Computational modeling of mechanical anisotropy in the cornea and sclera.
ABSTRACT To determine the biomechanical deformation of the cornea resulting from tissue cutting and removal by use of a new computational model and to investigate the effect of mechanical anisotrophy resulting from the fibrillar architecture.
Department of Mechanical Engineering, Stanford University, Stanford, California, USA.
A mathematical model for a typical lamella that explicitly accounts for the strain energy of the collagen fibrils, extrafibrillar matrix, and proteoglycan cross-linking was developed. A stromal model was then obtained by generalized averaging of the lamella properties through the stromal thickness, taking into account the preferred orientations of the collagen fibrils, which were obtained from x-ray scattering data.
The model was used to predict astigmatism induced by a tunnel incision in the sclera, such as is used for cataract extraction and intraocular lens implantation. The amount of induced cylinder was in good agreement with published clinical data. Results show it is important for the model to incorporate preexisting corneal physiological stress caused by intraocular pressure.
The mathematical model described appears to provide a framework for further development, capturing the essential features of mechanical anisotropy of the cornea. The tunnel incision simulation indicated the importance of the anisotropy in this case.
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ABSTRACT: The interlacing and cross angles between the collagen lamellae within the human corneal stroma were studied by means of scanning electron microscopy (SEM). For SEM, cells and noncollagenous extracellular matrix were removed with 10% sodium hydroxide. Transmission electron microscopy (TEM) preparations were performed according to standard procedures. The interlacing of lamellae was studied within the limbal, paracentral, and central regions of five different layers. The cross angles between the longitudinal axes of adjacent lamellae were measured. The distribution of these angles within defined layers and regions was compared. Special attention was paid to the interlacing of the lamellae. Lamellae split in an anteroposterior direction as well as horizontally into branches and are interlaced by crossing the fissures between the branches. Smaller lamellae cross through clefts of neighboring lamellae. The cross angles show a high variability of 1 degree - 90 degrees. With the exception of the limbal region of the layer adjacent to Descemet's membrane, the distribution of cross angles is similar. A frequent occurrence of cross angles <30 degrees (68%) in this limbal layer can be explained by a pseudocircular orientation (ligamentum circulare corneae) of the lamellae. The present study shows that the three-dimensional organization of the collagen lamellae is characterized by a greater extent of lamellar interlacing than has been assumed until now.Cornea 09/1998; 17(5):537-43. · 1.75 Impact Factor
Chapter: Structural MaterialsCVD of Nonmetals, 12/2007: pages 321 - 366; , ISBN: 9783527614813
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ABSTRACT: To determine the magnitude and duration of change on the horizontal and vertical meridians of the cornea after five different incisions for cataract. Retrospective comparative interventional study of five commonly used incisions for cataract surgery: extracapsular cataract extraction (ECCE), 6-mm superior scleral tunnel (6Sup), 3-mm superior scleral tunnel (3Sup), 3-mm temporal scleral tunnel (3Temp), and 3-mm temporal corneal incision (3Cor). A total of 662 cases with preoperative regular astigmatism, measured with keratometry. The mean net change on each meridian was computed at 1 day, 1 week, 2 weeks, 1 month, 1.5 months, 2 months, 4 months, 6 months, and 12 months and at succeeding 6-month intervals after surgery. Best-fit parameters were calculated for the observed changes in the horizontal and vertical keratometry values after each incision. To determine when the cornea stabilized, average change on the horizontal and vertical meridians was compared with an estimate of the accuracy of keratometry measurement. The pattern of change on the horizontal and vertical meridians and time for the cornea to stabilize after each incision. The initial and final net changes after a superior incision decrease with length. A sigmoid equation describes the course of the changes on the horizontal and vertical meridians after the superior incisions. The changes after the temporal incisions depend linearly on time after surgery. Considering the uncertainty of keratometry, the corneal meridians stabilized 4.5 months after ECCE, 1.2 months after 6Sup, and 0.3 months after 3Sup. No significant change was detected on the horizontal and vertical meridians after 3Temp and 3Cor. The magnitude and the duration of keratometric change on the horizontal and vertical meridians of the cornea depend on the length and location of the incision. Within the limits of measurement error, no significant change in corneal curvature was detected after either small temporal incision.Ophthalmology 10/2003; 110(9):1807-13. · 5.56 Impact Factor