Calin Vaida 1 , Doina Pisla 1 , Josef Schadlbauer 2 , Manfred Husty 2 - PowerPoint PPT Presentation

Calin Vaida 1 , Doina Pisla 1 , Josef Schadlbauer 2 , Manfred Husty 2 and Nicolae Plitea 1 1 Research Center for Industrial Robots Simulation and Testing, Technical University of Cluj-Napoca, Romania 2 Unit for Geometry and CAD, University of Innsbruck, Austria Nantes, July 9 th , 2015

Introduction Brachytherapy Robotics in brachytherapy PARA-BRACHYROB - The medical parallel robot Singularities analysis using the Jacobi matrices The kinematics using Study parameters Singular poses of the manipulator Results interpretation and implementation The experimental model Conclusions

Brachytherapy (BT) , also known as internal radiotherapy, sealed source radiotherapy, curietherapy or endocurietherapy, is an advanced cancer treatment technique, where radioactive seeds are delivered directly in the tumor area . It involves the placement of tiny radioactive miniaturized sources precisely in the tumor area , delivering high dosage of radiation in the cancerous cells. Its effectiveness is clearly demonstrated, its side effects are reduced to a minimum, but it involves an important condition : the catheters delivering the radioactive sources must be placed precisely as the radiation dose decreases abruptly from the base and incorrect positioning causes the necrosis of healthy tissue without affecting the tumor.

Why is BT undervalued? A report presented in the AAPM (American Association of Physicists in Medicine- prof. Podder and Fichtinger) meeting in 2010, shows that robotic BT is underdeveloped as most of the solutions target only the prostate , without any device capable of performing the BT tasks on larger areas of the body. EUCLIDIAN MrBOT

The development of a robotic system, able to perform general BT procedures, capable of targeting any organs A new approach in the thoracic and abdominal areas, like liver, lungs, paravertebral areas, breast, kidney, etc. CT scan with needle placement (arrow) CT-Sim scan with laser positioning system for transpulmonary biopsy (Courtesy of the Oncology Institute Cluj-Napoca, Romania)

Evolution of robotic brachytherapy A new report presented in the AAPM (written by the same task force leaded by prof. Podder and Fichtinger) dating from august 2014, illustrates the progress made in the last four years, defining more clearly several aspects for robotic brachytherapy:  Specific criteria for the robots;  Emphasis on safety issues;  Testing protocols for new robotic solutions validation;  The need for further researches as still most robotic solutions cover only prostate brachytherapy with one solution focused on lung treatment.

Patent pending, 2013 q , q , q 1 2 3 Kinematic scheme of the medical parallel robot

The medical task of the robot : The robot should introduce, based on radiologic data, needles with diameters varying from 0.6 mm up to 2 mm and lengths from 100 mm up to 250 mm, on distances up to 200 mm, following a linear trajectory. For this task the robotic system receives a set of two points: point I ( 𝑌 𝑗 , 𝑍 𝑗 , 𝑎 𝑗 ) - the insertion point and point T ( 𝑌 𝑈 , 𝑍 𝑈 , 𝑎 𝑈 ) - the target point. In addition, a third point is introduced in the algorithm, the current robot position, point C ( 𝑌 𝐷 , 𝑍 𝐷 , 𝑎 𝐷 , 𝜘 𝐷 , 𝜄 𝐷 ). Based on this data, the final needle orientation is computed:       = atan 2 Y Y , X X  IT T I T I      2   2    = atan 2 ( Y Y ) ( X X ) , Z Z  IT T I T I I T   

The medical task of the robot : This task will be achieved through a motion decomposed in two different parts: • the approach stage (from point C to I), when the first five actuators are used, to reach the point of entry inside the patient, with the final orientation, having the pose ( 𝑌 𝐽𝑈 , 𝑍 𝐽𝑈 , 𝑎 𝐽𝑈 , 𝜘 𝐽𝑈 , 𝜄 𝐽𝑈 ); • the needle insertion stage (from point I to T), when the sixth actuator is used to push the needle, on a straight line, to reach the target point having the pose ( 𝑌 𝑈 , 𝑍 𝑈 , 𝑎 𝑈 , 𝜘 𝑈 , 𝜄 𝑈 ). The system should also allow the control of the insertion force into the patient’s tissue.

Kinematic model was presented in [Plitea et al, 2014] The system of implicit functions, which results using the geometrical relations between the coordinates of the active joints, the needle tip and the geometrical parameters of the structure, is:         f : Z l ( q 2 l ) cos ( ) q 1 E 1 6 c 1           2   2   f : X ( q 2 l ) sin ( ) cos ( ) b d ( q q ) cos ( q )   2 E 6 c 1 1 2 1 3              2   2  f : Y ( q 2 l ) sin ( ) sin ( ) b d ( q q ) sin ( q )    3 E 6 c 1 1 2 1 3          f : Z l ( q l ) cos ( ) q  4 E 2 6 c 4  2  2  2   2  2        f : X X Y ( q l ) sin ( ) 2 ( q l ) sin ( ) 5 O 2 E E 6 c 6 c    2 2               ( X X ) cos ( ) Y sin ( ) 2 X X b d E O 2 E O 2 E 2 2  2   2      2 ( q q ) 2 b d ( q q )  5 4 2 2 5 4

Kinematic model Where matrix A is: and matrix B is:    f  1  0 0 1 0      1 0 0 0 0          f f f f f    2 2 2  2 2 0 0 1 0 0          q q q   1 2 3          f f f f f   3 3 3  3 3  0 1 0 0 0 A B          q q q     1 2 3    f  0 0 0 1 0   4 0 0 1 0     f f     5 5 0 0 0           f f f f  q q  5 5 5 5   4 5 0        X Y  E E     T and     T X X , Y , Z , , , q q , q , q , q , q E E E 1 2 3 4 5     T T                 X X , Y , Z , , , q q , q , q , q , q E E E 1 2 3 4 5     T T                             X X , Y , Z , , , q q , q , q , q , q E E E 1 2 3 4 5 Safety in use

The determinants of A Jacobi and B Jacobi matrices are:     2  2         det ( A ) = 2 l sin ( ) ( X X ) sin ( ) Y cos ( ) c O 2 E E          2   2   2   2 ( q q ) ( q q ) b d ( q q ) b d ( q q )     2 1 5 4 1 1 2 1 2 2 5 4     det ( B ) = 2   2  2   2 d ( q q ) d ( q q ) 1 2 1 2 5 4 det ( A ) = 0 - this situation corresponds to the case when the distance between the two l c = 0 𝐷 1 𝐷 2 Cardan joints is zero, meaning that the points and superpose; This situation cannot materialize in practice and can be discarded; sin 2  -this equation characterizes the vertical position of the needle module, when ( ) = 0 the two Cardan joints are positioned on a vertical axis (parallel with the OZ axis). In this configuration the robot gains one degree of freedom, allowing the rotation of the needle positioning module around the axis defined by the points 𝐷 1 𝐷 2 and . In the robot control algorithm this situation will be avoided by 𝜄 𝐽𝑈 ≠ 𝜌 imposing that 2

Y   E       which is equivalent with tan ( ) = ( X X ) sin ( ) Y cos ( ) = 0  O 2 E E X X O 2 E Considering the fact that the needle tip coordinates (point E) will be always located Y between the two robot arms, the ratio will be always positive, meaning that E  X X O 2 E       3        the angle will take values in the domain  ,   ,2      2 2 The configuration corresponds to the case when the coordinates of and E q , q , C , C 4 5 1 2 are located in the same plane. In the control algorithm this situation will be tested when a trajectory is generated, and in case a singular configuration an alternate trajectory will be computed.