Population balances in case of crossing characteristic curves: Application to T-cells immune response

The progression of a cell population where each individual is characterized by the value of an internal variable varying with time (e.g. size, weight, and protein concentration) is typically modeled by a Population Balance Equation, a first order linear hyperbolic partial differential equation. The characteristics described by internal variables usually vary monotonically with the passage of time. A particular difficulty appears when the characteristic curves exhibit different slopes from each other and therefore cross each other at certain times. In particular such crossing phenomenon occurs during T-cells immune response when the concentrations of protein expressions depend upon each other and also when some global protein (e.g. Interleukin signals) is also involved which is shared by all T-cells. At these crossing points, the linear advection equation is not possible by using the classical way of hyperbolic conservation laws. Therefore, a new Transport Method is introduced in this article which allowed us to find the population density function for such processes. The newly developed Transport method (TM) is shown to work in the case of crossing and to provide a smooth solution at the crossing points in contrast to the classical PDF techniques.Comment: 18 pages, 10 figure

Local metabolic changes in subcutaneous adipose tissue during intravenous and epidural analgesia.

BACKGROUND: This clinical study aimed at investigating the impact of postoperative thoracic epidural analgesia on extracellular glycerol concentration and glucose metabolism in subcutaneous adipose tissue, using the microdialysis technique. The sympathetic nervous activity, which can be attenuated by epidural anesthesia, influences lipolysis and the release of glycerol. METHODS: Fourteen patients who underwent major abdominal or thoraco-abdominal surgery were studied postoperatively over 3 days. For postoperative analgesia the patients were prospectively randomized to receive either thoracic epidural analgesia with a bupivacaine/morphine infusion (EPI-group, n=6) or a continuous i.v. infusion of morphine (MO-group, n=8). The concentration of glycerol, glucose and lactate in the abdominal and deltoid subcutaneous adipose tissue were measured using a microdialysis technique. RESULTS: The abdominal glycerol levels were equal in both groups. In the deltoid region of the EPI-group, glycerol concentrations started to increase on Day 2, and reached significantly higher levels on Day 3 compared with the MO-group. The glucose and lactate levels showed no differences between groups in the two regions. CONCLUSION: The uniform glycerol levels in abdominal subcutaneous adipose tissue in conjunction with the difference in glycerol levels in the deltoid area indicate that the local lipolysis is different in the two study groups. This might be explained by a regional metabolic influence of thoracic epidural analgesia, possibly via the sympathetic nervous system

Conservative vs liberal fluid therapy in septic shock (CLASSIC) trial-Protocol and statistical analysis plan

Introduction Intravenous (IV) fluid is a key intervention in the management of septic shock. The benefits and harms of lower versus higher fluid volumes are unknown and thus clinical equipoise exists. We describe the protocol and detailed statistical analysis plan for the conservative versus liberal approach to fluid therapy of septic shock in the Intensive Care (CLASSIC) trial. The aim of the CLASSIC trial is to assess benefits and harms of IV fluid restriction versus standard care in adult intensive care unit (ICU) patients with septic shock. Methods CLASSIC trial is an investigator-initiated, international, randomised, stratified, and analyst-blinded trial. We will allocate 1554 adult patients with septic shock, who are planned to be or are admitted to an ICU, to IV fluid restriction versus standard care. The primary outcome is mortality at day 90. Secondary outcomes are serious adverse events (SAEs), serious adverse reactions (SARs), days alive at day 90 without life support, days alive and out of the hospital at day 90 and mortality, health-related quality of life (HRQoL), and cognitive function at 1 year. We will conduct the statistical analyses according to a pre-defined statistical analysis plan, including three interim analyses. For the primary analysis, we will use logistic regression adjusted for the stratification variables comparing the two interventions in the intention-to-treat (ITT) population. Discussion The CLASSIC trial results will provide important evidence to guide clinicians' choice regarding the IV fluid therapy in adults with septic shock.Peer reviewe

Minimally invasive surgery and cancer: controversies part 1

Perhaps there is no more important issue in the care of surgical patients than the appropriate use of minimally invasive surgery (MIS) for patients with cancer. Important advances in surgical technique have an impact on early perioperative morbidity, length of hospital stay, pain management, and quality of life issues, as clearly proved with MIS. However, for oncology patients, historically, the most important clinical questions have been answered in the context of prospective randomized trials. Important considerations for MIS and cancer have been addressed, such as what are the important immunologic consequences of MIS versus open surgery and what is the role of laparoscopy in the staging of gastrointestinal cancers? This review article discusses many of the key controversies in the minimally invasive treatment of cancer using the pro–con debate format

Linear Mathematical Models in Chemical Engineering

Understanding the mathematical modeling of chemical processes is fundamental to The successful career of a researcher in chemical engineering. This book reviews, introduces, and develops the mathematics that is most frequently encountered in sophisticated chemical engineering models. The result of a collaboration between a chemical engineer and a mathematician, both of whom have taught classes on modeling and applied mathematics, The book provides a rigorous and in-depth coverage of chemical engineering model formulation and analysis as well as a text which can serve as an excellent introduction to linear mathematics for engineering students. There is a clear focus in the choice of material, worked examples, and exercises that make it unusually accessible to The target audience. The book places a heavy emphasis on applications to motivate the theory, but simultaneously maintains a high standard of rigor to add mathematical depth and understanding.https://repository.lsu.edu/facultybooks/1355/thumbnail.jp

Linear Mathematical Models in Chemical Engineering

Mathematics remains a core area of engineering. Formulating and analyzing mathematical models of basic engineering systems is an essential skill that all engineering students should endeavor to acquire. This book will serve as an excellent introduction to linear mathematics for engineering students, both seniors and graduate students. It is the result of a collaboration between a chemical engineer and a mathematician, both of whom have taught classes on modelling and applied mathematics. It provides a broad collection of chemical engineering modelling examples to train students in model formulation and model simplification as well as give a thorough coverage of the mathematical tools used to analyze and solve linear chemical engineering models. Solution manual is provided for free to instructors who adopt this textbook. Please send your request to [email protected]://repository.lsu.edu/facultybooks/1018/thumbnail.jp

Population balances in biomedical engineering

xi + 182 hlm.; 23.5 c

Population balances in biomedical engineering : segretion through the distribution of cell states

ix,170 pages : illustration ; 24 cm