Kinematic and mechanical modelling of a novel 4-DOF robotic needle guide for MRI-guided prostate intervention

Abstract

Traditionally ultrasound-guided biopsy has been used to diagnose prostate cancer despite of its poor soft tissue contrast and frequent false negative results. Magnetic Resonance Imaging (MRI) has the advantage of excellent soft tissue contrast for guiding and monitoring prostate biopsy. However, its working area and access in the confined MRI bore space limit the use of interventional guide devices including robotic systems. To provide robotic precision, greater access, and compact design, we designed a novel robotic mechanism that can provide four degrees of freedom (DOF) manipulation in a compact form comparable to size of manual templates. To develop the mechanism, we established a mathematical model of inverse and forward kinematics and prototyped a proof-of-concept needle guide for MRI guided prostate biopsy. The mechanism was materialized using four discs that house small passive spherical joints that can be moved by rotating the discs consisting of grooved profile. With an initial needle insertion angle range of ±15°, we identified mathematical and kinematic parameters for the mechanism design and fabricated the first prototype that has dimension of 40 × 110 × 180 mm³. The prototype demonstrated that the unique robotic manipulation can physically be delivered and could provide precise needle guidance including angulated needle insertion with higher structural rigidity.

Keywords: Biopsy needle angulation; Kinematics; Parallel robot; Prostate cancer.

Fig. 1.

Existing biopsy needle guiding template for comparison. (a) Manual template developed by Tokuda et al. [18] (b) 4-DOF parallel manipulator robot developed by Li et al. [7] (c) MRBot developed by Cunha et al. [19] (d) Ultrasonic motor operated biopsy robot developed by Song et al. [16]. Reproduced with permission from Ref. [7,19] and [16].

Fig. 2.

Schematics for the mathematical model (a) two double discs (black and cyan) are concentric and parallel with each other. Each double discs have f₁ (magenta color) and f₂ (blue color) profile on it. (b) An equivalent model of the 4-DOF mechanism, simplified for kinematics analysis including the angle of rotation for the profiles, intersecting points (P₁ and P₂), direction vector ($\overrightarrow{P_{12}}$), and the target point (P).

Fig. 3.

(a) The exploded view of the 4-DOF robot. (b) Motion transmission mechanism with the timing belt and motors. The 4-DOF mechanism (D) is composed of front double-disc (D₁₂) and rear double-disc (D₃₄). Components: (A) biopsy needle; (B) ball-joint; (C) rear cover; (D) disc1 of D₁₂; (E) disc2 of D₁₂; (F) disc3 of D₃₄; (G) disc4 of D₃₄; (H) front cover; (I) support link (J) disc’s lateral support; (K) timing belt; (L) base; (M) motor housing; (N) motor; (O) gearbox; (P) transmission shaft; (Q) drive pulley; (R) grooved profile on D₄; (S) grooved profile on D₃; (T) transmission shaft and pulley bracket. (c) 4-DOF robot placed on the MRI operating table while the patient is in lithotomy position for the transperineal needle biopsy.

Fig. 4.

The timing belt drive parameters and dimensions.

Fig. 5.

3D printed prototype along with the mechanical components with its outer dimensions and the full setup for the robotic operation. (a) Isometric view. (b) Top view. (c) Left hand side view. (d) Mechatronic setup for the 4-DOF robot. Components: (1) needle; (2) four discs (D₁, D₂, D₃ and D₄); (3) grooved profile; (4) front and rear cover; (5) motor casing; (6) four motors; (7) disc’s lateral support; (8) four timing belts; (9) driving pulley and (10) base.

Fig. 6.

(a) Perpendicular intersection of the two groves creating a square-shape pocket to firmly hold and allow the hollow spherical ball to move smoothly. (b) Chamfer created on the disc face to accommodate the needle angulation.

Fig. 7.

(a) Intersection grid of profile f₁ and f₂ when both discs are symmetrically rotated at an interval of π/24. (b) Intersection grid of profile f₁ and f₂ when one of disc are kept static and other rotates at an interval of π/48. (c) Point cloud created by forward kinematics on the discs and conical works space generated by utilizing inverse kinematics considering 15° constrain to reach certain points (small black sphere at the apex). (d) Point cloud on the insertion plane (i.e. first plane form the direction of needle insertion) and black circular region satisfying the limiting cone.

Fig. 8.

(a) Geometric parameters to describe the working envelope of a biopsy needle through our device and the 2D working envelope. (b) 3D envelope generated by revolving the 2D envelope which encompasses the prostate including a probable insertion cone. Spherical black ball, two circular black discs, l_needle, l_thickness, l_prostate and d_curve represents the prostate, the two double disc pairs, biopsy needle length, thickness of the device, position of the prostate and radius of the profile respectively.