MR-Conditional SMA-Based Origami Joint

Abstract

Foldable origami structures have been implemented into robotics as a way of compacting joints and circuitry into smaller structures. This technique is especially useful in minimally invasive surgical instruments, where the goal is to create slimline devices that can be inserted through small incisions. Origami also has the potential to cut costs by reducing the amount of material required for assembly. Origami devices are especially suitable for MRI-guided procedures, where instruments must be nonmagnetic because origami is more suitable for flexible, non-metallic materials. MR conditional surgical instruments enable intraoperative MRI procedures that provide superior imaging capabilities to physicians to allow for safer procedures. This work presents an MR conditional joint developed using origami techniques that reduces costs by eliminating assembly of various components and has potential applications in endoscopy. The joint is a compliant rolling-contact element that employs curved-folding origami techniques. A chain of these joints can be constructed from a single sheet of material, eliminating assembly of numerous materials to produce a final product, which is specifically advantageous for constructing low-cost, disposable surgical devices. The prototype contains a degree of bending of ±9 degrees per joint, a response time of less than 4 seconds and an actuation force of 0.5 N using a 1.25 A current. The MRI results showed a minimal artifact of less than 1 mm measured from the boundary of the joint chain and a SNR reduction of less than 10%.

I. Introduction

MINIMALLY invasive surgery (MIS) has quickly become one of the most promising fields for surgical procedures. The goal of MIS is to minimize incisions to reduce postoperative pain and blood loss, speed recovery, and lessen scarring [1, 2]. MIS procedures have been enabled by the advance of microfabrication of various medical devices. However, a major drawback to this technique is the increased costs due to investment in the equipment required and the use of disposable instruments [3]. The cost of disposable MIS devices can be significantly reduced through simplification of fabrication techniques. Origami provides distinct efficiency in creating three-dimensional geometry without assembly by folding a single sheet of material [4]. The implementation of origami structures into minimally invasive surgical instruments is a promising new field that has numerous applications [5-8]. Recently, there has been an emerging field using origami to create compliant mechanisms, which can provide alternative ways to develop joints that achieve a particular range of motion [9, 10]. Devices that can provide precise navigation through curved anatomical pathways are crucial during these types of surgery, which makes the dexterity of origami structures especially useful in MIS [11].

Magnetic resonance imaging (MRI) provides high contrast visualization of soft tissue, making it ideal for image-guided procedures. Currently, most MRI is diagnostic due to the inherent limitations present within a strong magnetic field. However, research shows that MRI can be used for intraoperative procedures such as navigating catheters in cardiovascular interventions [12]. The American Society for Testing and Materials (ASTM) standard F2503-13 [13] classifies devices for the MR environment. MR conditional items are those that have been demonstrated to pose no known hazards in a specified MRI environment.

In this study, we design and model a chain of compliant rolling-contact element joints [14]. The origami joints are derived from curved-folding origami techniques that enable the capability of being assembled from a single sheet of material. Many traditional endoscopes contain a series of pin joints for manipulation [15]. The origami joints used in this study aim to reduce the complications that arise in pin joints such as backlash and wear. The origami joints can be completely assembled from a single sheet of material, greatly reducing the cost of fabrication by eliminating assembly of various components.

The origami joints were actuated using shape-memory alloy (SMA). SMA is an alloy that can recover an apparent permanent strain once heated to its activation temperature [16]. SMA is in the martensite phase at lower temperatures and can be easily deformed. When the SMA is heated, it returns to its pre-deformed shape set at the austenite phase [17]. Previous similar studies have shown to provide around 3 N of force using SMA [18]. Real-time active water cooling can be used with SMA to avoid tissue burning and to increase actuation bandwidth [19].

The geometry of the joint was analyzed to derive equations that define the location of the end-effector position. Mathematical software was used to model the resulting equations to visualize the physical range of the joint. The desired position of the end-effector could then be found by utilizing inverse kinematics.

The origami joint chain was introduced into the MRI environment to evaluate its MRI compatibility. The ability of the device to be MR conditional allows it to be used in MRI-guided surgical procedures, making it a valuable additional tool to assist surgeons in navigating anatomical pathways.

The novel contributions in this paper include: 1) For the first time, a joint chain is developed based on origami principles and smart actuators, 2) the joint chain is low-cost and disposable as it can be assembled from a single sheet of material, and 3) the joint chain is MR conditional.

II. Materials and Methods

2.1. Origami Folding Plan of the Joint Chain

The flat printed folding pattern of a chain of four origami joints is presented in Fig. 1a. The design can be laser cut, significantly reducing fabrication time. Black lines represent where the structure is cut, and red lines represent where it is folded. The folding pattern of a single origami joint is shown in Fig. 1b. Two rolling surfaces are connected by flexible bands, which forms a functional joint (Fig. 1c). A link connects each joint with an orientation of 90 degrees to the next adjacent joint, which provides for multiple degrees of freedom. The joint and link structures were designed so that a lumen is available for a catheter or other instruments to go through the joint chain. The position of the structure can be modeled using forward kinematic equations.

Fig. 1.

(a) Printed folding pattern of an origami chain of four joints; (b) folding pattern for a single origami joint; (c) final folded form of a single origami joint [14].

2.2. Kinematic Model for Planar Origami Joint

The kinematics of the origami joint are used to describe the joint chain’s end effector position in relation to the angle of deflection of each joint. A mathematical model can be derived by building up from a single joint to a chain of n joints (Fig. 2).

Fig. 2.

Geometric analysis of the origami joint structure; (a) origami joint cam; (b) geometry to determine D from the angle of rotation of the origami joint; (c) 2-D geometric representation of the rotation in space of a chain of origami joints.

The point of contact between the two halves of a single origami joint with relation to its deflection angle can be determined from the total deflection θ of the joint and the radius of the cam R (Fig. 2a). Nelson et al [14] determined that the structure of the origami joint is modelled by a cylindrical cam. The equation of the length L of a single panel is shown by

$$L=2R\sin \frac{\theta }{2}$$ (1)

Using the Pythagorean Theorem, D can be determined by

$$R^2=D^2+{\left(\frac{L}{2}\right)}^2$$ (2)

Substituting for L and rearranging.

$$D=R\sqrt{1-{\left(\sin \frac{\theta }{2}\right)}^2}$$ (3)

D can then be used to determine the relationship between the angle of rotation of the joint, α, and the (x, y) coordinates of the point of contact between the two rolling elements in the origami joint (Fig. 2b). From Fig.2 and the law of sines,

$$\frac{\sin (90+\alpha )}{R}=\frac{\cos \alpha }{R}=\frac{\sin \beta }{D}$$ (4)

Solving for β and substituting for β,

$$\beta ={\sin }^{-1}\left(\frac{D}{R}\cos \alpha \right)$$ (5)

$$c+(90+\alpha )+{\sin }^{-1}\left(\frac{D}{R}\cos \alpha \right)=180$$ (6)

Solving for c,

$$c=90-\alpha -{\sin }^{-1}\left(\frac{D}{R}\cos \alpha \right)$$ (7)

Then using the law of sines again,

$$r=\frac{R\sin c}{\cos \alpha }=\frac{R\sin 90-\alpha -{\sin }^{-1}\left(\frac{D}{R}\cos \alpha \right)}{\cos \alpha }$$ (8)

Substituting for D,

$$r=\frac{R\sin 90-\alpha -{\sin }^{-1}\left(\sqrt{1-{\left(\sin \frac{\theta }{2}\right)}^2}\cos \alpha \right)}{\cos \alpha }$$ (9)

Let γ be the numerator of r.

$$\gamma =R\sin 90-\alpha -{\sin }^{-1}\left(\sqrt{1-{\left(\sin \frac{\theta }{2}\right)}^2}\cos \alpha \right)$$ (10)

r can be expressed as

$$r=\frac{\gamma }{\cos \alpha }$$ (11)

x and y are found in terms of r by

$$x=r\cos \alpha$$ (12)

$$y=r\sin \alpha$$ (13)

Thus, when given the coordinates to the origin of the origami joint (x_o, y_o), one can find the coordinates (x, y) of the point of contact of the joint. Take, for example. Fig. 2c, which shows the geometry of a chain of two origami joints in a two-dimensional plane (a structure with one degree of freedom). The coordinates of the points of contact between each joint, (x_n, y_n) can be determined by finding the origin coordinates (x_on, y_on) and adding the results from (12) and (13). Assuming the first origin coordinates are (0, 0) the next origin coordinates for the next joint in the chain is determined by

$$x_{o_2}=x_1+t_1\cos {\alpha }_1$$ (14)

$$y_{o_2}=y_1+r_1+t_1\sin {\alpha }_1$$ (15)

Where t is the thickness of each link (Fig. 2c). The point of contact of the second joint is at

$$x_2=x_{o_2}+r_2\cos (-90+{\alpha }_1+{\alpha }_2)$$ (16)

$$y_2=y_{o_2}+r_2\sin (-90+{\alpha }_1+{\alpha }_2)$$ (17)

For n joints, the point of contact of the n-th joint is at

$$\begin{gathered} x_n=\sum _{i=1}^n\left[\frac{{\gamma }_i}{\cos {\alpha }_i}\cos \left((i-1)\left(-\frac{\pi }{2}\right)+\sum _{j=1}^i{\alpha }_j\right)\right] \\ +\sum _{i=1}^{n-1}\left[t_i\cos \left((i-1)\left(-\frac{\pi }{2}\right)+\sum _{j=1}^i{\alpha }_j\right)\right] \\ +\sum _{i=2}^{n-1}\left[\frac{{\gamma }_i}{\cos {\alpha }_i}\cos \left((i-2)\left(-\frac{\pi }{2}\right)+\sum _{j=1}^{i-1}{\alpha }_j\right)\right] \end{gathered}$$ (18)

$$\begin{gathered} y_n=\sum _{i=1}^n\left[\frac{{\gamma }_i}{\cos {\alpha }_i}\sin \left((i-1)\left(-\frac{\pi }{2}\right)+\sum _{j=1}^i{\alpha }_j\right)\right]+\frac{{\gamma }_1}{\cos {\alpha }_1} \\ +\sum _{i=1}^{n-1}\left[t_i\sin \left((i-1)\left(-\frac{\pi }{2}\right)+\sum _{j=1}^i{\alpha }_j\right)\right] \\ +\sum _{i=2}^{n-1}\left[\frac{{\gamma }_i}{\cos {\alpha }_i}\sin \left((i-2)\left(-\frac{\pi }{2}\right)+\sum _{j=1}^{i-1}{\alpha }_j\right)\right] \end{gathered}$$ (19)

2.3. Shape Memory Alloy Actuation

Each origami joint can be actuated with shape-memory alloy (SMA) springs made of nitinol wire. The SMA springs are conditioned so that when heat is applied, they return to their tightly wound memory shape. Each joint contains two SMA springs: one on both the right and left sides. When an electrical current is applied to one of the SMA springs, it returns to its memory shape, which causes the other spring to stretch (Fig. 3a). This effectively actuates the joint in one direction. The direction of actuation of the joint can be regulated by controlling the current applied to each spring. The size of the origami joint prototype shown in Fig. 3b is approximately 12 mm x 12 mm x 12 mm and the cost is less than one US dollar.

Fig. 3.

(a) Progression of actuation of a two origami joints from 0° - 20°; (b) size comparison of an origami joint prototype to a human pinky; (c) CAD model of origami joint chain.

2.4. Electronic Circuitry

Each origami joint is connected to four cables that provide electricity to actuate the two springs. The cables are fed through the central lumen of the device. An open-loop control circuit was developed based on H-bridge electronics and pulse width modulation (PWM) to regulate the input current to achieve a desired bending angle output.

2.5. Origami Joint SMA Performance Analysis

The performance of the SMA was analyzed through experiments which compared current vs bending angle, current vs temperature, current vs force, and response time vs angle at various currents. Upon loading and unloading the SMA with current, hysteresis was observed and recorded. The force generated was measured by actuating the joint with weights hanging from one side of the structure. As more current was applied, more weight could be lifted. The actuation angle was measured using a protractor, and the SMA temperature was measured using a temperature probe.

2.6. Origami Joint Material Properties

The prototype in Fig. 3 is constructed by folding the origami pattern in Fig. 1 from cardstock and further strengthened by inserting a photopolymer. The mechanical properties of the photopolymer are given in Table 1.

Table 1.

Photopolymer Properties

Mechanical Properties	Measurement	Method
Ultimate Tensile Strength	38 MPA	ASTMD 638-10
Young's Modulus	1.6 Gpa	ASTMD 638-10
Elongation at Failure	12%	ASTMD 638–10
Flexural Modulus	1.25 Gpa	ASTMC 790–10
Thickness	1 mm	n/a

III. Results

3.1. Origami Joint SMA Performance Results

The performance results of the SMA are shown in Fig. 4. The results show that the degree of bending is approximately ±9 degrees per joint with the current limited to 1.5 A. The SMA reached a temperature of approximately 150 degrees Celsius at a current of 1.25 A. The joint has a response time of < 4 seconds and an actuation force of 0.5 N with 1.25-A current. The results of the observed hysteresis of the SMA upon loading and unloading of current is shown in Fig. 4e. The results indicate that the bending angle, actuation force and SMA temperature have a predictable response curve with respect to the applied current, making the origami chain feasible for use in endoscopic applications with future improvements.

Fig. 4.

Performance of the SMA actuation in a single origami joint; (a) current vs bending angle; (b) current vs force; (c) current vs temperature; (d) response time vs bending angle; (e) hysteresis of loading /unloading.

3.2. MRI Compatibility Evaluation

The origami joint was tested using a 3T MRI scanner according to ASTMF2503-13 [13]. The scientific rationale was first employed based on the component materials of the joint. The joint was then tested for the static magnetic field-induced displacement force (ASTM F2052) and torque (ASTM F2213) by suspending the manipulator at the entrance of the MR system bore by a string and measuring the string deflection angle and observing the torque. The RF field-induced heating (ASTM F2182, ISO TS 10974) and gradient field-induced heating and vibration (ISO 10974) were performed by direct observation. The gradient and RF field-induced voltage tests (ISO TS 10974) were also performed by direct observation. By these experiments, the origami joint is validated as MR conditional in a 3T environment. MR images were taken of the prototype and the results showed a minimal artifact size of <1 mm measured from the boundary of the joint (Fig. 5a). The signal-to-noise ratio (SNR) reduction was measured by comparing a baseline measurement with no device present to measurements with the device present at power levels of 0%, 25%, 50%, 75%, and 100% using gradient echo (GE) and spin echo (SE) sequences. The results provided in Fig. 5d show a SNR reduction of less than 10%.

Fig. 5.

(a) MRI images of an origami joint chain; (b) Photo of the control box inside the MRI scanner; (c) Block diagram displaying the control of the joint chain inside the MRI; (d) SNR reduction of gradient echo (GE) and spin echo (SE) sequences.

IV. Conclusion

MR conditional surgical devices provide a means for interventional procedures with the guidance of high-quality imaging. The structure of the MR conditional flexible SMA-based origami joint chain is fabricated from a single sheet of material, which makes it a low cost and disposable surgical instrument. The origami joints are actuated via SMA springs that are attached to the sides of the joints. There is a lumen integrated into the joints through which a camera, catheter, or some other surgical instrument can be threaded. The geometry of the structure was analyzed and a 2-D end-effector range plot was produced. The mechanical performance evaluation resulted in ±9 degrees of bending in the origami joint with just 1.5 A of current. The device was tested according to the ASTM standards [13], and the resulting images exhibited minimal artifacts, verifying it as an MR conditional device. Future work includes experimenting with various materials to make the structure more rigid, performing horizontal loading and parasitic motion analyses, and further miniaturizing the design by approximately 50% to match industry standard endoscopes. This work presents a novel application of origami and SMA to produce an MR conditional joint that has potential applications in endoscopy.