Conclusion

(1)

Project-team INRIA-UPMC-CNRS REO Laboratoire Jacques-Louis Lions, CNRS UMR 7598, Université Pierre et Marie Curie, Place Jussieu 4, Paris Cedex 05, France

Abstract

Input data for integrative investigation of complex, dynamical biological phenomena and physiological apparatus include knowledge accumulated at various length scales, from molecular biology to physiology on the one hand, and histology to anatomy on the other hand. Tier architecture of living systems is characterized by its communication means and regulation procedures, enabling to integrate environmental changes to adapt. Multiple molecules interact to create the adaptable activity of the cells, tissues, organs, and body.

The huge quantity of these molecules forms a complex reaction set with feedback loops and a hierarchical organization. Studies from molecular cascades primed by mechanical stresses to cell, then to tissues and organs need to be combined to study living systems with complex dynamics; but future investigations are still needed to mimic more accurately system functioning and interaction with the environment, using multiscale modeling. An integrative model also incorporates behavior at various time scales, including response characteristic times, cardiac and breathing cycles (s), and diurnal periodicities (h; Table 12.1), to efficiently describe the structure–function relationships of the explored physiological system.

Table 12.1.

Scales from molecules to tissue dynamics.

Element	Space scale	Time scale
Atom	0.1 nm	μs
Molecule	nm	ms
Polymer	50 nm	s
Cell	10–50 μm	mn
Tissue	1–10 cm	hour–day

Mathematical description of large, complex biochemical reaction networks, in which molecules are nodes, and modeling of the dynamics of interactions (scaffolding, reaction, transcription, etc.) relies on computational simulations. A biochemical reaction network is defined by: (1) a set of variables — the state variables — that define the state of the system and (2) rules of temporal changes and possible transport of involved variables. The network behavior can be analyzed in a single cells and extended to multicellular systems, especially in tumor models.

Numerous process can be modeled to quickly assess effects of parameters, all other agents remaining constant, once the mathematical model has been validated. The advantage of mathematical models is they yield complete quantity fields, whereas measurements are made only at some points or correspond to averages of exploration windows of the field of the investigated variable. Moreover, mathematical models and numerical simulations support proper design of experiments.

Cells react to various types of external stimuli, in particular, mechanical stresses. In physiological apparatus aimed at conveying flows, the magnitude and direction of mechanical stresses applied by the flowing fluid on the wetted surface of conduit wall (i.e., vascular endothelium with its glycocalyx or respiratory epithelium with the mucus layer and periciliary fluid) as well as within the vessel wall varies during the cardiac and breathing cycles.

The heart, pump embedded in the blood circuit, generates an unsteady flow with a given frequency spectrum in a network of blood vessels characterized by a complicated architecture and variable geometry both in space and time, in addition to between-subject changes. Vessel geometry varies over short distances. The vascular network of curved blood vessels is composed of successive geometrical singularities, mainly branchings.

The thoracic muscular cage, which covers the distal part of the respiratory tract, cyclically (but not symmetrically) inflates and deflates, thereby lowering and heightening the intrathoracic pressure, and hence alternatively dilating and collapsing lung alveoli and intrathoracic airways and enabling inhalation and exhalation of air. The respiratory tract is characterized by a large wetted surface inside a small volume, especially in its proximal and distal regions, i.e., the nose and thorax. In the nose, turbinates allow heat and water exchange, but render air currents less simple. In addition, the laryngeal constriction, the aperture of which varies during the breathing cycle, provokes air jet. The bronchial tree is a network of successive branchings at inspiration, or junctions at expiration, between short, more or less curved pipes of corrugated walls in large bronchi due to the presence of partial or complete cartilaginous rings in large bronchi.

Therefore, blood and air streams correspond to time-dependent, three- dimensional, developing, as these fluids flow in conduit entrance length, where the boundary layer develop (Vol. 7). Moreover, blood vessels and airways are deformable. Changes in transmural pressure (the pressure difference between the pressure at the wetted surface of the lumen applied by the moving fluid on the deformable conduit wall and the pressure at the external wall side that depends on the activity on the neighbor organs) can also influence the shape of vessel cross-section, especially when it becomes negative (collapsing regime).

In the arterial compartment, the change in cross-section shape can result from taper, when the trunk gives rise to lateral branches before bifurcating. More generally, possible prints of adjacent organs with more or less progressive constriction and enlargment, and adaptation to branching (transition zone) are also responsible for three-dimensional flows. These flows are commonly displayed by virtual transverse currents, even in approximately straight segments up- and downstream from geometrical singularities (end effects), especially when the explored vessel section differ from the local cross-section.

Local changes in the direction of stress components can also be caused by flow separation and flow reversal during the cardiac and respiratory cycles. Flow separation is set by an adverse pressure gradient when inertial forces and fluid vorticity are high enough, especially in branching segments. Due to its time-dependent feature, flow separation regions spread over a variable length during the flow cycle and can move. The location and variable size of the flow separation region depends on the flow distribution between branches that can vary during the flow cycle.

Complete flow reversal happens during alternations from inspiratory decelerating flow phase and expiratory accelerating flow phase and conversely. Partial or complete flow reversal occurs during the diastole of the left ventricle in elastic arteries, such as the aorta, and most of the muscular arteries, such as brachial and femoral arteries (but not in carotid arteries with their particular rheology). In arteries, flow reversal can actually be observed either in a region near the wall, more or less wide with respect to the position of the local center of vessel curvature, or in the entire lumen.

Consequently, the stress field experienced by mural tissues is strongly variable both in time and space. Cellular sensors then process mechanical signals by ensemble averaging not only to raise the signal-to-noise ratio, but also to adequately adapt the local size of the conduit lumen, i.e., the local flow resistance to maintain either flow rate or pressure, only in the case of sustained, abnormal stress field.

Sensing and adaptation to an applied mechanical stress field is not restrained to cells at the interface between a bioconduit and a biofluid or within the wall itself, but to any cell type in any site of the organism that can bear a stress field. Bone remodeling is a typical example of adaptation of a tissue to the gravity and lifestyle. Cells adjust their behavior to their environment rheology, especially when they migrate.

“ We are threatened with suffering from three directions: from our own body, which is doomed to decay and dissolution and which cannot even do without pain and anxiety as warning signals; from the external world, which may rage against us with overwhelming and merciless forces of destruction; and finally from our relations to other men. The suffering which comes from this last source is perhaps more painful than any other. ” (S. Freud, Das Unbehagen in der Kultur, 1930 [Civilization and Its Discontents])

Traditional Chinese medicine defines acupuncture points, or acupoints, for therapeutic objectives, more than 2500 years ago. An acupuncture needle is inserted into selected acupoints on the body’s surface, on which mechanical (needling with lifting–thrusting cycle or twisting), electrical (electro-needling), or other types (e.g., heat [moxibustion]) of physical stimulations are exerted, in particular to cause analgesia. Afferent fibers of peripheral nerves are stimulated to elicit the De–Qi sensation and signal to adequate zones in the central nervous system. Acupoints are loci through which Qi is transferred to the body’s surface.

Meridians (Chinese: Jing) and collaterals (Chinese: Luo) are communication paths for Qi, the vital energy master of body fluids, which can be transported to acupoints. These spatially restricted sites that do not correspond to a specialized biological tissue, but to localized structural and fonctional units, are loci from which energy pours and pervade into the body’s tissues.

Acupuncture is aimed at relieving a pathological state by liberating the sequestered energy and rearranging the balance of Yin and Yang to ensure homeostasis. A disease is indeed supposed to result from an imbalance between Yin and Yang.

“ The negative and positive spiritual forces (Kuei-Shen) are the spontaneous activity of the two material forces (Yin and Yang). ” (Chang Tsai [1020-1078])

Yang and Yin are 2 fundamental opposing, complementary, and interdependent 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 completely Yin or Yang; everything is a mixture of the two. In particular, Yang may be considered as mental activity in its strength aspect, Yin mental activity in its imaginative aspect; in other words, Yang constructs, Yin instructs, or conversely. Yin is related to static and hypoactive phenomena, Yang to dynamic and hyperactive processes, or conversely.

“ Greater activity is called major Yang, whereas greater tranquillity is named major Yin. Lesser activity is termed minor Yang, whereas lesser tranquillity is designated as minor Yin… Yang cannot exist by itself; it can exist only when it is supported by Yin. Hence, Yin is the foundation of Yang. Similarly, Yin cannot alone manifest itself; it can manifest itself only when accompanied by Yang. Hence, Yang is the expression of Yin. ” (Shao Yong [1012-1077])

Insertion into the skin of thin needles is the most common technique. Manual manipulation or electrical stimulation is then achieved. Any acupoint localized in the vicinity of bones, aponeuroses, muscles, and tendons that contain neural units with somatosensory receptors. It is characterized by a large density of mastocytes that can secrete high concentrations of vaso- and neuroactive molecules, the latter targeting the central nervous system via both nervous transmission and blood convection. This pool of mastocytes reside close to neurovascular bundles, in a region where capillaries, lymphatic vessels, and nervous structures abound. Free nerve endings and cutaneous receptors (Merkel, Meissner, Ruffini, and Pacinian corpuscles), 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 [1584]. The mechanical stress field can activate Aα, Aβ, and Aδ fibers, as well as C-fibers of nervous structures at acupoints.¹ Other features include a large skin electrical conductance and high ionic concentrations (K⁺, Ca ${}^{++}$ , Fe ${}^{++}$ , Mn ${}^{++}$ , Zn ${}^{++}$ , and PO₄ ^3 −) [1585].²

Acupuncture can be assumed to be based on the chemical response especially of mastocytes at acupoints to the sensed mechanical stresses caused by needle motions. Other cells, such as neurons, macrophages, fibroblasts, and lymphocytes can contribute to the emission of local and endocrine signals (Table 12.2).

Table 12.2.

Signaling mediators released at acupoints (Source:[1586]; CGRP: calcitonin gene-related peptide; MOR: μ-opioid receptor). Mechanical stresses can activate Aα, Aβ, and Aδfibers, as well as C-fibers of nervous structures at acupoints and augment locally the vascular permeability to accelerate the transfer of mediators to the flowing blood.

Mediators	Releasing cells	Receptors
		Effects
Acetylcholine	Neuron, keratinocyte	M₂
Adenosine		A₁
ATP	Epidermal cells	P2X, P2Y
Bradykinin	Local cells	B₁, B₂
CGRP	Epidermal cells, T cell,
	macrophage
Cytokines (interleukins, tumor-necrosis factor-α
IL1β/6/8,	Local cells	Enhanced excitability
TNFα		of afferent fibers
IL4/10	Local cells	Inhibition of inflammatory
		signals in afferent terminals
β-endorphin	Fibroblasts,leukocytes,	MOR
	keratinocyte, melanocyte
Histamine	Mastocyte	H₁, H₃
GABA	Macrophage, lymphocyte	GABA_A
Glutamate	Macrophage, epidermal cells
Nitric oxide	Many cell types	Inhibition of substance-P
		release from nerve terminals
		Stimulation of acetylcholine
		and β-endorphin secretion
Noradrenaline	Sympathetic nerve	α2AR
Serotonin	Mastocyte, platelet,	5HT₁,
		5HT₃ (afferent nerve)
Somatostatin	Merkel cell, keratinocyte	SstR
Substance-P	Mastocyte, fibroblast,
	platelet, macrophage,
	keratinocyte
Prostaglandins	Local cells	EP

Mastocytes free numerous types of molecules, such as calcitonin gene-related peptide (CGRP), heparin, histamine, leukotrienes (LTb4, LTc4, LTd4, and LTe4), platelet-activating factor, prostaglandin-E2, serotonin, substance-P, and thromboxane-A2 (Table 12.3; Vol. 3 – Chap. (7. G-Protein-Coupled Receptors). Mastocytes also secrete peptidases (e.g., tryptase), growth factors (e.g., FGF, gmCSF, and NGF), and cytokines (e.g., interleukins and tumor-necrosis factor). Nerve endings are stimulated and release substance-P that further activates mastocytes and triggers the production of nitric oxide.

Table 12.3.

Released molecules by the mastocyte and their effects. Acupuncture can be modeled by an immediate and a late response. Nerves and mastocytes exchange chemical messengers such as substance-P. The latter stimulates histamine and nitric oxide (NO) release. Calcitonin gene-related peptide (CGRP) causes a vasodilation; nitric oxide cooperates with CGRP to increase its positive inotropic effect that raises the local blood flow in dilated vessels. Histamine is quickly catabolized, thereby acting near the site of release. Resulting vasodilation and increased vessel wall permeability support the transfer of chemical mediators into the blood circulation. The NO concentration rises and enhances the vasodilation. Serotonin has a biphasic effect, as it triggers a vasoconstriction and promotes NO release, hence a subsequent vasodilation. Nerve growth factor (NGF), tumor-necrosis factor (TNF) and interleukins (IL) are potent mastocyte chemoattractants. Mastocyte chemotaxis is supported by matrix degradation by secreted peptidases.

Agent	Effects
CGRP	Vasodilation,
	positive chronotropy, inotropy, and lusitropy,
	mastocyte degranulation
Heparin	Blood clot prevention
Histamine	Vasodilation (directly and via NO),
	nerve stimulation
Leukotrienes	Vasodilation, vascular permeability elevation
IL, NGF, TNF	Chemotaxis
Prostaglandin-D2	Nerve stimulation
Prostaglandin-E2	Vasodilation,
	inhibition of mediator release
Serotonin	Vasoconstriction followed by NO-mediated vasodilation
Thromboxane-A2	Vasoconstriction, platelet aggregation
Tryptase, chymase	Matrix degradation for enhanced cell migration

A self-sustained process is created via the recruitment of circulating mastocytes and excitation of regional pools of mastocytes. This traditional procedure of Chinese medicine relies on intra-, auto-, juxta-, para-, and endocrine signaling aimed at triggering mastocyte chemotaxis and sending messages via: (1) nerves for an immediate ( $\mathcal{O}$ [1 s–1 mn]), fast, and transient response of the central nervous system responsible of hyperemia in a given local region of the brain, in which neurons then secrete endocannabinoids, enkephalins, endomorphins, dynorphins, and other analgesic subtances, in particular, as well as a permanent response ensured by the continuous flux of activators; and (2) blood and lymph vessels for a delayed, slower, and sustained reaction based on transmission of substances that are conveyed throughout the brain, but preferentially to the highly perfused zone. Target nervous centers then reply by regulating the behavior of proper peripheral organs.

Any mastocyte in the local vasculature moves along the chemoattractant gradient, hence undergoes a transmigration (across blood vessel wall to exit blood, remaining granulated outside a region of triggering mechanical stress (x ≫ Δ x) and liberating its granule content, once it reaches a region close to the acupoint (0—Δx), where it can sense a significant magnitude of the mechanical stress. Two mastocyte states indeed exist according to its localization w.r.t. the acupoint (non-degranulated and degranulated).

Chemical mediators are supposed to be quasi-instantaneously released by the mechanotransduction process that mainly relies on an sudden, rapid, and copious calcium entry in the mastocyte cytosol. This calcium wave that gush and pervade the mastocyte enables it to discharge chemoattractants, nerve messengers, cardiovascular stimulants, and endocrine messengers. On the other hand, the regeneration of granules content inside the mastocyte is delayed and slow.

Following chemotaxis from regional pools and blood, newly arrived mastocytes at acupoints experience a degranulation triggered by the stress field. The resulting self-sustained process enables the local elevation of vascular permeability for improved cardiac output and enhanced endocrine signaling, vasodilation associated with a resulting increase in blood flow (remote cardiac effect), endocrine signaling to central nervous system that supports a delayed and permanent response from neurons situated in a brain region characterized by hyperemia, which can receive set of action potentials during a long period.

The mathematical model of acupunture can be represented by the set of equations that incorporates 2 equation related to the populations of non-degranulated and degranulated mastocytes, n _nd(t, x) and n _d(t, x) being the density of non-degranulated and degranulated mastocytes; 3 equations that describe the temporal evolution of concentrations of chemoattractant (c(t, x)), liberated nerve stimulant (s _n(t, x)), and endocrine activator (s _e(t, x)) of some sites of the central nervous system, when convection (i.e., Stokes flow of extracellular water triggered by needle motions) in the extracellular matrix remains negligible:

$\begin{array}{rcl}{ \partial }_{t}{n}_{nd}(t,\mathbf{x}) -{\mathcal{D}}_{m}{\nabla }^{2}{n}_{ nd}(t,\mathbf{x})& & \end{array}$

(12.1)

$\begin{array}{rcl}+\nabla \cdot ({\mathsf{S}}_{ca}\nabla c(t,\mathbf{x}) \cdot {n}_{nd}(t,\mathbf{x}))& =& -\mathsf{L}\Phi(x){n}_{nd}(t,\mathbf{x}) + \mathsf{R}{n}_{d}(t,\mathbf{x}); \\{\partial }_{t}{n}_{d}(t,\mathbf{x})& =& \mathsf{L}\Phi(x){n}_{nd}(t,\mathbf{x}) -\mathsf{R}{n}_{d}(t,\mathbf{x});\end{array}$

(12.2)

$\begin{array}{rcl} \\ {\partial }_{t}c(t,\mathbf{x}) -{\mathcal{D}}_{c}{\nabla }^{2}c(t,\mathbf{x})& =& \mathsf{L}\Phi (x){n}_{ nd} -{\mathsf{D}}_{c}c(t,\mathbf{x});\end{array}$

(12.3)

$\begin{array}{rcl} {\partial}_{t}{s}_{n} -{\mathcal{D}}_{n}{\nabla }^{2}{s}_{ n}& =&\mathsf{L}\Phi (x){n}_{nd} -{\mathsf{D}}_{n}{s}_{n}; \end{array}$

(12.4)

$\begin{array}{rcl}{\partial }_{t}{s}_{e} -{\mathcal{D}}_{e}{\nabla }^{2}{s}_{ e}& =& \mathsf{L}\Phi (x){n}_{nd} -{\mathsf{D}}_{e}{s}_{e},\end{array}$

(12.5)

where Φ(x) is the magnitude of applied mechanical stress

(0 ≤ Φ(x) ≤ 1, 0 ≤ x ≤ Δx);

${\mathcal{D}}_{m/c/n/e}$ the diffusion coefficient of mastocyte, chemoattractant, nervous messenger, and endocrine mediator; D the degradation rate; L the release rate

( ${\mathsf{L}}_{c}\, \equiv \,{\mathsf{L}}_{n}\, \equiv \,{\mathsf{L}}_{e}\, \equiv \,\mathsf{L}$ );

R the regeneration rate of degranulated masotocytes; S _cathe mastocyte sensitivity to chemoattractant, a measure of the chemoattractant power.

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Jun 3, 2017 | Posted by admin in CARDIOLOGY | Comments Off

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