(cite) at the meso-scale: device validation

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COMPRESSION INSTRUMENT FOR TISSUE EXPERIMENTS (CITE) AT THE MESO-SCALE: DEVICE VALIDATION Douglas W. Evans1,2,3, Padma Rajagopalan4,2, Raffaella DeVita5,2, Jessica L. Sparks1,2,3 1. Department of Biomedical Engineering, Wake Forest University School of Medicine, NC 2. Virginia Tech – Wake Forest University School of Biomedical Engineering and Sciences, NC 3. Virginia Tech – Wake Forest Center for Injury Biomechanics, NC 4. Department of Chemical Engineering, Virginia Polytechnic Institute and State University, VA 5. Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, VA

ABSTRACT Liver sinusoidal endothelial cells (LSECs) are the primary site of numerous transport and exchange processes essential for liver function. LSECs rest on a sparse extracellular matrix layer housed in the space of Disse, a 0.5-1μm gap separating LSECs from hepatocytes. To develop bioengineered liver tissue constructs, it is important to understand the mechanical interactions among LSECs, hepatocytes, and the extracellular matrix in the space of Disse. Currently the mechanical properties of space of Disse matrix are not well understood. The objective of this study was to develop and validate a device for performing mechanical tests at the meso-scale (100nm-100μm), to enable novel matrix characterization within the space of Disse. The device utilizes a glass micro-spherical indentor attached to a cantilever made from a fiber optic cable. The sample’s position is accurately controlled by a custom 3-axis translation table used to bring the specimen in contact with the indentor and deform the cantilever. A position detector monitors the location of a laser passing through the cantilever and allows for the calculation of subsequent tissue deformation. The design allows micro-newton and nano-newton stress-strain tissue behavior to be quantified. To validate the device’s precision and accuracy, 11 samples of silicon rubber in two formulations were tested to experimentally confirm their Young’s moduli. Prior macroscopic unconfined compression tests determined the formulations of EcoFlex030 (n=6) and EcoFlex010 (n=5) to posses Young’s moduli of 92.67±6.22 and 43.10±3.29 kPa respectively. Optical measurements taken utilizing CITE’s position control and fiber optic cantilever found the moduli to be 106.4 kPa and 47.82 kPa. Keywords: Space of Disse, Spherical Indentation, Hertz Contact, Liver Biomechanics

INTRODUCTION Liver sinusoidal endothelial cells (LSECs) form the primary boundary between the blood and the hepatocytes. This location is vital for an organ responsible for removing toxins and secreting proteins to the blood. LSECs rest on a sparse extracellular matrix layer housed in the space of Disse, a 0.5-1μm gap separating LSECs from hepatocytes. The ECM in the space of Disse is primarily composed of fibronectin which acts to bind the hepatocytes and LSECs to bundles of collagen type I arranged as support cables for the interstitium [1]. Currently the mechanical properties of the space of Disse are not well understood and knowledge in this area can be used to create realistic bioengineered liver constructs. Indentation testing can be used to quantify biologic structures on the scale of the space of Disse. Nanoindentation utilizing atomic force microscopy has been used to determine the local mechanical properties of very small biologic samples such as individual cells and bacteria [2]. AFM can create

force-displacement curves which can be analyzed to provide information such as elasticity, adhesion, hardness, and friction. The specimen is contacted with a specifically designed tip usually with a radius of curvature of 50-100nm attached to a microscopic cantilever with experimentally determined stiffness. The vertical displacement of the cantilever is tracked by a laser and results in an instrument that is capable of detecting applied forces as small as 10pN. The ability to probe sub-cellular structures with accuracy makes AFM a desirable tool for many biomedical applications; however at the same time it poses problems for probing the space of Disse. Unlike a cell on which specific places can be targeted for indentation, the space of Disse is mostly an open void. The mechanical properties of the area arise from the amount and orientation of the ECM creating the void as well as the fluid contained within the space. Therefore to characterize the region, a larger indenter (10-100μm) is necessary to capture the bulk properties of the void. The objective of this study was to develop and validate a device for performing mechanical tests at the meso-scale (100nm-100μm). The design of the Compression Instrument for Tissue Experiments at the meso-scale (CITE) was inspired by a previously developed embryonic tissue testing apparatus and includes similar design features that have been implemented to modify commercial AFMs for cell biology [3] [4]. The device utilizes a glass micro-spherical indentor attached to a cantilever made from a fiber optic cable to enable novel matrix characterization within the space of Disse. CITE Components CITE functions by accurately controlling sample position and monitoring subsequent deformation of a fiber optic cantilever to obtain force-displacement data. Sample position is controled using a custom 3axis translation table (USEuro-Tek) with 102nm resolution. The table is used to move a sample upwards into contact with a glass microsphere (Cosphereic) indenter with diameter 20μm to 59μm. The indenter is glued to a segment of fiber optic cable with experimentally determined stiffness acting as a cantilever. The fiber segment is fixed to a laser diode module (Newport) which transmits light at 830nm through the cable. A PSM-10 position sensing module (On-Trak) is positioned in front of the free tip of the fiber and monitors the subsequent tissue deformation. Position data is aquired using a USB-6009 14-bit DAQ (National Instruments) that samples the analog signals. An AxioCam MRc attached to a LD-Plan Neofluar 40x objective (Zeiss) is positioned horizontally to image the indentation. This work aims to validate our technique of using a microsphere attached to a fiber optic cable to perform indentation tests and obtain accurate material properties at the meso-scale relevant for Space of Disse characterization. In this current study, tissue deformation data collection was limited to AxioCam image analysis. Fiber-Optic Stiffness Experiments In order to determine the force associated with each indention the stiffness of the fiber optic cantilever first must be known. Fiber optic cable segments (Thor Labs AFS-105/125) are first stripped of their protective plastic coating using a pair of fiber strippers. Segment stiffness was determined experimentally for individual cables by incrementally hanging wire weights (4.23-10.01mg) at various positions on the cable and monitoring subsequent bending. The cable stiffness was calculated as the slope of the linear regression for the force vs displacement data. Segment length can be altered to achieve desired cable stiffness. For the cable used in all 11 silicone rubber indentations, cable stiffness was determined experimentally by hanging 9 different weights at the location of the glued microsphere. The first step was to properly

orient the cable for the indentation tests. This was achieved by angling the laser module so that the tip of the cable would not re-contact the test specimen due to the cable’s deflection under its own weight. A mounted camera was then used to take two pictures of the cable under only a gravitational load. An additional two pictures were taken documenting the cable position for each weight. Vertical displacement of the weight was measured using ImageJ from a horizontal reference marker located in each picture. Care was taken to perform the stiffness experiment and indentation tests in this exact position so that cable stiffness was not also dependent on initial laser angle. Silicone Rubber Two formulations of silicone rubber, EcoFlex030 and EcoFlex010 (Smooth-On Inc.), were tested to develop experimental technique and validate the use of CITE for indentation testing at the meso scale. Prior to testing with the CITE device, the material was tested using a Bose-Electroforce mechanical testing system. Samples were cylindrical in shape with a nominal diameter of 36 mm and height of 24 mm. Unconfined compression experiments gathering engineering stress and strain determined EcoFlex030 to have a Young’s modulus of 92.67±6.22 kPa and EcoFlex010 a modulus of 43.10±3.29 kPa. Indentation Tests Using CITE Acquiring force-displacement data began with focusing the AxioCam and Zeiss objective on the glass microsphere indenter attached to the cantilever. The material sample tested was positioned on the translation table and brought into the plane of focus below the indenter. The sample was raised by 1.02μm increments (10 translation table encoder counts) until contact was first made between the microsphere and the surface of the material. At this position an image was taken with the AxioCam. The translation table was then raised by 51.4μm (500 encoder counts) where another image was obtained. The vertical camera position was then adjusted to center the image and another picture was captured. The process of incrementally moving the sample 51.4μm and gathering data was repeated until approximately half of the indenter had penetrated the sample. The process was then reversed lowering the table 51.4μm until the indentor lost contact with the sample. Hertz Model The indentation test provides force-displacment data which then must be translated into meaningful material properties using a mathmatical model. The Hertz model is the basis of contact mechanics and is commonly used for describing the behavior of indentation tests. The solution for the Hertz model for a rigid sphere contacting an elastic half plane is:[5] 4ER 2 δ 2 F= 3 (1 − υ 2 ) 1

3

(1) (2)

where F is the force of indention, E is Young’s modulus, R is the radius of the indentor, δ is the depth of indentation, and ν is Poisson’s ratio. The Hertz model is valid under the assumption that the material is isotropic and linear elastic and is techincally limited to the range α/R < 0.1. This theoretical limit is frequently violated and has been shown by Yoffe [6] to introduce an error based on Poisson’s ratio, where a material with ν =.4, will have an error in E of 1.4% at α/R ≈ 0.5 and 1.0% at α/R ≈ 0.8.

The information gathered from the indentation tests provides displacement information of the sample Z1 and the displacement of the fiber optic cable Z2 which are related to the indentation depth by: Z 2 = Z1 − δ

(3)

F = K Z2

(4)

The force of indentation is determined by:

where K is the experimentally determined stiffness for the cantilever. Combining equations 1-3 leads to the expression for determining Young’s modulus based on the displacements gathered from the indentation experiments:

(5)

RESULTS Fiber-Optic Stiffness Experiments The effective stiffness of each fiber optic cantilever depends on the location of the microsphere indenter from the fixed end of cable. This distance was defined as the effective length, Leff. This length is crucial to the results of each indentation test, as a cable too stiff will lead to insufficent bending to determine force and a cable too compliant will lead to insufficent indentation to determine a Young’s modulus. To properly place the indentor, the stiffness of a stripped AFS-105/125 cable was characterized as a function of Leff. Figure 1a shows the results from hanging weights (4.23-10.01 mg) at different positions and the least-squares linear regression line for each position (0.9653 ≤ R2 ≤ 0.9987). Figure 1b plots the stiffness obtained from the slope of each regression line against Leff and the least squares regression power curve that fits the data (R2=0.9920) with the equation: K = 8.4505 *10 −7 L eff

−3.3448

(6)

The cable created for the silicone indentation tests had the microsphere located 60.33 mm from the fixed point of the cable. The linear regression on the force displacement data (n=20) shown in Figure 2 results in a stiffness of 0.0104 N/m (R2=0.9988).

Figure 1: (a) Force-deflection data obtained from hanging weights at various positions (various values for Leff) on a stripped AFS-105/125 fiber optic cable. (b) Stiffness verse length of the stripped AFS-105/125 fiber optic cable and fitted power curve (R2=0.9920).

Experimental Stiffness

140 120 Force (μN)

Silicone Rubber Indentation Tests Indentation tests were performed on two formulations of silicone rubber, EcoFlex030 and EcoFlex010. The test utilized a microsphere indenter with R=17.6 μm that was fixed to the fiberoptic cable at a length of Leff=60.33 mm. Poisson’s ratio was assumed to be .5. The Hertz model (Eq. 1) was fitted to the data using a least squares algorithm to determine Young’s modulus. Results of the microsphere indentation tests for EcoFlex030 (n=6) and EcoFlex010 (n=5) are displayed in Figure 3 with Young’s moduli of E= 106.4 and 47.82 kPa respectively.

100 80 60 40 20 0 0

3000

6000

9000

12000

Vertical Displacement (μm) Figure 2: Force-displacement data (n=20) for the cantilever used in all 11 silicone experiments. Linear regression provides a stiffness value of 0.0104 N/m (R2=0.9988).

Figure 3: Force-indentation data obtained for two formulations of silicon rubber using CITE. Average data for EcoFlex030 (n=6) and EcoFlex010 (n=5) are displayed with their fitted Hertz model using a least squares method resulting in E=106.4 kPa and E=47.82 kPa respectively.

DISCUSSION/CONCLUSIONS The stiffness of segments of AFS-105/125 fiber optic cable (Thor Labs) can be accurately estimated as a function of Leff (Eq. 6). Applying the equation to the 60.33mm segment of cable used for the silicone experiments estimates the stiffness to be 0.0101 N/m where experimental stiffness measurements found the stiffness to be 0.0104 N/m, an error of 2.97%. This amount of error is reasonable, since the purpose

of the regression equation is only to estimate the proper location for the placement of the microsphere indentor. The Young’s moduli determined from the CITE measurements were 106.4 kPa for EcoFlex030 and 47.82 kPa for EcoFlex010. Both exceeded the moduli values obtained via macroscopic unconfined compression tests by 14.82% and 10.95% respectively. The values fall just outside of the 95% confidence intervals of (86.14-99.20) kPa for EcoFlex030 and (39.65-46.55) kPa for EcoFlex010. Possible sources of error in CITE measurements include experimental error, irregularities of the sample surface and limitations due to the assumptions made by the Hertz model. To account for this future work can include a correction factor reported by Yoffe for α/R > 0.1 [6]. Other work dealing with the unconfined compression of EcoFlex030 and EcoFlex010 has shown that the material is not lineary elastic. Fortunately, a method for modifying the Hertz solution for material beyond the linear elastic realm has been reported by Lin et al. and could be applied to CITE-generated data in future work [7]. The data presented shows that microsphere indentation using a fiber optic cantilever is capable of performing indentation tests at the mesoscale. Neglecting the position detector data was an attempt to limit possible sources of error. However the process introduced uncertainty associated with manually analyzing image data. Replacing the manual image analysis with an automated process including the position detector may help strengthen the results.

ACKNOWLEDGMENTS This research was funded through an SBES Seed Grant (2009-2010) awarded to Dr. Jessica Sparks (PI), Dr. Padma Rajagopalan (Co-PI), and Dr. Raffaella De Vita (Co-PI).

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