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Force detection, center of pressure tracking, and energy harvesting froma piezoelectric knee implantTo cite this article: Mohsen Safaei et al 2018 Smart Mater. Struct. 27 114007

 

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Force detection, center of pressure tracking,and energy harvesting from a piezoelectricknee implant

Mohsen Safaei1 , R Michael Meneghini2 and Steven R Anton1

1Department of Mechanical Engineering, Tennessee Technological University, Cookeville, TN 38505United States of America2Department of Orthopaedic Surgery, Indiana University School of Medicine, Indianapolis, IN 46202United States of America

E-mail: santon@tntech.edu

Received 13 June 2018, revised 18 July 2018Accepted for publication 1 August 2018Published 25 September 2018

AbstractRecent developments in the field of orthopedic materials and procedures have made the totalknee replacement an option for people who suffer from knee diseases and injuries. One of theongoing debates in this area involves the correlation of postoperative joint functionality tointraoperative alignment. Due to a lack of in vivo data from the knee joint after surgery, theestablishment of a well-quantified alignment method is hindered. In order to obtain informationabout knee function after the operation, the design of a self-powered instrumented knee implantis proposed in this study. The design consists of a total knee replacement bearing equipped withfour piezoelectric transducers distributed in the medial and lateral compartments. Thepiezoelectric transducers are utilized to measure the total axial force applied on the tibial bearingthrough the femoral component of the joint, as well as to track the movement in the center ofpressure (CoP). In addition, the generated voltage from the piezoelectrics can be harvested andstored to power embedded electronics for further signal conditioning and data transmissionpurposes. Initially, finite element analysis is performed on the knee bearing to select the bestlocation of the transducers with regards to sensing the total force and location of the CoP. Aseries of experimental tests are then performed on a fabricated prototype which aim to investigatethe sensing and energy harvesting performance of the device. Piezoelectric force and center ofpressure measurements are compared to actual experimental quantities for twelve differentrelative positions of the femoral component and bearing of the knee implant in order to evaluatethe performance of the sensing system. The output voltage of the piezoelectric transducers ismeasured across a load resistance to determine the optimum extractable power, and then rectifiedand stored in a capacitor to evaluate the realistic energy harvesting ability of the system. Theresults show only a small level of error in sensing the force and the location of the CoP.Additionally, a maximum power of 269.1 μW is achieved with a 175 kΩ optimal resistive load,and a 4.9 V constant voltage is stored in a 3.3 mF capacitor after 3333 loading cycles. Thesensing and energy harvesting results present the promising potential of this system to be used asan integrated self-powered instrumented knee implant.

Keywords: total knee replacement, piezoelectric sensing, energy harvesting, orthopedic implant,biomedical sensors

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Smart Materials and Structures

Smart Mater. Struct. 27 (2018) 114007 (13pp) https://doi.org/10.1088/1361-665X/aad755

0964-1726/18/114007+13$33.00 © 2018 IOP Publishing Ltd Printed in the UK1

1. Introduction

Significant improvements in surgical technologies have madetotal knee replacement (TKR) an option for those who sufferfrom pain or loss of function in the knee. Today, despiterecent developments, only about 80% of patients that undergoTKR are satisfied with their surgery in terms of pain relief andfunction for daily activities [1]. It was shown in 1986 thatseveral factors, such as alignment of extremities and pros-thetic components, and ligament tensioning, can cause pros-thetic loosening after surgery [2]. Recent studies still reportloosening and instability as some of the major reasons forknee failure a few years after the operation [3]. Today, anobjective and well-accepted measure of knee joint stabilitydoes not exist and better clinical assessments are needed inorder to develop such a measure [4]. There are provenmethods for bone alignment and knee implant componentposition, but ligament alignment and tensioning is still mostlyperformed based on the assessment of the surgeon’s tactilefeedback. It has been predicted that about 40% of early kneefailures can be avoided using proper fixation and ligamentbalancing during surgery [5]. Although the importance ofbalance has been proven, the lack of in vivo data has limitedthe establishment of a correlation between intra- and post-operative loading condition, and alignment is currently notwell-quantified [6].

In order to predict the functionality of the knee joint aftersurgery, the use of computational modeling has been sug-gested. However, postoperative interactions between articulargeometries, passive ligamentous constrains, and musclecontribution is not well-defined. The most promoted limita-tions of current simulations to predict the loading condition ofdaily activities are oversimplified passive soft tissue repre-sentations and lack of data from joint balance after surgery[7]. In an effort to obtain postoperative data from kneereplacements, an intelligent remote monitoring system wasproposed by Masyib et al [8]. The system consisted of amaster and slave sensor attached with straps to the top andbottom of the knee joint to measure the relative flexionbetween the femur and tibia during daily activities. Using amodem and GSM network, data can be transmitted to theclinic’s server to evaluate the progression and regression ofthe knee based on the attainable degree of flexion. The datacollected with this instrumentation mostly helps phy-siotherapists track the external functionality of the knee but itcannot provide postoperative in vivo measurements.

D’lima et al as one of the pioneering groups workingon in-vivo knee force and moment measurement, presented aninstrumented tibial tray using 4 load cells powered by anexternal coil around the patient’s knee [9]. The device pre-sented by Heinlein et al [10] was the first attempt to developan in-vivo system capable of six force and moment comp-onent measurements. The device consisted of 6 strain gaugesand a telemetry system located in the stem of a two-piecetibial component with an external coil as the power source,resulting in an overall thickness increase of the tibial trayof 5 mm. The results of tibiofemoral force measurementobtained postoperatively from implanted devices designed by

both D’lima and Heinlein present a good fit with modelingsimulation results for normal function of the knee [9, 10]. Inanother study, Crescini et al [11] presented a new design foran instrumented polyethylene bearing with 3 magnetoresistivesensors and an embedded wireless data transmission circuit.This system was inductively powered by an external coil andwas evaluated under sinusoidal input force to verify themeasurement system. The obtained results showed variabilityin measured data which was speculated to be a result ofnonlinear material behavior and hysteresis effects. The mainlimitation with the abovementioned knee sensory systems isthe external power source requirement of the devices. Thiscan limit the application of the system to laboratories andobviate the device to perform continuously at the patient’sconvenience.

Piezoelectric transducers present the potential to beimplemented in various sensing and energy harvestingapplications [12, 13]. Several wearable and implantablepiezoelectric energy harvesters have been introduced in theliterature in order to provide the required energy for low-power electronics by harvesting energy from human motion[14, 15]. In 2005, Platt et al [16] showed that it is feasible toutilize piezoelectric transducers in TKR as sensors and energyharvesters. More recently, Almouahed et al [17, 18] sug-gested utilizing piezoelectric ceramics in the tibial componentof a total knee replacement to measure the total axial forceapplied to the bearing and to track the location of the center ofpressure (CoP). Center of pressure is defined as the point ofapplication of the sum of the medial and lateral forces (i.e. theforces acting in the medial and lateral compartments) actingbetween the femoral component and the ultra-high molecularweight (UHMW) polyethylene bearing of the knee joint. Forreference, a schematic of a TKR is illustrated in figure 1(a).Although the proposed system can provide self-poweredin vivo measurement during normal function of the joint, theoriginal implant design is modified to implement the sensorysystem. The change in the overall dimension and design ofthe knee implant requires manufacturers and surgeons tomodify their design and surgical techniques, which have beenobtained as a result of several years of experience.

In order to tackle the power source and implant designmodification limitations of existing approaches, a noveldesign of a TKR bearing with embedded piezoelectric trans-ducers is proposed in this study. Implanted piezoelectrictransducers in the UHMW bearing of the TKR can provideself-powered sensing ability directly from the bearing as aresult of the applied force through the femoral component[19]. Furthermore, by encapsulating the piezoelectric trans-ducers inside the existing knee bearing, the original design ofthe implant can be preserved. The conceptual design exploredin this study aims to provide the ability of sensing knee loadsand transmitting data once per day with the help of the powerharvested from daily activities. In addition, the application ofembedded piezoelectrics can be extended to structural healthmonitoring (SHM) on the bearing to monitor for loosening,wear, and fracture in the implant (which will be the focus ofour future work). The design consists of two lead zirconatetitanate (PZT) transducers located in each of the medial and

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Smart Mater. Struct. 27 (2018) 114007 M Safaei et al

lateral compartments of the UHMW insert (total of fourPZTs). First, the arrangement of piezoelectric transducersinside the bearing is varied and the best arrangement isselected using finite element (FE) simulation. Next, the abilityof the employed PZT elements to detect the total applied forceon the bearing and track the movement of the center ofpressure is experimentally investigated through a series oftwelve tests that vary the relative position of the femoralcomponent and UHMW bearing. Finally, the energy har-vesting capability of the design in harvesting power fromnormal knee function is studied. A series of resistor sweeptests are first performed to obtain the maximum theoreticalharvestable power from the device. The practical attainablepower is then measured using a bridge rectifier and capacitorcircuit.

2. Design

Measuring the quantity of total force and tracking the location ofthe center of pressure on the knee bearing surface are theintended sensing functions for the instrumented TKR in thisstudy. Four piezoelectric transducers, located on the bottomsurface of the UHMW bearing, are employed to measure theforce and location quantities. Figure 1(b) shows this instru-mented TKR bearing design with the incorporated piezo-electrics; two piezoelectrics are placed in each compartment ofthe bearing (medial and lateral) to ensure measurement of eachcompartmental force, thus allowing calculation of the totalapplied force and the CoP. In addition to sensing, the piezo-electric transducers are able to harvest energy from the com-pression load acting on the bearing during walking. Theintended functionality of this system is to measure the desiredquantities and transmit to an external computer once a day, thus,the amount of energy harvested and stored during the day shouldbe sufficient to power the sensory system during the sensingoperation (which is likely to take less than one minute).

Due to the importance of axial alignment of the kneejoint [2], the compressive axial force between the femoral andtibial components of the TKR is considered as the main forcecomponent acting on the joint. As a result of the applied forceon the bearing, reaction forces are created on each piezo-electric transducer. By measuring these individual forcequantities, the amount of total axial force on the UHMW

component as well as the location of the CoP can be calcu-lated. Recall, CoP is the average location of contact areas onthe bearing in which the total force is acting. In other words,CoP is the point where the moment of the total force appliedto the bearing is zero. Tracking the movement of the CoPprovides valuable information about medial-lateral and ante-rior-posterior alignment of the joint, as well as the contactmechanism of the femoral component and tibial bearing [20].The location of the CoP for a bearing with two contact points(CPs) located on the medial and lateral compartments of thebearing is shown later in figure 4(a).

3. Finite element simulation

3.1. Simulation setup

Based on the conceptual design shown in figure 1(b), a FEstudy is performed in this section on a knee implant con-sisting of a femoral component and an instrumented kneebearing with four embedded piezoelectric transducers. Theaim of the FE analysis is to investigate the effect of the dif-ferent locations of piezoelectrics (i.e. arrangement of thesensors) inside the bearing on the sensing performance of thedevice. Therefore, several patterns of piezoelectric locationsare chosen for the system and the ability of the piezoelectricelements to measure the total force applied to the bearing andthe location of the CoP is studied. The FE analysis is con-ducted using ANSYS software and the FE model is shown infigure 2(a). The model consists of SOLID187 elements (3D10-node tetrahedral solid element with three translationaldegrees of freedom) for the femoral component and bearing,SOLID227 elements (3D 10-node coupled-field tetrahedralsolid element with five translational, thermal, and electricaldegrees of freedom) for the piezoelectric elements, andCONTA174 and TARGE170 (surface elements with the samegeometric characteristics as the solid elements) for contactsurfaces, and contains 384 231 nodes and 256 392 elements.The element size for PZTs, and bearing and femoral comp-onent are 0.6 mm and 1.2 mm, respectively, with a maximumaspect ratio of 8. The mesh is finely refined on the contactsurfaces and on the corners, and a mesh refinement study isinitially conducted to ensure that the simulation results con-verged. Frictional boundary conditions are applied between

Figure 1. Schematic of (a) total knee replacement (right knee), and (b) UHMW bearing with four embedded piezoelectric transducers.

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Smart Mater. Struct. 27 (2018) 114007 M Safaei et al

the femoral component and bearing as well as between thePZTs and bearing with a friction coefficient of 0.12 [21].

The CAD geometry of the femoral and tibial componentsis obtained by 3D scanning a real knee implant, and thebearing is modified in order to accommodate four piezo-electric transducers. Four 8 mm diameter and 2 mm depthpockets are removed from the bottom surface of the bearing.Piezoelectric disc transducers with a diameter of 8 mm andthickness of 2.5 mm are used. The pockets are designed to beshallower than the piezoelectric transducers in order to ensurefull load transmissibility to the PZTs during the tests and,therefore, maximum sensing capability of the system [19].The material for the bearing is chosen to be PLA (polylacticacid) in order to match the material used in the experiment(see section 4.1). The piezoelectric transducers are 25-layerNCE51 (PZT-5A) PZT stacks (CTS Ceramics DenmarkA/S). The material properties of PLA and the piezoelectrictransducers are listed in table 1. The piezoelectric transducersare polarized in the y-direction.

Two angular parameters, as shown in figure 2(b), aredefined in order to control the location of the piezoelectrictransducers. The locations of PZT1 and PZT2 are specified withangular parameters α1 and α2, respectively. The α1 parameter isallowed to take on values of 50°, 90°, and 130°, and the α2

parameter is allowed to take on values of 50°, 70°, 90°, and 130°in order to investigate twelve different patterns. Note, PZT3 andPZT4 are located in a symmetric arrangement to PZT1 andPZT2, respectively. A realistic knee loading profile obtainedfrom OpenSim (an open source biomechanical simulation soft-ware) is utilized as the axial input load (y-direction infigure 2(a)) of the system [19]. The force profile is shown infigure 3. The knee bearing and femoral component are initiallycenter-aligned based on the geometric centers of the compo-nents, and constrained in the x- and z-directions for all simula-tions. The bottom face of the piezoelectric transducers isrestrained in all directions. The effective force applied to eachPZT and the pressure distribution on the contact surface of thebearing and femoral component are collected from the transientFE simulation with an initial timestep of 0.01 s and 120 steps.The true locations of the contact areas are obtained from thepressure distribution result on the top surface of the bearing, andthe true location of the CoP is calculated from the averagelocation of the contact points. The location of the CoP asmeasured by the four piezoelectric transducers can be calculatedusing the equilibrium of moments as follows:

xx F

F, 1CoP

i i i

T

1

4å= = ( )

zz F

F, 2CoP

i i i

T

1

4å= = ( )

where xCoP and zCoP are the Cartesian coordinates of the CoP, xiand zi are the coordinates of ith piezoelectric transducer, Fi is thereaction force on ith transducer, and FT is the total force appliedon the bearing, which is the summation of the individual forces,as given by

F F. 3Ti

i1

4

å==

( )

On the other hand, the true location of the CoP can becalculated as the average location of the nodal pressuresobtained for all of the nodes located on the top surface ofthe bearing as follows:

Figure 2. (a) FE model of femoral component and instrumented bearing, and (b) angular parameters defined for FE analysis.

Figure 3. Realistic knee load profile obtained from OpenSim.

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Smart Mater. Struct. 27 (2018) 114007 M Safaei et al

xx P

P, 4CoP

n i

Nin

in

T

1tå

= = ( )

zz P

P, 5CoP

n i

Nin

in

T

1tå

= = ( )

where xCoPn and zCoP

n are the true location of the CoP obtainedfrom nodal pressure quantities, xi

n and zin are the coordinates of

ith node, Pin is the nodal pressure of ith node, Nt is the total

number of nodes located on the top surface of the bearing, andPT is the total pressure on the top surface.

3.2. Simulation results

Results of the FE simulations performed for different angles ofα1 and α2 are summarized in table 2. Twelve simulations areaccomplished and the error in the total force and deviation in thelocation of the CoP are calculated using equations (1)–(5). It canbe seen from the results that the error in measured total forcequantities is zero for all simulations, which indicates convergenceof the FE model. On the other hand, the deviation in the locationof the CoP varies with the change in the angular parameters.Based on the results, the arrangement used in Simulation 1 withα1=130° and α2=90° demonstrates the minimum deviationin the measured location of the CoP obtained from the PZTsfrom the true location obtained from the pressure distribution onthe top surface of the bearing. Figure 4(a) represents the pressuredistribution on the bearing obtained from Simulation 1. For moreclarity, the locations of the two CPs on the compartments ofthe bearing and of the CoP are shown in this figure as well.Figure 4(b) shows the exact location of the piezoelectric trans-ducers for this chosen arrangement (Simulation 1). The max-imum total deviation of the location of the CoP for thisarrangement is only 0.32 mm. The chosen arrangement is utilizedin the next section to fabricate a prototype of the device in orderto experimentally investigate the sensing and energy harvestingperformance of the suggested system.

4. Experiment

4.1. Fabrication

A prototype of the instrumented TKR bearing is fabricated via3D printing based on the design chosen from the FE simu-lation, shown in figure 4(b). 3D printing offers the ability toquickly and easily develop and test prototypes of various

designs, therefore, it is selected as the fabrication methodused in this work. Printable UHMW filament is not currentlyavailable on the market, therefore, PLA is chosen. Althoughthe material properties of PLA are not identical to UHMW,the two materials exhibit similar mechanical behavior undercompressive loading, therefore, PLA is deemed a suitablematerial for use in this study [23]. Similar to the design usedin the FE simulation, four pockets are placed on the bottomsurface of the bearing symmetrically to accommodate thepiezoelectric transducers. Pockets shallower than the PZTsguarantee full force transmissibility to the transducers andmaximum sensing and energy harvesting performance. Asdescribed in section 3.1, the piezoelectric transducers are25-layer NCE51 (PZT-5A) PZT stacks. Stack geometries canprovide relatively high coupling properties which are optimalfor sensing applications. Additionally, the matched impe-dance of piezoelectric stacks for optimum energy harvestingis on the order of hundreds of kΩ (as opposed to MΩ forsimilar monolithic transducers), which is appropriate forrealistic energy harvesting circuitry [24].

The material properties of the piezoelectric stacks andPLA material have been previously listed in table 1. Themanufactured knee bearing with incorporated PZTs is shownin figure 5. It can be seen that an arrangement of grooves isincorporated on the bottom face of the bearing for routing ofthe wires soldered to the piezoelectric electrodes and con-nected to the data acquisition circuitry. It is necessary to notethat in the eventual design of the instrumented implant, theexternal leads will be removed and a set of embedded elec-tronics will be incorporated to perform data acquisition,processing, and transmission, as well as power storing.

4.2. Test setup

In order to investigate the performance of the integratedbearing and piezoelectric system, a series of tests is performedon the fabricated prototype. The aim of the experimental testsis to evaluate the ability of the fabricated system to measurethe total axial applied force and the location of the CoP on thebearing, as well as harvest energy during the loading cycle.Figure 6(a) shows the overall experimental setup used to testthe prototype instrumented knee bearing, which allows theload to be applied to the bearing through the femoral comp-onent of the TKR. A closer view of the test setup detailing thefemoral fixture, the femoral component, the knee bearing withembedded PZT transducers, and the bearing fixture is shown

Table 1. Material properties for PLA and piezoelectric materials.

Material Properties PLA Bearing [22] NCE51 (PZT-5A) Piezoelectric

Young’s modulus [GPa] 3.5 52Poisson’s Ratio 0.42 0.35Density [kg m−3] 1240 7850Piezoelectric Constant, d33 [pC N−1] ___ 443×10−12

Piezoelectric Constant, d31 [pC N−1] ___ −180×10−12

Piezoelectric Constant, d15 [pC N−1] ___ 590×10−12

Relative Permittivity, T33 0e e/ ___ 1900

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Smart Mater. Struct. 27 (2018) 114007 M Safaei et al

in figure 6(b). Initially, the relative position of the femoralcomponent and bearing is set to an arbitrary zero position inwhich the femoral component and the bearing are visuallycenter-aligned in both medial-lateral and anterior-posteriordirections.

The realistic knee loading profile described in section 3.1is utilized as the axial input load of the load frame. Thegenerated voltage from the piezoelectrics is collected via twodistinct sets of circuits; one circuit for sensing and two typesof circuits for energy harvesting, and measured using an NI

9215 data acquisition module and a LabVIEW program(National Instrument Corp.). The sensing circuit is designedto measure the output voltage of each piezoelectric indivi-dually in order to sense the quantity of applied force on eachtransducer. The energy harvesting circuits, on the other hand,are designed to extract the maximum power from all thepiezoelectric generators across a load resistance, and to rectifyand store the total generated power from all the piezoelectricsin a single storage device. In practice, in a real instrumentedknee implant, the energy stored via the energy harvesting

Figure 4. (a) Pressure distribution on the bearing obtained from FE analysis, and (b) chosen arrangement of PZT sensors (top view).

Figure 5. Fabricated instrumented knee bearing equipped with four piezoelectric stacks (a) top view, and (b) bottom view.

Table 2. Simulation parameters and results.

Simulation No. Angle α1 Angle α2 Error in Total Force Deviation in x (mm) Deviation in z (mm) Total Deviation (mm)

1 130.00 90.00 0.00% 0.26 0.19 0.322 90.00 90.00 0.00% 0.86 0.44 0.973 70.00 90.00 0.00% 0.89 0.65 1.104 50.00 90.00 0.00% 1.06 1.01 1.465 130.00 50.00 0.00% 0.67 0.79 1.046 90.00 50.00 0.00% 0.85 1.23 1.497 70.00 50.00 0.00% 1.34 0.15 1.358 50.00 50.00 0.00% 1.39 0.01 1.399 130.00 130.00 0.00% 0.76 0.08 0.7610 90.00 130.00 0.00% 0.85 0.91 1.2511 70.00 130.00 0.00% 1.10 2.10 2.3712 50.00 130.00 0.00% 1.09 2.90 3.10

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circuit would be used to power an embedded sensory circuitthat collects, processes, and transmits the data.

4.2.1. Sensing tests. In order to measure the force andlocation of the CoP, the individual voltage signals from eachpiezoelectric transducer must be obtained and processed. Todo so, a load resistance of 100 kΩ is placed in parallel witheach piezoelectric element and the voltage signal is measuredacross the resistor. The circuit diagram utilized for datacollection from each piezoelectric transducer is presented infigure 7. The voltage signals are processed with the help of aMATLAB code to obtain the measured force and location ofthe CoP. The actual location of the CoP on the bearing surfaceis obtained from an image processing code for the recordedcontact areas using a medium-range Prescale pressuresensitive film (Fujifilm Corp.) placed on the interface of thetibial component and the bearing. Twelve tests are performedon the fabricated bearing to investigate the ability of thesensory system to measure the force and track the location ofthe CoP for different contact locations. For the first six tests(Test 1–6), the translational location of the femoralcomponent on the bearing is varied in the medial-lateraldirection, and for the second six tests (Test 7–12), the locationis varied in the anterior-posterior direction using the bearingfixture shown in figure 6(b). The movement directions areshown in figure 1(a). Different translational locations areachieved by moving the bearing along the medial-lateral (x)and anterior-posterior (z) axes in 1.5 mm increments. For Test1 and Test 7, the bearing and femoral component are visuallycenter-aligned, and the relative locations for the remainder ofthe tests are varied with reference to these two initiallocations. The relative location of the femoral component andthe bearing for all the sensing tests is listed in table 3. Note,

due to the curved interface of the femoral component andbearing, it is expected that the increments in CoP movementwill not be equal to the 1.5 mm increments of the kneebearing movement. In order to calculate the force from thecollected voltage signals, the first order governing equation ofa piezoelectric stack connected to a load resistance under low-frequency uniaxial compression loading is employed [25]:

CdV t

dt

V t

Rd

dF t

dt, 6p

eff eff33+ =

( ) ( ) ( ) ( )

where V(t) is the generated voltage, F(t) is the applied forceon the PZT, R is the resistive load connected to the PZT, d eff

33is the effective piezoelectric strain coefficient, given by

d Nd , 7eff33 33= ( )

where N is the number of piezoelectric layers, and d33 is thepiezoelectric strain coefficient. Cp

eff is the effectivecapacitance of the PZT stack, given as

CN A

h, 8p

effT33e

= ( )

where T33e is the dielectric permittivity, A is the cross-sectional

area of the stack, and h is the thickness of each layer. It shouldbe noted that the highest excitation frequency found in theOpenSim knee load profile is several orders of magnitude lessthan the fundamental thickness resonance frequency of thestack, thereby warranting the use of a non-resonant first-ordermodel. The force quantities measured on each piezoelectrictransducer can be used to calculate the total applied force bysimple summation of the four reaction forces, as presented inequation (3). The location of the CoP can then be calculatedusing the moment equilibrium equations expressed inequations (1) and (2).

4.2.2. Energy harvesting tests. The instrumented bearingproposed in this work consists of four piezoelectric transducers,therefore, various writing configurations of the PZTs are possible.The electrical configuration of the PZTs (series versus parallelversus combination of series and parallel) affects the generatedvoltage and optimal resistive load for maximum generatedpower. In piezoelectric energy harvesting systems, the amount ofharvestable power depends on the relative impedance of the load

Figure 6. Experimental compression testing setup including (a) overall setup and (b) close-up view of the instrumented bearing and femoralcomponent installed in the load frame.

Figure 7. Schematic diagram of sensing circuit.

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Smart Mater. Struct. 27 (2018) 114007 M Safaei et al

and the piezoelectric generators, with optimal extracted poweroccurring when the impedance is matched [26]. In order todetermine the ideal electrical configuration, three unique wiringconfigurations are first investigated in this section to determinethe most appropriate configuration suitable to power a low-powerwireless biomedical sensing circuit from the literature in terms ofgenerated voltage level and optimal resistive load. Once the idealconfiguration is selected, the optimum extractable power(theoretical power) from the piezoelectric system is determinedthrough a series of resistor sweep tests. Following this analysis ofthe maximum theoretical harvestable power, a second set ofexperiments is conducted to determine the practical harvestablepower (practical power) through a bridge rectifier andsmoothing/storage capacitor energy harvesting circuit.

First, three combinations of piezoelectric wiring connectionsare considered, and the behavior of each case is investigatedanalytically and numerically to determine the best configuration.It is necessary to note that the analytical solution is conducted foran arbitrary harmonic loading condition to obtain a parametricunderstanding of the ratios of optimum resistor, optimum power,and peak voltage for each configuration to those of a single PZTsystem and for the sake of comparison. Afterward, quantitativeresults are also developed for the actual OpenSim load profileusing a numerical solution. Figure 8 shows the three arrange-ments considered, whereby the PZT transducers are placed inseries, parallel, and a combination of series and parallel(figures 8(a)–(c), respectively).

For a single piezoelectric transducer under a dynamic loadof F(t) and connected in parallel to a resistor R, the governingelectromechanical equation is presented in equation (6). Forharmonic excitation, the peak voltage can be obtained from

equation (6) as

Vj d F

j C, 9

R p

331

w

w=

+( )

where ω is the frequency of excitation and j is the imaginaryunit. Then, the peak power can be written as P ,V

R

2

= and theoptimum resistive load to obtain the maximum power can becalculated from 0.dP

dR= As a result, the optimum resistive load

(Ropt) is

Rj C

1. 10opt

pw= ( )

Based on equations (6), (9), and (10), the governing equation,optimum resistor, maximum power, and peak voltage with theoptimum resistor for all three energy harvesting circuits shown infigure 8 are developed and listed in table 4 in comparison with asingle PZT connected to a resistive load. Although the forceprofile used in this study (OpenSim profile) is not harmonic, dueto the periodic behavior and consistent frequency content of theprofile, the relative ratios of optimum resistor, maximum power,and peak voltage provided in table 4 (presented in ‘Harmonic’columns) are valid for the sake of comparison. On the other hand,substituting the OpenSim force profile and the material propertiesof PZT stacks, as listed in table 1, into equation (6), the optimumresistor, maximum power, and peak generated voltage quantitiesare also numerically calculated and added to table 4 for eachconfiguration (presented in ‘OpenSim’ columns).

A published study on the development of a low-powerwireless circuit designed for knee implants shows a 1.2 V to3.6 V voltage requirement and an equivalent circuit resistanceof about 31 kΩ [27]. Based on the requirements of the

Figure 8. Schematic diagram of considered wiring configurations where PZTs are placed in (a) series, (b) parallel, and (c) combination ofseries and parallel.

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Smart Mater. Struct. 27 (2018) 114007 M Safaei et al

aforementioned circuit, the configuration with all four PZTsconnected in parallel to a resistive load is chosen as the idealarrangement for the energy harvesting tests in this work.

In order to determine the optimum extractable power(theoretical power) from the piezoelectrics, the load resistor isswept from 10 kΩ to 1 MΩ and the voltage across the resistoris measured. Again, the voltage signals are imported into aMATLAB program in order to process and calculate theaverage generated power by the piezoelectrics. The averagepower is calculated as

Pv

R, 11avg

rms2

= ( )

where, vrms is the RMS voltage given by

vT

v t dt1

, 12rms

T

0

2ò= ( ) ( )

in which, T is the time period of voltage signal.While the theoretical power can be obtained using this

technique, the practical harvestable power from the piezoelectricsystem will be less than the theoretical value due to losses in thecircuitry required to condition the harvested energy for use. Inreal-world applications, the generated voltage from the piezo-electric transducers under cyclic loading is in the form of a timevarying signal with a high level of fluctuation, therefore, it needsto be rectified and stored prior to use. Thus, in addition to the

theoretical power circuitry introduced for the resistor sweeptests, a practical energy harvesting circuit consisting of a basicbridge rectifier and smoothing/storage capacitor is also used inthis work. The circuit diagram for this energy harvesting circuitis illustrated in figure 9, where the four piezoelectrics areconnected in parallel to the bridge rectifier (since the mechanicalloading on each transducer is in phase, voltage cancellation isnot of concern). The stored energy in the capacitor is measuredusing the NI DAQ in terms of the capacitor voltage.

4.3. Test results

4.3.1. Sensing test results. Figure 10(a) presents the totalforce profile measured from the piezoelectric transducersalong with the actual applied force to the knee bearingmeasured by the built-in load cell of the load frame for Test 1(recall, twelve tests are conducted, as described previously intable 3). Note, a 20-point moving average filter has beenapplied to the voltage signals to help eliminate measurementnoise. Comparing the two diagrams, it can be seen that themeasured force profile matches with the applied force profilefor higher quantities of force. On the other hand, deviations ofthe measured force from the actual profile at the beginningand end of the test (where lower force amplitudes occur) arenoticeable. The error in these areas can be partially attributedto low signal-to-noise ratio in the collected data in these

Table 3. The relative location of femoral component and bearing for the sensing tests.

Relative location in mm Relative location in mm

Test No. x-direction z-direction Test No. x-direction z-direction

Test 1 0 0 Test 7 0 0Test 2 −1.5 0 Test 8 0 −1.5Test 3 −3 0 Test 9 0 −3Test 4 −4.5 0 Test 10 0 −4.5Test 5 +1.5 0 Test 11 0 +1.5Test 6 +3 0 Test 12 0 +3

Figure 9. Schematic diagram of energy harvesting circuit including rectifier and power storage.

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regions and the corresponding inaccuracies caused by filteringthe data. Moreover, preliminary tests on the piezoelectricstacks show nonlinear behavior in the d33 coefficient, while aconstant coefficient is used for data processing in this study.This error can be reduced or potentially eliminated by testingin a low-noise environment, using more precise dataacquisition equipment and signal processing techniques, andapplying a variable piezoelectric strain coefficient in thecalculation. Similarly, the force profile is obtained for all ofthe other tests and the error in measured peak forces is plottedin figure 10(b) for all twelve tests. Overall, the error in forcesensing is less than 2.5% of the total force applied to thebearing for all twelve tests.

In addition to force amplitudes, the location of the CoP isanalyzed. Figure 11 shows the measured locations of CPs andCoP from the pressure sensitive films for Test 1. Themeasured CoP locations for the six tests with the bearingmoved in the x-direction and the six tests with the bearingmoved in the z-direction are compared to the true CoPlocations recorded by the pressure films and plotted infigures 12(a) and (b), respectively. Comparing the measuredlocation of the CoP from the piezoelectric sensors with theactual coordinates obtained from the pressure sensitive films,the deviation in calculated CoP location from the actuallocation can be obtained. Note, while the knee bearing ismoved along the x- and z-axis with 1.5 mm increments,movement of the true location of the CoP represents uneven

increments due to the complex contact surfaces of the femoralcomponent and the bearing. From the two plots, it can beobserved that the piezoelectric sensors are able to track themovement in the location of the CoP for a wide range ofbearing and femoral component relative movement with asmall deviation of less than 0.5 mm.

4.3.2. Energy harvesting test results. First, the resistor sweeptest is performed on the piezoelectric system. The averagepower harvested from the piezoelectrics is plotted infigure 13(a) along with the average power calculated

Figure 10. (a) Comparison of measured and true total applied force profile for test 1, and (b) error in measured total force for 12 experiments.

Figure 11. Measured contact areas (red areas), centers of contactareas (blue plus signs), and CoP (red dot) from pressure sensitivefilm for Test 1 (all dimensions are in mm).

Table 4. Characteristics of electrical circuits for various wiring configurations of PZTs.

Optimum Resistor Maximum Power Peak Voltage

Configuration Governing equation Harmonic OpenSim Harmonic OpenSim Harmonic OpenSim

Single PZT C dpdV t

dt

V t

R

dF t

dt33+ =( ) ( ) ( ) Ropt 600 kΩ P 0.067 mW Vp 6 V

PZTs in series C dpdV t

dt

V t

R

dF t

dt

433+ =( ) ( ) ( ) 4Ropt 2400 kΩ 4P 0.268 mW 4Vp 24 V

PZTs in parallel C d4 pdV t

dt

V t

R

dF t

dt33+ =( ) ( ) ( ) R

4opt 150 kΩ 4P 0.268 mW Vp 6 V

Combination of series andparallel PZTs

C d2 pdV t

dt

V t

R

dF t

dt

233+ =( ) ( ) ( ) Ropt 600 kΩ 4P 0.268 mW 2Vp 12 V

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analytically using equations (6) and (11). The diagram showsthat the simulation and experimental results are in goodagreement. A maximum extracted power of 269.1 μW isachieved with a 175 kΩ optimal resistive load experimentally,whereas, the simulation shows a maximum average power of268.4 μW for an optimum resistive load of 150 kΩ (aspreviously presented in table 4).

Next, in order to determine a better understanding of theamount of practical harvestable energy, the total voltagesignal obtained from the piezoelectrics using the bridgerectifier and smoothing/storage capacitor is obtained. The testis run for 4000 s, which is equivalent to 3333 gait cycles. It isnecessary to note that an average of about 10 000 steps (gaitcycles) per day is reported for a healthy person [28, 29].However, considering the reduced level of activity in patientsafter knee surgery, a reduced number of steps (gait cycles) perday is expected during the recovery period, therefore, 3333gait cycles can be considered a reasonable representation ofthe total daily number of steps for a patient after undergoing aknee replacement procedure. Figure 13(b) shows the capacitor

voltage diagram versus time. Although the piezoelectrictransducers were continuously charging the capacitor, it canbe seen that the voltage reaches the steady state quantity of4.9 V after about 3000 s. The constant voltage of the capacitorrepresents the maximum voltage generated from the piezo-electric transducers after the bridge rectifier (which includeslosses in the diodes) and accounts for self-discharge in thecapacitor as well as loading from the data acquisition system.It should be noted that the amount of voltage loss in thecircuit can be decreased using more ideal components such aslow-loss diode bridges and thin film batteries or super-capacitors. The total energy stored in the capacitor after 3000cycles is calculated from figure 13(b) as 40 mJ (13.3 μWaverage power). It has been reported that an embedded low-power data processing and transmission system designed fororthopedic implants consumes 45 μW and 3.2 mW in datacollecting and transmission modes, respectively [27]. As aresult, the amount of power stored in the capacitor issufficient for 9 min of sensing and data processing, and 5 sof data transmitting. Considering the target function of the

Figure 12. Comparison of measured locations of CoP by PZTs and true locations from pressure sensitive films for (a) Tests 1–6 when thebearing is moved in x-direction, and (b) Tests 7–12 when the bearing is moved in z-direction.

Figure 13. Energy harvesting results showing (a) average power versus resistive load, and (b) voltage on 3.3 mF storage capacitorversus time.

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instrumented implant developed in this work (harvestingthroughout the day and sensing/data transmitting onceper day), these results show promising potential of embeddedPZTs to supply power to a low power force measuring andtelemetry system for knee implants. Note, the power rectifiedand stored in the capacitor is about 20 times less than themaximum power obtained from the piezoelectric harvestersusing the resistor sweep tests (theoretical power). Therefore,using more advanced electronics with impedance matchingcapability, the energy harvesting efficiency of the system canbe improved and the duty cycle of sensing and energyharvesting system can be reduced.

5. Conclusion

A novel design of an instrumented knee implant with fourembedded piezoelectric transducers for sensing force magnitudeand tracking center of pressure (CoP), as well as energy har-vesting for self-powered operation is proposed in this study. Aduty cycle operation is considered for the device wherebyenergy is harvested from daily activities and then used at the endof the day to power the sensing and data transmission electro-nics. First, the best arrangement of piezoelectric transducers isselected via finite element (FE) analysis with regard to thesensing performance of the device in detecting force magnitudeand CoP location. Next, a 3D printed prototype of the devicewith the chosen sensor configuration is fabricated and employedin a series of experimental tests. Using a load frame, a realisticknee compression load profile is applied on the instrumentedbearing via the femoral component of an actual knee implant.Sensing and energy harvesting tests are conducted individuallywith different electrical circuits. The sensing ability of the deviceis studied by processing the individual generated voltage signalsfrom the piezoelectric transducers measured across simpleload resistors. The total applied force and the location ofthe CoP are measured by the piezoelectrics and compared to thetrue quantities obtained from the load frame and pressure sen-sitive films placed on the top surface of the bearing. Two circuitsare considered for the energy harvesting tests, both of whichplace all four PZTs in parallel. First, the optimum theoreticalharvestable power is determined by a resistor sweep circuitwhere a simple load resistor is placed across the piezoelectrics.Next, a voltage rectifier and storage capacitor circuit is employedto obtain the practical harvestable power from the PZTs. Thesensing results showed an error of less than 2.5% in force sen-sing and a deviation of less than 0.5 mm in tracking the locationof the CoP when the relative positions of the femoral componentand bearing are varied. The resistor sweep tests showed that withan optimum load, an average power of up to 269.1 μW(theoretical power) can be harvested from the piezoelectrictransducers. In addition, the average rectified and stored power(practical power) was found to be 13.3 μW and was shown to besufficient to power a biomedical sensing and data transmissioncircuit from the literature with a low duty cycle. The promisingsensing and energy harvesting results obtained in this studyshow the potential of the instrumented knee implant to beemployed as a self-powered knee sensory system.

Acknowledgments

Research reported in this publication was supported by theNational Institute of Arthritis And Musculoskeletal And SkinDiseases of the National Institutes of Health under AwardNumber R15AR068663. The content is solely the responsi-bility of the authors and does not necessarily represent theofficial views of the National Institutes of Health.

ORCID iDs

Mohsen Safaei https://orcid.org/0000-0002-8312-3000Steven R Anton https://orcid.org/0000-0003-2777-5458

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