Dynamics and pattern formation in invasive tumor growth

In this work, we study the in-vitro dynamics of the most malignant form of the primary brain tumor: Glioblastoma Multiforme. Typically, the growing tumor consists of the inner dense proliferating zone and the outer less dense invasive region. Experiments with different types of cells show qualitatively different behavior. Wild-type cells invade a spherically symmetric manner, but mutant cells are organized in tenuous branches. We formulate a model for this sort of growth using two coupled reaction-diffusion equations for the cell and nutrient concentrations. When the ratio of the nutrient and cell diffusion coefficients exceeds some critical value, the plane propagating front becomes unstable with respect to transversal perturbations. The instability threshold and the full phase-plane diagram in the parameter space are determined. The results are in a good agreement with experimental findings for the two types of cells.Comment: 4 pages, 4 figure

The Benefits of a More Physically Active Workforce in the Corporate World

With the ever-expanding knowledge of the benefits of physical activity and good general health for all aspects of our lives, it should be quite surprising that activity levels are declining at accelerating rates. After taking a deeper look into the probable cause for this phenomenon, it becomes clearer that the increasing pressures of workplace culture are leading to more sedentary lifestyles. This paper looks at the benefits of physical activity on people and on corporations, specifically workplace disease prevention and wellness programs, to see if there exists a mutualistic relationship between the two. For people, physical activity was consistently found to benefit our sleep quality, risk of disease, mood, productivity, and much more. Within the context of companies, physically active employees were proven to reduce absenteeism, productivity loss, and health care costs. After thorough review of several case studies and academic journals, it appears there is a strong connection between physically active employees and beneficial cost-saving opportunities for corporations. In fact, the average ROI of wellness programs ranges between 5.5 and 6.1 to 1, meaning a company can receive/save $5.5 to$6.1 for every $1 invested into the health of their employees through these programs. More specifically, when investing adequately into wellness programs (about$400/employee), absenteeism and disease management programs were found to save companies an average of $1,432 and$1,632 respectively per employee per year. These findings supports the idea that companies can realize tremendous cost-savings and employees can become healthier at the same time

Management preferences in stage I non-seminomatous germ cell tumours of the testis: an investigation among patients, controls and oncologists.

Increasingly, treatment choices leading to the same survival outcome can be offered to cancer patients (e.g. mastectomy or conservative surgery in early breast cancer). Two approaches available for post-orchidectomy, stage I patients with non-seminomatous germ cell tumours of the testis (NSGCTT), particularly those at high risk of relapse, include immediate adjuvant chemotherapy (two courses) or surveillance, with chemotherapy (typically four courses) given only on relapse. The aim of this study was to investigate which approach patients prefer. Questionnaires were given to newly diagnosed NSGCTT patients, to patients with previous experience of the two options and to non-cancer controls, including specialist testicular tumour oncologists. Participants were asked to choose between immediate chemotherapy, surveillance or for the doctor to decide, at recurrence risk levels ranging from 10% to 90%. Questionnaires were returned by 207 subjects in nine different groups. The risk thresholds at which subjects' management preference changed, within apparently homogeneous groups, varied greatly, although at least one subject in each group selected adjuvant chemotherapy at the lowest (10%) level of risk. Subjects tended to favour options of which they had previous experience. Cancer patients wanted the doctor to decide more frequently than controls. The wide variability observed makes it difficult to predict which option an individual will select. Personality factors and personal circumstances, other than specific experience and knowledge, are obviously influential. Many patients would prefer their doctor to decide, but variability among oncologists is as great as that among their patients

The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerated advancing or retreating plate. Part 1. The principal flow

The free surface and flow field structure generated by the uniform acceleration (with dimensionless acceleration σ) of a rigid plate, inclined at an angle α ∈ (0, π/2) to the exterior horizontal, as it advances (σ > 0) or retreats (σ < 0) from an initially stationary and horizontal strip of inviscid, incompressible fluid under gravity, are studied in the small-time limit via the method of matched asymptotic expansions. This work generalises the case of a uniformly accelerating plate advancing into a fluid as studied in Needham et al. (2008). Particular attention is paid to the innermost asymptotic regions encompassing the initial interaction between the plate and the free surface. We find that the structure of the solution to the governing initial boundary value problem is characterised in terms of the parameters α and μ (where μ = 1+σ tan α), with a bifurcation in structure as μ changes sign. This bifurcation in structure leads us to question the well-posedness and stability of the governing initial boundary value problem with respect to small perturbations in initial data in the innermost asymptotic regions, the discussion of which will be presented in the companion paper Gallagher et al. (2016) . In particular, when (α, μ) ∈ (0, π/2) × R+, the free surface close to the initial contact point remains monotone, and encompasses a swelling jet when (α, μ) ∈ (0, π/2)×[1,∞), or a collapsing jet when (α, μ) ∈ (0, π/2) × (0, 1). However, when (α, μ) ∈ (0, π/2) × R−, the collapsing jet develops a more complex structure, with the free surface close to the initial contact point now developing a finite number of local oscillations, with near resonance type behaviour occurring close to a countable set of critical plate angles α = α∗n ∈ (0, π/2) (n = 1, 2, . . .)

The evolution problem for the 1D nonlocal Fisher-KPP equation with a top hat kernel. Part 1. The Cauchy problem on the real line

We study the Cauchy problem on the real line for the nonlocal Fisher-KPP equation in one spatial dimension, $$u_t = D u_{xx} + u(1-\phi*u),$$ where $\phi*u$ is a spatial convolution with the top hat kernel, $\phi(y) \equiv H\left(\frac{1}{4}-y^2\right)$. After showing that the problem is globally well-posed, we demonstrate that positive, spatially-periodic solutions bifurcate from the spatially-uniform steady state solution $u=1$ as the diffusivity, $D$, decreases through $\Delta_1 \approx 0.00297$. We explicitly construct these spatially-periodic solutions as uniformly-valid asymptotic approximations for $D \ll 1$, over one wavelength, via the method of matched asymptotic expansions. These consist, at leading order, of regularly-spaced, compactly-supported regions with width of $O(1)$ where $u=O(1)$, separated by regions where $u$ is exponentially small at leading order as $D \to 0^+$. From numerical solutions, we find that for $D \geq \Delta_1$, permanent form travelling waves, with minimum wavespeed, $2 \sqrt{D}$, are generated, whilst for $0 < D < \Delta_1$, the wavefronts generated separate the regions where $u=0$ from a region where a steady periodic solution is created. The structure of these transitional travelling waves is examined in some detail

Perioperative donor bone marrow infusion augments chimerism in heart and lung transplant recipients

Background.: We and others have demonstrated that a low level of donor cell chimerism was present for years after transplantation in tissues and peripheral blood of heart and lung recipients; it was associated, in the latter, with a lower incidence of chronic rejection. To augment this phenomenon, we initiated a trial combining simultaneous infusion of donor bone marrow with heart or lung allotransplantation. Methods.: Between September 1993 and January 1995, 15 nonconditioned patients received either heart (n = 10) or lung (n = 5) allografts concurrently with an infusion of unmodified donor bone marrow (3.0 × 108 cells/kg), and were maintained on an immunosuppressive regimen consisting of tacrolimus and steroids. Results.: There was no complication associated with the infusion of donor bone marrow. Chimerism was detectable in 73% of bone marrow-augmented patients up to the last sample tested. Of the 5 control recipients who did not receive bone marrow infusion, only 1 had detectable chimerism by flow on postoperative day 15, which dwindled to an undetectable level by postoperative day 36. None of the patients had evidence of donor-specific immune modulation by mixed lymphocyte reaction. Conclusions.: The combined infusion of donor bone marrow and heart or lung transplantation, without preconditioning of the recipient, is safe and is associated with an augmentation of donor cell chimerism. © 1995 The Society of Thoracic Surgeons