Two-Relaxation-Time Lattice Boltzmann Scheme: About Parametrization,Velocity, Pressure and Mixed Boundary Conditions

We develop a two-relaxation-time (TRT) Lattice Boltzmann model for hydrodynamic equations with variable source terms based on equivalent equilibrium functions. A special parametrization of the free relaxation parameter is derived. It controls, in addition to the non-dimensional hydrodynamic numbers, any TRT macroscopic steady solution and governs the spatial discretization of transient flows. In this framework, the multi-reflection approach [16, 18] is generalized and extended for Dirichlet velocity, pressure and mixed (pressure/tangential velocity) boundary conditions. We propose second- and third-order accurate boundary schemes and adapt them for corners. The boundary schemes are analyzed for exactness of the parametrization, uniqueness of their steady solutions, support of staggered invariants and for the effective accuracy in case of time dependent boundary conditions and transient flow. When the boundary scheme obeys the parametrization properly, the derived permeability values become independent of the selected viscosity for any porous structure and can be computed efficiently. The linear interpolations [5, 46] are improved with respect to this property.     

A Well-Balanced Gas Kinetic Scheme for Navier-Stokes Equations with Gravitational Potential

The hydrostatic equilibrium state is the consequence of the exact balance between hydrostatic pressure and external force. Standard finite volume cannot keep this balance exactly due to their unbalanced truncation errors. In this study, we introduce an auxiliary variable which becomes constant at isothermal hydrostatic equilibria and propose a well-balanced gas kinetic scheme for the Navier-Stokes equations. Through reformulating the convection term and the force term via the auxiliary variable, zero numerical flux and zero numerical source term are enforced at the hydrostatic equilibrium state instead of the balance between hydrostatic pressure and external force. Several problems are tested to demonstrate the accuracy and the stability of the new scheme. The results confirm that, the new scheme can preserve the exact hydrostatic solution. The small perturbation riding on hydrostatic equilibria can be calculated accurately. More importantly, the new scheme is capable of simulating the process of converging towards hydrostatic equilibria from a highly unbalanced initial condition. The ultimate state of zero velocity and constant temperature is achieved up to machine accuracy. As demonstrated by the numerical experiments, the current scheme is very suitable for small amplitude perturbation and long time running under gravitational potential.     

A High-Order Accurate Gas-Kinetic Scheme for One- and Two-Dimensional Flow Simulation

This paper develops a high-order accurate gas-kinetic scheme in the framework of the finite volume method for the one- and two-dimensional flow simulations, which is an extension of the third-order accurate gas-kinetic scheme [Q.B. Li, K. Xu, and S. Fu, J. Comput. Phys., 229(2010), 6715-6731] and the second-order accurate gas-kinetic scheme [K. Xu, J. Comput. Phys., 171(2001), 289-335]. It is formed by two parts: quartic polynomial reconstruction of the macroscopic variables and fourth-order accurate flux evolution. The first part reconstructs a piecewise cell-center based quartic polynomial and a cell-vertex based quartic polynomial according to the "initial" cell average approximation of macroscopic variables to recover locally the non-equilibrium and equilibrium single particle velocity distribution functions around the cell interface. It is in view of the fact that all macroscopic variables become moments of a single particle velocity distribution function in the gas-kinetic theory. The generalized moment limiter is employed there to suppress the possible numerical oscillation. In the second part, the macroscopic flux at the cell interface is evolved in fourth-order accuracy by means of the simple particle transport mechanism in the microscopic level, i.e. free transport and the Bhatnagar-Gross-Krook (BGK) collisions. In other words, the fourth-order flux evolution is based on the solution (i.e. the particle velocity distribution function) of the BGK model for the Boltzmann equation. Several 1D and 2D test problems are numerically solved by using the proposed high-order accurate gas-kinetic scheme. By comparing with the exact solutions or the numerical solutions obtained the second-order or third-order accurate gas-kinetic scheme, the computations demonstrate that our scheme is effective and accurate for simulating invisid and viscous fluid flows, and the accuracy of the high-order GKS depends on the choice of the (numerical) collision time.     

Repeatability of the moments of the truncated forced expiratory spirogram.

It is proposed that if the spirogram is truncated for moment analysis, this should be done with respect to volume and not time. Errors are incurred when the moments of one spirogram are compared with those of another. These errors are maximal with no truncation and are reduced by truncation. A method is described for deriving sequential truncated moments of the forced expiratory spirogram. The repeatability and discriminatory power of the truncated moments were assessed over five consecutive days in 21 symptom-free subjects and were compared with conventional spirometric tests. The first and second moments about the origin of the spirogram (alpha 1 and alpha 2), the moment ratio (square root alpha 2/alpha 1) and the forced expiratory time to truncation (FET) are progressively less repeatable within individuals the later the truncation point. The discriminatory power of alpha 1 and alpha 2 and FET declines with later truncation but the discriminatory power of the moment ratio is maximal with truncation at 85% forced vital capacity (FVC) an diminishes sharply if truncation is beyond 95% FVC. At 75% FVC truncation alpha 1 is as good as FEV1% in discriminating between our subjects, whereas alpha 1 at 100% FVC is only half as good as FEV1%. The moment ratio at 90% FVC truncation is highly reproducible (mean within person coefficient of variation 2.1%), has important discriminatory power and is little influenced by events early in the spirogram (correlation with FEV1% r = -0.61, p less than 0.001). The moment ratio at 90% of FVC has attributes which may be useful in detecting early airway obstruction and its further study is warranted in order to establish its normal range and predictive value.     

Study of Simple Hydrodynamic Solutions with the Two-Relaxation-Times Lattice Boltzmann Scheme

For simple hydrodynamic solutions, where the pressure and the velocity are polynomial functions of the coordinates, exact microscopic solutions are constructed for the two-relaxation-time (TRT) Lattice Boltzmann model with variable forcing and supported by exact boundary schemes. We show how simple numerical and analytical solutions can be interrelated for Dirichlet velocity, pressure and mixed (pressure/tangential velocity) multi-reflection (MR) type schemes. Special care is taken to adapt them for corners, to examine the uniqueness of the obtained steady solutions and staggered invariants, to validate their exact parametrization by the non-dimensional hydrodynamic and a "kinetic" (collision) number. We also present an inlet/outlet "constant mass flux" condition. We show, both analytically and numerically, that the kinetic boundary schemes may result in the appearance of Knudsen layers which are beyond the methodology of the Chapman-Enskog analysis. Time dependent Dirichlet boundary conditions are investigated for pulsatile flow driven by an oscillating pressure drop or forcing. Analytical approximations are constructed in order to extend the pulsatile solution for compressible regimes.     

Effects of Instability Versus Traditional Resistance Training on Strength,Power and Velocity in Untrained Men

The purpose of this study was compare the effects of a traditional and an instability resistance circuit training program on upper and lower limb strength, power, movement velocity and jumping ability. Thirty-six healthy untrained men were assigned to two experimental groups and a control group. Subjects in the experimental groups performed a resistance circuit training program consisting of traditional exercises (TRT, n = 10) or exercises executed in conditions of instability (using BOSU® and TRX®) (IRT, n = 12). Both programs involved three days per week of training for a total of seven weeks. The following variables were determined before and after training: maximal strength (1RM), average (AV) and peak velocity (PV), average (AP) and peak power (PP), all during bench press (BP) and back squat (BS) exercises, along with squat jump (SJ) height and counter movement jump (CMJ) height. All variables were found to significantly improve (p <0.05) in response to both training programs. Major improvements were observed in SJ height (IRT = 22.1%, TRT = 20.1%), CMJ height (IRT = 17.7%, TRT = 15.2%), 1RM in BS (IRT = 13.03%, TRT = 12.6%), 1RM in BP (IRT = 4.7%, TRT = 4.4%), AP in BS (IRT = 10.5%, TRT = 9.3%), AP in BP (IRT = 2.4%, TRT = 8.1%), PP in BS (IRT=19.42%, TRT = 22.3%), PP in BP (IRT = 7.6%, TRT = 11.5%), AV in BS (IRT = 10.5%, TRT = 9.4%), and PV in BS (IRT = 8.6%, TRT = 4.5%). Despite such improvements no significant differences were detected in the posttraining variables recorded for the two experimental groups. These data indicate that a circuit training program using two instability training devices is as effective in untrained men as a program executed under stable conditions for improving strength (1RM), power, movement velocity and jumping ability.

Key Points

• Similar adaptations in terms of gains in strength, power, movement velocity and jumping ability were produced in response to both training programs.
• Both the stability and instability approaches seem suitable for healthy, physically-active individuals with or with limited experience in resistance training.
• RPE emerged as a useful tool to monitor exercise intensity during instability strength training.

Key words: Unstable surfaces, strength training, back squat, bench press, jumping ability     

Rotational Slip Flow in Coaxial Cylinders by the Finite-Difference Lattice Boltzmann Methods

Recent studies on applications of the lattice Boltzmann method (LBM) and the finite-difference lattice Boltzmann method (FDLBM) to velocity slip simulations are mostly on one-dimensional (1D) problems such as a shear flow between parallel plates. Applications to a 2D problem may raise new issues. The author performed numerical simulations of rotational slip flow in coaxial cylinders as an example of 2D problem. Two types of 2D models were used. The first were multi-speed FDLBM models proposed by the author. The second was a standard LBM, the D2Q9 model. The simulations were performed applying a finite difference scheme to both the models. The study had two objectives. The first was to investigate the accuracies of LBM and FDLBM on applications to rotational slip flow. The second was to obtain an experience on application of the cylindrical coordinate system. The FDLBM model with 8 directions and the D2Q9 model showed an anisotropic flow pattern when the relaxation time constant or the Knudsen number was large. The FDLBM model with 24 directions showed accurate results even at large Knudsen numbers.     

Extended theory of selective photothermolysis

BACKGROUND AND OBJECTIVE: We present a new theory of selective thermal damage of non-uniformly pigmented structures in biological tissues. Spatial separation of the heavily pigmented areas and the target requires limitation of the pigment temperature and heat diffusion from the pigmented to the targeted areas. STUDY DESIGNS/MATERIALS AND METHODS: A concept of selective target damage by heat diffusion is presented for three target geometries: planar, cylindrical, and spherical. An in vitro experiment is described in which the dependence of thermal damage on pulsewidth at constant fluence was evaluated. RESULTS: The in vitro experiment showed that the size of the damage zone for similar hair follicles was pulsewidth-independent over a very broad range of pulsewidths (30-400 ms). We formulated a new theory (extended theory of photothermolysis) to interpret the experimental results. CONCLUSIONS: Based on this new theory, the treatment pulsewidth for non-uniformly pigmented targets is significantly longer than the target thermal relaxation time (TRT). The theory provides new recommendations for photoepilation and photosclerotherapy parameters.     

Prospective assessment of health‐related quality of life in men with late‐onset hypogonadism who received testosterone replacement therapy

The objective of this study was to characterise the status of health‐related quality of life (HRQOL) in Japanese men with late‐onset hypogonadism (LOH) treated with testosterone replacement therapy (TRT). HRQOL in 69 consecutive Japanese men with LOH undergoing TRT for at least 6 months was prospectively evaluated before and 6 months after the initiation of TRT using the Medical Outcomes Study 8‐Item Short‐Form Health Survey (SF‐8). All eight‐scale scores except for bodily pain (BP) in the 69 patients at 6 months after the introduction of TRT significantly improved compared with those before TRT; however, all scale scores except for BP in the 69 patients were significantly inferior to those in age‐matched Japanese controls irrespective of the timing of SF‐8. Multivariate analyses of several parameters revealed that both age and Aging Male Symptom (AMS) score had an independent impact on mental health (MH), despite the lack of an independent association between any score and the remaining factors examined. TRT appeared to significantly improve the status of HRQOL in men with LOH; however, even after the introduction of TRT, HRQOL associated with MH remained significantly impaired in elderly men and/or those with a high AMS score.     

Testosterone replacement therapy and the risk of prostate cancer. Is there a link?

Substantial evidence supports the value of testosterone replacement therapy (TRT) in improving quality of life in men with proven aging male syndrome (AMS). Benefits of TRT include improved bone mineral density, reduced fracture risk, increased muscle mass, and improved mood, sense of well being, and libido, among others. There is currently a heated debate about the theoretical association between TRT and the initiation, progression, and aggressiveness of prostate cancer; however, this link has not been uniformly studied, and any results have been contradictory and nonconclusive. Although no clear evidence links TRT to prostate cancer, the possibility of increasing the risk of a clinical manifestation of a latent pre-existing malignancy can influence the decision about TRT use. Current recommendations are to exclude prostate cancer before initiating TRT in men over age 40 and to closely monitor men in the first year of testosterone replacement, followed by observation in subsequent years.     

Testosterone and the prostate: Implications for the treatment of hypogonadal men

Late-onset hypogonadism (LOH) and testosterone replacement therapy (TRT) are subjects of much recent research. Because aging men are at risk for benign prostatic hyperplasia (BPH) and prostate cancer, elucidating the relationship between testosterone and these diseases is crucial to ensure its safe administration. It is known that testosterone supplementation may worsen active prostate cancer and that its blockade or removal slows the disease’s progression. However, recent studies have attempted to show that, in individuals in whom prostate cancer has been ruled out, TRT may simply restore serum testosterone levels to within normal limits without significant adverse affects on the prostate. Patients undergoing TRT should be monitored carefully for any evidence of prostatic disease.     

A Nearly Analytical Discrete Method for Wave-Field Simulations in 2D Porous Media

The nearly analytic discrete method (NADM) is a perturbation method originally proposed by Yang et al. (2003) [26] for acoustic and elastic waves in elastic media. This method is based on a truncated Taylor series expansion and interpolation approximations and it can suppress effectively numerical dispersions caused by the discretizating the wave equations when too-coarse grids are used. In the present work, we apply the NADM to simulating acoustic and elastic wave propagations in 2D porous media. Our method enables wave propagation to be simulated in 2D porous isotropic and anisotropic media. Numerical experiments show that the error of the NADM for the porous case is less than those of the conventional finite-difference method (FDM) and the so-called Lax-Wendroff correction (LWC) schemes. The three-component seismic wave fields in the 2D porous isotropic medium are simulated and compared with those obtained by using the LWC method and exact solutions. Several characteristics of wave propagating in porous anisotropic media, computed by the NADM, are also reported in this study. Promising numerical results illustrate that the NADM provides a useful tool for large-scale porous problems and it can suppress effectively numerical dispersions.     

Efficacy of testosterone replacement therapy on pain in hypogonadal men with chronic pain syndrome: A subanalysis of a prospective randomised controlled study in Japan (EARTH study)

The present study investigated the efficacy of 6 months of testosterone replacement therapy (TRT) on chronic pain syndrome in late-onset hypogonadal (LOH) men. Sixty hypogonadal patients with chronic pain syndrome (31 patients in TRT group and 29 controls) were extracted from a previous randomised controlled study in Japan. Chronic pain was evaluated based on bodily pain (BP) subscale of Short-form (36) Health Survey (SF-36), and patients with a score of 50.0 or less were defined as suffering from chronic pain. SF-36 scores, Aging Male Symptoms (AMS) scale, international prostatic symptoms score (IPSS) and prostate-specific antigen (PSA) levels at baseline and a 6-month visit for the two groups were collected and compared. There were no statistically significant differences in baseline backgrounds between the two groups. Six-month TRT could contribute to significant improvements in BP, mental health of SF-36 and sleep disturbance (AMS question 4). Though the PSA level in the TRT group also significantly elevated at 6 months, the increase was not clinically significant. No significant improvements were evident in any characteristics in the controls. In conclusion, 6-month TRT can improve pain and some aspects of quality of life in LOH men with chronic pain.     

A Fourth Order Numerical Method for the Primitive Equations Formulated in Mean Vorticity

A fourth-order finite difference method is proposed and studied for the primitive equations (PEs) of large-scale atmospheric and oceanic flow based on mean vorticity formulation. Since the vertical average of the horizontal velocity field is divergence-free, we can introduce mean vorticity and mean stream function which are connected by a 2-D Poisson equation. As a result, the PEs can be reformulated such that the prognostic equation for the horizontal velocity is replaced by evolutionary equations for the mean vorticity field and the vertical derivative of the horizontal velocity. The mean vorticity equation is approximated by a compact difference scheme due to the difficulty of the mean vorticity boundary condition, while fourth-order long-stencil approximations are utilized to deal with transport type equations for computational convenience. The numerical values for the total velocity field (both horizontal and vertical) are statically determined by a discrete realization of a differential equation at each fixed horizontal point. The method is highly efficient and is capable of producing highly resolved solutions at a reasonable computational cost. The full fourth-order accuracy is checked by an example of the reformulated PEs with force terms. Additionally, numerical results of a large-scale oceanic circulation are presented.     

Tensile properties of human knee joint cartilage. II. Correlations between weight bearing and tissue pathology and the kinetics of swelling

The nonequilibrium or kinetic swelling behavior of normal, fibrillated, and osteoarthritic (OA) (removed from total knee joint replacements) human knee joint cartilage has been measured using our isometric tensile apparatus (ITA). We found that large local variations exist in the manner with which human knee joint cartilage swells, including anisotropic effects, inhomogeneities, and dependence on local biochemical composition and pathological condition. The ITA provides three convenient biomechanical parameters--peak stress (sigma p), stress relaxation (sigma R), and diffusion coefficient (D)--to quantify the kinetics of swelling. We used these parameters to quantify and differentiate the kinetic swelling behavior of normal, fibrillated, and osteoarthritic cartilage, as well as the swelling behavior of cartilage from high and low weight-bearing areas. Also, these kinetic swelling parameters correlated very well, though by varying degrees, with such biochemical measures as collagen/proteoglycan ratio, hexosamine content/wet weight, and hydroxyproline content/dry weight, providing important insight into the mechanisms and processes involved during the course of swelling. Hence, the kinetic swelling behavior of cartilage should be used to provide important information not obtainable from equilibrium swelling studies.     

Quantitative measure of the output of the deep abdominal vessels with a new device Duplex. Preliminary results

Deep abdominal vessels blood flow can be measured noninvasively with the relation Q = V x A, where Q = flow, V = blood velocity and A = area of the considered vessel. In most Duplex devices, V is only calculated as a mean by the Doppler effect and A estimated by an echograph. Our newly developed multi-gated pulsed Doppler provides the velocity profile across the vessel, so minimizing errors in flow determination. On fifty healthy volunteers, we found flow of 717 +/- 238 ml/min for the portal vein, 1594 +/- 293 ml/min for the upper abdominal aorta and 794 +/- 168 ml/min for the lower aorta. These results are obtained through many technical and practical problems, but are feasible, even if still subject to errors. Further investigation will determine if the technique is also suitable for patients. Better assessment of deep abdominal vessels hemodynamics may be expected.     

Comparison of Simulations of Convective Flows

We show that a single particle distribution for the "energy-conserving" D2Q13 lattice Boltzmann scheme can simulate coupled effects involving advection and diffusion of velocity and temperature. We consider various test cases: non-linear waves with periodic boundary conditions, a test case with buoyancy, propagation of transverse waves, Couette and Poiseuille flows. We test various boundary conditions and propose to mix bounce-back and anti-bounce-back numerical boundary conditions to take into account velocity and temperature Dirichlet conditions. We present also first results for the de Vahl Davis heated cavity. Our results are compared with the coupled D2Q9-D2Q5 lattice Boltzmann approach for the Boussinesq system and with an elementary finite differences solver for the compressible Navier-Stokes equations. Our main experimental result is the loss of symmetry in the de Vahl Davis cavity computed with the single D2Q13 lattice Boltzmann model without the Boussinesq hypothesis. This result is confirmed by a direct Navier Stokes simulation with finite differences.     

Hypogonadism and urologic surgeries: a narrative review

Background and ObjectivePrevious studies indicated that the treatment of male hypogonadism can be beneficial for intraoperative and postsurgical outcomes. In this study, we aimed to determine the impact of male hypogonadism on urologic surgeries. We provided an overview of the key studies in the field with the focus on the outcomes of urologic surgeries in hypogonadal men with/without testosterone replacement therapy (TRT).MethodsWe performed a literature review in PubMed and Google Scholar databases for the most relevant articles pertaining to the outlined topics without placing any limitations on publication years or study designs. We included full-text English articles published in peer reviewed journals between January 1970 and March 2022.Key Content and FindingsAndrogen deficiency is a common finding after major urologic surgeries. Although guidelines recommend against TRT in men with prostate carcinoma, recent investigations showed no association between TRT and disease progression and recurrence. Indeed, recent evidence suggested that low androgen levels could be related to high grade prostate carcinoma and increased risk of upgrading from low to high grade disease. Investigations on the application of TRT in benign prostatic hyperplasia (BPH) patients also revealed contrasting results. While some studies suggested higher rates of prostate-related events in men who received TRT, others showed that TRT could alleviate urinary symptoms in hypogonadal men with BPH. Decreased testosterone level is commonly seen in bladder cancer patients. The treatment of perioperative androgen deficiency can reduce postoperative morbidities and lower the risk of recurrence in these patients. Low testosterone levels are observed in approximately half of the men who undergo artificial urinary sphincter (AUS) placement and can increase the risk of complications.ConclusionsThe role of testosterone treatment in patients with urologic diseases such as prostate carcinoma and BPH is controversial. Further investigations are needed to determine the impact of hypogonadism and TRT on the outcomes of urologic surgeries in patients with androgen deficiency.     

Some Random Batch Particle Methods for the Poisson-Nernst-Planck and Poisson-Boltzmann Equations

We consider in this paper random batch interacting particle methods for solving the Poisson-Nernst-Planck (PNP) equations, and thus the Poisson-Boltzmann (PB) equation as the equilibrium, in the external unbounded domain. To justify the simulation in a truncated domain, an error estimate of the truncation is proved in the symmetric cases for the PB equation. Then, the random batch interacting particle methods are introduced which are $\mathcal{O}(N)$ per time step. The particle methods can not only be considered as a numerical method for solving the PNP and PB equations, but also can be used as a direct simulation approach for the dynamics of the charged particles in solution. The particle methods are preferable due to their simplicity and adaptivity to complicated geometry, and may be interesting in describing the dynamics of the physical process. Moreover, it is feasible to incorporate more physical effects and interactions in the particle methods and to describe phenomena beyond the scope of the mean-field equations.     

Testosterone replacement in prostate cancer survivors with hypogonadal symptoms

Study Type – Therapy (case series)
Level of Evidence 4

OBJECTIVE

To describe the clinical outcomes of prostate cancer survivors who were treated with high‐dose testosterone‐replacement therapy (TRT) for the relief of hypogonadal symptoms.

PATIENTS AND METHODS

We reviewed the records of 96 patients who received TRT after initial management for prostate cancer from 2000 to 2007.

RESULTS

In all, 41 men had prostate‐specific antigen (PSA) progression (PSA Working Group) while on TRT, but only seven had radiographic progression of disease. Fifty‐six men discontinued TRT due to increasing PSA levels, and 59% of these men had significant reductions in PSA level with no additional intervention. In all, 31 men remain on TRT with no PSA or radiological progression at a median of 36.7 months; nine men stopped TRT for reasons other than progression. Characteristics associated with continuing TRT were radical prostatectomy as primary management, a low PSA level when starting TRT, and concurrent use of dutasteride. Hypogonadal symptoms were alleviated in most cases.

CONCLUSIONS

While most men in this series had increasing PSA levels during TRT, stopping TRT typically resulted in PSA declines. A subset of men were able to remain on TRT for several years without disease progression.