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Microindentation Sensor System Based on an Optical Fiber Bragg Grating for the Mechanical Characterization of Articular

Cartilage by Stress-Relaxation

G. Marchi a*, V. Baier a, P. Alberton b,e, P. Foehr c, R. Burgkart c, A. Aszodi b,e, H. Clausen-Schaumannd,e,f, J. Rothsa

aMunich University of Applied Sciences, Photonics Laboratory , Department of Applied Sciences and Mechatronics, Lothstr. 34, Munich, Germany, 80335

b Laboratory of Experimental Surgery and Regenerative Medicine, Clinic for General, Trauma and Reconstructive Surgery, Ludwig Maximilian University, Nussbaumstr. 20, 80336, Munich, Germany

cDepartment of Orthopaedics and Sportsorthopaedics, Klinikum rechts der Isar, Technical University of Munich, Ismaningerstr. 22, Munich, Germany, 81675

dMunich University of Applied Sciences, Nanoanalytics and Biophysics Laboratory , Department of Applied Sciences and Mechatronics, Lothstr. 34, Munich, Germany, 80335

eCenter for Applied Tissue Engineering and Regenerative Medicine – CANTER, Munich University of Applied Sciences, Lothstr. 34, Munich, Germany, 80335

fCenter for Nanoscience (CeNS), Ludwig-Maximilians-Universität, Geschwister-Scholl Platz 1, 80539 Munich, Germany

Abstract. A novel microindentation sensor system, with the potential to be integrated into arthroscopic instrumentation is presented to assess biomechanical properties of the articular cartilage. The piezoelectric driven indentation device was realized by using the tip of an optical fiber with an integrated fiber Bragg grating for force sensing. The performance of the system was demonstrated by ex vivo stepwise indentation experiments performing 15 steps each 20 µm in depth, on explants of bovine femoral condyle cartilage. Parameters describing the relaxation were extracted using a viscoelastic model, which includes two relaxation time constants, one in the order of 0.2 to 3 seconds and the other in the order of 10 to 40 seconds. All model parameters showed increasing values with indentation depth. The plots of the model parameters against the indentation depth suggested that the faster relaxation process was mainly influenced by the superficial zone of the articular cartilage while the middle zone cartilage contributed predominantly to the slower relaxation process. The small indenter size allowed the assessment of the spatial distribution of the mechanical characteristics of the cartilage, which was determined within a frame of 3x5 mm2 on each sample. A stronger dependence of the model parameters along the medial-lateral axis than the posterior-anterior direction of the knee was found. In conclusion the device presented showed the potential to discriminate between the superficial and middle zone of the articular cartilage and to assess with high resolution changes in the constitution of the tissue. Keywords: Cartilage, Indentation, Fiber Bragg grating, Stress-relaxation, Maxwell-Wiechert * E-mail: marchi@hm.edu

1 Introduction

Articular cartilage is a specialized, viscoelastic load-bearing connective tissue of the joint. Structurally, it is characterized by a high degree of anisotropy and is divided into four zones with distinct organization of the extracellular matrix and cells [1-3]. The uppermost superficial zone (10-20% of the total thickness) is mainly composed of collagen fibrils and elongated chondrocytes both oriented parallel to the articular surface. The middle zone lies directly beneath (40-60% of total thickness) where the sparse, rounded chondrocytes are embedded in a dense collagen-proteoglycan matrix. In the deep zone (30% of total thickness), the chondrocyte and proteoglycan density is the highest, the collagen fibers are oriented perpendicular to the surface, and the chondrocytes are typically organized into columns. The final layer is the calcified zone (10% of total thickness), which connects the cartilage to the underlying subchondral bone. Osteoarthritis, a debilitating disorder of the articular cartilage, affects initially the superficial zone, and then progress towards the bone disrupting the other layers [4]. Biomechanical investigations of cartilage (unconfined and confined compression, indentation, tension, and shear) have been performed for several decades in order to gain a better understanding of articular cartilage

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functions, of the progression of osteoarthritis [5], to classify the degeneration grades of osteoarthritis [6] and to characterize implants and substitutive tissues [7-10]. In particular indentation experiments, where the testing probe has much smaller dimensions than the sample, have been used to characterize cartilage in vivo [11-13]. In the field of direct biomechanical testing the typical dimensions of the indentation probes are on the order of 1 mm in diameter [14-19] with few exceptions, where the probes were smaller than 1 mm [11, 20, 21]. The capability to measure the spatial distribution of the mechanical characteristics of articular cartilage is especially important for investigating localized defects or the boundaries between different tissues, e.g. between an autologous implant and the native cartilage that surrounds it [22, 23]. In vitro studies of articular cartilage using atomic force microscopy clearly demonstrated that a high spatial resolution combined with high force sensitivity allows for the early detection of degenerative diseases, such as osteoarthritis [24]. In order to achieve high spatial resolution and a sufficiently high sensitivity, new instruments with smaller indenter size high force sensitivity and the potential for integration in arthroscopic instruments are desirable. Here we report on a novel microindentation system based on optical fiber technology, which has the potential to be integrated into arthroscopic instruments. In the presented configuration, the microindenter is realized by the tip of an optical fiber with 125µm diameter, allowing mechanical characterizations with high spatial resolution. An integrated fiber Bragg grating (FBG) acts as a force sensor [25]. The indentation movement is accomplished by a piezoelectric actuator that pushes the optical fiber into the tissue. The optical fiber transmits both the mechanical load and the sensor signal. Due to the high mechanical stiffness and the good signal transmission characteristics of the optical fiber it is possible to install the actuator at a certain distance from the fiber tip, that is it can be located outside the body and no electrical signals will be needed inside the sensor head. The indentation response of cartilage strongly depends on the shape and size of the indenter employed [19, 26, 27]. In order to characterize the performance of our novel system in vitro stepwise indentation experiments were performed on two samples of bovine condyle cartilage where for each indentation step the tissue relaxation was measured. Data reduction was achieved by describing the tissue relaxation with a Maxwell-Wiechert viscoelastic model and a limited number of model parameters. An analysis of the dependence of the parameter values upon indentation depth and upon the location on the sample is presented as well.

2 Materials and Methods

2.1 Indentation sensor head

A schematic representation of the sensor head used in this study is depicted in Figure 1. A Type I FBG of

4 mm length and 30% reflectivity was inscribed in a photosensitive fiber (GF1B, Nufern, East Granby) using the phase mask technique [28]. After the inscription, the fiber was cleaved at 1 cm from the FBG and spliced with a piece of coreless fiber (FG125LA, Thorlabs Inc., Newton). The coreless fiber was itself cleaved at 3 cm distance from the splice point.

Figure 1: Schematic drawing of the assembly of the sensor head

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The function of the coreless fiber was to reduce interference effects due to Fresnel reflections from the cleaved tip [29]. Reflectivity spectra of the sensor, taken with an FBG-interrogator (I4, FAZ Technology Ltd., Dublin) after various steps of sensor construction, are depicted in Figures 2a-c. Starting with a clean FBG reflectivity spectrum of the pristine fiber (Figure 2a), the FBG spectrum is superimposed by strong interference signals when the sensor fiber was cleaved 1 cm behind the FBG (Figure 2b). These interference signals are diminished by the spliced coreless fiber (Figure 2c). The immersion in polyphosphate buffered saline solution (PBS) used to preserve biological samples improved the signal quality furthermore (Figure 2d). The coating of the sensor fiber was then removed on a length of 7 cm from the tip and the bare fiber was inserted into a glass capillary (150 µm inner diameter, 360 µm outer diameter and 5 cm length) to prevent the fiber from bending during indentation. The sensor fiber was positioned so that the coreless fiber tip protruded 1-1.5 mm out of the glass capillary (Figure 1). In the final step of production, the capillary was glued on an aluminum plate with epoxy glue. The bare optical fiber outside the capillary was also fixed on the plate with Cerastil V336 glue (Cerastil V336, Panacol, Steinbach). The Cerastil glue was chosen because it showed an almost elastic response to stress (see Section 2.4).

2.2 Articular cartilage samples

One knee from 18 months old steers were acquired from a local slaughterhouse. Cylindrical osteochondral plugs of 8 mm diameter were harvested from the medial femoral condyle (Figure 2a),

Figure 2: Reflectivity spectra of the FBG after different steps of sensor head construction: a) Original reflectivity spectrum, b) Reflectivity spectrum after cleaving of the fiber 1 cm from the FBG, c) Reflectivity spectrum after splicing the cleaved fiber with a 4 cm long piece of coreless fiber, d) Reflectivity spectrum after the immersion of the probe tip in PBS solution.

Figure 3: a) Bovine femoral condyle which was used to prepare articular cartilage explants. The coordinates X and Y correspond to the medial-lateral and posterior-anterior direction respectively. The locations where the samples were extracted are indicated in the picture. b) View of articular surface of Sample 1 and c) of Sample 2. The small notches indicated by the arrows mark the direction towards the patellar groove.

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wrapped in PBS (pH=7.4) soaked gauze and stored at -21°C until used. On each sample, the direction of the patellar groove was marked with a small notch (Figure 2b and 2c) to give an orientation reference. Two samples (Sample 1 and Sample 2 in Figure 2a) were measured in the experiment. In both samples, the articular cartilage with a thickness of about 1 mm was left attached to the subchondral bone. Before starting, each osteochondral sample was thawed for at least 20 minutes at room temperature. Afterwards, the bottom of the sample was glued to a glass Petri dish with Braun hystoacril glue (Hystoacril, Braun Melsungen AG, Melsungen) for biological tissues. After the glue had hardened in few minutes, the sample was fully immersed in PBS and after additional 20 minutes, the indentation measurement started

2.3 Experimental setup

A schematic of the complete experimental setup is depicted in Figure 4. The sensor head was fixed on a positioning system that allowed its vertical translation along the fiber axis (z axis). Before starting the automatic measurements, a manual micrometer stage (UMR8.25, Newport, Corporation, Irvine) and a microscope camera were used to approach the sensor head tip approximately 1-2 mm above the sample surface. An additional stepper motor driven translation stage (8MT167-25LS, Standa Ltd., Vilnius) mounted on the manual translation stage allowed the automatic positioning of the sensor tip at 2.5 µm above the sample surface (see section 2.5). The sensor head was fixed on a piezoelectric stage (HERA 625.1, Physik Instrumente GmbH, Karlsruhe) that was mounted on the step motor driven stage. The piezo stage had a resolution of 2 nm, a maximum travel of 500 µm and a maximum speed of 2 mm/s. The piezo stage was used to provide the movement during the indentation procedure. The piezo stage was driven by a piezo controller (E753, Physik Instrumente GmbH, Karlsruhe) which could be programmed for stepwise movements and the acquisition in real time of the position of the piezo stage. Beneath the indenter probe, two motorized stages formed an x-y stage for the automatic positioning of the sample parallel to the table surface. The Petri dish containing the cartilage sample was mounted on a goniometer (GNL10/M, Thorlabs GmbH, Dachau) which, with the help of the microscope camera, allowed the horizontal adjustment of the sample surface perpendicular to the fiber axis. Acquisition of the Bragg wavelengths was achieved with an interrogator of type I4 (FAZ Technology Ltd., Dublin) with a resolution of 100 fm at 1 kHz acquisition rate. The interrogator, the piezo controller and the

Figure 4: Schematic drawing of the setup. The reference coordinate system is also shown to clarify the sample orientation during the measurements

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motorized stages were connected to a desktop computer, which was used to synchronize the movements and to collect the data. The setup was shielded with a plastic cover to avoid temperature changes induced by air draft.

2.4 Experimental characterization of the sensor head

Under the assumption that friction between the sensor fiber and the capillary was negligible, the compressive force acting on the tip of the sensor fiber is given by

𝐹 = Δ𝜆𝐵𝜆0

𝑎2𝜋𝐸𝑓𝑖𝑏

(1−𝑝𝑒𝑓𝑓) ,

(1) where 𝐸𝑓𝑖𝑏 is the Young’s modulus of the GF1B fiber, 𝑝𝑒𝑓𝑓 is the optoelastic coefficient, 𝜆0 is the Bragg wavelength of the FBG when no force was applied, Δ𝜆𝐵 is the wavelength change due to the compressive load on the fiber and 𝑎 is the radius of the fiber (here, a = 62.5 µm). The values of 𝐸𝑓𝑖𝑏 and 𝑝𝑒𝑓𝑓 for a fiber of type GF1B were experimentally determined by Jülich et al. [30, 31] to be 𝐸𝑓𝑖𝑏 = 73.1 ± 1.3 GPa and 𝑝𝑒𝑓𝑓 = 0.211 ± 0.003 . The force sensitivity was experimentally validated by pressing the sensor head on a high-precision scale (Scout Pro, OHAUS, Greifensee). A calibration curve was obtained by plotting the force measured by the sensor head against the reference force measured by the scale (Figure 5a). A linear regression 𝑦 = 𝐴𝑥 + 𝐵 was applied to the experimental data giving a slope of 𝐴 = 0.998 ± 0.004 and an intersection of 𝐵 = −2.5 ± 0.5 mN. The fit slope is very close to unity and the intersection gives an indication that there might be small static friction in the order of 2.5 mN. As the viscoelastic behavior of the sensor head, potentially induced by the glue used for its fabrication, would bias the determination of the viscoelastic behavior of the biological materials, the time response of the sensor head was also investigated. The sensor head was pressed against a rigid metal surface with a fast step of the Z-axis step motor. The size of the step was adjusted so that the experienced forces were in the same range as the ones expected during cartilage indentation. The Bragg wavelengths were recorded as a function of time and were then converted to force values using (Eq. 1) and dividing it by the slope 𝐴. The results of the measurements are summarized in Figure 5b. As can be seen in the inset of Figure 5b, a ringing is visible after the impact of the sensor tip on the metal surface. The ringing extinguished within approximately 100 ms and afterwards the measured force values remained constant and no relaxation was observed.

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2.5 Indentation procedure

The measurement procedure started with an automatic routine that determined the contact point between the fiber indenter and the sample surface. This was performed by lowering the fiber probe with the Z-motor in steps of 2.5 µm and measuring the wavelength difference before and after each step. When a difference of 2 pm, corresponding to a force of 1.5 mN, was measured, the Z-motor made a single 2.5 µm step upwards to detach the probe from the sample. Having the fiber probe in this reference position, no stress was applied to the indenter and the Bragg wavelength was measured for 120 seconds. The wavelength data collected during this period were averaged and the mean values were assumed as the reference Bragg wavelengths 𝜆0 (Eq, 1). From this position, the fiber indenter was driven stepwise into the sample by the piezo stage. At each step, the indenter was moved 20 µm downwards with an average velocity of 270 µm/s and then it remained at its position for 140 seconds (Figure 7, gray dots). The Bragg wavelength and the piezo position data were collected simultaneously for 120 seconds with an acquisition rate of 1 kHz and 546 Hz respectively. Before the next step was initiated, it took additional 20 seconds to transfer the data from the piezo controller to the control software. After 15 steps were completed, reaching a total depth of 300 µm, the Z-motor retracted the indenter and the sample was moved by the X-Y stages to the next position. For each sample indentation, measurements were performed at 15 X-Y positions following a grid pattern, with the positions being 1 mm apart (Figure 9f). At each position, the same measurement cycle was repeated, starting with the determination of the contact point.

2.6 Relaxation model

An analytical model based on a Prony series was used to describe the experimentally observed stress relaxation process. The purpose of the model was to allow data reduction by providing time-dependent relaxation functions with fit parameters that characterize the mechanical properties of articular cartilage. In the literature, Prony series models have been adopted extensively to describe cartilage viscoelastic behavior [15, 18, 19, 32-34]. Because the maximum depth of the indentation was 300 µm only the superficial and middle zones of cartilage are expected to have contributed significantly to the relaxation process. Therefore, in our experiments the bovine articular cartilage was assumed as a bilayered tissue (Figure 6a). In Figure 6b is depicted the generalized Maxwell-Wiechert viscoelastic model used to analyze the relaxation, with three springs of elasticity 𝑘𝑒, 𝑘1, 𝑘2 and two dashpots of viscosity 𝜂1 and 𝜂2. The model adopted had two Maxwell elements (representing the Prony series terms) because of the good agreement with the experimental data achieved (see section 3). In this model the force response 𝐹(𝑡) to an indentation step 𝑧(𝑡) = 𝑧0𝜃(𝑡) (𝜃(𝑡) is the Heaviside step function) is given as

𝐹(𝑡) = 𝑧0 (𝑘𝑒 + 𝑘1𝑒−𝑡 𝜏1⁄ + 𝑘2𝑒−𝑡 𝜏2⁄ ) = 𝐾𝑒 + 𝐾1𝑒−𝑡 𝜏1⁄ + 𝐾2𝑒−𝑡 𝜏2⁄ , (2) where the time constants 𝜏1 and 𝜏2 are given by the expressions,

Figure 6: a) Model assumed for the cartilage tissue during microindentation. b) Two elements Maxwell-Wiechert viscoelastic model used to describe the mechanical behavior of the cartilage under relaxation.

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𝜏1 = 𝜂1/𝑘1, 𝜏2 = 𝜂2/𝑘2 (3) and

𝐾𝑒 = 𝑧0𝑘𝑒, 𝐾1 = 𝑧0𝑘1, 𝐾2 = 𝑧0𝑘2 . (4) The model includes the presence of two relaxation mechanisms, which are characterized by the parameters 𝜏1, 𝐾1 and 𝜏2, 𝐾2. The parameters 𝐾1 and 𝐾2 represent the contributions of each process to the short-term stiffness of the tissue, and 𝐾𝑒 describes its stiffness at equilibrium. Using this linear model each indentation step is treated with a linear approach, but the values of the parameters 𝐾𝑒, 𝐾1, 𝐾2, 𝜏1, 𝜏2 are allowed to change with depth, leading to a non-linear description for the full indentation process.

3 Results and discussion

A typical stepwise indentation relaxation measurement series is shown in Figure 7 (black dots). At the end of the indentation ramp the measured forces reached peak values (peak force), followed by a relaxation process when the indenter remained at a constant depth and ~120 seconds after the step, the measured forces approached almost asymptotic values (equilibrium forces). Other investigators have

reported similar behavior for relaxation measurements on cartilage [17, 35-37]. The peak force as well as the equlibrium force values increased with indentation depth. In addition, the time necessary to reach the equilibrium values (relaxation time) increased with depth. It is important to remark that no discontinuities in the force data were observed. This indicates that no material ruptures or cuts into the cartilage surface caused by the edges of the fiber indenter occurred. Incremental force values, which are the differences between the measured forces and the steady state force values of the preceding indentation step, were calculated. Figure 8 depicts the incremental force values (gray dots) as a function of time elapsed after the beginning of each step movement. In order to reduce the data, step response functions based on the Maxwell-Wiechert model (see Section 2.6, Eq. 2), were fitted to the measured incremental force values (Figure 8, black lines). The fit functions agree remarkably well with the measured force data for all indentation depths. For Sample 1, the depth dependent fit parameters 𝐾𝑒, 𝐾1, 𝐾2, 𝜏1, 𝜏2 from all 15 indentations sites are plotted as a function of indentation depth in Figure 9

Figure 7: Exemplary stepwise indentation relaxation measurement series performed at Position 4 of Sample 1. The force measured from the FBG is represented by the black dots, the piezo position by the gray dots.

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and for Sample 2 in Figure 10. All data recorded at the same indentation depth exhibited only a limited variation. All parameters values increased with indentation depth and were for both samples very similar. The equilibrium stiffness is described by the parameter 𝐾𝑒, which showed for both samples and for all positions an almost linear increase. The values of 𝐾𝑒 reached maximum values at 𝑧 =300 µm between 13 mN and 18 mN for Sample 1 and between 9 mN and 12 mN for Sample 2. The parameter 𝐾1 (Figure 9b and 10b) describes the stiffness related to a fast relaxation mechanism, connected to the fast relaxation constant 𝜏1 (Figure 9d and 10d). For both samples, the profile of 𝐾1 showed a strong increase below 𝑧~80 µm and a moderate increase at deeper indentation depths. At 𝑧 = 300µm the variation of 𝐾1 was larger for Sample 2 (12 mN to 30 mN) than for Sample 1 (17 mN to 25 mN). For both samples the fast relaxation constant 𝜏1 had values of about 𝜏1 = 0.2 s at small indentation depths and it increased almost linearly to values between 𝜏1 = 3.0 s and 𝜏1 = 4.5 s at 300 µm indentation depth. Parameter 𝐾2 (Figure 9c and 10c) represents the stiffness connected with the slow relaxation process. For all measurements we observed small values of 𝐾2 (𝐾2 < 2.5mN) at small indentation depths of 𝑧 ≤ 80µm, followed by a steady increase up to values of 𝐾2 ≅ (15 mN to 25 mN) at 𝑧 = 300µm. The measured time constant 𝜏2 showed a large variability at small indentation depths. As mentioned above, the sensor head was influenced by friction on the order of 𝐹 ≃ 2.5 mN. Therefore, the measurements of 𝜏2, which were connected with small 𝐾2 values, were probably biased by the effect of static friction and were not considered for further evaluation (open gray symbols in Figure 9e and 10e). The non-biased values of 𝜏2 (full black symbols in Figure 9e and 10e) showed a linear increase from 𝜏2 ≃ 15 s at 𝑧 = 100 µm to 𝜏2 ≃ 25 s at 𝑧 = 300 µm. It is noticeable that the changes in the patterns of 𝐾1 (strong increase followed by a moderate increase), 𝐾2 (low values started to increase linearly) and 𝜏2 (high dispersed values changed into a linear pattern) were occurring at almost the same indentation depth of 𝑧 ≃ 80µm, suggesting a correlation between the changes. We speculate that this behavior is associated with the multilayer structure of the cartilage. At small indentation depths (𝑧 ≤ 80µm) we observed high 𝐾1 values up to 15 mN that relaxed with 𝜏1 time constant, and found 𝐾2 values smaller than 6 mN that were associated with 𝜏2 time constant. Therefore, the parameters 𝐾1 and 𝜏1 could be associated to the superficial zone influence which is the first layer interested from indentation. The slow relaxation

Figure 8: Incremental force values (i. e. the difference between the measured force and the steady state force of the preceding step) as function of time elapsed after the beginning of each step (gray) and fits of model-based step response functions (black). The curves correspond to steps at different indentation depths (for example step from 0µm to 20µm depth for lowest curve, step from 180µm to 300µm depth for the upmost curve).

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process, described by the time constant 𝜏2, contributed only at indentation depths larger than 𝑧 ≃ 80µm.

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Hence, the parameters 𝐾2 and 𝜏2 could be mainly associated with the dynamic of the middle zone. The superficial zone of the cartilage tissue is principally constituted from collagen fibrils with few proteoglycan components. In the middle zone, the collagen to proteoglycans ratio is instead lower. This leads to the association of the parameter 𝜏1 with the relaxation time of the superficial collagen fibers and the parameter 𝜏2 with the relaxation time of the deeper proteoglycan-collagen matrix. In the next step, the small-scale spatial variations of the fit parameters were investigated. In Figure 11 the values of all fit parameters from both samples measured at indentation depths of 𝑧 = 300 µm are shown as a function of their X coordinate position. It can be seen that the variation of the parameters was in general much larger in the X-direction (medial-lateral) than in the Y-direction (posterior-anterior). For example, the parameter 𝐾1 measured on Sample 2 showed a maximum change of 3.7 mN along the Y-direction compared to a change of 14 mN in X-direction. Both samples showed approximately similar values although they were well separated in the Y-direction (refer to Figure 3a). This indicated that the mechanical properties of cartilage exhibited more pronounced changes in the X-direction. For both samples, the stiffness parameter 𝐾1 decreased in the positive X-direction and the relaxation times 𝜏1 and 𝜏2 increased (Figure 11b, 11d and 11e). The parameters 𝐾𝑒 and 𝐾2 displayed different trends in both samples (Figures 11a and 11c). For Sample 1, there was a slight increase in positive X-direction whereas for Sample 2 there was a slight decrease. These observations imply that the tissue structure underlying the different relaxation mechanisms is influenced by a variety of factors and a larger sample number is necessary after this pilot study to unravel the single mechanisms responsible for the relaxation

4 Conclusions In this article, a new microindentation system based on a piezo actuator and optical fiber sensor technology is presented. The tip of an optical fiber with a diameter of 125 µm forms a cylindrical indenter and includes a force sensor in the form of an integrated fiber Bragg grating. Owing to its small dimensions and the simplicity of the sensor construction, this sensor design has the potential to be integrated into arthroscopic instrumentation. Because of the high spatial resolution capability of the

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Figure 11: a-e) Values of model parametersat different Y-positions measured at 300 µm depth versus the X- coordinate of the measured position.

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indentation system, it was possible to perform indentation measurements at 15 different locations on the same sample, within a 3 × 5 mm2 area. The novel microindentation system was validated with in vitro by stepwise relaxation measurements on two healthy bovine femur condyle cartilage samples. Both samples were extracted from the same medial condyle at almost the same medial-lateral position (X direction, see Figure 3a) but far apart along the posterior-anterior direction of the knee (Y direction, see Figure 3a). It was found that the relaxation after each step could be described very accurately with a two elements Maxwell-Wiechert model, that included a fast and a slow relaxation processes with relaxation times 𝜏1 and 𝜏2 on the order of 1-5 seconds and 10-40 seconds respectively, and stiffness parameters 𝐾1, 𝐾2 and 𝐾𝑒, the latter being the equilibrium stiffness. It was found that all parameters increase with indentation depth. The dependence of the stiffness parameters 𝐾1 and 𝐾2 on depth showed a strong increase of 𝐾1 and almost negligible values of 𝐾2 at small indentation depths (𝑧 ≤ 80 µm). We therefore assume that this behavior is linked to the specific characteristics of the superficial zone of articular cartilage. The parameter 𝐾1 can be interpreted as a quantity which describes the fast relaxation stiffness characteristics of the collagen rich superficial zone. The slow relaxation would reflect the biomechanical properties of the middle zone. Comparing the parameters measured on each sample, we observed that only the steady state stiffness parameter 𝐾𝑒 showed significantly smaller values for Sample 2 than for Sample 1. All other parameters (𝐾1, 𝐾2, 𝜏1, 𝜏2) were found to be in the same range for both samples. For all parameters a dependence on the medial-lateral direction (X direction) was found, which was particularly pronounced for parameters 𝐾1, 𝜏1, 𝜏2. This indicates that the cartilage structure exhibits a clear spatial variation of the parameters. In conclusion, the presented indentation system has shown the potential to differentiate between the response of the superficial and middle zones of the articular cartilage and to assess changes in the constitution of the tissue with high resolution. To support our conclusions, further investigations on a large number of samples and on extracellular matrix digested specimens are planned in future to support this study. Acknowledgements The research was funded from the Deutsche Forschungsgemeinschaft (DFG) [grants RO 4145/4-1, CS 409/2-1 and AS 150/10-1]. Parts of the study were granted by the German Federal Ministry of Education and Research (BMBF) [grant number 0315577C (QuReGe)] and the Bavarian State Ministry for Science and Education (CANTER Forschungsschwerpunkt). The authors would like to thank Rolf Kuttler of the Photonics Laboratory at the Munich University of Applied Sciences (MUAS) for invaluable IT support, and Professor Erwin Steinhauser from MUAS for his precious suggestions. References [1] R. J. Williams, L. Peterson, and B. Cole, Cartilage repair strategies: Springer, 2007. [2] X. Zhang, D. Blalock, and J. Wang, "Classifications and Definitions of Normal Joints,"

Osteoarthritis-Progress in Basic Research and Treatment (2015), 2015. [3] V. C. Mow, S. Kuei, W. M. Lai, and C. G. Armstrong, "Biphasic creep and stress relaxation of

articular cartilage in compression: theory and experiments," Journal of biomechanical engineering, vol. 102, pp. 73-84, 1980.

[4] K. Pritzker, S. Gay, S. Jimenez, K. Ostergaard, J.-P. Pelletier, P. Revell, D. Salter, and W. Van den Berg, "Osteoarthritis cartilage histopathology: grading and staging," Osteoarthritis and Cartilage, vol. 14, pp. 13-29, 2006.

[5] S. Knecht, B. Vanwanseele, and E. Stüssi, "A review on the mechanical quality of articular cartilage–implications for the diagnosis of osteoarthritis," Clinical biomechanics, vol. 21, pp. 999-1012, 2006.

[6] R. Kleemann, D. Krocker, A. Cedraro, J. Tuischer, and G. Duda, "Altered cartilage mechanics and histology in knee osteoarthritis: relation to clinical assessment (ICRS Grade)," Osteoarthritis and Cartilage, vol. 13, pp. 958-963, 2005.

12

[7] L. Peterson, M. Brittberg, I. Kiviranta, E. L. Åkerlund, and A. Lindahl, "Autologous chondrocyte transplantation biomechanics and long-term durability," The American journal of sports medicine, vol. 30, pp. 2-12, 2002.

[8] A. I. Vasara, M. T. Nieminen, J. S. Jurvelin, L. Peterson, A. Lindahl, and I. Kiviranta, "Indentation stiffness of repair tissue after autologous chondrocyte transplantation," Clinical orthopaedics and related research, vol. 433, pp. 233-242, 2005.

[9] C. Lee, A. Grodzinsky, H. P. Hsu, and M. Spector, "Effects of a cultured autologous chondrocyte‐seeded type II collagen scaffold on the healing of a chondral defect in a canine model," Journal of Orthopaedic Research, vol. 21, pp. 272-281, 2003.

[10] D. Maier, K. Braeun, E. Steinhauser, P. Ueblacker, M. Oberst, P. C. Kreuz, N. Roos, V. Martinek, and A. B. Imhoff, "In vitro analysis of an allogenic scaffold for tissue‐engineered meniscus replacement," Journal of Orthopaedic Research, vol. 25, pp. 1598-1608, 2007.

[11] P. Hansma, H. Yu, D. Schultz, A. Rodriguez, E. A. Yurtsev, J. Orr, S. Tang, J. Miller, J. Wallace, and F. Zok, "The tissue diagnostic instrument," Review of Scientific Instruments, vol. 80, p. 054303, 2009.

[12] G. G. Niederauer, G. M. Niederauer, L. C. Cullen Jr, K. A. Athanasiou, J. B. Thomas, and M. Q. Niederauer, "Correlation of cartilage stiffness to thickness and level of degeneration using a handheld indentation probe," Annals of biomedical engineering, vol. 32, pp. 352-359, 2004.

[13] T. Lyyra, J. Jurvelin, P. Pitkänen, U. Väätäinen, and I. Kiviranta, "Indentation instrument for the measurement of cartilage stiffness under arthroscopic control," Medical engineering & physics, vol. 17, pp. 395-399, 1995.

[14] M. R. DiSilvestro and J.-K. F. Suh, "A cross-validation of the biphasic poroviscoelastic model of articular cartilage in unconfined compression, indentation, and confined compression," Journal of biomechanics, vol. 34, pp. 519-525, 2001.

[15] K. E. Keenan, S. Pal, D. P. Lindsey, T. F. Besier, and G. S. Beaupre, "A viscoelastic constitutive model can accurately represent entire creep indentation tests of human patella cartilage," Journal of applied biomechanics, vol. 29, p. 292, 2013.

[16] F. Richard, M. Villars, and S. Thibaud, "Viscoelastic modeling and quantitative experimental characterization of normal and osteoarthritic human articular cartilage using indentation," Journal of the mechanical behavior of biomedical materials, vol. 24, pp. 41-52, 2013.

[17] J. Mäkelä and R. Korhonen, "Highly nonlinear stress-relaxation response of articular cartilage in indentation: Importance of collagen nonlinearity," Journal of biomechanics, vol. 49, pp. 1734-1741, 2016.

[18] T. Osawa, T. Matsumoto, H. Naito, and M. Tanaka, "Evaluation of viscoelastic property of articular cartilage based on mechanical model considering tissue microstructure," Journal of Biomechanical Science and Engineering, vol. 7, pp. 31-42, 2012.

[19] A. Seifzadeh, D. Oguamanam, N. Trutiak, M. Hurtig, and M. Papini, "Determination of nonlinear fibre-reinforced biphasic poroviscoelastic constitutive parameters of articular cartilage using stress relaxation indentation testing and an optimizing finite element analysis," Computer methods and programs in biomedicine, vol. 107, pp. 315-326, 2012.

[20] X. Li, Y. H. An, Y. D. Wu, Y. C. Song, Y. J. Chao, and C. H. Chien, "Microindentation test for assessing the mechanical properties of cartilaginous tissues," Journal of Biomedical Materials Research Part B: Applied Biomaterials, vol. 80, pp. 25-31, 2007.

[21] S. S. j. F. Lavoie, A. Moreau, C. E. Aubin, E. Quenneville, M. Garon and M.D. Buschmann, "Mapping Biomechanical Properties of Mouse Articular Surfaces Using Indentation: Preliminary Results," in BMeS 2014, San Antonio, 2014.

[22] S. Marlovits, P. Singer, P. Zeller, I. Mandl, J. Haller, and S. Trattnig, "Magnetic resonance observation of cartilage repair tissue (MOCART) for the evaluation of autologous chondrocyte transplantation: determination of interobserver variability and correlation to clinical outcome after 2 years," European journal of radiology, vol. 57, pp. 16-23, 2006.

[23] T. Schubert, S. Anders, E. Neumann, J. Scholmerich, F. Hofstadter, J. Grifka, U. Muller-Ladner, J. Libera, and J. Schedel, "Long-term effects of chondrospheres on cartilage lesions in an autologous chondrocyte implantation model as investigated in the SCID mouse model," International journal of molecular medicine, vol. 23, p. 455, 2009.

13

[24] M. Stolz, R. Gottardi, R. Raiteri, S. Miot, I. Martin, R. Imer, U. Staufer, A. Raducanu, M. Düggelin, and W. Baschong, "Early detection of aging cartilage and osteoarthritis in mice and patient samples using atomic force microscopy," Nature nanotechnology, vol. 4, pp. 186-192, 2009.

[25] A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. Koo, C. Askins, M. Putnam, and E. J. Friebele, "Fiber grating sensors," Journal of lightwave technology, vol. 15, pp. 1442-1463, 1997.

[26] M. L. Oyen, T. A. Shean, D. G. Strange, and M. Galli, "Size effects in indentation of hydrated biological tissues," Journal of Materials Research, vol. 27, pp. 245-255, 2012.

[27] B. Briscoe, K. Sebastian, and M. Adams, "The effect of indenter geometry on the elastic response to indentation," Journal of Physics D: Applied Physics, vol. 27, p. 1156, 1994.

[28] K. Hill, B. Malo, F. Bilodeau, D. Johnson, and J. Albert, "Bragg gratings fabricated in monomode photosensitive," Appl. Phys. Lett, vol. 62, p. 1035, 1978.

[29] G. Marchi, M. Jost, A. Steinkopff, C. Prein, A. Aszodi, H. Clausen-Schaumann, and J. Roths, "All optical indentation probe for endoscopic diagnosis of ostheoarthritis," in SPIE Optical Metrology, 2015, pp. 95291A-95291A-9.

[30] F. Jülich, "Charakterisierung von Faser-Bragg-Gitter Sensorelementen," Master, Physikalische Technik, University of Applied Sciences, Munich, 2009.

[31] F. Jülich, L. Aulbach, A. Wilfert, P. Kratzer, R. Kuttler, and J. Roths, "Gauge factors of fibre Bragg grating strain sensors in different types of optical fibres," Measurement Science and Technology, vol. 24, p. 094007, 2013.

[32] J.-K. Suh and S. Bai, "Finite element formulation of biphasic poroviscoelastic model for articular cartilage," Transactions-American Society of Mechanical Engineers Journal of biomechanical Engineering, vol. 120, pp. 195-201, 1998.

[33] W. Ehlers and B. Markert, "A linear viscoelastic biphasic model for soft tissues based on the theory of porous media," Transactions-American Society of Mechanical Engineers Journal of biomechanical Engineering, vol. 123, pp. 418-424, 2001.

[34] L. Li and W. Herzog, "The role of viscoelasticity of collagen fibers in articular cartilage: theory and numerical formulation," Biorheology, vol. 41, pp. 181-194, 2004.

[35] L. Li, J. Soulhat, M. Buschmann, and A. Shirazi-Adl, "Nonlinear analysis of cartilage in unconfined ramp compression using a fibril reinforced poroelastic model," Clinical Biomechanics, vol. 14, pp. 673-682, 1999.

[36] M. T. Nieminen, J. Töyräs, J. Rieppo, J. M. Hakumäki, J. Silvennoinen, H. J. Helminen, and J. S. Jurvelin, "Quantitative MR microscopy of enzymatically degraded articular cartilage," Magnetic resonance in medicine, vol. 43, pp. 676-681, 2000.

[37] G. Zhang, A. Thambyah, and N. Broom, "A microstructural investigation of the depth-dependent response of cartilage during stress relaxation," in IOP Conference Series: Materials Science and Engineering, 2009, p. 012013.