Determinants of whole-body maximal aerobic performance in young male and female athletes: The roles of lower extremity muscle size, strength and power

This study sought to determine whether lower extremity muscle size, power and strength could be a determinant of whole-body maximal aerobic performance in athletes. 20 male and 19 female young athletes (18 ± 4 years) from various sporting disciplines participated in this study. All athletes performed a continuous ramp-incremental cycling to exhaustion for the determination of peak oxygen uptake (V˙O2peak: the highest V˙O2 over a 15-s period) and maximal power output (MPO: power output corresponding to V˙O2peak). Axial scanning of the right leg was performed with magnetic resonance imaging, and anatomical cross-sectional areas (CSAs) of quadriceps femoris (QF) and hamstring muscles at 50% of thigh length were measured. Moreover, bilateral leg extension power and unilateral isometric knee extension and flexion torque were determined. All variables were normalised to body mass, and six independent variables (V˙O2peak, CSAs of thigh muscles, leg extension power and knee extension and flexion torque) were entered into a forward stepwise multiple regression model with MPO being dependent variable for males and females separately. In the males, V˙O2peak was chosen as the single predictor of MPO explaining 78% of the variance. In the females, MPO was attributed to, in the order of importance, V˙O2peak (p < 0.001) and the CSA of QF (p = 0.011) accounting for 84% of the variance. This study suggests that while oxygen transport capacity is the main determinant of MPO regardless of sex, thigh muscle size also has a role in whole-body maximal aerobic performance in female athletes.

Empirical modeling of the percent depth dose for megavoltage photon beams

Introduction This study presents an empirical method to model the high-energy photon beam percent depth dose (PDD) curve by using the home-generated buildup function and tail function (buildup-tail function) in radiation therapy. The modeling parameters n and μ of buildup-tail function can be used to characterize the Collimator Scatter Factor (Sc) either in a square field or in the different individual upper jaw and lower jaw setting separately for individual monitor unit check. Methods and materials The PDD curves for four high-energy photon beams were modeled by the buildup and tail function in this study. The buildup function was a quadratic function in the form of dd2+n with the main parameter of d (depth in water) and n, while the tail function was in the form of e−μd and was composed by an exponential function with the main parameter of d and μ. The PDD was the product of buildup and tail function, PDD = dd2+n·e−μd. The PDD of four-photon energies was characterized by the buildup-tail function by adjusting the parameters n and μ. The Sc of 6 MV and 10 MV can then be expressed simply by the modeling parameters n and μ. Results The main parameters n increases in buildup-tail function when photon energy increased. The physical meaning of the parameter n expresses the beam hardening of photon energy in PDD. The fitting results of parameters n in the buildup function are 0.17, 0.208, 0.495, 1.2 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The parameter μ can be treated as attenuation coefficient in tail function and decreases when photon energy increased. The fitting results of parameters μ in the tail function are 0.065, 0.0515, 0.0458, 0.0422 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The values of n and μ obtained from the fitted buildup-tail function were applied into an analytical formula of Sc = nE(S)0.63μE to get the collimator to scatter factor Sc for 6 and 10 MV photon beam, while nE, μE, S denotes n, μ at photon energy E of field size S, respectively. The calculated Sc were compared with the measured data and showed agreement at different field sizes to within ±1.5%. Conclusions We proposed a model incorporating a two-parameter formula which can improve the fitting accuracy to be better than 1.5% maximum error for describing the PDD in different photon energies used in clinical setting. This model can be used to parameterize the Sc factors for some clinical requirements. The modeling parameters n and μ can be used to predict the Sc in either square field or individual jaws opening asymmetrically for treatment monitor unit double-check in dose calculation. The technique developed in this study can also be used for systematic or random errors in the QA program, thus improves the clinical dose computation accuracy for patient treatment.

Is there really a proportional relationship between VO2max and body weight? A review article

Maximum oxygen uptake (VO2max) is a “gold standard” in aerobic capacity assessment, playing a vital role in various fields. However, ratio scaling (VO2maxbw), the present method used to express relative VO2max, should be suspected due to its theoretical deficiencies. Therefore, the aim of the study was to revise the quantitative relationship between VO2max and body weight (bw). Dimensional analysis was utilized to deduce their theoretical relationship, while linear or nonlinear regression analysis based on four mathematical models (ratio scaling, linear function, simple allometric model and full allometric model) were utilized in statistics analysis to verify the theoretical relationship. Besides, to investigate the effect of ratio scaling on removing body weight, Pearson correlation coefficient was used to analyze the correlation between VO2maxbw and bw. All the relevant data were collected from published references. Dimensional analysis suggested VO2max be proportional to bw23. Statistics analysis displayed that four mathematical expressions were VO2max = 0.047bw (p<0.01, R2 = 0.68), VO2max = 0.036bw+0.71 (p<0.01, R2 = 0.76), VO2max = 0.10bw0.82 (p<0.01, R2 = 0.93) and VO2max = 0.23bw0.66–0.48 (p<0.01, R2 = 0.81) respectively. Pearson correlation coefficient showed a significant moderately negative relation between VO2maxbw and bw (r = -0.42, p<0.01), while there was no correlation between VO2maxbw0.82 and bw (r = 0.066, p = 0.41). Although statistics analysis did not fully verify the theoretical result, both dimensional and statistics analysis suggested ratio scaling distort the relationship and power function be more appropriate to describe the relationship. Additionally, we hypothesized that lean mass, rather than body weight, plays a more essential role in eliminating the gap between theoretical and experimental b values, and is more appropriate to standardize VO2max, future studies can focus more on it.

Liouville-type results for positive solutions of pseudo-relativistic Schrödinger system

In this paper, we are concerned with the physically engaging pseudo-relativistic Schrödinger system: \[ \begin{cases} \left(-\Delta+m^{2}\right)^{s}u(x)=f(x,u,v,\nabla u) & \hbox{in } \Omega,\\ \left(-\Delta+m^{2}\right)^{t}v(x)=g(x,u,v,\nabla v) & \hbox{in } \Omega,\\ u>0,v>0 & \hbox{in } \Omega, \\ u=v\equiv 0 & \hbox{in } \mathbb{R}^{N}\setminus\Omega, \end{cases} \] where $s,t\in (0,1)$ and the mass $m>0.$ By using the direct method of moving plane, we prove the strict monotonicity, symmetry and uniqueness for positive solutions to the above system in a bounded domain, unbounded domain, $\mathbb {R}^{N}$ , $\mathbb {R}^{N}_{+}$ and a coercive epigraph domain $\Omega$ in $\mathbb {R}^{N}$ , respectively.

Partial regularity for minimizers of discontinuous quasiconvex integrals with general growth

We prove the partial Hölder continuity for minimizers of quasiconvex functionals \begin{equation*} \mathcal{F}({\bf u}) \colon =\int_{\Omega} f(x,{\bf u},D{\bf u})\,\textrm{d} x, \end{equation*} where $f$ satisfies a uniform VMO condition with respect to the $x$ -variable and is continuous with respect to ${\bf u}$ . The growth condition with respect to the gradient variable is assumed a general one.

Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres

In this paper we consider the unfolding of saddle-node \[ X= \frac{1}{xU_a(x,y)}\Big(x(x^{\mu}-\varepsilon)\partial_x-V_a(x)y\partial_y\Big), \] parametrized by $(\varepsilon,\,a)$ with $\varepsilon \approx 0$ and $a$ in an open subset $A$ of $ {\mathbb {R}}^{\alpha },$ and we study the Dulac time $\mathcal {T}(s;\varepsilon,\,a)$ of one of its hyperbolic sectors. We prove (theorem 1.1) that the derivative $\partial _s\mathcal {T}(s;\varepsilon,\,a)$ tends to $-\infty$ as $(s,\,\varepsilon )\to (0^{+},\,0)$ uniformly on compact subsets of $A.$ This result is addressed to study the bifurcation of critical periods in the Loud's family of quadratic centres. In this regard we show (theorem 1.2) that no bifurcation occurs from certain semi-hyperbolic polycycles.

The transmission of drug-resistant strains of HIV in heterosexual populations based on genetic sequences

Background China’s National Free Antiretroviral Treatment Program (NFATP) has substantially reduced morbidity and HIV/AIDS incidence since 2003. However, HIV resistance to antiretroviral drugs (ARVs) has been a major challenge for the current treatment of HIV/AIDS in China. Methods In the current study, we established a nested dynamic model to predict the multi-drug resistance dynamics of HIV among the heterosexual population and evaluated the impact of intervention measures on the transmission of drug resistance. We obtained an effective reproductive number R e d from each sub-model held at different stages of the dynamic model. Meanwhile, we applied Bayesian phylogenetic methods to infer the weighted average effective reproductive number R e g from four HIV subtypes that sampled from 912 HIV-positive patients in China. It is an original and innovative method by fitting R e d to R e g by Markov Chain Monte Carlo (MCMC) to generate unknown parameters in R e d. Results By analyzing the HIV gene sequences, we inferred that the most recent common ancestor of CRF01AE, CRF07BC, CRF08BC, and CRFBC dated from 1994, 1990, 1993 and 1990, respectively. The weighted average effective reproductive number R e g dropped from 1.95 in 1994 to 1.73 in 2018. Considering different interventions, we used a macro dynamic model to predict the trend of HIV resistance. The results show that the number of new infections and total drug resistance under the baseline parameter (S1) are 253,422 and 213,250 in 2025, respectively. Comparing with the numbers under the target treatment rate (S2), they were 219,717 and 236,890, respectively. However, under the ideal treatment target (S3, the treatment rate reaches 90% and the treatment success rate reaches 90%), the number of new infections shows a declining trend and will decrease to 46,559 by 2025. Compared with S1 and S2, the total number of resistance also decreased to 160,899 in 2025. Conclusion With the promotion of NFATP in China, HIV resistance to ARVs is inevitable. The strategy of increasing the treatment rate would not only ineffectively curb the epidemic, but also deteriorate drug resistance issue. Whereas, a combination of intervention strategies (the treatment rate reaches 90% and the treatment success rate reaches 90%) can greatly reduce both infection and drug resistance rate than applying one strategy alone.

Cluster size distribution of cells disseminating from a primary tumor

The first stage of the metastatic cascade often involves motile cells emerging from a primary tumor either as single cells or as clusters. These cells enter the circulation, transit to other parts of the body and finally are responsible for growth of secondary tumors in distant organs. The mode of dissemination is believed to depend on the EMT nature (epithelial, hybrid or mesenchymal) of the cells. Here, we calculate the cluster size distribution of these migrating cells, using a mechanistic computational model, in presence of different degree of EMT-ness of the cells; EMT is treated as given rise to changes in their active motile forces (μ) and cell-medium surface tension (Γ). We find that, for (μ > μmin, Γ > 1), when the cells are hybrid in nature, the mean cluster size, N ¯ ∼ Γ 2 . 0 / μ 2 . 8, where μmin increases with increase in Γ. For Γ ≤ 0, N ¯ = 1, the cells behave as completely mesenchymal. In presence of spectrum of hybrid states with different degree of EMT-ness (motility) in primary tumor, the cells which are relatively more mesenchymal (higher μ) in nature, form larger clusters, whereas the smaller clusters are relatively more epithelial (lower μ). Moreover, the heterogeneity in μ is comparatively higher for smaller clusters with respect to that for larger clusters. We also observe that more extended cell shapes promote the formation of smaller clusters. Overall, this study establishes a framework which connects the nature and size of migrating clusters disseminating from a primary tumor with the phenotypic composition of the tumor, and can lead to the better understanding of metastasis.

Verifying non-isomorphism of groups

The concept of isomorphism is central to group theory, indeed to all of abstract algebra. Two groups {G, *} and {H, ο}are said to be isomorphic to each other if there exists a set bijection α from G onto H, such that $$\left( {a\;*\;b} \right)\alpha = \left( a \right)\alpha \; \circ \;(b)\alpha $$ for all a, b ∈ G. This can be illustrated by what is usually known as a commutative diagram:

L p -trace-free generalized Korn inequalities for incompatible tensor fields in three space dimensions

For $1< p<\infty$ we prove an $L^{p}$ -version of the generalized trace-free Korn inequality for incompatible tensor fields $P$ in $W^{1,p}_0(\operatorname {Curl}; \Omega ,\mathbb {R}^{3\times 3})$ . More precisely, let $\Omega \subset \mathbb {R}^{3}$ be a bounded Lipschitz domain. Then there exists a constant $c>0$ such that \[ \lVert{ P }\rVert_{L^{p}(\Omega,\mathbb{R}^{3\times 3})}\leq c\,\left(\lVert{\operatorname{dev} \operatorname{sym} P }\rVert_{L^{p}(\Omega,\mathbb{R}^{3\times 3})} + \lVert{ \operatorname{dev} \operatorname{Curl} P }\rVert_{L^{p}(\Omega,\mathbb{R}^{3\times 3})}\right) \] holds for all tensor fields $P\in W^{1,p}_0(\operatorname {Curl}; \Omega ,\mathbb {R}^{3\times 3})$ , i.e., for all $P\in W^{1,p} (\operatorname {Curl}; \Omega ,\mathbb {R}^{3\times 3})$ with vanishing tangential trace $P\times \nu =0$ on $\partial \Omega$ where $\nu$ denotes the outward unit normal vector field to $\partial \Omega$ and $\operatorname {dev} P : = P -\frac 13 \operatorname {tr}(P) {\cdot } {\mathbb {1}}$ denotes the deviatoric (trace-free) part of $P$ . We also show the norm equivalence \begin{align*} &\lVert{ P }\rVert_{L^{p}(\Omega,\mathbb{R}^{3\times 3})}+\lVert{ \operatorname{Curl} P }\rVert_{L^{p}(\Omega,\mathbb{R}^{3\times 3})}\\ &\quad\leq c\,\left(\lVert{P}\rVert_{L^{p}(\Omega,\mathbb{R}^{3\times 3})} + \lVert{ \operatorname{dev} \operatorname{Curl} P }\rVert_{L^{p}(\Omega,\mathbb{R}^{3\times 3})}\right) \end{align*} for tensor fields $P\in W^{1,p}(\operatorname {Curl}; \Omega ,\mathbb {R}^{3\times 3})$ . These estimates also hold true for tensor fields with vanishing tangential trace only on a relatively open (non-empty) subset $\Gamma \subseteq \partial \Omega$ of the boundary.