biomedical infophysics models of meridian channel system · 2011. 12. 7. · or propagation of...

Article ID: WMC002555 ISSN 2046-1690

Biomedical Infophysics Models of Meridian ChannelSystemCorresponding Author:Dr. Kang Cheng,Scientist, Biomedical InfoPhysics, Science Research Institute - United States of America

Submitting Author:Dr. Kang Cheng,Scientist, Biomedical InfoPhysics, Science Research Institute - United States of America

Article ID: WMC002555

Article Type: Original Articles

Submitted on:06-Dec-2011, 07:39:41 PM GMT Published on: 07-Dec-2011, 05:12:36 PM GMT

Article URL: http://www.webmedcentral.com/article_view/2555

Subject Categories:BIOPHYSICS

Keywords:Interstices, Electrolytes, Thermodynamics, Electrodynamics, Entropy, Statistical, Fluid

How to cite the article:Cheng K , Zou C . Biomedical Infophysics Models of Meridian Channel System .WebmedCentral BIOPHYSICS 2011;2(12):WMC002555

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Biomedical Infophysics Models of Meridian ChannelSystemAuthor(s): Cheng K , Zou C

Abstract

In our recent previous study, we in anatomy andhistology modeled meridian channels as aphysiological system based on published biomedicaldata. We think, the meridian system is mostlyconstructed with interstices in or between otherphysiological systems; major components in themeridians are loosen connective tissues that consist ofelectrolytes, cells and proteins; the electrolytes providerich fluids and ions for processing, propagation ortransportation of information, matter and energy in themeridians. In this research, we propose infophysicsmodels to answer how information, matter and energyare processed, propagandized, or transported in themer id ians. We apply thermodynamics tomacroscopically present relationships of entropy,energy, work, heat, pressure, volume and temperature;physics involves the two laws of thermodynamics, vander Waal’s equation, Gibbs equation and Maxwell’sequations of thermodynamics. We apply classicstatistical mechanics to microscopically elucidateinformation amount and matter (or energy) flux for thecomplicated irreversible process; physics involvesGibbs entropy, Onsager method or formulation, suchas heat conduction density (Fourier law), particlediffusion density (Fick law), electric current density(Ohm law), or shear stress of viscosity (Newton law),Poisson-Boltzmann equation and Boltzmann equation.We apply electrodynamics to macroscopically describeelectromagnetic fields and ions motion; physicsinvolves Maxwell’s equations of electrodynamics,Newtonian momentum transfer equation, Ohm’s law,Lorentz forces, Bernoulli’s separation method,conservations of charges and masses, and Poynting’stheorem. We apply constitutive equation in fluidmechanics to indicate stress - strain relationship. Weapply Schrodinger equation in quantum statisticalmechanics to estimate ion channel currents. We alsothink information has different expressions and levels(forms). In a view of sciences, there are expressions ofphysics, chemistry, physiology, medicine, et al. In aview of arts, there are expressions of songs, music,photos, draws, tables, words, et al. In a view ofphysics, the highest level of information containsrelated or correlated equations, such as Maxwell

equations of electromagnetism or thermodynamics,Newton’s laws of mechanics, Einstein’s relativities; thehigher level of information is a theoretic formula, suchas Schrodinger equation, Boltzmann entropy formula,Newton’s gravitational law; the middle level ofinformation is a function, such as a natural exponentialfunction; the basic level of information is a property oran attribute of a function, e.g., a frequency of a wavefunction. Lower level information can be resolved orexpressed with or included in higher level information,e.g., dual properties of wave and particle of anelectron can be expressed with a probability wavefunction, and the function can be included in andresolved with Schrodinger equation.Keywords: Interstices, Electrolytes, Thermodynamics,Electrodynamics, Entropy, Statistical, Fluid

Introduction

Scientists or clinicians have proposed many models orhypotheses to discover the mechanisms of meridian (-collateral) channels in human bodies. One ofhypotheses is that the Chinese medicine system is aspecial channel network comprising of the skin withabundant nerves and nociceptive receptors of varioustypes and deeper connective tissues inside the bodywith the flowing interstitial fluid system [1]. Anotherhypothesis of multi-factors is involved in directcommunication pathway of the cell junction (speciallykeeping the relevant cellular direct communicationrelation in individual development), the extra-cellularmatrix stress network system and its biophysicalmessage transmission--force--meridian signstransformation-inter-cellular massage integration [2]Mathematical [3], informative [4] and birdcage [5]models have been proposed too. However themechanism of the meridian channel system is stillunclear. In our recent previous study [6], we in anatomy andhistology modeled meridian channels as aphysiological system based on published biomedicaldata [7-9]. We think, the meridian system is mostlyconstructed with interstices in or between systems ofthe integumentary, the nervous, the muscular, thecardiovascular, the skeletal, the lymphatic, theendocrine, the respiratory, the digestive, the urinaryand the reproductive; major components in the



meridians are loosen connective tissues that consist ofelectrolytes, cells and proteins; the electrolytes providerich fluids and ions for processing, propagation ortransportation of information, matter and energy in themeridians. The meridian system is mostly inlongitudinal direction (ascending from toes or fingers),is approximately symmetric about the middle line (fromthe nose to the umbilicus or spinal cord), and isroughly parallel to systems of the integumentary, thenervous, the muscular, the cardiovascular, the skeletal,the lymphatic, and the endocrine. We hypothesizedthe orientation, the symmetry and the parallel of thesystems are formed during the embryo’s development.Similar to systems of the nervous, the cardiovascular,the lymphatic, the endocrine, the respiratory, thedigestive and the urinary, the meridian system shouldbe unblocked according to the theory of Chinesemedicine. If the systems are blocked, some diseasescould occur. However, we have not modeled how information,matter and energy are processed, propagandized ortransported in the meridian system and we have notfound any related report in a view of biomedicalinfophysics. We think storage, propagation (ortransportation) and processing of information arephysical. In this paper, we consider infophysics as acombination of information and physics, and presentour infophysics models for processing, transportationor propagation of information, matter and energy in themeridian system. We believe our models in this paperwill be helpful to keep health people from or treatpatients with the meridian diseases.

Models

We think information has different expressions andlevels (forms) [6]. In a view of sciences, there areexpressions of physics, chemistry, physiology,medicine, et al. In a view of arts, there are expressionsof songs, music, photos, draws, tables, words, et al. Ina view of physics, the highest level of informationcontains related or correlated equations, such asMaxwell equations of electromagnetism orthermodynamics, Newton’s laws of mechanics,Einstein’s relativities; the higher level of information isa theoretic formula, such as Schrodinger equation,Boltzmann entropy formula, Newton’s gravitational law;the middle level of information is a function, such as anatural exponential function; the basic level ofinformation is a property or an attribute of a function,e.g., a frequency or an amplitude of a wave function.Lower level information can be (approximately)resolved or expressed with or included in higher level

information, e.g., dual properties of wave and particleof an electron can be expressed with a probabilitywave function, and the function can be included in andresolved with Schrodinger equation. The levels fromthe middle to the highest are correspondent toapproach the natural laws; the basic levels arecorrespondent to approach properties or attributes ofthe natural objects. See Fig. 1.Fig. 2 illustrates our framework of main networks ofinformation, matter and energy in a human body. Inthis investigation, we focus on the meridian network;and we first introduce our meridian models inphysiology; then based on the physiological model, wepropose our models for processing, transportation orpropagation of information, matter and energy in themeridians in physics.A. BiomedicineFig. 3 shows our model of meridian channel system forhuman embryos in physiology, anatomy and histology.The meridians are interstices around systems of thenervous, the cardiovascular, the digestive and thecells. We believe the meridian system is formed duringembryos developing in parallel to other physiologicalsystems, such as the nervous, the cardiac vascular,the muscle and the skin [6].Fig. 4 shows our model of meridian channel system ofhuman adults. The meridians are interstices in orbetween systems of the integumentary, the nervous,the muscular, the cardiovascular and the skeletal. Thenervous system samples, collects, encodes, decodes,transmits and processes information from othersystems and controls the other systems [1]. Our modeling results suggest that, the meridiansystem is mostly constructed with interstices in orbetween other physiological systems; majorcomponents in the meridians are loosen connectivetissues that consist of electrolytes, cells and proteins,the electrolytes provide rich fluids and ions forprocessing, transportation or propagation ofinformation, matter and energy in the meridians(6).B. InfophysicsA biological system obeys laws of physics andchemistry [10]. We mostly model processing,propagation or transportation of information, matterand energy in the meridian system with laws andtheorems in physics, though chemistry is involved too.The dominative laws and theorems in physics involvethermodynamics, classic statistical mechanics,electrodynamics, fluid mechanics and dynamics,quantum statistical mechanics.

Application



A. Electric shock

If we accidentally get an electric shock by touching acharged object with our hands, we will feel externallyapplied electric currents flow along our arms6. Theexternally applied electric currents or fieldsapproximately follow Ohm’s law of electricity (equation14), ions motion approximately follows equations 18 or22. We would like explain the phenomenon in this way:the externally applied electric currents or fields flow inour meridian channel system, the applied fieldsstimulate our nervous sensors along the meridians,the sensors sample and collect the information, thenerves transmit the information to our brains, see Fig.4. This evident strongly supports our models ofmeridian channel system.

B. Interstitial fluid flow

Experimental data of interstitial fluid flow [1, 26] couldbe described with equations 26 and 27.

C. Interstices

We can see interstices when we cut fresh meat, suchas beefs or porks. We consider the interstices as themeridian channels.

Discussion

Though, we can solve the equations with the boundaryconditions in theory, it is very difficult to obtainanalytical solutions of the equations today. Futurestudy could be how to solve the equations analyticallyor digitally; and how to fit the experimental data withthe calculated results. We believe our models are alsoapplicable to other biomedical systems in principle.

Conclusion

Information has different expressions and levels(forms). In a view of sciences, there are expressions ofphysics, chemistry, physiology, medicine, et al. In aperspective of physics, the highest level of informationcontains related or correlated equations, such asMaxwell equations of electromagnetism orthermodynamics, Newton’s laws of mechanics,Einstein’s relativities; the higher level of information isa theoretic formula, such as Schrödinger equation,Boltzmann entropy formula, Newton’s gravitational law;the middle level of information is a function, such as anatural exponential function; the basic level ofinformation is a property or an attribute of a function.Lower level information can be resolved or expressedwith or included in higher level information.

Acknowledgment

The authors thank Miss Vivien Cheng of PrincetonUniversity for comments and English corrections.

References

1. P.C. Fung, “Probing the mystery of Chinesemedicine meridian channels with special emphasis onthe connective tissue interstitial fluid system,mechanotransduction, cells durotaxis and mast celldegranulation,” Chin. Med. 4, 10:1-6, (2009).2. J.D. Chen, “On structure characteristics andmechanisms of channels and collaterals,” 29(4):293-6(2009).3. Y. Liu, L. Chen, P. Fan, X. Wu, “Createmathematical model and analysis of correlationbetween traditional Chinese medicinal characteristicsand neurobehavioral effects,” Zhongguo Zhong YaoZa Zhi. 34(3):251-4 (2009).4. X.L. Chang, “Anatomical visibility of the meridianinformation channels,” Zhen Ci Yan Jiu. 33(6):420-2(2008).5. K.T. Yung, “Birdcage model for the Chinesemeridian system: part VI. meridians as the primaryregulatory system,” Am J Chin Med. 33(5):759-66(2005).6. K. Cheng and C. Zou, “Information models ofacupuncture analgesia and meridian channels,”I n f o r m a t i o n 1 ( 2 ) , 1 5 3 - 1 6 8 ( 2 0 1 0 ) ;doi:10.3390/info1020153.7. M. H. Ross and W. Pawlina, Histology: A Text andAtlas: With Correlated Cell and Molecular Biology(Lippincott Williams & Wilkins, Philadelphia, PA, USA,2006).8. S. McCann, J. Tillotson and S.E. Reichert, AnatomyColoring Book (Kaplan Publishing, New York, NY,USA, 2008).9. B. M. Patten, Human Embryology, Edited by ClarkEdward Corliss (McGraw-Hill, New York, NY, USA,1982).10. B. Alberts, et al, Molecular Biology of The Cell(Garland Science, New York, NY, USA, 2007).11. G. Barrow, Physical Chemistry (Mcgraw-HillCollege, New York, NY USA, 1996).12. Moore WJ, Physical Chemistry, LongmanPublishing Group; New York, NY, USA, 1998).13. D. Chandler, Introduction to Modern StatisticalMechanics (Oxford University Press, New York, NY,USA, 1987).14. J.W. Gibbs, Elementary Principles in StatisticalMechanics - Developed with Special Reference to the



Rational Foundation of Thermodynamics (Dover, NY,USA, 1901).15. C.E. Shannon, “A mathematical theory ofcommunication,” Bell System Technical Journal,July/October (1948).16. R.W. Hamming, Coding and Information Theory(Prentice-Hall Inc. Wood Cliffs, NJ, USA, 1986). 17. E.Schrödinger, What is Life? and Mind and Matter(Cambridge University Press. New York, NY, USA,1968).18. K. Cheng and C. Zou, “Four dimensionalBioChemInfoPhysics models of cardiac cellular andsub-cellular vibrations (oscillations),” OnLine Journalof Biological Sciences, 9(2), 52-61 (2009).19. M.A. Uman, Introduction to Plasma Physics(McGraw Hill, New York, NY, 1964).20. H. Sagan, Boundary and Eigenvalue Problems inMathematical Physics (Dover Publications, New York,NY, USA, 1989).21. K. Cheng and C. Zou, “BioInfoPhysics models ofneuronal signal processes based on theories ofelectromagnetic fields,” American Journal ofNeuroscience, 1(1), 13-20 (2010).22. Y.C. Fung, Biomechanics, Mechanics Properties ofLiving Tissues (Springer, New York, NY, USA, 1996).23. Y.C. Fung, Biodynamics, Circulation (Springer,New York, NY, USA, 2010).24. K. Cheng, P.P. Tarjan, C. Zou, “Schrodingerequation, Maxwell-Boltzmann distribution and singlechannel current,” Biomed Sci Instrum. 29, 361-367(1993).25. K. Cheng, “Improved 3-D quantum mechanicalmodels of ion movements in a cylindrical ion-channel,”Proceedings of the 16th Southern BiomedicalEngineering Conference, Broadwater Beach Resort,Bilaxi, Mississippi, USA, 1997, edited by J.D.Bumgardner, A.A. Puckett [IEEE: Piscataway, NJ,USA, pp. 220-223 (1997)].26. Y. Xu, W. Zhang, Y. Tian, R. Wang, L. Wang, T.Huang and G. Wang, “Preliminary observation of theblocking effect produced by injecting polyacnylamidehydrogel on low hydraulic resistance channel alongmeridian,” Sheng Wu Yi Xue Gong Cheng Xue Za Zhi.26(4):776-9 (2009).



FIG. 1. Our framework of information levels (forms).

Framework of Information Levels

Basic

An Equation

A Function

A Property or a Tribute of a function

High

To approach thenatural laws.

To approach a property ora tribute of a natural object.

Related Equations

Illustrations

Illustration 1

Fig 1



FIG. 2. Our framework of main networks of information, matter and energy in ahuman body. The arrows indicate exchanges of information, matter and energy.

Framework of Main Networks in a Human Body

Neural Network

Meridian Network

Lymphatic Network

Cardiovascular Networks

Illustration 2

Fig 2



Illustration 3

FIG. 3. Our model of meridian channels for a part of selected cross section of a human embryo during the 5th week, the directionsof meridian channel currents are assumed. The biological data and draw is from published references [9].



Illustration 4

FIG. 4. Our model of meridian channels of human adults. The directions of meridian channel currents are assumed.



1. ThermodynamicsThermodynamics plays very important roles in biological systems [10]. Therefore,thermodynamics should do so in the meridian channel system too.

The first law of thermodynamics is, (1)

where, U, Q and W respectively denote energy, heat and work for the meridiansystem. The first law indicates conservation of energy.

The second law of thermodynamics in mathematics is [11 – 12],

(2)

where S, Q and T respectively denote entropy, heat and absolute temperature of asystem. Equation 2 represents a theorem of entropy increase for the meridian andother physiological systems and their environments.

For equilibrium isotherms states of a meridian system, we apply van der Waal’sequation,

(3)

Illustration 5

Model Detail Page



where, P, V and T are respectively pressure, volume and absolute temperature; n ismole number; R is gas constant per mole; a and b are constants.

For nonequilibrium states system, the Postulate of Local (cellular) Equilibrium hasbeen introduced. Gibbs equation has been applied to each cell in the system [11 – 12],

(4)

where i is defined as the chemical potential by Gibbs and ni is the number of molesof components. Equation 4 also means energy conservation.

Maxwell’s equations of thermodynamics present relationships of entropy,temperature, pressure and volume, they are,

(5)

(6)

(7)

(8)Equation 5 means that changing pressure in a constant volume and in an entropydomain is equivalent to changing temperature with constant entropy and in a volumedomain. In a similar way, we can describe equations 6 - 8. We consider Equations 1 –8 as thermodynamics expression of information.



2. Classic statistical mechanicsClassic statistical mechanics is a microscopic state description for macroscopicthermodynamics. Based on Boltzmann’s statistical entropy of equilibrium states of asystem, Gibbs proposed a more general statistical entropy to describe the order for theboth equilibrium and non-equilibrium systems [13]. Gibbs entropy formula involvespartition function and microstate energies [13 – 14], and it is,

(9)

where

(10)

(11)where, kB is Boltzmann’ constant; n denotes a microstate, Nn is the number ofmicrostates, n is a chemical potential and pn is its probability that it occurs duringthe system's fluctuations. We consider equations 9 - 11 as information expressions inmicroscopic statistical mechanics and represent entropy, i.e., orders or disorders forthe meridian system states. And we also apply Gibbs entropy formula to calculate thecorrespondent information amount, based on Shannon’s information concept [15 –16],



(12)

(13)

where, subscript a and b are respectively after and before.Schrodinger discussed genetic information in a biological system with order,

disorder and Boltzmann’s entropy in 1945 [17]. Shannon clearly proposed hisdefinition of information (amount) with entropy for a communication channel systemin 1948 [15 – 16]. We think, Shannon’s information concept for a communicationchannel system is in principle equivalent to equation 13 with Gibbs entropy formulafor a meridian channel (classical statistical mechanical) system.

Onsager method or formulation is suitable to describe the complicated irreversibleprocess. The formulation is based on the Principle of Microscopic Reversibility [12].We can write a flux (transportation), for a linear procedure in thermodynamics, as:



(14)

(15)

where, respectively, Jk is kth thermodynamic flux, such as heat conduction density(Fourier law), particle diffusion density (Fick law), electric current density (Ohmlaw), or shear stress of viscosity (Newton law); Xl is lth thermodynamic force, such astemperature gradient (T), concentration gradient (C), electric potential gradient(V), or velocity gradient (v); Lkl is the direct (or cross) force coefficient, such asheat convention coefficient, diffusion coefficient, conductivity, or coefficient ofviscosity. Equation 15 is Onsager relation. Formula for a non-linear procedure is morecomplicated, but the Onsager relation is still valid. The local entropy production rateis,

(16)

Poisson-Boltzmann equation of electric potential is [11 – 12],

(17)



where r2 is a 3-D spatial Laplace mathematic operator, is charge density, iselectric permittivity, -e is electron charge, zi is number of charges on the ion, Ci is theaverage number of ions of kind i in unit volume of tissue fluid.

If we considered the electrolytes as quasi liquid plasma in physics [18], Boltzmannequation is [19],

(18)

(19)

where, i and n respectively denote ions and neutral particles; f denotes a Boltzmanndistribution function; u and r respectively denote velocities and space coordinates; ris a 3D spatial nabla mathematic operator.



3. ElectrodynamicsBiological fluids in the meridian system are mostly electrolytes. Electrodynamics (orelectromagnetism) must play very important roles for the meridian systems [6].Maxwell’s two complementary equations of electromagnetism present relationshipsof electric field, magnetic field and electric current, and they are,

(20)

(21)

where, E and H are respectively electric and magnetic field intensity vectors; and are respectively tensors of permittivity, conductivity and permeability. Equations 20and 21 mean temporal changing electric (magnetic) field produces spatial rotationalmagnetic (electric) field. Temporal and spatial frequencies may be involved. If weconsidered the electrolytes as quasi liquid plasma in physics [18], a Newtonianmomentum transfer equation for macroscopic particles (e.g. ions) in an electro – hydrodynamic system is [19],

(22)



where, vi, mi, ni, ci and qi are respectively the velocity, the mass, the particleconcentration, the effective collision frequency (Ohm’s law related) and the electriccharge of the free ions. Pi represents the pressure in the fluid. E and B are electric andmagnetic fields respectively; X means a mathematical cross product (Lorentz forcesrelated). Fv is a sum of externally applied hydrodynamic volume forces(force/volume) [19].

The related electric charge density is c(x, y, z, t) = ni qi in meridians. Thelongitudinal direction is along a (changing) z axis, x and y are in the transversaldirections; t is time; we assume, Bernoulli’s separation method and superpositionprinciple are applicable to the spatial and temporal variables [20] and x, y, z and t areindependent from each other, to simplify our models and to get analytic solutions.

Based on principle of conservation of charges, we can obrain related equations ofelectric field intensity (EFI),

(23)



where Je is the electric current density. An expression of conservation of masses issimilar to equation 23, but mass density replaces charge density and mass flow densityreplaces the electric current density. We defined EFI as information intensity (II) inour presvious study21 and we think an object claims its terotory with its II producedwith its matter (charge or mass) and informs its targets how to respond to its claim: toleave or to come.Poynting’s theorem also plays important roles in processing, propagation ortransportation of information, matter and energy in electrodynamics21. We considerEquations 20 – 23 as electrodynamics expression of information.

We approximately used Fourier series (FS) to model (electric) acupunctureinformation or signals received by nervous sensors in the meridians [6], it is,

(24)



Where, Q is electric charge; we assume Bernoulli’s separation method is applicable tothe spatial (z) and temporal (t) variables [20]; kz is a wave number in z (informationpropagation) direction; = 2f, and f are fundamental angular frequency andfrequency, respectively; an and bm are constants. After the 1/2 and signs are includedin the an or bm, the electric current in z propagation direction is:

(25)

where z0 is a unit vector in z direction. The current is frequency encoded. We canexecute the superposition theory for two signals, one is pain and another one isacupuncture, in pairs for m and n numbers in equation 25, to explain analgesia withacupuncture [6].



4. Fluid mechanicsConstitutive equation is also very important to describe the meridian system.Interstitial fluid can be considered as quasi incompressible Newtonian viscous fluid[22 – 23]. Therefore, a constitutive equation can be used to represent its stress - strain(tensors) relationship,

(26)

where ij is Kronecker delta, and

(27)

is the strain rate tensor, and and are two material constants. We considerEquations 26 – 27 are information expression in fluid mechanics.



5. Quantum statistical mechanicsIn quantum statistical mechanics, Schrodinger equation for motion of a

microscopic particle in a cylindrical coordinate system is,

(28)

where is a probability wave function, H is Hamilton’s energy operator (Hamiltonianoperating) and h is Plank constant. We define - as a probability field intensity,where is a spatial mathematic nabla operator. A general solution for a stationarystate Schrodinger equation in quantum statistical mechanics is,

(29)



where potential field is assumed to be independent of time, r, , z and t are spatial andtemporal coordinates respectively; n denotes a integer, cn, n and En are constants,probability wave functions and energies for microstates. The equation and thefunction have been assumed to be suitable to describe particle movements in verynarrow spaces such as cellular ion channels [24 – 25]. Equation 29 is an informationexpression of probability wave function; and the related probability density (PD) canbe obtained from equation 29, and it is,

(30)

when n1 n2, the terms in equation 28 are interferences. Equation 28 is aninformation expression of probability density and demonstrates where particles existprobably. Comparing equations 9 and 30, we think cn2cn1*, n2*n1 and exp()terms in equation 30 respectively play the same roles as KB, Pn and ln() terms do inequation 9. We consider Equations 28 – 30 as information expression in quantumstatistical mechanics.



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biomedical infophysics models of meridian channel system · 2011. 12. 7. · or propagation of...

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