Exact sharp-fronted solutions for nonlinear diffusion on evolving domains

Models of diffusive processes that occur on evolving domains are frequently employed to describe biological and physical phenomena, such as diffusion within expanding tissues or substrates. Previous investigations into these models either report numerical solutions or require an assumption of linear diffusion to determine exact solutions. Unfortunately, numerical solutions do not reveal the relationship between the model parameters and the solution features. Additionally, experimental observations typically report the presence of sharp fronts, which are not captured by linear diffusion. Here we address both limitations by presenting exact sharp-fronted solutions to a model of degenerate nonlinear diffusion on a growing domain. We obtain the solution by identifying a series of transformations that converts the model of nonlinear diffusion on a growing domain to the porous medium equation on a fixed domain, which admits known exact solutions. We determine expressions for critical time scales and domain growth rates such that the diffusive population never reaches the domain boundaries and hence the solution remains valid

Exact solutions for diffusive transport on heterogeneous growing domains

From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is a common phenomenon. Mathematical models have been widely employed to investigate diffusive processes on growing domains. However, a standard assumption is that the domain growth is spatially uniform. There are many relevant examples where this is not the case, such as the colonisation of growing gut tissue by neural crest cells. As such, it is not straightforward to disentangle the individual roles of heterogeneous growth and diffusive transport. Here we present exact solutions to models of diffusive transport on domains undergoing spatially non-uniform growth. The exact solutions are obtained via a combination of transformation, convolution and superposition techniques. We verify the accuracy of these solutions via comparison with simulations of a corresponding lattice-based random walk. We explore various domain growth functions, including linear growth, exponential growth and contraction, and oscillatory growth. Provided the domain size remains positive, we find that the derived solutions are valid. The exact solutions reveal the relationship between model parameters, such as the diffusivity and the type and rate of domain growth, and key statistics, such as the survival and splitting probabilities

Predicting population extinction in lattice-based birth-death-movement models

The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to obtain predictions about the ultimate survival or extinction of the population. A common model employed to describe population dynamics is the lattice-based random walk model with crowding (exclusion). This model can incorporate behaviour such as birth, death and movement, while including natural phenomena such as finite size effects. Performing sufficiently many realisations of the random walk model to extract representative population behaviour is computationally intensive. Therefore, continuum approximations of random walk models are routinely employed. However, standard continuum approximations are notoriously incapable of making accurate predictions about population extinction. Here, we develop a new continuum approximation, the state space diffusion approximation, which explicitly accounts for population extinction. Predictions from our approximation faithfully capture the behaviour in the random walk model, and provides additional information compared to standard approximations. We examine the influence of the number of lattice sites and initial number of individuals on the long-term population behaviour, and demonstrate the reduction in computation time between the random walk model and our approximation

Programable Sound Absorption Performance Enabled by 3D Printing

Design of acoustic materials can be achieved through the connection between their geometry and acoustical performance. Here, we propose 3D-printing as an enabling technology that allows us to precisely control an acoustic material’s micro-geometry and orientation, which then eliminates microscopic geometry bias due to conventional manufacturing process, thus realizing precise material characterization at the 3D-printing CAD programming stage. This concept was practiced in the current study focusing on 3D-printing fibrous sound absorbing layers. A fused deposition modeling (FDM) method was applied to produce the fibers. A Tarnow-based airflow resistivity model was implemented together with Johnson-Champoux-Allard and Biot theories for modeling the geometry-performance connection for the fibers. The sound absorption prediction accuracy of the model was validated by E-1050 standing wave tube measurements on the printed sample

Comparison of Neuromuscular Injuries to the Surgeon during Hand-Assisted and Standard Laparoscopic Urologic Surgery

Background and Purpose: Hand-assisted procedures have assumed a greater role in the practice of many laparoscopists. We surveyed major laparoscopy program directors to compare the incidence and location of neuromuscular injury to the surgeon during hand-assisted laparoscopic (HAL) and standard laparoscopic (SL) surgery. Materials and Methods: A questionnaire on neuromuscular injuries was e-mailed to 42 laparoscopic program directors. Respondents were instructed to report only injuries or pain associated with laparoscopic surgery when they were the primary responsible surgeon and not during open or endoscopic procedures. Results: Surveys were returned from 23 attending laparoscopic surgeons and 2 laparoscopic fellows. Surgeons reported an average of 3.9 HAL and 6.3 SL cases per month as the primary surgeon. The HAL was completed with the GelPort, LapDisk, Omniport, or a combination of devices 55%, 22%, 5%, and 14%, respectively, of the time. Comparing HAL with SL, there was significantly more hand/wrist, forearm, and shoulder pain/injuries associated with HAL (P < 0.004). There was significantly more neck pain associated with SL than HAL (P < 0.003), but no significant difference in lower-back pain (P = 0.40). Comparing the two most commonly used hand-assist devices (GelPort and LapDisk), the LapDisk demonstrated significantly more hand/wrist pain or injury (P = 0.001). Conclusion: Hand-assisted laparoscopy is associated with more frequent neuromuscular strain to the upper extremity than SL, but SL surgeons experience more neck pain or injury. Surgeon discomfort is also dependent on the type of hand-assist device. The long-term consequences of physical strain on the laparoscopic surgeon are unknown currently, but measures to minimize neuromuscular strain should be considered.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63117/1/end.2005.19.377.pd

Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics

We present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee effects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods often calibrate Allee effect models to match observed global population dynamics without providing any mechanistic insight. By introducing a stochastic individual-based model, with proliferation, death and motility rates that depend on local density, we present a modelling framework that translates particular global Allee effects to specific individual-based mechanisms. Using data from ecology and cell biology, we unpack individual-level mechanisms implicit in an Allee effect model and provide simulation tools for others to repeat this analysis

Sleep regularity and predictors of sleep efficiency and sleep duration in elite team sport athletes

Background Many elite athletes have suboptimal sleep duration and efficiency, potentially due to factors that may impact sleep onset and offset times. Variability in sleep onset and offset may negatively influence sleep. The sleep regularity index (SRI) is a novel metric for sleep regularity, however there are no published descriptions of SRI in elite athletes. Further, contributors to sleep efficiency and duration in elite athletes using objective measures have not been explored. Methods Sleep was monitored over a minimum of seven consecutive days (7 to 43)—in 203 elite team sport athletes (age range = 19–36 years; female, n = 79; male, n = 124, total sleep nights = 1975) using activity monitoring and sleep diaries. The sleep regularity index (SRI) was calculated to reflect the night-to-night shifts in sleep by accounting for changes in sleep onset and sleep offset. Sleep characteristics were compared between regular and irregular sleepers and important contributors to sleep efficiency and total sleep time were assessed using multiple linear regression models. Results The median sleep regularity index and interquartile range were 85.1 (81.4 to 88.8). When compared to irregular sleepers, regular sleepers demonstrated (1) significantly greater sleep efficiency (p = 0.006; 0.31 medium effect size [ES]), (2) significantly less variability in total sleep time (− p ≤ 0.001; − 0.69, large ES) and sleep efficiency (− 0.34, small ES), (3) similar total sleep time and (4) significantly less variation in sleep onset (p ≤ 0.001; − 0.73, large ES) and offset (p ≤ 0.001; − 0.74, large ES) times. Sleep characteristics explained 73% and 22% of the variance in total sleep time and sleep efficiency, respectively. The most important contributor to total sleep time was a later sleep offset time, while the most important contributors to sleep efficiency were an earlier bedtime and less variable sleep onset times. Conclusions Bedtime and a consistent sleep onset time are important factors associated with sleep efficiency in athletes, while sleep offset is an important factor for total sleep time. Coaches and staff can assist their athletes by providing training schedules that allow for both regularity and sufficiency of time in bed where possible