NEUROSCIENTIST USES MECHANICAL EVENT SIMULATION SOFTWARE TO LEARN MORE ABOUT EYE DEVELOPMENT

Eye examinations of children have indicated that critical changes occur in eyesight over the first eight years of life. Using Mechanical Event Simulation software from Pittsburgh-based Algor, Inc., Dr. Alan Springer at the New York Medical College in Valhalla, New York created a virtual biomechanical model of retinal development. He believes that a greater understanding of early eye development could lead to advances in the treatment of eye diseases and abnormalities.

April 30, 1999, Pittsburgh, Pennsylvania -- At this very moment, the sophisticated design of your eyes is enabling you to read these words. The geometric shape of each part of your eye and the correct arrangement of cells make the miracle of sight possible. Neuroscientist Alan Springer, Ph.D., at the New York Medical College in Valhalla, New York is studying how the shape of important eye tissues and the arrangement of light-sensing cells develop. He has created a virtual biomechanical model of the development of a key area of the eye, called the fovea, using the Mechanical Event Simulation software of Pittsburgh-based Algor, Inc.

The virtual biomechanical model supports Dr. Springer's hypothesis that eye growth and stretching of tissue causes cells to passively assume the shape and distribution necessary for good vision. A greater understanding of eye development could lead to unimaginable advances in the treatment of eye diseases and abnormalities.

Focusing on a Small but Important Part of the Retina
As light enters your eye, a lens directs the light onto the retina, the interior back surface of your eye. The fovea, a small region in the center of the retina, contains a higher density of light-sensing photoreceptors than in the surrounding retina, thus providing high visual acuity. Dr. Springer’s research focuses on how photoreceptors become concentrated in the fovea when a newborn's retina contains an even layer of photoreceptors. His virtual biomechanical model simulates foveal development and supports Dr. Springer's hypothesis that eye growth and retinal stretch cause cells to passively rearrange during the development of the human fovea.

Vision Impairment Linked to Improper Eye Development
Scientists believe that two vision disorders may be related to improper eye growth. A recent study of induced myopia (near-sightedness) by a colleague of Dr. Springer’s (Dr. Troilo) concluded that myopic eyes are larger and have a higher density of photoreceptors in the fovea than normal eyes. Strabismus, a disorder of the eye in which both eyes cannot fixate on the same point at the same time, is believed by Dr. Springer to be caused by uneven rates of eye growth. The link between eye growth and strabismus is supported by experiments in animals in which one eye is enlarged; not only does strabismus result in some of these experiments, but also the fovea is located differently in each eye. These results suggest that there may be a connection between eye growth, the development of the fovea and strabismus. A greater understanding of the factors involved in eye development could have a profound effect on the treatment of these disorders.

Medical researchers have observed the changes that take place in the retina during eye development. The retina consists of an outer layer of photoreceptors and an inner layer consisting of nerve cells (ganglion and inner nuclear cells). The photoreceptor layer is initially one cell thick. At the beginning of an unborn child's third trimester, the inner retinal layer, in the area that will become the fovea, is thicker than the surrounding retina (Figure 1A). Between the third trimester and about five to eight years of age, retinal cells in the inner layer move centrifugally away from the center of the fovea, resulting in a cone-shaped pit (Figure 1B). The pit starts as a mere shallow notch and then grows larger over time. This movement removes cells that presumably obstruct light from impinging on the underlying photoreceptors.

At the same time, photoreceptors move centripetally toward the center of the fovea. This centripetal movement results in a high number of photoreceptors arranged in a multilayered mass at the center of the fovea (Figure 1C). In addition to observing cell movement, scientists have noticed that the photoreceptors in the foveal region are thinner and more elongated than those in the peripheral retina.

Figure 1: A. At the beginning of an unborn child's third trimester, a thick spot develops in the part of the retina that will become the fovea. B. Between the third trimester and about five to eight years of age, cells in the inner layer of the retina move centrifugally away from the center of the fovea, resulting in a conical-shaped pit. C. The pit starts as a mere notch and then grows larger over time. At the same time, photoreceptors move centripetally, toward the center of the fovea, resulting in a high number of photoreceptors, arranged in a multilayered mass at the center of the fovea.

Although medical researchers and doctors have observed the changes that take place, they have not come to a consensus on how or why the changes come about. Possible explanations could relate to genetics, biochemistry or the active movement of cells during eye development. Dr. Springer believes that the retina stretches like an inflating balloon as the eye grows. The formation of the fovea results from active eye growth and the ensuing passive stretching of the retina. In addition to explaining the cell movements that scientists observe, the theory that the retina stretches as the eye grows predicts the differences in the shapes of photoreceptors in the fovea and the peripheral retina.

Modeling Eye Tissue
Eye growth takes place over the course of about eight years. Because of the length of time involved, eye growth research is not amenable to experiments with real tissues. Algor's Mechanical Event Simulation software offered the opportunity to isolate the biomechanics of eye growth and investigate that topic in a short amount of time.

Dr. Springer was concerned with how the shape of the fovea changes over time (displacement). Graphical representations of the displaced shapes generated from his simulations could be compared to the changes in shape that researchers have observed in human eyes at various stages of development. Stress results were not as useful. Usually, engineers are interested in how stress values from an analysis compare quantitatively to the strength of the material used, as measured by the yield and ultimate stresses. However, Dr. Springer was not concerned with the failure of eye material. Thus, he could disregard quantitative stress results.

Dr. Springer determined that it would be most useful to simplify the scenario as much as possible. The nature of human eye material was an area where simplification of the model was especially important. The eye has many layers and each layer is not homogenous. Since the process is so slow, the tissues are continuously stretching and then setting. Dr. Springer found that for the purposes of learning about the qualitative changes in foveal shape, the nonlinear and Mooney-Rivlin material models could supply meaningful results. He used published values for the collective material properties of eye tissues.

The actual forces involved in eye growth are still a mystery. For the purposes of conceptualizing retinal growth, Dr. Springer followed the analogy that the retina stretches like an inflating balloon as the eye grows. In two of his models, he applied pressure to the inner surface of the eye to cause displacement. In the other model, a force applied to one end caused displacement by simulating the tangential forces that accompany pressure.

Dr. Springer also decided to begin by working with models that reflected the development of the foveal pit from a notch. If Mechanical Event Simulation could predict the changes in the shape of the notch, Dr. Springer could later focus on whether or not the notch's origination also has a biomechanical explanation.

Two-Dimensional Model Using Tangential Forces
In keeping with Dr. Springer's attempt to make his models as simple as possible, he began with a 2-dimensional model and used tangential forces, rather than a radial force such as pressure, to simulate stretching. The model represented the inner retinal layers with a small notch. The model was fixed on one end and displaced in the X direction with a force applied to the other end (Figure 2).

Figure 2: A. Dr. Springer's first model represented the inner layer of the retina with a small notch. B. With increasing tangential force, the notch grows larger and the outer edge of the retina beneath the foveal pit deflects upward.

"As I expected, the notch grew larger over the course of the virtual event," said Dr. Springer. "However, I had not expected to see the outer edge of the retina beneath the foveal pit deflect upward. These results suggest that as the retina stretches, the notch in the inner retinal layer undergoes tension directed toward its inner surface. These tensile stresses could be transmitted to the underlying photoreceptor layer. Thereby, the photoreceptors could be passively drawn centripetally to the area underlying the center of the base of the notch."

To confirm the qualitative aspect of these deformations, Dr. Springer made a notched sheet of rubber. When stretched by hand, the region under the notch deflected inwardly, as did the Algor model.

Two- and Three-Dimensional Pressure/Inflation Models
To confirm the results from his first model, Dr. Springer created a curved, 2-dimensional model of the inner retinal layer with a notch. Dr. Springer used Mooney-Rivlin material properties to simulate the elastic nature of the tissue. Boundary conditions fixed the model at both ends and pressure applied to the inner surface caused displacement. The results were similar to those obtained using a tangential stretching force. As the pressure increased, the notch widened and the material overlying the notch was displaced less than the material more distant from the notch (Figure 3).

Figure 3: Dr. Springer applied pressure to a curved, 2-dimensional model. The notch widened and the material overlying the notch was displaced less than the material more distant from the notch. This result is analogous to the notch region deflecting toward the inner surface of the model.

Dr. Springer also examined the behavior of a 3-dimensional elastic hemisphere having a notch in its inner surface. "The 3-dimensional model has been important for presentation purposes," commented Dr. Springer. "When non-engineers can see the displacement in 3 dimensions, it is easier for them to understand."

Boundary conditions fixed the nodes at the base of the hemisphere and pressure was applied to the inner surface of the model causing displacement. As pressure increased, the hemisphere became thinner, the notch in the inner surface widened and the outer surface of the hemisphere overlying the notch deflected toward the inner surface of the hemisphere (Figure 4). Changes in the displaced model following inflation were consistent with those obtained for the 2-dimensional models.

Figure 4: Dr. Springer applied pressure to a 3-dimensional hemisphere (here shown sliced in half). Insets show the initial shape of the fovea and its deflected shape.

Layer Interaction Model
All three models suggest that as a developing retina is stretched by growth, the foveal notch in the inner layer of the retina may act to deflect the cells away from the outer surface of the retina. Such movement could serve to draw cone photoreceptors centripetally, toward the center of the fovea. To examine the interaction between the inner retinal and photoreceptor layers, Dr. Springer added a model representing the photoreceptor layer to his first model. Beam elements connected the original model of the inner retinal layer to the model representing the photoreceptor layer. Their high modulus of elasticity prevented the beams from stretching. The beams allowed the interaction of stresses occurring in the inner retinal and photoreceptor layers as the model was stretched and deformed.

As with the first model, Dr. Springer fixed the nodes on one end of the layer interaction model and applied a force to the other end. To simulate the contour found in a normal retina, Dr. Springer constrained the nodes on the outer surface of the photoreceptor layer. They were constrained in the X, but not the Y, plane. After the combined model was stretched, the notched area of the inner retinal layer deflected upward and, via the beams, pulled the photoreceptor layer centripetally toward the center of the notch (Figure 5). Extending this result to the retina, eye growth-induced retinal stretch would result in the passive centrifugal movement of the inner retinal layer cells away from the center of the fovea and the centripetal movement of photoreceptors toward the center of the fovea. These stresses would also elongate the photoreceptor material under the notch in the Y plane. Therefore, the same force could account for the elongated shape of the photoreceptors as well as the centripetal accumulation of photoreceptors in the fovea. Stretching of the inner layer of the retina may generate the force that induces the centripetal visocelastic flow of the underlying cone cells.

Directions for Further Mechanical Event Simulation Study
Dr. Springer's research to date supports the hypothesis that the development of the fovea from a notch to a pit is biomechanical in nature. How the notch forms in the first place is an issue he plans to study. Dr. Springer plans to work with virtual models to evaluate a biomechanical hypothesis of foveal pit formation.

Directions for Clinical Research
In connection with his hypothesis, Dr. Springer is initiating clinical research into strabismus. Currently, doctors surgically treat eyes that cannot both be fixed on the same point at the same time. However, sufferers of strabismus are left with some residual visual problems. Working with the idea that strabismus is caused by uneven rates of eye growth, Dr. Springer thinks it may be treatable with corrective lenses during the "critical period" of development in which the brain learns about eye fixation. The growth of the eyes at different rates is thought to make it difficult for the brain to learn how to fixate the eyes. Lenses might be able to train eyes to fixate until the slower-growing eye "catches up" to the other.

Today’s Work May Result in Technologies Beyond Imagination
"A better understanding of eye development could very well lead to better treatment of poor vision due to improper eye growth," said Dr. Springer. "Or, we may be able to treat retinal or other eye diseases. The long-term outcome of our research is impossible to predict."

When Anton Van Leeuwenhoek discovered bacteria in the late 17^th century, he could not have imagined a world in which death from bacterial infection is rare. Countless scientific discoveries, the implications of which were rarely understood in their time, were required to form the foundation of the medically advanced world we live in. As with much scientific research, the technologies that might result from Dr. Springer's work are beyond imagination.