Lifelong dynamics of human CD4+CD25+ regulatory T cells: insights from in vivo data and mathematical modeling.

Despite their limited proliferation capacity, regulatory T cells (T(regs)) constitute a population maintained over the entire lifetime of a human organism. The means by which T(regs) sustain a stable pool in vivo are controversial. Using a mathematical model, we address this issue by evaluating several biological scenarios of the origins and the proliferation capacity of two subsets of T(regs): precursor CD4(+)CD25(+)CD45RO(-) and mature CD4(+)CD25(+)CD45RO(+) cells. The lifelong dynamics of T(regs) are described by a set of ordinary differential equations, driven by a stochastic process representing the major immune reactions involving these cells. The model dynamics are validated using data from human donors of different ages. Analysis of the data led to the identification of two properties of the dynamics: (1) the equilibrium in the CD4(+)CD25(+)FoxP3(+)T(regs) population is maintained over both precursor and mature T(regs) pools together, and (2) the ratio between precursor and mature T(regs) is inverted in the early years of adulthood. Then, using the model, we identified three biologically relevant scenarios that have the above properties: (1) the unique source of mature T(regs) is the antigen-driven differentiation of precursors that acquire the mature profile in the periphery and the proliferation of T(regs) is essential for the development and the maintenance of the pool; there exist other sources of mature T(regs), such as (2) a homeostatic density-dependent regulation or (3) thymus- or effector-derived T(regs), and in both cases, antigen-induced proliferation is not necessary for the development of a stable pool of T(regs). This is the first time that a mathematical model built to describe the in vivo dynamics of regulatory T cells is validated using human data. The application of this model provides an invaluable tool in estimating the amount of regulatory T cells as a function of time in the blood of patients that received a solid organ transplant or are suffering from an autoimmune disease.

Case studies and mathematical models of ecological speciation. 1. Cichlids in a crater lake.

A recent study of a pair of sympatric species of cichlids in Lake Apoyo in Nicaragua is viewed as providing probably one of the most convincing examples of sympatric speciation to date. Here, we describe and study a stochastic, individual-based, explicit genetic model tailored for this cichlid system. Our results show that relatively rapid (<20,000 generations) colonization of a new ecological niche and (sympatric or parapatric) speciation via local adaptation and divergence in habitat and mating preferences are theoretically plausible if: (i) the number of loci underlying the traits controlling local adaptation, and habitat and mating preferences is small; (ii) the strength of selection for local adaptation is intermediate; (iii) the carrying capacity of the population is intermediate; and (iv) the effects of the loci influencing nonrandom mating are strong. We discuss patterns and timescales of ecological speciation identified by our model, and we highlight important parameters and features that need to be studied empirically to provide information that can be used to improve the biological realism and power of mathematical models of ecological speciation.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Segmentation and grid generation for numerical simulations of vad connections with patient-specific data

Objectives: We are interested in the numerical simulation of the anastomotic region comprised between outflow canula of LVAD and the aorta. Segmenta¬tion, geometry reconstruction and grid generation from patient-specific data remain an issue because of the variable quality of DICOM images, in particular CT-scan (e.g. metallic noise of the device, non-aortic contrast phase). We pro¬pose a general framework to overcome this problem and create suitable grids for numerical simulations.Methods: Preliminary treatment of images is performed by reducing the level window and enhancing the contrast of the greyscale image using contrast-limited adaptive histogram equalization. A gradient anisotropic diffusion filter is applied to reduce the noise. Then, watershed segmentation algorithms and mathematical morphology filters allow reconstructing the patient geometry. This is done using the InsightToolKit library (www.itk.org). Finally the Vascular Model¬ing ToolKit (www.vmtk.org) and gmsh (www.geuz.org/gmsh) are used to create the meshes for the fluid (blood) and structure (arterial wall, outflow canula) and to a priori identify the boundary layers. The method is tested on five different patients with left ventricular assistance and who underwent a CT-scan exam.Results: This method produced good results in four patients. The anastomosis area is recovered and the generated grids are suitable for numerical simulations. In one patient the method failed to produce a good segmentation because of the small dimension of the aortic arch with respect to the image resolution.Conclusions: The described framework allows the use of data that could not be otherwise segmented by standard automatic segmentation tools. In particular the computational grids that have been generated are suitable for simulations that take into account fluid-structure interactions. Finally the presented method features a good reproducibility and fast application.

Mastectomy, body deconstruction, and impact on identity: a qualitative study.

Objectives This qualitative study aims at understanding the consequences of body deconstruction through mastectomy on corporality and identity in women with breast cancer. Design Nineteen women were contacted through the hospital. All had to undergo mastectomy. Some were offered immediate breast reconstruction, others, because of cancer treatments, had no planned reconstruction. A qualitative reflexive methodological background was chosen. Method Women were invited to participate in three semi-structured interviews, one shortly before or after mastectomy, and the other interviews later in their illness courses, after surgery. All interviews were transcribed verbatim. Thematic analysis was performed. The analysis of the first interview of each woman is presented in this article. Results Mastectomy provokes a painful experience of body deconstruction. Even when immediate reconstruction is proposed, contrasted feelings and dissonance are expressed when comparing the former healthy body to the present challenged body entity. Body transformations are accompanied with experiences of mutilation, strangeness, and modify the physical, emotional social, symbolic and relational dimensions of the woman's gendered identity. Although the opportunity of breast reconstruction is seen as a possible recovery of a lost physical symmetry and body integrity, grieving the past body and integrating a new corporality leads to a painful identity crisis. Conclusion With mastectomy, the roots of the woman's identity are challenged, leading to a re-evaluation of her existential values. The consequences of mastectomy transform the woman's corporality and embodiment, and question her identity. Psychological support is discussed in the perspective of our results.

Mastectomy, Body De-Construction and Impact on Identity: A qualitative study

Objectives: This qualitative study aims at understanding the consequences of body deconstruction through mastectomy on corporality and identity in women with breast cancer. Design: Nineteen women were contacted through the hospital. All had to undergo mastectomy. Some were offered immediate breast reconstruction, others, because of cancer treatments, had no planned reconstruction. A qualitative reflexive methodological background was chosen. Method: Women were invited to participate in three semi-structured interviews, one shortly before or after mastectomy, and the other interviews later in their illness courses, after surgery. All interviews were transcribed verbatim. Thematic analysis was performed. The analysis of the first interview of each woman is presented in this article. Results: Mastectomy provokes a painful experience of body deconstruction. Even when immediate reconstruction is proposed, contrasted feelings and dissonance are expressed when comparing the former healthy body to the present challenged body entity. Body transformations are accompanied with experiences of mutilation, strangeness, and modify the physical, emotional social, symbolic and relational dimensions of the woman's gendered identity. Although the opportunity of breast reconstruction is seen as a possible recovery of a lost physical symmetry and body integrity, grieving the past body and integrating a new corporality leads to a painful identity crisis. Conclusion: With mastectomy, the roots of the woman's identity are challenged, leading to a re-evaluation of her existential values. The consequences of mastectomy transform the woman's corporality and embodiment, and question her identity. Psychological support is discussed in the perspective of our results.

Topographic ERP analyses: a step-by-step tutorial review.

In this tutorial review, we detail both the rationale for as well as the implementation of a set of analyses of surface-recorded event-related potentials (ERPs) that uses the reference-free spatial (i.e. topographic) information available from high-density electrode montages to render statistical information concerning modulations in response strength, latency, and topography both between and within experimental conditions. In these and other ways these topographic analysis methods allow the experimenter to glean additional information and neurophysiologic interpretability beyond what is available from canonical waveform analyses. In this tutorial we present the example of somatosensory evoked potentials (SEPs) in response to stimulation of each hand to illustrate these points. For each step of these analyses, we provide the reader with both a conceptual and mathematical description of how the analysis is carried out, what it yields, and how to interpret its statistical outcome. We show that these topographic analysis methods are intuitive and easy-to-use approaches that can remove much of the guesswork often confronting ERP researchers and also assist in identifying the information contained within high-density ERP datasets.

Unraveling the complex metabolic nature of astrocytes.

Since the initial description of astrocytes by neuroanatomists of the nineteenth century, a critical metabolic role for these cells has been suggested in the central nervous system. Nonetheless, it took several technological and conceptual advances over many years before we could start to understand how they fulfill such a role. One of the important and early recognized metabolic function of astrocytes concerns the reuptake and recycling of the neurotransmitter glutamate. But the description of this initial property will be followed by several others including an implication in the supply of energetic substrates to neurons. Indeed, despite the fact that like most eukaryotic non-proliferative cells, astrocytes rely on oxidative metabolism for energy production, they exhibit a prominent aerobic glycolysis capacity. Moreover, this unusual metabolic feature was found to be modulated by glutamatergic activity constituting the initial step of the neurometabolic coupling mechanism. Several approaches, including biochemical measurements in cultured cells, genetic screening, dynamic cell imaging, nuclear magnetic resonance spectroscopy and mathematical modeling, have provided further insights into the intrinsic characteristics giving rise to these key features of astrocytes. This review will provide an account of the different results obtained over several decades that contributed to unravel the complex metabolic nature of astrocytes that make this cell type unique.

Health education of diabetes as a chronic disease : transmission of information or active appropriation ?

Résumé du poster : Diabetes is both an important chronic disease and a real public health problem. It requires a great control over the body and a great mastery of the tools used in the daily struggle to reach a physiological balance. It is therefore a disease in which health education plays an important role, since patients are expected to reach a certain autonomy in the management of their disease. But how can the patients' autonomy be promoted? This is the question to which this study tried to answer from the perspective of socio-cultural psychology. The study was launched by the Cantonal Diabetes Program Vaud and aimed at evaluating a health education setting located in the east region of the Canton Vaud. It was based on both quantitative and qualitative methodological approaches. The results showed that there is a correlation between the number of hospitalizations and the quality of support provided by this particular health education setting. Moreover, the acquisition of expertise appears to be a distributed and collective process based upon the actors' active participation in various types of activities and involving and extended network. Further research is now required in order to examine how health education might be grasped through the lens of social-cultural psychology.

On some numerical aspects of an active strain model in cardiac mechanics

We are interested in the development, implementation and testing of an orthotropic model for cardiac contraction based on an active strain decomposition. Our model addresses the coupling of a transversely isotropic mechanical description at the cell level, with an orthotropic constitutive law for incompressible tissue at the macroscopic level. The main differences with the active stress model are addressed in detail, and a finite element discretization using Taylor-Hood and MINI elements is proposed and illustrated with numerical examples.

Topographic ERP analyses: a step-by-step tutorial review

In this tutorial review, we detail both the rationale for as well as the implementation of a set of analyses of surface-recorded event-related potentials (ERPs) that uses the reference-free spatial (i.e. topographic) information available from high-density electrode montages to render statistical information concerning modulations in response strength, latency, and topography both between and within experimental conditions. In these and other ways these topographic analysis methods allow the experimenter to glean additional information and neurophysiologic interpretability beyond what is available from canonical waveform analyses. In this tutorial we present the example of somatosensory evoked potentials (SEPs) in response to stimulation of each hand to illustrate these points. For each step of these analyses, we provide the reader with both a conceptual and mathematical description of how the analysis is carried out, what it yields, and how to interpret its statistical outcome. We show that these topographic analysis methods are intuitive and easy-to-use approaches that can remove much of the guesswork often confronting ERP researchers and also assist in identifying the information contained within high-density ERP datasets

Biases on the administered parenteral doses of an experimental drug during phase I clinical trials

Introduction: The pharmaceutical aspects of drug administration in clinical trials receive poor consideration compared with the important attention devoted to the analytical and mathematical aspects of biological sample exploitation. During PK calculations, many researchers merely use for dose the nominal amount declared, overlooking the noticeable biases that may result in the assessment of PK parameters. The aim of this work was to evaluate the biases related to doses injected of a biosimilar drug in 2 Phase I clinical trials. Patients (or Materials) and Methods: In trial A, 12 healthy volunteers received different doses of a biosimilar of interferon beta-1a by either subcutaneous (SC) or intravenous (IV) injection. The doses were prepared by partially emptying 0.5-mL syringes supplied by the manufacturer (drop count procedure). In trial B, 12 healthy volunteers received 3 different formulations of the drug by IV injection (biosimilar without albumin [HSA], biosimilar with HSA and original brand [Rebif®]) and 2 different formulations as multiple SC injections (biosimilar HSA-free and original brand). In both trials, the actual dose administered was calculated as: D = C·V - losses. The product titer C was assessed by ELISA. The volume administered IV was assessed by weighting. Losses were evaluated by in vitro experiments. Finally, the binding of 125I-interferon to HSA was evaluated by counting the free and HSA complexed molecule fractions separated by gel filtration. Results: Interferon was not significantly adsorbed onto the lines used for its IV administration. In trial A, the titer was very close to the one declared (96 ± 7%). In trial B, it differed significantly (156 ± 10% for biosimilar with/without HSA and 123 ± 5% for original formulation). In trial A, the dose actually administered showed a large variability. The real injected volume could be biased up to 75% compared with the theoretical volume (for the lower dose administered [ie, 0.03 mL]). This was mainly attributed to a partial re-aspiration of the drug solution before withdrawing the syringe needle. A strict procedure was therefore applied in trial B to avoid these inaccuracies. Finally, in trial B, 125I-Interferon beta-1a binding to HSA appeared time dependent and slow, reaching 50% after 16-hour incubation, which is close to steady state reported for the comparator Rebif®. Conclusion: These practical examples (especially biases on actual titer and volume injected) illustrate that actual dose assessment deserves attention to ensure accuracy for estimates of clearance and distribution volume in the scientific literature and for registration purposes, especially for bioequivalence studies.

A cellular system for spatial signal decoding in chemical gradients.

Directional cell growth requires that cells read and interpret shallow chemical gradients, but how the gradient directional information is identified remains elusive. We use single-cell analysis and mathematical modeling to define the cellular gradient decoding network in yeast. Our results demonstrate that the spatial information of the gradient signal is read locally within the polarity site complex using double-positive feedback between the GTPase Cdc42 and trafficking of the receptor Ste2. Spatial decoding critically depends on low Cdc42 activity, which is maintained by the MAPK Fus3 through sequestration of the Cdc42 activator Cdc24. Deregulated Cdc42 or Ste2 trafficking prevents gradient decoding and leads to mis-oriented growth. Our work discovers how a conserved set of components assembles a network integrating signal intensity and directionality to decode the spatial information contained in chemical gradients.