Localization of acupoints on a head based on a 3D virtual body

Localization of acupoints on a head based on a 3D virtual body

Lei Zhenga, Binjie Qina, Tiange Zhuanga,*, Ulf Tiedeb, Karl Heinz Hohneb

aDepartment of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, ChinabInstitute of Medical Informatics (IMI), University Hospital Hamburg-Eppendorf, Hamburg, Germany

Received 11 February 2004; received in revised form 15 March 2004; accepted 31 March 2004

Abstract

Modern computer science allows powerful and versatile computer-based knowledge representations of acupuncture, one part of

Traditional Chinese Medicine. For further research and development of acupuncture therapy, it is critical to define where to accurately

localize acupoints onto such a computer based pictorial representation of the human body. Using the segmentation and 3D visualization of

the VOXEL-MAN software system, original work for localizing the acupoints on a head based of a virtual body is reported in this paper.

The proposed 2D acupoint description links the description taken from literature for locating acupoints in Traditional Chinese Medicine to

the data in the absolute reference frame of a 3D virtual body. It offers a simple and useful way for the localization of acupoints on a 3D model,

especially one derived from the data from Visible Human Project.

q 2004 Elsevier B.V. All rights reserved.

Keywords: Traditional Chinese Medicine; Acupuncture and moxibustion; Localization of acupoints; Three-dimensional body model; Visible Human Project;

VOXEL-MAN

1. Introduction

The science of acupuncture and moxibustion is an

important part of Traditional Chinese Medicine Chinese

people have accepted it for thousands of years, because of

its magic curative effect, simple operation, low cost, and

few side effects. Now, use of the science of acupuncture and

moxibustion has even spread all over the world.

Acupuncture therapy heavily depends upon the precise

placement of the acupuncture needle at the proper point

on the body surface. Some of them are vital. Such points

are defined within the context of blood vessels and

nerves. Positioning errors in acupuncture treatment can

cause medical accidents. Therefore the accurate localiz-

ation of acupoints is a key issue in the acupuncture

research.

In traditional medicine, knowledge on acupuncture is

described in books and atlases, such as the anatomical charts

of acupuncture and moxibustion. However, modern com-

puter science, especially computerized three-dimensional

models [1,2], allows new, more standardized and reprodu-

cible computer-based representations of the human body.

We expect that the use of such models will not only

decisively advance learning and teaching acupuncture, but

also substantially contribute to the research concerning

Traditional Chinese Medicine (TCM) theory.

One of these models is the VOXEL-MAN [3] system,

which consists of a voxel based spatial model of the human

body linked to a semantic network containing the descrip-

tive information. One of the prerequisites, however, for

making use of this model for acupuncture, we need to

transfer the classical qualitative description of the acupoints

into the computer-based model. With the example of the

human head we therefore propose in this paper algorithms

for transferring the localizations of the acupoints of the

human head from classical atlases and books to the

computer based model.

2. Pre-processing

Spatial knowledge representation in medical imaging

and computer graphics is totally different from what is used

in the literature for locating acupoints in TCM. The first uses

an absolute reference frame, which has almost no relation to

the image content, while the latter employs a relative

reference frame relative to constituents of the body.

0262-8856/$ - see front matter q 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.imavis.2004.03.005

Image and Vision Computing 23 (2005) 1–9

www.elsevier.com/locate/imavis

* Corresponding author.

E-mail address: [email protected] (T.G. Zhuang).

http://www.elsevier.com/locate/imavis

Furthermore, computer based volume models are

discretized in voxels. In current research, a voxel of the

VOXEL-MAN is e.g. 1.08 mm in each dimension [3].

However, the basic unit for a relative reference frame used

by traditional acupoint localization is usually defined by

‘Bone Proportional Measurement’ [4] between landmarks

on the human body. It makes the acupoint position suitable

for everybody, no matter whether the boy is thin or fat or tall

or short.

To locate acupoints on a 3D human body model

accurately, we design a temporary reference frame (TRF)

to relate the absolute reference frame (ARF) of 3D medical

images to the relative reference frame (RRF) used in

traditional acupoint localization methods.

2.1. General definition

On a body or body image, we define the axis x of TRF as

the orientation from right to left, the axis y from anterior to

posterior and the axis z from inferior to superior Especially,

in this paper, we set the origin of TRF on the midpoint

between the two eyebrows, as shown in Fig. 1.

2.2. Plane yz

One property of a human body is its left-right symmetry,

which is also expressed on the human body image. A method

based on the use of moments could help us to find the

median longitudinal plane [5].

The ði; j; kÞ-moment of a three-dimensional digital image

is mijk ¼P

x;y;z xiyjzkf ðx; y; zÞ; where f ðx; y; zÞ is the grey

value function of the image. So the centroid ðgx; gy; gzÞ

is given by the first-order moments, that is ðgx; gy; gzÞ ¼

ðm100=m000;m010=m000;m001=m000Þ:

The central ði; j; kÞ-moment of the three dimensional

digital image is defined as mijk ¼P

x;y;z ðx 2 gxÞiðy 2 gyÞ

j

ðz 2 gzÞkf ðx; y; zÞ: So the principal axes of the image can be

defined as the eigenvectors of the matrix

I ¼

m020 þ m002 2m110 2m101

2m110 m200 þ m002 2m011

2m101 2m011 m200 þ m020

2664

3775:

To a symmetry 3D image, the centroid is on the median

longitudinal plane, while one of the principal axes of the image

is parallel to the normal direction of the median longitudinal

plane, as shown in Fig. 2.

Given the centroid ðgx; gy; gzÞ and the normal direction

ðpx; py; pzÞT; the parameters of the median longitudinal plane

equation a·x þ b·y þ c·z ¼ 1 are:

a

b

c

2664

3775 ¼

1

pxgx þ pygy þ pzgx

px

py

pz

2664

3775 ð1Þ

Now, the resulted median longitudinal plane is considered

to be the plane yz of TRF.

2.3. Axis z and plane xz

In order to define the axis z and the plane xz of TRF, we

proceed with the following steps:

† With the midpoint between the two eyebrows (point A)

and the corners of mouth (point B and C), the plane ABC

could be determined

† The intersecting line between the plane ABC and

the plane yz defined above is considered as the axis z

of TRF.

Fig. 1. Definition of TRF (1). Left: the position of the origin on a 3D virtual body. Right: the direction of the axes with the same view angle as the left.

L. Zheng et al. / Image and Vision Computing 23 (2005) 1–92

† The plane through the axis z; which is perpendicular to

the plane yz; is determined as the plane xz; as shown in

Fig. 3.

Given point AðxA; yA; zAÞ; point BðxB; yB; zBÞ; point

CðxC; yC; zCÞ and the median longitudinal plane, the plane

yzðayz·x þ byz·y þ cyz·z ¼ 1; Þ then the intersecting point of

the line BC and the plane yz; point A0ðxA0 ; yA0 ; zA0 Þ; satisfies

the following simultaneous equations

ayz·xA0 þ byz·yA0 þ cyz·zA0 ð2aÞ

xA0 2 xB

xC 2 xB

¼yA0 2 yB

yC 2 yB

ð2bÞ

xA0 2 xB

xC 2 xB

¼zA0 2 zB

zC 2 zB

ð2cÞ

From Eqs. (2a)–(2c), the coordinate vector is

xA0

yA0

zA0

2664

3775¼

a b c

yC2yB xB2xC 0

zC2zB 0 xB2xC

2664

3775

21

·

1

xByC2xCyB

xBzC2xCzB

2664

3775:

The axis z coinciding with the line A0A could be expressed as

the equation:

x2xA

xA0 2xA

¼y2yA

yA0 2yA

¼z2zA

zA0 2zA

:

Fig. 3. Definition of TRF (2). Left: the position of the reference points (point A;B and C). Right: the relationship of the points, axes and planes. Note: point B

and C are not always on the plane xz:

Fig. 2. The symmetry property of a virtual head. Left: a symmetry slice of the head. Right: the principal axes of the virtual head, while P1 is considered to point

out the normal direction of the median longitudinal section.

L. Zheng et al. / Image and Vision Computing 23 (2005) 1–9 3

The plane xz; in which point A and point A0 are located,

could be described as axz·xþbxz·yþcxz·z¼1: The para-

meters axz;bxz and cxz here satisfy the following simul-

taneous equations:

axz·ayzþbxz·byzþcxz·cyz¼0 ð3aÞ

axz·xA0 þbxz·yA0 þcxz·zA0 ¼1 ð3bÞ

axz·xAþbxz·yAþcxz·zA¼0 ð3cÞ

Thus we get

axz

bxz

cxz

2664

3775¼

ayz byz cyz

xA0 yA0 zA0

xA yA zA

2664

3775

21

·

0

1

1

2664

3775:

2.4. Reference frame transformation

The vector A0A��!

defines the direction of z of TRF, with

the corresponding unit vector uz ðuz1; uz2; uz3Þ ¼

ðA0A��!

Þ=ðlA0A��!

lÞ: The direction of x could be determined by

the normal to the plane yz; and the corresponding unit

vector is ux

ðux1; ux2; ux3Þ ¼ðayz; byz; cyzÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2

yz þ b2yz þ c2

yz

q :

The direction of y is calculated by the vector product of

u0z and u0

x; as uyðuy1; uy2; uy3Þ ¼ uz £ ux: Based on these

three vectors, we can form the coordinate rotation matrix

from ARF to TRF [6], that is

R ¼

ux1 ux2 ux3 0

uy1 uy2 uy3 0

uz1 uz2 uz3 0

0 0 0 1

26666664

37777775

ð4aÞ

The origin of TRF is AðxA; yA; zAÞ Then the coordinate

translation matrix from ARF to TRF is

T ¼

1 0 0 2xA

0 1 0 2yA

0 0 1 2zA

0 0 0 1

26666664

37777775

ð4bÞ

So the complete equation expressing the transformation

from the Pðx; y; zÞ in ARF to the P0ðx0; y0; z0Þ in TRF is

x0

y0

z0

1

26666664

37777775¼ R·T·

x

y

z

1

26666664

37777775

¼

ux1 ux2 ux3 0

uy1 uy2 uy3 0

uz1 uz2 uz3 0

0 0 0 1

26666664

37777775

·

1 0 0 2xA

0 1 0 2yA

0 0 1 2zA

0 0 0 1

26666664

37777775

·

x

y

z

1

26666664

37777775

ð4cÞ

The complete coordinate transformation is then the

composite matrix R·T ; while the coordinate transformation

from TRF to ARF is ðR·TÞ21:

3. Methods

The traditional methods for acupoints localization are

based on the measurement along the surface of a body with

‘cun’, a traditional Chinese measure which varies in length

for different parts of the body. In common parlance, it is said

that: ‘An acupoint is located at a distance of some ‘cun from

a certain landmark in particular direction….’ [4]. For

example, acupoint Quchai (BL 4) of the Bladder Meridian

of Foot-Taiyang is on the head, 0.5 cun within the hairline,

1.5 cun lateral to Shenting (DU 24), a point that is 0.5 cun

directly above the midpoint of the anterior hairline, as

shown in Fig. 4. The advantage of this kind of description is

that we can ignore the rugged and uneven feature of a

human body surface. The landmarks for localizing acu-

points are obvious, relatively fixed and universal to

everybody, though there are some individual differences.

Similarly, for the reasons above, the reconstructed

surface from varied raw data would be totally different. If

using the 3D coordinates directly to express the position for

Fig. 4. Several Acupoint labels from TCM.


each acupoint, it is difficult to apply the experience from the

TCM methods and hard to resolve the individual/data

differences. To solve the problems mentioned here, a 2D

acupoint description system is taken.

3.1. 2D acupoint description

Given a definite viewing direction, all visible points on

body surface have one projection plane that is perpendicular

to this direction These visible points have corresponding

projection points in this plane, and each projection point

could be back-projected to the body surface to get the

corresponding 3D coordinate.

In current research, there are three projection planes on

head for the 2D acupoint description system, as shown in

Fig. 5.

† Plane a is specially for locating the acupoints in the face.

It is a rectangle and covers the projection of the forehead,

the lower jaw and the outer canthi.

† Plane b is corresponding to the acupoints on the top-

head. It is part of a cylinder and covers the projection of

the forehead, the occiput and the temples.

† Plane g is for localizing acupoints on the side of the head.

It looks like a disk and is the projection plane of the

surface around the ear.

For the acupoints in different regions, corresponding

localization models are employed to describe them in TRF

based on the knowledge from TCM. When you need to

display acupoints on virtual human body, each point could

be back-projected to the body surface to get its 3D

coordinates. From now on, for convenience, the acupoints

localization is within the framework of 2D coordinate

description.

3.2. Model of median longitudinal circle

Traditionally the ‘vertical cun’ on the head is defined as

the surface distance from the anterior hairline to the

posterior hairline The right image of Fig. 6 shows the

definition of ‘vertical cun’ in Bone Proportional Measure-

ment, a commonly used method for locating acupoints.

Accordingly, the model of the median longitudinal circle is

given as follows.

Three points A;D and E; which are from the fixed

median longitudinal plane (plane yz), are taken to

determine the median longitudinal circle. As mentioned

above, point A is the midpoint between the two

eyebrows. Referring to Fig. 6, point D is the point at

the tip of the body in plane yz; which is easy to be

identified. It is a little bit complicated to get the third

point E; for neither tomograms nor 3D volume could

Fig. 5. 2D Acupoint description.


show the hairlines. Now we try to tackle the problem in

another way. Generally, there is a groove between the

lower lip and the chin in the face. Through this groove

there is a plane parallel to the plane xy: Then the

intersecting point between this plane and the median

longitudinal plane at back is defined as the point E: Point

E could be considered as the midpoint of posterior

hairline.

Suppose point A;D and E are on the median longitudinal

circle, the center of the circle, point Oðx0; y0; z0Þ; satisfies the

relation:

ðxi 2 x0Þ2 þ ðyi 2 y0Þ

2 þ ðzi 2 z0Þ2 ¼ r2

;

i ¼ A;D;E

ð5aÞ

x0 2 xA y0 2 yA z0 2 zA

xD 2 xA yD 2 yA zD 2 zA

xE 2 xA yE 2 yA zE 2 zA

��

��¼ 0 ð5bÞ

where r is the radius of the median longitudinal circle.

Eq. (5a) indicates that the distances between O and the other

three points are equal. Eq. (5b) means point O is also on the

median longitudinal plane defined by point A;D and E:

Under the standards of Bone Proportional Measurement,

on the intersecting arc line between the head surface and the

median longitudinal plane, as Fig. 6 shows, the anterior

hairline is identified by a distance of 3 cun from the

midpoint of two eyebrows (point A), while point E is located

at a distance of 15 cunfrom point A: That means, we can

define the length of arc AOE as 15 cun on median

longitudinal circle.

Through the arc AOE; the cylinder that is perpendicular

to the plane yz of TRF is considered to be the projection

plane b: And 1/15 of arc AOE is taken as the ‘vertical cun’

standard on the head of a 3D human body model.

3.3. Model of face meshes

Under the standard of Bone Proportional Measurement, it

is 9 cun in horizontal between two corners of hairline As

hair cannot be displayed on a 3D medical image, we try to

find another way to determine the horizontal cun.

Let us look at some examples from the traditional

methods at first [4,7]. Referring to Fig. 4, Shenting (DU 24)

is 0.5 cun directly above the midpoint of anterior hairline.

Touwei (ST 8) is at the hairline of the forehead, 4.5 cun

lateral to Shenting (DU 24). And Toulinqi (GB 15) is 0.5

cun within the anterior hairline directly above the pupil, on

the midpoint of the line connecting Shenting (DU 24) and

Touwei (ST 8). From the description above, we can

conclude that the pupil (point F) is 2.25 cun lateral to the

median longitudinal plane. We determine horizontal cun in

the face based on this knowledge.

The coordinate plane xz is considered to be the projection

plane a: Dividing the horizontal length of line AF by 2.25 is

taken as the ‘horizontal cun’ standard in the face. With the

‘horizontal cun’ standard for the face and the ‘vertical cun’

standard for the head, we get the model of face meshes on

the projection plane a; as shown in Fig. 7.

3.4. Model of bone projection

Usually the acupoints on the side-head are set using the

landmarks on the surface. Accordingly the model of bone

projection is applied to locate such acupoints, as shown in

Fig. 8.

3D medical volume of a human body not only shows the

surface of a body, but also contains its inner structures The

projection of some bone landmarks on plane yz could be tags

for localizing acupoints on 3D images. We define that

Fig. 6. Model of median longitudinal circle. Left: the reference points (point A;D and E) on median longitudinal circle. Right: definition of ‘vertical cun’

from TCM.


the position of mastoid process as point G; which is at a

distance of 3 cun from point A in the direction y [4,7].

The part of the plane yz; which is in the median

longitudinal circle, is considered to be the projection plane

g: And 1/3 of the length of line AG in direction y is the

horizontal cun standard on the side of the head of a 3D

human body model.

4. Results

With the knowledge of traditional methods for locating

acupoints, we get a standardized 2D description of

acupoints in TRF.

4.1. Standardized 2D description

For example, in typical acupoint terminology, acupoint

Quchai (BL 4) is described as: on head, 0.5 cun within

the hairline, 1.5 cun lateral to a point that is 0.5 cun

directly above the midpoint of the anterior hairline [4] So

it is on the top-head, with the coordinates 1.5 cun in

horizontal and 0.5 cun in vertical from the origin point A

on plane b; as:

Name Number Location (cun)

Horizontal Vertical

Quchai BL 4 1.5 0.5

The 2D description of all the 63 acupoints on head

surface is listed in the appendix. The list is suitable to any

individual, if we can get enough information about point A

to point G mentioned above from the image data.

Fig. 8. Model of bone projection. Left: the position of the reference point G: Right: the coordinate meshes on the side-head of the 3D virtual body.

Fig. 7. Model of face meshes. Left: the position of the reference point F: Right: the coordinate meshes in the face of the 3D virtual body.


4.2. 3D expression

Finally, as shown in Fig. 9, after back-projection, a set

of acupoints on the head of the 3D virtual body are

clearly displayed. Especially, some work has been

done based on the data from Visible Human Project

(VHP) [2].

5. Discussion

Although acupuncture has a history of more than two

thousand years, up to now, there are only a few references

relating acupuncture to modern computer-based imaging.

The development of VHP and VOXEL-MAN give us the

opportunity to explore a new field like 3D medical imaging

integrated with acupuncture. This paper tries to offer a

simple and useful way to systemically localize acupoints on

the 3D virtual body.

There are a total of 63 acupoints on the surface of the

head. It is troublesome to localize them one by one on

the virtual body. Meanwhile, because of the limitation of the

visual angle of the 3D image, the lack of being able to touch

the virtual body, and the quality of the visualization, even an

expert has to take some time to accurately localize an

acupoint on an image. The method proposed in this paper

lets the operator point out seven obvious landmarks

manually, and then systemically present the localization of

all acupoints.

Originally the method proposed here has been devel-

oped using the data of VOXEL-MAN: Brain and Skull.

To check the validation of the procedure, more work has

been done using the data of VOXEL-MAN: Visible

Human. The result seems to be acceptable to the doctors

we asked.

Of course, the work expressed in this paper is just

the beginning in a new field. The coordinates of the

acupoints under the standardized 2D description listed in

Table A1

Position of Acupoints in the face (Plane a)

Name Number Location (cun) Name Number Location (cun)

Horizontal Vertical Horizontal Vertical

Quanliao SI 18 3.5 2 Suliao DU 25 0 1.8

Chengqi ST 1 2.25 1 Shuigou DU 26 0 2.5

Sibai ST 2 2.25 1.5 Duiduan DU 27 0 3

Juliao ST 3 2.25 2.3 Jingming BL 1 0.75 0.8

Dicang ST 4 2.25 3.3 Zanzhu BL 2 0.75 0

Kouheliao LI 19 0.75 2.5 Sizhukong SJ 23 4.5 0

Yingxiang LI 20 1.1 2 Tongziliao GB 1 4.5 1

Chengjiang RN 24 0 4

Fig. 9. 3D description of Acupoints. Left: based on VOXEL-MAN: brain and skull. Right: based on VOXEL-MAN: visible human.


the appendix could be further adjusted, if they were applied

to more data.

Acknowledgements

We thank Martin Riemer and Andreas Pommert, IMI,

University Hospital Hamburg-Eppendorf, Germany,

for technical supporting of the VOXEL-MAN. We are

also grateful to Zhenguo Yan, who substantially provides the

knowledge of the Traditional Chinese Medicine.

Appendix A

Tables A1–A3

References

[1] K.H. Hohne, B. Pflesser, A. Pommert, M. Riemer, T. Schiemann,

R. Schubert, U. Tiede, A new representation of knowledge concerning

human anatomy and function, Nature Med. 1 (1995) 506–511.

[2] A. Pommert, K.H. Hohne, B. Pflesser, E. Richter, M. Riemer,

T. Schiemann, R. Schubert, U. Schumacher, U. Tiede, Creating a

high-resolution spatial/symbolic model of the inner organs based on the

visible human, Med. Image Anal. 5 (2001) 221–228.

[3] K.H. Hohne (Eds.), VOXEL-MAN, Part 1: Brain and Skull, Version

1.0, (CD-ROM for UNIX Workstations, ISBN 3-540-14517-6,

Springer, Berlin, 1995, Electronic Media, Heidelberg.

[4] Z.G. Yan (Eds.), English–Chinese Practical Anatomical Charts of

Acupuncture and Moxibustion, Publishing House of Shanghai

University of TCM, 1993.

[5] G. Lohmann, Volumetric Image Analysis, Wiley, New York, 1999,

pp. 53–59.

[6] D. Hearn, M.P. Baker, Computer Graphics, second ed., Prentice Hall,

New Jersey, 1994.

[7] Z.G. Yan (Eds.), Normal Human Anatomy, Shanghai Scientific and

Technical Publishers, 1995 (in Chinese).

Table A3

Position of Acupoints on the side-head (Plane g)



Daying ST 5 1.3 4.2 Shangguan GB 3 2 1.8

Jiache ST 6 1.8 3.8 (Touwei) ST 8 2 -1

Xiaguan ST 7 2 2.5 Hanyan GB 4 2.1 -0.5

Tinggong SI 19 2.3 2.5 Xuanlu GB 5 2.2 0

Yifeng SJ 17 2.6 3.5 Xuanli GB 6 2.3 0.5

Qimai SJ 18 3.5 3 Qubin GB 7 2.5 1.2

Luxi SJ 19 3.5 2 Shuaigu GB 8 3.2 -0.3

Jiaosun SJ 20 3.2 1.2 Tianchong GB 9 3.7 -0.3

Ermen SJ 21 2.3 2.3 Fubai GB 10 4 1

Erheliao SJ 22 2.5 1.5 Touqiaoyin GB 11 4 2.3

Tinghui GB 2 2.2 2.8 Wangu GB 12 3.5 3.5

Table A2

Position of Acupoints on the top-head (Plane b)



Yamen DU 15 0 11.5 Tongtian BL 7 1.5 4

Fengfu DU 16 0 11 Luoque BL 8 1.5 5.5

Naohu DU 17 0 9.5 Yuzhen BL 9 1.3 9.5

Qiangjian DU 18 0 8 Tianzhu BL 10 1.3 12

Houding DU 19 0 6.5 Benshen GB 13 3 0.5

Baihui DU 20 0 5 Yangbai GB 14 2.25 -2

Qianding DU 21 0 3.5 Toulinqi GB 15 2.25 0.5

Xinhui DU 22 0 2 Muchuang GB 16 2.25 1.5

Shangxing DU 23 0 1 Zhengying GB 17 2.25 2.5

Shenting DU 24 0 0.5 Chengling GB 18 2.25 4

Meichong BL 3 0.75 0.5 Naokong GB 19 2.25 9.5

Quchai BL 4 1.5 0.5 Fengchi GB 20 2.25 11

Wuchu BL 5 1.5 1 Touwei ST 8 4.5 0.5

Chengguang BL 6 1.5 2.5


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Localization of acupoints on a head based on a 3D virtual body