Sensors and Actuators A 135 (2007) 323–328
Fiber grating sensor for pressure mapping during total knee arthroplasty Lipi Mohanty a,∗ , Swee Chuan Tjin a , Denny T.T. Lie b , Silvino E.C. Panganiban b , Pierce K.H. Chow c a
Photonics Research Centre, School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore b Department of Orthopedics, Singapore General Hospital, Outram Road, Singapore 169608, Singapore c Department of Experimental Surgery, Singapore General Hospital, Outram Road, Singapore 169608, Singapore Received 16 January 2006; received in revised form 14 June 2006; accepted 17 July 2006 Available online 28 August 2006
Abstract Pressure mapping at the knee joint provides information regarding the contact stress, contact area and the alignment of the tibiofemoral interface. In this paper, preliminary cadaveric studies of a pressure-mapping sensor are presented. The sensor is made of fiber Bragg grating arrays embedded into the tibial spacer. The sensor can be used for in vitro and in vivo studies of the tibiofemoral interface. The results show that the sensor can detect malalignment and distribution of contact stresses in extension and flexion. This pressure-mapping tibial spacer sensor can be used for alignment of prostheses during total knee joint replacement surgery. © 2006 Elsevier B.V. All rights reserved. Keywords: Fiber bragg gratings; Pressure sensors; Knee arthroplasty; Tibiofemoral pressure mapping; Instrumented tibial spacer
1. Introduction Pressure mapping at the tibiofemoral interface is of interest to many groups involved in related surgical procedures, biomechanics studies and prostheses research and manufacturing. Many valuable studies have been reported on the contact stresses [1], contact area measurement [2], and polyethylene wear patterns [3]. Different methods of measurement and estimation have also been used for stress or pressure quantification [4–7]. Currently, two main methods of pressure mapping are prevalent—Fujifilm and Tekscan sensing systems. Though the systems have their specific advantages, the sensors have to be introduced between the tibial and femoral articulating surfaces and can alter the natural contact topology [8]. As the knee joint is a complex structure of various curved surfaces, a sensor that can adapt to complex contours is required for pressure mapping. Due to their flexibility, sensing and multiplexing capability, fiber Bragg gratings (FBGs) can be chosen as the sensing medium. Fiber grating sensors have a grating built into the core of the optical fiber where the period of the grating changes with applied
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perturbations and is encoded in the reflected or transmitted wavelength [9]. The wavelength encoding gives the added advantage of multiplexing by which a single strand of fiber can bear multiple sensors of different wavelength along the length and can be used to configure sensor arrays. In this paper, a novel fiber optic sensor (instrumented tibial spacer) is reported that can be used to correct malalignment during total knee replacement surgery. The basic design and working principle of the sensor are presented and results of preliminary cadaveric tests are also given. The sensor constitutes an FBG array embedded in fiber-reinforced composite. The actual fiber sensor lies beneath the contact surface, inside the instrumented tibial spacer (ITS), and hence does not disturb the natural contact characteristics of the region. The shape of the articulating surface is retained. During a total knee joint replacement procedure, the ITS sensor can slide in place of the prosthetic spacer. The femur can be rolled over the ITS sensor and the alignment checked from the pressure map displayed. Any malalignment can be corrected with repeated checking. After measurements are taken and required alignment has been achieved, the ITS sensor can be replaced by the actual tibial prosthetic spacer and the knee joint can be sutured. This ITS sensor can act as a valuable guide to surgeons during the surgical procedure. Also, the ITS sensor can be built into many of the
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Fig. 1. Reference and shifted spectra of fiber grating due to the application of pressure. The fourth sub-grating shows a shift in central wavelength.
designs of the tibial spacer prosthesis and into various polymeric materials. 2. The sensor design The sensor is comprised of optical fibers with sampled chirped gratings inscribed on each fiber to generate four to five sub-gratings that act as sensing points [10]. These sub-gratings can give the magnitude and position of loading simultaneously. Fig. 1 shows the reflected spectrum of a sampled chirped fiber grating. Each peak corresponds to a single sub-grating along the fiber that forms one sensing point. The central wavelength of each peak is the reference and any shift in the peak occurs due to a proportional magnitude of stress acting on the sub-grating. The figure shows two traces (line spectra) that are recorded when the fiber sensor is loaded and unloaded. The fourth sub-grating shows a wavelength shift as compared to the reference spectrum (unloaded). The wavelength shift (change in the position of the central wavelength of the peak) is proportional to the magnitude of the applied load. Each sub-grating is also uniquely identified by a specific position on the sensor. The central wavelength of the affected sub-grating can identify the location of the load, as the wavelength scale is directly proportional to the distance on the optical fiber. The gratings were embedded in a stack of unidirectional fiberreinforced composite in a specific design [10] to create an array of 2D sensing points. This process of embedding enhances the sensitivity of the FBG to transverse loading, when the FBG is placed away from the neutral layer. The transverse loading of the sensor results in axial tensile strain experienced by the optical fiber. This strain results in a change in the fiber grating period and a consequent change in the reflected spectrum at the specified point. A tensile strain results in the grating central wavelength shifting to a higher wavelength. This wavelength shift is proportional to the applied stress and the proportionality factor is influenced by the embedding design. The unidirectional composite used for embedding the sensor also significantly reduces
Fig. 2. Illustration showing the layout of the sub-gratings in the sensor (one condyle). The circular areas denote the spread of stress over many sub-gratings.
the effect of birefringence (and the resulting spectral distortion) when the fiber-reinforcements of the composite are parallel to the optical fiber. Fig. 2 shows the array of fiber gratings with five sub-gratings in each fiber. It demonstrates the effect of a force on several subgratings. The principle illustrated in the figure can be used to generate the pressure map at the tibiofemoral interface. Recently, we have reported the laboratory testing and calibration of such fiber grating sensor using this concept [11]. The applied pressure distributes the stress over a certain area covering several sub-gratings. From the reflected spectra of the gratings, the magnitude and location of the affected sub-gratings can be noted. It has been found that the shift in the central wavelength of each sub-grating, in the chirped sampled grating, increases monotonically with an increase in the applied force [10]. When a surface comes into contact with the sensor, the distribution of the pressure determines the shift in central wavelength of the various sub-gratings. The sub-grating that experiences the maximum pressure will show maximum wavelength shift whereas adjacent sub-gratings will show less shift. This method gives the location and magnitude of the load even when the load is not directly applied to any of the sub-gratings. The composite stack, with the fiber gratings, was cured in a mould to conform to the condylar surface of the Zimmer IB-II tibial spacer. A tibial spacer sample moulded with polymethyl methacrylate (PMMA) was layered with silicone rubber and the embedded sensor array was attached to both grooves. Such a design results in an array of 23 sensing points in each condyle of the tibial spacer. Fig. 3(a) shows a picture of the ITS sensor during the process of moulding. Two arrays of fiber sub-gratings are laid out in the two condyles. The fiber connections can be from the anterior or posterior end. After this stage, a thin layer of PMMA is poured on the sensor array to coat the lateral and medial condyles. This process results in covering the entire sensor with PMMA, and is convenient for sterilization, without
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Fig. 4. The loading and unloading plots of wavelength shift and applied force of a single sub-grating in the ITS.
Fig. 3. (a) A picture of the embedded fiber gratings covering the two condyles of the tibial spacer. (b) The vertical cross section (not to scale) of the instrumented tibial spacer showing the layers of different materials.
using reagents that would corrode the PMMA (or alternative polymer used). The schematic of the vertical cross section of the sensor is shown in Fig. 3(b). The embedded array of FBGs is less than 1 mm thick and the layer of silicone rubber is approximately 1 mm thick. The overall dimensions of the final ITS sensor are the same as the Zimmer IB-II. Though PMMA has different properties and is more brittle than ultra high molecular weight polyethylene (UHMWPE), the popular material for tibial spacers, it has been used for this sensor as it can be moulded at room temperature in the laboratory, without any specialized equipment. The same sensor design concepts can be incorporated in a UHMWPE spacer with separate calibration. 3. Experimental methods The fiber grating measurements were recorded using a standard experimental setup of a light source, a circulator and a spectrum analyzer. Though all tests were carried out statically, they can be done dynamically with a commercially available interrogation system. A repeated loading/unloading test done for calibrating the ITS is presented to demonstrate the response of the sensor to a vertical load. Fig. 4 shows the loading and unloading plots of wavelength shift as a function of applied force of a single subgrating in the ITS. In this case a femoral implant was placed on the ITS and it was loaded with a Chatillon force gauge. As the vertical force applied to the ITS increases, the wavelength shift registered by the sub-grating also increases monotonically. The deviation from linearity may be because increasing the force results in a larger contact area between the femoral implant and
the tibial spacer. The change in area of contact due to changing applied load is a consequence of a concave solid surface of one material (ITS) being in contact with a convex solid surface (femoral implant) of another material. Assuming that the interrogation system, comprising of a tunable laser source and an optical spectrum analyzer, has an accuracy of 15 pm and a resolution of 1 pm, it can be calculated that the sensor has an accuracy of 0.125 MPa with a sensitivity of 120 pm/MPa. The sensor resolution is about 8 kPa. These values are determined from the force/wavelength shift plot with the contact area approximated using principles of Hertz mechanics. Further details can be found in Ref. [11]. For the cadaveric tests, cadaveric parts were obtained from the Health Sciences Authority of Singapore under the Medical Research Act. The cadaveric knees were prepared for total knee joint replacement surgery. The femur and tibia were cut and shaped to accommodate the femoral implant and the tibial tray. The femoral implant was positioned on to the cut end of the femur, and the tibial tray was inserted without using cement at any stage. In place of the UHMWPE tibial spacer, the ITS was inserted. As the ITS sensor is identical to the prosthetic spacer, there is no change required in the procedure. Fig. 5 shows the ITS sensor inserted in place of a tibial spacer into a cadaveric knee joint. The operating procedure of total knee replacement remains the same in case of the sensor. This allows the surgeons to use the ITS sensor conveniently. The cut was sutured with the ITS sensor in the knee joint. Several tests were conducted at various angles of flexion. To study the pressure maps at various angles of flexion, the femur was clamped and the tibia was allowed to hang freely as shown in the setup (Fig. 6) of the cadaveric knee. The patella tendon was used to control the angles of flexion. The patella tendon was stringed and the string was run through a pulley. As the pulley moved vertically, it pulled the string and consequently tugged at the tendon changing the flexion angle of the tibia. The
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Fig. 5. A picture of the cadaveric knee joint with the fiber optic sensor inserted.
vertical motion of the pulley was controlled to obtain specific angles of flexion. For each angle of flexion, the central wavelengths of the sub-gratings were recorded. These wavelengths give the pressure distribution on the sensor array. The measured wavelengths of the gratings, under the effect of load, were compared with the reference wavelengths and the difference was recorded as wavelength shifts. These wavelength shifts are different for different loads. These wavelength shifts were input into a Matlab program to give the display or map of the load distribution. The load magnitude was obtained from the initial calibration done in the laboratory. A three dimensional surface is generated with the colour map giving the load magnitudes in terms of wavelength shifts. The map can be plotted as discrete points; in this case interpolation has been used to give continuous colour patterns. 4. Results and discussion
Fig. 6. The picture shows a cadaveric knee setup at 60◦ flexion with the sensor sutured inside. The optical spectrum analyzer is in the foreground.
Fig. 7 shows the response of one condyle in the ITS at various angles of flexion, from 70◦ to 40◦ . The magnitude of the pressure and the contact region also change. Such a pressure map can be used to infer the magnitude of load applied, the area affected and the alignment of the femoral component with reference to the tibial spacer. As the tests are not based on a load-bearing model, the magnitude of the pressures measured at the tibiofemoral interface by the ITS sensor are not absolute; the maps give the distribution of differential pressures. However, the maps show the efficacy of using the sensor to determine pressure patterns and absolute loads when necessary. Fig. 8 shows the pressure map for the medial and lateral condyles of a cadaveric knee. The pressure is unequally distributed in the condyles. This sensor shows that the ITS sensor can determine varus–valgus malalignment. The pressure map
Fig. 7. Pressure maps of one condyle at various angles of flexion: 70◦ , 60◦ , 50◦ and 40◦ . The icon in the left corner denotes the actual region covered by the pressure map (rectangle) in the tibial spacer. The condylar regions are denoted by the ellipses. The scale bar on the right is in MPa.
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Fig. 8. Pressure maps of the lateral and medial condyles of one knee in extension. The icon in the left corner denotes the actual region covered by the pressure map (rectangle) in both the grooves of the tibial spacer. The scale bar is in MPa.
shows that the contact for the left condyle is towards the posterior edge whereas for the right condyle it is towards the centre. This analysis of the pressure map verifies that the contact between the femur and tibial sensor is unbalanced. Fig. 9 shows the pressure map of a single condyle under a vertical load of 45 N. The sensor shows that there is a small rotation of the femoral implant that is causing loss of congruency (no contact in the centre) between the tibial spacer and the femoral implant articulating surfaces. This test shows that the ITS sensor can detect rotational malalignment. The above pressure maps in the figures show that the fiber optic sensor array in the ITS can detect the distribution of pressure, as required for a pressure-mapping sensor. The ITS sensor was sutured inside the cadaveric knee as a substitute for the UHMWPE tibial prosthesis. This method of testing confirms that the ITS sensor can be used for pressure mapping and prostheses
Fig. 9. Pressure maps of lateral condyle of another cadaver in extension. The scale bar is in MPa.
alignment during the process of surgery. Currently, surgeons use methods such as soft tissue balancing to reduce the wear of prostheses [12]. This sensor can supplement the existing techniques and reduce the chances of malalignment. Femoral rotation can be checked before cementing the implant. Severe deformities such as bow-legs and knock-knees due to surgical malalignment may be avoided before too much bone is cut off. The pressure maps also show the behavior of the knee in various modes of extension, flexion and rotation. The angles of flexion repeat a cycle of contact, the exact contact area and loads are however, different. Also, the axis of contact, determined at the point of fitting the femoral implant, remains the same for all the angles of flexion. Any tilt in the axis of contact is a consequence of femoral rotation that is relative to the position of the tibial spacer. Proper orientation of the implants can change stress distributions to a large extent, reducing subsequent complications of the knee, patella and the hip. The advantage of this sensor is that it can be used dynamically during the process of surgery with minimal disruption to the usual procedure. Also, the sensor can be customized for any curvature and design of the tibial spacer. The conforming surface allows the pressure distribution to be natural, unlike having to insert a sensor in between the articulating surfaces. However, the accuracy of the ITS sensor in predicting the contact pressure is also influenced by the stiffness of the sensor being similar to that of the prosthetic spacer. The maps in Figs. 7–9 show peak stresses of 3.5–5 MPa and a recent FEM study [13] reports compressive stresses of 2.55 MPa on the tibial cartilage in a healthy knee. However, the study [13] also mentions the significance of differing values of Young’s modulus and Poisson’s ratio of knee tissues used in the estimation, which are different from the ITS. Quantitative comparison of this sensor can be made with other methods when sufficient statistical data has been obtained under identical loading conditions. The ITS sensor can also be used in vitro for studying the biomechanics of the prosthetic knee joint especially for curved and conforming designs. The sensor can be used by prosthe-
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sis manufacturers to improve the design of implants. The core design concept can lead to similar sensors for the patella and the acetabular socket in the hip. 5. Conclusions This paper presents a novel fiber Bragg grating pressuremapping sensor that can be used during total knee joint replacement surgery. The array of fiber gratings gives the pressure distribution across the tibiofemoral interface. The pressure maps can give information on the femoral rotation and varus–valgus. The instrumented tibial spacer sensor can slide onto the tibial tray or base plate and provide a simple method to avoid malalignment during total knee arthroplasty. Acknowledgements The authors are grateful to Zimmer Inc. for providing the tools for the cadaveric testing. They would also like to thank Mr. Robert Ng of DES, SGH Singapore, for his help. References [1] C.S. Colsman, S. Ostermeier, C. Hurschler, C.J. Wirth, Acta Orthop. Scand. 73 (2002) 638. [2] M.L. Harris, P. Morberg, W.J.M. Bruce, W.R. Walsh, J. Biomech. 32 (1999) 951. [3] S. Schmitt, M. Harman, S. Wohlgemuth, H.P. Scharf, J. Biomech. 34 (2001) S70, Abstracts. [4] R.K. Kdolsky, B.A. Arabid, M. Fuchs, R. Schabus, V. Vecsei, Wien. Klin. Wochenschr. 116 (2004) 196. [5] D.D. D’Lima, C.P. Townsend, S.W. Arms, B.A. Morris, C.W. Colwell Jr., J. Biomech. 38 (2005) 299. [6] J.J. Liau, C.K. Cheng, C.H. Huang, W.H. Lo, Clin. Biomech. 17 (2002) 140. [7] T.P. Andriacchi, C.O. Dyrby, T.S. Johnson, Clin. Orthop. Relat. Res. 1 (410) (2003) 44. [8] J.J. Liau, C.K. Cheng, C.H. Huang, W.H. Lo, Clin. Biomech. 17 (2002) 698.
[9] A. Othonos, K. Kalli, Fiber Bragg Gratings: Fundamentals of Applications in Telecommunications and Sensing, Artech House, Boston, 1999. [10] L. Mohanty, S.C. Tjin, N.Q. Ngo, Sens. Actuators A: Phys. 117 (2005) 217. [11] L. Mohanty, S.C. Tjin, Appl. Phys. Lett. 88 (2006) 083901. [12] P. Gopinath, S.J. Varkey, J. Orthop. 1 (1) (2004), e2. [13] E. Peˇna, B. Calvo, M.A. Mart´ınez, M. Doblar´e, J. Biomech. 39 (2006) 1686.
Biographies Lipi Mohanty received her BSc Degree in Physics (Honours) from Ravenshaw College, Cuttack, India. She received her MSc Degree from Indian Institute of Technology, Delhi, India and her PhD degree from Nanyang Technological University (NTU), Singapore. Currently, she is working as a Research Fellow in NTU. Her research interests are in fiber optics and biophotonics. Swee Chuan Tjin received his PhD from the Department of Medicine at the University of Tasmania, Australia. He is currently the Director of the Photonics Research Centre and Associate Professor in the Division of Microelectronics, School of Electrical and Electronics Engineering, Nanyang Technological University (NTU), Singapore. He is also the Assistant Director of Research, NTU. His research interests are in biosensors, fiber optic sensors, and biomedical engineering. Dr. Denny Lie is a Consultant Orthopaedic Surgeon in the Orthopaedics Department of Singapore General Hospital. He completed his PhD at Imperial College, London. He is Co-Director, Master of Science in Biomedical Engineering programme, Nanyang Technological University; Clinical Teacher at the Medical Faculty of the National University of Singapore and Deputy Director of the Department of Experimental Surgery. Dr. Silvino Panganiban, MD, has completed his orthopaedic surgery training in the Philippines. He is sports medicine training fellow with the Department of Orthopaedic Surgery, Singapore General Hospital. Pierce Chow, MD, PhD, is a clinician scientist and the Director of the Department of Experimental Surgery, an AAALAC accredited translational research laboratory at the Singapore General Hospital (SGH). He holds concurrent appointments as senior Consultant Surgeon at SGH and visiting Associate Professor at the Nanyang Technological University. His research interests include preclinical development and testing of biomedical devices and clinical trials of these devices.