In virtual surgery of minimally invasive vascular intervention, the force feedback is transmitted through the flexible guide wire. The disturbance caused by the flexible deformation would affect the fidelity of the VR (virtual reality) training. SMC (sliding mode control) strategy with delayed-output observer is adopted to suppress the effect of flexible deformation. In this study, the control performance of the strategy is assessed when the length of guide wire between actuator and the operating point changes. The performance assessment results demonstrate the effectiveness of the proposed method and find the optimal length of guide wire for the force feedback control.
Virtual surgery is an effective training method to help novice surgeons to avoid operative errors during a real surgical process [
Image information has emerged quickly enough, thanks to the development of
Interventional cardiovascular surgery is a complex surgery. Before the surgery, doctors need to conduct a large number of surgical trainings. In recent decades, the design of VR simulator of vascular intervention surgery has aroused interests of engineering. The Simbionics company in America developed the
In above simulators of minimally invasive vascular intervention, there is a problem that the flexible deformation of the guide wire would lead to disturbance in force feedback transmission [
To solve this problem, researchers generally use the passage of guide wire to simulate real vessel [
Several control strategies can be used in the force feedback system. However, some limitations exist. For instance, the output feedback variable structure control can suppress plant model uncertainty efficiently; however, the control input is too large during the transient stage, which may violate saturation constraint [
In this study, the SMC (sliding mode control) strategy with delayed-output observer is used to suppress the effects of system lags on system fidelity while maintaining system robustness. As the length of guide wire between actuator and operating point is different, the disturbance of flexible deformation is related to the length of guide wire between the actuator and the operating point. The control performance needs to be assessed when the length of guide wire changes. And the optimal length of guide wire can be determined through the performance assessment.
The rest of the paper is organized as follows. In Section
Intracoronary Stenting surgery is performed to treat the stenosis or blockage of vessels [
Minimally invasive vascular intervention.
There are several branches along the path of the vessels; the surgeon needs to skillfully operate the guide wire to reach the target place. One important requirement for the surgeon is to avoid producing too much resistance force between the guide wire and the walls of vessels; otherwise, the thin and delicate walls of vessels may be damaged by the guide wire.
In the force feedback control system of VR simulator, the input of the force feedback control represents resistance of the vessels in real surgery. The feedback force felt by the human hands is generated by actuators and it is transfered via surgical instruments (the guide wire, guide catheter, the thin guide wire, and ballon catheter). The VR simulator renders image information on the computer monitor, while the force feedback is provided by a device. Novice surgeons could be trained through the virtual surgery with the image and force feedback, as shown in Figure
Virtual reality simulator of minimally invasive vascular intervention surgery.
The displacement of the surgical instruments is measured by encoders. The three actuators generate the force feedback of the surgical instruments separately. The VR training requires the force feedback to be the same as the real surgery. Figure
Force feedback device of minimally invasive vascular intervention; Actuator 1 creates the feedback force of the guide catheter and the thin guide wire; Actuator 2 creates the feedback force of the balloon catheter; Actuator 3 creates the feedback force of the guide wire.
The guide wire has two degrees of freedom (DOF): forward-backward movement and rotation. The guide wire in the virtual surgery is flexible. In the forward-backward direction, the deformation of the guide wire between the Actuator 3 and the operating point of human hand needs to be taken into consideration [
Force feedback control system of virtual surgery.
There are parameter variations and response lags in the system. They would affect the force feedback control.
In Intracoronary Stenting surgery [
Force status of the guide wire.
The guide wire is under uniformly distributed load
Using the Lagrange equation, it can be shown that
Equation (
It can be shown that
where
From (
As there is flexible deformation in the guide wire [
SMC has the quality of fast response and good transient performance [
The measurement output is
It is noted that the
Equation (
Considering the response lag
The error caused by system lags
To compensate the error in (
Define the observation error as
From (
The stability requirement of (
It means that
The sliding mode surface is chosen as
And the Lyapunov function is chosen as
The designed control law of sliding mode control is
From (
Because the observer is convergent,
It can be shown that
It means that the control law satisfies Lyapunov stability.
Equation (
The force feedback measurement device.
A sensor measures the force feedback in real-time. The sensor is hollow and the guide wire passes through it. The proposed device is suitable to measure a large range of motion of deformable tools, such as the guide wire.
To model the parameter variation of the control system, the process model in system identification tool of matlab is adopted to simulate the force transmission of the guide wire. Consider
The response process of a constant force after transmission via guide wire is measured, as shown in Figure
Identification of the force feedback control system.
Identification of the system
Error between simulated force and measured force
From (
Then
In the identification, the loss function is
In VR training, a virtual force model is established to give feedback force [
Research reveals that the real time force feedback needs a refresh rate of more than 300 HZ in order to achieve realistic requirements [
Control performance of regular SMC strategy is shown in Figure
Performance of force feedback control when using regular SMC. The disturbance is sine wave plus random interference (the amplitude is 0.11 N).
Under the control of regular SMC strategy, the response lag is about 48 ms. The SMC with delayed-output observer is used to suppress the response lag, seen in Figure
Performance of force feedback control when using SMC with delayed-output observer. The disturbance is sine wave plus random interference (the amplitude is 0.11 N).
Comparing Figure
As it is discussed in Section
The controller design focuses on development of the control strategy and its application, while the performance assessment is concerned about whether the designed controller is in accordance with the required performance at the operating stage [
Various assessment methods are used in surgical training [
To assess performance of virtual vascular intervention surgery, a specific control performance metric for the virtual surgery is needed. Reference [
In this section, a minimum variance controller is designed and the associated minimum variance performance will be found for the control system of virtual vascular intervention surgery [
The force feedback control system.
As shown in Figure
In Section
The control input is defined as
So the minimum variance of output can be obtained by the coefficients
From (
Equation (
Then, (
as it can be derived that
From (
If we design
it can be shown from the output with minimum variance from (
From (
The
The mathematical expectation of
Then, the model prediction error can be shown as
When using the minimum variance controller,
The output
It is equivalent to
The minimal variance of output is as follows:
We can see that the output variance
The advantage of this performance index is that minimal variance benchmark can be calculated from routine operating data by estimating the impulse response from noise-to-output transfer function. This definition of the controller performance index satisfies
As shown in (
Force feedback control when length of the guide wire between actuator and the operating point is 8 cm.
Force feedback control when length of the guide wire between actuator and the operating point is 18 cm.
As shown in Figure
As shown in Figure
Performance index of the force feedback control system when the length of guide wire changes.
According to the specification for structural design of virtual surgery, the length of guide wire
Based on the performance index, it can be seen that the control system can be further improved. As we can see from Figures
In virtual surgery of minimally invasive vascular intervention, the response lag caused by flexible deformation of the guide wire would affect the fidelity of the force feedback control system. In this study, the SMC with delayed-output observer is adopted to eliminate the effects of flexible deformation. The whole control strategy is easy to implement and is well accepted in the field.
In our force feedback control system, the requirement of fidelity of the virtual vascular intervention surgery is to reduce the control force error between the virtual and real surgery. The minimum variance is chosen as the performance benchmark to assess the control performance of the virtual surgery. The results of performance assessment reveals the optimal length of guide wire between actuator and operating point. And this method can be used to assess other lengths of surgical instruments in the VR simulator.
As shown in Figures
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research is supported by the Key Program of National Science and Technology supported Program of China (2009BAI71B06) and the Key Project of Chinese National Science Foundation (61190124).