A Fast and Stable Guidewire Model for Minimally Invasive
Vascular Surgery based on Lagrange Multipliers
Xiao-Ran Cheng
1,2
, Qing-Kun Song
1
, Xiao-Liang Xie
2
, Long Cheng
2
,
Li Wang
2
, Gui-Bin Bian
2
, Zeng-Guang Hou
2∗
, Tingwen Huang
3
, Pusit Prasong
2
1
Automation Department, Harbin University of Science and Technology
Harbin 150000, China.
2
State Key Laboratory of Management and Control for Complex Systems
Institute of Automation, Chinese Academy of Sciences
Beijing 100190, China.
3
Texas A&M University at Qatar, Doha 23874, Qatar.
Abstract—The simulator based on interactive virtual reality
can solve many drawbacks in traditional surgery training, and
it is widely used to train apprentices. A real-time and realistic
guidewire model is a challenging task for the simulator, which is
used to simulate minimally invasive vascular surgery. In this pa-
per, we propose a fast and stable physical model to simulate the
behavior of the guidewire. And Cosserat theory of elastic rods is
used to simulate the bending and twisting of the guidewire, the
inextensibility of which is maintained with Lagrange multipliers.
Then an operation method is proposed to control the virtual
guidewire effectively. Finally, some experiments are conducted
to demonstrate the effectiveness of our guidewire model and the
operation method.
Keywords—Cosserat theory of elastic rods, Lagrange multi-
pliers, guidewire model
I. INTRODUCTION
Coronary heart disease has been the leading cause of death-
s worldwide. Percutaneous coronary intervention surgery is
widely used to treat the coronary heart disease. During the
operation, operators thread the guidewire into lesion position
in a complex 3D blood vessel through a 2D screen. Thus, an
excellent instrument manipulation skill is required to avoid
causing serious injury to patients. So, apprentices need to
receive a lot of training before they become qualified doctors.
Traditional operation training which is mainly based on living
animals is expensive.
An alternative is the simulator based on interactive virtual
reality. Apprentices can practice the same surgery at anytime
and anywhere. And they practice the surgery in a virtual
environment, so a lot of money can be saved, and it also
reduces the damage to health of the apprentices.
In the simulator, one core part is the physical model of
the virtual guidewire. To simulate the guidewire, a hybrid
mass-spring particle system was proposed by Luboz et al.[1].
Later, they adopted some realistic instrument behaviors into
this system to reduce the modeling error [2]. However, the
modified model still couldn’t simulate the large nonlinear
geometric deformation because of the inherent drawback
of the mass-spring model. Duriez et al. [3] proposed a
guidewire model based on incremental Finite Element Model
(FEM) and substructure decomposition was introduced to op-
timize their model. Unfortunately, the accuracy of this model
gradually reduced in each incremental step. A guidewire
model based on dynamic Lagrangian splines constrained by
Lagrangian multipliers was proposed by Lenoir [4]. This
model could effectively model the guidewire, but it could not
simulate the twisting effect of the guidewire. Alderliesten et
al. [5] introduced more complex bending energies into the
guidewire model and the model achieved a high accuracy,
but this model was not real-time.
Elastic rods model can effectively simulate one-
dimensional elastic objects. In [6], Pai proposed a guidewire
model based on the Cosserat theory of elastic rods [7].
Bergou et al. [8] presented an elastic rods model which
could accurately simulate the bending and twisting. Based
on his work, a guidewire model was presented by Tang et
al. [9][10]. Wang et al. [11] proposed a fast guidewire model
by introducing a dynamically adaptive discrete setting. Spill-
mann and Teschner [12] introduced the unit quaternions into
the elastic rods model. Based on [12], unit quaternions were
integrated into the guidewire model in our previous work
[13]. In our previous work, we use penalty method to realize
the inextensibility of the guidewire. Unfortunately, when we
push or pull the guidewire, the motion of the guidewire will
look like spring and this will partly influence the immersion
of the simulator. To overcome this disadvantage, a method of
Lagrange multipliers which is inspired by [14] is adopted.
Thus, the guidewire model can reach the steady state
in a very short time. We also propose an effective and
stable method to control the moving of the guidewire. Some
simulations are also done to demonstrate the effectiveness of
our method.
The organization of this paper is as follows. The guidewire
model and control method are described in section II. In
section III, the experimental results are evaluated and in
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