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Research Papers

# Experimental Surface Strain Mapping of Porcine Peripapillary Sclera Due to Elevations of Intraocular Pressure

[+] Author and Article Information
Michaël J. Girard

Department of Biomedical Engineering, Tulane University, 6823 St. Charles Avenue, New Orleans, LA 70118; Ocular Biomechanics Laboratory,  Devers Eye Institute, Legacy Health System, 1225 NE 2nd Avenue, Portland, OR 97232mgirard@deverseye.org, michael.girard@mac.com

J. Crawford Downs

Ocular Biomechanics Laboratory,  Devers Eye Institute, Legacy Health System, 1225 NE 2nd Avenue, Portland, OR 97232

Claude F. Burgoyne

Optic Nerve Head Research Laboratory,  Devers Eye Institute, Legacy Health System, 1225 NE 2nd Avenue, Portland, OR 97232;

J.-K. Francis Suh

Moksan BioEng LLC, 605 Middle Street Unit #25, Braintree, MA 02184

J Biomech Eng 130(4), 041017 (Jun 20, 2008) (6 pages) doi:10.1115/1.2948416 History: Received July 22, 2007; Revised April 18, 2008; Published June 20, 2008

## Abstract

To experimentally characterize 2D surface mapping of the deformation pattern of porcine peripapillary sclera following acute elevations of intraocular pressure (IOP) from $5mmHgto45mmHg$. Four porcine eyes were obtained within $48h$ postmortem and dissected to the sclera. After the anterior chamber was removed, each posterior scleral shell was individually mounted at the equator on a custom-built pressurization device, which internally pressurized the scleral samples with isotonic saline at $22°C$. Black polystyrene microspheres ($10μm$ in diameter) were randomly scattered and attached to the scleral surface. IOP was incrementally increased from $5mmHgto45mmHg$$(±0.15mmHg)$, and the surface deformation of the peripapillary sclera immediately adjacent to the dural insertion was optically tracked at a resolution of $2μm∕pixel$ one quadrant at a time, for each of four quadrants (superior, nasal, inferior, and temporal). The 2D displacement data of the microsphere markers were extracted using the optical flow equation, smoothed by weighting function interpolation, and converted to the corresponding Lagrangian finite surface strain. In all four quadrants of each eye, the principal strain was highest and primarily circumferential immediately adjacent to the scleral canal. Average maximum Lagrangian strain across all quadrants for all eyes was $0.013±0.005$ from $5mmHgto10mmHg$, $0.014±0.004$ from $10mmHgto30mmHg$ and $0.004±0.001$ from $30mmHgto45mmHg$, demonstrating the nonlinearity in the IOP-strain relationship. For each scleral shell, the observed surface strain mapping implied that the scleral stiffness was relatively low between $5mmHg$ and $10mmHg$, but dramatically increased for each IOP elevation increment beyond $10mmHg$. Peripapillary deformation following an acute IOP elevation may be governed by the underlying scleral collagen microstructure and is likely in the high-stiffness region of the scleral stress-strain curve when IOP is above $10mmHg$.

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## Figures

Figure 1

Schematic showing a cross section of the custom-built pressurization apparatus. The posterior scleral shell was first mounted onto the plastic ring, and then clamped at the equator by moving the vertical stage toward the clamping stage. The saline outflow was interrupted after saline filled the posterior shell cavity and IOP reached 5mmHg. The scleral surface was imaged as IOP was increased from 5mmHgto45mmHg with an increment of 1mmHg.

Figure 2

(a) Diagram of the posterior scleral shell of a left eye (OS) showing the position of the four fields of view within which 2D scleral deformation patterns were determined. Each field of view is 4×4mm2 with a single image resolution of 2μm∕pixel. (b) Image of a nasal quadrant with microsphere markers present on the surface of the shell and a magnified view of three microspheres showing their contours and centroids.

Figure 4

Experimental displacement field for a 4×4mm2 location at the surface of a spherical rubber balloon. The microscope head was oriented perpendicular to the balloon surface and the displacement field was generated for a pressure ranging from 70mmHgto80mmHg.

Figure 5

Principal direction associated with maximum principal strain for a porcine scleral shell (OS) due to an IOP increase from 10mmHgto30mmHg. All four porcine eyes that were tested showed the same specific patterns, for all four quadrants and for all IOP ranges (i.e., 5–10mmHg, 10–30mmHg, and 30–45mmHg).

Figure 6

Maximum principal strain magnitude for a porcine scleral shell (OS) due to an IOP increase from 10mmHgto30mmHg. All four porcine eyes that were tested showed the same specific patterns, for all four quadrants and for all IOP ranges (i.e., 5–10mmHg, 10–30mmHg, and 30–45mmHg).

Figure 7

Mean maximum increase of the maximum principal strain as a function of IOP for each of the four porcine eyes, showing the high degree of nonlinearity in the response. For each eye, means were calculated for all four quadrants pooled together. As IOP increases, porcine sclera becomes considerably stiffer.

Figure 3

The optical flow displacement vector was used as an initial guess to derive the true displacement vector. The steps were as follows and were repeated for each 1mmHg IOP increase: (1) The coordinates of the particle centroids were determined on the first image. (2) The optical flow algorithm was executed to derive the predicted displacements. (3) For each particle, the optical flow displacement vector was added to the particle centroid coordinates, and a two pixel diameter search area was created. (4) The matching particle centroid on the second image was found in the search area. (5) For each particle, subtracted centroid coordinates yielded the true displacement vector.

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