In traditional Chinese medicine, internal organs imply ve viscera and six bowels. Five viscera mean liver, heart, spleen, lung and kidney, and six bowels mean gallbladder, small intestine, stomach, large intestine, urinary bladder and triple energizer. Also, meridian system represents the passage of metabolites in the human body. In this paper, we deal with construction of Petri net model of internal organs and meridian based on traditional Chinese medicine. At rst, we introduce relations of mutual generation and mutual restriction between ve viscera to make a basic Petri net model of ve viscera based on ve-elements theory. Analyzing the relation between ve viscera and six bowels, we propose a model of internal organs that include ve viscera and six bowels. After that, through investigating the syndrome of internal organs as well as the function of pericardium meridian, we propose a Petri net model including internal organs and meridians by combining the model of internal organs with meridians. Finally, we do simulation of the proposed model by using CPN Tools to show how our model works.
Traditional Chinese medicine or oriental medicine has been widely applied in
treating disease in China as well as in various asian countries since ancient times.
This is because of its less secondary e ect and possible curing for ahead sick and
incurable disease. Especially acupuncture and moxibustion therapy that
stimulate acupuncture points in meridian system to treat disease have spread rapidly
since the times when acupuncture and moxibustion therapy were admitted by
WHO in 1989 and 361 acupuncture points were standardized by WHO in 2006.
However mechanism of meridian system is still not scienti cally elucidated and
many of related researches and treatments have been made empirically and
clinically. Therefore it is required to develop new knowledge to elucidate acupuncture
and moxibustion treatment [
In traditional Chinese medicine, internal organs include ve viscera and six
bowels. Five viscera mean liver, heart, spleen, lung and kidney, and six bowels
mean gallbladder, small intestine, stomach, large intestine, urinary bladder and
triple energizer. Five viscera and six bowels imply the systematic functions of
human body rather than internal organs of human anatomy. Five viscera and six
bowels are closely related each other and have the correspondence relationship
between liver and gallbladder, heart and small intestine, spleen and stomach,
lung and large intestine, kidney and urinary bladder, respectively. Once one
becomes sick, the other has high possibility of abnormalities. Such relationship is
expressed in ve-elements theory of traditional Chinese medicine [
Recently, ve viscera of traditional Chinese medicine have been studied through
modeling and quantitatively analyzing [
In this paper, we are to propose a method of modeling both internal organs
and meridian system by using discrete Petri nets as the rst step towards
elucidating meridian system. Section 2 introduces ve-elements theory in traditional
Chinese medicine and gives basic knowledge of Petri nets. Section 3 describes
a model of internal organs including both ve viscera and six bowels based on
ve-elements theory. Section 4 introduces a concept of \syndrome" used in
traditional Chinese medicine and describes syndrome of ve viscera and six bowels
as well as the function of a meridian, pericardium meridian, to propose a Petri
net model including internal organs and meridian system. Section 5 shows
simulation of the proposed model by using CPN Tools [
According to ancient Chinese ve-elements theory, the ve elements, wood, re,
earth, metal and water are indispensable to the daily life of mankind. And in
veelements theory of traditional Chinese medicine, ve viscera, liver, heart, spleen,
lung and kidney, are mapped to the ve elements respectively. Liver ows Qi
through over the body free of all care, as a tree getting taller; Heart warms the
body as re; Spleen produces nutrients, as soil that produce all things; Lung
takes down Qi and Bodily Fluid, as astringent action of the metal; Kidney pools
Mind and adjusts the moisture of the body, as water that ows to the low place
from on high [
In ve-elements theory, there are generation and restriction relationships
between ve viscera. Generation is that of mother-to-child relationship to give
birth to the other party and is circulating in the order of wood ! re ! earth
! metal ! water [
In addition, ve viscera and six bowels have relations that interact with each other. That is, liver and gallbladder, heart and small intestine, spleen and stomach, lung and large intestine, and kidney and urinary bladder interact with each other, respectively. Triple energizer consists of upper energizer, middle energizer and lower energizer, which are the paths for Qi and Bodily Fluid to pass. Since triple energizer does not corresponds to any one of ve viscera, we are not to deal with it in this paper. 2.2
A Petri net is one of several mathematical modeling languages for the description
of concurrent systems [
Colored Petri nets (CPN) is extended from Petri nets by adding colors to
tokens and is a discrete-event modeling language combining the capabilities of
Petri nets with the capabilities of a high-level programming language. It allows
tokens to have a data value attached to them. This attached data value is called
token color. A Petri net is a tuple CP N =(P; T; A; ; C; N; E; G; I ) [
In Sun's model [
Excess and disease state with power of restriction ((a2; b2]), and severe state of excess (b2; 1).
Among ve viscera, there are generation and restriction relationships. In the
case of heart, it is generated by liver but restricted by kidney, which is shown in
Fig.3. Meanwhile, liver may loss its energy itself. Therefore, the state of liver at
time t, f (t), is expressed by the following equation that is modi ed from Sun's
model [
Here, we propose a Petri net model of ve viscera based on Sun's model. Firstly, we give a model for a single viscus as shown in Fig.4. Places, pin and pstate, are called input place and state place, and the token in state place is called state token whose value expresses the state of the viscus. tin is called input transition that works to calculate the state value of Eq. (1). tstate is called state transition and works to generate a state of the viscus. The token with calculated state value passes through pin and tstate and then arrive at pstate. tout is called output transition and works to generate and restrict other viscera.
Fig.5 shows a Petri net model including relationship of generation and restriction between viscera. This model is comprised of three single viscus models, the models of liver, heart and spleen, which are connected by places ps1, p1k and ps2. Places ps1 and p1k express liver's generation and restriction a ection to heart and spleen, respectively, and these two places are respectively called generationoutput place and restriction-output place of liver. Tokens in generation-output and restriction-output places are respectively called generation token and restriction token. Similarly, ps2 is generation-output place of heart.
Since liver generates heart and restricts spleen, state token of liver ows through output transition to1ut to generation-output place ps1 (that is also an input place of heart model) and to restriction-output place p1k (that is also an input place of spleen model). In the same way, state token of heart ows to generation-output place ps2 that is an input place of spleen model. The Petri net shown in Fig.6 can be treated as a model of any one pair of ve viscera and six bowels (say liver and gallbladder). Hence to make a full model that includes both ve viscera and six bowels, we need only to consider how to connect these models together into one model.
Five viscera and six bowels are in the relationship of the front and back, such as liver and gallbladder, heart and small intestine, spleen and stomach, lung and large intestine, and kidney and urinary bladder. Each of these pairs interacts with each other to maintain life. Such a pair, for example liver and gallbladder, is modeled by Petri net as shown in Fig.6. This model is made by adding transitions tzf and tfz and connecting them to the single model of liver and gallbladder. tzf and tfz represent the a ections from liver to gallbladder and from gallbladder to liver, respectively.
Synthesizing the models we have made till now, we can complete a model of internal organs. The process is summarized as follows: (1) Make a single model for each of ve viscera as Fig.4; (2) Connect these single models according to generation and restriction relationship between ve viscera as Fig.5; (3) Add to the model of each viscus by the model of its pair partner of six bowels as Fig.6. Then the complete model is obtained as shown in Fig.7. 4
4.1
In traditional Chinese medicine, meridian system is considered as important
channels to transfer Qi (means energy) and blood in human body. Meridian
system is divided into meridians and collaterals [
Meridians consist of twelve principal meridians and eight extra meridians.
Twelve principal meridians include three Yin and three Yang meridians of hand
and also three Yin and three Yang meridians of foot. Here, Yin and Yang are
the concept of duality forming a whole and mean respectively sunny side and
shady side (e.g., the palm and the back of the hand). Yin meridians belong to
ve viscera and Yang meridians belong to six bowels. Each principal meridian
has acupuncture points. In eight extra meridians, only Renmai and Dumai have
acupuncture points. Twelve principal meridians along with Renmai and Dumai
are thought of main meridians [
Acupuncture points exist in twelve principal meridians, Renmai and Dumai.
Through these acupuncture points, Qi passes inside and outside of body and
thus various diseases can be prevented and cured by stimulating these
acupuncture points [
In traditional Chinese medicine, \syndrome" is a measure to evaluate the state
and physical condition of human body [
On the other hand, when the states of internal organs are no longer
normal, various functions will be modulated by each organ. For example, in liver
the dispersing and dredging function and the capability to store the blood are
probably decreased; in heart abnormalities may occur in the blood stream; in
spleen the functions of transportation and transformation, which send up the
lucid Yang and govern the blood, may be decreased; in lung dissipating and
exerting e ect may become weak; and in kidney functions of storing the essence of
life and regulating the metabolism of water are probably decreased. In the case
of six bowels, the abnormalities related to digest, absorption and excretion may
probably occur. [
Combining these syndromes due to the modulations of internal organs with the e ect of acupuncture points of pericardium meridian, we can make a table representing the relationship between each internal organ and each acupuncture point of pericardium meridian as shown in Table.1, in which notion \*" shows the e cacious relations. For example, the acupuncture point Quze is supposed to be e cacious against the symptoms related to liver, heart, lung and kidney, as well as stomach and large intestine.
Here, we construct a model of pericardium meridian and combine it with the model of internal organs proposed in the last section according to Table 1. As we have stated, meridians and acupuncture points connect skin and inner organs of body. Stimulating an acupuncture point, the signal is transmitted to the meridian and then circulation of Qi and ood is improved, which makes internal organs active. In the case of Quze, when it is stimulated, liver, heart, lung and kidney, as well as stomach and large intestine, are activated.
Based on the above, we modeled the in uence of a single acupuncture on a single organ as shown in Fig.9. Acupuncture point is represented by a transition, stimulation of the acupuncture point is represented by ring the transition. Fitting together with state token of the single organ, the token generated by the ring goes through transition tp to the input place of the organ, and it further moves to the state place (Output&State Place). Thus activation of the organ is represented.
Applying the same way as Fig.9 for all the organs according to Table 1, we nally get a complete model of internal organs and pericardium meridian as shown in Fig.10. Note that plural tokens generated by plural acupuncture points are accumulated at one place. 5
We have done simulation by using CPN Tools [
Note that all the constants are temporarily decided for the simulation.
Simulations have been done based on the above parameters. We suppose that initially stomach is in weak state with state token value \1" and all the other organs are in normal state with \3". Among acupuncture points, Quze, Neiguan, Daling and Laogong have in uence on stomach, and we choose Daling to do the stimulation for 50 times. Simulation results are shown in Fig.12 and Fig.13.
From Fig.12 and Fig.13 we can observe the following phenomenons. At rst, weak stomach adversely a ects spleen directly, and thus spleen weakens rapidly and its state value becomes lower than 2.5. Due to weakening of spleen and also the relationship of generation and restriction between ve viscera, all the viscera gradually weaken except heart. On the other hand, spleen directly strengthens stomach and the acupuncture point, Daling, is stimulated continuously. These actions strengthen stomach rapidly and as the result stomach recovers its state value to 2.5 when Daling is stimulated 22 times. After that, all the organs recover gradually and nally get to health state with state values almost 3 when Daling is stimulated 50 times. Of particular interest is that any organs of six bowels are almost not a ected by stomach except large intestine. 6
We have proposed a method of constructing Petri net model for internal organs and meridians based on traditional Chinese medicine. According to ve-elements theory and the control model proposed by Sun et al., we have proposed a Petri net model of ve viscera by considering the generation and restriction relationship between ve viscera. Taking into account of the relationship of front and back between ve viscera and six bowels (except triple energizer), we have made a model of internal organs. Through investigating the syndrome of internal organs as well as the function of pericardium meridian, we have proposed a Petri net model including internal organs and meridians by combining the model of internal organs with meridians. Finally, we do simulation to show how our model works by using CPN Tools.
It should be pointed out that this work does not intend to be a scienti c contribution to medical science in the sense as it is usually understood. As the future works, we are to (1) decide parameters for all the transitions and places, as well as for tokens and arcs on the basis of the data of acupuncture treatment site; (2) do simulation to verify the validity of the proposed model and the parameters, in order to improve the model; (3) develop a method to construct a Petri net model for the whole human body.
The authors would like to thank Ms. Misato Maesaka for her e orts in doing simulation and handling simulation data. This work was supported by JSPS KAKENHI Grant Number 25540135 (Grant-in-Aid for Challenging Exploratory Research).