Supersolutions for a class of semilinear heat equations

A semilinear heat equation $u_{t}=\Delta u+f(u)$ with nonnegative initial data in a subset of $L^{1}(\Omega)$ is considered under the assumption that $f$ is nonnegative and nondecreasing and $\Omega\subseteq \R^{n}$. A simple technique for proving existence and regularity based on the existence of supersolutions is presented, then a method of construction of local and global supersolutions is proposed. This approach is applied to the model case $f(s)=s^{p}$, $\phi\in L^{q}(\Omega)$: new sufficient conditions for the existence of local and global classical solutions are derived in the critical and subcritical range of parameters. Some possible generalisations of the method to a broader class of equations are discussed.Comment: Expanded version of the previous submission arXiv:1111.0258v1. 14 page

Mononuclear Cells From Human Lung Parenchyma Support Antigen‐Induced T Lymphocyte Proliferation

We have previously demonstrated that there is a subpopulation of loosely adherent pulmonary mononuclear cells that can be isolated from minced and enzyme‐digested lung tissue with a potent capacity to stimulate allogeneic T lymphocyte proliferation. We now demonstrate that these cells are also capable of stimulating an autologous mixed leukocyte reaction (AMLR) and presenting antigen to autologous T lymphocytes. These loosely adherent mononuclear cells (LAM) were more effective than either alveolar macrophages or monocytes as antigen‐presenting cells. Depletion of phagocytic or Fc receptor‐positive cells from the LAM population enhanced the stimulation of an reaction AMLR while preserving antigen‐induced T lymphocyte proliferation. These results indicate that there are nonphagocytic, Fc receptor‐negative accessory cells in human lung parenchyma capable of activating resting T cells in an AMLR and supporting antigen‐specific T lymphocyte proliferation. The identity of these cells is uncertain, but the data strongly suggest that the cell is not a classical monocyte‐derived macrophage. These antigen‐presenting cells may be critical in the initiation of immune responses within the lung.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141257/1/jlb0336.pd

Separation of Potent and Poorly Functional Human Lung Accessory Cells Based on Autofluorescence

Human alveolar macrophages obtained by bronchoalveolar lavage are usually poor accessory cells in in vitro lymphoprollferation assays. However, we recently described a subpopulation of pulmonary mononuclear cells, obtained from minced and enzyme‐digested lung, which were potent stimulators of allogeneic T‐lymphocyte proliferation. These cells were enriched in loosely adherent mononuclear cell (LAM) fractions, but further study of these accessory cells was hampered by the heterogeneous nature of LAM. It was observed that in the majority of lung tissue sections, most alveolar macrophages were autofluorescent, whereas most interstitial HLA‐DR positive cells were not. Therefore autofluorescence was utilized to fractionate LAM in an attempt to remove alveolar macrophages and selectively purify interstitial accessory cells. LAM were separated by flow cytometry using forward and side scatter to exclude lymphocytes, and red autofluorescence to obtain brightly autofluorescent (A pos) and relatively nonautofluorescent (A neg) mononuclear cells. Although both populations contained over 80% HLA‐DR positive cells, A pos cells were poor accessory cells, whereas A neg cells were extremely potent stimulators of a mixed leukocyte reaction at all stimulator ratios tested. When A pos cells were added to A neg cells, T‐cell proliferation was markedly suppressed in the majority of experiments. Morphologically, A pos cells appeared similar to classical alveolar macrophages with 95% of the cells being large and intensely nonspecific esterase positive. In contrast, the majority of A neg were smaller, B‐cell antigen‐negative, nonspecific esterase negative, and had a distinctive morphology on Wright‐stained smears. We conclude that fractionation of LAM based on autofluorescence is a powerful tool to isolate and characterize lung mononuclear cells that act either as stimulators or as suppressors of immune responses in the lung.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141667/1/jlb0458.pd

A particle system with explosions: law of large numbers for the density of particles and the blow-up time

Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for diffusion/creation/annihilation of particles, we obtain a stong law of large numbers for the density of particles in the supremum norm. The limiting object is a classical solution to the semilinear heat equation u_t =u_{xx} + f(u). If f(u)=u^p, 1<p \le 3, we also obtain a law of large numbers for the explosion time

A note on maximal estimates for stochastic convolutions

In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces.Comment: Minor correction

Previous tonsillectomy modifies odds of tonsil and base of tongue cancer

BACKGROUND: Tonsillectomy is a commonly performed surgical procedure that involves removal of the palatine tonsils. The purpose of this study is to examine the association between previous tonsillectomy and odds of oropharyngeal squamous cell carcinoma (OPSCC) in a large population-based case-control study. We hypothesise that previous tonsillectomy is associated with a decreased odds of tonsil cancer with no impact on the odds of developing base of tongue (BOT) cancer. METHODS: This was a population-based, frequency-matched case-control study with multinomial logistic regression, including 1378 controls, 108 BOT cancer cases, and 198 tonsil cancer cases. Demographic and risk factor data were collected using a structured questionnaire during an in-home visit conducted by trained nurse-interviewers. The human papillomavirus (HPV) tumour status was determined through Luminex-based multiplex PCR and p16 status by immunohistochemistry. RESULTS: Previous tonsillectomy was associated with a nearly two-fold increased odds of BOT cancer (OR=1.95, 95% CI 1.25-3.06, P=0.003) and a large decrease in the odds of tonsil cancer (OR=0.22, 95% CI 0.13-0.36, P<0.001). When HPV status was considered, tonsillectomy was associated with a decreased odds of HPV-positive tonsil cancer (OR=0.17, 95% CI 0.08-0.34, P<0.001) and an increased risk of HPV-positive BOT cancer (OR=2.46, 95% CI 1.22-4.95, P=0.012). When p16 status was considered, tonsillectomy was associated with an increased odds of p16-positive BOT cancer (OR=2.24, 95% CI 1.16-4.35, P=0.017) and a decreased odds of p16-positive tonsil cancer (OR=0.14, 95% CI 0.07-0.31, P<0.001). CONCLUSIONS: Previous tonsillectomy modifies the odds of both tonsil and BOT cancer, with decreased odds of tonsil cancer and increased odds of BOT cancer. A history of previous tonsillectomy may play a role in OPSCC risk stratification when considered along with other covariates such as sexual history, smoking status, and age

PET performance evaluation of a pre-clinical SiPM-Based MR-Compatible PET Scanner

We have carried out a PET performance evaluation a silicon photo-multiplier (SiPM) based PET scanner designed for fully simultaneous pre-clinical PET/MR studies. The PET scanner has an inner diameter of 20 cm with an LYSO crystal size of 1.3 by 1.3 by 10 mm. The axial PET field of view (FOV) is 30.2 mm. The PET detector modules, which incorporate SiPMs, have been designed to be MR-compatible allowing them to be located directly within a Philips Achieva 3T MR scanner. The spatial resolution of the system measured using a point source in a non-active background, is just under 2.3 mm full width at half maximum (FWHM) in the transaxial direction when single slice rebinning (SSRB) and 2D filtered back-projection (FBP) is used for reconstruction, and 1.3 mm FWHM when resolution modeling is employed. The system sensitivity is 0.6% for a point source at the center of the FOV. The true coincidence count rate shows no sign of saturating at 30 MBq, at which point the randoms fraction is 8.2%, and the scatter fraction for a rat sized object is approximately 23%. Artifact-free images of phantoms have been obtained using FBP and iterative reconstructions. The performance is currently limited because only one of three axial ring positions is populated with detectors, and due to limitations of the first-generation detector readout ASIC used in the system. The performance of the system as described is sufficient for simultaneous PET-MR imaging of rat-sized animals and large organs within the mouse. This is demonstrated with dynamic PET and MR data acquired simultaneously from a mouse injected with a dual-labeled PET/MR probe

Hospitalists in Teaching Hospitals: Opportunities but Not Without Danger

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73210/1/j.1525-1497.2004.42002.x.pd

Oral health and human papillomavirus-associated head and neck squamous cell carcinoma

BACKGROUND: Indicators of poor oral health, including smoking, have been associated with increased risk of head and neck squamous cell carcinoma, especially oropharyngeal squamous cell carcinoma (OPSCC), yet few studies have examined whether this association is modified by human papillomavirus (HPV) status. METHODS: Data from interviews and tumor HPV status from a large population-based case-control study, the Carolina Head and Neck Cancer Study (CHANCE), were used to estimate the association between oral health indicators and smoking among 102 HPV-positive patients and 145 HPV-negative patients with OPSCC and 1396 controls. HPV status was determined by p16INK4a (p16) immunohistochemistry. Unconditional, multinomial logistic regression was used to estimate odds ratios (ORs) for all oral health indictors adjusting for important covariates. RESULTS: Routine dental examinations were associated with a decreased risk of both HPV-negative OPSCC (OR, 0.52; 95% confidence interval [CI], 0.35-0.76) and HPV-positive OPSCC (OR, 0.55; 95% CI, 0.36-.86). Tooth mobility (a proxy for periodontal disease) increased the risk of HPV-negative disease (OR, 1.70; 95% CI, 1.18-2.43) slightly more than the risk for HPV-positive disease (OR, 1.45; 95% CI, 0.95-2.20). Ten or more pack-years of cigarette smoking were strongly associated with an increased risk of HPV-negative OPSCC (OR, 4.26; 95% CI, 2.85-6.37) and were associated less with an increased risk of HPV-positive OPSCC (OR, 1.62; 95% CI, 1.10-2.38). CONCLUSIONS: Although HPV-positive and HPV-negative HNSCC differ significantly with respect to etiology and tumorigenesis, the current findings suggest a similar pattern of association between poor oral health, frequency of dental examinations, and both HPV-positive and HPV-negative OPSCC. Future research is required to elucidate interactions between poor oral health, tobacco use, and HPV in the development of OPSCC. Cancer 2017;71–80. © 2016 American Cancer Society

Elderly Patients With Squamous Cell Carcinoma of the Head and Neck and the Benefit of Multimodality Therapy

Limited data are available regarding outcomes in elderly head and neck cancer patients. This retrospective study was designed to characterize head and neck cancer in geriatric patients