A mathematical model of mast cell response to acupuncture needling

International audienceWe introduce a new model of mast cell response to acupuncture needling based on the Keller-Segel model for chemotaxis. The needle manipulation induces the release of a chemoattractant by the mast cells. We show, in a simplified case, that blow-up of the solution occurs in finite time for large initial data concentrated around the acupoint. In those conditions, blow-up is the result of aggregation of cells and could indicate the efficiency of the acupuncture manipulation of the needle at one acupoint

A Biological Model of Acupuncture and its Derived Mathematical Modeling and Simulations

International audience(Aims) Acupuncture was employed since 2 millenaries, but the underlying mechanisms are not globally handled. The present study is aimed at proposing an explanation by pointing out involved processes and a convincing modeling to demonstrate its efficiency when carried out by trained practitioners. (Method) In the absence of global knowledge of any mechanism explaining the acupuncture process, a biological model is first developed, based on stimulation in a given domain around the needle tip of a proper mastocyte population by a mechanical stress, electrical, electromagnetic, or heat field. Whatever the type of mechanical or physical stimuli, mastocytes degranulate. Released messengers either facilitate the transfer of main mediators, or target their cognate receptors of local nerve terminals or after being conveyed by blood their receptors on cerebral cells. Signaling to the brain is fast by nervous impulses and delayed by circulating messengers that nevertheless distribute preferentially in the brain region of interest due to hyperemia. The process is self-sustained due to mastocyte chemotaxis from the nearby dense microcirculatory circuit and surrounding mastocyte pools, which are inadequate for acupuncture, but serve as a signal relay. A simple mathematical model is solved analytically. Numerical simulations are also carried out using the finite element method with mesh adaptivity. (Results) The analytical solution of the simple mathematical model demonstrates the conditions filled by a mastocyte population to operate efficiently. A theorem gives the blow-up condition. This analytical solution serves for validation of numerical experiments. Numerical simulations show that when the needle is positioned in the periphery of the acupoint or outside it, the response is too weak. This explains why a long training is necessary as the needle implantation requires a precision with a magnitude of the order of 1 mm. (Conclusion) The acupoint must contain a highly concentrated population of masto-cytes (e.g., very-high–amplitude, small-width Gaussian distribution) to get an initial proper response. Permanent signaling is provided by chemotaxis and continuous recruitment of mastocytes. Therefore, the density and distribution of mastocytes are crucial factors for efficient acupuncture as well as availability of circulating and neighboring pools of mastocytes

Semaine d'Etude Mathématiques et Entreprises 2 : Analyse multivariées pour la production d'aluminium

Ce rapport présente l'étude statistique, menée au cours de la deuxième Semaine d'Étude Maths-Entreprises, d'un problème industriel rencontré par Rio Tinto Alcan. Productrice d'aluminium par électrolyse, cette entreprise cherche à expliquer des fluctuations de procédé. À partir d'un ensemble de mesures sur les anodes et sur les cuves à électrolyse, nous proposons d'utiliser des méthodes d'analyse multivariée pour construire des modèles explicatifs. Le but étant de permettre aux usines d'éviter les périodes avec des fluctuations. Dans une première section, nous présentons le problème et ses enjeux. Nous détaillons dans les sections suivantes les différentes méthodes explorées et les résultats obtenus : l'analyse du coefficient de corré- lation en présence d'un déphasage et l'auto-corrélation, l'analyse en composantes principales, les arbres de décisions, le clustering et la régression linéaire. Des résultats complémentaires sont donnés en annexe

Modélisation et simulation de transport pendant l'acupuncture

L’objectif de cette thèse est d’appréhender la complexité des mécanismes biologiques de l’acupuncture afin de construire un modèle mathématique multi-échelle. Ce modèle est étudié théoriquement et numériquement. L’acupuncture est une des plus vielles pratiques de l’histoire de la médecine et une partie intégrante de la médecine traditionnelle chinoise. Dans sa pratique la plus classique, une ou plusieurs aiguilles sont placées à des endroits spécifiques, nommés points d’acupuncture. L’aiguille est ensuite manipulée en utilisant des mouvements de rotation et de translation de façon à stimuler le point d’acupuncture. Les effets cliniques de l’acupuncture pourraient être le résultat d’effet de cascades de réactions produites par les interactions entre l’hypoderme et les systèmes nerveux, endocrinien et immunitaire. Le travail présenté s’articule sur la modélisation de l’insertion d’une aiguille dans le tissu conjonctif de l’hypoderme. Un modèle d’écoulement en milieu poreux du liquide interstitiel de l’hypoderme a permis d’étudier numériquement les composantes de contrainte qui agissent sur les récepteurs à la surface des cellules du tissu et notamment des mastocytes.Un modèle mathématique de la réponse chimiotactique des mastocytes à une contrainte physique créée par le traitement d’acupuncture est développé. Ce modèle prend en compte les mécanismes de signalisation cellulaire. La contrainte physique induit la libération rapide et continue, grâce au recrutement chimotactique de mastocytes, d’attractants et de médiateurs chimiques. Le modèle est basé sur le modèle de chimiotaxie de type Keller-Segel.The objective of this thesis is to comprehend the complexity of the underlying basis of acupuncture. Acupuncture needling is investigated in order to establish a multiscale model that takes into account the complexity of biology but is mathematically simple enough to run simulations.Acupuncture is one of the oldest practices in the history of medicine and is the core of Traditional Chinese Medicine. Once needles are inserted in the right locations, called acupoints, they are manipulated via manual needling to stimulate the acupoint. The physiological reactions of acupuncture needling lead to therapeutic effects which can be explained by a series of interactions between the skin and the nervous, the endocrine, and the immune systems.In the present work, the thrusting and lifting of an acupuncture needle inserted in subcutaneous connective tissue is modeled. A porous media model is used to run simulations and compute the pressure and shear stress affecting the organization of fibers and of isolated cells in their matrix. A mathematical model was conceived to take into account cell signaling. There is ample evidence that needle manipulation in acupuncture can cause degranulation of mastocytes directly through a physical stress to occur. Activated mastocytes rapidly release granules containing chemical mediators. These chemical mediators play a key role recruiting mastocytes in their environment and are known to affect the excitability of nerve endings as well as local microcirculation permeability and size for the appropriate transfer of long-term acting endocrine signals. The process is sustained by the recruitment of mastocytes through chemotaxis

Modélisation et simulation de transport pendant l'acupuncture

The objective of this thesis is to comprehend the complexity of the underlying basis of acupuncture. Acupuncture needling is investigated in order to establish a multiscale model that takes into account the complexity of biology but is mathematically simple enough to run simulations.Acupuncture is one of the oldest practices in the history of medicine and is the core of Traditional Chinese Medicine. Once needles are inserted in the right locations, called acupoints, they are manipulated via manual needling to stimulate the acupoint. The physiological reactions of acupuncture needling lead to therapeutic effects which can be explained by a series of interactions between the skin and the nervous, the endocrine, and the immune systems.In the present work, the thrusting and lifting of an acupuncture needle inserted in subcutaneous connective tissue is modeled. A porous media model is used to run simulations and compute the pressure and shear stress affecting the organization of fibers and of isolated cells in their matrix. A mathematical model was conceived to take into account cell signaling. There is ample evidence that needle manipulation in acupuncture can cause degranulation of mastocytes directly through a physical stress to occur. Activated mastocytes rapidly release granules containing chemical mediators. These chemical mediators play a key role recruiting mastocytes in their environment and are known to affect the excitability of nerve endings as well as local microcirculation permeability and size for the appropriate transfer of long-term acting endocrine signals. The process is sustained by the recruitment of mastocytes through chemotaxis.L’objectif de cette thèse est d’appréhender la complexité des mécanismes biologiques de l’acupuncture afin de construire un modèle mathématique multi-échelle. Ce modèle est étudié théoriquement et numériquement. L’acupuncture est une des plus vielles pratiques de l’histoire de la médecine et une partie intégrante de la médecine traditionnelle chinoise. Dans sa pratique la plus classique, une ou plusieurs aiguilles sont placées à des endroits spécifiques, nommés points d’acupuncture. L’aiguille est ensuite manipulée en utilisant des mouvements de rotation et de translation de façon à stimuler le point d’acupuncture. Les effets cliniques de l’acupuncture pourraient être le résultat d’effet de cascades de réactions produites par les interactions entre l’hypoderme et les systèmes nerveux, endocrinien et immunitaire. Le travail présenté s’articule sur la modélisation de l’insertion d’une aiguille dans le tissu conjonctif de l’hypoderme. Un modèle d’écoulement en milieu poreux du liquide interstitiel de l’hypoderme a permis d’étudier numériquement les composantes de contrainte qui agissent sur les récepteurs à la surface des cellules du tissu et notamment des mastocytes.Un modèle mathématique de la réponse chimiotactique des mastocytes à une contrainte physique créée par le traitement d’acupuncture est développé. Ce modèle prend en compte les mécanismes de signalisation cellulaire. La contrainte physique induit la libération rapide et continue, grâce au recrutement chimotactique de mastocytes, d’attractants et de médiateurs chimiques. Le modèle est basé sur le modèle de chimiotaxie de type Keller-Segel

Modeling and simulation of transport during acupuncture

The objective of this thesis is to comprehend the complexity of the underlying basis of acupuncture. Acupuncture needling is investigated in order to establish a multiscale model that takes into account the complexity of biology but is mathematically simple enough to run simulations. Acupuncture is one of the oldest practices in the history of medicine and is the core of Traditional Chinese Medicine. Once needles are inserted in the right locations, called acupoints, they are manipulated via manual needling to stimulate the acupoint. The physiological reactions of acupuncture needling lead to therapeutic effects which can be explained by a series of interactions between the skin and the nervous, the endocrine, and the immune systems. In the present work, the thrusting and lifting of an acupuncture needle inserted in subcutaneous connective tissue is modeled. A porous media model is used to run simulations and compute the pressure and shear stress affecting the organization of fibers and of isolated cells in their matrix. A mathematical model was conceived to take into account cell signaling. There is ample evidence that needle manipulation in acupuncture can cause degranulation of mastocytes directly through a physical stress to occur. Activated mastocytes rapidly release granules containing chemical mediators. These chemical mediators play a key role recruiting mastocytes in their environment and are known to affect the excitability of nerve endings as well as local microcirculation permeability and size for the appropriate transfer of long-term acting endocrine signals. The process is sustained by the recruitment of mastocytes through chemotaxis

On three-dimensional ALE finite element model for simulating deformed interstitial medium in the presence of a moving needle

International audienceThe effect of inserted needle on the subcutaneous interstitial flow is studied. Our goal is to describe the physical stress affecting cells during acupuncture needling. The convective Brinkman equations are considered to describe the flow through a fibrous medium. Three-dimensional simulations are carried out by employing an ALE finite element model. Numerical studies illustrate the acute physical stress developed by the implantation of a needle

On Three-Dimensional ALE Finite Element Model For Simulating Interstitial Medium Deformation in the Presence of a Moving Needle

International audienceThe effects of inserted needle on the subcutaneous interstitial flow is studied. A goal is to describe the physical stress affecting cells during acupuncture needling. The convective Brinkman equations are considered to describe the flow through a fibrous medium. Three-dimensional simulations are carried out employing an ALE finite element model. Numerical studies illustrate the acute physical stress developed by the implantation of a needle