Design of Virtual Fixtures for Robotic Cholecystectomy

Abstract

Background and Objective:

With the ongoing developments in robotic surgery, the associated adverse events need to be carefully evaluated. Virtual fixtures (VFs), a safety design feature against unintended motion during robotic surgery, have been proposed, but the methodology for designing VFs remains experimental. In this study, we propose a novel methodology for designing VFs for robotic cholecystectomy.

Materials and Methods:

Laparoscopic cholecystectomy (LC) was performed in 24 patients with cholecystitis. Active working space (AWS), the distance between instrument heads (DBIH), motion speed of bilateral hands, and instrument heads were calculated and analyzed.

Results:

DBIH was 14.78 ± 6.94 cm. Diameter of right and left AWS was 15.81 ± 3.69 cm and 15.33 ± 1.52 cm, respectively. DBIH was found to significantly correlate with the surgeon's experience. Bilateral AWS was found to be significantly associated with body circumference at Murphy's point level. However, no association was observed between bilateral AWS and surgeon's experience.

Conclusions:

A novel methodology to build VFs for designing VFs for robotic cholecystectomy is established. Surgeon's experience appears to play an important role in determining the DBIH during robotic laparoscopic cholecystectomy, but does not affect bilateral AWS.

Introduction

Robotic surgery is being used extensively in gynecology and urology.¹ With the ongoing developments in robotic surgery, the associated adverse events need to be evaluated. Retrospective review of data submitted to Food and Drug Administration revealed a total of 10,624 documented adverse events over a 14-year period. These adverse events included parts of the device falling into the body cavity, robot software errors, video/imaging errors, electrical arcing of instruments, and unintended motion of instruments. Among these adverse effects, unintended motion of instruments alone accounted for two deaths and injuries to 52 patients.² In view of the above, there is an urgent need to develop safety design features against unintended motion of robotic systems. In this regard, features such as haptic feedback and virtual fixtures (VFs) appear promising.

Guidance VFs and forbidden region VFs are the two main types of VFs that have been studied,³ with the latter reportedly having a better performance than the former in surgery.

Before applying VFs in robotic surgery, we need to scale the size and the shape of VFs, and a reasonable way to achieve this is to obtain data from the surgical procedure itself. For this, a parameter called working space has been proposed for laparoscopic surgery. The concept was initially proposed to measure the space that a robot arm would be able to operate in.⁴ Arkenbout et al. used this term to illustrate the activity range of the miniature head of the instrument.⁵ Vlot et al., and Tan et al., through a series of studies, assessed the determinants for optimizing laparoscopic working space.^6–11

The working space required for a surgical robot is larger than a patient's abdominal cavity and could possibly damage the patient's organs and tissues if optimal working space is not defined.

The concept of VFs has been introduced to restrict the movement of the robot inside certain regions of working space, but there are still issues that need to be resolved.^12,13 The design of VFs is a key factor for its successful application. Current design of VFs mainly relies on several regular geometric models such as spheres, cubes, and their combinations thereof, while the position and size of VF models have the abdominal cavity as a static reference. Three-dimensional (3D) computed tomography (CT) and image rebuild have also been introduced, but the complexity of the methodology is a significant barrier to its wider use.^14–16

Instrument designers are interested in the space an instrument is actively working in. This is referred to as the fundamental working space that a laparoscopic surgical robot would require. Measuring this space during actual surgical procedure has never been done before. In this VF design, the active working space (AWS) is defined as the free space, while the remaining space in the abdominal cavity is defined as forbidden region VFs. These forms of VFs are based on real-world surgical experience and may help improve safety of robotic surgery. Also of interest are the factors that determine the size of the VFs.

This study was conducted to determine the reasonable active working space during laparoscopic cholecystectomy (LC) and its application in designing surgical robot VFs.

Materials and Methods

Patients

Twenty-four patients diagnosed with having cholecystitis between June 2015 and July 2015 at the Department of General Surgery, Third Xiangya Hospital of Central South University, who underwent laparoscopic cholecystectomy were enrolled in the study. Exclusion criteria were history of any open abdominal surgery; intrahepatic bile duct lesions, compromised cardiac or lung function; severe alcohol or drug dependence; severe hypertension; diabetes; unstable psychiatric illness; and the presence of an active ulcer.

The study was approved by the Institutional Review Board of the Third Xiangya Hospital, Central South University. Written informed consent was obtained from all participants before enrollment.

Study protocol

A magnetic field tracking device with two 6DOF miniature sensors (3D Guidance trakSTAR, Model 180 Sensor; Ascension Technology Corporation) was used for instrument tracking. Sensors were sterilized with ethylene oxide. The tip of each sensor was attached at the handle of the instrument, using a transparent film dressing (Tegaderm Film 1626w; 3M Corporation), coaxially to the rod 38 cm away from the tip of the instrument. Bodies of sensors were protected by a protective cover, which did not interfere with the sensor signal (3L Medical Products Group). The instrument was manipulated with an electric hook using the right hand (Yida Medical Apparatus Corporation) and with a dissecting forceps using the left hand (Karl Storz). An electronic CO₂ insufflator (Endoflator; Karl Storz) was used for abdominal insufflation. During surgery, the supraumbilical midline from xiphoid to umbilicus was demarcated. Two main stages of the surgery were cutting of the bile duct and vessels and excision of the gallbladder. The tracking instrument was calibrated before its use to ensure the reliability of its output. The positions of the instrument head were then calculated by direction and position of sensors installed 38 cm away from it. This method has been shown to be reliable in a surgical robot motion tracking test.¹⁷

Two types of working spaces were defined in this study: active working space (AWS) of left- and right-hand instruments and distance between instrument heads (DBIH). Active working space was defined as the position set of the instrument head. To measure AWS, we used a sphere to cover the position set. Considering the outlier of the position set, we defined a marginal value such that 90% of the position set was covered in this sphere. To calculate the center of the sphere, a method of least squares was adopted. AWS was defined as the diameter of this sphere at a marginal value of 90%. DBIH was defined as the distance between the positions of two instrument heads. Both left- and right-hand speeds were defined as the speed of hand movement instantaneous, calculated by the distance of two adjacent positions of sensors divided by a time interval of 50 ms. The speed of both left and right heads of the instruments was defined as the speed of instrument head movement instantaneous, calculated by direction and position of sensors positioned 38 cm away.

Outcome measurements

Age, sex, height, body weight, and body circumference (BC) at Murphy's point plane (@Murphy) and umbilical plane (@Umbilicus) were measured before the operation. Heart rate, blood pressure, and respiratory rate were monitored during the surgery. Data on 3D space coordinates from the two 6DOF sensors were recorded by CUBES program (Ascension Technology Corporation) installed on a laptop PC (T420; Thinkpad by Lenovo). Outcomes were processed on Matlab 7.0 (Mathworks).

Statistical analyses

Statistical analyses were performed using SPSS for Windows, version 13.0 (IBM). Data on all continuous variables are expressed as mean ± standard deviation (SD). The Spearman correlation coefficient was used to examine the relationship between intraoperative measurements and the other variables. Stepwise multivariate regression analysis was performed to assess the independent association of intraoperative measurements with the preoperative data. The significance level of this study was set at a two-tailed α = 0.05.

Results

Operation outcomes

All operations were successful. No significant intraoperative complications were observed, and the patients were discharged 3 days after surgery. Neither mortality nor significant morbidity was noted. Complete resolution or significant improvement in major symptoms was reported in all cases.

Basic characteristics of the patients and data on key parameters

Preoperative data are summarized in Table 1. Median total key operation time was 9 minutes (range 7–15 minutes). Data on DBIH, AWS, hand speed, and instrument head speed are presented in Table 2. Bilateral hand speed and head speed were maintained at a low level with intermittent bursts of speed. This is in conformity with the real motion of laparoscopic instruments observed on screen during surgeries: most of the time these consist of fine movements, with episodes of fast movement.

Table 1.

Baseline Patient Characteristics

Number of patients	24
Age (years)	49.96 ± 5.76 (38–55)
Sex (% male)	16.67
Height (cm)	155.52 ± 6.11 (148–170)
Weight (kg)	53.43 ± 7.87 (44–67)
BC@Murphy (cm)	82.43 ± 10.32 (68–102)
BC@Umbilicus (cm)	82.61 ± 13.72 (64–98)

BC@Murphy, body circumference at Murphy's point level; BC@Umbilicus, body circumference at the umbilicus level.

Table 2.

General Operative Parameters

	N	Mean ± SD
DBIH (cm)	24,000	14.78 ± 6.94 (0.72–53.67)
Diameter of AWS of right hand (cm)	24	15.81 ± 3.69 (11.53–28.35)
Diameter of AWS of left hand (cm)	24	15.33 ± 1.52 (12.97–21.61)
Hand speed (right) (cm/s)	24,000	1.64 ± 11.40 (0–1342.69)
Hand speed (left) (cm/s)	24,000	1.08 ± 3.86 (0–354.28)
Head speed (right) (cm/s)	24,000	1.70 ± 11.59 (0–1342.06)
Head speed (left) (cm/s)	24,000	1.36 ± 7.63 (0–566.82)

AWS, active working space; DBIH, distance between instrument heads; SD, standard deviation.

Relationship between working space, operator experience, and preoperative characteristics

Weight of the patient was found to have a significant negative correlation with both left (R = −0.421, P < .01) and right (R = −0.222; P < .01) AWS. BC@Murphy's point was significantly associated with left (R = 0.328, P < .01) and right (R = 0.306, P < .01) AWS (Table 3). The experience of the operating surgeon was not significantly associated with either left or right AWS and neither did the height nor did the BC@Umbilicus point. A stepwise multivariate regression model was applied with bilateral AWS as the dependent variable and the weight, height, BC@Umbilicus, BC@Murphy, and surgeon's experience as independent variables. Regression coefficients indicate that weight of the patient and BC@Murphy's point contributed most to the variability in AWS. All five independent variables could explain 38.1% of the observed variance in left AWS, and four independent variables (excluded height) in the group could explain 31.1% of the observed variance in right AWS according to R square (Tables 4 and 5).

Table 3.

Correlation Between Distance Between Heads, Active Working Space, and Surgeon's Experience, Patients' Height and Weight, BC@Murphy, and BC@Umbilicus

	Distance between heads		Active working space (left)		Active working space (right)
	r	P	r	P	r	P
Surgeon's experience	0.530	.00^*	0.128	.00	0.121	.00
Height (cm)	−0.116	.00	−0.161	.00	0.136	.00
Weight (kg)	−0.108	.00	−0.222	.00^*	−0.421	.00^*
BC@Murphy (cm)	−0.208	.00^*	0.328	.00^*	0.306	.00^*
BC@Umbilicus (cm)	−0.054	.00	0.126	.00	0.117	.00

Significant correlation.

BC@Murphy, body circumference at Murphy's point level; BC@Umbilicus, body circumference at the umbilicus level.

Table 4.

Stepwise Multivariate Regression Analysis for Right AWS

	Unstandardized coefficient
	B	Standard error	Standardized coefficient Beta	t	P
Constant	93.127	1.709		54.487	.000
Surgeon's experience	0.325	0.027	0.676	10.008	.000
BC@Umbilicus	−0.397	0.020	−0.849	−10.350	.000
BC@Murphy	0.606	0.026	1.693	23.601	.000
Weight	−0.427	0.028	−0.911	−15.440	.000
Height	−0.394	0.036	−0.652	−10.939	.000

AWS, active working space; BC@Murphy, body circumference at Murphy's point level; BC@Umbilicus, body circumference at the umbilicus level.

Table 5.

Stepwise Multivariate Regression Analysis for Left AWS

	Unstandardized coefficient
	B	Standard error	Standardized coefficient Beta	t	P
Constant	14.598	0.335		43.547	.000
Surgeon's experience	0.101	0.046	0.052	2.205	.028
BC@Umbilicus	−0.051	0.007	−0.462	−7.379	.000
BC@Murphy	0.139	0.009	0.943	15.329	.000
Weight	−0.124	0.006	−0.644	−20.214	.000

Height was excluded from the stepwise regression analysis.

AWS, active working space; BC@Murphy, body circumference at Murphy's point level; BC@Umbilicus, body circumference at the umbilicus level.

Relationship between DBIH, operator experience, and patient characteristics

The operating surgeon's experience was significantly associated with DBIH. Spearman's rank correlation coefficient was 0.530 (P < .01). BC@Murphy's point (R = −0.208, P < .01) had a significant association with DBIH. Height (R = −0.116, P < .01), weight (R = −0.108, P < .01), and BC@Umbilicus (R = −0.054, P < .01) did not show any significant association with DBIH (Table 3). A stepwise multivariate regression model was applied with DBIH as the dependent variable and the weight, height, BC@Umbilicus, BC@Murphy, and surgeon's experience as independent variables (Table 6). Regression coefficients indicate that all five independent variables were related to DBIH; among these, surgeon's experience contributed most to the variability in DBIH. All five independent variables could explain ∼50% of the observed variance in DBIH.

Table 6.

Stepwise Multivariate Regression Analysis for DBIH

	Unstandardized coefficient
	B	Standard error	Standardized coefficient Beta	t	P
Constant	93.127	1.709		54.487	.000
Surgeon's experience	10.448	0.105	0.661	99.072	.000
BC@Umbilicus	−0.804	0.007	−1.591	−112.908	.000
BC@Murphy	0.944	0.009	1.403	100.814	.000
Weight	0.612	0.011	0.695	58.144	.000
Height	−0.805	0.014	−0.708	−55.760	.000

BC@Murphy: body circumference at Murphy's point level, BC@Umbilicus: body circumference at the umbilicus level; DBIH, distance between instrument heads.

Relationship between operator experience and hand speed

Surgeon's experience was not found to be significantly associated with bilateral hand speed (left r = 0.179, P < .01; right r = 0.101, P < .01) and bilateral instrument head speed (left r = 0.131, P < .01; right r = 0.128, P < 0.1) (Table 7).

Table 7.

Correlation Between Hand Speed, Head Speed of Instrument, and Surgeon's Experience

	Hand speed (left)		Hand speed (right)		Head speed (left)		Head speed (right)
	r	P	r	P	r	P	r	P
Surgeon's experience	0.179	.00	0.101	.00	0.131	.00	0.128	.00

Discussion

Recently, VF has become a popular topic of study in robot surgery. The concept of VFs was first proposed by Louis Rosenberg in 1992 at the USAF Armstrong Laboratory and refers to a general class of guidance models that help a robotic manipulator perform a task by limiting its movement in restricted regions and/or influencing its movement along the desired path.¹⁸ It was developed to solve the problem of delay and to improve the operability of the teleoperation system.

Rosenberg constructed eight types of VFs in a peg-and-hole task and found them to be helpful in reducing the operation time.¹⁹ There are two basic categories of VFs: guidance VFs and forbidden region VFs.²⁰ Due to the openness of surgical instruments and the skill of the surgeon, guidance VFs were not considered initially. Forbidden region VFs were later introduced to avoid major accidents. Due to its greater torque, inappropriate handling of the surgical robot may result in injury to organs. In addition, in a surgical robot that lacks a mechanism of force feedback, any maloperation is liable to inflict excessive force on the organs.

The VFs bring in an automated protective mechanism within the robotic surgical system that does not require any manual intervention. VFs could be regular or irregular. Irregular ones are more suitable for online-generating mode, but were not investigated in the present study. We suggest that regular VFs are better in our study because we detected a shape similar to spheres and also it is easier to achieve. The use of VFs in robotic surgery can help restrict movements of the robot and is particularly of value during teleoperations. In a teleoperation robotic system, such as Da Vinci robotic surgery system, VFs can be implemented on both the master and slave manipulators.²¹

The shapes and sizes of VFs need to be measured during actual surgeries instead of their being based on assumptions. The force feedback mechanism confers a considerable leverage to the operator by allowing for finer intraoperative manipulation, especially when tactile sensations may not be adequately perceivable otherwise.²²

Dynamic modeling of the human body, a key input for virtual fixture design and analysis, has been largely missing in most of the earlier studies. Conventional VF modeling is based on the use of CT or magnetic resonance imaging radiographs for reconstruction of static 3D models of human organs.^14–16 The more advanced methods for real-time measurement of human organs are based on complex image processing technologies²³ that involve a time-consuming positioning step, which makes it unrealistic. In our study, we demonstrate a more advanced method of modeling, which is based on real-world intraoperative data and which may serve to overcome the limitations of the other two methods.

In the present study, there was no significant association between the surgeon's experience and bilateral AWS, which indicates that treatment outcomes may no longer be a direct function of surgeon's skills. However, Kowalewski et al. evaluated a different motion path score for surgeons with different experience levels, but the path length was relevant to time spent, while 3D Tool path plots of different surgeons seemed much the same in volume.²⁴

In the present study, a significant negative association was observed between bilateral AWS and weight, while a significant positive association was observed between bilateral AWS and BC@Murphy. This indicates that a larger BC@Murphy makes AWS bigger bilaterally, while lower body weight enlarged AWS bilaterally. Increased body weight is likely to be associated with an increase in abdominal visceral fat,²⁵ which serves to limit the room for manipulation during robotic cholecystectomy. Increased BC@Murphy may be relevant to a bigger shape of the body and bigger organs such as the liver and the gallbladder.

We also observed a significant correlation between the operating surgeon's experience and the DBIH, which indicates that experienced surgeons may require less DBIH. This is probably attributable to the standardized steps and the relatively lesser need for additional active working space during robotic cholecystectomy. Significant negative association between BC@Murphy and DBIH was found, indicating that when space is too small, a repetitive dragging motion between two instruments for a clear view of organ structure is needed.

We did not observe any significant association between the surgeon's experience and bilateral head speeds of instruments, which indicates that average motion speed of the surgical robot instrument head is likely to be well suited to most surgeons. This finding seems to contradict those from a study by Rivard et al. However, in the said study, a VR laparoscopic training system was used, in which speed is indirectly estimated by the duration of surgery and these two differences may contribute to the contradiction.²⁶

To make measurements of size and shape of VFs easier for different types of surgical procedures, a new kind of tracking system such as an optical tracking system or infrared ray tracking system, such as Microsoft Kinect sensor, may have to be introduced.²⁷ Further studies are required to build a reference database to determine the exact relationship between AWS required for robotic surgery in relation to specific types of surgeries and specific patient characteristics. The complete building of the VF system for a guidance system in robot surgery needs more data from different surgeries to be developed and validated.

Conclusion

A novel methodology to build VFs for designing VFs for robotic cholecystectomy is established. Surgeon's experience plays an important role in determining the size of DBIH during robotic laparoscopic cholecystectomy, but does not appear to affect bilateral AWS.

Footnotes

Acknowledgment

This article is funded by Project 51290290 supported by National Natural Science Foundation of China.

Disclosure Statement

No competing financial interests exist.

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