Comparison of the Effectiveness of Two Types of Single Port Minimal Invasive Neurosurgical Robots to Ablation and Resection of Brain Tumor

Background :Using minimally invasive neurosurgical robots is one of the most desirable ablation methods and resection of brain tumors. In this study, forward kinematics and Jacobian matrix calculated for two single-port robots for comparing the effectiveness of two types of single port minimal invasive surgical robots to ablation and resection of brain tumor Methods : The motion analysis of robots type 1 and 2 has compared to each other. Ablation manipulator in robot type 1 has five degrees of freedom, but in robot type 2, three revolute degrees of freedom of this manipulator has replaced with a revolute joint perpendicular to the previous three revolute joints. Results : Results showed that for resection surgery, in the same conditions, robot type 2 damaged 58.9 mm 3 more of cerebral cortex tissue than robot type 1 to resect the brain tumors. To establish a static balance, robot type 2 needs to tolerate at least 41% more internal loading than robot type 1. The maximum velocity for robot type 1 in the contact location between the end-effector and the tumor is 1.7 times more than robot type 2. The maximum end-effector force of robot type 1 to apply the tumor for ablation surgery is more than 1.8 times in robot type 2, but the maximum moment and power for ablation surgery and resection of these two robots were the same less than 1% difference. Conclusion : Despite the more straightforward mechanism, a minimum number of joints, and better kinematics range of robot type 2, robot types 1 has the possibility for transformation, establishes the static balancing, and does a better ablation surgery with less damage to the brain.

Int Clin Neurosci J. Vol 7, No 4, Autumn 2020 202 journals.sbmu.ac.ir/Neuroscience http the second method is the small surgical site's small size, which results in less pain for the patient after the surgery, shorter recovery duration, and, therefore, fewer hospital costs. 1,20 Hu et al introduced a semi-autonomous surgical robot that can resection of a brain tumor. 23 It should note that this robot has stereo visual feedback too. They used two plans to resection the tumor and compared the autonomous motion control method and visual endeffector sensing for each plan. Chinbe et al. designed a finger-attachment manipulator system for a resection brain tumor which operates based on pulling force feedback 24 . Their focus was on robots with more accuracy and safe resection. Azarnoush et al. used a special manipulator for brain tumor resection in which safety has improved during resection by utilizing modulating resident force application 25 . Niccolini et al. proposed a platform for neuro-endoscopy, which results in more accuracy of robots both in autonomous and hands-on control methods by using an accurate tool 26 . Lefranc et al. also introduced a frameless robot for posterior fossa biopsy 27 . This proposed platform results in more accuracy and safety in comparison with normal biopsies in neurosurgery. Maddahi et al. built a robot-assisted micro-neurosurgery, which creates the optimal position, orientation, and force using a hand-controller in the robot workspace area 28 . Ross et al. designed a manipulator with two axes that operated the tumor resection by a cutting laser 29 . They used a feed-forward to provide automated soft tissue resection in these robots.
Despite sensitivities in neurosurgery and several limitations in robot workspace, improving robots' work efficiency by optimizing their joints is not studied before. Therefore, the present study attempts to answer this need in single-port minimal invasive surgery for brain tumor removal while preserving the accuracy and design considerations. This goal aims two types of single-port minimal invasive surgery robots have considered, and their performance has compared.

Materials and Methods
According to the present study's purpose, a single-port minimal invasive surgery robot is named robot type 1 and has compared with the developed model of this robot named robot type 2. Robot type 1 has tubular housing in its arm and end-effector, containing two small manipulators (Figure 1). This tubular housing has a 20 mm diameter and enables a robot for translation movement along the horizontal axis. After skull drilling ( Figure 1a) and placing a trocar, this tubular housing had placed to make a tumor pathway. It should note that the trocar diameter and endoscope of this robot are 20.2 mm and 10 mm, respectively. This robot consists of two manipulators (Figure 1b). The first manipulator has 5 degrees of freedom and allows for resection and ablation of tumors from the brain cortex ( Figure 2 -Zoom A and B). These 5 degrees of freedom consist of 4 revolute degrees of freedom and one prismatic degree of freedom. Revolute degree of freedom is for end-effector proper access to all the tumor parts ( Figure 2 -Zoom B). One prismatic degree of freedom had used for covering all the tumor volumes for accessing the tumor's depth in the brain cortex. The second manipulator is called suction and has 4 degrees of freedom. This manipulator sucks the separated tumor parts and removes them from the brain. This manipulator has three revolute degrees of freedom for accessing all the resected tumor volume and one prismatic degree of freedom to remove a tumor from the skull. The diameter of these manipulators is 4 mm. It should note that the ablation manipulator has one more revolute degree of freedom than a suction manipulator, which is because of the installed gripper in the endeffector of this manipulator.
In robot type 2, at the junction of the manipulator to the tubular housing, instead of using three revolute joints like in robot type 1 ( Figure 3 -Zoom A), 1 is a joint perpendicular to the other three revolute joints used. The important fact is that this new robot's ease of operation or higher efficiency depends on its output and kinematic and kinetic functions, which will discuss in the following

Transformation and spatial description
Forward kinematic analysis is one of the most important methods for a robot transformation description. Therefore, for both robot types, the table of Denavit-Hartenberg (D-H) parameters was calculated (Tables 1  and 2).
The transformation matrix derived from Equation 1 is a compilation of R 3×3 and P 3×3 matrices 22 , calculated for both robot types using forward kinematics.
Equations 2 and 3 describe the transformation matrix for robots type 1 and 2, respectively.
The transformation matrix had used for comparing orientation, spatial description, and location of type1 and type 2 robots. By multiplying this matrix with robot end-effector location, initial location, and orientation calculated.
In these calculations, Sθ and Cθ are Sin(θ) and Cos(θ), respectively and head center is considered as the origin of coordinates. Thus, tumor location which is the final destination of the robot's end-effector was considered in the same condition for both robot types at position [35,35, 0] T (numbers unit is mm). The location of the initial origin for both robot types was compared due to   . According to these equations, the distance traveled by robot type 1 and robot type 2 for accessing the same tumor is 68.2 and 71.2 mm, respectively. Therefore, although robot type 2 uses fewer joints and has a simpler mechanism, it has limited ability for spatial movement and transformation in comparison with robot type 1. According to Equation 6, during resection surgery robot type 2 damaged cerebral cortex tissue 58.9 mm 3 more than robot type 1 for resection of ablated tumors. Since robot type 2 damages cortex more than robot type 1, using it may increase the chances of post-surgery damages in the patient which can cause a longer recovery process.

Jacobian matrix
The Jacobian determinant had used when making a change of variables when evaluating multiple integrals of a function over a region within its domain. The Jacobian can also solve differential equations at an equilibrium point or approximate solutions near an equilibrium point. For evaluating and comparing manipulators balancing for both robot types, their joints' input needs to be analyzed and compared with each other. To do this, the Jacobian matrix for both robot types calculated. This matrix has six rows, and the number of its columns equals the number of that robot joints. The first three rows (Jv) derived from matrix P 3×1 relative to joints variables (q) and the second 3 rows derived from matrix R of each joint relative to another joint. Equations 7 and 8, show a Jacobian matrix for robot type 1 and type 2, respectively.
Robot's external loading, which is the tumor weight, should be applied in both robot types. According to a normal and minimum weight for a brain tumor, this number for each robot type considered being 0.5N, so that robots have compared in the same condition. Thus, both robots' external loading matrix has considered being [0, -0.5 N, 0] T . Equations 9 and 10 are calculated from multiplying transpose of the Jacobian matrix of robot type 1 and robot type 2 with an external loading matrix. The results showed that joints input matrix for robot type 1 and type 2 for establishing static balancing is [0, 0.27, 0, 0.21, 0] T and [0, 0.38, 0] T , respectively. This means that for establishing static balancing in robot type 1, the second and fourth joints should engage, and in the same

Discussions
After analyzing and comparing joints' inputs from both robots to establish static balancing, motion analysis compares these two robots described in this section. Static balance refers to the ability of stationary on the object to its balance. This happens when the object's center of gravity is on the axis of rotation. Whereas dynamic balance is an object's ability to balance while in motion or when switching between positions First, the 3D model for these two robot types has designed using CATIA Version 5R21 software (Dassault Systems, Waltham, Massachusetts, USA) (Figures 2 and 3). These models had transferred to MSC Adams Version 2018 software (MSC Software Corp, Santa Ana, California, USA) for motion simulation. Computer simulation is a common method in biology field analysis [30][31][32][33][34][35][36][37][38][39] . Therefore, in this study, two robot types were compared using Euler-Lagrange, kinetic, and kinematic equations in MSC Adams software. Figure  4 shows that in the same condition, maximum velocity in the contact location of the end-effector with the tumor for robot type 1 is 1.7 times more than the maximum velocity for robot type 2. This shows that robot type 1 is more effective than type 2. Motion period in robot type 1 has two peaks, while robot type 2 has only one peak. This means that robot type 2 has a better kinematic range, but robot type 1 can move more delicately, especially during ablation.
The kinetic view shows that the maximum end-effector force of robot type 1 applied to the tumor is more than 1.8 times than in robot type 2 ( Figure 5). This means that ablation is more comfortable in robot type 1 because, in the same conditions, robot type 1 can perform ablation 80% better than robot type 2. On the other hand, the maximum moment for both robot types is the same with less than a 1% difference ( Figure 6). This means that the end-effector's output power during ablation and resection is the same for both types. Moment graph in robot type 2 is linear, while this graph is parabolic in robot type 1. Linear moment graph in robot type 2 is a significant disadvantage in these robots during surgeries since it prevents smooth motion for the robot. Therefore, this issue turns out to be a significant weakness of robot type 2.

Conclusion
Robot type 1 and robot type 2 have almost the same endeffector output power for ablation and resection. On the other hand, robot type 2 has a more straightforward mechanism, fewer joints, and a better kinematic range than robot type 1. However, the results of this study show that for ablation and resection of a brain tumor, it is better to use single port minimal invasive surgical robots type 1. Because in the same conditions, the damaged volume of cerebral cortex tissue during resection is more for robot type 2, which results in post-surgery risks. Moreover, robot type 2 needs more internal loading in its joints for establishing static balancing. Robot type 1 has more smooth motions while it has better performance for ablation by 80%.