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Facial Surgery Simulation Using 3D Bubble Mesh

Eiji Takahashi and Toyohisa Kaneko

Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Japan 441-8580

SUMMARY

This paper is concerned with the simulation of facial

changes after removing some part of a bone in the face. It

uses a spring network model in order to represent the facial

tension after surgery. It is shown that a spring network

model works better when node distances in the model are

uniformly equal. The first part of the paper describes how

to allocate nodes at equal distances using a bubble-mesh

scheme, which has been utilized in CAD/CAM. Nodes

should move along the facial surface continuously. But the

first technique utilized was to let the nodes move only on a

limited number of discrete points. The second technique

was to start with an overcrowded initial condition and to

reduce excess nodes so as to reduce computation time.

Using the network model, we successfully performed a

surgery simulation experiment and produced a facial image

which was quite similar to that of an actual patient after

32(1): 19, 2001

Key words: Bubble mesh, network model, defor-

mation simulation, virtual surgery, upper jaw cancer

1. Introduction

Surgery simulation, which is a virtual reality applica-

tion, has attracted much attention recently. Our attention

has been focused on facial surgery because the face is the

most noticeable feature. A typical example is to remove a

part of jawbone in order to treat upper jaw cancer. This kind

of surgery has a strong impact on a patient. We want to

develop a system to predict the facial appearance after

surgery. Such a system is useful for communication be-

tween a doctor and his patient as a tool for informed

consent.

Regarding research on facial surgery by Keeve and

colleagues [13], their system was developed so as to

predict postsurgery facial appearance for treating such de-

creases as hereditary deformation of the head. Their model

divides the soft tissue region between the cranium and the

surface skin into two layers. Their spring network model is

therefore largely unbalanced between the direction along

the surface and its perpendicular direction. It is thought that

such an unbalanced model has a directional problem in

simulating force. The approach taken by Hattori and co-

workers [4, 5] allocated an equidistance grid, which ex-

ceeds the size of an organ and shrinks its size to fit the organ.

But the node distribution is as yet not quite equal, particu-

larly on the surface.

When a mass-spring network was employed, it was

experimentally shown that a network with equal node dis-

tribution could carry out better deformation simulation [6].

Our requirement is that the node allocation on the surface

as well as the internal region be distributed as equally as

possible.

The node allocation problem has been investigated as

a meshing problem in such areas as CAD/CAM, CG, and

hydrodynamics. There are a number of mesh generation

techniques [710]. We looked for a technique that could

meet our requirements. The bubble mesh algorithm [11, 12]

seems to meet our requirements. It allocates bubbles on the

surface and then in the internal region. The balance between

the attracting force and repelling force results in bubble

allocation.

Systems and Computers in Japan, Vol. 32, No. 1, 2001

Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J83-D-II, No. 3, March 2000, pp. 9961004

Based on this bubble allocation algorithm, we suc-

cessfully made a facial surgery simulation system. We

implemented this system using a force-feedback device in

which cutting a part of muscle is simulated by cutting

springs and muscle healing is simulated by adjusting the

hardness via the spring constants.

This paper is organized as follows. Section 2 de-

scribes a node allocation scheme for medical data based on

the bubble mesh algorithm. Section 3 describes the application

to surgery simulation. The conclusions are in Section 4.

2. Bubble Mesh Algorithm for 3D Medical

Data

The bubble mesh algorithm is applicable to 3D ana-

lytical data with nodes, edges, surfaces, and internal re-

gions. Bubbles are allocated based on the attracting and

repelling force between bubbles. However, no such infor-

mation is included in CT data, which are volume data. Thus,

the well-known marching cubes algorithm [13] was applied

to derive such data.

It was found that computation was slow when we

generated bubbles in a low-density region and eliminated

some bubbles in high-density regions. Hence, we decided

to accelerate the process by using bubble elimination alone

by starting from a state of excess bubble allocation.

The process of bubble allocation in the head is as

follows:

1. Apply the marching cubes algorithm using proper

threshold values to delineate air, muscle, and bones, and

derive surface polygonal data.

2. Allocate bubbles on the skin surface and on the

bone.

3. Allocate especially large bubbles in order to plug

eyeholes and ear holes.

4. Allocate bubbles in the muscle (space between the

skin surface and bone surface).

In the following subsection, we will describe the

bubble allocation and bubble elimination process.

2.1. The principle of the bubble mesh

algorithm

2.1.1. Force between bubbles

The force between two bubbles is similar to the

molecular force operative between two molecules. If bub-

bles are touching, the force is zero. If bubbles are mutually

overlapping, the force is positive (repelling). And if bubbles

are apart, the force is negative (attracting). The force is

represented as the following polynomial.

where w is the ratio of r (bubble distance) over r

touching distance given the stable distance) (Fig. 1). A, B,

C, and D are derived using the boundary conditions given

in Eq. (2). d

is the largest distance where the bubble force

can be applied, and k

is the spring constant with w = 1.0.

Since we consider the repelling force alone, fw 0 for

w t 1.0.

2.1.2. Bubble movement

The i-th bubble moves according to the following

equation:

where F

is the force for the i-th bubble, m

is the mass of

the i-th bubble, x

is its location, and c is the viscosity

constant. Let W be a small increment in time. The bubble

location at time t + W is given as

If a bubble moves, it affects all other bubbles. Therefore,

computation time becomes enormous if every step in com-

puting mutual force is considered. To make it faster, we

compute bubble movement independently. After a cycle of

computation of bubble movement, all bubbles move at

once.

2.1.3. Elimination of bubbles

As mentioned, we start with an overcrowded state of

bubbles. Then bubbles are eliminated if at least one of the

following conditions holds:

(1)

(2)

Fig. 1. Internal bubble force.

(3)

(4)

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