# Strain Sensors For Knee Prosthesis English Language Essay

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Finite Element Analysis is the most frequently used technique to evaluate the artificial implants, mainly to investigate the influence of load application and identify fragile regions to avoid premature prosthesis failure \cite{Bergmann2008}.

If FEA contributes to extend the life of the orthopedic implant other factors significantly impact on the prosthesis lifetime.

Several different artificial knee implant designs are commercially available but misalignment, leading to knee imbalance, and wearing are still the major reasons for revision.

Forces acting directly on the artificial joint affect the knee balance and induce wear of the bearing surface, which is associated to prosthesis loosening, consequently impacting on the implant lifetime \cite{D'Lima2006a}.

One of the most affected components of the artificial knee implant is the ultra-high-molecular-weight polyethylene (UHMWPE) insert, due to its geometry and the high forces acting upon it \cite{Arami2011}.

Therefore monitoring the strain, associated to knee imbalance and forces acting upon the prosthesis, can help on the development of new articulating components, lead to a better understanding of the artificial knee biomechanics, support improvements on the mathematical models that describes the constitutive model of the materials and the knee behavior, improve prosthesis alignment during surgery and give continuous feedback on the status of the artificial knee implant.

Valuable efforts have been made to design implantable systems for monitoring biomedical implants, either using strain gauges, fiber Bragg gratings or Tekscan sensing systems \cite{Taylor1998c, Kirking2006, Heinlein2007, Mohanty2007}.

Though the systems have their specific advantages many require alterations of the current prosthesis designs or can only be used during surgery not being suitable for implantation.

To overcome these limitations sensors can be fabricated using biocompatible materials, such as polyimide, and embedded into the polyethylene insert without introducing design changes \cite{Crescini2009a, Crescini2011}.

Polymer-based microelectromechanical systems (MEMS) are increasingly being used in biomedical applications \cite{Grayson2004} and, recently, micro-machined polyimide sensors have been used as sensing elements in a broad range of biomedical applications, e.g. deep brain recording and stimulation \cite{Mercanzini2008} and contact lens pressure sensors for glaucoma \cite{Leonardi2009}.

In this chapter we present a versatile MEMS strain-sensing device for the monitoring of loads acting upon an artificial knee implants, at the level of the UHMWPE insert.

The goal of evaluating the strain is to help surgeons on the alignment of prosthesis, which can improve the knee balance and provide a follow-up tool to help monitoring the artificial knee along its lifetime assuring the overall integrity of the prosthetic limb.

Likewise, the strain monitoring, which is associated to loads acting upon the prosthesis, can lead to a better understanding of the artificial knee biomechanics and help in the development of new generation of implants.

Moreover, the continuous monitoring of the strain evolution can be used to track the wear of the UHMWPE insert.

The basic design and working principle of the sensors are presented as well as results of the preliminary bench tests.

The manufacturing process is based on polyimide micro-machining, which allows to adapt the shape and design of the micro-devices.

The sensors are based on polyimide-metal-polyimide sandwich structures that are embedded into the UHMWPE part.

\section{Finite element analysis}

Finite Element Analysis (FEA) is an effective tool to investigate the distribution of the stress and strain in various kinds of engineering structures \cite{Kasi2011}.

In this article, FEA was used to investigate the distribution of strain in an artificial knee implant and assist on the strain gauges placement inside the ultra-high-molecular-weight polyethylene insert (UHMWPE).

The Computer Aided Design (CAD) model was obtained from the manufacturer of an artificial knee, Symbios Orthop\'edie SA (Yverdon-Les-Bains, Switzerland), and the 3D finite element model built into a commercial FEA software, COMSOL Multiphysics (v4.2).

The components of the CAD model are presented in Fig. \ref{fig-cad}, and comprise the femoral component (FC), the UHMWPE insert, the tibial component (TC) and the guide pin. The location of the strain sensors in a cross-sectioned UHMWPE insert is also depicted in Fig. \ref{fig-cad}.

The original CAD description of the prosthesis is overly complicated, therefore simplifications were made to generate a 3D model suitable for computing. The simplified 3D model is sketched in Fig. \ref{fig-design}.

\begin{figure}[htp]

\centering

\includegraphics[width = \linewidth ]{./images/ch4/Slide13.jpg} \\

\caption{Components of the CAD model comprising the femoral component (FC), the UHMWPE insert, the tibial component (TC) and the guide pin, and a UHMWPE insert cross-section depicting the location of the strain sensors.}

\end{figure}

FEA was modeled in the structural mechanics module of COMSOL in stationary mode assuming a linear elastic behavior for all parts.

The fundamental considerations of this approach are to assume a small strain (or stress) and the linear relationship between components stress/strain (i.e. Young's modulus).

The material properties (Young's modulus $E$ and Poisson constant $\nu$) used in the FEA are the following: for the FC and TC (made of a Co-Cr-Mo alloy) $E$~=~115~GPa, $\nu$~=~0.3, and for the UHMWPE $E$~=~0.34~GPa, $\nu$~=~0.4.

To establish boundary conditions for the simulation the following constraints were added to the model.

Between the FC and the UHMWPE insert a contact interface is established.

A surface constraint is defined on the guide pin hole to keep the alignment between the UHMWPE insert and the TC.

Boundary condition uniaxial loads acting on the prosthesis were applied to the upper flat area of the FC, in the z-axis direction, varying from 200~N up to 3100~N, and defined as such to be in accordance with the biomechanical conditions in the human body.

To complete the model, a fixed constraint is defined at the bottom surface of part of the TC to avoid overall implant displacement which can introduce discrepancies in the simulations.

Unstructured progressive triangular meshing algorithm, to form tetrahedral elements, was utilized for meshing the model. The minimum and maximum element size was defined as 0.1~mm and 1~mm, respectively.

The meshed structure consisted of 116933 tetrahedron elements and the convergence criteria for simulations was established by a MUMPS solver.

FEA was used to investigate the distribution of strain inside the UHMWPE insert and to identify regions for placement of strain gauges sensors.

In order to comply with implant regulatory standards the sensors where placed in the xy-plane at 6~mm from the FC/UHMWPE bearing surface (refer to Fig. \ref{fig-cad}).

\begin{figure}[htp]

\centering

\includegraphics[width = 0.6\linewidth ]{./images/ch4/Slide14.jpg} \\

\caption{Simplified 3D CAD model used in the FEA.}

\label{fig-design}

\end{figure}

\section{Results of finite element analysis}

Fig. \ref{fig-feares1} shows the evolution of the x-component strain, in the previously defined xy-plane (at 6~mm from the FC/UHMWPE bearing surface), for different applied loads. Highly positive strain values, associated with tensile strain in the x-axis direction, are visible under the contact points of the FC/UHMWPE bearing surface. Negative strain values, associated with compressive strain in the x-axis direction are also visible on the surroundings of the tensile region.

Moreover, from this investigation we could identify a xz-plane with good strain symmetry at nearly 1/3 of the UHMWPE height (14~mm), therefore these region is suitable for positioning the sensors.

\begin{figure}[htp]

\centering

\includegraphics[width = \linewidth ]{./images/ch4/Slide04.jpg} \\

\caption{Evolution of the x-component strain, in the xy-plane at 6~mm from the FC/UHMWPE bearing surface, for different applied loads.}

\label{fig-feares1}

\end{figure}

At the intersection between the defined xy- and xz-plane a line is defined and used to position and orient the strain sensors.

Fig. \ref{fig-feares2} presents the evolution of the x-component strain at the intersection of xy- and xz-planes, along the UHMWPE width, for different applied loads.

The insert in Fig. \ref{fig-feares2} shows the line of intersection between the xy- and xz-planes where the strain values were taken.

Highly compressive strain is visible in a region that extends roughly for 6~mm, having its maximum nearly 13~mm along the UHMWPE width.

Therefore, the strain sensors were defined to be located in the compressive strain region with their center located at 13~mm along the UHMWPE insert width,

while passive strain sensors were located in regions of zero strain to compensate for overall temperature variations.

\begin{figure}[htp]

\centering

\includegraphics[width = \linewidth ]{./images/ch4/Slide06.jpg} \\

\caption{Evolution of the x-component strain at the line of intersection between the xy- and the xz-planes, along the UHMWPE width, for different applied loads.}

\label{fig-feares2}

\end{figure}

\section{Sensor design, fabrication and packaging}

The strain sensors resistance was defined to be 3.2~k$\Omega$ in order to decrease power consumption and facilitate readout by the Sensimed wireless telemetry chip.

The strain sensors to be embedded into the UHMWPE were built in polyimide-metal-polyimide sandwich structures by dry etching, using standard photolithography manufacturing processes.

Polyimide (PI) is an excellent material for biomedical microdevices due to its chemical and thermal stability, low water uptake and biocompatibility \cite{Richardson1993a}.

Such PI properties are crucial because the sensors are placed under bearing surfaces which are prone to wear and it will not risk patients health.

Furthermore, PI is widely used in MEMS devices, therefore suitable for mass production.

The total thickness of the sensor is about 10~$\mu$m.

A cross-sectional view of the microfabrication process is presented in Fig. \ref{fig-fab}.

\begin{figure}[htp]

\centering

\includegraphics[width = \linewidth ]{./images/ch4/Slide2.jpg}

\caption{Cross section view of the fabrication process.}

\label{fig-fab}

\end{figure}

The detailed microfabrication process comprises the following steps:

A sacrificial layer of tungsten (100~nm) and aluminum (1~$\mu$m) is first deposited through thermal evaporation onto a carrier silicon wafer (Fig. \ref{fig-fab}(a)).

A 5~$\mu$m layer of PI (PI2611, HD Microsystems) is applied on top of the aluminum by spin-coating and cured at 300~$\ensuremath{^\circ}$C for 1~h in nitrogen atmosphere (Fig. \ref{fig-fab}(b)).

A titanium adhesion layer (20~nm) and platinum layer (180~nm) are then sputtered onto the cured polyimide.

The strain gauges are patterned by reactive ion etching in Cl$_{2}$ using a patterned photoresist as an etch mask (Fig. \ref{fig-fab}(c)).

A second layer of PI, 5~$\mu$m in thickness, is spin-coated and likewise cured (Fig. \ref{fig-fab}(d)).

An etch mask of sputtered SiO$_{2}$ (500~nm) is deposited onto the sandwich structure and then patterned by reactive ion etching using a photoresist etch mask.

This oxide layer is then used as hard mask during the subsequent oxygen-plasma etch of the polyimide to define both the structure outline and open contact pads to the strain gauges (Fig. \ref{fig-fab}(e)).

The polyimide devices are detached from the silicon carrier wafer by anodic metal dissolution in a 10~wt\% sodium chloride solution: the substrates are immersed in the salt solution at room temperature with a platinum counter electrode, and a constant positive potential (0.7~V) is applied to the aluminum layer.

The anodic metal dissolution process dissolved the aluminum, leaving the tungsten on the substrate and releasing the polyimide-metal-polyimide structures (Fig. \ref{fig-fab}(f)).

\begin{figure}[htp]

\centering

\includegraphics[width = 0.6\linewidth ]{./images/ch4/Slide18.jpg}

\caption{Polyimide-metal-polyimide micro-machined structure.}

\label{fig-structure}

\end{figure}

The packaging of the device consists of bonding a surface-mount connector (Samtec, Inc.) to the contact pads using a conductive epoxy.

The connector provides the link between the strain gauges and the electronic circuitry.

Despite the fact that the utilization of a connector prevents the usage of this device \textit{in vivo}, the technology versatility allows for design changes without prejudicing the device feasibility.

A fabricated polyimide-metal-polyimide structure is shown in Fig. \ref{fig-structure}.

It consists of four strain gauges, two active gauges positioned (according simulation results) under the contact bearing surfaces, and two passive gauges towards the center of the artificial knee in regions of zero stain (according simulations).

To complete the fully packaged strain-sensing device the sensors are embedded into the UHMWPE insert.

For that, the UHMWPE insert is sectioned in two parts, the polyimide-metal-polyimide sandwich is positioned, and the UHMWPE parts re-joined and sealed using a biocompatible epoxy glue.

A cross-sectioned UHMWPE insert with the strain sensors positioned for final assembly is presented in Fig. \ref{fig-package}A and the complete packaged device is shown in Fig. \ref{fig-package}B.

The packaged device is capable of continuous real-time measurement.

The built strain-sensing devices are versatile, simple, cost effective, and are ready to be integrated with implantable wireless telemetry, which can increase monitoring efficiency outside healthcare facilities.

\begin{figure}[htp]

\centering

\includegraphics[width = \linewidth ]{./images/ch4/Slide17.jpg}

\caption{(A) A cross-sectioned UHMWPE insert with the strain sensors positioned for final assembly and (B) the complete packaged device re-joined and sealed using a biocompatible epoxy glue.}

\label{fig-package}

\end{figure}

\section{Experimental setup and results}

The experimental study was carried out in a mechanical knee simulator (MTS Bionix Servohydraulic Test Systems).

The tests were performed using static and dynamic axial load conditions (perpendicular to the referred xy-plane) similar to those encountered \textit{in vivo}.

The strain-sensing device is attached to the knee simulator and subjected to loads varying from 200~N up to 3100~N.

The applied forces are close-loop controlled by a load cell, attached underneath the strain-sensing device, and connected to the knee simulator controller.

The fully packaged strain-sensing device is connected in a Wheatstone bridge configuration using external standard resistors with similar impedance to those in the polyimide-metal-polyimide sandwich. The bridge is DC powered with 2.5~V.

The output signals are recorded with a National Instruments acquisition board (NI-Daqpad-6015) through a signal conditioning unit (SC-2345) connected to a full-bridge input channel (SCC-SG04).

For displaying and recording the measurements a LabView (National Instruments) interface is configured.

The signal conditioner's gain and span controls for the strain-sensing devices are set to obtain a full-scale electrical output signals.

Results for the identification (fitting) of parameters of the strain-sensing device are presented in Fig. \ref{fig-expres}.

The curve presents both the expected strain (simulated x-component strain) and the measured strain as a functions of applied loads.

The measured strain was calculated from the output voltage of the Wheatstone bridge, according the equation presented in Fig. \ref{fig-wbs}B, being the input voltage 2.5~V and the gauge factor 2.

These results indicate that the measured strain is %within $\pm$10\% from

in accordance with the simulated strain, and that applied forces can be estimated from measured strain.

Therefore, validating the results obtained from the numerical model.

Despite the overall non-linear behavior of the device, the measured data presents a linear region within forces varying from 0~N up to 1500~N.

This is the range of forces exerted upon the knee during normal walking activities.

A linear regression in this range of forces (from 0~N to 1500~N) indicates an average device sensitivity of 2.4~$\mu$V/N (adjusted R-square~=~0.99).

\begin{figure}[htp]

\centering

\includegraphics[width = 0.95\linewidth ]{./images/ch4/Slide8.jpg} \\

\caption{Simulated x-component strain and measured strain as a functions of applied loads.}

\label{fig-expres}

\end{figure}

Tests of the assembled device were also carried out dynamically.

Fig. \ref{fig-expres1} shows a series of slow (Fig. \ref{fig-expres1}A) and fast (Fig. \ref{fig-expres1}B) dynamic loading/unloading and the sensor's output as a function of time.

The influence of the UHMWPE viscoelastic behavior on the measurements can be verified in Fig. \ref{fig-expres1}A, where non-linearities, i.e. creep, can be observed in the measurements.

Creep has an undeniable influence on the repeatability of the measurements affecting device accuracy in long-term measurements.

A good sensor response to fast dynamic loading can be verified in Fig. \ref{fig-expres1}B, thus allowing the sensor to be used for measuring knee forces during walking.

\begin{figure}[htp]

\centering

\includegraphics[width = \linewidth ]{./images/ch4/Slide22.jpg} \\

\label{fig-expres1}

\end{figure}

\section{Viscoelasticity and Creep}

Viscoelasticity is the study of materials with mechanical characteristics of both solid and fluid materials, and as such it implies that its properties are function of time, with the material possessing a "memory" of past events \cite{Brinson_Brinson_2008}.

A Viscoelastic material exhibit time dependent strain, since it has elements of both elasticity and viscosity.

The elasticity (in an ordered solid) is usually the result of the elongation of chemical bonds along the crystallographic planes.

The viscosity, whereas, can be defined as a result of the diffusion of atoms or molecules inside an amorphous material.

These materials can be modeled to determine their stress or strain interactions as well as their temporal dependencies.

These models are employed to predict a material's response under different loading conditions being most common the Maxwell model, the Kelvin-Voigt model, and the Standard Linear Solid (SLS) Model \cite{Jr_Sharpe_2008}.

In Fig. \ref{fig-models} we present these models with it respective constitutive equations.

Viscoelastic behavior

has elastic and viscous components modeled as linear combinations of springs and dashpots, respectively.

Each model differs in the arrangement of an equivalently electrical circuits, where stress is represented by voltage, and the derivative of strain by current.

The elastic modulus of a spring is analogous to a circuit's capacitance (it stores/restores energy) and the viscosity of a dashpot to a circuit's resistance (it dissipates energy).

\begin{figure}[htp]

\centering

\includegraphics[width = \linewidth]{./images/apA/slide1.jpg}

\caption{Most common viscoelastic models employed to predict material's response under different loading conditions \cite{Jr_Sharpe_2008}.}

\label{fig-models}

\end{figure}

The most widely used among these models is the SLS model because it can describe stress relaxation and creep behavior.

In this approach the springs represents deformations due to bending and stretching of intermolecular bonds, and the dashpot represents deformation due to viscous effect.

In the SLS model, the total stress is decomposed into rate dependent stress component in the spring $E_{2}$ and the dashpot $\eta$, and rate independent equilibrium stress in the spring $E_{1}$. The governing equation for the total stress in the SLS can be solved to define the stress-strain relationship at constant strain rate where creep and stress relaxation can be modeled. Despite this approach provides a model for the behavior of viscoelastic material its application to dynamic systems is cumbersome and analytical relationships are preferred.

For the case of many plastics the creep and stress relaxation behavior is subject to an empirical approach employing the following equation:

\begin{eqnarray}

\varepsilon (t) = & \varepsilon _{0} + m * t^{n}

\label{eqn:empirical}

\end{eqnarray}

where $\varepsilon _{0}$ is the instantaneous strain and, $m$ and $n$ are material constants which depends on the applied stress.

In our experiments with the strain gauge sensors embedded in the UHMWPE, when applying a static force, a drift of the recorded values is observed over time and a similar behavior appears when releasing the force, affecting the measurements.

In Fig. \ref{fig-creeping} and \ref{fig-relaxing} we present the response over time when applying and releasing forces on the implant, respectively, showing the necessity to model these phenomenons in order to gain insight on the behavior of the strain sensors inside the UHMWPE insert.

\begin{figure}[htp]

\centering

\includegraphics[width = 0.8\linewidth]{./images/apA/creeping.png}

\caption{Sensor's response over time for several constant forces applied.}

\label{fig-creeping}

\end{figure}

\begin{figure}[htp]

\centering

\includegraphics[width = 0.8\linewidth]{./images/apA/relaxing.png}

\caption{Sensor's response over time when the applied constant forces are released.}

\label{fig-relaxing}

\end{figure}

A first attempt to model this creep and relaxation, is to assume that the sensor response and the creep or relaxation can be separated in two phases, the immediate sensor response due to the application or the release of the force, and the creep or stress relaxation.

The goal would be to fit the creep and stress relaxation part for each force and therefore being able to build a model to remove it.

The point that identifies the transition between the two phases is selected manually and a step function for the force is assumed to be the input.

This procedure must be followed because the MTS Load frame is not able to generate this kind of ideal patterns.

The hydraulic actuator is relatively slow and the PID controller is a trade-off between decreasing the time response of the output and avoiding side effects such as overshoots of the signal or loss of stability.

For modeling this creep and stress relaxation, the curves presented in Fig. \ref{fig-creeping} and \ref{fig-relaxing} are fitted with a power function ($f(x)=a*x^{b}$), according recent work by H. Liu \textit{et. al.} \cite{Liu_Polak_Penlidis_2008}, therefore following a traditional empirical approach.

Using the power function model the evolution of the parameters "a" and "b" as a function of the force is shown for creep and stress relaxation in Fig. \ref{fig-evol}.

\begin{figure}[htp]

\centering

\includegraphics[width = \linewidth]{./images/apA/Slide2.jpg}

\caption{Evolution of the fitting parameters "a" and "b", for both creep and stress relaxation, as a function of the force.}

\label{fig-evol}

\end{figure}

The model presented for fitting the creep and stress relaxation signals provides an initial approach towards understanding creep and stress relaxation on the knee implants.

It is difficult to build an accurate and reliable model using this approach, at least with the experimental set-up used.

The ideal goal would be to compensate on-line the effect of the creep and relaxation.

However, the main issue for performing an on-line compensation is that the model for creep and stress relaxation is self-dependent, meaning it is dependent on the applied force which has to be measured.

Moreover, creep and stress relaxation are dependent on the history of the forces which were previously applied on the material.

Furthermore, if a small error is computed using the model it will be propagated over time making the predictions unreliable.

The future work is to explore more complex models to model creep and stress relaxation.

These models should be then tested on new recordings to be validate as well as the setup needs to be modified.

To analyze the influence of the creep on the measurements the experimental creep curve was extracted from the data.

The creep is plotted versus the logarithm of time.

The experimental curves indicates the creep is dependent on the applied load as well as on the time.

When analyzing Fig. \ref{fig-creep} we are able to determine the proposed sensor is accurate for measuring events happening within a 1s time window, with errors below 8\% the applied load.

For measurements lasting 10s and 100s the creep introduces substantial drift on the measurement, respectively, 38\% and 85\% the applied load.

However, in slow pace walking a single load cycle is within a 1s time window, therefore in gait studies it is important to monitor events happening bellow a 0.1s time window, region where errors are below 3\%.

The developed device has thus the potential to measure \textit{in vivo} activity and help to improve TKA surgery and postoperative follow-up.

In TKA surgery the device can be used to assist in the ligament balance, which is currently only qualitatively assessed, and is crucial for the stability and lifetime of implants.

During the postoperative physical therapy the device can provide information regarding the artificial knee implant function and help to improve overall rehabilitation and treatment of patients with total knee implants.

\begin{figure}[htp]

\centering

\includegraphics[width = \linewidth ]{./images/ch4/creepn.png} \\

\caption{Experimental creep curves for different loading levels versus the logarithm of time.}

\label{fig-creep}

\end{figure}

\section{Discussion}

In this chapter, a polymer-based strain-sensing device was developed for monitoring an artificial knee implant.

The experimental data demonstrates the sensor is capable of measuring the strain associated to the total axial forces exerted on the UHMWPE insert in the range of approximately 4 times body weight with a good sensitivity and accuracy for events happening within 1s time window.

This device has been designed to monitor the total load and simple alterations on the strain-sensor design can allow the measurements of forces in each individual compartment of the UHMWPE insert, allowing for the monitoring of instantaneous artificial knee balance.

Other alterations can also be made in the design to allow the measurement of other force components (e.g. momentum) and temperature monitoring, to investigate the effect of different activities, such as walking and cycling, on the implant wear rate.

Improvements on the sensors design and packaging, as well as increasing the number of strain-sensors on the device can allow the mapping of strain in other regions of interest in the UHMWPE.

Although, \textit{in vivo} measurements of the knee joint forces are broadly available, very little is know on the evolution of artificial knee implants after TKA and the aging of such prosthesis, hence the proposed device will allow studies of biomechanics on the prosthetic knee and improve implant design.

The results demonstrated that the proposed strain-sensor represents a promising new system for \textit{in vivo} load monitoring of medical implants with the advantage that this device can be introduced into the surgery procedure with minimal disruption to usual protocols.

Also we expect this sensor could be used to investigate the creep deformation on the UHMWPE.

Creep is a property of viscoelastic materials \cite{Phan2008} which introduces non-linearities on the system and are a cause for errors in long-term measurements.

The understanding of the creep behavior of the UHMWPE can also help on accurate quantify the prosthesis wear \cite{El-Domiaty2002}.

The strain-sensing device is simple to package and represents a cost effective solution since it does not imply changes on current artificial knee implant designs.

Future applications include the ability to validate mathematical models that describes the knee biomechanics, the capability to study the effect of postoperative physical therapy and evaluate the knee balance to improve overall rehabilitation.

Moreover, it can be customized for different models of prosthesis combined with various materials, therefore the proposed autonomous sensor can lead to new redesigns regarding the function of knee implants

and the treatment of patients with total knee implants.

Additionally, the device could be integrated with low-power wireless telemetry, which will allow for long-term measurements \textit{in vivo}.

\section{Conclusion}

We demonstrated a polyimide-based MEMS strain-sensing device for monitoring knee implants. Throughout the design process, FEA modeling results were used to optimize device placement inside an artificial knee component (UHMWPE). The PI-based technology is well suited for biomedical applications and can provide a significant cost advantage since it does not imply changes on current prosthesis.

The device was subjected to tests in a mechanical knee simulator using static and dynamic axial load conditions similar to those encountered \textit{in vivo}.

Results indicated the measured strain is in accordance with simulated strain and that the applied forces can be estimated from measured strain.

The experimental data demonstrates the sensor is capable of measuring the strain associated to the total axial forces in the range of approximately 4 times body weight with a good sensitivity and accuracy for events happening within a 1~s time window.

Compared with the current available technology either using strain gauges, fiber Bragg gratings or Tekscan sensing systems \cite{Taylor1998c, Kirking2006, Heinlein2007, Mohanty2007} or even most recent solutions, such as the one provide by OrthoSensor (which followed a similar approach though providing a disposable instrument) the system developed in this thesis provides a suitable solution for implantation while the available solutions can only be used during surgery.

This advantage comes at the cost of having sensors embedded on the UHMWPE insert which is a viscoelastic material and therefore are prone to creep and stress relaxation.

In the current application, where high forces can be exerted, the UHMWPE may be deformed beyond the limit where linear viscoelasticity is accurate, and traditional plasticity models are not accurate since the applied loads are not monotonic.

To overcome these limitations it is necessary to developed an advanced thermo-mechanical constitutive model for UHWMPE where the developed sensors can provide valuable information on the behavior of the material.

Afterwards, the constitutive model could be used to perform real-time estimation and compensation of creep and stress relaxation.

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