men 75.2 [±6.1 SD] and in women 78.6 [±5.9] years). Conference attendees emphasized the importance of evaluating the influence of body mass on cutpoints. Based on the analyses presented in this series, the final recommended cutpoints for weakness are grip strength <26kg for men and <16kg for women, and for low lean mass, appendicular lean mass adjusted for body mass index <0.789 for men and <0.512 for women. Conclusions. These evidence-based cutpoints, based on a large and diverse population, may help identify participants for clinical trials and should be evaluated among populations with high rates of functional limitations

Grip Strength Cutpoints for the Identification of Clinically Relevant Weakness

Background. Weakness is common and contributes to disability, but no consensus exists regarding a strength cutpoint to identify persons at high risk. This analysis, conducted as part of the Foundation for the National Institutes of Health Sarcopenia Project, sought to identify cutpoints that distinguish weakness associated with mobility impairment, defined as gait speed less than 0.8 m/s. Methods. In pooled cross-sectional data (9,897 men and 10,950 women), Classification and Regression Tree analysis was used to derive cutpoints for grip strength associated with mobility impairment. Results. In men, a grip strength of 26–32 kg was classified as “intermediate” and less than 26 kg as “weak”; 11% of men were intermediate and 5% were weak. Compared with men with normal strength, odds ratios for mobility impairment were 3.63 (95% CI: 3.01–4.38) and 7.62 (95% CI 6.13–9.49), respectively. In women, a grip strength of 16–20 kg was classified as “intermediate” and less than 16 kg as “weak”; 25% of women were intermediate and 18% were weak. Compared with women with normal strength, odds ratios for mobility impairment were 2.44 (95% CI 2.20–2.71) and 4.42 (95% CI 3.94–4.97), respectively. Weakness based on these cutpoints was associated with mobility impairment across subgroups based on age, body mass index, height, and disease status. Notably, in women, grip strength divided by body mass index provided better fit relative to grip strength alone, but fit was not sufficiently improved to merit different measures by gender and use of a more complex measure. Conclusions. Cutpoints for weakness derived from this large, diverse sample of older adults may be useful to identify populations who may benefit from interventions to improve muscle strength and function

High-intensity interval training and beta-hydroxy-beta-methylbutyric free acid improves aerobic power and metabolic thresholds

Background: Previous research combining Calcium beta-hydroxy-beta-methylbutyrate (CaHMB) and running high-intensity interval training (HIIT) have shown positive effects on aerobic performance measures. The purpose of this study was to examine the effect of beta-hydroxy-beta-methylbutyric free acid (HMBFA) and cycle ergometry HIIT on maximal oxygen consumption (VO(2)peak), ventilatory threshold (VT), respiratory compensation point (RCP) and time to exhaustion (T-max) in college-aged men and women. Methods: Thirty-four healthy men and women (Age: 22.7 +/- 3.1 yrs; VO(2)peak: 39.3 +/- 5.0 ml center dot kg(-1)center dot min(-1)) volunteered to participate in this double-blind, placebo-controlled design study. All participants completed a series of tests prior to and following treatment. A peak oxygen consumption test was performed on a cycle ergometer to assess VO(2)peak, Tmax, VT, and RCP. Twenty-six participants were randomly assigned into either a placebo (PLA-HIIT) or 3 g per day of HMBFA (BetaTor (TM) ) (HMBFA-HIIT) group. Eight participants served as controls (CTL). Participants in the HIIT groups completed 12 HIIT (80-120% maximal workload) exercise sessions consisting of 5-6 bouts of a 2: 1 minute cycling work to rest ratio protocol over a four-week period. Body composition was measured with dual energy x-ray absorptiometry (DEXA). Outcomes were assessed by ANCOVA with posttest means adjusted for pretest differences. Results: The HMBFA-HIIT intervention showed significant (p \u3c 0.05) gains in VO(2)peak, and VT, versus the CTL and PLA-HIIT group. Both PLA-HIIT and HMBFA-HIIT treatment groups demonstrated significant (p \u3c 0.05) improvement over CTL for Tmax, and RCP with no significant difference between the treatment groups. There were no significant differences observed for any measures of body composition. An independent-samples t-test confirmed that there were no significant differences between the training volumes for the PLA-HIIT and HMBFA-HIIT groups. Conclusions: Our findings support the use of HIIT in combination with HMBFA to improve aerobic fitness in college age men and women. These data suggest that the addition of HMBFA supplementation may result in greater changes in VO(2)peak and VT than HIIT alone

High-intensity interval training and beta-hydroxy-beta-methylbutyric free acid improves aerobic power and metabolic thresholds

Background: Previous research combining Calcium beta-hydroxy-beta-methylbutyrate (CaHMB) and running high-intensity interval training (HIIT) have shown positive effects on aerobic performance measures. The purpose of this study was to examine the effect of beta-hydroxy-beta-methylbutyric free acid (HMBFA) and cycle ergometry HIIT on maximal oxygen consumption (VO(2)peak), ventilatory threshold (VT), respiratory compensation point (RCP) and time to exhaustion (T-max) in college-aged men and women. Methods: Thirty-four healthy men and women (Age: 22.7 +/- 3.1 yrs; VO(2)peak: 39.3 +/- 5.0 ml center dot kg(-1)center dot min(-1)) volunteered to participate in this double-blind, placebo-controlled design study. All participants completed a series of tests prior to and following treatment. A peak oxygen consumption test was performed on a cycle ergometer to assess VO(2)peak, Tmax, VT, and RCP. Twenty-six participants were randomly assigned into either a placebo (PLA-HIIT) or 3 g per day of HMBFA (BetaTor (TM) ) (HMBFA-HIIT) group. Eight participants served as controls (CTL). Participants in the HIIT groups completed 12 HIIT (80-120% maximal workload) exercise sessions consisting of 5-6 bouts of a 2: 1 minute cycling work to rest ratio protocol over a four-week period. Body composition was measured with dual energy x-ray absorptiometry (DEXA). Outcomes were assessed by ANCOVA with posttest means adjusted for pretest differences. Results: The HMBFA-HIIT intervention showed significant (p \u3c 0.05) gains in VO(2)peak, and VT, versus the CTL and PLA-HIIT group. Both PLA-HIIT and HMBFA-HIIT treatment groups demonstrated significant (p \u3c 0.05) improvement over CTL for Tmax, and RCP with no significant difference between the treatment groups. There were no significant differences observed for any measures of body composition. An independent-samples t-test confirmed that there were no significant differences between the training volumes for the PLA-HIIT and HMBFA-HIIT groups. Conclusions: Our findings support the use of HIIT in combination with HMBFA to improve aerobic fitness in college age men and women. These data suggest that the addition of HMBFA supplementation may result in greater changes in VO(2)peak and VT than HIIT alone

Tracking changes in the upper boundary of the heavy-intensity exercise domain: end-test power versus respiratory compensation point

The aim of this study was to compare how respiratory compensation point (RCP) and end-test power (EP) change in response to the same four-week high intensity interval training (HIIT). The power output associated with RCP and EP before and after HIIT were recorded in 24 recreationally-active participants (14 men and 10 women). RCP was determined from an incremental exercise test and EP was derived from a three-minute maximal effort test on a cycle ergometer. A significant time (pretest/posttest) × measurement (EP/RCP) interaction was found (F(1, 23)=5.119, p<.05). Results from a paired-sample t-test indicated that both EP (t(23)= -5.221, p<.05) and RCP (t(23)=-3.049, p<.05) increased significantly from pretest to posttest. Furthermore, a small effect size (d=.36, 90%CI=[.13, .58]) was calculated for the pre/posttest changes in the examined thresholds indicating greater potential improvements in EP compared to RCP. The pre/posttest change in EP (mean=21 W, 90%CI=[14, 28 W]) exceeded its standard error of estimate (14 W), while RCP did not. Correlation analysis revealed that EP correlated with RCP at both pretest (r=.813, p<.05) and posttest (r=.873, p<.05), however, delta values between the two measures were not significantly related. Both EP and RCP can be used to assess the change of aerobic capacity after HIIT, but may be reflective of different physiological adaptations. Further, EP may be preferred over RCP when assessing the effects of HIIT

Indoor Air Quality Survey of Nail Salons in Boston

Employees in nail salons, largely Vietnamese immigrant women in Boston, are exposed to a range of volatile organic chemicals from the products used in salons, including solvents, glues and polishes. Some of these chemicals have the potential to cause short and long-term adverse health effects. Only limited research has been performed on assessing occupational exposures. This project aimed to characterize total volatile organic compound (TVOC) and PM(2.5) concentrations in nail salons as a function of ventilation, building characteristics, customer and employee occupancy, and type of services being performed. Students conducted sampling in 21 salons in Boston, MA from September to December, 2011. Study visits included: indoor environmental quality measurements (TVOCs, PM(2.5) and carbon dioxide), site observations, and an interview. CO(2) levels in 15 of 21 salons exceeded 800 ppm, suggesting that these salons may have insufficient ventilation. Higher TVOC and PM(2.5) levels were found in salons with less ventilation (as estimated using CO(2) concentrations). Contrary to our a priori hypothesis, average levels of TVOCs, CO(2) and PM(2.5) were consistent throughout salons, indicating that exposures may not be restricted to areas in the salon where work is being performed (e.g., at the manicure table). Higher TVOC concentrations were observed when tasks were being performed, yet were not dependent upon the number of tasks being performed. Improving ventilation conditions in salons to meet minimum outdoor air delivery requirements can reduce exposures to TVOCs