924 resultados para Potential theory (Mathematics)


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Aims and objectives. To explore the psychosocial needs of patients discharged from intensive care, the extent to which they are captured using existing theory on transitions in care and the potential role development of critical care outreach, follow-up and liaison services. Background. Intensive care patients are at an increased risk of adverse events, deterioration or death following ward transfer. Nurse-led critical care outreach, follow-up or liaison services have been adopted internationally to prevent these potentially avoidable sequelae. The need to provide patients with psychosocial support during the transition to ward-based care has also been identified, but the evidence base for role development is currently limited. Design and methods. Twenty participants were invited to discuss their experiences of ward-based care as part of a broader study on recovery following prolonged critical illness. Psychosocial distress was a prominent feature of their accounts, prompting secondary data analysis using Meleis et al.’s mid-range theory on experiencing transitions. Results. Participants described a sense of disconnection in relation to profound debilitation and dependency and were often distressed by a perceived lack of understanding, indifference or insensitivity among ward staff to their basic care needs. Negotiating the transition between dependence and independence was identified as a significant source of distress following ward transfer. Participants varied in the extent to which they were able to express their needs and negotiate recovery within professionally mediated boundaries. Conclusion. These data provide new insights into the putative origins of the psychosocial distress that patients experience following ward transfer. Relevance to clinical practice. Meleis et al.’s work has resonance in terms of explicating intensive care patients’ experiences of psychosocial distress throughout the transition to general ward–based care, such that the future role development of critical care outreach, follow-up and liaison services may be more theoretically informed.

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HUMOR: OUR VIEW FOR MATHEMATICS TEACHING Our assumptions and context. Process humor and be able to produce is clearly a sign of intelligence, revealing, when done well, complex reasoning. Humor has an important social role, assuming as a cognitive experience that as well as creating a sense of well-being, predisposes people to work and can improve the productivity of that work. Mathematics is a discipline in which the reasoning occupies a very prominent place, both as a science as a school area. At the same time, students' interest for mathematics is not always the same and some have initially not very favorable feelings (Toh, 2009; Wanzer, Frymier & Irwin, 2010). Recent curriculum changes to the teaching of mathematics have been, in most countries of the world, showing the need for students to develop skills of critical nature, such as communication, thinking and problem solving along with the acquisition of mathematical knowledge. Also in Portugal, it is claimed the importance of promoting learning that combine the construction of mathematical knowledge with its use, when performing mathematical tasks and communicating mathematical ideas and mathematical reasoning. In the early years of schooling, corresponding to primary education in many countries, the use of texts such as short stories or comics, from which we can develop challenging mathematical tasks, is reported in the literature as having potential to promote learning specified in curricular documents (Wanzer, Frymier., & Irwin, 2010). In particular, some texts focus on mathematical topics in a humorous way and to be understood, students must develop their mathematical competence. The development of mathematical tasks from stories and other humorous presents big challenges to teachers (Flores & Moreno, 2011). Our questions. In this context, we put some questions: Primary teachers use in their classes tasks or situations that present, in a humorous way, mathematical ideas? What resources do they use? Also: How to select, adapt or build texts and tasks which have, in a humorous way, mathematical ideas with didactic potential for education in the early years of schooling? If the resources for this purpose have been produced and if teachers have been sensitized for their use, are they able to integrate them in their classes? Our intentions. This research project seeks to address these questions, focused on: (i ) assessment of teachers’ practices and underlying knowledge, resources available for the use of texts with mathematical ideas presented in a humorous way; (ii) selection, adaptation and construction of mathematical tasks from texts that present, in a humorous way, mathematical ideas with didactic potential in education for the early years of schooling; and ( iii ) integration and use, by primary school teachers, of texts that present , in a humorous way, contexts for the teaching of mathematics. So, the project is organized into three tasks and as a methodological design that combines qualitative elements with quantitative elements, the first one prevailing.

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In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as ``stoquastic'' or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above. I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically. Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing ``Fundamental Gap Conjecture''.

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Over the last decade, a new idea challenging the classical self-non-self viewpoint has become popular amongst immunologists. It is called the Danger Theory. In this conceptual paper, we look at this theory from the perspective of Artificial Immune System practitioners. An overview of the Danger Theory is presented with particular emphasis on analogies in the Artificial Immune Systems world. A number of potential application areas are then used to provide a framing for a critical assessment of the concept, and its relevance for Artificial Immune Systems.

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Over the last decade, a new idea challenging the classical self-non-self viewpoint has become popular amongst immunologists. It is called the Danger Theory. In this conceptual paper, we look at this theory from the perspective of Artificial Immune System practitioners. An overview of the Danger Theory is presented with particular emphasis on analogies in the Artificial Immune Systems world. A number of potential application areas are then used to provide a framing for a critical assessment of the concept, and its relevance for Artificial Immune Systems. Notes: Uwe Aickelin, Department of Computing, University of Bradford, Bradford, BD7 1DP

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As climate change continues to impact socio-ecological systems, tools that assist conservation managers to understand vulnerability and target adaptations are essential. Quantitative assessments of vulnerability are rare because available frameworks are complex and lack guidance for dealing with data limitations and integrating across scales and disciplines. This paper describes a semi-quantitative method for assessing vulnerability to climate change that integrates socio-ecological factors to address management objectives and support decision-making. The method applies a framework first adopted by the Intergovernmental Panel on Climate Change and uses a structured 10-step process. The scores for each framework element are normalized and multiplied to produce a vulnerability score and then the assessed components are ranked from high to low vulnerability. Sensitivity analyses determine which indicators most influence the analysis and the resultant decision-making process so data quality for these indicators can be reviewed to increase robustness. Prioritisation of components for conservation considers other economic, social and cultural values with vulnerability rankings to target actions that reduce vulnerability to climate change by decreasing exposure or sensitivity and/or increasing adaptive capacity. This framework provides practical decision-support and has been applied to marine ecosystems and fisheries, with two case applications provided as examples: (1) food security in Pacific Island nations under climate-driven fish declines, and (2) fisheries in the Gulf of Carpentaria, northern Australia. The step-wise process outlined here is broadly applicable and can be undertaken with minimal resources using existing data, thereby having great potential to inform adaptive natural resource management in diverse locations.

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Background: Depression is a major health problem worldwide and the majority of patients presenting with depressive symptoms are managed in primary care. Current approaches for assessing depressive symptoms in primary care are not accurate in predicting future clinical outcomes, which may potentially lead to over or under treatment. The Allostatic Load (AL) theory suggests that by measuring multi-system biomarker levels as a proxy of measuring multi-system physiological dysregulation, it is possible to identify individuals at risk of having adverse health outcomes at a prodromal stage. Allostatic Index (AI) score, calculated by applying statistical formulations to different multi-system biomarkers, have been associated with depressive symptoms. Aims and Objectives: To test the hypothesis, that a combination of allostatic load (AL) biomarkers will form a predictive algorithm in defining clinically meaningful outcomes in a population of patients presenting with depressive symptoms. The key objectives were: 1. To explore the relationship between various allostatic load biomarkers and prevalence of depressive symptoms in patients, especially in patients diagnosed with three common cardiometabolic diseases (Coronary Heart Disease (CHD), Diabetes and Stroke). 2 To explore whether allostatic load biomarkers predict clinical outcomes in patients with depressive symptoms, especially in patients with three common cardiometabolic diseases (CHD, Diabetes and Stroke). 3 To develop a predictive tool to identify individuals with depressive symptoms at highest risk of adverse clinical outcomes. Methods: Datasets used: ‘DepChron’ was a dataset of 35,537 patients with existing cardiometabolic disease collected as a part of routine clinical practice. ‘Psobid’ was a research data source containing health related information from 666 participants recruited from the general population. The clinical outcomes for 3 both datasets were studied using electronic data linkage to hospital and mortality health records, undertaken by Information Services Division, Scotland. Cross-sectional associations between allostatic load biomarkers calculated at baseline, with clinical severity of depression assessed by a symptom score, were assessed using logistic and linear regression models in both datasets. Cox’s proportional hazards survival analysis models were used to assess the relationship of allostatic load biomarkers at baseline and the risk of adverse physical health outcomes at follow-up, in patients with depressive symptoms. The possibility of interaction between depressive symptoms and allostatic load biomarkers in risk prediction of adverse clinical outcomes was studied using the analysis of variance (ANOVA) test. Finally, the value of constructing a risk scoring scale using patient demographics and allostatic load biomarkers for predicting adverse outcomes in depressed patients was investigated using clinical risk prediction modelling and Area Under Curve (AUC) statistics. Key Results: Literature Review Findings. The literature review showed that twelve blood based peripheral biomarkers were statistically significant in predicting six different clinical outcomes in participants with depressive symptoms. Outcomes related to both mental health (depressive symptoms) and physical health were statistically associated with pre-treatment levels of peripheral biomarkers; however only two studies investigated outcomes related to physical health. Cross-sectional Analysis Findings: In DepChron, dysregulation of individual allostatic biomarkers (mainly cardiometabolic) were found to have a non-linear association with increased probability of co-morbid depressive symptoms (as assessed by Hospital Anxiety and Depression Score HADS-D≥8). A composite AI score constructed using five biomarkers did not lead to any improvement in the observed strength of the association. In Psobid, BMI was found to have a significant cross-sectional association with the probability of depressive symptoms (assessed by General Health Questionnaire GHQ-28≥5). BMI, triglycerides, highly sensitive C - reactive 4 protein (CRP) and High Density Lipoprotein-HDL cholesterol were found to have a significant cross-sectional relationship with the continuous measure of GHQ-28. A composite AI score constructed using 12 biomarkers did not show a significant association with depressive symptoms among Psobid participants. Longitudinal Analysis Findings: In DepChron, three clinical outcomes were studied over four years: all-cause death, all-cause hospital admissions and composite major adverse cardiovascular outcome-MACE (cardiovascular death or admission due to MI/stroke/HF). Presence of depressive symptoms and composite AI score calculated using mainly peripheral cardiometabolic biomarkers was found to have a significant association with all three clinical outcomes over the following four years in DepChron patients. There was no evidence of an interaction between AI score and presence of depressive symptoms in risk prediction of any of the three clinical outcomes. There was a statistically significant interaction noted between SBP and depressive symptoms in risk prediction of major adverse cardiovascular outcome, and also between HbA1c and depressive symptoms in risk prediction of all-cause mortality for patients with diabetes. In Psobid, depressive symptoms (assessed by GHQ-28≥5) did not have a statistically significant association with any of the four outcomes under study at seven years: all cause death, all cause hospital admission, MACE and incidence of new cancer. A composite AI score at baseline had a significant association with the risk of MACE at seven years, after adjusting for confounders. A continuous measure of IL-6 observed at baseline had a significant association with the risk of three clinical outcomes- all-cause mortality, all-cause hospital admissions and major adverse cardiovascular event. Raised total cholesterol at baseline was associated with lower risk of all-cause death at seven years while raised waist hip ratio- WHR at baseline was associated with higher risk of MACE at seven years among Psobid participants. There was no significant interaction between depressive symptoms and peripheral biomarkers (individual or combined) in risk prediction of any of the four clinical outcomes under consideration. Risk Scoring System Development: In the DepChron cohort, a scoring system was constructed based on eight baseline demographic and clinical variables to predict the risk of MACE over four years. The AUC value for the risk scoring system was modest at 56.7% (95% CI 55.6 to 57.5%). In Psobid, it was not possible to perform this analysis due to the low event rate observed for the clinical outcomes. Conclusion: Individual peripheral biomarkers were found to have a cross-sectional association with depressive symptoms both in patients with cardiometabolic disease and middle-aged participants recruited from the general population. AI score calculated with different statistical formulations was of no greater benefit in predicting concurrent depressive symptoms or clinical outcomes at follow-up, over and above its individual constituent biomarkers, in either patient cohort. SBP had a significant interaction with depressive symptoms in predicting cardiovascular events in patients with cardiometabolic disease; HbA1c had a significant interaction with depressive symptoms in predicting all-cause mortality in patients with diabetes. Peripheral biomarkers may have a role in predicting clinical outcomes in patients with depressive symptoms, especially for those with existing cardiometabolic disease, and this merits further investigation.

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The aim of this study is to investigate the effectiveness of problem-based learning (PBL) on students’ mathematical performance. This includes mathematics achievement and students’ attitudes towards mathematics for third and eighth grade students in Saudi Arabia. Mathematics achievement includes, knowing, applying, and reasoning domains, while students’ attitudes towards mathematics covers, ‘Like learning mathematics’, ‘value mathematics’, and ‘a confidence to learn mathematics’. This study goes deeper to examine the interaction of a PBL teaching strategy, with trained face-to-face and self-directed learning teachers, on students’ performance (mathematics achievement and attitudes towards mathematics). It also examines the interaction between different ability levels of students (high and low levels) with a PBL teaching strategy (with trained face-to-face or self-directed learning teachers) on students’ performance. It draws upon findings and techniques of the TIMSS international benchmarking studies. Mixed methods are used to analyse the quasi-experimental study data. One -way ANOVA, Mixed ANOVA, and paired t-tests models are used to analyse quantitative data, while a semi-structured interview with teachers, and author’s observations are used to enrich understanding of PBL and mathematical performance. The findings show that the PBL teaching strategy significantly improves students’ knowledge application, and is better than the traditional teaching methods among third grade students. This improvement, however, occurred only with the trained face-to-face teacher’s group. Furthermore, there is robust evidence that using a PBL teaching strategy could raise significantly students’ liking of learning mathematics, and confidence to learn mathematics, more than traditional teaching methods among third grade students. Howe ver, there was no evidence that PBL could improve students’ performance (mathematics achievement and attitudes towards mathematics), more than traditional teaching methods, among eighth grade students. In 8th grade, the findings for low achieving students show significant improvement compared to high achieving students, whether PBL is applied or not. However, for 3th grade students, no significant difference in mathematical achievement between high and low achieving students was found. The results were not expected for high achieving students and this is also discussed. The implications of these findings for mathematics education in Saudi Arabia are considered.

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Selon la théorie de l’auto-détermination, l’autonomie est un besoin universel de base qui, lorsque soutenu, permet aux individus de mieux fonctionner et de vivre plus de bien-être psychologique (p. ex., Deci & Ryan, 2008). Le style parental des parents qui soutiennent l’autonomie de leur enfant est caractérisé par le soutien du fonctionnement autodéterminé de ce dernier. Sa définition traditionnelle inclut des pratiques telles qu’offrir des explications et des choix lors des requêtes, communiquer de l’empathie, et encourager les prises d’initiatives tout en minimisant l’utilisation d’un langage contrôlant (p. ex., Soenens et al., 2007). Les bénéfices d’un style parental qui soutient l’autonomie d’un enfant ont été bien documentés (p. ex., Grolnick, Deci, & Ryan, 1997), toutefois, peu d’études ont été effectuées auprès des bambins. Or, cette thèse visait à enrichir la littérature sur le « parentage » en explorant les pratiques soutenantes qui sont utilisées par des parents de bambins dans un contexte de socialisation (étude 1), ainsi qu’en examinant les facteurs qui peuvent brimer leur mise en pratique (étude 2). La première étude a examiné un grand nombre de pratiques de socialisation que les parents qui favorisent davantage le soutien à l’autonomie (SA) pourraient utiliser plus fréquemment lorsqu’ils font des demandes à leurs bambins. Cette étude nous a permis d’explorer comment les parents manifestent leur SA et si le SA dans ce type de contexte est associé à un plus grand niveau d’internalisation des règles. Des parents (N = 182) de bambins (M âge = 27.08 mois) ont donc été invités à rapporter la fréquence avec laquelle ils utilisent 26 pratiques potentiellement soutenantes lorsqu’ils demandent à leurs bambins de compléter des tâches importantes mais non intéressantes et de rapporter à quel point ils valorisent le SA. Huit pratiques ont été identifiées comme étant soutenantes: quatre façons de communiquer de l’empathie, donner des explications courtes, expliquer pourquoi la tâche est importante, décrire le problème de façon informative et neutre, et mettre en pratique le comportement désiré soi-même. De plus, l’ensemble des huit pratiques corrélait positivement avec le niveau d’internalisation des bambins, suggérant aussi que celles-ci représentent bien le concept du SA. Des études futures pourraient tenter de répliquer ces résultats dans des contextes potentiellement plus chargés ou ébranlants (p. ex., réagir face à des méfaits, avec des enfants souffrant de retard de développement). La deuxième étude a poursuivi l’exploration du concept du SA parental en examinant les facteurs qui influencent la fréquence d’utilisation des stratégies soutenantes dans des contextes de socialisation. Puisque la littérature suggère que le stress parental et le tempérament difficile des bambins (c.-à-d., plus haut niveau d’affectivité négative, plus faible niveau de contrôle volontaire/autorégulation, plus faible niveau de surgency) comme étant des facteurs de risque potentiels, nous avons exploré de quelle façon ces variables étaient associées à la fréquence d’utilisation des stratégies soutenantes. Les buts de l’étude étaient: (1) d’examiner comment le tempérament des bambins et le stress parental influençaient le SA parental, et (2) de vérifier si le stress parental médiait la relation possible entre le tempérament des bambins et le SA parental. Le même échantillon de parents a été utilisé. Les parents ont été invités à répondre à des questions portant sur le tempérament de leur enfant ainsi que sur leur niveau de stress. Les résultats ont démontré qu’un plus grand niveau d’affectivité négative était associé à un plus grand niveau de stress parental, qui à son tour prédisait moins de SA parental. De plus, le stress parental médiait la relation positive entre l’autorégulation du bambin et le SA parental. Des recherches futures pourraient évaluer des interventions ayant pour but d’aider les parents à préserver leur attitude soutenante durant des contextes de socialisation plus difficiles malgré certaines caractéristiques tempéramentales exigeantes des bambins, en plus du stress qu’ils pourraient vivre au quotidien.

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Using the one-loop Coleman-Weinberg effective potential, we derive a general analytic expression for all the derivatives of the effective potential with respect to any number of classical scalar fields. The result is valid for a renormalisable theory in four dimensions with any number of scalars, fermions or gauge bosons. This result corresponds to the zero-external momentum contribution to a general one-loop diagram with N scalar external legs. We illustrate the use of the general result in two simple scalar singlet extensions of the Standard Model, to obtain the dominant contributions to the triple couplings of light scalar particles under the zero external momentum approximation.

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We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture medium is driven. We employ a multiphase formulation of the type presented by G. Lemon, J. King, H. Byrne, O. Jensen and K. Shakesheff in their study (Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol. 52(2), 2006, 571–594) restricted to two interacting fluid phases, representing a cell population (and attendant extracellular matrix) and a culture medium, and employ the simplifying limit of large interphase viscous drag after S. Franks in her study (Mathematical Modelling of Tumour Growth and Stability. Ph.D. Thesis, University of Nottingham, UK, 2002) and S. Franks and J. King in their study Interactions between a uniformly proliferating tumour and its surrounding: Uniform material properties. Math. Med. Biol. 20, 2003, 47–89). The novel aspects of this study are: (i) the investigation of the effect of an imposed flow on the growth of the tissue construct, and (ii) the inclusion of a chanotransduction mechanism regulating the response of the cells to the local mechanical environment. Specifically, we consider the response of the cells to their local density and the culture medium pressure. As such, this study forms the first step towards a general multiphase formulation that incorporates the effect of mechanotransduction on the growth and morphology of a tissue construct. The model is analysed using analytic and numerical techniques, the results of which illustrate the potential use of the model to predict the dominant regulatory stimuli in a cell population.

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Landscape is interpreted as the creation of a cultural expression through human ideology and representing a living heritage. Since landscapes are continually evolving, it arouses challenges for sustainability in preserving significant cultural landscape which rested in evolving and transitional world. Kinta Valley former mining landscape can be described as ‘relic landscape’ and this landscape type is one of the sub category under organically evolved cultural landscape (or vernacular landscape) as incorporated in UNESCO Operational Guidelines [18:8]. The main contribution of this paper lies within the gap of knowledge and practise of cultural landscape conservation in Malaysia emphasizing on the cultural values embedded within the heritage mining landscape of Kinta Valley of Perak State, Malaysia. Concerning to the significance heritage values that lies within the Kinta Valley former mining landscape through the lens of cultural landscape theory and practice, this paper highlights on the potential and challenges faced by the Perak state government in establishing mining cultural landscape conservation which can be incorporated within the state and districts planning gazetted documents. Palang & Fry [15] remark that the interface between culture and landscape is very important to understand as it will lead to interpretations of future and current issues of past landscape developments and interventions. United Nations [17] emphasize that sustainable cultural landscape composing of ‘socially, economically and environmentally durable’ and therefore preserving the heritage mining landscape will unravel and unveil the valley sustainability. In addition, qualifying the cultural landscape significance crafted by past tin mining activities in Kinta Valley has resulted in the establishment of heritage values of state and national significance. Therefore potential and challenges of preserving this heritage landscape will be disclose and thereupon embellish the Malaysian culture heritage in general especially in enduring Perak State culture heritage and sustainability.

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This chapter argues that theories about privacy would benefit from embracing deliberative democratic theory on the grounds that it addresses harms to democracy, and widens our understandings of privacy infringements in social networking environments. We fi rst explore how social networking services (SNS) have evolved through diff erent phases and how they enable political deliberation. Subsequently, we discuss more traditional individualistic and intersubjective theories of privacy in relation to social networking and point out their limitations in identifying and redressing social networking-related harms. We then critique emerging claims concerning the social value of privacy in the context of the social Web. Here we point out how these theories might identify non-individualized harms, yet, at the same time, suff er important challenges in application. We conclude by arguing that deliberative democratic theory can add some critical insights into the privacy harms encountered on the contemporary “social Web” that are only imperfectly understood by individualistic and social conceptions of privacy

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The Mathematics Teacher Education Collective (MTEC) — a self-study group based at the University of British Columbia, Canada — collaborates to enhance our pedagogical practice in mathematics teacher education through analysing, constructing, and reflecting on variations to assessment tasks. The theoretical framework underlying the establishment of the MTEC is based on Lave and Wenger’s (1991) view of learning through a Community of Practice (CoP). “Communities of practice are groups of people who share a concern or a passion for something they do and learn how to do it better as they interact regularly” (Wenger-Trayner, 2011, http://wenger-trayner.com/theory/). Three characteristics are viewed as crucial to the CoP: domain, community, and practice. The shared domain for MTEC is a commitment to gaining a deeper understanding of practice as mathematics teacher educators. In particular, as members we are interested in better understanding the role and development of tasks for learning to teach mathematics. As a community MTEC engages “in joint activities and discussions, [that] help each other, and share information” (Wenger-Trayner, 2011, http://wenger-trayner.com/theory/), with the goal to build relationships that provide members with opportunities to learn from one other. MTEC members are practitioners in the field. The success of the MTEC is based on the sharing, evaluation and critical reflection of assessment tasks and pedagogical approaches refined by the CoP.

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The use of human mesenchymal stem cells (hMSCs) in regenerative medicine is a potential major advance for the treatment of many medical conditions, especially with the use of allogeneic therapies where the cells from a single donor can be used to treat ailments in many patients. Such cells must be grown attached to surfaces and for large scale production, it is shown that stirred bioreactors containing ~200 μm particles (microcarriers) can provide such a surface. It is also shown that the just suspended condition, agitator speed NJS, provides a satisfactory condition for cell growth by minimizing the specific energy dissipation rate, εT, in the bioreactor whilst still meeting the oxygen demand of the cells. For the cells to be used for therapeutic purposes, they must be detached from the microcarriers before being cryopreserved. A strategy based on a short period (~7 min) of very high εT, based on theories of secondary nucleation, is effective at removing >99% cells. Once removed, the cells are smaller than the Kolmogorov scale of turbulence and hence not damaged. This approach is shown to be successful for culture and detachment in 4 types of stirred bioreactors from 15 mL to 5 L.