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 Vh. . . 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
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 Rd (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.
Introduction
Contents
0.1 Acupuncture . . . 24 0.1.1 History of acupuncture . . . 25 0.1.2 Traditional theory behind acupuncture . . . 26 0.2 Underlying acupuncture mechanisms . . . 29 0.3 Contribution of this thesis . . . 31
This thesis aims at modeling and simulating transport processes of physical and chem-ical signals during acupuncture. It is divided into five chapters, grouped into three parts.
Each chapter contains an introduction to the topic which will be examined and provides relevant references.
The two main objectives of this work are (i) to understand the biomechanics of acupunc-ture 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 acupunc-ture 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 prac-tice 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.
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 ChiChi-nese 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 burn-ing 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.
0.1. ACUPUNCTURE
The popularity of acupuncture practices has now attracted mainstream medical at-tention 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 acupunc-ture 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 acupunc-ture, 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 stim-ulate 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 phenom-ena,yáng to dynamic and hyperactive processes, or conversely. " [6]
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]