Modeling and simulation of transport during acupuncture

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國立臺灣大學工學院工程科學及海洋工程學系博士論文

Department of Engineering Science and Ocean Engineering College of Engineering

National Taiwan University Doctoral Thesis

亞霓

Yannick Deleuze

Advisors : Tony Wen-Hann Sheu, Ph.D. and Marc Thiriet , M.D., Ph.D.

中華民國104年九月 September, 2015

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Yannick Deleuze

Modeling and simulation on transport phenomena during acupuncture

Under the supervision of

Marc Thiriet ^and Tony W.H. Sheu

ÉCOLEDOCTORALE SCIENCESMATHÉMATIQUES DE PARIS CENTRE

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NIVERSITÉ

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DEPARTMENT OFENGINEERINGSCIENCE AND OCEANENGINEERING

COLLEGE OFENGINEERING

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^NIVERSITY

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OCTORAL

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ISSERTATION

Modeling and simulation of transport during acupuncture

By : Yannick DELEUZE

Advisors : Marc THIRIET, M.D., Ph.D. and Tony W. H. SHEU, Ph.D.

Submitted in partial fulfillment of the requirement for the degree of Doctor of Philosophy

specialized in Engineering Science at National Taiwan University

and

the degree of Doctor of science, specialized in Applied Mathematics at University Pierre and Marie Curie

Reviewers :

HUANG Huaxiong York University

MAURY Bertrand Université Paris-Sud

Defended publicly on the 22/09/2015 in Taipei in front of a Committee composed of :

THIRIET Marc UPMC Advisor

SHEU Tony W.H NTU Advisor

PIRONNEAU Olivier UPMC Examiner

MAURY Bertrand Université Paris-Sud Reviewer

LIN Jaung-Geng China Medical University Examiner

TSAI Wu-Ting NTU Examiner

CHU Yeh-Shiu National Yang-Ming University Examiner

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Laboratoire Jacques-Louis Lions Université Pierre et Marie Curie Boîte courrier 187

75252 Paris Cedex 05 France

École Doctorale de Sciences Mathé- matiques de Paris Centre (ED 386)

Université Pierre et Marie Curie Boîte courrier 290

4, Place Jussieu 75252 Paris Cedex 05 France

Scientific Computing and Cardiovascular Simulation Laboratory

Department of Engineering Science and Ocean Engineering

National Taiwan University

No. 1, Sec. 4, Roosevelt Rd., Daan District, Taipei City 106

Taiwan

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À mes parents, mon frère, et ma femme

"Ceux qui vivent, ce sont ceux qui luttent."

Victor Hugo

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Acknowledgements

I am heartily thankful to my supervisors, Tony Sheu and Marc Thiriet, for allowing me to work on this exciting subject and giving me the opportunity to be part of this international project. Their enthusiasm, encouragement, understanding, guidance, and support have made this work a thoughtful and rewarding journey.

I owe my deepest gratitude to Huaxiong Huang and Bertrand Maury to have accepted to read and review my thesis. I would like to thank Olivier Pironneau, Bertrand Maury, Benoit Perthame, Jaung-Geng Lin, Wu-Ting Tsai, and Yeh-Shiu Chu to have accepted to be part of my dissertation Committee.

I thank the UPMC for the funding of my doctoral studies. I thank the FSMP, the CASTS, the "Bureau de Représentation de Taipei en France”, and the Department of Engineering Science and Ocean Engineering for the several partial fundings during my master and doctoral studies.

My work has been made possible thanks to the efforts and scientific excellency of the researchers and professors in the LJLL, SCCS, and CASTS that generously shared their time and ideas. A special thanks to Nadine Foucart, Salima Lounici, Danielle Boulic, Liliane Ruprecht, Christian David, Khashayar Dadras, and Antoine Le Hyaric for their help both in France and during my stay in Taiwan. Thanks also to Ms Huang and Ms Wang for the precious help and counsels during my stay in the NTU.

I would like to thank the teachers who led me to the world of research through their in- spirational teaching. I would like to cite in particular Yvon Maday, Jean-Pierre Françoise, Pascal Frey, Frédéric Hecht, Albert Goldbeter, Alessandra Carbone, David Holcman, and Olivier Pironneau. I also would like to show my gratitude to Benoit Perthame who has introduced me to the world of interactions between mathematics and biology. I would also like to thank Benoit for his collaboration and proofreading for parts of the work presented in chapter 4 and his precious advices during our encounters both in France and Taiwan.

Thanks to Frédéric Hecht for generously sharing his time and ideas with the use of the software FreeFem++.

I also would like to thank Hiroshi Suito for inviting me to share my work in Japan. I really enjoyed the rewarding experience. During the several conferences and events along my doctoral studies, I met remarkable researchers that had the kindness to interact with me and whose work have inspired me. I would like to cite, among others, Norikazu Saito,

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Olivier Pironneau, Pascal Frey, Kenji Takizawa, Bertrand Maury.

The dual degree project between France and Taiwan has been made possible with the great help of the International Relations Department in UPMC and the Office of Interna- tional Affairs in NTU. I would like to thank in particular Patricia Zizzo for her help and advices during the elaboration of the project.

I don’t forget the students and post-doctors of UPMC and NTU with who I had friendly, helpful, and productive discussions: Juliette, 承佑, 育瑋, 聖宗, Lise-Marie, Nicole, Charles, Vincent, Mamadou, Pierre, Marie, Paul, Jean-Paul, Grégoire, Claire, Maxim, Céline,仕超, 燿宇, 向成, 豫潔, 林樂, 日陽, 聖鋒, 禹鑫, 哲安, 嘉敏, 倫語.

I’m very grateful for the unconditional support of my wife Camille, my parents, my brother, and family during the completion of the project.

And finally, thanks to my all my friends and especially to Guillaume, Thibault, Thibault, Sébastien, and the Orry team for their friendship during all these years.

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Abstract

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, such as lifting and thrusting or rotating, to stimulate the acupoint. The same acupoints can also be stimulated by other techniques such as moxibustion, acupressure, electroacupuncture, and more recently, laser acupuncture. Growing public interest for acupuncture treatments has led the scientific community to investigate the underlying physiological basis of acupuncture. The physiological re- actions 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. This loose connective tissue is composed of cells and an extracellular matrix of collagen and elastic fibers embedded in gel made of glycoproteins and proteoglycans. 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. The predicted pressure and shear stress show that the implantation of a needle can produce local mechanical stimulation in its environment.

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 trans- fer of long-term acting endocrine signals. The process is sustained by the recruitment of mastocytes through chemotaxis.

The mathematical model of the mastocyte response to acupuncture needling relies on the macroscopic description of chemotaxis. Its simplest form describes the evolution of the density of mastocytes and the concentration of a chemoattractant emitted only

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by mastocytes when activated by the mechanical stress induced by needle manipulation.

Blow-up of the solution in finite time is proven to occur for large initial data concentrated around the acupoint in a simplified model. A numerical study infers the theoretical results and the observed blow-up is interpreted as a self-sustained response of stimulation and recruitment of mastocytes at the acupoint.

Keywords : acupuncture; mastocyte; chemotaxis ; fluid-structure interaction; fluid- fibrous porous medium interaction ; chemotaxis-fluid model; numerical simulation ; finite element method; FreeFem++

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Résumé

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 clas- sique, 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. Ces mêmes points peuvent être stimulés par d’autres techniques telles que la moxibustion, l’acupression, l’électro- acupuncture et l’acupuncture par laser.

L’intérêt croissant pour l’acupuncture a incité la communauté scientifique à s’intéresser aux bases physiologiques de l’acupuncture. Les effets cliniques de l’acupuncture pour- raient 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. Ce tissu conjonctif lâche est composé de cellules et d’une matrice extracellulaire. Cette dernière est constituée principalement d’un maillage de fi- bres de collagène et d’élastine stabilisées ainsi que d’un fluide formé de protéoglycanes et de glycoprotéines. Les mastocytes sont des cellules du système immunitaire présentes dans l’hypoderme. Ces dernières contiennent dans leur cytoplasme de très nombreuses granulations contenant des médiateurs vaso-actifs et neuro-actifs ainsi que des attractants chimiques. Ces attractants jouent un rôle important pour le recrutement de mastocytes.

Les médiateurs neuro-actifs sont impliqués dans l’excitabilité des terminaisons nerveuses pour permettre l’émission de potentiels d’action transmis jusqu’au système nerveux central. Les médiateurs vaso-actifs augmentent notamment la perméabilité vasculaire et la microcirculation pour permettre une production, à long terme, de signaux endocriniens.

Activés par un signal externe, les mastocytes dégranulent et libèrent les médiateurs de manière très rapide.

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 ré- cepteurs à la surface des cellules du tissu et notamment des mastocytes. La pression et le cisaillement calculés renforcent l’hypothèse selon laquelle que l’insertion de l’aiguille

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peut produire une stimulation mécanique suffisante pour activer les mastocytes proches du point d’acupuncture.

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 libéra- tion 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. Il décrit l’évolution de la densité de mastocytes et de la concentration des médiateurs chimiques libérés par les mastocytes après avoir été activés. Dans sa ver- sion la plus simplifiée, la solution du système d’équation aux dérivées partielles devient singulière en un temps fini pour des conditions initiales suffisamment grandes et concen- trées autour du point acupuncture. Dans ces conditions, l’explosion en temps fini de la solution résulte de l’agrégation des cellules et pourrait mesurer l’efficacité de la manipulation de l’aiguille sur le point d’acupuncture. L’étude numérique confirme les résultats théoriques. La stimulation en dehors d’un point d’acupuncture n’est que légèrement am- plifiée. Selon le modèle proposé, la présence d’un nombre important de mastocytes au point d’acupuncture est impérative pour qu’une réponse appropriée soit observée.

Mots clés : acupuncture; chimiotaxie; mastocyte; intéraction fluide-structure; intérac- tion fluide-milieu poreux fibreux; modèle de chimiotaxie-fluide; simulation numérique;

méthode des éléments finis; FreeFem++

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Conclusion and future work 157

Bibliography 158

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List of Figures

1 Foundation in traditional Chinese medicine: A qì-blood-tissue fluid triple

coupling circulation system . . . 27

2 Meridians and acupuncture points in traditional Chinese medicine . . . . 28

3 Correspondence between the meridians, zàng-fˇu organs and the y¯ın and the yáng in traditional Chinese medicine . . . 29

4 Meridian compartment model . . . 31

1.1 Locoregional activation of mastocytes . . . 41

1.2 Chemical messengers released by mastocytes upon stimulation . . . 43

2.1 Uniform square mesh and rectangle mesh . . . 52

2.2 Mesh representing a plum blossom of the Taiwan national flower . . . 53

2.3 Meshes of Taiwan generated from an image . . . 55

2.4 3d mesh of Taiwan generated from an image . . . 56

2.5 Mesh generated with the truncation tool . . . 57

2.6 Mesh of two collated rectangles . . . 57

2.7 Mesh adaptation with the splitmesh function . . . 58

2.8 Mesh adaptation with the adaptmesh function . . . 59

2.9 Mesh manipulation with the movemesh function . . . 60

2.10 Solution of the Poisson’s equation on a Taiwan shaped mesh . . . 64

2.11 Mesh and numerical solutions of the heat equation . . . 66

2.12 Numerical simulation of flow in idealized 2D aneurysm model, stenosis model, bifurcation model, and bended tube model . . . 70

2.13 Moving meshes in FreeFem++ . . . 74

2.14 Numerical simulation of flow accelerated from rest by an oscillating cir- cular cylinder . . . 74

2.15 Comparison of the predicted and referenced solutions at t = ⁹₂T . . . 75

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LIST OF FIGURES

2.16 Comparison of the computed and referenced solutions at t = ⁵⁵₁₂T . . . 75

2.17 Comparison of the computed and referenced solutions at t = ⁵⁹₁₂T . . . 76

3.1 Schematic of the computational domain . . . 81

3.2 Illustration of the prescribed needle position and the corresponding generated meshes . . . 83

3.3 The simulated velocity magnitude resulting from the needle motion in interstitial fluid . . . 86

3.4 The simulated pressure profiles resulting from the needle motion in interstitial fluid . . . 87

3.5 The simulated pressure profiles at different vertical locations . . . 88

3.6 The simulated mean shear stress on the cell surface . . . 89

3.7 The simulated pressure profiles resulting from the motion of a needle in interstitial fluid at acupoint . . . 90

3.8 The α_f profiles given at the acupoint, close to the acupoint, and far from the acupoint . . . 91

3.9 The simulated velocity and pressure profiles with an interstitial cell . . . . 93

3.10 Evolution of the pressure and the shear stress distributions along the cell surface . . . 94

4.1 Stress function Φ in 1D . . . 101

4.2 Convergence rates for the P1-P2 finite elements . . . 119

4.5 Influence of the chemotactic sensitivity parameter S with a mesh size ∆x = 1/16 . . . 121

4.8 Gaussian spatial distribution of mastocytes in a bounded domain . . . 124

4.9 Stress function Φ defined as a bump function . . . 124

4.10 Needling at acupoint and non-acupoint . . . 125

4.11 Needling outside an acupoint . . . 126

4.12 Granulated mastocyte density dynamics . . . 126 5.1 Boundary conditions for the the chemotaxis–diffusion–convection system 133

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LIST OF FIGURES

5.2 The computed rates of convergence for the coupled set of Navier-Stokes

and Keller-Segel equations . . . 138

5.3 Examples of convection cells for the chemotaxis–diffusion–convection, Rayleigh-Bénard convection, and double diffusive convection . . . 139

5.4 Time evolution of the cell density . . . 140

5.5 Time evolution of the cell density number at the surface . . . 141

5.6 The stable and unstable regions of the dimensionless chemotaxis–diffusion– convection coupling system . . . 144

5.7 Numerical results for the cell density with respect to the deterministic initial conditions . . . 145

5.15 Initial random condition and the corresponding numerical results for the cell density . . . 150

5.16 Growth rate of plume amplitude . . . 152

5.17 Numerical solution of the double diffusive system . . . 154

5.18 Numerical solution of the Rayleigh-Bénard system . . . 154

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List of Tables

1.1 Scales and sizes in the hypodermis . . . 36

1.2 Cells of the subcutaneous loose connective tissue . . . 36

1.3 Vasoactive mediators . . . 38

1.4 Neuroactive mediators . . . 38

1.5 Autocrine mediators . . . 39

3.1 Nomenclature and parameter dimensions . . . 78

4.2 Repartition of the mass in a Gaussian distribution in the full domain . . . 123

5.2 Representative dimensionless numbers involved in the double diffusive convection, chemotaxis–diffusion–convection, and Rayleigh-Bénard convection . . . 131

5.3 Phenomenological analysis based on time scales of the three competitive mechanisms: chemotaxis, diffusion, and convection of bacteria . . . 143

5.4 The predicted number of plumes, wavenumber and wavelength for ` = 2 . 150 5.5 The predicted number of plumes, wavenumber and wavelength for ` = 3 . 151 5.6 The predicted number of plumes, wavenumber and wavelength for ` = 4 . 151 5.7 The predicted number of plumes, wavenumber and wavelength for ` = 5 . 151 5.8 The predicted growth rate of the plume amplitudes for two simulations subject to the random initial condition . . . 153

5.9 Recapitulative of the physical mechanisms involved in the double diffusive convection, chemotaxis–diffusion–convection, and the Rayleigh- Bénard convection . . . 155

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List of FreeFem++ Scripts

2.1 Exemples of variable types, function declarations, and operators . . . 50 2.2 Script to build a mesh of square domain plotted in figure 2.1. . . 51 2.3 Script to build the mesh of a rectangle domain plotted in figure 2.1. . . 52 2.4 Script to build the mesh plotted in figure 2.2. . . 53 2.5 Script to build 2d and 3d meshes from an image . . . 53 2.6 Script to build a truncated mesh. An exemple is plotted in figure 2.5. . . . 55 2.7 Script to add two meshes to form a single mesh . . . 56 2.8 Script to split mesh triangles with splitmesh. . . 58 2.9 Script to adapt a mesh with the function adaptmesh. . . 58 2.10 Mesh manipulation with the movemesh function . . . 60 2.11 Declaration of finite element spaces. . . 61 2.12 Declaration of finite element functions in the space V_h. . . 61 2.13 Solving the Poisson’s equation in 2d with the keyword solve. . . 62 2.14 Solving the Poisson’s equation in 2d with the keyword problem. . . 63 2.15 Solving the Poisson’s equation in 2d with the keyword varf. . . 63 2.16 Solving the heat equation in FreeFem++ . . . 65 2.17 Solving the incompressible Navier-Stokes equations . . . 68 2.18 Solving the incompressible Navier-Stokes equations in a moving domain

with the ALE method . . . 73

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Notations

References

A number in brackets, example (1.2), refers to the equation (2) of chapter 1. The numbers in square brackets like [1] indicate a reference in the bibliography. Figures and parts of figures use numerals and labels enclosed in parentheses, respectively. For exemple, figure 4.12 refers to the figure 12 of chapter 4 and figure 5.3 (a) refers to subfigure (a) of figure 3 of chapter 5. Tables and scripts use numerals, for exemple table 3.1 refers to table 1 of chapter 3 and script 2.16 refers to script 16 of chapter 2.

Differential operators

The classical grad, div, and laplacian operators are denoted respectively as

∇c, ∇ · u, ∇²u.

Geometry of the domains

The domain of a PDE is in general denoted by Ω, which is a bounded open set in R^d (d = 2, 3), it’s volume element by dx and its boundary by ∂Ω or Γ. The domain is sufficiently regular to define an outward normal unit vector n(x) for almost all x of the boundary ∂Ω. Domains with corners are also admitted. |Ω| denotes the area of Ω.

Function spaces

C⁰(Ω) is the space of continuous functions on Ω L¹(Ω) is the space of integrable functions on Ω.

L¹₊(Ω) is the space of nonnegative integrable functions on Ω.

L²(Ω) is the space of square integrable functions on Ω.

H¹(Ω) is the Sobolev space of order 1.

H₀¹(Ω) is the space of H¹(Ω) functions with zero trace on ∂Ω.

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Introduction

The two main objectives of this work are (i) to understand the biomechanics of acupuncture needling; more specifically, understand how the pressure and stress field affect the network of fibers and cells of subcutaneous tissues during the manipulation of an acupuncture needle; and (ii) to understand the response of mastocytes and the transmission of information to the vascular and nervous systems.

0.1 Acupuncture

Although an extensive portrayal of thousands of years of acupuncture theory and practice is beyond the scope of this thesis, a brief description is useful for the discussion of modeling and simulation in acupuncture. For more details, readers can refer to Cheng [2]

for example.

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0.1. ACUPUNCTURE

0.1.1 History of acupuncture

This section is the fruit of an exchange with Dr Gilles Cury, general secretary of the

“Association Française d’Acupuncture¹” (http://acupuncture-france.com/.

Accessed January 26, 2015.).

Acupuncture and moxibustion are two age-old medical techniques of Traditional Chi- nese medicine. Their names come from the Chinese words “zhen jiu" meaning needle and moxibustion, respectively. The name acupuncture takes its form from the Latin words

“acus”, meaning needle, and “puncture". Acupuncture is in fact a therapeutic practice based on inserting needles into the skin at acupoints. The name moxibustion is formed from the word “moxa” and “combustion”. Moxibustion is a therapeutic practice of burning moxa sticks next to the skin to stimulate acupoints.

Acupuncture and moxibustion practices date back more than 3000 years. Acupuncture has been practiced in Asia for at least 2500 years. In China, written texts and graphics related to acupuncture and moxibustion date back over 2000 years [3]. The foundation of acupuncture lays in Taoist principles. The “Huáng Dì Nèi J¯ıng” (黃帝內經), translated

“The Yellow Emperor’s Classic of Medicine", one of the first known documentations of Chinese medicine, has been accepted as one of the fundamental doctrinal sources of Chinese medicine.

Traditional Chinese medicine was brought to Europe, notably to France, at the end of the 17th century. The Jesuits, among which the Belgian Philippe Couplet, were the first to provide documents in French about Chinese medicine. In 1805, the manual "De l’acupuncture", written by Dr. Félix Vicq d’Azir, was published in France. Afterwards, experimentation started, especially by doctors Louis Berlioz and Jules Cloquet. There was a growing interest in acupuncture at the end of the 19th century. During this period, enthusiasm for China reached the arts and sciences because of its mysteries and wonders.

It was not until recent years that acupuncture gained wider attention in America and Europe. In France, acupuncture really began in the 1930’s with George Soulié-de-Morant, the French consul in Kunming, China. Upon his return to France in 1929, thanks to his knowledge of the Chinese language, he published, together with Dr. Ferreyrolles, an article entitled “l’acupuncture en Chine vingt siècles avant JC et réfléxothérapie moderne”

in the journal “l’homéopathie française”. Later, in 1934, he published "L’acupuncture chinoise", a work of several volumes achieved in the 1950’s, that served for the teaching of acupuncturists in France. The museum “Musée de la médecine traditionelle chinoise en occident" directed by professor Ting Hor in Kunming, in the Yunnan province of China, is dedicated to George Soulié-de-Morant for his great role in introducing acupuncture in the West. In 1971, Reston Reston [4], a journalist covering President Nixon’s trip to China, developed appendicitis and wrote a long article that drew attention in the United States on how acupuncture treatments helped relieve his pain.

1French Association of Acupuncture.

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0.1. ACUPUNCTURE

The popularity of acupuncture practices has now attracted mainstream medical attention and acupuncture has become the subject of scientific investigation [5]. Today in France, the number of acupuncturists is estimated at 2000. Although a diploma of ca- pacity in acupuncture is required to practice (3 years after being qualified as Medical Doctor), the acupuncture specialty has not been recognized yet. Only four universities in Paris, Nantes, Strasbourg and Montpellier-Nîmes provide the diploma in acupuncture. In obstetrics, an inter-university degree is open to obstetricians and midwives.

Acupuncture treatments are reimbursed by the French medical care system within strict provisions. Accreditation of France (La Haute Autorité de Santé) has limited acupuncture treatments to alternative treatments to chemotherapy, analgesic treatment, treatment for depression and anxiety, and treatment for alcohol and tobacco withdrawal. However, acupuncture can treat a wider range of symptoms.

Several research projects dedicated to acupuncture are currently being carried out in France and acupuncture is increasingly recognized by professionals and administra- tion. Acupuncture and moxibustion practices were recognized in 2010 by UNESCO and inscribed on the Representative List of the Intangible Cultural Heritage of Humanity.

They have also been endorsed by the American National Institutes of Health, the National Health Service of the United Kingdom and the World Health Organization. Today, Taiwan remains one of the most important places for the practice of traditional acupuncture.

0.1.2 Traditional theory behind acupuncture

The foundation of Chinese acupuncture has a basis in Taoist principles. In acupuncture, the internal organs are assumed to be interconnected with one another by a system of complex channels called “meridians”. The meridians are pathways in which the vital energy qì (chinese: 氣) flows throughout the body. The flow of qì regulates bodily health and reflects illness. Acupuncture needling is used to treat and prevent many diseases. In fact, all symptoms can be treated with acupuncture. Hair-thin needles are used to stimulate specific points on the body, acupoints (chinese: xuè, 穴), in order to balance y¯ın (chinese:陰) and yáng (chinese: 陽) by removing blocks in the flow of qì [2]. During the needle insertion and manipulation process, dé qì (chinese: 得氣) sensation is experienced when the needle has been placed at a proper location.

"Yáng and y¯ın are 2 fundamental opposing, complementary, and inter- dependent forces found in all things in the universe, with traces of one in the other, that support each other and can transform into one another. Nothing in the universe is completelyy¯ın or yáng; everything is a mixture of the two. In particular,yáng may be considered as mental activity in its strength aspect, y¯ın mental activity in its imaginative aspect; in other words, yáng constructs, y¯ın instructs, or conversely. Y¯ın is related to static and hypoactive phenomena,yáng to dynamic and hyperactive processes, or conversely. " [6]

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0.1. ACUPUNCTURE

Qì, blood, and body fluids are the fundamental substances which maintain the normal vital activities of the body. Qì refers to both the essential substances of the human body and the functional activities of the organs and tissues. All the vital activities of the body are explained by the change and movement of qì. Blood circulates throughout the organs, the skin, muscles, tendons and bones. Blood nourishes and moistens various tissues and organs from the inside. Body fluid is the collective term for all the normal fluids of the body : saliva, gastric juice, tears, sweat, urine. Body fluids nourish various parts of the body. Together they are the material foundation for the physiological functions of the zàng-fˇu (chinese: 臟腑) organs, tissues and meridians. Their close and complex relationships manifest in physiology and are important in determining the treatment [2].

"When the liver receives blood, it gives rise to vision ; when the feet receive blood, they are capable of walking ; when the palms receive blood, they are capable of holding ; and when the fingers receive blood, they are capable of grasping."[2]

Qì

tissue fluid blood

Qì being comma

nder of blood Q ì bein

g comma nder

of bloo d Blood is the mother of qì Tissu

e fluid ca n carry

qì

homogeny of tissue fluid and blood

Figure 1: Foundation in traditional Chinese medicine: A qì-blood-tissue fluid triple coupling circulation system.

The meridians (chinese: j¯ıng, 經) and collaterals (chinese: luò, 絡) are pathways along which the qì and blood flow (see figure 2). They are connected to the zàng-fˇu organs internally and extend over the body externally, thereby forming a network and linking tissues and organs into a whole [2]. Acupoints are distributed mostly along the major meridians and collaterals. There are around 400 acupoints scattered throughout the body.

Each acupoint is either related to a zàng or a fˇu organ (see figure 3).

The system of zàng organs includes the Heart, the Lung, the Spleen, the Liver and the Kidney. They manufacture and store essential substances, qì, blood, and body fluid

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0.1. ACUPUNCTURE

Figure 2: Meridians and acupuncture points in traditional Chinese medicine. / (Im- age modified from KVDP, 2010. Chinese meridians. Licensed under public domain via Wikimedia Commons. https://commons.wikimedia.org/wiki/File:

Chinese_meridians.JPG)

[2]. The system of fˇu organs includes the Gall Bladder, the Stomach, the Small Intestine, the Bladder and the Triple Heater. They receive and digest food ; transmit and excrete wastes [2]. The zàng-fˇu are not equivalent to the anatomical organs and their names are capitalized in the text.

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0.2. UNDERLYING ACUPUNCTURE MECHANISMS

經絡

五行

木

火

土水金

12 main meridians

3 Yin meridians

in hand 3 Yang meridians

in hand 3 Yin meridians

in foot 3 Yang meridians

in foot

+ extras meridians (collateral, superficial...) spleen

liver kidney

large intestine triple heater small intestine

stomach gall bladder bladder pericardium heart lung

臟腑陰陽

心

心包肺

大腸三焦

小腸脾

肝腎

胃

膀胱膽

穴

Yannick Deleuze - 100 8 15

Figure 3: Correspondence between the meridians, zàng-fˇu organs and the y¯ın and the yáng in traditional Chinese medicine.

0.2 Underlying acupuncture mechanisms

Acupuncture is a minimally invasive procedure. It involves a penetration of the skin with hair thin needles to stimulate acupoints in order to restore the balance and flow of qì through meridians. There is a great demand for explanations regarding the basic concepts such as qì, meridians, and acupuncture points. The absence of scientific background of the acupuncture biochemical mechanisms has motivated us to carry out modeling and numerical simulation of both macroscopic and microscopic aspects of the acupuncture process.

The anatomical and physiological natures of acupoints and meridians are not yet well understood [7]. Still, the effects of acupuncture can be explained by interactions among the nervous, circulatory, endocrine, and immune systems. Recent investigations have shown evidence that meridians and acupuncture points are correlated with subcutaneous loose connective tissue [8]. The subcutaneous connective tissue is composed of cells embedded in the extracellular matrix mainly constituted by collagen and elastic fibers in a gel of glycoproteins and proteoglycans. Mastocytes play a major role in acupuncture.

They are scattered throughout tissue, yet their density is higher near acupoints [9].

The insertion of thin needles into the skin is the most common technique. The needles are then manually manipulated at acupoints. Acupoints are located near bones, aponeuroses ², muscles, and tendons that contain neural units with somatosensory receptors.

2An aponeurosis is a sheet of pearly white fibrous tissue which takes the place of a tendon in sheet-like muscles having a wide area of attachment.

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Acupoints are characterized to have a large density of mastocytes. This pool of mastocytes resides close to neurovascular bundles, in regions where capillaries, lymphatic vessels, and nervous structures abound. Other features of acupoints include larger skin electrical conductance and higher ionic concentrations [10].

During acupuncture needling, mechanical stimuli result from the local deformation of the connective tissue imposed by a sequence of needle motions. This stress field is sensed by the local population of mastocytes that react by degranulation. Other cells, such as neurons, macrophages, fibroblasts, and lymphocytes can contribute to the emission of local and endocrine signals.

Nerve endings are stimulated and can release substances that further activate mastocytes. A self-sustained process is created via the recruitment of circulating mastocytes and excitation of regional pools of mastocytes. This traditional Chinese medicine procedure relies on signaling aimed at triggering mastocyte chemotaxis and sending messages via released molecules. Released molecules include vaso- and neuroactive messengers, the latter targeting the central nervous system via both nervous transmission and blood convection. Targeted nervous regions then respond by regulating the behavior of peripheral organs.

Taxis refers to the collective motion of cells or an organism in response to an attractant gradient. The nature of the attractant stimulus can be of chemical (chemotaxis), physical (baro-, electro-, magneto-, phono-, photo-, and thermotaxis), or mechanical (hapto- and rheotaxis) origins. Chemotaxis refers to cell movement primed by an external chemical signal that can either be emitted by the same population of cells or created by an external source [11].

In this scenario, a meridian can be assumed to be a neurovascular signaling tract. A compartmental model can then be designed (see figure 4). Compartment 1 is related to the signal transmission of external stimuli via mechano-, electro-, thermo, phototransduction. Compartment 2 is the acupoint region with three components: (1) mastocytes, (2) blood and lymph vessels, and (3) nerves. Chemoattractants increase the mastocyte population by recruiting the nearby mastocytes; autocrine signals intensify a self-sustained response. Compartment 3 is related to signal transmission to the central nervous system, either very rapidly via nervous impulses, or delayed via messenger convection through the blood circulation. A feedforward loop associated with elevated cardiac function enables an increased blood flow for a relevant material transport. Com- partment 4 deals with signal processing with a quick and late response corresponding to a fast and delayed input. Compartment 4 represents outputs sent from the central nervous system and the body’s response.

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0.3. CONTRIBUTION OF THIS THESIS

Trigger

mechano-, electro-, thermo, photo-transduction

autocrine signaling + chemotaxis cell recruitment O[1h]

Compartment 1

R 1,1 R 1,2 Heart

CNS

R 2,1 R 2,2

I+

C+

local flow increased

R CNS

delayed (τ)

convective impulsive

delayed (τ’) (EC pulse, fast)

external stimuli!

needle insertion zone O[1min]

Compartment 2

signal development!

acupoint region N Vx

Compartment 3

signal transmission!

to central nervous system (CNS)

Compartment 4

signal processing!

CNS to peripheral organ + other responses

Mastocyte degranulation

Figure 4: Meridian compartment model

0.3 Contribution of this thesis

This thesis makes contributions to the fields of mathematical modeling in medicine and life sciences.

In chapter 1, the mechanism of acupuncture is introduced. This first chapter is purely bibliographical and describes the physiological basis of acupuncture as well as the current research in acupuncture. During a traditional acupuncture treatment, a needle is inserted into the skin and the tip of the needle reaches the subcuteaneous tissue, namely, the hypodermis. Cells of the immune system such as mastocytes are stressed by the needle manipulation. In turn, chemical messengers, released by the mastocytes, participate in the biochemical response of acupuncture. Nerve messengers stimulate nerve endings to send quick information to the central nervous system. Endocrine messengers produce a slower response targeting the heart and the brain. Chemoattractants play an important role to sustain and strengthen the process by recruiting neighboring mastocytes.

Chapter 2 introduces the finite element software FreeFem++ used in this work. FreeFem++

is a finite element software with an interpreted language used to solve partial differential equations using the finite element method. Construction and manipulation of the mesh of the geometry, discretization of the weak form, and visualization of the solutions are done within a single framework.

Chapter 3 contains a biomechanical model of the interaction of an acupuncture needle with the interstitial fluid of the hypodermis. Acupuncture can be assumed to be based on

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the chemical response of mastocytes and other cells at acupoints to the sensed mechanical stresses caused by the needle motion.

The extracellular matrix forms a fibrous media in which interstitial fluid can flow. The interstitial fluid flow is modeled as a Brinkman’s flow in a fibrous media deformed by a moving needle. The model equations are solved with an arbitrary Lagrangian–Eulerian (ALE) finite element scheme. The numerical results reinforce the hypothesis that the mechanical stimuli are localized and acute at the acupoint. The change in the fluid pressure and shear stress field can be sensed by local pools of mastocytes and activate a mechanotransduction process.

Chapter 4 presents a novel mathematical model of the chemotactic response of mastocytes to the physical stress. Mastocytes are presumed to play a major role in acupuncture.

The physical stress field, described in chapter 3, is sensed by the local population of mastocytes which in turn degranulate. A self-sustained process is created via recruitment of the circulating mastocytes and excitation of regional pools of mastocytes.

Emphasis is put into the model of mastocyte response to acupuncture needling and is based on the Keller-Segel model for chemotaxis. The effect of physical stress is assumed to be a forcing term in the model. The mathematical analysis focuses on the simple leading situation dominated by the granulated mastocytes and the chemoattractant. This reduced model is of the nonlinear degenerate parabolic type. It is shown that the solution is positive and that it blows up in the sense that a weighted L1 norm does not stay positive if the forcing term times the initial condition is large. The blow-up is interpreted as a hyper reactivity at the acupoint where a large quantity of mastocytes are present.

Conversely if the forcing term times the initial condition is not large, the solution to the coupled nonlinear partial differential equations exists. In this case, the action of acupuncture is considered ineffective. The theoretical results serve as a validation of numerical experiments. Numerical simulations show that when the needle is positioned in the pe- riphery of the acupoint or outside it, the response is too weak. The acupoint must contain a highly concentrated population of mastocytes to get a proper initial response. Permanent signaling is provided by chemotaxis and continuous recruitment of mastocytes.

Chapter 5 describes the coupling of chemotaxis and fluid flow. Although, this chapter does not directly focus on acupuncture but gives insight into the interaction between the chemotaxis of cells with an incompressible fluid when the external force is gravity. The chemotaxis–diffusion–convection coupling system is presented in the particular case of suspensions of swimming microorganisms which are denser than the fluid in which they are immersed in. The system describes a form of buoyant convection in which the fluid develops convection cells and plume patterns. The numerical results indicate that the chemotaxis can stabilize the overall chemotaxis/fluid system when the chemotaxis head and sensitivity is large.

In addition, a comparison of the differential system of chemotaxis–diffusion–convection, double diffusive convection, and Rayleigh-Bénard convection is established. A set of evidences shows that even if the physical mechanisms are different, the dimensionless

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systems are strongly related to each other.

As a conclusion, some directions for future research are pointed out.

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Chapter 1 Literature survey of acupuncture study

1.1 Introduction . . . 35 1.1.1 Subcutaneous connective tissue . . . 35 1.1.2 Mastocytes . . . 36 1.2 Underlying acupuncture mechanisms . . . 37 1.2.1 Stimulation of acupoints . . . 37 1.2.2 Biochemical signaling at acupoints . . . 42 1.3 Modeling in acupuncture . . . 44 1.3.1 Electroosmotic meridian model . . . 44 1.3.2 Interstitial flow in acupuncture . . . 45 1.3.3 Mastocyte dynamics of degranulation . . . 46 1.4 Concluding remarks . . . 47

Abstract

The aim of this chapter is to provide the fundamental basis for the modeling and simulation presented in this study. The content of this chapter is purely bibliographical and summarizes the physiology of tissues involved in acupuncture, details of current research in acupuncture, and previous mathematical models in acupuncture.

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1.1. INTRODUCTION

1.1 Introduction

This section provides the physiological basis of the different components involved in the mechanism of acupuncture.

1.1.1 Subcutaneous connective tissue

The skin consists of three layers of tissue known as the epidermis, dermis, and hypodermis. The hypodermis is the subcutaneous connective tissue that provides (1) structural and mechanical support, (2) transport of nutrients, metabolites and waste between the blood and tissues, (3) storage of energy, (4) immunological defense. For a complete description of the extracellular matrix one can refer to [12, 13]. The hypodermis is a loose connective tissue that lies above skeletal muscles and forms a continuous body-wide network including subcutaneous and interstitial connective tissues surrounding all muscles, organs, nerves, blood vessels, and lymphatic system [14]. Like other types of connective tissues, the loose connective tissue is made of scattered cells immersed in the extracellular matrix and contains an abundant ground substance and relatively sparse fibers.

The extracellular matrix is a key participant in mechanotransduction¹, or mechanisms allowing cells to perceive and interpret mechanical forces. The extracellular matrix skele- ton is made of collagen and elastin fibers. Collagen fibers ensure progressive resistance to deformation and, hence, have low extensibility [15]. The collagen molecules are crosslinked to form the collagen fibers. Collagen fibers of type III and I are mainly found in the connective tissues [12]. Type I is a tensile fiber, usually forming wavy bundles, which does not ramify and is associated with the resistance and rupture of the connective tissue [12, 16]. Elastic fibers, thinner than collagen fibers, enable strain and tissue resilience, the energy being reinstated upon stress removal [15]. The tissue is structured in multiple layers of thin collagen sheets loosely interconnected by elastin fibers to limit distension and prevent tearing [17].

The ground substance is a non-cellular component occupying the space between cells and fibers. The ground substance consists of water, proteoglycans, glycoproteins, and other macromolecules, thereby forming a viscous hydrated gel that can stabilize fiber network or can undergo fluidization under stress [18]. Proteoglycans control the level of hydration of connective tissues, and thus partially determine the physical properties of connective tissues [12]. The aqueous phase of the ground substance is the essential medium between cells and bloods through which all nutrients and wastes must pass [19].

The connective tissue has three scales of heterogeneity :

• mesoscopic scale (0.01 to 1 mm) : dividing the connective tissue into different compartments

1Mechanotransduction refers to the various mechanisms by which cells convert mechanical stimuli into biochemical activity.

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1.1. INTRODUCTION

• microscopic scale (1 to 10 µm) : description of each compartment (collagen, elastin,...)

• nanoscopic scale ( < 1 µm) : cellular structure

The size and scale of each component of the extracellular matrix are listed in table 1.1.

diameter references

epidermis 10 - 100 µm [20]

dermis 1000 - 3000 µm [20]

hypodermis 1000 - 10000 µm [20]

collagen fiber (type I) 1 - 20 µm [12, 16, 20]

elastin fiber 0.1 - 1 µm [12, 16, 20]

Mastocyte 2 - 12 µm [21]

acupuncture needle 100 - 300 µm

Table 1.1: Scales and sizes in the hypodermis

1.1.2 Mastocytes

1.1.2.1 Loose connective tissue cells

Cell types of connective tissue include both resident cells (e.g., fibroblasts, mastocytes, and macrophages) and immigrant cells (e.g., monocytes, lymphocytes, and granulocytes) (see table 1.1.2.1). Fibroblasts, which are matrix-secreting cells, account for 70-80% of the cells [22]. The wandering cells of connective tissue are involved mainly in immune defense and inflammation. Macrophages are large phagocytic cells found in stationary form in the tissues or as mobile cells that are found especially at sites of infec- tion. Mastocytes are found in numbers in connective tissue. They contain granules storing chemical mediators. Mastocytes are able to release their granule contents within minutes for intra-, auto-, juxta-, paracrine signaling and to resynthesize their content.

Resident cells Immigrant cells Fibroblasts Lymphocytes

Fibrocytes Granulocytes Adipocytes Monocytes Macrophages Mastocytes Mastocytes Macrophages

Table 1.2: Cells of the subcutaneous loose connective tissue

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1.1.2.2 Mastocytes

Mastocytes of the connective tissue are believed to play an important role in acupuncture [9]. Mastocytes are tissue-resident sentinels of the immune system. In particular, they are found in tissues close to the external environment [23]. Mastocytes are well known for their role in the inflammatory process where they accumulate at the site of inflammation in response to a chemical mediator [24]. However, they also appear to have a protective role [25]. Mastocytes contain granules storing inflammatory mediators, including histamine, serotonin, and chemotactic factors, in particular for eosinophils and neutrophils [12]. Mastocytes are scattered throughout the connective tissues of the body especially neurovascular bundles.

1.1.2.3 Released chemical mediators from mastocytes

Mastocytes contain granules storing chemical mediators. They release the content of their granules into the surrounding tissues by exocytosis² within minutes.

The cytoplasmic granules include stimulants that aim at triggering action potential to nearby nerve endings, that can lead for example to liberate opioids and analgesic in the brain [27] (see table 1.4). Some stimulants increase the blood vessel lumen as well as its permeability and increase blood flow rate after reaching the heart [28, 29] (see table 1.3).

Mastocytes also release chemoattractants that participate in cell recruiting (see table 1.5).

1.2 Underlying acupuncture mechanisms

This section describes the underlying basis of acupuncture needling involving signal transduction through the connective tissues together with the immune system, the endocrine system and the nervous system to explain how the signals are transported from acupoints to close and distant tissues and organs of the body.

1.2.1 Stimulation of acupoints

Whatever the technique chosen to stimulate the acupoint, physical stimuli are sent to the subcutaneous connective tissue. In turn, mastocytes rapidly release vesicles containing chemical mediators that participate in biochemical responses that induce the acupuncture effects.

2process by which the contents of a cell vesicle are released to the exterior through fusion of the vesicle membrane with the cell membrane [26].

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Table 1.3: Vasoactive mediators

Effect Mediators

Vasodilation Histamine [30]

Histamine + NO [31]

Serotonin [32]

Substance-P + NO [32]

CGPR [33]

LktC₄, LktD₄, LktE₄ [12]

PGE₂ [34, 35]

Vascular permeability LktB₄, LktC₄, LktD₄ [12]

Vasoconstriction Serotonin [32]

TXA₂ [12, 36]

Anticoagulant Heparin [12]

Positive chronotropy CGRP [37]

PGE₂ [34, 35]

Positive inotropy CGRP + NO [38, 39, 39]

PGE₂ [34, 35]

Table 1.4: Neuroactive mediators Nerve ending stimulation Histamine [23]

PGD2

LktC

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Table 1.5: Autocrine mediators Chemotaxis for mastocytes IL [40]

TNFα [41]

Tryptase [42]

NGF [43]

Mastocyte degranulation and secretion Substance-P [44]

CGRP [45]

1.2.1.1 Acupoints

At the present moment, the anatomy and physiology of acupoints are not clearly defined but recent studies have revealed some of their specific properties. Acupoints are mainly located in the loose connective tissue not far from bones, aponeuroses, muscles, and/or tendons and close to dense neurovascular bundles [46]. Acupoints differentiate from nonacupoint locations by displaying high density of mastocytes [9], high density of capillaries [47], high collagen concentration [48], high skin electrical conductance [49, 50] and high ionic concentrations (K⁺, Ca²⁺, Fe²⁺, Mn²⁺, Zn²⁺, PO³₄⁻). Free nerve endings, cutaneous receptors, sarcous sensory receptors (muscle spindles and tendon organs), and their afferent fibers, as well as somatic efferent fibers innervating muscles, small nerve bundles, and plexi are observed in acupoints [51].

1.2.1.2 Needle and collagen fiber deformation

The needle is inserted in the hypodermis. After a short term of needle manipulation, the needle is retained about 20 minutes with possible restimulation at the acupoint. When the desired effect has been achieved, the needle is removed from the acupoint.

The mechanical signal induced by the needle manipulation causes the collagen fibers to wrap around the needle body [8]. When the needle is coupled to tissues, needle manipulation engenders the deformation of the extracellular matrix. The reorganization of the extracellular matrix affects the interstitial pressure and flow producing mechanical stimuli that are perceived by the mechanosensitive proteins on the surface of cells [52]. Masto- cytes react to the mechanical stimulus and calcium signaling. There is ample evidence that activation and degranulation of mastocytes are increased with shear stress [53] and heating during moxibustion as well [54]. Mathematical models have been established for the dynamics of mastocyte degranulation with calcium signaling induced by laser irradiation [55] and induced by shear stress [53]. Dé qì sensation could be a response to the

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wrapping of connective tissues around the needle body [52].

1.2.1.3 Extracellular matrix and mastocyte interaction

Mastocytes are scattered throughout the connective tissues of the body especially be- neath the skin near blood and lymphatic vessels and within nerves. Experimentation showed that needle manipulation in acupuncture causes degranulation of mastocytes to occur [9, 48]. In particular, inhibition of mastocyte degranulation annihilates the analgesic effect of acupuncture [9].

There is an evidence that the shear and pressure stresses from the winding of connective tissues with the needle are transmitted to the extracellular matrix of the subcutaneous connective tissue and lead to the excitation of receptors on the mastocyte membrane [48].

In turn, there are several signaling pathways associated with a rapid entry of calcium (Ca²⁺) waves in the mastocyte cytosol leading to mastocyte degranulation. The mastocytes release, within minutes after activation, numerous chemoattractants, neural stimulants, and endocrine mediators that are diffused in the tissue and interplay with blood vessels and nerve endings, thereby causing a cascade of biological effects and resulting in the alteration of systems, tissues and organs (see figure 1.1).

1.2.1.4 Other acupuncture treatments

The same acupoint can be stimulated by acupressure, moxibustion, electroacupunture and, more recently, by laser acupuncture. Acupressure, or needleless acupuncture, stim- ulates the acupoints by applying finger pressure near these points that in turn creates a local mechanical stress. Electroacupuncture (or percutaneous electrical nerve stimulation) [56] creates a local electrical field by applying a small electric current between a pair of acupuncture needles at acupoints. Laser acupuncture [57] is an optical method used to stimulate acupoints with laser irradiation. Laser acupuncture does not seem to work via physical processes such as excitation with an electromagnetic wave and heating. Laser acupuncture seems to trigger phototransduction pathways. Moxibustion is a popular alternative therapy that involves burning a mugwort stick (or moxa candle) and moving it back and forth above a short meridian segment centered at a given acupoint.

To reduce the risk of burns, indirect moxibustion using both needles and ignited moxa is currently more popular. This practice involves inserting a needle into an acupoint. The tip of the needle is then ignited to supply heat flux to the acupoint and surrounding area. To sum up, mastocytes can be activated by a mechanical stress field (mechanotransduction), heating (thermotransduction), electrical field (electrotransduction), or an electromagnetic wave (phototransduction).

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Vθ VP Needle

Mast cell Collagen fibers

Nerve Blood vessel Cell

recruitment

Degranulation

Nerve stimulation

Propagation of mediators Mechanical

Stimuli

Stimulation

Histamine LktC4

PGD2 Tryptase

IL TNFα

NGF

Histamine Substance P + NO SerotoninLktE4

CGRP

LktD4 LktC4 PGE2

PGE2 CGRP+NO LktD4

Subs. PCGRP Epidermis

Dermis

Hypodermis

Figure 1.1: Locoregional activation of mastocytes. Acupuncture needling sends mechanical stimuli capable of activating mastocytes in acupoints, causing their degranulation via mechanotransduction.

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1.2.2 Biochemical signaling at acupoints

In response to external stimuli, mastocytes rapidly release vesicles containing chemical mediators (see tables 1.3, 1.4, and 1.5). These chemical messengers can be grouped intp three major groups: nerve messengers, endocrine messengers and chemoattractants (see figure 1.2).

1.2.2.1 Nerve messengers

The release of a nerve messengers immediately (O[ s- mn]) affects the excitability of the nerve endings triggering fast short-lived action potentials [6]. Secretion of neuropep- tides, like substance-P and CGRP, released from mastocytes could stimulate nerve endings sending neural signals from the acupoint site along the respective fibers to the given local regions of the central nervous system. This process is responsible for hyperemia and regulates the secretion of neurotransmitters (substance-P) and analgesic substances such as endocannabinoids, enkephalins, endomorphins, dynorphins [27, 58]. Nerve endings release substance-P that further activates mastocytes and triggers the production of nitric oxide. Nitric oxide levels decrease in the central nervous system and increase in the plasma and organs [58]. This interaction corresponds to an impulsive (fast) response to acupuncture.

1.2.2.2 Endocrine messengers

The release of endocrine messengers and vasoactive mediators participates in the increase of blood vessel lumen size (vasodilation) and wall permeability as well as cardiac function, thus increasing the local blood flow and enhancing the exchanges of chemical mediators to the brain [28, 29]. NO together with other chemicals mediators is known to affect the local blood circulation increasing the blood flow [59]. Some of the vasoactive mediators have a positive chronotropic effect on the heart rate and inotropic effect on the heart contractions that can maintain blood pressure. Vasoactive mediators, like leukotrienes, increase blood vessel permeability allowing the flow of chemical mediators or cells to the blood. These chemical signals are transported in the blood throughout the central nervous system, tissues and organs. They are however preferentially conveyed to the previously activated and highly perfused region of the central nervous system. Neu- rons from this region can then receive sets of action potentials for a long period of time and respond by regulating the behavior of the appropriate peripheral organs. This interaction corresponds to a delayed (slow) response to acupuncture.

1.2.2.3 Chemoattractants

The effective action time of chemical mediators is short due to the presence of degrad- ing enzymes. For this reason, a high and continuous secretion of messengers is ensured

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by mastocyte recruitment through chemotaxis. Following chemotaxis, newly arrived mastocytes at acupoints experience a degranulation triggered by the stress field. The arrival of new mastocyte pools from nearby capillaries and regional mastocyte populations en- sures a continuous flux of activators. Simultaneously, the already degranulated mastocytes at acupoints resynthesize chemical messengers. The regeneration of granules is slow (O[ mn- h]). The resulting self-sustained process enhances the exchange of messengers with nerve endings, enables the local elevation of vascular permeability for the increase of cardiac output, and enhances vasodilation associated with a resulting increase in blood flow. It also supports endocrine signaling to the central nervous system and especially neurons situated in a brain region characterized by hyperemia. This process corresponds to a permanent response to acupuncture.

MASTOCYTE

Vasodilation ( ) Vasoconstriction( )

Mastocyte degranulation and secretion

C+ and I+ effects

Increase local blood flow/pressure Vascular permeability

( )

Histamine

Substance P + NO

Nerve ( ) stimulation Mastocyte chemotaxis

( )

Histamine

Histamine + NO

PGE2 Serotonin

Serotonin

LktE4

CGRP

Substance P

CGRP+NO

CGRP

CGRP LktD4

LktD4 LktC4 LktB4

LktC4

PGE2

TXA2

NGF Tryptase IL

TNFα

LktC4 PGD2

Vx

N

MC

Substance P

Figure 1.2: Chemical messengers released by mastocytes upon stimulation can be grouped into three major groups: nerve messengers (N), endocrine messengers (Vx) and chemoattractants (MC).

In summary, the classical method of acupuncture relies on the following set of events:

(1) generation of a local stress field caused by the needle manipulation; (2) mechanotransduction of sensed local tension into chemical signals, i.e., increase in cytosolic Ca²⁺concentration, granule exocytosis, and substance release; (3) triggering of action potentials (early, quick response) by nerve stimulants bound to cognate receptors on local nerve terminals and activation of the target brain region that is associated with a local functional hyperemia (local increase in blood flow due to nervous activity); (4) chemotaxis of neighboring mastocytes and degranulation of newly arrived mastocytes at acupoints that enables a sustained process, degranulation being effective only near the needle, where the

Modeling and simulation of transport during acupuncture

Department of Engineering Science and Ocean Engineering College of Engineering

Yannick Deleuze

Modeling and simulation on transport phenomena during acupuncture

Under the supervision of

Marc Thiriet and Tony W.H. Sheu

NIVERSITÉ

IERRE ET

ARIE

URIE

ATIONAL

AIWAN

NIVERSITY

D

D

Modeling and simulation of transport during acupuncture

À mes parents, mon frère, et ma femme

Acknowledgements

Abstract

Résumé

Contents

Conclusion and future work 157

Bibliography 158

List of Figures

List of Tables

List of FreeFem++ Scripts

Notations

Introduction

Contents

0.1.1 History of acupuncture

0.1.2 Traditional theory behind acupuncture

Qì

tissue fluid blood

經絡

五行

臟腑 陰陽

穴

Chapter 1

Literature survey of acupuncture study

Contents

1.1.1 Subcutaneous connective tissue

1.1.2 Mastocytes

1.2.1 Stimulation of acupoints

1.2.2 Biochemical signaling at acupoints

Marc Thiriet ^and Tony W.H. Sheu

^ATIONAL

^AIWAN

^NIVERSITY

臟腑陰陽