Characterization of the vitreoretinal interface and vitreous in the porcine eye as it changes with age

Cases of child abuse, specifically abusive head trauma (AHT) or shaken-baby syndrome (SBS), have long been associated clinically with retinal hemorrhages (RH). Previous research has shown that the vast majority (~85%) of AHT cases present with some type of RH. Traumatic RH is initiated by an external application of forces and accelerations to the head, but the mechanism by which this causes RH in infants is still unknown. The most prominent theory suggests that collagen-mediated adhesion between the vitreous and retina causes traction on the retina during rapid head rotation, damaging retinal blood vessels. To date, this theory has never been proven. In order to better understand the mechanisms of traumatic RH in infants, age-related changes of the vitreous and vitreoretinal interface were investigated. First, dynamic shear tests were conducted using a novel rheological interconversion technique to characterize the changes in material properties with developmental age of porcine vitreous. Next, scanning electron microscopy (SEM) and energy dispersive X-Ray spectroscopy (EDS) studies were performed on specimens from the vitreoretinal interface to quantitatively evaluate changes in collagen with age and in different regions of the eye. In dynamic shear, there was a statistically significant difference among the three age groups at varying shear rates (frequencies) for both storage (G′) and loss (G″) shear modulus. In particular, younger porcine vitreous had significantly higher (G′) and (G″) than vitreous from older animals. Given the unavoidable time degradation of vitreous, vi the interconversion technique used to characterize the porcine vitreous dynamic properties provided more reliable data over a wider range of frequencies (0.01 Hz - 1 Hz) than previous studies. SEM image analysis of the vitreoretinal interface resulted in a significantly higher percent collagen in eyes from 3- to 5-day-old piglets compared to 4-week-old piglets (p=0.002). Statistically significant regional differences were hindered by large variances due to charging artifacts and extraneous collagen from the vitreous body. The EDS analysis resulted in significant differences in carbon (p=0.009), nitrogen (p=0.025), silicon (p≤0.001), and sulfur (p=0.007) with respect to age. Regional significant differences were also found for sulfur (p=0.002).

CHARACTERIZATION OF THE VITREORETINAL INTERFACE AND VITREOUS IN THE PORCINE EYE AS IT CHANGES WITH AGE by Patrick Ryan Moran A thesis submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Master of Science Department of Mechanical Engineering The University of Utah December 2012 Copyright © Patrick Ryan Moran 2012 All Rights Reserved iv The University of Utah Graduate School STATEMENT OF THESIS APPROVAL The thesis of Patrick Moran has been approved by the following supervisory committee members: Brittany Coats , Chair 05/24/2012 Date Approved Bart Raeymaekers , Member 05/24/2012 Date Approved Kenneth L. DeVries , Member 05/24/2012 Date Approved and by Timothy Ameel , Chair of the Department of Mechanical Engineering and by Charles A. Wight, Dean of The Graduate School. v ABSTRACT Cases of child abuse, specifically abusive head trauma (AHT) or shaken-baby syndrome (SBS), have long been associated clinically with retinal hemorrhages (RH). Previous research has shown that the vast majority (~85%) of AHT cases present with some type of RH. Traumatic RH is initiated by an external application of forces and accelerations to the head, but the mechanism by which this causes RH in infants is still unknown. The most prominent theory suggests that collagen-mediated adhesion between the vitreous and retina causes traction on the retina during rapid head rotation, damaging retinal blood vessels. To date, this theory has never been proven. In order to better understand the mechanisms of traumatic RH in infants, age-related changes of the vitreous and vitreoretinal interface were investigated. First, dynamic shear tests were conducted using a novel rheological interconversion technique to characterize the changes in material properties with developmental age of porcine vitreous. Next, scanning electron microscopy (SEM) and energy dispersive X-Ray spectroscopy (EDS) studies were performed on specimens from the vitreoretinal interface to quantitatively evaluate changes in collagen with age and in different regions of the eye. In dynamic shear, there was a statistically significant difference among the three age groups at varying shear rates (frequencies) for both storage (G′) and loss (G″) shear modulus. In particular, younger porcine vitreous had significantly higher (G′) and (G″) than vitreous from older animals. Given the unavoidable time degradation of vitreous, vi the interconversion technique used to characterize the porcine vitreous dynamic properties provided more reliable data over a wider range of frequencies (0.01 Hz - 1 Hz) than previous studies. SEM image analysis of the vitreoretinal interface resulted in a significantly higher percent collagen in eyes from 3- to 5-day-old piglets compared to 4-week-old piglets (p=0.002). Statistically significant regional differences were hindered by large variances due to charging artifacts and extraneous collagen from the vitreous body. The EDS analysis resulted in significant differences in carbon (p=0.009), nitrogen (p=0.025), silicon (p≤0.001), and sulfur (p=0.007) with respect to age. Regional significant differences were also found for sulfur (p=0.002). iv vii TABLE OF CONTENTS ABSTRACT ............................................................................................................................. iii LIST OF FIGURES ............................................................................................................... viii LIST OF TABLES .................................................................................................................. xii ACKNOWLEDGEMENTS ................................................................................................... xiii INTRODUCTION .....................................................................................................................1 Chapter 1 AGE DEPENDENT MATERIAL PROPERTIES OF PORCINE VITREOUS....................3 1.1 Abstract ........................................................................................................................... 3 1.2 Introduction ..................................................................................................................... 4 1.3 Methods and Materials ................................................................................................... 5 1.3.1 Polystyrene-Toluene Solution (PS) ............................................................................5 1.3.2 Agarose .......................................................................................................................5 1.3.3 Matrigel.......................................................................................................................6 1.3.4 Synthetic Material Mechanical Testing ......................................................................7 1.3.5 Porcine Vitreous Preparation and Testing ..................................................................8 1.4 Data Analysis ................................................................................................................ 9 1.4.1 Interconversion Technique .........................................................................................9 1.4.2 Statistics ....................................................................................................................10 1.5 Results ......................................................................................................................... 11 1.5.1 Polystyrene-Toluene Solution ..................................................................................11 1.5.2 Agarose .....................................................................................................................14 1.5.3 Matrigel.....................................................................................................................16 1.5.4 Porcine Vitreous .......................................................................................................22 1.6 Discussion .................................................................................................................... 26 viii 1.7 Conclusion .................................................................................................................... 35 2 BIOLOGICAL SAMPLE PREPARATION FOR SEM IMAGING OF PORCINE RETINA ..................................................................................................................................37 2.1 Abstract ......................................................................................................................... 37 2.2 Introduction ................................................................................................................... 38 2.3 Scanning Electron Microscopy Methods and Materials ............................................... 38 2.3.1 Specimen en bloc dissection .....................................................................................38 2.3.2 Critical Point Drying (CPD) .....................................................................................39 2.3.3 Hexamethyldisilazane (HMDS)................................................................................40 2.3.4 Environmental Scanning Electron Microscopy (ESEM) ..........................................40 2.4 Results .......................................................................................................................... 40 2.5 Discussion .................................................................................................................... 48 2.6 Conclusion ..................................................................................................................... 49 3 QUANTIFICATION OF THE COLLAGEN CONTENT AT THE VITREORETINAL INTERFACE...........................................................................................................................50 3.1 Abstract ......................................................................................................................... 50 3.2 Introduction .................................................................................................................. 51 3.3 Methods and Materials .................................................................................................. 52 3.3.1 Sample Extraction and Preparation ..........................................................................52 3.3.2 SEM Imaging and EDS ............................................................................................53 3.4 Data Analysis ................................................................................................................ 54 3.4.1 SEM Analysis ...........................................................................................................54 3.4.2 EDS Analysis ............................................................................................................54 3.4.3 Statistics ....................................................................................................................55 3.5 Results .........................................................................................................................55 3.5.1 Image Segmentation Analysis ..................................................................................55 3.5.2 EDS Analysis ............................................................................................................57 3.6 Discussion .................................................................................................................... 58 3.7 Conclusion .................................................................................................................... 64 vi ix CONCLUSIONS AND FUTURE WORK ..............................................................................66 Appendices: A. CUSTOM PARALLEL PLATE CLEAT DESIGN...........................................................69 B. INTERCONVERION.........................................................................................................76 C. MATLAB CODE ...............................................................................................................80 D. DATA FOR CHAPTER 1..................................................................................................90 REFERENCES ......................................................................................................................102 vii x LIST OF FIGURES 1: Various plate geometries were used to reduce wall slip between sample and rheometer. C1) Cleat geometry sold commercially by TA Instruments: 90o x 0.5mm deep, apex to apex, steel. C2) Custom built geometry for large samples: 0.6mm x0.6mm x0.9mm (LxWxH) 20 mm and 24 mm diameter ABS. C3) Custom built geometry for small samples; 0.6mm x0.6mm x0.9mm (LxWxH) 13.70mm diameter ABS. .................................. 8 2: Interconversion technique used to calculate frequency dependent material properties of vitreous from creep testing...................................................................................................... 10 3: Representative creep compliance curve for polystyrene-toluene. ...................................... 12 4: Verification of the interconverted storage modulus for polystyrene solution. The interconverted G′ PS data was not statistically different from the oscillation G′ data up to 10 Hz frequency range (*p˂0.05). .......................................................................................... 13 5: Verification of the interconverted loss modulus for polystyrene solution. The interconverted G″ data became significantly different from the oscillation G″ data around 10 Hz (*p<0.05). ..................................................................................................................... 14 6: Representative creep compliance curve for Agarose (○). Averaging this original creep-ringing region resulted in a damped compliance curve (■) .......................................... 15 7: Verification of the interconverted storage modulus for agarose. The interconverted G′ was not statistically different from the oscillation G′ data over the entire interconverted frequency spectrum. ................................................................................................................ 16 8: Verification of the interconverted loss modulus for agarose. Compared to the G″ from forced oscillation tests, the interconverted G″ was statistically different for seven of the 12 frequencies in the interconverted frequency spectrum (*p˂0.05, **p˂0.005). ................. 17 9: Representative creep compliance curve for Matrigel (○). Averaging this original creep-ringing region resulted in a damped compliance curve (■). ......................................... 19 10: Verification of the interconverted storage modulus for Matrigel. The interconverted G′ was not statistically different from the forced oscillation G′ over the entire interconverted frequency spectrum. ........................................................................................ 20 xi 11: Verification of the interconverted loss modulus for Matrigel. Compared to the oscillation G″ data, the interconverted G″ was statistically different for four frequencies (*p˂0.05, **p˂0.005). ............................................................................................................ 21 12: Representative porcine vitreous creep compliance curve (○). Averaging this original creep-ringing region resulted in a damped compliance curve (■) .......................................... 23 13: Mean ± SD of storage modulus of porcine vitreous at three stages of development. Statistical differences (p˂0.05) between the 5-day-old porcine vitreous and 4-week-old porcine vitreous are indicated by (*). In comparison to the 2-month-old vitreous, the 5-day-old porcine vitreous was significantly different (p˂0.05) at frequencies represented by (**) . The 4-week-old porcine vitreous was significantly different from the 2-month-old porcine vitreous (p˂0.05) for nearly the entire frequency range (#). ............................... 24 14: Age-dependent loss modulus of porcine vitreous. Statistical differences (p˂0.05) between the 5-day-old and 4-week-old porcine vitreous are indicated by (*). In comparison to the 2-month-old vitreous, the 5-day-old porcine vitreous was significantly different (p˂0.05) at frequencies represented by(**) . The 4-week-old porcine vitreous was not significantly different from the 2-month-old porcine vitreous (p˂0.05) for nearly the entire frequency range (#). ................................................................................................ 25 15: Analysis of the increased G" error associated with a lower tanδ value. The tanδ associated with the 3- to 5-day-old (◊ tanδ=0.33), 4-week-old (Δ tanδ=0.45), and 2-month-old (□ tanδ=0.62) corresponds to a coefficient of non-determination of 0.64, 0.47, and 0.23, respectively. ............................................................................................................ 27 16: 5-day-old porcine vitreous comparison of the G' values calculated using the interconversion technique (○) versus using a frequency sweep (●). ...................................... 29 17: 4-week-old porcine vitreous comparison of the G' values calculated using the interconversion technique (○) versus using a frequency sweep (●). ...................................... 30 18: 5-day-old porcine vitreous comparison of the G″ values calculated using the interconversion technique (□) versus using a frequency sweep (●). ...................................... 31 19: 4-week-old porcine vitreous comparison of the G″ values calculated using the interconversion technique (□) versus using a frequency sweep (●). ...................................... 32 20: Comparison of the interconverted storage modulus for fixed and fresh sheep eyes. ....... 34 21: Comparison of the interconverted loss modulus for fixed and unfixed sheep eyes. ........ 35 22: Spherical artifacts (arrows) found in the collagen matrix of the porcine retina. The dehydration procedure was thought to be the cause of the artifact and was changed for subsequent specimens. Imaged using the Everhart-Thornley detector in high vacuum with a magnification of 8000x and 20kV accelerating voltage. ............................................. 42 ix xii 23: Retina sample that was critical-point dried using a more gradual dehydration protocol to mitigate the spherical artifacts of Figure 1. Imaged using Helix (SE) detector in low vacuum with a magnification of 8000x, 0.298 Torr chamber pressure, and accelerating voltage of 7kV......................................................................................................................... 43 24: Retina sample critical-point dried without osmium fixation using Helix detector in low vacuum. Image taken at a magnification of 8000x, 0.261 Torr chamber pressure, and accelerating voltage of 7kV. ................................................................................................... 44 25: Retina sample critical-point dried with osmium fixation using Helix detector in low vacuum. Image taken at 8000x magnification, 0.376 Torr chamber pressure, and 7 kV accelerating voltage. ............................................................................................................... 45 26: Retina sample prepared with HMDS dehydration and imaged using Helix detector in low vacuum. Magnification of 8000x was used with a 7kV accelerating voltage and 0.301 Torr chamber pressure. ........................................................................................................... 46 27: ESEM image taken of retinal surface at 6.499 Torr of water vapor with a magnification of 4000x and 7kV accelerating voltage. The presence of vitreous (99% water) impedes visualization of the collagen matrix on the retina. Attempts to minimize vitreous were unsuccessful, and specimen became thermally damaged (i.e. retina layers curling) within 20 minutes of application of the beam. .......................................................... 47 28: Sample collection from each eye. A) Boxes 1N, 2N, and 3N indicate the nasal orientation of the vitreous base region, equator region, and posterior pole region, respectively. Boxes 1T, 2T, and 3T indicate the temporal orientation of the vitreous base, equator, and posterior pole, respectively. B) Boxes 1N and 1T signify the nasal and temporal locations, respectively, of the trephine cut through the vitreous base region. ......... 52 29: Representative EDAX spectrum for the seven elements (green box) investigated. Statistical analysis was performed on the corresponding atomic percent values (red box). The "Ka" values after the elemental name indicates which orbital shell the signal originated. ............................................................................................................................... 56 30: Age and region statistics (Mean ± SD). Significant differences (p<0.005) in age (**) were identified, but no regional differences were found. ....................................................... 57 31: Representative SEM image of collagen with retina visible in background. Image of 4-week-old retina taken from the posterior pole. 8000x magnification. ................................. 59 32: Image segmentation results of contrasted collagen (white) and retina (black). The corresponding collagen content was 20.85%. ......................................................................... 59 33: Representative SEM image of collagen without visible retina. Image of 2-month-old retina taken from the equator. 8000x magnification. .............................................................. 60 x xiii 34: Image segmentation results of contrasted collagen (white) and retina (black). The corresponding collagen content was 38.68%. ......................................................................... 60 35: Comparison of the mean sulfur differences with age in the three regions (vitreous base, equator, posterior pole). ................................................................................................. 64 36: Various plate geometries were used to reduce wall slip between sample and rheometer. C1) Cleat geometry sold commercially by TA Instruments: 90o x 0.5mm deep, apex to apex, steel. C2) Custom built geometry for large samples: 0.6 x0.6 x0.9mm (LxWxH) 20 mm and 24 mm diameter ABS. C3) Custom built geometry for small samples; 0.6 x0.6 x0.9mm (LxWxH) 13.70mm diameter ABS.............................................. 71 37: PDMS validation with cleat geometries C1, C2, and smooth. Gap correction factors: C1=325μm, C2=393 μm. ........................................................................................................ 72 38: Bruker Contour K1 optical interferometry data report. .................................................... 74 39: Voigt single element model. ............................................................................................. 78 xi xiv LIST OF TABLES 1: Agarose statistical p-values comparing shear moduli which correspond to the G′ and G″ plots above. ........................................................................................................................ 18 2: Matrigel statistical p-values comparing shear moduli which correspond to the G′ and G″ plots above. ........................................................................................................................ 21 3: Significance level testing of G′ and G″ between age groups of porcine vitreous from 0.015 - 1.0 Hz. ........................................................................................................................ 26 4: Operating parameters used in the SEM studies of collagen content. .................................. 53 5: Chemical composition statistical analysis results for the four chemical components of interest (Mean ±SD). Significance in age (bold) found for all four elements, but only sulfur showed regional difference effects (italics*). ............................................................... 61 6: Interconverted creep data for porcine vitreous ................................................................... 91 7: Force oscillation data from porcine vitreous ...................................................................... 93 8: Fresh vs. fixed interconversion comparison for sheep eyes ............................................... 94 9: Forced oscillaiton and interconverted agarose data ............................................................ 94 10: Forced oscillation and interconversion data for PS .......................................................... 96 11: Forced oscillation and interconversion data for Matrigel ............................................... 100 ACKNOWLEDGEMENTS I owe a huge debt of gratitude to my advisor, Dr. Brittany Coats, for her academic and career guidance over the past two years. She has been a great mentor and friend, and I am forever grateful for her diligent work and positive attitude not to mention her phenomenal editing skills. I also want to thank my Injury Biomechanics lab members for the many hours of hard work and fond memories. Also, I would like to acknowledge the Micron Microscopy Core Facilities, HSC Core Research Facilities, and Dixon Laser Institute for their guidance and technical expertise. To my parents, thank you for the many years of love and support you have shown me throughout my academic career. I only hope that you are as proud of me as I am blessed to have such wonderful role models. Finally, I would like to dedicate this thesis in loving memory of my grandfather, Col. Elwood Mathison. INTRODUCTION Abusive Head Trauma (AHT) is one of the leading causes of child abuse related fatalities in the United States [6]. Patients may present with a wide range of symptoms making diagnosing AHT very challenging for clinicians. AHT cases have a high incidence of eye and brain injury, but it is unclear what types of accidental scenarios in children also result in similar injuries. Differences between accidental and inflicted trauma could be better identified if the mechanisms of each injury were known. One injury in particular, retinal hemorrhage, is common in AHT and has also been reported in accidental trauma [1]. While it is generally understood that large angular accelerations of the head can lead to RH, the mechanisms are unknown. One prominent theory is that during head rotation, the vitreous pulls on the retina in regions of the eye with strong vitreoretinal adhesion and causes damage to the retinal vessels. The adhesion between the vitreous and retina is thought to be mediated by collagen fibers spanning the vitreoretinal interface. To better understand the potential mechanisms of RH, and expand our understanding of the biomechanics of the pediatric eye, we investigated the age dependent changes in vitreous material properties as well as the associated structural changes in collagen content at the vitreoretinal interface. Rheological studies have demonstrated that the material properties of vitreous vary between species [7] and region [8]; however, no studies have quantified how the vitreous properties change with age. Similarly, the amount of collagen in the vitreous and at the vitreoretinal interface has never been quantified to identify changes with age or region [9] [10] [11]. To fill these gaps in the literature, dynamic shear moduli of vitreous were calculated at various stages of early development using an advanced rheological technique known as interconversion. Scanning electron microscopy (SEM) was then used to analyze the vitreoretinal interface, specifically the quantity of collagen fibers. Due to the limited availability of human eyes for testing, we decided to refine our techniques and initiate the analysis using formalin fixed pig eyes. Pig eyes have similar anatomical characteristics such as a multilayered retina, well-defined vascular arcade, and a vessel-free zone similar to the human macula [12]. Additionally, changes in pig collagen content in vitreous and at the vitreoretinal interface with age appear to parallel human changes with age [10]. Eyes from three age groups were selected for analysis based on their relative brain development to humans: 5-day-old (infant), 4-week-old (toddler), and 2-month-old (adolescent). CHAPTER 1 AGE DEPENDENT MATERIAL PROPERTIES OF PORCINE VITREOUS 1.1 Abstract It has been shown that vitreous material properties significantly affect finite element modeling predictions of retinal stress during repetitive head rotation in infants [1]. However, no material property data for pediatric vitreous exists. Therefore, we sought to identify the age-dependent material properties of porcine vitreous during dynamic oscillatory (shear) loading. As with most biological tissues, the pediatric vitreous exhibited a viscoelastic material response which was characterized by a storage modulus (G′) and loss modulus (G″) representing the elastic and viscous behavior, respectively. These moduli were extremely difficult to characterize at high shear rates due to inertial effects, so an advanced rheological interconversion technique was used to extract high frequency moduli from creep data. Verification of the technique was performed with synthetic materials that span the viscous and elastic behavior spectrum. The technique was then used to characterize the dynamic material properties of vitreous in 3- to 5-day, 4-week, and 2-month-old porcine eyes. The interconversion technique resulted in a good approximation of G‟ for all materials, but the accuracy of G″ was reduced in materials with a predominantly elastic response (tanδ << 1). Storage and loss 4 modulus of vitreous from 5-day-old pigs were significantly greater than the moduli of vitreous from 2-month-old pigs. Significant differences were also found between the vitreous from 5-day and 4-week-old pigs, but only for two of the frequencies examined. Vitreous from 4-week and 2-month-old pigs also had significant differences in the storage and loss modulus, but only over some frequencies. The age dependent changes in material properties of porcine vitreous validate the need for future rheological studies on the material properties of human infant eyes to determine if the biomechanical changes in the pediatric eye contribute to the presence of retinal hemorrhages caused by AHT. 1.2 Introduction Vitreous is a transparent gel-like substance located between the retina and lens in the eye. It is composed of a heterogeneous network consisting of 99 wt% water, 0.9 wt% salts, 0.1 wt% heterotypic collagen fibrils (collagen type II,V/XI and IX), and a hyaluronan network [5]. Characterizing the viscoelastic moduli of such a complex fluid with oscillation testing is a significant rheological challenge as it is susceptible to low signal-to-noise ratios at low frequencies, resonant effects, and tool inertial effects at the higher frequencies (1-10Hz). To overcome these obstacles and obtain data over a spectrum of clinically relevant frequencies, we converted time-dependent (TD) data from creep testing to estimate the frequency-dependent (FD) data typically measured with oscillation testing. A polystyrene-toluene solution (PS), agarose mixture, and Matrigel® were selected to verify the interconversion technique because their viscous and elastic characteristics encapsulate the viscoelastic response of vitreous. Once verified, the interconversion technique was applied to porcine vitreous at different stages of 5 development (5-day, 4-week, and 2-months old) to identify the age-dependent viscoelastic response of vitreous. 1.3 Methods and Materials To identify the frequency dependent response of vitreous, time domain data from creep tests were converted to frequency domain using a specialized spectral conversion technique (described in detail in section 3.1). To validate this technique we tested three synthetic materials (PS, agarose, and Matrigel) in creep and dynamic oscillation to compare the dynamic moduli from both methods. The rheological characterization was conducted by dynamic shear tests on the samples using an AR-G2 rheometer (TA Instruments, New Castle, DE). 1.3.1 Polystyrene-Toluene Solution (PS) Polystyrene atactic flakes (Polysciences, Inc., Warrington, PA) with a molecular weight of 50,000 Da were dissolved in Toluene to a final concentration of approximately 60% by mass. Small volumes (0.6cm3-2.5cm3) of the solution were placed on the rheometer plates and maintained at a temperature of 20° C for testing. 1.3.2 Agarose Dry agarose (Sigma-Aldrich, St. Louis, MO) was mixed with deionized water to a concentration of 1% by volume. After thoroughly mixing, the agarose was heated in the microwave until it began to boil. The mixture was stirred a second time and poured into a Petri dish, covered, and immediately cooled in a fridge at 9°C for at least 12 hours to 6 gel completely. Using a 20 mm trephine, agarose samples were delicately removed from the Petri dish and placed on the rheometer parallel plates maintained at 20°C for testing. 1.3.3 Matrigel Matrigel (BD Biosciences, Bedford, MA) is a basement membrane matrix primarily composed of laminin and collagen type IV. Matrigel is stored frozen between -10°C and -20°C. Heating it to ~4°C liquefies the Matrigel. Increasing the temperature to 22-35°C will initiate cross-linking and result in a semisolid gel. For this analysis, Matrigel was initially thawed and liquefied by placing it on ice in a refrigerator and maintaining a temperature range of 2-6° C for 24 hours. Once liquid, the Matrigel (100% concentration) was divided into 0.25 mL aliquots and refrozen until testing. Extra care was taken during the aliquot process to ensure that nothing above 10° C came into contact with the Matrigel as this could cause premature gelation. To create uniformly sized gel samples for rheometry testing, a steel washer (thickness=2mm, ID=13.7mm) was used as a mold. The washer was placed on the rheometer plates preset to a temperature of 8°C. Dow Corning high vacuum grease (Auburn, MI) was used on the underside of the washer to prevent leaking. Aliquotted Matrigel samples were re-thawed by placing on ice in the refrigerator for 24 hours. Once liquid, the Matrigel was transferred (0.15 mL to 0.25 mL) into the center of the washer using a 200 μL pipeteman (VWRbrand, Radnor, PA) with a chilled pipette tip. The temperature of the rheometer plates was increased to 37.5°C to initiate gel formation and then held constant for 30 minutes. Once completely gelled, the washer was carefully lifted off of the parallel plates leaving the cylindrical Matrigel specimen intact. Testing was performed at 37.5°C. 7 1.3.4 Synthetic Material Mechanical Testing To characterize the dynamic material properties using oscillation testing methods and the interconversion technique, each sample (n=6 for each material) was subjected to the following tests: dynamic strain sweep, dynamic frequency sweep (forced oscillation), and creep-recovery. The order of the frequency and creep testing was rotated (i.e. frequency/creep, creep/frequency) from one sample to the next to account for carryover effects due to the dependent testing. Strains sweeps were performed over three decades (0.1-100% strain) at 1 Hz to establish the linear viscoelastic region (LVR). Forced oscillations were swept over three decades from 0.1-100 radians per second with a 1% (PS, agarose) or 20% (Matrigel) strain amplitude that was previously found to lie within in the LVR of these materials. For creep testing, PS, agarose, and Matrigel were subjected to a torque of 35 μNm, 15 μNm, and 5 μNm, respectively, and held for 90 seconds. The stresses resulting from these torques were found to lie in the LVR for each material. Early in testing it became apparent that the forced oscillation tests were susceptible to slipping at the boundary of the parallel plates and the sample. To eliminate these effects, commercial cross-hatched parallel plate geometries (C1) and in-house custom parallel plate geometries (C2, C3) were designed to better grip the samples during testing (Fig. 1). Development and verification of the custom parallel plate geometries can be found in Appendix A. PS and agarose testing were completed using the C1 geometry; Matrigel testing was performed using the C3 geometry for the top plate and the C1 geometry for the bottom plate. 8 Figure 1: Various plate geometries were used to reduce wall slip between sample and rheometer. C1) Cleat geometry sold commercially by TA Instruments: 90o x 0.5mm deep, apex to apex, steel. C2) Custom built geometry for large samples: 0.6mm x0.6mm x0.9mm (LxWxH) 20 mm and 24 mm diameter ABS. C3) Custom built geometry for small samples; 0.6mm x0.6mm x0.9mm (LxWxH) 13.70mm diameter ABS. 1.3.5 Porcine Vitreous Preparation and Testing Eyes from 3-to 5-day-old (n=8), 4-week-old (n=8) and 2-month-old (n=6) old pigs were fixed in 10% formalin at the conclusion of nonocular related animal studies and transferred to phosphate buffered saline (PBS) for storage until testing. On the date of testing, the extraocular tissue (muscle, fat, etc.) was removed using forceps, and the optic nerve was transected at the sclera and optic nerve junction to allow direct access to the peripapillary sclera. The sclera and choroid were dissected up to the corneoscleral junction by accessing the small cavity between the choroid and retina and bluntly dissecting with forceps. The retina was then carefully peeled away from the vitreous leaving only the vitreous and hyaloid membrane. The entire vitreous and hyaloid membrane was placed onto the C2 custom rheometer plates maintained at 37.5°C. A solvent trap covered the specimen to maintain a humid environment. Two vitreous samples (5-day-old and 4-week-old) were subjected to a time sweep for 12 minutes at 0.1 Hz and 1% strain to identify how the dynamic shear moduli change C3 C3 C2 C1 9 with time. Three additional samples (5-day, 4-week, and 2-month) were subjected to a strain sweep over three decades (0.1-100% strain) at 0.1 Hz to identify the linear viscoelastic region of vitreous. The remaining 17 samples (3-to 5-day, n=6; 4-week, n=6; 2-monthNm torque) to determine their shear moduli using the interconversion technique. 1.4 Data Analysis 1.4.1 Interconversion Technique All creep tests were converted post hoc to FD data using a previously developed interconversion technique [13] composed of three steps. First, TD creep data are fit to an intermediate material function known as the retardation spectrum (Fig.2). This retardation spectrum is then interconverted to another material function, the relaxation spectrum. Finally, the relaxation spectrum is used to produce FD oscillation data. This final step requires an input of the frequency range over which to convert the creep data. The lower limit of the converted frequency data must correspond to the reciprocal of the total time for the creep data. For example, one creep test ran for 100 seconds, so the lower limit of the frequency range input for our data was 0.01 Hz or 0.1 rad/s. Similarly, the upper limit of the converted frequency data must correspond to the reciprocal of the lowest value resolvable from the creep tests. This value can vary depending on the material response, the sensitivity of the load cell, and the presence and duration of a toe region. The three-step interconversion process was performed using the Advanced Polymer Library software (TA Instruments, New Castle, DE). A more in depth description of interconversion theory is provided in Appendix B. 10 Figure 2: Interconversion technique used to calculate frequency dependent material properties of vitreous from creep testing. Creep ringing is a phenomenon that results from the coupling of the sample‟s inertia with the rheometer‟s inertia [14] and has an appearance of an under-damped system. Interconversion of data with creep ringing can cause large amounts of error. In order to remove this potential error, an averaging technique was developed using MATLAB (Mathworks, Inc. v. 7.9.0) in which the ringing was damped by averaging the peak-to-valley distances. All the peak and valley data points were selected for averaging with the origin included as a valley. By averaging the peak-to-valley data, the system was effectively critically damped and noise was removed from the system. 1.4.2 Statistics Statistical analysis was performed on PS, Matrigel, and agarose using SPSS PASW 18 (IBM, Armonk, NY). Paired samples t-test (α=0.05) was used at each frequency of the interconverted spectrum to test for significant differences between G′ and G″ obtained from forced oscillation versus G′ and G″ calculated from interconverted Creep: J(t) •Time dependent functionRetardation Spectrum: L(λ)Relaxation Spectrum: H(τ)Oscillation: G'(ω) G"(ω) •Frequency dependent function [Interconversion] 11 creep test data. The interconverted frequency spectrum was defined by the upper and lower frequency limits input during step 3 of the interconversion process. Material property differences among porcine vitreous at different ages (section 3.1) were analyzed using a univariate one-way ANOVA test. The null hypothesis (H0) statement was as follows: μ5day = μ4week = μ2months for both G′ and G″. The alternative hypothesis (HA) was: μ5day ≠ μ4week ≠ μ2months for both G′ and G″. A 95% confidence interval (α=0.05) was used and independence was assumed since only the interconverted data was used in the age comparison. 1.5 Results 1.5.1 Polystyrene-Toluene Solution The dynamic moduli of polystyrene-toluene solution were initially difficult to calculate due to memory effects. This was corrected by preconditioning the PS with a single oscillation test and creep test prior to collecting data for analysis. The creep test of the predominantly viscous PS solution resulted in little to no creep ringing (Fig. 3). Therefore, the interconversion of this data was completed without averaging any data points. The paired t-tests indicated that only the last two frequencies of G′ and last frequency of G″ calculated from the creep data were statistically different from G′ and G″ calculated from oscillation data. The deviations at these higher frequencies were most likely caused by the presence of a slight toe region and some minor noise in the PS creep data for the first ~0.1 seconds. Therefore, interconversion was identified as a valid method of analysis for PS up to approximately 10 Hz (Fig. 4-5). 12 0 10.000 20.000 30.000 40.000 50.000 60.000 70.000 80.000 90.000 time (s) 0 1.0000E-4 2.0000E-4 3.0000E-4 4.0000E-4 5.0000E-4 6.0000E-4 7.0000E-4 8.0000E-4 9.0000E-4 1.0000E-3 c o m p l ia n c e J ( t ) ( 1 / P a ) Polystryrene-Toluene Creep Test Figure 3: Representative creep compliance curve for polystyrene-toluene 13 Figure 4: Verification of the interconverted storage modulus for polystyrene solution. The interconverted G′ PS data were not statistically different from the oscillation G′ data up to 10 Hz frequency range (*p˂0.05). * * * * 14 Figure 5: Verification of the interconverted loss modulus for polystyrene solution. The interconverted G″ data became significantly different from the oscillation G″ data around 10 Hz (*p<0.05). 1.5.2 Agarose Performing a creep test on this elastic dominant material resulted in significant free oscillations (e.g., creep-ringing) for the initial 5 to 7 seconds of the test (Fig. 6). The ringing was eliminated by using the averaging technique described earlier. The interconversion technique resulted in a good approximation of G′ for the entire interconverted frequency spectrum (Fig. 7), but the interconverted G″ showed less agreement with the oscillation data (Fig. 8). Specifically, the interconverted G″ was significantly different from the oscillation G″ between 0.04 - 0.63 Hz (Fig. 8). The * * * * 15 0 10.000 20.000 30.000 40.000 50.000 60.000 70.000 80.000 90.000 time (s) 0 2.5000E-4 5.0000E-4 7.5000E-4 1.0000E-3 1.2500E-3 1.5000E-3 c o m p l ia n c e J ( t ) ( 1 / P a ) Agarose Creep Test Figure 6: Representative creep compliance curve for Agarose (○). Averaging this original creep-ringing region resulted in a damped compliance curve (■). 16 Figure 7: Verification of the interconverted storage modulus for agarose. The interconverted G′ was not statistically different from the oscillation G′ data over the entire interconverted frequency spectrum. maximum error was 38.5% at 0.1Hz. The minimum error was 4% at 1.6Hz as seen in Table 1. 1.5.3 Matrigel The Matrigel samples demonstrated ringing effects for the longest duration (approx. 20 to 40 seconds) during the creep tests (Fig. 9). These effects were removed by using the aforementioned averaging technique. As shown in Fig. 10, the interconversion technique resulted in nearly identical G′ values for the entire interconverted frequency 17 Figure 8: Verification of the interconverted loss modulus for agarose. Compared to the G″ from forced oscillation tests, the interconverted G″ was statistically different for seven of the 12 frequencies in the interconverted frequency spectrum (*p˂0.05, **p˂0.005). spectrum. The interconverted G″, however, was only valid to about 0.1 Hz (Fig. 11). The maximum error (194%) occurred at the endpoint of the interconverted frequency spectrum. Both agarose and Matrigel had limited high frequency ranges due to tool inertial effects. This occurred around 4 Hz for agarose and 0.5 Hz for Matrigel. The interconverted data were able to extend the reliable frequency range for G′ of agarose and Matrigel to 13 Hz and 2 Hz, respectively (Table 2). * * ** * ** * * * * * * * * * 18 Table 1: Agarose statistical p-values comparing shear moduli that correspond to the G′ and G″ plots above. G′ G″ Frequency (Hz) 0.015 p=.559 p=.437 0.025 p=.424 p=.125 0.04 p=.382 p=.020 0.063 p=.449 p=.004 0.1 p=.672 p=.003 0.16 p=.906 p=.010 0.25 p=.985 p=.030 0.4 p=.852 p=.023 0.63 p=.756 p=.045 1 p=.649 p=.171 1.6 p=.626 p=.594 2.5 p=.683 p=.175 19 Figure 9: Representative creep compliance curve for Matrigel (○). Averaging this original creep-ringing region resulted in a damped compliance curve (■). 010.00020.00030.00040.00050.00060.00070.00080.00090.000time (s)02.5000E-35.0000E-37.5000E-30.0100000.0125000.0150000.017500compliance J(t) (1/Pa)Matrigel Creep Test20 Figure 10: Verification of the interconverted storage modulus for Matrigel. The interconverted G′ was not statistically different from the forced oscillation G′ over the entire interconverted frequency spectrum. time (s) 21 Figure 11: Verification of the interconverted loss modulus for Matrigel. Compared to the oscillation G″ data, the interconverted G″ was statistically different for four frequencies (*p˂0.05, **p˂0.005). Table 2: Matrigel statistical p-values comparing shear moduli that correspond to the G′ and G″ plots above. Frequency (Hz) 0.015 0.025 0.040 0.063 0.10 0.16 0.25 0.40 G′ p=.410 p=.286 p=.234 p=.200 p=.117 p=.163 p=.158 p=.150 G″ p=.039 p=.118 p=.135 p=.102 p=.065 p=.014 p=.002 p=.003 * * * * ** * ** * 22 1.5.4 Porcine Vitreous The creep response of the porcine eyes appeared to be predominantly more viscous, similar to the PS, but creep ringing was observed for the initial ten seconds of the test at a relatively low ringing frequency (Fig. 12). The ringing was corrected using the same protocol used for agarose and Matrigel. Low ringing frequencies in the creep tests and a relatively long toe region restricted the resolvable upper limit of the interconverted frequency spectrum to 1 Hz. This was still better than our early forced oscillation tests of vitreous which had an upper limit of 0.3 Hz due to tool inertial effects. In general, storage and loss modulus calculated from the interconverted creep data decreased with age, but this was only significant between the 3- to 5-day-old eyes and the 2-month-old eyes. Further examination using a Games-Howell means comparison found significant differences with age across the entire frequency range for the storage modulus (G′) comparing 5-day-old vitreous to 2-month-old vitreous, but only one frequency (0.25 Hz) for the loss modulus (G″) was significantly different between the two ages. The storage modulus of the 5-day-old vitreous was significantly different from the 4-week-old porcine vitreous for only two frequencies. Loss modulus (G″) comparisons between the 5-day to 4-week-old porcine vitreous and 4-week to 2-month-old porcine vitreous were statistically significant for four and two frequencies, respectively (Table 3). Based on the earlier validation tests with synthetic materials, the evaluation of the interconversion likely resulted in more error for G″ values than G′. 23 0 10.000 20.000 30.000 40.000 50.000 60.000 70.000 80.000 90.000 time (s) 0 0.17500 c o m p l ia n c e J ( t ) ( 1 / P a ) Porcine Vitreous Creep Test Figure 12: Representative porcine vitreous creep compliance curve (○). Averaging this original creep-ringing region resulted in a damped compliance curve (■). 24 Figure 13: Mean ± SD of storage modulus of porcine vitreous at three stages of development. Statistical differences (p˂0.05) between the 5-day-old porcine vitreous and 4-week-old porcine vitreous are indicated by (*). In comparison to the 2-month-old vitreous, the 5-day-old porcine vitreous was significantly different (p˂0.05) at frequencies represented by (**) . The 4-week-old porcine vitreous was significantly different from the 2-month-old porcine vitreous (p˂0.05) for nearly the entire frequency range (#). * * * * # * # * # * # # * # * # * # * ** * ** * ** * ** * ** * ** * ** * ** * ** * ** * 25 Figure 14: Age-dependent loss modulus of porcine vitreous. Statistical differences (p˂0.05) between the 5-day-old and 4-week-old porcine vitreous are indicated by (*). In comparison to the 2-month-old vitreous, the 5-day-old porcine vitreous was significantly different (p˂0.05) at frequencies represented by(**) . The 4-week-old porcine vitreous was not significantly different from the 2-month-old porcine vitreous (p˂0.05) for nearly the entire frequency range (#). ** * ** * ** * ** * ** * ** * ** * * * * * * * # * # * 26 Table 3: Significance level testing of G′ and G″ between age groups of porcine vitreous from 0.015 - 1.0 Hz. Frequency (Hz) Comparisons 0.015 0.025 0.040 0.063 0.10 0.16 0.25 0.40 0.63 1.0 5 dy vs. 4 wk G′ p=.010 p=.071 p=.086 p=.099 p=.099 p=.086 p=.067 p=.052 p=.048 p=.057 G″ p=.114 p=.108 p=.087 p=.073 p=.008 p=.007 p=.023 p=.212 p=.407 p=.731 5 dy vs. 2 mo G′ p=.002 p=.024 p=.028 p=.035 p=.041 p=.040 p=.034 p=.027 p=.026 p=.033 G″ p=.030 p=.036 p=.039 p=.042 p=.005 p=.006 p=.022 p=.146 p=.404 p=.691 4 wk vs. 2 mo G′ p=.598 p=.043 p=.050 p=.047 p=.039 p=.029 p=.019 p=.011 p=.016 p=.154 G″ p=.072 p=.063 p=.038 p=.018 p=.914 p=.956 p=.984 p=.992 p=.998 p=.994 1.6 Discussion The results of this study show that the process of converting creep compliance TD data to FD data, G′ (ω) and G″ (ω), is successful but has some limitations. Viscous dominant materials, such as the PS solution, can be directly interconverted without any additional data analysis (e.g., averaging) and with good accuracy for predicting G′ and G″ up to 10 Hz. However, with elastic dominant materials, such as agarose and Matrigel, significant error can occur due to free oscillations (creep ringing). In fact, there appears to be a relationship between the accuracy of the interconversion method and the ratio of the viscous to elastic mechanical response of the material, tanδ (Fig. 15). Predictions of 27 Figure 15: Analysis of the increased G" error associated with a lower tanδ value. The tanδ associated with the 3- to 5-day-old (◊ tanδ=0.33), 4-week-old (Δ tanδ=0.45), and 2-month-old (□ tanδ=0.62) corresponds to a coefficient of non-determination of 0.64, 0.47, and 0.23, respectively. G″ for PS, which has an average tanδ of 0.61, were accurate over a wide range of frequencies (0.01Hz-10Hz). However, Matrigel and agarose, which have a much smaller tanδ (0.13 and 0.06, respectively) had significantly more error in the G″ data (Fig. 15). Creep ringing of the material is a significant contribution to error and our averaging technique may have been unable to eliminate it completely.1 A low signal-to-noise ratio may also contribute to the problem. When G′ is larger than G″, the subdominant signal 1 The averaging technique takes a single peak and average it with a single neighboring valley. Averaging each peak with the neighboring valley on each side of the peak would result in additional data points and could potentially improve the accuracy of the interconversion. Matrigel Agarose PS 28 (e.g., G″) can be less accurate and may be noisy [15]. Both of these sources for error are predisposed to elastic materials, so the interconversion technique is much more accurate for predominantly viscous materials. Porcine vitreous has a tanδ more comparable to PS, but it changes with age (Fig. 15). We conclude that the interconverted G′ and G″ porcine data provides reliable results for frequencies up to 1Hz, but it is slightly more accurate in calculating G" in eyes from older children than for infants. Additional verification of the validity of this technique for the infant age group should be performed using materials with tanδ ≈ 0.3. The actual error in G″ when using the interconversion method on vitreous cannot be directly measured as it was with the synthetic materials due to continual water loss of vitreous during testing [4]. In a preliminary examination, we found that G′ and G″ values dropped 20%-60% depending on the age of the animal within 90 seconds after the start of testing. More variation occurred after 90 seconds. Each forced oscillation test took 390 seconds to complete a frequency sweep (0.1-100rad/s). This means that the properties of vitreous changed throughout the sweep and any subsequent creep testing on the same sample would be incomparable. Similarly, each creep test lasted 90 seconds and any subsequent oscillation testing was bound to result in different dynamic moduli. One benefit of the interconversion technique is that high frequency rate information is gleamed within the first second of testing. In this regard, using the interconversion technique on vitreous can result in much more accurate measurements of dynamic viscoelastic moduli at high frequencies. Post-hoc oscillation tests were conducted on 5-day-old vitreous (n=1) and 4-week-old vitreous (n=1) to compare the error between the two testing methods. The G′ values of the 5-day-old vitreous fell within the error bars 29 over the frequency spectrum where the oscillation testing is valid (Fig. 16). The 4-week-old vitreous oscillation data showed worse correlation (Fig. 17), but at both ages the G′ values were reduced for the oscillation test which is what we expect with longer test times. The G″ values for both the 5-day and 4-week-old porcine vitreous were similarly reduced for the oscillation testing (Fig. 18, 19). As expected from the tanδ analysis, the G″ for the younger age eye showed more error. Figure 16: 5-day-old porcine vitreous comparison of the G' values calculated using the interconversion technique (○) versus using a frequency sweep (●). 30 Figure 17: 4-week-old porcine vitreous comparison of the G' values calculated using the interconversion technique (○) versus using a frequency sweep (●). 31 Figure 18: 5-day-old porcine vitreous comparison of the G″ values calculated using the interconversion technique (□) versus using a frequency sweep (●). 32 Figure 19: 4-week-old porcine vitreous comparison of the G″ values calculated using the interconversion technique (□) versus using a frequency sweep (●). Other disadvantages of the standard oscillation testing over the interconversion technique are the effects of resonant frequencies [15] and tool inertia [16]. Tool inertia effects occur when the loss angle (phase angle between strain input and stress response) rapidly increases to 180 degrees. At this point, the signal is largely dominated by inertia and it becomes difficult to determine the true sample loss angle thus resulting in errors [17]. In our case, instrument inertia (~19 μNm/s2) significantly affected the ability to measure agarose, Matrigel, and vitreous properties at high frequencies. Creep tests are not susceptible to such inertial issues because the stress response is supplied by the rotational inertia (~2 μNm/s2) rather than the instrument‟s motor inertia (~19 μNm/s2) 33 [15] [18]. Resonance effects amplify a material‟s response which leads to erroneous G′ and G″ values. These effects can occur during both creep and stress-controlled forced oscillation experiments, but the advantage of the creep test is that only one perturbative stress state is used. Oscillation tests go through multiple stress states, increasing resonance and potentially leading to strain hardening of the material [16]. Therefore, given a predominantly viscous material that is susceptible to significant material property changes with time, the benefits of the interconversion method using a creep test appear to significantly outweigh any limitations, and will result in much more accurate high frequency moduli compared to properties derived from forced oscillation testing. Statistical tests on the pediatric porcine vitreous indicate that the storage modulus and loss modulus decrease with developmental age. Significant differences were strongest comparing the storage modulus of the 5-day porcine vitreous to the two older age groups. Large variations within the age groups due to vitreous orientation, precision of dissection, and pre-loading2 could have confounded the statistical analysis. As a result, the statistical power of our experiment was relatively low at some of the higher frequencies where larger variance occurred (β = 0.45). This may be resolved by increasing the sample size. A decrease in moduli with age is consistent with the age-related structural changes of vitreous reported in the literature [19]. Vitreous is largely composed of collagen fibers that traverse the eye. These fibers are thought to provide structure to the vitreous and dictate the elastic response of the eye. Research has shown that these collagen fibers degrade with age [20], reducing the structural integrity of the vitreous and lowering the elastic response [21] [10]. 2 Pre-loading occurs as a result of lowering the plate geometries onto the sample and therefore changes from sample to sample. This may be significant as vertical displacement is controlled manually. 34 Figure 20: Comparison of the interconverted storage modulus for fixed and fresh sheep eyes. Eyes used in the analysis were fixed in formalin and likely had altered properties compared to in vivo vitreous. However, the comparative differences with age are likely still valid. To estimate the effects of formalin fixation on the absolute measurement of G′ and G″, 132 day old fetal sheep eyes were either fixed in formalin (n=2) or unfixed (n=1). The unfixed eye was tested within 2 hours post-mortem. Eyes were creep tested and interconverted to a frequency spectrum. The storage modulus of the fixed sheep eye was anywhere from 2.5 to 5 times larger than the fresh sheep eye depending on frequency (Fig. 20), and the sheep eye that was fixed had a loss modulus that was anywhere from 1.5 to 5.5 times larger depending on frequency (Fig. 21). The statistical significance of 35 these results cannot be evaluated due to the sample size (n=1) for the fresh sheep eye, but it is clear that performing mechanical tests on fixed eyes results in an overestimation of the in vivo dynamic moduli. Future work will characterize the dynamic mechanical response of vitreous in fresh tissue. 1.7 Conclusion Interconversion of time-dependent data to obtain frequency-dependent data appears to be a viable technique to obtain dynamic properties of viscoelastic materials Figure 21: Comparison of the interconverted loss modulus for fixed and unfixed sheep eyes. 36 when oscillation testing is unavailable. The technique has certain limitations. Small differences in creep data can result in large errors in the resulting interconverted FD data due to the nature of the interconversion technique, so care needs to be taken when obtaining creep compliance data. Elastic dominant materials result in creep ringing which can invalidate the technique. This can be improved by using a peak-to-valley averaging technique, but it may not eliminate all of the errors. Future investigations should refine the averaging technique to lead to a more accurate G″ over a wider range of frequencies. Interconversion effectively extended the reliable G′ and G″ of vitreous by 0.7 Hz. As expected, the elastic and viscous response of porcine vitreous decreased with age. This trend, however, was only significant between the 3-to 5-day-old and 2-month-old eyes. Other comparisons had large variances resulting in a low statistical power. These comparisons can be improved with more consistent dissection techniques, controlling specimen orientation during testing, and increasing the sample size. The formalin fixation of the eyes increased both the G′ and G″ resulting in an overestimation of the in vivo moduli values. Future work should repeat testing on unfixed tissue to verify changes of shear moduli with age are similar to those reported in this study. 37 CHAPTER 2 BIOLOGICAL SAMPLE PREPARATION FOR SEM IMAGING OF PORCINE RETINA * Moran P., Coats B., "Biological Sample Preparation for SEM Imaging of Porcine Retina," Microscopy Today, vol. 20, no. 2, pp. 28-31, March 2012. 2.1 Abstract Vitreous is a clear, gel-like material, composed predominantly of water. Biological tissues such as vitreous (i.e., composed mainly of fluids) present difficulties for SEM analysis-both for sample preparation and subsequent imaging. Standard SEM imaging generally requires a high vacuum environment in order to maximize the mean free path of air and improve image resolution. Biological specimens immediately dehydrate in such harsh conditions. In order to successfully image the surface of the retina, a controlled dehydration of the vitreous is required. The unique composition of vitreous makes this process difficult to achieve without creating artificial changes to the sample. To minimize drying artifacts, and optimize image resolution of the vitreoretinal interface, three sample preparation protocols were investigated (ESEM, HMDS, and critical point drying). ESEM was not able to achieve the desired resolution requirements to image collagen in vitro. HMDS and critical point drying (CPD) of the porcine vitreous 38 both resulted in similar image quality, but HMDS was significantly less time consuming. Gradual ethanol drying prior to HMDS or CPD affected the propensity for drying artifacts and thus is an important consideration. 2.2 Introduction Sample preparation is a critical step in SEM imaging. This is especially true for biological samples because of charge build-up and sensitivity to vacuum and electron beam damage. In terms of ultrastructure imaging, a variety of advancements in detectors and approaches have improved biological imaging such that fewer steps are required for sample preparation. However, the conventional approach incorporating osmium tetroxide fixing, ethanol dehydrating, critical point drying, and coating still finds useful application. Three biological sample preparation methodologies for imaging the ultrastructure of immature porcine retina were compared. The three preparation methods examined are critical point drying (CPD), hexamethyldisilazane (HMDS) dehydration, and direct imaging by environmental scanning electron microscopy (ESEM). Preparation methodologies were evaluated based on resulting image quality and reduced potential for artifacts. 2.3 Scanning Electron Microscopy Methods and Materials 2.3.1 Specimen en bloc dissection Porcine eyes were fixed for 5 days in a 10% formalin solution and then transferred to phosphate buffered saline (PBS). Extraocular tissue was dissected away, and globes were hemisected anteroposteriorly along the sagittal plane with a scalpel. A 39 core through the retinal layers, choroid, and sclera was made with a 4 mm diameter trephine and placed on an aluminum stub using carbon dots or an aluminum crucible (for direct examination in ESEM). 2.3.2 Critical Point Drying (CPD) The first step in the CPD process was to dehydrate the specimen with ethanol. In general, more gradual dehydration minimizes surface tension effects, but there is some ambiguity as to the duration and incrementation of this important step for fragile biological tissues. We selected a dehydration procedure that is standard at our facility for liver and kidney specimens: samples were dried in 70% ethanol for 12 hours and increased to 95% ethanol for two changes lasting 1 hour each. To ensure complete ethanol saturation, the dehydration solution was increased to 100% ethanol for three changes lasting 1 hour each. All samples were critical-point dried using a PELCO CPD2 Critical Point Dryer (Ted Pella Inc., Redding, CA). Temperature and pressure were closely monitored to ensure the samples were not prematurely dried or thermally damaged. Six samples were prepared with 2% osmium tetroxide, and six samples were prepared without osmium tetroxide to determine if post fixation improved imaging and minimized charging artifacts and thermal damage. Additionally, all samples were sputter-coated with ~10 nm of gold-palladium and imaged using a Helix detector in low vacuum on the FEI NovaNano 630. The Helix detector is an FEI NovaNano detector that allows imaging of nonconductive samples in low vacuum mode. Pressures were varied from 0.25-0.4 Torr, but the accelerating voltage remained at 7kV. 40 2.3.3 Hexamethyldisilazane (HMDS) Ethanol dehydration was implemented, as described above, followed by three changes of 100% HMDS (Ted Pella, Inc.) for 30 minute durations. After the third change, specimens remained in HMDS until all of the solution evaporated. Samples were sputter coated with gold-palladium and imaged on an FEI Quanta 600 FEG in high vacuum with an Everhart-Thornley detector and also an FEI NovaNano 630 in low vacuum with a Helix detector. 2.3.4 Environmental Scanning Electron Microscopy (ESEM) ESEM imaging captures specimens in their natural hydrated state and can augment information obtained in other SEMs using extensive sample preparation. Unfortunately, examining the ultrastructure of the retina in its natural state is hindered by the vitreous of the eye. Vitreous is a viscous substance (composed of 99% water by volume) that sits atop the retina surface. Therefore, retina was dissected as described previously, but the specimens were dehydrated slightly in 70% ethanol for 1 hour, and vitreous was physically removed by gently suctioning with a medicine dropper. ESEM was performed on a FEI Quanta 600 FEG with a Peltier stage and gaseous secondary electron detector. 2.4 Results All SEM imaging methods, except the ESEM, allowed resolution of the filament-like collagen matrix. Initially, the CPD and HMDS samples were found to have peculiar spherical artifacts in the collagen matrix (Fig. 22). By adjusting the accelerating voltage, 41 chamber pressure, and ethanol procedure individually (not shown), we determined that these artifacts were the result of the ethanol dehydration protocol. Accordingly, a modified dehydration protocol was implemented to incorporate more gradual ethanol increases. The ethanol concentration in the dehydrating solution was increased from 30% to 50% and incrementally increased by 10% up to 100%. The duration of each iteration was 10 minutes. Two additional increments at 100% for 30 minutes ensured complete ethanol saturation throughout the tissue. By modifying the ethanol dehydration protocol to slow the dehydrating process, the artifacts were significantly decreased (Fig. 23). Subtle changes were made to chamber pressure and working distance to analyze the resulting images qualitatively. Samples without osmium tetroxide from the CPD preparation yielded crisp images of the collagen matrix on the retina surface using the Helix detector at low vacuum (Fig. 24). Specimens subsequently treated with osmium tetroxide, also imaged at low vacuum with a Helix detector, yielded indistinguishable results (Fig. 25). A comparison of the HMDS image (Fig. 26) with the CPD images (Fig.. 24-25) showed no distinct difference between the two preparation methods. No charging or drying artifacts were observed. The ESEM was unable to resolve collagen fibers on the retinal surface (Fig. 27). Multiple attempts with varying temperature and pressure parameters yielded no progress in the imaging results. Furthermore, air drying during imaging posed a significant problem because of the curling of the thin layers of the retina. 42 Figure 22: Spherical artifacts (arrows) found in the collagen matrix of the porcine retina. The dehydration procedure was thought to be the cause of the artifact and was changed for subsequent specimens. Imaged using the Everhart-Thornley detector in high vacuum with a magnification of 8000x and 20kV accelerating voltage. 43 Figure 23: Retina sample that was critical-point dried using a more gradual dehydration protocol to mitigate the spherical artifacts of Fig. 1. Imaged using Helix (SE) detector in low vacuum with a magnification of 8000x, 0.298 Torr chamber pressure, and accelerating voltage of 7kV. 44 Figure 24: Retina sample critical-point dried without osmium fixation using Helix detector in low vacuum. Image taken at a magnification of 8000x, 0.261 Torr chamber pressure, and accelerating voltage of 7kV. 45 Figure 25: Retina sample critical-point dried with osmium fixation using Helix detector in low vacuum. Image taken at 8000x magnification, 0.376 Torr chamber pressure, and 7 kV accelerating voltage. 46 Figure 26: Retina sample prepared with HMDS dehydration and imaged using Helix detector in low vacuum. Magnification of 8000x was used with a 7kV accelerating voltage and 0.301 Torr chamber pressure. 47 Figure 27: ESEM image taken of retinal surface at 6.499 Torr of water vapor with a magnification of 4000x and 7kV accelerating voltage. The presence of vitreous (99% water) impedes visualization of the collagen matrix on the retina. Attempts to minimize vitreous were unsuccessful, and specimen became thermally damaged (i.e. retina layers curling) within 20 minutes of application of the beam. 48 2.5 Discussion In our study, CPD and HMDS preparation methods both provided acceptable image quality and minimal artifacts. While CPD is the most common preparation method, HMDS requires no specialized equipment or precise monitoring of the samples, resulting in lower time and cost commitments than CPD. For immature porcine retina, we found that the HMDS images were indistinguishable from CPD images, and therefore conclude that HMDS is suitable for delicate tissues as long as imaging is conducted in low vacuum. This agrees with other studies that have shown the efficacy of HMDS [22] [23] on non-retina animal tissues. However, CPD still appears to be the preferable method for plant specimens [23]. The ESEM approach was by far the least time consuming of all the methods tested, and the costs were minimal. Unfortunately, imaging the retina surface using this technique proved difficult because of the thickness of the vitreous fluid layer, the poorer image resolution, and the finite duration of the specimen in the ESEM chamber before it became thermally damaged by the electron beam. ESEM has been used to resolve features on the nanometer scale, but this can be difficult with a wet sample [24]. Collagen fibers on the retinal surface are on the order of 10 nm in diameter. The small size of the collagen matrix and the presence of vitreous on the retina surface make ESEM imaging a poor choice for investigating retina ultrastructure. Another challenge with ESEM imaging is the limited time for imaging of the biological specimen inside the chamber. Despite having some control over pressure and temperature, biological specimens are very susceptible to beam damage and deterioration, and samples may only be imaged once. Typically, biological specimens can be imaged 49 for 30-60 minutes before significant drying artifacts damage the sample [25] [26]. In our study, the retina lasted 20 minutes, perhaps because of the thin (~200 μm) and multilayered structure. 2.6 Conclusion Scanning electron microscopy of biological specimens is such that subtle changes in sample preparation can alter image quality as well as introduce artifacts. From our investigation of preparation methodologies for a delicate biological tissue (i.e., retina), we conclude that the CPD and HMDS preparation techniques both result in similar image quality, but HMDS clearly has the advantage of being less time consuming and less costly. If specimens come from previously fixed tissue, additional fixation with osmium tetroxide is unnecessary when using a Helix detector in low vacuum. Regardless of preparation method, gradual ethanol gradient steps should be used to reduce the potential for drying artifacts. ESEM was not found to be useful for imaging collagen in retina samples given the resolution requirements, the natural presence of vitreous on the surface, and the thin multi-layered structure that is extremely susceptible to thermal damage. 50 CHAPTER 3 QUANTIFICATION OF THE COLLAGEN CONTENT AT THE VITREORETINAL INTERFACE 3.1 Abstract Collagen at the vitreoretinal interface is thought to play an important role in the adhesion of the vitreous to the retina resulting in retinal detachment or retinal hemorrhages when stressed. Qualitative studies have reported regional and age-related differences in collagen at the vitreoretinal interface, but these differences have never been quantified. In this chapter we created an image segmentation algorithm to quantify collagen at the vitreoretinal interface from scanning electron microscope images. Energy dispersive X-Ray spectroscopy (EDS) was also used to determine if there exist differences in chemical composition. Three age groups and three regions of the eye were investigated. Collagen content was significantly different for different ages as determined from both SEM and EDS image segmentation. No regional effects were observed using image segmentation algorithms; however, the EDS found significant differences by region in sulfur content. This suggests that collagen and retina do vary with age and region, and correlating chemical properties with ultrastructure information can provide a more complete quantification of the vitreoretinal interface. Future studies should investigate the region and age-related changes in chemical composition, 51 specifically of sulfur, in hydrated and unfixed porcine eyes to verify our EDS findings. Additional SEM image segmentation studies should also be conducted on unfixed eyes using a preparation protocol that limits the extraneous vitreous body included in the specimen extraction and analysis. 3.2 Introduction As shown in Chapter 1, there is an age dependent change in dynamic viscoelastic material properties of porcine vitreous; however, little is known about the structure and function of the vitreous [27]. Previous studies have observed age-related changes in the vitreous as well as at the vitreoretinal interface [10] [26] using dark-field slit illumination. These studies suggest that adhesion at the vitreoretinal interface is a source of many traction related eye injuries such as posterior vitreous detachment (PVD). In addition, traction between the retina and vitreous has been suggested to cause retinal hemorrhages (RH) in traumatic (SBS or AHT) and nontraumatic events [1]. For improved diagnosis and prevention of these diseases, it is important to understand the age and region dependent characteristics of the vitreoretinal interface. Of particular interest is collagen because it is thought to be responsible for adhesion between the vitreous and retina. Several scanning electron microscopy (SEM) studies [19] [28] [10] have visually investigated collagen ultrastructure at the vitreoretinal interface and evaluated the regional distribution of collagen qualitatively within the eye [11]. However, to our knowledge, no studies have attempted to quantify the age and region-related changes in collagen content at the interface. We have expanded upon previous analysis methods to incorporate image segmentation algorithms and EDS to quantify collagen content at the 52 vitreoretinal interface and identify changes with age (3- to 5-days, 4 weeks, 2 months) and region (vitreous base, equator, posterior pole). 3.3 Methods and Materials 3.3.1 Sample Extraction and Preparation The methods for preparing eyes and creating SEM specimens were previously described in Chapter 2. The left and right eye from two animals for each age group (3-to 5-days, 4-weeks, and 2-month) were dissected for analysis. Two samples (one nasal, one temporal) were removed from three regions (vitreous base, equator, posterior pole) for a Figure 28: Sample collection from each eye. A) Boxes 1N, 2N, and 3N indicate the nasal orientation of the vitreous base region, equator region, and posterior pole region, respectively. Boxes 1T, 2T, and 3T indicate the temporal orientation of the vitreous base, equator, and posterior pole, respectively. B) Boxes 1N and 1T signify the nasal and temporal locations, respectively, of the trephine cut through the vitreous base region. 53 total of six samples taken from each eye (Fig. 28). For consistency, samples extracted from the nasal orientation were also located on the superior surface of the eye, and those from the temporal orientation were located on the inferior surface of the eye. This was applied to both left and right eyes. 3.3.2 SEM Imaging and EDS All imaging was conducted using the FEI NovaNano 630 (Hillsboro, OR) with a Helix detector. The operating conditions were maintained with the parameters provided in Table 4. Immersion mode was used to improve resolution capabilities in low vacuum. In Chapter 2, gold-palladium was used to coat SEM specimens, but carbon was used for the current experiments because of its better capability with EDS analysis [29]. This change is minor and did not damage the sample. Carbon coating was done using the Denton Vacuum Desk II (Moorestown, NJ). A final carbon coating thickness between 10nm and 30nm was achieved. EDS was performed on all six specimens taken from a single 5-day-old (n=1) and 2-month-old (n=1) eye. For each specimen, a regular SEM image was taken first and then the EDS was performed. Seven different elements were determined relevant for the EDS Table 4: Operating parameters used in the SEM studies of collagen content. PARAMETER VALUE Pressure 0.25-0.40 Torr Vacuum Low Voltage 7 kV Magnification 8000 x Current ~0.25 nano-Amperes (nA) 54 analysis: carbon, nitrogen, oxygen, sodium, silicon, phosphorus, and sulfur. The EDAX detector (EDAX Inc., Mahwah, NJ) attached to the FEI NovaNano 630 was adjusted such that the detector was located ~49mm from the sample. Each spectrum was collected for 2 minutes. 3.4 Data Analysis 3.4.1 SEM Analysis An image segmentation program to quantitatively evaluate the collagen content at the vitreoretinal interface was developed using MATLAB. The code (Appendix C) exploits the inherent contrast differences between the retina and collagen that result from SEM. Each image is pre-adjusted to filter the 10 percent darkest and 10 percent lightest pixels. This reduces the effects of charging, which saturates the pixels, and dark regions where the contrast is poor. The pixels were then normalized to a 0-255 grayscale range. An absolute threshold of 153 was selected as the optimal grayscale threshold for all images based on preliminary examination of several images. This threshold was not changed throughout analysis. Pixels above the threshold were considered collagen fibers and pixels below the threshold were considered retina. The total percent collagen was defined by Equation [1]. 𝐶𝑜𝑙𝑙𝑎𝑔𝑒𝑛 𝑃𝑖𝑥𝑒𝑙𝑠𝑇𝑜𝑡𝑎𝑙 𝑃𝑖𝑥𝑒𝑙𝑠 ×100 [1] 3.4.2 EDS Analysis EDS quantification of the elemental components at the vitreoretinal interface was computed within the NovaNano 630 EDAX detector and software. Briefly, the software 55 counts the atomic particles of various elemental components and normalizes them from background noise (Fig. 29). The resulting counts are reported and identifiable peaks are given as weight and atomic percent values of the selected elements. Elemental quantification uses the ZAF method which accounts for the interactions between the specimen and elements‟ characteristic x-ray that reduce the signal: z-number effects, absorbance effects, and fluorescent affects. For our analysis, we compared the atomic percent (At %) values for statistically significant differences between ages and regions. 3.4.3 Statistics A two-way ANOVA was used to determine if the collagen quantity determined from the image segmentation program was significantly different among age groups (3-to 5-day, 4-week, 2-month) and regions (vitreous base, equator, posterior pole). A multivariate two-way ANOVA was used to analyze significant differences in the seven chemical components resulting from EDS analysis of specimens from two of the animal ages (3-to 5-day, 2-month) and the three eye regions examined. A level of p<0.05 was defined as significant. 3.5 Results 3.5.1 Image Segmentation Analysis No significant differences in collagen content were found among the three regions (p=0.248), but age did significantly affect collagen content (p=0.002) (Fig. 30). The interaction between the two independent variables (age and region) was also statistically significant (p≤0.001). Occasionally, collagen fibers were easy to distinguish from the 56 Figure 29: Representative EDAX spectrum for the seven elements (green box) investigated. Statistical analysis was performed on the corresponding atomic percent values (red box). The "Ka" values after the elemental name indicates which orbital shell the signal originated. 57 Figure 30: Age and region statistics (Mean ± SD). Significant differences (p<0.005) in age (**) were identified, but no regional differences were found. background retina (Fig. 31- 32), but the majority of the SEM images were dominated by collagen from the vitreous and made identifying retina difficult (Fig. 34). In some images there were charging artifacts which affected quantification of collagen. Significant interaction effects between age and region were identified. 3.5.2 EDS Analysis The achievable signal count, measured in counts per second (CPS), was between 500 and 900 during the EDS testing. There were significant differences between the two ages for four of the chemical components. As shown in Table 5, carbon (p=0.009), nitrogen (p=0.025), silicon (p≤0.001), and sulfur (p=0.007) had significant age 01020304050607080901003-5 day4 week2 month% COLLAGENAGEVitreous BaseEquatorPosterior Pole******58 differences (bold) with carbon, silicon, and sulfur being higher in older animals, and nitrogen being smaller. There were also significant regional differences in the presence of sulfur (p=0.002) (Table 5) with significantly lower amounts of sulfur in the vitreous base compared to the equator or posterior pole. No significant interaction effects between age and region were found. 3.6 Discussion To quantify collagen at the vitreoretinal interface, image segmentation of SEM images and EDS analysis were performed. Image segmentation of images resulted in significant differences with age, but not with region. This is contradictory to observed levels of collagen in different regions of the eye. Previous literature has identified a significant increase in the collagen fibers of the vitreoretinal interface of the vitreous base relative to the equator and posterior pole, while the differences between the equator and posterior pole were comparable [19]. One reason for the discrepancy is likely that the SEM images in our analysis had copious amounts of collagen from the vitreous body. Our protocol used a trephine to create the specimens for SEM. The trephine cut through the vitreous of the eye before cutting through the retinal layers. This resulted in vitreous being incorporated into the retina samples. Vitreous naturally has a large amount of collagen which is fairly uniform throughout the vitreous. Once dried, the vitreous collagen stacked on top of the collagen at the vitreoretinal interface and made identifying regional variations difficult. Collagen in the vitreous does decrease with age [10] [27], which explains why the data were significantly affected by age, but not region. Carbon was chosen over gold-palladium coating due EDS analysis. Carbon has a lower 59 Figure 31: Representative SEM image of collagen with retina visible in background. Image of 4-week-old retina taken from the posterior pole. 8000x magnification. Figure 32: Image segmentation results of contrasted collagen (white) and retina (black). The corresponding collagen content was 20.85%. 60 Figure 33: Representative SEM image of collagen without visible retina. Image of 2-month-old retina taken from the equator. 8000x magnification. Figure 34: Image segmentation results of contrasted collagen (white) and retina (black). The corresponding collagen content was 38.68%. 61 Table 5: Chemical composition statistical analysis results for the four chemical components of interest (Mean ±SD). Significance in age (bold) found for all four elements, but only sulfur showed regional difference effects (italics*). Element Group Age Mean Std. Deviation Carbon Total 5-day 62.8733 1.91538 2-month 66.0433 1.67382 Nitrogen Total 5-day 13.125 1.28777 2-month 11.145 0.65613 Silicon Total 5-day 0.3283 0.04309 2-month 1.0933 0.18694 Sulfur Vitreous Base 5-day 0.14* 0.01414 2-month 0.18* 0.02828 Equator 5-day 0.205* 0.00707 2-month 0.24* 0.01414 Posterior Pole 5-day 0.205* 0.00707 2-month 0.235* 0.00707 Total 5-day 0.1833 0.03445 2-month 0.2183 0.03312 62 absorbance than the gold-palladium meaning that more of the elements are analyzed resulting in better accuracy. Unfortunately, biological specimens can still manifest charge build-up on the imaging surface. Charging causes regions of intense saturation on SEM images and can hinder the image segmentation algorithms which rely heavily on the contrast between collagen and retina. From sample to sample, the charging varied from being very prominent to none at all, possibly due to the nonuniformity of the deposition of the carbon. Large variations in the standard deviation (SD) likely resulted from the variation in charging. Utilizing EDS to qualitatively analyze the amount of a collagen can be advantageous especially if used effectively in conjunction with using ultrastructure imaging [30] [31]. EDS provides information about subsurface details of the samples by analyzing energy levels of the electrons ejected from the element‟s electron shell. In this way, chemical information from the surface and deeper (~1 μm based on Monte Carlo simulations) can be analyzed and quantified. It is difficult, however, to identify the exact depth of the analysis. According to a previous study, the x-rays may analyze within 5μm of the sample [31]. The retinal thickness is on the order of 300μm thick, so the chemical components from our analysis were likely on the surface of the retina or within the top layer of the retina. Absolute quantification of the chemical composition of collagen or retina is impractical given the chemical fixatives and desiccants used to dry the sample. As such, this study only sought to qualitatively compare how elemental constituents of the vitreous and retina varied with age and region. Four elemental components significantly differed between the two age groups: Silicon, nitrogen, carbon, and sulfur. Silicon is not native to 63 the eye, but is found in HMDS. Therefore, the presence of this chemical is likely an artifact of the HMDS drying protocol. Nitrogen is an element found in the eye, but it is also found in HMDS. Therefore, it is unclear if the significance is real or an artifact of the drying protocol. Carbon is a known element of both collagen and retina, so we cannot determine if a significant difference in carbon means an increase in the collagen-retina ratio or vice versa. HMDS and ethanol also contain carbon so the significance may also be a drying artifact. To our knowledge, the collagen fibers within the vitreous are not known to contain sulfur, but sulfur has been identified as a constituent of melanosomes found in the retinal pigment epithelium (RPE) [30] [32]. The RPE is located within 200μm of the retina, so it is uncertain if the measured sulfur is from the RPE or a retinal layer closer to the vitreoretinal interface. Regardless, the reported sulfur content could indicate that a higher ratio of retina to collagen is present (Fig. 35). Sulfur in the vitreous base (0.16 ± 0.029) was significantly lower than that in the posterior pole (0.22 ± 0.018) or equator (0.223 ± 0.022). This is consistent with previous observations of collagen at the vitreoretinal interface [19]. 3.7 Conclusion Careful preparations were made to ensure the repeatability and reliability of our image segmentation results; however, the eye preparation method extracted extraneous vitreous body, and therefore collagen fibers, at the vitreoretinal interface which artificially increased the reported collagen fiber content. In addition, charging artifacts, inherent to biological specimens, created large sample to sample variability. As such, the image segmentation of SEM images alone did not allow for meaningful conclusions 64 Figure 35: Comparison of the mean sulfur differences with age in the three regions (vitreous base, equator, posterior pole). about the age and region dependent quantity of collagen fibers. EDS identified significant differences in sulfur across three regions of the eye, and significant differences in carbon, nitrogen, silicon, and sulfur for two ages. The results of nitrogen and silicon are likely not meaningful due to their presence in HMDS. A comprehensive analysis of the effect of chemical fixation with formalin and chemical dehydration with HMDS should be evaluated. Carbon, being present in both collagen and retina, limits the conclusions that can be gleaned regarding collagen content. Sulfur showed an increase with age which may be indicative of more amounts of retina relative to collagen. Sulfur content was lower in the vitreous base, suggesting amounts of collagen in that region compared to the equator and posterior pole. These findings are 0.070.090.110.130.150.170.190.210.230.250.27Vitreous BaseEquatorPosterior PoleESTIMATED MARGINAL MEANS OF SULFUR REGIONS5 day2 month65 supported by previous studies that have reported collagen content being highest in the vitreous base [11] [19]. However, these results provide only a qualitative description of the age dependent changes in collagen fiber. To quantify these changes in a more meaningful way (i.e., image segmentation analysis) a change in the methodology for extracting the samples for SEM imaging would be necessary such that only collagen fibers at the vitreoretinal interface are evaluated. 66 CONCLUSIONS AND FUTURE WORK Interconversion of time-dependent data to obtain frequency-dependent data has been shown to be a viable technique to obtain dynamic properties of viscoelastic materials when oscillation testing is unavailable. This technique is most effective for materials whose response is more viscous (i.e., polymer-melts such as PS) as certain limitations have been identified when the inertia-elastic coupling between the sample and the rheometer result in creep-ringing. These elastic dominant effects must be removed before using the technique. We have shown that by using an averaging technique over the region where the ringing occurs, we can reduce these errors such that the storage modulus (G′) of the material is accurate over the entire interconverted frequency spectrum. However, the interconverted loss modulus (G″) continues to be inaccurate. To improve the accuracy of G″ over a wider range of frequencies in elastic dominant materials, future investigations should refine the averaging technique. One suggestion is to find the midpoint between each peak and valley of the oscillation and use that as a data point. This will result in twice the amount of data that is currently used to create the creep compliance curve. Interconversion effectively calculated G′ and G″ of porcine vitreous over a broader frequency range compared to forced oscillation data. Using the interconversion technique, G′ was calculated from 0.01Hz-1.0Hz and G″ from 0.01Hz-1.0 Hz while only 0.01Hz- 0.3Hz were able to be trusted from oscillation data. The dynamic shear moduli 67 of porcine vitreous decreased with age, but this was only significant between 3-to 5-day-old and 2-month-old eyes. Other comparisons (3-to 5-day to 4-week; 4-week to 2-month) had large variances that could be improved with more consistent dissection techniques, controlling specimen orientation during testing, and increasing the sample size. Due to the overestimation of G′ and G″ resulting from formalin fixation, future work should repeat the testing on unfixed tissue to verify changes of shear moduli with age. In addition, regional shear moduli should be investigated, using the interconversion technique, to determine significant differences between anterior and posterior vitreous. Our investigation of preparation methodologies indicated that for delicate biological tissue, such as the retina, CPD or HMDS preparation techniques are both appropriate. HMDS is clearly more advantageous as it is less costly and time consuming. Regardless of preparation method, gradual ethanol gradient steps are critical to reducing drying artifacts. Isolating the vitreoretinal interface at different regions and developmental ages was achieved. However, the eye preparation method also extracted extraneous vitreous body, and therefore collagen fibers, at the vitreoretinal interface. Significant age differences were found using the image segmentation algorithm, but the excess collagen at the vitreoretinal interface was a confounding variable. In addition, charging artifacts saturated the contrast in certain images. This caused difficulties for quantifying collagen using image segmentation methods and resulted in large regional and age standard deviations. Future studies should investigate appropriate methods to remove the extraneous vitreous body at the vitreoretinal interface. This may included repeated flushing of the surface or potentially using CPD as it is inherently more abrasive to the 68 samples3. Quantifying the collagen at the vitreoretinal interface may also be more reliable using transmission electron microscopy (TEM). This circumvents the issues of extraneous collagen fibers because TEM generates cross-sectional images that show insertion points for the individual collagen fibers. Additionally, adhesion testing of the vitreoretinal interface could be incorporated into future studies to test for regional and age dependent, in addition to direction (anisotropy), force measurements. Preliminary vitreoretinal adhesion studies in our lab have demonstrated the ability to measure adhesion between the retina and vitreous. EDS was used to identify qualitative changes in the seven elements measured by the EDAX detector. Significant regional differences in sulfur were identified while age differences included four of the seven elements: carbon, nitrogen, silicon, and sulfur. Chemical fixatives and desiccants likely contributed to the age differences associated with carbon, nitrogen, and silicon. Sulfur, being a known constituent in the melanosomes of RPE, may be indicative of actual differences in the collagen content, where an increase in sulfur content indicates an increase in retina and associated decrease in collagen. In our study, sulfur increased with age and was higher in the posterior pole and equator than the vitreous base which is comparable to observations reported in the literature. In addition to the SEM image segmentation analysis on unfixed eyes, future EDS analysis should validate the qualitative findings of this study with eyes that are unfixed and hydrated. 3 As liquid carbon dioxide in the CPD chamber passes the critical point, a turbulent environment (boiling) is created. This may be assist in removing the extra vitreous body in a consistent manner. 69 APPENDIX A CUSTOM PARALLEL PLATE CLEAT DESIGN 70 Previous research [33] has shown that certain materials, specifically vitreous, are prone to wall slip phenomena. Preliminary investigation in our lab confirmed that pediatric vitreous also suffers from wall slip [34]. To eliminate these effects we created four custom cleat designs and optimized for slip prevention by varying both the height and cross-sectional area parameters. Two cleat heights (0.6mm and 0.9mm) and two, square cross-sectional areas (0.45 x0.45mm and 0.6 x0.6mm) were used in our investigation of mitigating wall slip. The design parameters were evaluated on porcine vitreous and the 0.6 x0.6x0.9mm (LxWxH) geometry was the most successful at suppressing slip [34]. Three cleats (Fig. 36) were used to mitigate slip for the vitreous and materials used for verification: a commercial geometry (C1) and two custom parallel plate geometries (C2, C3) that had the same cleat design, but different overall diameters. The custom cleat designs, C2 and C3, were used to mitigate the apparent slip in vitreous and Matrigel, while the commercial cleat design, C1, was used to mitigate the slip in PS and agarose. The cleat geometries were successful in suppressing the slip, but to accurately interpret data gathered while using these modified geometries, an „effective gap height‟ had to be determined because the no-slip boundary layer was different with each geometry. Following the same techniques used by Nickerson and Kornfield [33], effective gap heights for the new geometries were derived by performing experiments on well-characterized fluids such as a low viscosity standard Newtonian oil (Cannon Oils, State College, PA) and polydimethylsiloxane (PDMS) putty. Briefly, stepped flow tests with 71 Figure 36: Various plate geometries were used to reduce wall slip between sample and rheometer. C1) Cleat geometry sold commercially by TA Instruments: 90o x 0.5mm deep, apex to apex, steel. C2) Custom built geometry for large samples: 0.6 x0.6 x0.9mm (LxWxH) 20 mm and 24 mm diameter ABS. C3) Custom built geometry for small samples; 0.6 x0.6 x0.9mm (LxWxH) 13.70mm diameter ABS. shear rates sweeping from 1-80 s-1 were conducted on the standard oil to determine the viscosity. Four gap heights (500 μm, 1000 μm, 1500 μm, and 2000 μm) were tested on three geometries (smooth, C1, and C2) at 22 oC. The C3 geometry had identical cleat dimensions as C2 thus calculation of the effective gap height was not repeated for C3. Standard oil is not prone to wall slip effects, so viscosity measured with the smooth parallel plate geometry established was identified as the true viscosity (ηtrue) and viscosity measured with the cleated geometries was defined as the measured viscosity (ηmeas). The effective gap correction factor, δ, was found by performing a nonlinear least-squares fitting of Eq. [2] for each geometry. η𝑚𝑒𝑎𝑠η𝑡𝑟𝑢𝑒=𝑔𝑎𝑝𝑚𝑒𝑎𝑠 𝑔𝑎𝑝𝑚𝑒𝑎𝑠+𝛿 [2] 72 Figure 37: PDMS validation with cleat geometries C1, C2, and smooth. Gap correction factors: C1=325μm, C2=393 μm. 0.10001.00010.00100.01000ang. frequency (rad/s)100.01000100001.000E5G' (Pa)100.01000100001.000E5G'' (Pa)PDMS Validation C2 geometryPDMS Validation C1 geometryPDMS smooth geometry73 Gap correction values are independent of the materials tested [33], so the gap correction factors and effective gap heights (gapmeas + δ) were validated by performing frequency tests from 0.1-100 rad/s of PDMS putty in the linear viscoelastic region (1% strain). The true viscoelastic moduli (smooth geometry) of the PDMS were higher than the measured uncorrected viscoelastic moduli (slip suppressing geometries). By applying the gap correction factor post-hoc the viscoelastic moduli showed very good agreement (Fig. 37). The depth of the no-slip boundary layer (for our custom cleat design was 390 m. This is much larger than the 157 m depth of the no-slip boundary layer for the custom cleat design developed by Nickerson et al. for testing the dynamic properties of adult porcine vitreous [33]. Their optimal cleat design was 0.45 x 0.45 x 0.6 mm, and is much smaller than the dimensions of our cleat design. Their smaller design is likely due to differences in the manufacturing processes. They machined their cleat out of aluminum, while our custom cleat design was made from ABS plastic using 3-D printing (University of Utah BioDesign Lab). This resulted in a quick and inexpensive way to develop and test cleat geometries, but the actual dimensions of the cleat varied from what was specified for 3-D printing. As verified using a Contour K1 optical interferometer (Bruker, Tuscan, AZ), the geometries were circular (diameter = 0.75mm) rather than square (0.6mm x 0.6mm) in shape and the height for the 0.9mm design was actually 0.85mm (Fig. 38). Nickerson et al. did not perform optical measurements on their finalized cleat design, but it is likely that their tolerances may have been tighter because it 74 Figure 38: Bruker Contour K1 optical interferometry data report. 75 was machined rather than printed. Despite these differences, the ABS cleat geometries were successful in preventing slip for immature vitreous [34]. Frequency-dependent sweeps from 0.1-100 rad/s without the cleat profile resulted in noisy data at low frequencies (0.1-1 rad/s). Wall slip was associated with these low frequency limitations and was mitigated using the new cleat designs. 76 APPENDIX B INTERCONVERSION 77 Interconversion is a mathematically intensive process whereby an experimentally inaccessible material function such as the retardation spectrum or relaxation spectrum is derived from an experimentally accessible material function (creep compliance or oscillation test, respectively). To complete the interconversion there are two approaches. The discrete interconversion approach analytically evaluates a Voigt or Kelvin (Fig. 39) element‟s characteristic compliance Jk and timescale λk by fitting the experimental creep compliance data to Equation [3]. Due to this being an ill-posed mathematical process, small differences in experimental data can lead to large differences in the spectral result. This is counteracted by using nonlinear regularization procedures resulting in the determination of a discrete retardation spectrum with a "strength" Jk and location λk, where the location corresponds to the time required for the extension of the spring to its equilibrium length during retardation by a dashpot [35]. Conversion to the relaxation spectrum is an exact integral transformation resulting in the element‟s characteristic modulus, Gi and timescale τi [36] [36]. As shown in Equation 4, the relaxation modulus is easily defined from the relaxation spectrum. The corresponding dynamic functions, G‟ and G", are obtained by the Fourier transforms of Equation 4, resulting in Equation 5 and Equation 6. 𝐽 𝑡 =𝐽0+ 𝐽𝑘𝑚𝑘=1 1−𝑒 −𝑡𝜆𝑘 +𝑡𝜂0 [3] 𝐺 𝑡 =𝐺𝑒+ 𝐺𝑖𝑒(−𝑡𝜏𝑖 )𝑛𝑖=1 [4] 𝐺′ 𝜔 =𝐺𝑒+𝜔 𝐺 𝑡 −𝐺𝑒 𝑠𝑖𝑛𝜔𝑡 𝑑𝑡∞0 [5] 𝐺" 𝜔 =𝜔 𝐺 𝑡 −𝐺𝑒 𝑐𝑜𝑠𝜔𝑡 𝑑𝑡∞0 [6] 78 Figure 39: Voigt single element model. An alternative approach is the continuous interconversion as shown in Equation 7, which uses numerical techniques to determine the spectra. This is a generalized discrete interconversion approach in that an infinite amount of elements instead of an exact integral are used to calculate the spectra. Once one spectrum is determined for the entire time scale, the corresponding spectra can be calculated. The interconversion between material spectral functions is not included, but a complete description can be found in [35]. 𝐽 𝑡 =𝐽𝑜+ 𝐿(𝜆) 1−𝑒−𝑡𝜆 𝑑𝑙𝑛𝜆∞−∞+𝑡𝜂𝑜 [7] 𝐺′ 𝜔 = 𝜔2𝜏21+𝜔2𝜏2𝐻 𝜏 𝑑𝑙𝑛𝜏∞−∞ [8] 𝐺" 𝜔 = 𝜔𝜏1+𝜔2𝜏2𝐻 𝜏 𝑑𝑙𝑛𝜏∞−∞ [9] 79 For our analysis, we opted to use the discrete approach. The error associated with creep-ringing was reduced to make the interconversion more effective, but materials with an elastic dominant response still resulted in significant error for G″. This error was determined to be less pronounced when tanδ of the material was close to 1. 80 APPENDIX C MATLAB CODE 81 ANALYZING INTERCONVERTED DATA %Statistical Analysis of Porcine Eye clear clc close all %parameters N = 6; df = 5; t = 2.571; freq_interval = [0.01592; 0.02522; 0.03998; 0.06336; 0.1004; 0.1592; 0.2522;... 0.3998; 0.6336; 1.004]; %Load the creep data creep10 =load('convert_eye_23_GA_discrete.txt'); creep11 =load('convert_eye_32_GA_discrete.txt');... creep12 =load('convert_eye_39_GA_discrete_new.txt'); creep13 =load('convert_eye_47_GA_discrete_new.txt');... creep14 =load('convert_eye_59_GA_discrete.txt'); creep15 =load('convert_eye_61_GA_discrete.txt'); freq1 = load('freq_eye_20_GA.txt'); freq2 = load('freq_eye_40_GA.txt'); %Organize G' and G" in terms of their discrete data points %G' for creep data c1 = [creep10(1,1), creep11(1,1), creep12(1,1), creep13(1,1), creep14(1,1), creep15(1,1)]; c2 = [creep10(2,1), creep11(2,1), creep12(2,1), creep13(2,1), creep14(2,1), creep15(2,1)]; c3 = [creep10(3,1), creep11(3,1), creep12(3,1), creep13(3,1), creep14(3,1), creep15(3,1)]; c4 = [creep10(4,1), creep11(4,1), creep12(4,1), creep13(4,1), creep14(4,1), creep15(4,1)]; c5 = [creep10(5,1), creep11(5,1), creep12(5,1), creep13(5,1), creep14(5,1), creep15(5,1)]; c6 = [creep10(6,1), creep11(6,1), creep12(6,1), creep13(6,1), creep14(6,1), creep15(6,1)]; c7 = [creep10(7,1), creep11(7,1), creep12(7,1), creep13(7,1), creep14(7,1), creep15(7,1)]; c8 = [creep10(8,1), creep11(8,1), creep12(8,1), creep13(8,1), creep14(8,1), creep15(8,1)]; c9 = [creep10(9,1), creep11(9,1), creep12(9,1), creep13(9,1), creep14(9,1), creep15(9,1)]; c10 = [creep10(10,1), creep11(10,1), creep12(10,1), creep13(10,1), creep14(10,1), creep15(10,1)]; %G" for creep data c_1 = [creep10(1,2), creep11(1,2), creep12(1,2), creep13(1,2), creep14(1,2), creep15(1,2)]; c_2 = [creep10(2,2), creep11(2,2), creep12(2,2), creep13(2,2), creep14(2,2), creep15(2,2)]; c_3 = [creep10(3,2), creep11(3,2), creep12(3,2), creep13(3,2), creep14(3,2), creep15(3,2)]; c_4 = [creep10(4,2), creep11(4,2), creep12(4,2), creep13(4,2), creep14(4,2), creep15(4,2)]; c_5 = [creep10(5,2), creep11(5,2), creep12(5,2), creep13(5,2), creep14(5,2), creep15(5,2)]; c_6 = [creep10(6,2), creep11(6,2), creep12(6,2), creep13(6,2), creep14(6,2), creep15(6,2)]; c_7 = [creep10(7,2), creep11(7,2), creep12(7,2), creep13(7,2), creep14(7,2), creep15(7,2)]; c_8 = [creep10(8,2), creep11(8,2), creep12(8,2), creep13(8,2), creep14(8,2), creep15(8,2)]; c_9 = [creep10(9,2), creep11(9,2), creep12(9,2), creep13(9,2), creep14(9,2), creep15(9,2)]; c_10 = [creep10(10,2), creep11(10,2), creep12(10,2), creep13(10,2), creep14(10,2), creep15(10,2)]; %Find the Mean of each data point for G' and G" %Mean of Creep G' MGc = [mean(c1); mean(c2); mean(c3); mean(c4); mean(c5); mean(c6); mean(c7); ... mean(c8); mean(c9); mean(c10)]; 82 %Mean of Creep G" MGGc = [mean(c_1); mean(c_2); mean(c_3); mean(c_4); mean(c_5); mean(c_6); ... mean(c_7); mean(c_8); mean(c_9); mean(c_10)]; % %% %est std. dev Y creep G' stdY_Gc = [std(c1); std(c2); std(c3); std(c4); std(c5); std(c6); std(c7); ... std(c8); std(c9); std(c10)]; %est std. dev Y creep G" stdY_GGc = [std(c_1); std(c_2); std(c_3); std(c_4); std(c_5); std(c_6); std(c_7); ... std(c_8); std(c_9); std(c_10)]; %est std. dev M creep G' stdM_Gc = [stdY_Gc(1,1)/sqrt(N); stdY_Gc(2,1)/sqrt(N); stdY_Gc(3,1)/sqrt(N); stdY_Gc(4,1)/sqrt(N); stdY_Gc(5,1)/sqrt(N); stdY_Gc(6,1)/sqrt(N); stdY_Gc(7,1)/sqrt(N); stdY_Gc(8,1)/sqrt(N); stdY_Gc(9,1)/sqrt(N);... stdY_Gc(10,1)/sqrt(N)]; %est std. dev M creep G" stdM_GGc = [stdY_GGc(1,1)/sqrt(N); stdY_GGc(2,1)/sqrt(N); stdY_GGc(3,1)/sqrt(N); stdY_GGc(4,1)/sqrt(N); stdY_GGc(5,1)/sqrt(N); stdY_GGc(6,1)/sqrt(N); stdY_GGc(7,1)/sqrt(N); stdY_GGc(8,1)/sqrt(N); stdY_GGc(9,1)/sqrt(N);... stdY_GGc(10,1)/sqrt(N)]; %Plot the mean plus 2 std dev. (95% CI) from the mean for creep G' and G" data size = 7; e = stdY_Gc; figure(1) %Plot of 95% CI mean creep with oscillation data loglog(freq_interval, MGc,'or', 'linewidth', 2) hold on plot(freq_interval(1:size), freq2(1:size,1), '*k','linewidth',4) errorbar(freq_interval,MGc, e, 'r') xlabel('frequency, [Hz]') ylabel('G'' [Pa]') legend('Mean Interconverted G''', 'Oscillation G''') title('Interconverted G'' vs. Oscillation G''') e = stdY_GGc; figure(2) %Plot of 95% CI mean creep with oscillation data loglog(freq_interval, MGGc,'sqb', 'linewidth', 2) hold on plot(freq_interval(1:size), freq2(1:size,2), '*k','linewidth',4) h = errorbar(freq_interval,MGGc, e, 'b') xlabel('frequency, [Hz]') ylabel('G" [Pa]') legend('Mean Interconverted G"', 'Oscillation G"') title('Interconverted G" vs. Oscillation G"') 83 IMAGE SEGMENTATION clear clc close all %Open the SEM image file; image=imread('Helix_4week_Post_Temp_004.tif'); %Initialize the variables col_count=0; ret_count=0; max=0; min=255; b=size(image,2); %Crop the parameter bar from the bottom of images image1(:,:)=image(1:833,1:b); figure(1) imshow(image1); title('original image'); %Adjust the image to remove 10% of the brightest pixels image1 =imadjust (image1, [0.0 0.9],[]); %Determine max and min gray in image for row = 1:size(image1,1) for col = 1:size(image1,2) if image1(row,col)>max max=image1(row,col); end if image1(row,col)<min min=image1(row,col); end end end %Set absolute threshold value threshold=0.6*max; %fully contrast the image diff=double(max-min); for row = 1:size(image1,1) for col = 1:size(image1,2) %normalize all pixels in image to 0-255 grayscale range image2(row,col)=(255/diff)*(image1(row,col)-min); end end %create all black and all white image, the white representing collagen for row = 1:size(image2,1) for col = 1:size(image2,2) if image2(row,col)>threshold 84 contrast_image(row,col)=255; col_count=col_count+1; else contrast_image(row,col)=0; ret_count=ret_count+1; end end end %Calculate the percent collagen percent_col=(col_count/(col_count + ret_count))*100 %Plot images figure(2) imshow(image1); title('adjusted image'); figure(3) imshow(contrast_image); title('cologen contrast'); 85 CREEP RINGING AVERAGING %Averaging Creep data Method for Vitreous clear clc close all %Load creep data with ringing included creep62= load('creep_eye_62_GA.txt'); %Show the creep ringing figure(1) plot(creep62(:,2), creep62(:,1), 'ok') %Access the structure. Specifically the DataIndex of all the Peaks and %valleys of the ringing k = 0; for i = 1: 4 %Index changes depending on the number of peaks/valleys k = k + 1; y(k,1) = creep_peak(i).DataIndex; z(k,1) = creep_valley(i).DataIndex; end %Find the compliance values and respective times for the peaks "x" and %valleys "z" x = creep62(y,:); w = creep62(z,:); %Average the peaks and valley compliance values and times u = 0; for j = 1: 4 % the data index "4" indicates there were 4 peaks & 4 valleys u = u + 1; c_t_avg(u,1) = (x(j,1) + w(j,1))./2; c_t_avg(u,2) = (x(j,2) + w(j,2))./2; end %Plot the resulting non-ringing data region figure(2) plot(c_t_avg(:,2), c_t_avg(:,1), 'k') 86 GAP CORRECTIONS %Curve fitting the viscosity data to find delta %09/29/11 close clc clear %Average viscosities of the 3 different geometry types at 4 different gaps cross = [0.677; 0.733; 0.765; 0.818]; %cross-hatch geometry cleat6 = [0.671; 0.719; 0.806; 0.768]; %cleat geometry (0.6 x0.45 x 0.45) cleat9 = [0.707; 0.659; 0.728; 0.733]; %cleat geometry (0.9 x0.6 x 0.6) cleat6_1 = [0.653; 0.758; 0.812; 0.93]; %cleat geometry (0.6 x0.6 x0.6) %Measured gap separation for each test gap = [500; 1000; 1500; 2000]; %Initial guess delta0 = [0.1]; options = optimset('Display','iter','MaxFunEvals',2000,'MaxIter',500,'LargeScale','off'); %Solve for the variable...delta = gap heigth adjustment delta(1) = lsqcurvefit(@myfun,delta0,gap,cross) %delta for x-hatch delta(2) = lsqcurvefit(@myfun,delta0,gap,cleat6)%delta for 0.6mm cleat delta(3) = lsqcurvefit(@myfun,delta0,gap,cleat9)%delta for 0.9mm cleat delta(4) = lsqcurvefit(@myfun,delta0,gap,cleat6_1)%delta for the 0.6 x 0.6 mm cleat %Plot the viscosity ratio vs. the gap measured figure(1) x_hatch_geom = myfun(delta(1),gap); cleat_geom1 = myfun(delta(2),gap); cleat_geom2 = myfun(delta(3),gap); cleat_geom3 = myfun(delta(4),gap); hold on grid on %Plot the relation between gap and the output of the myfun function (i.e. %n_meas/n_true) plot(gap,x_hatch_geom,'bl','linewidth',1) %plot(gap,cleat_geom1,'r','linewidth',2) plot(gap,cleat_geom2,'g','linewidth',3) %plot(gap,cleat_geom3,'k','linewidth',2) legend('C1 geometry','C2 geometry') xlabel('gap [μm]') ylabel('\eta_m_e_a_s / \eta_t_r_u_e') title('Gap correction factors') 87 CALCULATING AND COMPARING TANδ %Tandelta Analysis of Porcine Eyes close clear clc %parameters N = 6; df = 5; t = 2.571; freq_interval = [0.01592; 0.02522; 0.03998; 0.06336; 0.1004; 0.1592; 0.2522]; %Load the creep data %5-day creep10 =load('freq_eye_37_GA.txt'); creep11 =load('freq_eye_44_GA.txt');... creep12 =load('freq_eye_46_GA.txt'); creep13 =load('freq_eye_62_GA.txt');... creep14 =load('freq_eye_63_GA.txt'); creep15 =load('freq_eye_65_GA.txt'); %4-week creep16 =load('freq_eye_23_GA.txt'); creep17 =load('freq_eye_32_GA.txt');... creep18 =load('freq_eye_39_GA.txt'); creep19 =load('freq_eye_47_GA.txt');... creep20 =load('freq_eye_59_GA.txt'); creep21 =load('freq_eye_61_GA.txt'); %2-month creep22 =load('freq_eye_50_GA.txt'); creep23 =load('freq_eye_51_GA.txt');... creep24 =load('freq_eye_52_GA.txt'); creep25 =load('freq_eye_55_GA.txt');... creep26 =load('freq_eye_56_GA.txt'); %Organize G' and G" in terms of their discrete data points %G' for creep data %5-day c1 = [creep10(1,1), creep11(1,1), creep12(1,1), creep13(1,1), creep14(1,1), creep15(1,1)]; c2 = [creep10(2,1), creep11(2,1), creep12(2,1), creep13(2,1), creep14(2,1), creep15(2,1)]; c3 = [creep10(3,1), creep11(3,1), creep12(3,1), creep13(3,1), creep14(3,1), creep15(3,1)]; c4 = [creep10(4,1), creep11(4,1), creep12(4,1), creep13(4,1), creep14(4,1), creep15(4,1)]; c5 = [creep10(5,1), creep11(5,1), creep12(5,1), creep13(5,1), creep14(5,1), creep15(5,1)]; c6 = [creep10(6,1), creep11(6,1), creep12(6,1), creep13(6,1), creep14(6,1), creep15(6,1)]; c7 = [creep10(7,1), creep11(7,1), creep12(7,1), creep13(7,1), creep14(7,1), creep15(7,1)]; %4-week c01 = [creep16(1,1), creep17(1,1), creep18(1,1), creep19(1,1), creep20(1,1), creep21(1,1)]; c02 = [creep16(2,1), creep17(2,1), creep18(2,1), creep19(2,1), creep20(2,1), creep21(2,1)]; c03 = [creep16(3,1), creep17(3,1), creep18(3,1), creep19(3,1), creep20(3,1), creep21(3,1)]; c04 = [creep16(4,1), creep17(4,1), creep18(4,1), creep19(4,1), creep20(4,1), creep21(4,1)]; c05 = [creep16(5,1), creep17(5,1), creep18(5,1), creep19(5,1), creep20(5,1), creep21(5,1)]; c06 = [creep16(6,1), creep17(6,1), creep18(6,1), creep19(6,1), creep20(6,1), creep21(6,1)]; c07 = [creep16(7,1), creep17(7,1), creep18(7,1), creep19(7,1), creep20(7,1), creep21(7,1)]; %2-month c001 = [creep22(1,1), creep23(1,1), creep24(1,1), creep25(1,1), creep26(1,1)]; c002 = [creep22(2,1), creep23(2,1), creep24(2,1), creep25(2,1), creep26(2,1)]; c003 = [creep22(3,1), creep23(3,1), creep24(3,1), creep25(3,1), creep26(3,1)]; c004 = [creep22(4,1), creep23(4,1), creep24(4,1), creep25(4,1), creep26(4,1)]; 88 c005 = [creep22(5,1), creep23(5,1), creep24(5,1), creep25(5,1), creep26(5,1)]; c006 = [creep22(6,1), creep23(6,1), creep24(6,1), creep25(6,1), creep26(6,1)]; c007 = [creep22(7,1), creep23(7,1), creep24(7,1), creep25(7,1), creep26(7,1)]; %G" for creep data %5-day c_1 = [creep10(1,2), creep11(1,2), creep12(1,2), creep13(1,2), creep14(1,2), creep15(1,2)]; c_2 = [creep10(2,2), creep11(2,2), creep12(2,2), creep13(2,2), creep14(2,2), creep15(2,2)]; c_3 = [creep10(3,2), creep11(3,2), creep12(3,2), creep13(3,2), creep14(3,2), creep15(3,2)]; c_4 = [creep10(4,2), creep11(4,2), creep12(4,2), creep13(4,2), creep14(4,2), creep15(4,2)]; c_5 = [creep10(5,2), creep11(5,2), creep12(5,2), creep13(5,2), creep14(5,2), creep15(5,2)]; c_6 = [creep10(6,2), creep11(6,2), creep12(6,2), creep13(6,2), creep14(6,2), creep15(6,2)]; c_7 = [creep10(7,2), creep11(7,2), creep12(7,2), creep13(7,2), creep14(7,2), creep15(7,2)]; %4week c_01 = [creep16(1,2), creep17(1,2), creep18(1,2), creep19(1,2), creep20(1,2), creep21(1,2)]; c_02 = [creep16(2,2), creep17(2,2), creep18(2,2), creep19(2,2), creep20(2,2), creep21(2,2)]; c_03 = [creep16(3,2), creep17(3,2), creep18(3,2), creep19(3,2), creep20(3,2), creep21(3,2)]; c_04 = [creep16(4,2), creep17(4,2), creep18(4,2), creep19(4,2), creep20(4,2), creep21(4,2)]; c_05 = [creep16(5,2), creep17(5,2), creep18(5,2), creep19(5,2), creep20(5,2), creep21(5,2)]; c_06 = [creep16(6,2), creep17(6,2), creep18(6,2), creep19(6,2), creep20(6,2), creep21(6,2)]; c_07 = [creep16(7,2), creep17(7,2), creep18(7,2), creep19(7,2), creep20(7,2), creep21(7,2)]; %2-month c_001 = [creep22(1,2), creep23(1,2), creep24(1,2), creep25(1,2), creep26(1,2)]; c_002 = [creep22(2,2), creep23(2,2), creep24(2,2), creep25(2,2), creep26(2,2)]; c_003 = [creep22(3,2), creep23(3,2), creep24(3,2), creep25(3,2), creep26(3,2)]; c_004 = [creep22(4,2), creep23(4,2), creep24(4,2), creep25(4,2), creep26(4,2)]; c_005 = [creep22(5,2), creep23(5,2), creep24(5,2), creep25(5,2), creep26(5,2)]; c_006 = [creep22(6,2), creep23(6,2), creep24(6,2), creep25(6,2), creep26(6,2)]; c_007 = [creep22(7,2), creep23(7,2), creep24(7,2), creep25(7,2), creep26(7,2)]; %Find the Mean of each data point for G' and G" %Mean of Creep G' 5-day MGc = [mean(c1); mean(c2); mean(c3); mean(c4); mean(c5); mean(c6); mean(c7)]; %Mean of Creep G' 4-week MGc0 = [mean(c01); mean(c02); mean(c03); mean(c04); mean(c05); mean(c06); mean(c07)]; %Mean of Creep G' 2-month MGc00 = [mean(c001); mean(c002); mean(c003); mean(c004); mean(c005); mean(c006); mean(c007)]; %Mean of Creep G" 5-day MGGc = [mean(c_1); mean(c_2); mean(c_3); mean(c_4); mean(c_5); mean(c_6); ... mean(c_7)]; %Mean of Creep G" 4-week MGGc0 = [mean(c_01); mean(c_02); mean(c_03); mean(c_04); mean(c_05); mean(c_06); ... mean(c_07)]; %Mean of Creep G" 4-week MGGc00 = [mean(c_001); mean(c_002); mean(c_003); mean(c_004); mean(c_005); mean(c_006); ... mean(c_007)]; 89 %Calculate the Tandelta at each frequency tandelt_5day = MGGc./MGc; tandelt_4week = MGGc0./MGc0; tandelt_2month = MGGc00./MGc00; %Average the Tandeltas avg_tandelt_5d = mean(tandelt_5day) avg_tandelt_4wk = mean (tandelt_4week) avg_tandelt_2mo = mean (tandelt_2month) 90 APPENDIX D DATA FOR CHAPTER 1 91 Table 6: Interconverted creep data for porcine vitreous Porcine Eye Data 3-5-day 4-week 2-month freq G' [Pa] G" [Pa] G' [Pa] G" [Pa] G' [Pa] G" [Pa] 1 11.5 5.411 10.73 8.23 2.378 1.742 2 12.54 6.694 14.15 9.024 2.905 2.01 3 13.7 8.681 17.91 8.457 3.445 2.229 4 15.04 11.82 20.8 6.735 3.854 2.538 5 17.07 16.87 22.44 4.825 4.142 3.197 6 21.08 24.52 23.21 3.335 4.454 4.457 7 29.47 34.44 23.55 2.375 5.03 6.577 8 44.65 43.57 23.71 1.874 6.3 9.818 9 65.19 46.16 23.83 1.758 8.99 14.24 10 84.12 39.98 24 1.988 13.93 19.34 1 16.42 8.672 4.715 3.288 2.434 0.9788 2 17.85 10.49 5.548 3.567 2.497 1.187 3 20.4 13.85 6.151 4.049 2.58 1.641 4 25.36 18.1 6.579 5.131 2.752 2.424 5 33.44 21.16 7.062 7.201 3.146 3.642 6 42.84 20.6 7.992 10.69 3.998 5.362 7 50.27 16.79 10.12 16.08 5.6 7.452 8 54.57 12.27 14.9 23.54 7.966 9.582 9 56.68 8.734 24.45 31.75 10.73 11.78 10 57.8 6.519 39.45 36.8 13.97 14.66 1 42.16 20.6 3.245 1.451 2.155 1.018 2 46.16 27.2 3.448 1.601 2.559 1.105 3 54.32 36.87 3.642 2.037 3.008 1.034 4 69.27 46.64 3.974 2.847 3.35 0.8302 5 90.02 50.82 4.684 4.084 3.542 0.6138 6 109.8 46.85 6.147 5.629 3.634 0.4586 7 123.5 39.39 8.681 6.915 3.678 0.3804 8 131.9 33.99 11.9 7.064 3.71 0.3761 9 139 32.53 14.67 5.927 3.753 0.4428 10 148.3 33.51 16.36 4.307 3.835 0.5765 1 15 8.979 4.735 2.504 2.095 1.552 2 17.97 10.8 5.326 2.843 2.692 1.903 3 22.32 12.03 5.806 3.322 3.543 2.048 4 27.07 11.76 6.105 4.236 4.389 1.83 5 31.11 10.38 6.293 5.952 4.969 1.395 6 34.27 8.583 6.489 8.911 5.273 0.9736 7 36.59 6.592 6.86 13.76 5.411 0.6631 92 Porcine Eye Data 3-5-day 4-week 2-month freq G' [Pa] G" [Pa] G' [Pa] G" [Pa] G' [Pa] G" [Pa] 8 38.03 4.688 7.723 21.47 5.474 0.4667 9 38.79 3.155 9.763 33.42 5.511 0.361 10 39.14 2.055 14.31 51.3 5.551 0.3227 1 14.95 5.042 7.793 4.612 1.782 1.571 2 15.31 6.295 9.066 5.07 2.121 1.623 3 15.94 8.822 10.21 5.545 2.329 1.867 4 17.35 12.99 10.98 6.478 2.498 2.439 5 20.48 19.07 11.49 8.482 2.727 3.474 6 26.8 26.76 12.02 12.19 3.155 5.157 7 37.84 34.34 13.02 18.41 4.058 7.732 8 53.56 38.22 15.34 28.28 5.977 11.35 9 69.95 35.39 20.75 43.03 9.627 15.72 10 81.89 27.73 32.54 63.01 15.28 20.03 1 20.13 15.6 6.602 5.953 2 25.48 19.4 9.036 6.774 3 33.85 22.09 11.95 6.654 4 43.46 21.16 14.4 5.505 5 50.98 16.99 15.89 4.016 6 55.28 12.14 16.62 2.759 7 57.3 8.255 16.94 1.895 8 58.18 5.657 17.07 1.383 9 58.57 4.141 17.14 1.153 10 58.81 3.474 17.2 1.166 Table 6: Continued 93 Table 7: Force oscillation data from porcine vitreous Porcine Eye Data 3-5-day 4-week freq G' [Pa] G" [Pa] G' [Pa] G" [Pa] 1 10.56 5.676 6.463 2.62 2 14.76 8.175 4.883 2.03 3 19.68 9.595 4.565 2.218 4 25.09 10.7 4.623 2.615 5 27.64 10.93 4.913 3.297 6 32.24 10.62 5.318 4.13 7 35.92 10.56 5.926 5.421 1 20.01 7.713 2 21.04 5.477 3 16.11 5.491 4 18.01 5.151 5 19.55 5.926 6 20.82 6.367 7 21.87 7.218 94 Table 8: Fresh vs. fixed interconversion comparison for sheep eyes Sheep Eye Data Fixed Fresh freq G' [Pa] G" [Pa] G' [Pa] G" [Pa] 1 47.02 43.28 16.16 7.287 2 61.91 48 17.65 8.721 3 75.51 52.24 20.05 10.77 4 89.34 59.25 23.25 12.77 5 106.4 69.34 26.38 14.72 6 129.2 81 28.95 17.84 7 159.2 89.91 31.63 23.51 8 191.9 90.19 35.66 32.52 9 217.3 84.02 41.92 45.13 10 232.1 81.31 50.47 62.39 11 239.5 90.43 62.38 87.51 1 35.41 38.8 2 48.82 46.08 3 62.96 52.65 4 78.63 60.37 5 96.85 68.16 6 114.9 75.73 7 131.2 88.11 8 150.4 111.5 9 183 147.1 10 241.5 185.6 11 326.5 203.5 Table 9: Forced oscillaiton and interconverted agarose data Agarose Forced Oscillation Interconverted freq G' [Pa] G" [Pa] G' [Pa] G" [Pa] 1 1197 122.7 1218 100.6 2 1241 105.8 1244 99.41 3 1276 97.25 1270 103.9 4 1308 90.94 1304 111 5 1335 85.37 1344 111.1 6 1358 85.32 1381 101.6 7 1386 84.17 1408 90.38 8 1403 75.54 1431 83.72 95 Agarose Forced Oscillation Interconverted freq G' [Pa] G" [Pa] G' [Pa] G" [Pa] 9 1431 74.45 1456 78.99 10 1450 75.57 1482 70.27 11 1470 77.82 1502 57.88 12 1493 78.39 1515 46.52 1 1103 84.02 1033 101.1 2 1133 80.08 1059 97.44 3 1159 77.56 1084 99.8 4 1184 75.03 1115 104.4 5 1206 73.26 1151 103.2 6 1228 71.1 1182 96.33 7 1247 68.99 1208 90.82 8 1267 67.33 1234 88.98 9 1286 65.88 1263 86.58 10 1305 64.7 1293 77.83 11 1325 65.32 1318 61.79 12 1344 67.44 1333 43.98 1 962.3 86.6 1224 106.2 2 1001 77.95 1250 103.8 3 1028 73.97 1277 107.8 4 1053 70.61 1311 112.8 5 1075 67.12 1348 112.7 6 1094 65.09 1383 109.3 7 1114 63.25 1417 105.2 8 1131 59.46 1450 98.05 9 1150 57.95 1478 88.1 10 1165 57.2 1503 78.47 11 1181 58.2 1526 69.39 12 1199 59.1 1547 57.68 1 1176 96.54 989.8 95.38 2 1208 97.08 1016 94.23 3 1236 95.31 1041 97.23 4 1264 92.33 1072 101.9 5 1289 90.57 1107 101.4 6 1313 91.75 1138 95.67 7 1337 89.16 1164 90.76 8 1357 81.97 1190 88.04 9 1377 83.46 1217 83.14 10 1400 80.47 1239 74.83 Table 9: Continued 96 Agarose Forced Oscillation Interconverted freq G' [Pa] G" [Pa] G' [Pa] G" [Pa] 11 1420 78.2 1253 69.02 12 1441 76.11 1260 72.36 1 1258 90.25 1083 120.5 2 1290 87.51 1114 115 3 1319 84.57 1143 117.4 4 1347 81.19 1178 124.7 5 1370 77.62 1222 126.3 6 1392 78.31 1262 118.9 7 1417 77.6 1295 111.3 8 1434 70.36 1326 108.5 9 1458 68.71 1362 104.7 10 1477 69.6 1399 91.82 11 1496 70.93 1426 71.48 12 1517 71.55 1443 50.77 1 985 92.67 994.7 83.79 2 1019 86.28 1018 83.25 3 1049 82.15 1041 85.71 4 1076 77.64 1067 91.56 5 1101 74.29 1100 93.77 6 1122 72.72 1131 87.71 7 1142 69.95 1156 78.65 8 1164 67.04 1175 72.7 9 1181 65.93 1194 69.76 10 1197 62.52 1213 68.05 11 1216 65.25 1230 68.69 12 1230 62.22 1250 71.93 Table 10: Forced oscillation and interconversion data for PS Polystyrene-Toluene Forced Oscillation Interconverted freq G' [Pa] G" [Pa] G' [Pa] G" [Pa] 1 3413 1863 2369 1348 2 4102 2124 2698 1421 3 4645 2350 3019 1631 4 5389 2719 3470 1977 5 6146 3125 4113 2333 Table 9: Continued 97 Polystyrene-Toluene Forced Oscillation Interconverted freq G' [Pa] G" [Pa] G' [Pa] G" [Pa] 6 6951 3595 4834 2604 7 7938 4181 5510 2911 8 9358 5135 6225 3418 9 10660 5991 7132 4109 10 12180 7081 8194 4905 11 13880 8522 9295 5967 12 16700 10790 10550 7593 13 18970 12960 12220 10010 14 22760 16570 14750 13510 15 26240 20480 19170 18120 16 31770 26250 26790 22560 1 3051 1740 3262 1762 2 3698 1973 3845 1829 3 4356 2312 4318 1874 4 4889 2538 4729 2064 5 5815 3060 5225 2444 6 6615 3463 5888 2939 7 7522 3939 6680 3522 8 8599 4638 7631 4282 9 9802 5417 8877 5187 10 11460 6632 10350 6076 11 13110 7777 11720 7061 12 14370 9173 12840 8587 13 16740 11450 13630 11240 14 19630 14340 14100 15880 15 23370 18190 14330 23760 16 28560 23380 14430 36710 1 2894 1660 3568 1872 2 3519 1923 4105 2028 3 4136 2213 4619 2271 4 4692 2466 5242 2666 5 5464 2933 6071 3099 6 6249 3366 6987 3462 7 7189 3889 7842 3918 8 8235 4560 8778 4714 9 9650 5535 10120 5828 10 11050 6481 11950 6913 11 12690 7862 13800 7784 Table 10: Continued 98 Polystyrene-Toluene Forced Oscillation Interconverted freq G' [Pa] G" [Pa] G' [Pa] G" [Pa] 12 14570 9438 15130 8956 13 16960 11770 15850 11370 14 19750 14560 16200 15980 15 23360 18270 16390 23970 16 28430 23200 16580 37110 1 2925 1673 3916 2040 2 3486 1899 4471 2170 3 4119 2164 5000 2439 4 4697 2424 5675 2877 5 5411 2763 6571 3334 6 6209 3245 7536 3730 7 7183 3790 8458 4261 8 8151 4358 9519 5131 9 9138 5042 10980 6259 10 10510 6095 12810 7408 11 12140 7427 14690 8556 12 14090 9045 16240 10080 13 16460 11290 17220 12790 14 19360 13980 17720 17830 15 23100 17770 17940 26560 16 27040 22220 18030 40980 1 2568 1500 3353 1911 2 314