- Email: [email protected]
A multiaxial force-sensing implantable tibial prosthesis
ARTICLE IN PRESS
Journal of Biomechanics 39 (2006) 1744–1751
Technical note
www.elsevier.com/locate/jbiomech www.JBiomech.com
A multiaxial force-sensing implantable tibial prosthesis Bryan Kirking, Janet Krevolin, Christopher Townsend, Clifford W. Colwell Jr., Darryl D. D’Lima Orthopaedic Research Laboratories, Shiley Center for Orthopaedic Research & Education at Scripps Clinic, CA, USA Accepted 10 May 2005
Abstract Accurate in vivo measurement of tibiofemoral forces is important in total knee arthroplasty. These forces determine polyethylene stresses and cold-flow, stress distribution in the implant, and stress transfer to the underlying implant bone interface. Theoretic estimates of tibiofemoral forces have varied widely depending on the mathematical models used. The six degrees of freedom of motion, complex articular surface topography, changing joint-contact position, intra- and extra-articular ligaments, number of muscles crossing the knee joint, and the presence of the patellofemoral joint contribute to the difficulty in developing reliable models of the knee. A prototype instrumented total knee replacement tibial prosthesis was designed, manufactured, and tested. This prosthesis accurately measured all six components of tibial forces ðR2 40:997Þ. The prosthesis was also instrumented with an internal microtransmitter for wireless data transmission. Remote powering of the sealed implanted electronics was achieved using magnetic coil induction. This device can be used to validate existing models of the knee that estimate these forces or to develop more accurate models. In conjunction with kinematic data, accurate tibiofemoral force data may be used to design more effective knee-testing rigs and wear simulators. Additional uses are intraoperative measurement of forces to determine soft-tissue balancing and to evaluate the effects of rehabilitation, external bracing, and athletic activities, and activities of daily living. r 2005 Elsevier Ltd. All rights reserved. Keywords: Tibiofemoral forces; Telemetry; Knee biomechanics; Total knee arthroplasty; In vivo forces
1. Introduction Over two hundred thousand knee joints are surgically replaced every year (National Hospital Survey, 2004) with the number expected to double by the year 2030 due to the increase in population and the increase in life expectancy (US Bureau of the Census, 1994; AAOS Dept of Research and Scientific Affairs, 1994). Current total knee implant designs have a reasonable survival rate of 10–15 years (Weir et al., 1996; Nafei et al., 1996; Aglietti et al., 1999; Falatyn et al., 1995; Buehler et al., 2000). However, polyethylene wear has become a major factor associated with implant loosening and revision Corresponding author. Suite 140, 11025 N Torrey Pines Road, La Jolla, CA92037. Tel.: +1 858 332 0166; fax: +1 858 332 0140. E-mail address: [email protected] (D.D. D’Lima).
0021-9290/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2005.05.023
surgery (Bugbee et al., 1998; Whiteside, 1994; Cameron and Jung, 1993; Mintz et al., 1991). With the increase in life expectancy and the increase in arthroplasties performed in younger patients, longer survival is essential. Knee wear is dependent on several interrelated parameters that make it difficult to predict the effect of design changes. Clinical studies can be used to evaluate the efficacy of design changes or surgical techniques; however, the need for large cohorts and long-term follow-up preclude their use (Weir et al., 1996; Nafei et al., 1996; Diduch et al., 1997). In vitro and mathematical models are commonly used as cost- and time-effective screening tools before clinical evaluation (Yashar et al., 1997; Ezzet et al., 2001; Petersilge et al., 1994; Grady-Benson et al., 1992; Nagamine et al., 1995; Singerman et al., 1996). The knee, however, is a complex joint that is difficult to model accurately. Although
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significant advances have been made in mathematical modeling, these have yet to be conclusively validated in vivo. Accurate measurement of knee forces can lead to a better understanding of the stresses seen in total knee arthroplasty and will enable more clinically applicable mathematical and in vitro modeling of the knee, which can then be used to develop and evaluate relevant improvements in implant design. Perry et al. measured tibial forces in vitro using a tibial plate connected to an instrumented shaft (Perry et al., 1975). An instrumented tibia that transmitted knee forces through four posts to strain gages in the tibial tray has been reported (Kaufman et al., 1996). We have also reported the results of testing a prototype telemetry tibial replacement system using radiofrequency transmission of tibiofemoral compressive forces and location (D’Lima et al., 1999). This telemetry system was found to accurately transmit the signal through bone, cement, and soft tissues with a range of approximately 3 m. In addition, the system also worked intraoperatively (Morris et al., 2001); however, only axial compression and center of pressure were measured. Shear in the anterior–posterior and mediolateral direction and axial torques (all important components of knee forces) were not measurable. To address this deficiency, a total knee replacement tibial prosthesis was designed that accurately measured all six components of tibial forces.
2. Methods 2.1. Overview The design was based on a commercially available tibial tray, polyethylene insert, and instrumentation. The tibial prosthesis was an assembly of two structural components (Fig. 1). The proximal section (holding the polyethylene insert) was connected to the distal section (cemented in the tibia) through a shrink-fit cylindrical stem. The proximal section was the sensing element and was instrumented with strain gages that measured stem deformation under load. A microprocessor was used to acquire, multiplex, and transmit the strain-gage data through a radiofrequency transmitter and an antenna. The proximal section (Fig. 1a) consisted of the tibial tray and a load-sensing component. A conventional tibial-tray design (NK-II, Centerpulse, Austin, TX) connected to a hollow stem was machined out of titanium alloy as a single piece (Ti6Al4V). The tibial tray contained the standard locking mechanism for holding a standard polyethylene insert. The inner surface of the hollow stem, which also housed the microtransmitter, was instrumented with 12 strain gages. The tibial tray was proximally unconstrained. The distal portion of the strain-gaged stem was inserted via a rigid shrink-fit into the distal section.
Fig. 1. (a) Proximal tray-stem section. (b) Distal Shell. (c) Assembled implant. The stem was shrink-fit into the shell using a temperature differential during assembly. The gap between the proximal tray and the distal shell allowed loads to be transmitted to the upper portion of the stem. Strain gages were bonded to the inner surface of the stem. The microtransmitter and internal power induction were assembled in the stem of the implant.
The distal section (shell, Fig. 1b) was comprised of a flat platform and a hollow shoulder, which was cemented in the tibia. Knee forces were transmitted through the femoral–articular surface, through the polyethylene insert, to the tibial tray of the proximal
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section, and finally transmitted via the shrink-fit interface to the distal shell. Strains measured in the straingaged stem (connected at one end to the shell and at the other end to the unconstrained tray) were used to compute the net forces acting on the device. The tibial tray was unconstrained due to a gap (width ¼ 0.635 mm) between the tibial tray and the shell. This gap was chosen as adequate for measuring mediolateral and anteroposterior moments without closure, while allowing for closure of the gap and for protection of the strain gages due to overload. The inner diameter of the stem was 16 mm, as this was the minimum diameter required to house the prototype microtransmitter. The minimum thickness of the stem wall was estimated to be 2 mm (resultant outer diameter ¼ 20 mm), which can theoretically withstand fatigue due to 10 million cycles of a bending moment of 20 N m (assuming a fatigue stress for Ti4Al6V ¼ 396 MPa). The proximal tray-stem and distal shell were assembled using a thermal shrink-fit between the hollow strain-gaged stem and the shoulder of the shell. Using a coefficient of thermal expansion of 6.39 106/1C for the titanium alloy (Gere and Timoshenko, 1997) and the above nominal inner and outer diameters for the stem, a minimum temperature differential of 6.34 1C/mm of expansion was needed. This yielded a minimum temperature differential of 317 1C for a nominal shrink-fit interference of 0.05 mm. In actuality, a temperature differential of approximately 700 1C was used. The shell was heated in an oven to approximately 500 1C, while the stem was cooled in liquid nitrogen to 195 1C. The shell and stem were assembled and were clamped together until temperature equilibrium was achieved and the shrink-fit was stable. A combination of analytic solutions supported by linear finite-element analysis was used to optimize placement of the strain gages. Three-element stackedrosette 1000-O strain gages (4 rosettes, total 12 gages, Vishay Micro-Measurements, Malvern, PA) were bonded to the inner surface of the stem using transducer-grade epoxy. Each rosette was made of three gages: one oriented along the vertical z-axis, one oriented at 451 to the z-axis and the other at +451 to the z-axis. One rosette each was bonded at anterior, posterior, medial, and lateral surfaces, 16 mm below the bottom of the tibial tray (midway between top of the hollow stem and the most proximal level of the shrink-fit between the tray and the shell). Custom fixtures were used during the procedure to ensure gage location, orientation, and bonding pressure. 2.2. Calibration The device was secured in a mounting fixture that was aligned with the axis of a six degrees of freedom load cell
(AMTI, Watertown, MA), which served as the measurement standard (Fig. 2). Individual components of force were separately applied to the surface of the tray. For each applied force, continuous data were synchronously logged from the measurement standard and the strain gages. The offset between the location of the measurement standard and the surface of the tray was used to transform forces and moment output from the measurement standard to yield forces and torques at the tray surface. One set of loads was used to determine the calibration matrix, while a different set was used to measure error. Calibration loads were selected in the range of 600–+ 4000 N for Fz (vertical load), and 600–+600 N for Fx, and Fy (anteroposterior and mediolateral loads,
Fig. 2. Implant Calibration: The implant was mounted on a custom device (on linear bearings to prevent unintended side loads) in line with a six-component load cell. Loads were applied to the top of the tray and were measured by the load cell. Simultaneously, strains were measured from the 12 strain gages. Multiple linear regressions were used to relate the measured strains with applied loads and to determine the linearity response.
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respectively). Moments were selected in the range of 25–+25 N m. Multiple linear regressions (one per force component) were used to relate the 12 simultaneous strain measurements to each component of force. Additionally, the error between the forces predicted by strain-gage measurement and those recorded by the measurement standard were calculated. To determine the accuracy under dynamic conditions, measurements were made using a sinusoidal loading waveform at varying frequencies up to 2 Hz. 2.3. Telemetry system Voltage output from the twelve 1000-O resistive strain gauges were multiplexed into an instrumentation amplifier. The output of the instrumentation amplifier was digitized by a 12-bit analog-to-digital converter (ADC). Multiple digital samples were digitally filtered by the onboard microprocessor (PIC16f876, Microchip Technology, Chandler, AZ). The microprocessor then serially modulated a 418 MHz frequency shift-keyed radio transmitter (pulse-code modulation) with the digital data. A short radio antenna was attached to a hermetically sealed feed-through to allow for highfrequency transmission out of the implant. A polyethylene cap was added to protect the antenna from damage during the implantation process. Each data packet consisted of a header byte, 12 channels of sensor data (2 bytes each), power-level data (2 bytes), and a checksum (sum of preceding bytes, 2 bytes in size). The header byte was used as a flag for reading the start of the data packet, the checksum byte was used to check the integrity of the data and to test for missing bytes. The pulse-code modulated (PCM) receiver contained a receiving antenna, a matched radiofrequency oscillator, and a level converter to generate RS-232 signals from the incoming PCM data stream. Custom PC-based software was developed to read, display, and store received data. A PC received the RS-232 signal, which was read by custom software and was synchronized with data from other instruments. The microtransmitter was powered using magnetic near-field coupling. An external coil (driven with AC current) generated an AC voltage in the internal coil (Fig. 3). This voltage was then rectified and filtered to provide the DC power required to operate the telemetry system. A function generator was used to provide a 3-V AC signal at 1.6 kHz to a 100-W audio-power amplifier, which amplified the signal and drove the external (primary) coil. The power amplifier delivered 1.0 A of current at 35 V to the external coil. An external coil of 17 cm in diameter was chosen to allow it to be placed around the patient’s leg. The external coil was constructed of 35 turns of 16-gauge magnet wire, with an impedance of 10 O at the 1.6 kHz frequency. The internal (secondary) coil, housed in the stem of the
Fig. 3. (a) Photograph of the implant being assembled with the telemetry system. (b) Close-up view: shows the onboard microprocessor and the internal power induction coil. (c) Photograph of a subject wearing the power induction coil (C) around foam padding about the upper tibia. An amplifier (A) powers the induction coil. The receiving antenna (R) receives the radiofrequency signal which is then recorded on a notebook PC.
implant, consisted of 2000 turns of magnet wire wound on a high-permeability ferrite core. Under static (unloaded conditions) the telemetry system was tested up to 12 h duration at a time. The electronics were also subjected to high temperature ‘‘burn in’’ and shaker tests (10 Hz) to determine failure due to fatigue. To test the integrity of the telemetry system, a fresh-frozen cadaveric knee specimen was thawed and a total knee replacement performed. The instrumented tibial prosthesis was cemented into the tibia. The knee was then mounted on a dynamic quadriceps-driven (closed kinetic chain) knee extension rig and tibial forces measured. Forces were initially measured using the prosthesis in a fully wired configuration and again through the telemetry system. The
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number of checksum errors was used to determine the stability of the telemetry signal during dynamic loading knee motion. 2.4. Structural testing Six components (tibial trays with stems) were mounted on a fixture designed for cantilever testing on Shore Western Fatigue Frames (Shore Western, Monrovia, CA). The components were fatigue tested in air at room temperature in accordance with ASTM standards (ASTM F1800-97, 2004). The lateral half of the tray was rigidly clamped while the unsupported medial half was loaded. A cyclic load of 667.5 N was applied in the form of a sinusoidal waveform at 15 Hz for 10 million cycles. 2.5. Strength of the shrink-fit Four shells were heated in an oven to approximately 500 1C. Four stems were cooled in liquid nitrogen to 195 1C. Each stem-shell pair was assembled and clamped together until temperature equilibrium was achieved and shrink-fit was completed. Each stem-shell assembly was mounted on a MTS Bionix testing machine and then peak resistance to axial torque was measured at 0.131/s. Standard NK-II cruciate-retaining femoral components were also tested against corresponding modular inserts in off-the-shelf tibial trays. An axial load of 2670 N was applied across the femorotibial articulation. The maximum torque resistance at the femorotibial articulation (between the femoral component and polyethylene insert) was measured.
3. Results 3.1. Calibration A highly linear response ðR2 40:997Þ was noted between measured and predicted forces (Fig. 4). After calibration, a dynamic force was applied and strains were measured. A very close agreement between the measured and predicted forces was found. The maximum error, average absolute error, and percent fullscale error in the prediction of each force channel are listed in Table 1. The experimental determination of the calibration matrix effectively minimized errors in locating or aligning the strain gages, accounted for cross talk between various force components, and automatically weighted the contribution of each strain gage to calculate each component of applied load. After static calibration, the dynamic response of the strain gages was compared with that of the external load cell (Fig. 5). To test the value of redundant strain gages, in the event of a failure of a single strain gage, the contributions of each of the 12 gages were individually removed from the
Fig. 4. Calibration results. A highly linear response was seen between externally applied loads and those predicted by the instrumented device ðR2 49:997Þ. (a) Fz (Vertical force (N)). (b) Fx (Anteroposterior Force, (N)). (c) Tz (Torque around the vertical axis, (N m)).
calibration matrix and predicted forces compared with measured forces. The 12-gage system appeared to be very robust to the loss of a single strain gage (Table 2).
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Table 1 Calibration error analysis
AAE MAE R2
Fx
Fy
Fz
Tx
Ty
Tz
0.67 2.54 0.999
1.00 4.73 0.998
3.92 14.80 0.997
0.15 0.65 0.998
0.15 0.85 0.999
0.16 1.12 0.998
AAE ¼ average absolute error (N for Fx, Fy, Fz; N m for Tx, Ty, Tz). MAE ¼ maximum absolute error (N for Fx, Fy, Fz; N m for Tx, Ty, Tz).
Fig. 5. Dynamic Testing: predicted forces closely matched measured forces during dynamic testing.
Table 2 Effect of loss of strain gages on accuracy Loss of:
Any one gage
All 45 gages
All +45 gages
All axial gages
AAE MAE R2
4.18 18.05 0.997
3.33 4.14 0.997
3.36 3.11 0.996
7.88 2.42 0.989
3.2. Telemetry In this configuration, the internal coil consistently generated approximately 40 mW of power, which was
more than adequate to power the strain gages and the telemetry system. Data were collected in both wired and wireless mode and were compared for integrity. Less than 2% of the data was flagged with errors in the
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checksum byte. Of the data that passed the checksum test, a 100% match was obtained between the wired and wireless recordings. 3.3. Structural testing All six of the tested specimens survived 10 million cycles at the maximum applied fatigue load without failure or fracture. The surface of each tray was inspected visually and microscopically for signs of fatigue and cracks but none were found. The maximum torque resistance at the shrink-fit (60–85 N-m) compared very favorably with the maximum torque resistance at the femorotibial articulation (16–24 N-m).
4. Discussion Singerman et al. reported on a similar force transducer design based on two concentric cylinders (Singerman et al., 1999). The inner cylinder was instrumented with strain gages while the outer cylinder was fixed to the bone. That transducer was used to measure tibial forces in normal cadaver knees and was inserted through a 1 cm resection of proximal tibial. Powering and data transmission, however, were through direct wiring. The design reported here accurately measured all six components of load and achieved wireless transmission of data with a net signal integrity of greater than 98%. The prototype implants also passed the specified structural testing. The shrink-fit could easily sustain axial torques transferred across the knee. The testing and calibration was done using uniaxial loading along the different axes. The error under these conditions was relatively small. It is possible that the error would be higher under simultaneous dynamic multiaxial loading conditions. Another potential area of concern was the gap between the tibial tray and the cemented platform. In the short term, bone particles and cement trapped in the gap may decrease the accuracy of the device. In the long term, biological tissue ingrowth into the gap may also affect measurements. Possible solutions are to use a sealant that will prevent ingress of debris and that will seal off the gap to tissue ingrowth without materially affecting the accuracy of the device. The increased dimensions of the tray (4 mm increased thickness) and the stem diameter may necessitate greater than typical bone resections. This could be addressed by careful patient selection and templating. Tibial forces are directly related to the transmission of stresses in the implant. These include contact stresses generated at the bearing surface and subsurface, stresses at the implant–cement–bone interface, and stresses transmitted to underlying bone. Stresses at the bearing surface are a major factor in generating wear and fatigue, which determine the life of the implant.
Stresses at the implant–cement interface are correlated with aseptic loosening, migration, and generation of third-body wear particles. Stresses transmitted to underlying bone result in remodeling, stress shielding, and osteoporosis. Accurate measurement of these forces could yield insight into the stresses generated during common activities of daily living. The tibiofemoral force data can be used to develop biomechanical knee models and in vitro wear tests and to evaluate the effect of improvements in implant design and bearing surfaces, rehabilitation protocols, and orthotics. This data could potentially lead to refinement of surgical techniques and to prosthetic design enhancements that could improve the function, longevity, and quality of life after total knee arthroplasty. While this device was based on a commercially available tray, it can easily be adapted to any similar tray designs available from other manufacturers. This will help to widen the applications for a similar instrumented device. References AAOS Dept of Research and Scientific Affairs, 1994. AAOS department of Research and Scientific Affairs. Aglietti, P., Buzzi, R., De Felice, R., Giron, F., 1999. The Insall–Burstein total knee replacement in osteoarthritis: A 10-year minimum follow-up. Journal of Arthroplasty 14, 560–565. ASTM F1800-97, 2004. Standard test method for cyclic fatigue testing of metal tibial tray component of total knee joint. Buehler, K.O., Venn-Watson, E., D’Lima, D.D., Colwell Jr., C.W., 2000. The press-fit condylar total knee system: 8- to 10-year results with a posterior cruciate-retaining design. Journal of Arthroplasty 15, 698–701. Bugbee, W.D., Ammeen, D.J., Parks, N.L., Engh, G.A., 1998. Four to 10-year results with the anatomic modular total knee. Clinical Orthopaedics, 158–165. Cameron, H.U., Jung, Y.B., 1993. Noncemented, porous ingrowth knee prosthesis: the 3- to 8-year results. Canadian Journal of Surgery 36, 560–564. Diduch, D.R., Insall, J.N., Scott, W.N., Scuderi, G.R., FontRodriguez, D., 1997. Total knee replacement in young, active patients. Long-term follow-up and functional outcome. Journal of Bone and Joint Surgery American Volume 79A, 575–582. D’Lima, D.D., Slamin, J.E., Morris, B.A., Colwell, C.W., 1999. An implantable telemetry system to measure intraarticular tibial forces. Transactions of the 45th Orthopaedic Research Society 24. Ezzet, K.A., Hershey, A.L., D’Lima, D.D., Irby, S.E., Kaufman, K.R., Colwell, C.W., 2001. Patellar tracking in total knee arthroplasty. Inset versus onset design. Journal of Arthroplasty 16, 838–843. Falatyn, S., Lachiewicz, P.F., Wilson, F.C., 1995. Survivorship analysis of cemented total condylar knee arthroplasty. Clinical Orthopaedics 317, 178–184. Gere, J.M., Timoshenko, S.P., 1997. Mechanics of Materials. PWS Publishing Company. Grady-Benson, J.C., Kaufman, K.R., Irby, S.E., Colwell, C.W.J., 1992. The influence of joint line location on tibiofemoral forces after total knee arthroplasty. Transactions of Orthopaedics Research Society 17, 324. Kaufman, K.R., Kovacevic, N., Irby, S.E., Colwell, C.W., 1996. Instrumented implant for measuring tibiofemoral forces. Journal of Biomechanics 29, 667–671.
ARTICLE IN PRESS B. Kirking et al. / Journal of Biomechanics 39 (2006) 1744–1751 Mintz, L., Tsao, A.K., McCrae, C.R., Stulberg, S.D., Wright, T., 1991. The arthroscopic evaluation and characteristics of severe polyethylene wear in total knee arthroplasty. Clinical Orthopaedics 273, 215–222. Morris, B.A., D’Lima, D.D., Slamin, J.E., Kovacevic, N., Arms, S.W., Townsend, C., Colwell Jr., C.W., 2001. e-Knee: evolution of the electronic knee prosthesis: telemetry technology development. Journal of Bone and Joint Surgery American Volume 83-A (Suppl 2), 62–66. Nafei, A., Kristensen, O., Knudsen, H.M., Hvid, I., Jensen, J., 1996. Survivorship analysis of cemented total condylar knee arthroplasty. A long-term follow-up report on 348 cases. Journal of Arthroplasty 11, 7–10. Nagamine, R., White, S.E., McCarthy, D.S., Whiteside, L.A., 1995. Effect of rotational malposition of the femoral component on knee stability kinematics after total knee arthroplasty. Journal of Arthroplasty 10, 265–270. National Hospital Survey, 2004. National Hospital Discharge Survey 1996–1999. Perry, J., Antonelli, D., Ford, W., 1975. Analysis of knee-joint forces during flexed-knee stance. Journal of Bone and Joint Surgery American Volume 57, 961–967. Petersilge, W.J., Oishi, C.S., Kaufman, K.R., Irby, S.E., Colwell Jr., C.W., 1994. The effect of trochlear design on patellofemoral shear
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and compressive forces in total knee arthroplasty. Clinical Orthopaedics 309, 124–130. Singerman, R., Dean, J.C., Pagan, H.D., Goldberg, V.M., 1996. Decreased posterior tibial slope increases strain in the posterior cruciate ligament following total knee arthroplasty. Journal of Arthroplasty 11, 99–103. Singerman, R., Berilla, J., Archdeacon, M., Peyser, A., 1999. In vitro forces in the normal and cruciate-deficient knee during simulated squatting motion. Journal of Biomechanical Engineering 121, 234–242. US Bureau of the Census, 1994. US Bureau of the Census, Current Population Reports, Series P25-1130. Weir, D.J., Moran, C.G., Pinder, I.M., 1996. Kinematic condylar total knee arthroplasty. 14-year survivorship analysis of 208 consecutive cases. Journal of Bone and Joint Surgery British Volume 78, 907–911. Whiteside, L.A., 1994. Cementless total knee replacement. Nine- to 11year results and 10-year survivorship analysis. Clinical Orthopaedics 309, 185–192. Yashar, A.A., D’Lima, D.D., Irby, S.E., Kaufman, K.R., Colwell Jr., C.W., 1997. The effect of mobile bearing knee replacement on three-dimensional kinematics. ORS 43, 262.
Journal of Biomechanics 39 (2006) 1744–1751
Technical note
www.elsevier.com/locate/jbiomech www.JBiomech.com
A multiaxial force-sensing implantable tibial prosthesis Bryan Kirking, Janet Krevolin, Christopher Townsend, Clifford W. Colwell Jr., Darryl D. D’Lima Orthopaedic Research Laboratories, Shiley Center for Orthopaedic Research & Education at Scripps Clinic, CA, USA Accepted 10 May 2005
Abstract Accurate in vivo measurement of tibiofemoral forces is important in total knee arthroplasty. These forces determine polyethylene stresses and cold-flow, stress distribution in the implant, and stress transfer to the underlying implant bone interface. Theoretic estimates of tibiofemoral forces have varied widely depending on the mathematical models used. The six degrees of freedom of motion, complex articular surface topography, changing joint-contact position, intra- and extra-articular ligaments, number of muscles crossing the knee joint, and the presence of the patellofemoral joint contribute to the difficulty in developing reliable models of the knee. A prototype instrumented total knee replacement tibial prosthesis was designed, manufactured, and tested. This prosthesis accurately measured all six components of tibial forces ðR2 40:997Þ. The prosthesis was also instrumented with an internal microtransmitter for wireless data transmission. Remote powering of the sealed implanted electronics was achieved using magnetic coil induction. This device can be used to validate existing models of the knee that estimate these forces or to develop more accurate models. In conjunction with kinematic data, accurate tibiofemoral force data may be used to design more effective knee-testing rigs and wear simulators. Additional uses are intraoperative measurement of forces to determine soft-tissue balancing and to evaluate the effects of rehabilitation, external bracing, and athletic activities, and activities of daily living. r 2005 Elsevier Ltd. All rights reserved. Keywords: Tibiofemoral forces; Telemetry; Knee biomechanics; Total knee arthroplasty; In vivo forces
1. Introduction Over two hundred thousand knee joints are surgically replaced every year (National Hospital Survey, 2004) with the number expected to double by the year 2030 due to the increase in population and the increase in life expectancy (US Bureau of the Census, 1994; AAOS Dept of Research and Scientific Affairs, 1994). Current total knee implant designs have a reasonable survival rate of 10–15 years (Weir et al., 1996; Nafei et al., 1996; Aglietti et al., 1999; Falatyn et al., 1995; Buehler et al., 2000). However, polyethylene wear has become a major factor associated with implant loosening and revision Corresponding author. Suite 140, 11025 N Torrey Pines Road, La Jolla, CA92037. Tel.: +1 858 332 0166; fax: +1 858 332 0140. E-mail address: [email protected] (D.D. D’Lima).
0021-9290/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2005.05.023
surgery (Bugbee et al., 1998; Whiteside, 1994; Cameron and Jung, 1993; Mintz et al., 1991). With the increase in life expectancy and the increase in arthroplasties performed in younger patients, longer survival is essential. Knee wear is dependent on several interrelated parameters that make it difficult to predict the effect of design changes. Clinical studies can be used to evaluate the efficacy of design changes or surgical techniques; however, the need for large cohorts and long-term follow-up preclude their use (Weir et al., 1996; Nafei et al., 1996; Diduch et al., 1997). In vitro and mathematical models are commonly used as cost- and time-effective screening tools before clinical evaluation (Yashar et al., 1997; Ezzet et al., 2001; Petersilge et al., 1994; Grady-Benson et al., 1992; Nagamine et al., 1995; Singerman et al., 1996). The knee, however, is a complex joint that is difficult to model accurately. Although
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significant advances have been made in mathematical modeling, these have yet to be conclusively validated in vivo. Accurate measurement of knee forces can lead to a better understanding of the stresses seen in total knee arthroplasty and will enable more clinically applicable mathematical and in vitro modeling of the knee, which can then be used to develop and evaluate relevant improvements in implant design. Perry et al. measured tibial forces in vitro using a tibial plate connected to an instrumented shaft (Perry et al., 1975). An instrumented tibia that transmitted knee forces through four posts to strain gages in the tibial tray has been reported (Kaufman et al., 1996). We have also reported the results of testing a prototype telemetry tibial replacement system using radiofrequency transmission of tibiofemoral compressive forces and location (D’Lima et al., 1999). This telemetry system was found to accurately transmit the signal through bone, cement, and soft tissues with a range of approximately 3 m. In addition, the system also worked intraoperatively (Morris et al., 2001); however, only axial compression and center of pressure were measured. Shear in the anterior–posterior and mediolateral direction and axial torques (all important components of knee forces) were not measurable. To address this deficiency, a total knee replacement tibial prosthesis was designed that accurately measured all six components of tibial forces.
2. Methods 2.1. Overview The design was based on a commercially available tibial tray, polyethylene insert, and instrumentation. The tibial prosthesis was an assembly of two structural components (Fig. 1). The proximal section (holding the polyethylene insert) was connected to the distal section (cemented in the tibia) through a shrink-fit cylindrical stem. The proximal section was the sensing element and was instrumented with strain gages that measured stem deformation under load. A microprocessor was used to acquire, multiplex, and transmit the strain-gage data through a radiofrequency transmitter and an antenna. The proximal section (Fig. 1a) consisted of the tibial tray and a load-sensing component. A conventional tibial-tray design (NK-II, Centerpulse, Austin, TX) connected to a hollow stem was machined out of titanium alloy as a single piece (Ti6Al4V). The tibial tray contained the standard locking mechanism for holding a standard polyethylene insert. The inner surface of the hollow stem, which also housed the microtransmitter, was instrumented with 12 strain gages. The tibial tray was proximally unconstrained. The distal portion of the strain-gaged stem was inserted via a rigid shrink-fit into the distal section.
Fig. 1. (a) Proximal tray-stem section. (b) Distal Shell. (c) Assembled implant. The stem was shrink-fit into the shell using a temperature differential during assembly. The gap between the proximal tray and the distal shell allowed loads to be transmitted to the upper portion of the stem. Strain gages were bonded to the inner surface of the stem. The microtransmitter and internal power induction were assembled in the stem of the implant.
The distal section (shell, Fig. 1b) was comprised of a flat platform and a hollow shoulder, which was cemented in the tibia. Knee forces were transmitted through the femoral–articular surface, through the polyethylene insert, to the tibial tray of the proximal
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section, and finally transmitted via the shrink-fit interface to the distal shell. Strains measured in the straingaged stem (connected at one end to the shell and at the other end to the unconstrained tray) were used to compute the net forces acting on the device. The tibial tray was unconstrained due to a gap (width ¼ 0.635 mm) between the tibial tray and the shell. This gap was chosen as adequate for measuring mediolateral and anteroposterior moments without closure, while allowing for closure of the gap and for protection of the strain gages due to overload. The inner diameter of the stem was 16 mm, as this was the minimum diameter required to house the prototype microtransmitter. The minimum thickness of the stem wall was estimated to be 2 mm (resultant outer diameter ¼ 20 mm), which can theoretically withstand fatigue due to 10 million cycles of a bending moment of 20 N m (assuming a fatigue stress for Ti4Al6V ¼ 396 MPa). The proximal tray-stem and distal shell were assembled using a thermal shrink-fit between the hollow strain-gaged stem and the shoulder of the shell. Using a coefficient of thermal expansion of 6.39 106/1C for the titanium alloy (Gere and Timoshenko, 1997) and the above nominal inner and outer diameters for the stem, a minimum temperature differential of 6.34 1C/mm of expansion was needed. This yielded a minimum temperature differential of 317 1C for a nominal shrink-fit interference of 0.05 mm. In actuality, a temperature differential of approximately 700 1C was used. The shell was heated in an oven to approximately 500 1C, while the stem was cooled in liquid nitrogen to 195 1C. The shell and stem were assembled and were clamped together until temperature equilibrium was achieved and the shrink-fit was stable. A combination of analytic solutions supported by linear finite-element analysis was used to optimize placement of the strain gages. Three-element stackedrosette 1000-O strain gages (4 rosettes, total 12 gages, Vishay Micro-Measurements, Malvern, PA) were bonded to the inner surface of the stem using transducer-grade epoxy. Each rosette was made of three gages: one oriented along the vertical z-axis, one oriented at 451 to the z-axis and the other at +451 to the z-axis. One rosette each was bonded at anterior, posterior, medial, and lateral surfaces, 16 mm below the bottom of the tibial tray (midway between top of the hollow stem and the most proximal level of the shrink-fit between the tray and the shell). Custom fixtures were used during the procedure to ensure gage location, orientation, and bonding pressure. 2.2. Calibration The device was secured in a mounting fixture that was aligned with the axis of a six degrees of freedom load cell
(AMTI, Watertown, MA), which served as the measurement standard (Fig. 2). Individual components of force were separately applied to the surface of the tray. For each applied force, continuous data were synchronously logged from the measurement standard and the strain gages. The offset between the location of the measurement standard and the surface of the tray was used to transform forces and moment output from the measurement standard to yield forces and torques at the tray surface. One set of loads was used to determine the calibration matrix, while a different set was used to measure error. Calibration loads were selected in the range of 600–+ 4000 N for Fz (vertical load), and 600–+600 N for Fx, and Fy (anteroposterior and mediolateral loads,
Fig. 2. Implant Calibration: The implant was mounted on a custom device (on linear bearings to prevent unintended side loads) in line with a six-component load cell. Loads were applied to the top of the tray and were measured by the load cell. Simultaneously, strains were measured from the 12 strain gages. Multiple linear regressions were used to relate the measured strains with applied loads and to determine the linearity response.
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respectively). Moments were selected in the range of 25–+25 N m. Multiple linear regressions (one per force component) were used to relate the 12 simultaneous strain measurements to each component of force. Additionally, the error between the forces predicted by strain-gage measurement and those recorded by the measurement standard were calculated. To determine the accuracy under dynamic conditions, measurements were made using a sinusoidal loading waveform at varying frequencies up to 2 Hz. 2.3. Telemetry system Voltage output from the twelve 1000-O resistive strain gauges were multiplexed into an instrumentation amplifier. The output of the instrumentation amplifier was digitized by a 12-bit analog-to-digital converter (ADC). Multiple digital samples were digitally filtered by the onboard microprocessor (PIC16f876, Microchip Technology, Chandler, AZ). The microprocessor then serially modulated a 418 MHz frequency shift-keyed radio transmitter (pulse-code modulation) with the digital data. A short radio antenna was attached to a hermetically sealed feed-through to allow for highfrequency transmission out of the implant. A polyethylene cap was added to protect the antenna from damage during the implantation process. Each data packet consisted of a header byte, 12 channels of sensor data (2 bytes each), power-level data (2 bytes), and a checksum (sum of preceding bytes, 2 bytes in size). The header byte was used as a flag for reading the start of the data packet, the checksum byte was used to check the integrity of the data and to test for missing bytes. The pulse-code modulated (PCM) receiver contained a receiving antenna, a matched radiofrequency oscillator, and a level converter to generate RS-232 signals from the incoming PCM data stream. Custom PC-based software was developed to read, display, and store received data. A PC received the RS-232 signal, which was read by custom software and was synchronized with data from other instruments. The microtransmitter was powered using magnetic near-field coupling. An external coil (driven with AC current) generated an AC voltage in the internal coil (Fig. 3). This voltage was then rectified and filtered to provide the DC power required to operate the telemetry system. A function generator was used to provide a 3-V AC signal at 1.6 kHz to a 100-W audio-power amplifier, which amplified the signal and drove the external (primary) coil. The power amplifier delivered 1.0 A of current at 35 V to the external coil. An external coil of 17 cm in diameter was chosen to allow it to be placed around the patient’s leg. The external coil was constructed of 35 turns of 16-gauge magnet wire, with an impedance of 10 O at the 1.6 kHz frequency. The internal (secondary) coil, housed in the stem of the
Fig. 3. (a) Photograph of the implant being assembled with the telemetry system. (b) Close-up view: shows the onboard microprocessor and the internal power induction coil. (c) Photograph of a subject wearing the power induction coil (C) around foam padding about the upper tibia. An amplifier (A) powers the induction coil. The receiving antenna (R) receives the radiofrequency signal which is then recorded on a notebook PC.
implant, consisted of 2000 turns of magnet wire wound on a high-permeability ferrite core. Under static (unloaded conditions) the telemetry system was tested up to 12 h duration at a time. The electronics were also subjected to high temperature ‘‘burn in’’ and shaker tests (10 Hz) to determine failure due to fatigue. To test the integrity of the telemetry system, a fresh-frozen cadaveric knee specimen was thawed and a total knee replacement performed. The instrumented tibial prosthesis was cemented into the tibia. The knee was then mounted on a dynamic quadriceps-driven (closed kinetic chain) knee extension rig and tibial forces measured. Forces were initially measured using the prosthesis in a fully wired configuration and again through the telemetry system. The
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number of checksum errors was used to determine the stability of the telemetry signal during dynamic loading knee motion. 2.4. Structural testing Six components (tibial trays with stems) were mounted on a fixture designed for cantilever testing on Shore Western Fatigue Frames (Shore Western, Monrovia, CA). The components were fatigue tested in air at room temperature in accordance with ASTM standards (ASTM F1800-97, 2004). The lateral half of the tray was rigidly clamped while the unsupported medial half was loaded. A cyclic load of 667.5 N was applied in the form of a sinusoidal waveform at 15 Hz for 10 million cycles. 2.5. Strength of the shrink-fit Four shells were heated in an oven to approximately 500 1C. Four stems were cooled in liquid nitrogen to 195 1C. Each stem-shell pair was assembled and clamped together until temperature equilibrium was achieved and shrink-fit was completed. Each stem-shell assembly was mounted on a MTS Bionix testing machine and then peak resistance to axial torque was measured at 0.131/s. Standard NK-II cruciate-retaining femoral components were also tested against corresponding modular inserts in off-the-shelf tibial trays. An axial load of 2670 N was applied across the femorotibial articulation. The maximum torque resistance at the femorotibial articulation (between the femoral component and polyethylene insert) was measured.
3. Results 3.1. Calibration A highly linear response ðR2 40:997Þ was noted between measured and predicted forces (Fig. 4). After calibration, a dynamic force was applied and strains were measured. A very close agreement between the measured and predicted forces was found. The maximum error, average absolute error, and percent fullscale error in the prediction of each force channel are listed in Table 1. The experimental determination of the calibration matrix effectively minimized errors in locating or aligning the strain gages, accounted for cross talk between various force components, and automatically weighted the contribution of each strain gage to calculate each component of applied load. After static calibration, the dynamic response of the strain gages was compared with that of the external load cell (Fig. 5). To test the value of redundant strain gages, in the event of a failure of a single strain gage, the contributions of each of the 12 gages were individually removed from the
Fig. 4. Calibration results. A highly linear response was seen between externally applied loads and those predicted by the instrumented device ðR2 49:997Þ. (a) Fz (Vertical force (N)). (b) Fx (Anteroposterior Force, (N)). (c) Tz (Torque around the vertical axis, (N m)).
calibration matrix and predicted forces compared with measured forces. The 12-gage system appeared to be very robust to the loss of a single strain gage (Table 2).
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Table 1 Calibration error analysis
AAE MAE R2
Fx
Fy
Fz
Tx
Ty
Tz
0.67 2.54 0.999
1.00 4.73 0.998
3.92 14.80 0.997
0.15 0.65 0.998
0.15 0.85 0.999
0.16 1.12 0.998
AAE ¼ average absolute error (N for Fx, Fy, Fz; N m for Tx, Ty, Tz). MAE ¼ maximum absolute error (N for Fx, Fy, Fz; N m for Tx, Ty, Tz).
Fig. 5. Dynamic Testing: predicted forces closely matched measured forces during dynamic testing.
Table 2 Effect of loss of strain gages on accuracy Loss of:
Any one gage
All 45 gages
All +45 gages
All axial gages
AAE MAE R2
4.18 18.05 0.997
3.33 4.14 0.997
3.36 3.11 0.996
7.88 2.42 0.989
3.2. Telemetry In this configuration, the internal coil consistently generated approximately 40 mW of power, which was
more than adequate to power the strain gages and the telemetry system. Data were collected in both wired and wireless mode and were compared for integrity. Less than 2% of the data was flagged with errors in the
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checksum byte. Of the data that passed the checksum test, a 100% match was obtained between the wired and wireless recordings. 3.3. Structural testing All six of the tested specimens survived 10 million cycles at the maximum applied fatigue load without failure or fracture. The surface of each tray was inspected visually and microscopically for signs of fatigue and cracks but none were found. The maximum torque resistance at the shrink-fit (60–85 N-m) compared very favorably with the maximum torque resistance at the femorotibial articulation (16–24 N-m).
4. Discussion Singerman et al. reported on a similar force transducer design based on two concentric cylinders (Singerman et al., 1999). The inner cylinder was instrumented with strain gages while the outer cylinder was fixed to the bone. That transducer was used to measure tibial forces in normal cadaver knees and was inserted through a 1 cm resection of proximal tibial. Powering and data transmission, however, were through direct wiring. The design reported here accurately measured all six components of load and achieved wireless transmission of data with a net signal integrity of greater than 98%. The prototype implants also passed the specified structural testing. The shrink-fit could easily sustain axial torques transferred across the knee. The testing and calibration was done using uniaxial loading along the different axes. The error under these conditions was relatively small. It is possible that the error would be higher under simultaneous dynamic multiaxial loading conditions. Another potential area of concern was the gap between the tibial tray and the cemented platform. In the short term, bone particles and cement trapped in the gap may decrease the accuracy of the device. In the long term, biological tissue ingrowth into the gap may also affect measurements. Possible solutions are to use a sealant that will prevent ingress of debris and that will seal off the gap to tissue ingrowth without materially affecting the accuracy of the device. The increased dimensions of the tray (4 mm increased thickness) and the stem diameter may necessitate greater than typical bone resections. This could be addressed by careful patient selection and templating. Tibial forces are directly related to the transmission of stresses in the implant. These include contact stresses generated at the bearing surface and subsurface, stresses at the implant–cement–bone interface, and stresses transmitted to underlying bone. Stresses at the bearing surface are a major factor in generating wear and fatigue, which determine the life of the implant.
Stresses at the implant–cement interface are correlated with aseptic loosening, migration, and generation of third-body wear particles. Stresses transmitted to underlying bone result in remodeling, stress shielding, and osteoporosis. Accurate measurement of these forces could yield insight into the stresses generated during common activities of daily living. The tibiofemoral force data can be used to develop biomechanical knee models and in vitro wear tests and to evaluate the effect of improvements in implant design and bearing surfaces, rehabilitation protocols, and orthotics. This data could potentially lead to refinement of surgical techniques and to prosthetic design enhancements that could improve the function, longevity, and quality of life after total knee arthroplasty. While this device was based on a commercially available tray, it can easily be adapted to any similar tray designs available from other manufacturers. This will help to widen the applications for a similar instrumented device. References AAOS Dept of Research and Scientific Affairs, 1994. AAOS department of Research and Scientific Affairs. Aglietti, P., Buzzi, R., De Felice, R., Giron, F., 1999. The Insall–Burstein total knee replacement in osteoarthritis: A 10-year minimum follow-up. Journal of Arthroplasty 14, 560–565. ASTM F1800-97, 2004. Standard test method for cyclic fatigue testing of metal tibial tray component of total knee joint. Buehler, K.O., Venn-Watson, E., D’Lima, D.D., Colwell Jr., C.W., 2000. The press-fit condylar total knee system: 8- to 10-year results with a posterior cruciate-retaining design. Journal of Arthroplasty 15, 698–701. Bugbee, W.D., Ammeen, D.J., Parks, N.L., Engh, G.A., 1998. Four to 10-year results with the anatomic modular total knee. Clinical Orthopaedics, 158–165. Cameron, H.U., Jung, Y.B., 1993. Noncemented, porous ingrowth knee prosthesis: the 3- to 8-year results. Canadian Journal of Surgery 36, 560–564. Diduch, D.R., Insall, J.N., Scott, W.N., Scuderi, G.R., FontRodriguez, D., 1997. Total knee replacement in young, active patients. Long-term follow-up and functional outcome. Journal of Bone and Joint Surgery American Volume 79A, 575–582. D’Lima, D.D., Slamin, J.E., Morris, B.A., Colwell, C.W., 1999. An implantable telemetry system to measure intraarticular tibial forces. Transactions of the 45th Orthopaedic Research Society 24. Ezzet, K.A., Hershey, A.L., D’Lima, D.D., Irby, S.E., Kaufman, K.R., Colwell, C.W., 2001. Patellar tracking in total knee arthroplasty. Inset versus onset design. Journal of Arthroplasty 16, 838–843. Falatyn, S., Lachiewicz, P.F., Wilson, F.C., 1995. Survivorship analysis of cemented total condylar knee arthroplasty. Clinical Orthopaedics 317, 178–184. Gere, J.M., Timoshenko, S.P., 1997. Mechanics of Materials. PWS Publishing Company. Grady-Benson, J.C., Kaufman, K.R., Irby, S.E., Colwell, C.W.J., 1992. The influence of joint line location on tibiofemoral forces after total knee arthroplasty. Transactions of Orthopaedics Research Society 17, 324. Kaufman, K.R., Kovacevic, N., Irby, S.E., Colwell, C.W., 1996. Instrumented implant for measuring tibiofemoral forces. Journal of Biomechanics 29, 667–671.
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