Biomechanical models contribute to a better understanding of both the normal and the diseased eye.
Squint, and you can almost make out that bird soaring over the horizon. But determining whether it’s a hawk or a raven will be nearly impossible for someone with myopia, also known as nearsightedness. In this common condition, light focuses on a spot in front of, rather than on, the retina. Eyeglasses can correct the defect, as can refractive surgery in which a lens-shaped portion of the cornea—the outer layer of the eye in front of the pupil—is removed in a precise way, pushing the focus back to the retina.
But when Anna Pandolfi, PhD, asked her doctor if her myopia could be treated with refractive surgery (commonly known by such trademark names as LASIK or LASEK), he said her eyes were “too thin” to endure the surgery.
Pandolfi, associate professor of structural mechanics in the structural engineering department at the Politecnico di Milano in Italy, wanted to know more: How did her eye abnormality affect the surgical outcome? After some initial research, she realized that researchers didn’t really know the answer: They couldn’t conduct experiments on humans without great risk to the patient; and there were no adequate computer models of the eye.
Pandolfi also realized that she could help. As a civil engineer with a longstanding interest in computational mechanics and the study of materials, she could create a computational model of the cornea that might help explain how refractive surgery would impact problematic eyes such as hers.
Pandolfi is not alone in realizing the need for computational modeling of the eye’s biomechanics. The risks of experimentation are too great. “You can’t start hacking around with peoples’ eyes to see what works,” says Harvey Burd, D. Phil., university lecturer in engineering science at the University of Oxford.
Moreover, given the eye’s multiple interconnected parts, each of which is comprised of layers of cells, connective tissue, and fluid that must all function properly to give us sight (our most valued sense), it’s perhaps no surprise that there are myriad biomechanical ways the eye can fail. The array of diseases and disorders that afflict the eye include glaucoma, cataracts, macular degeneration, and retinal detachment, to name just a few.
Despite the eye’s complexity, says Phil Luthert, PhD, professor of pathology at University College, London, it lends itself well to computational approaches. “There is something fantastically tractable about the eye,” he says. The discrete steerable globe has a blood supply; allows light in one end; and sends signals through the optic nerve at the other end. “The eye ought to be a really neat place to try to get an integrated model in the next ten years.”
Already, biomechanical models of practically every part of the eye—from the muscles that control eye movement to the cornea, lens, vitreous humour, sclera, lamina cribrosa and retina—are contributing to a better understanding of both the normal and the diseased eye.
What’s in the Blink of an Eye?
Biomechanics of eye muscles Eyes can move extremely fast. Indeed, the jerky eye movements called saccades are the fastest movements produced by the human body. Eyes also engage in smooth pursuit as they follow a moving object. And they converge and diverge as well—moving toward or away from each other to maintain binocular vision. The muscles and tissue that surround the eye control all of these movements.
Biomechanical models of the eye muscles can give insights into diseases in which the muscles fail. For example, a condition called strabismus can result when the eyes are not properly aligned; and gaze palsy prevents the eyes from moving in the same direction. Surgeries for these problems often go wrong because they involve guesswork about which muscles to shorten or lengthen. The model SEE++ can help guide surgeons to improve outcomes. It consists of three parts: a geometric model of the muscles; a muscle force model; and a kinematic model that brings the geometry and forces together to define stable eye positions.
Using SEE++, physicians can enter a patient’s response to diagnostic testing (such as the classic “head tilt test” in which tilting the head results in telltale eye movements) and try
A Model of Extraocular Muscles. The software program SEE++ creates individualized models of the eye muscles that can be used to both diagnose muscle problems and plan surgical treatments. Courtesy of: Thomas Kaltofen, www.see-kid.at.
to work backward to understand the muscle forces that cause the patient’s particular pathology. “It’s not always perfect,” says Thomas Kaltofen, a researcher at RISC Software GmbH, a limited liability company in Austria that developed the program. “There’s often more than one way to achieve a particular pattern.” But in conjunction with a physician’s expertise, the program can hone in on the causes of a particular pathology and then simulate how to correct it surgically. SEE++ is currently used for surgical planning, mostly in Austria. “
Often, we’re ruling things out as well as ruling them in. You get closer and closer to the pattern measured from the real patient and at some point assume that you might be simulating the actual case,” he says. “It works quite well when you have enough data.”
Kaltofen and his colleagues recently added the skull to the visualization, and hope to soon integrate it into the model as a constraint on muscle movement. They also plan to integrate a more flexible model of the signal that comes from the brain to the muscle; and add the capacity to simulate new, innovative surgeries.
Despite its usefulness, SEE++ simulates only static movements (where the eye ends up) rather than dynamic movements (the trajectory and accelerations it used to get there). A new model created by Dinesh K. Pai, PhD, professor of computer science at the University of British Columbia, takes this extra step. “Static movements assume you can ignore the inertial term—the effect of mass or accelerations—and that motions are balanced at all times,” he says. “But eye movements are some of the fastest movements we make; and the dynamics are significant.”
A Robotic Eye. Pai’s computational model of extra-ocular eye movements was the basis for this tendon-driven robotic eye, which can even engage in the extremely rapid eye movements known as saccades. Courtesy of: Dinesh Pai, Mahkameh Lakzadeh and Tony Hodgson.
Using their model, Pai and his colleagues have learned how to build robotic eyes that can do both saccades and smooth pursuit. Their model includes “pulleys,” the connective tissues that lie between the muscles on the sides and top of the eye. These tissues play a greater role than once believed. “Many surgeries cut away at these functionally important connective tissues. As a result, rates of success at eye surgery are relatively poor,” Pai says. “If we can model these, we can use the model for surgical planning.”
SEE++ has also added a model of the pulleys, Kaltofen says. Pulleys detour rather than going straight; and they move when the eye moves. So SEE++ includes pulleys in the geometric model as well as in the force and kinematic models. “The whole model changes by introducing this behavior, though it’s a slight change,” Kaltofen says. Why the pulleys move with the eye is not fully clear. They may help simplify the brain’s job of coordinating eye movements, Kaltofen says, “but that’s only one theory.” Research is ongoing.
The Window into the Eye: Models explain cornea’s transparency
The cornea is a curved lens that bends light toward a focal point inside the eye, providing about two-thirds of the eye’s optical power. Structurally, “the cornea is a perfect pressure vessel,” says Peter Pinsky, PhD, professor of mechanical engineering at Stanford University. “It’s floppy and flexible when isolated, but assumes a highly precise and stable shape when internally pressurized like a balloon.” It is also—rather remarkably—transparent, allowing about 90 percent of incident light to enter the eye.
Computational biomechanics can help provide a theoretical understanding of both corneal shape and transparency, issues that matter for a variety of clinical problems, Pinsky says. For example, corneal shape is an important issue for refractive surgery—the procedure Pandolfi was denied due to the thinness of her cornea. Also, in certain diseases such as keratoconus, corneal shape is severely changed as a result of ultrastructural rearrangements within the tissue. And other disease processes can compromise corneal transparency, leading to blindness.
Pinsky spent most of his career working on the theory side of finite element method (FEM)—a numerical technique that divides a complex object into simple elements that can be solved in relation to each other, often in a triangular mesh. But about 10 years ago, he began applying FEM to model the cornea. He’s specifically interested in how the cornea maintains transparency as well as why it assumes the shape it does.
Corneal Tissue “Unit Cell.” To model the nanoscale structure of the cornea, Pinsky and his colleagues worked with a unit cell (representative volume) of tissue, as illustrated here, showing collagen fibrils (cylindrical zones with blue ends) and GAGs arranged in a next-nearest neighbor connectivity (in the red zone-not explicitly modeled). The team used numerical methods to analyze the unit cell and obtain the free energies of the system. The color contours illustrate the electrostatic potential. Courtesy of: Peter Pinsky.
Prevailing theory holds that a cornea’s transparency stems from its nanoscale organization. Scientists know that within the stroma—the thickest layer of the cornea—lies an intricate system of ribbon-like fibers called lamellae. “These flattened strands lie one on top of another in up to 500 layers,” Pinsky says. The lamellae are also like large cables—cut through them and you will see the finer level of smaller cables made up of thousands of individual fibrils that are beautifully organized in an almost perfect regular lattice. But researchers don’t really know precisely how the fibrils are maintained in this pseudo-lattice arrangement as required for transparency.
Proteoglycan molecules—proteins with “GAG” (glycosaminoglycan) chains that branch out in a star-like structure—are known to play a critical role. Theory has it that these GAGs bridge from one collagen fibril to another to form an elastic network. But this doesn’t match up with imaging or fit what’s known about GAG chemistry, which suggests the fibrils and GAGs should be mutually repulsive, Pinsky says.
To study the phenomenon theoretically, Pinsky and his colleagues created a numerical model of a portion of the cornea. Working with a representative volume, they characterized the system in an idealized way—endowing the fibrils and proteoglycans with nicely organized properties and characterizing the system’s electrostatic and elastic energies. “We then try to find the model parameters that make the energy of the system stationary,” he says.
The result: The fibril lattice’s response to external forces is better explained by osmotic stress perturbations resulting from electrostatic interactions than by the GAG elastic bridging theory. And the model explains a curious quality of corneas: when isolated and placed in a salt bath, they swell enormously. No other theory successfully predicts this behavior of the cornea at various levels of hydration. The model is being applied to explain the fundamental mechanism for Fuch’s dystrophy, a condition in which the ion pumping mechanisms at the posterior surface of the cornea are compromised, resulting in swelling and a loss of corneal transparency.
The second thrust of Pinsky’s cornea work involves understanding how refractive surgery impacts the shape and health of the cornea. When removing part of the cornea or adding implants, Pinsky says, it is important to know how the cuts affect the tissue mechanics. Imaging is starting to provide a good 3-D understanding of how the lamellae are organized in the stromal layer of the cornea. And Pinsky’s lab has been doing experiments to mechanically test super-thin slices of the cornea. His group has also put all that data together to produce a predictive FEM model and a theory of the
A Weakened Cornea. Pandolfi’s finite element models of the cornea after refractive surgery revealed that the thinner cornea is under greater stress (top) and loses visual acuity more rapidly than normal corneas do if IOP goes up (graph, lower).
“This is of interest to the laser companies,” Pinsky says. “LASIK, which is really an ingenious procedure, is nevertheless a pretty significant attack on the cornea.” It involves cutting a flap, lifting it, and then vaporizing some of the stromal tissue in a precise way. The flap is then carefully repositioned over the cornea. But, says Pinsky, “the flap remains mechanically defunct because wound healing does not fully integrate it with the underlying stroma.” And the removal of tissue changes the state of stress in the remaining tissue. Using his models, Pinsky seeks to understand how the cornea responds to various surgical procedures with the goal of improving the predictability of outcomes. He also hopes the models will provide insight into how the lamellae rearrange to produce an altered corneal shape in keratoconus. Pandolfi is also interested in using FEM to understand how refractive surgery affects the eye, with a particular interest in problematic eyes like hers. Unlike Pinsky, she models the corneal material as a whole, rather than at a molecular level. “Once you have a numerical model, you can run a simulation to see if the eye can undergo a surgical intervention or not,” she says
To create her model, Pandolfi started with the geometry—building the exact shape of the cornea using photographs and measurements. “This was easy in that you have all the information you need,” Pandolfi says. Describing how the material behaves is trickier, she says, because the mechanical properties cannot be directly measured in living tissue. She only had data on how dead pig or human corneas behave in response to displacement. So, she used inverse analysis—feeding the model with the geometry of these tests and observed displacements—to discover the mechanical parameters.
Using this approach, Pandolfi showed that, after refractive surgery, the eye’s refractive power (visual acuity) is more sensitive to changes of intraocular pressure (IOP). “For an engineer, this is clear,” Pandolfi says. “The cornea is thinner so it is more sensitive to a change of IOP.” Pandolfi has now validated the results. In addition, she showed that after removing 10 percent of the cornea in a simulated refractive surgery, the remaining tissue is subjected to 15 to 20 percent more stress. It’s a noteworthy result given that some surgeries reduce corneal thickness by as much as 50 percent. Imagine thinning the cornea from the thickness of a soccer ball to that of a helium balloon: it becomes more stretchable in response to internal pressure, and this in turn affects the cornea’s ability to focus light in the right spot.
To date, Pandolfi’s model has relied on average values for the cornea’s geometry and material properties. Now she’s moving toward understanding the differences between different individual’s eyes. “We cannot speak about an ideal eye,” she says. “We have to speak about the range of variability of the parameters that define the real eye.” One of her students is using geometric data from 20 pre- and post-operative eyes and simulating how the surgeries likely affect IOP and the stress state inside the cornea.
Clear-eyed: Models of the lens explore cataract prevention and treatment
Behind the cornea lies the aqueous humor; and behind that floats the lens, a transparent unit that is responsible for about one-third of the eye’s optical power. Shaped like a lentil bean—round, and convex on both sides—the lens has an outer capsule made of stiff collagen elements in a flexible matrix. Inside, lens fibers stretch from the front to the back in onion-like layers.
With age, the lens can become opaque, a condition called age-related nuclear cataract that is treated by removing the natural lens and replacing it with an artificial one. Also with age, the lens loses its ability to adjust (or “accommodate”) its focus from objects in the distance to objects close by. Called presbyopia, this condition occurs in almost all adults after about age 50.
Using computer modeling, researchers are trying to get a better understanding of how the lens develops cataracts, how it responds to cataract surgery, and how it loses its ability to accommodate. “It’s a neat system for an integrative model because at the cellular level, the location of physiological components determines the local tissue’s optical function,” says Paul Donaldson, PhD, professor of optometry and vision science at the University of Auckland, New Zealand.
Nuclear cataracts develop as a result of protein cross-linking at the center of the lens. “It’s like molecules falling out of solution and scattering light,” Donaldson says. The cause is uncertain, but Donaldson believes that protein cross-linking might be driven by a failure of the lens to maintain its normal physiological environment—a process in which internal micro-circulation likely plays a key role. As we age, Donaldson proposes, the micro-circulation system runs down, losing its ability to deliver sufficient nutrients to the lens center and initiating the biochemical changes that lead to protein cross-linking and compromised lens transparency.
The existence of a lens micro-circulation system was first proposed by Donaldson’s collaborator, Richard Mathias, PhD, who is now professor of physiology and biophysics at the State University of New York, Stony Brook. He took electrical measurements, analyzed the circuits discovered, and modeled the resulting ion and water fluxes to demonstrate that micro-circulation occurs within the lens. Over time, Mathias’ model evolved to cover many physiological components of the lens, says Ehsan Vaghefi, PhD, a bioengineering researcher in the department of optometry and vision science, also at Auckland. But Mathias solved his model analytically and in one dimension, which tended to become exponentially time-consuming and complex. Building on this work, Donaldson and Vaghefi encapsulated Mathias’s analytical model into a 3-D finite element framework that includes parameters such as the spatial location of transporters and ion channels/pumps throughout the lens. They then used brute force (iterating through a series of approximate solutions) to solve numerical equations that describe fluid circulation at a microscopic level throughout the lens. After many iterations, the results converged on a solution.
Net Microcirculation in the Lens. This 3-D vector map shows the net current densities calculated by Vaghefi and Donaldson’s model of micro-circulation in the human lens when the model is stimulated with a simulated vibrating probe at the pole. According to the model, net flow moves inward at the poles and outward around the equatorial plane. Reprinted from Vaghefi E, et al., Development of a 3-D finite element model of lens microcirculation, BioMedical Engineering OnLine 2012, 11:69 doi:10.1186/1475-925X-11-69.
The advantage of this approach, Vaghefi says, is that the model can make predictions about what happens when the environment and/or physiology of the lens is perturbed. For example, the team has now shown that, in response to stimulation with an external probe, the model lens behaves the same way as a real lens.
Vaghefi and Donaldson both hope their model will be used as a tool to predict how age-dependent changes in lens physiology affect the progression of lens cataract—and ultimately improve treatment. “If we could up-regulate the circulation system of the lens,” Donaldson says, “we could deliver anti-oxidants to delay onset of cataract.” Delaying cataracts by just 5 to 10 years would actually cut their incidence in half, he notes, since many people will die of natural causes before they even get them.
Computer models of the lens could also help researchers design better cataract surgical procedures and lens replacements. Currently, cloudy cataract lenses are surgically replaced with new lenses that have a fixed optical power. “It’s a plastic lens that behaves like a spectacle lens but inside your eye,” Burd says. “A lot of people are trying to head toward a lens that can behave more like a natural lens.” But that, of course, requires a good understanding of the natural lens physiology.
To that end, Burd created a finite-element, multiscale model of the lens capsule—the outermost layer of the lens. Like the cornea, the lens capsule has a complex microscopic structure that affects the material’s behavior. So Burd’s millimeter-scale finite element model of the lens capsule includes micro-scale structural information about the behavior of collagen fibers embedded in an elastic matrix. The model could be used to evaluate how the implantation of new lenses stresses the lens capsule.
Burd has also modeled how the lens loses the ability to accommodate as we age. He and his colleagues have proposed an empirical model that represents the changes in the elasticity of the lens over time. Combining that with Burd’s lens capsule model, they showed that 80 percent of the age-related decline in lens accommodation is caused by increased stiffness in the lens fibers—not changes to the capsule itself. This suggests that inserting an appropriately flexible artificial lens within the capsule might help the lens retain its ability to accommodate. But, Burd says, researchers would have to know how such a surgery would alter the material properties of the lens capsule—another topic he hopes to address using his models.
Not a Dry Eye in the House: Fluid mechanics in the vitreous humour
Mixing Processes in the Vitreous. For some diseases, drugs are delivered to the retina by injection into the vitreous. Models of fluid flow in the vitreous can help researchers understand how much of the drug will actually reach the targeted cells before it is excreted. Here, Repetto and his colleagues modeled particle movement in the vitreous in an analytical model and showed that the mixing properties and fluid structures depend on fluid properties, such as viscosity, and eye motion (particularly, speed). Recently, Repetto’s team computationally reconstructed 2-D images of the speed of these flows to get a fully 3-D image of fluid motion in the vitreous humour. Reprinted from Stocchino A, et al., Mixing processes in the vitreous chamber induced by eye rotations, Phys Med Biol 55 (2010) 453-467, with permission from IOP Publishing.
Moving deeper into the eye, the next major structure is the vitreous humor—a gelatinous blob that fills the area between the lens and the retina. As the eye moves, so too does the blob, exerting mechanical forces on the surrounding tissue—primarily the retina. With age, the blob can become liquefied in parts and can also shrink and detach from the retina, allowing the liquefied portion to fill in the gap between the vitreous gel and the retina. This causes flashes of light and floaters in the visual field as the eye moves. More importantly, however, portions of the vitreous that are still attached to the retina can pull on or tear the retina. This, in some cases, leads to retinal detachment, a condition in which the photoreceptor-rich retina pulls away from the nourishing tissue behind the eye, resulting in blindness.
Interestingly, retinal detachment following vitreous detachment occurs more often in nearsighted eyes. Rodolfo Repetto, PhD, lecturer in hydraulics at Universita Degli Studi di Genova, and his colleagues hypothesized that mechanics plays a role. “Possibly myopic eyes’ oblong shape affects friction at the interface between the liquefied vitreous humor and the retina during eye movement,” Repetto says. His group’s computational models of fluid flow in the vitreous during saccades—rapid flickering motions of the eye—confirmed this hypothesis. “Even with a homogeneous fluid, the stresses within the vitreous and on the retina are significantly higher [in myopic eyes],” he says.
Repetto and his colleagues are also modeling the effect of surgical treatments for retinal detachment. Typically, surgeons attach a silicon band that deforms the eye shape into a slight hourglass shape, pulling the retina back in touch with the tissue behind it. “It works, but there was no understanding about what happens in terms of the motion of the fluid in the vitreous chamber,” Repetto says. His group showed that the motion and stresses in the humour are significantly altered. “Reattachment depends on the stresses generated from the inside on the retina,” he says. “It’s a first step toward understanding why the process works.”
Another surgery replaces the vitreous with an oil that pushes the retina back in contact with the essential underlying tissues. But sometimes the oil breaks down into an emulsion that is not transparent. Repetto’s group is modeling the oils to better understand why this happens. “It depends again on mechanics,” he says.
With an Eye to Glaucoma: Modeling the effects of intraocular pressure
At the back of the eye, more than a million nerve fibers (axons from ganglion nerve cells in the retina) extend through an opening known as the scleral canal within a zone called the optic nerve head (the eye’s “blind spot,” which has no photoreceptors). The lamina cribrosa (LC), a porous structure that resembles a loose foam, fills in the area around the nerves. In glaucoma, a disease whose most common symptom is elevated intraocular pressure (IOP), “the LC gets squished down, moves backwards, and becomes more like scar tissue,” says says Ross Ethier, PhD, senior research investigator with the department of bioengineering at Imperial College, London. Ultimately, these changes somehow damage and kill off the nerves passing through the scleral canal, causing blindness. But there’s little known about why one person might get glaucoma while another does not.
Ethier hypothesized that individual differences in the thickness of the sclera—the white of the eye—might mediate the effects of pressure on the optic nerve head. In humans, the thickness of the sclera is quite variable, so he and his team used 11 post-mortem eyes (7 normal and 4 with glaucoma) to build 11 finite element models of the scleral shell, each containing a model of an identical and idealized optic nerve head. In the models, scleral thickness turned out to be a significant factor in glaucoma risk: Differences in scleral thickness, particularly in the region next to the optic nerve head, produced significant variation in strains across the LC.
Rafael Grytz, PhD, is also interested in the effect of elevated eye pressure on the optic nerve head. He recently left the Devers Eye Institute Research Labs in Portland, Oregon, to become assistant professor of ophthalmology at the University of Alabama, Birmingham, where he will continue working on multiscale models to explore the biomechanics of the eye. “I look at glaucoma and other eye diseases and one thing that strikes me—and it’s the theme of my work—is that the biomechanical mechanisms are occurring and interacting across very different length scales,” he says.
Multiscale Eye Models. Grytz integrates eye models at a variety of scales. Courtesy of: Rafael Grytz.
Pressure creates a loading condition at the macroscale that translates down the scale of the collagen fibrils, the main load-bearing constituents of the LC. “If you load them beyond certain pressures, remodeling occurs,” he says. That, in turn, might have an impact on the nanoscale—interrupting axonal transport
So Grytz’s models start with a biomechanical model of how the individual collagen fibril responds to loaded forces. From this, he derives material properties of eye tissues at the microscale, and then simulates growth and remodeling of the entire eye with particular attention to how the LC thickens in the early stages of glaucoma. This involves creating a generic finite element model of the optic nerve head and modeling the living tissues of the scleral canal as an adapting mixture of components—collagen tissues, axons, etc. He found, first, that the mixture would create an LC all by itself under ordinary IOP. And that at elevated IOP, the LC thickened by recruiting collagen from the tissue behind the LC. Eventually, the simulated tissue reached a steady state where it no longer thickened. This was the first study to show that biomechanics could drive the growth and remodeling of the LC in a way that matched observations of early glaucoma in monkey eyes.
Grytz acknowledges that a major challenge remains: determining the mechanism that leads to the insult to the axons. Thus far, he has simulated the human eye coupled with the micro-architecture of the LC and axons passing through LC’s porous structure. Though still in the early stages, he says the simulation is fully coupled and shows that when he elevates IOP, the axons are highly shear deformed around the edges of the LC. “But there’s so much we still don’t understand, and I believe computer simulations will be a great benefit to explore this problem,” he says.
Looking Deep into the Eye: Retina modeling and simulation
The retina is perhaps the most complex component of the eye. In addition to 100 million photoreceptors and more than a million nerve cells that send visual signals to the brain, the retina is a highly layered anatomical and physiological structure. Existing models of the retina tend to simplify it into a slab of cells, says Vaghefi. “That’s not accurate.”
Luthert, who calls himself a “would-be” modeler of the retina, agrees. His “bugbear” with existing metabolic models of the retina is their use of systems biology without a spatial domain. “Biology occurs in a cell with a finite size and constraints about what can move where,” he says. “The cell in turn sits in a tissue with blood vessels that are constrained in space.” As a result, he says, multiscale modeling is needed to capture the metabolic and spatial elements within one integrated model.
So, a few years ago, Luthert joined with others to propose a multimillion-dollar grand scheme for computational modeling of the retina. The plan included several building blocks: a model of the cells that come together to create the outer retina; a model of blood flow in the retina; and the incorporation of imaging data to refine the models and then make them patient-specific.
Though the European Commission’s Research and Innovation Department didn’t fund the grant, Luthert remains completely committed to the plan. “It’s absolutely the way forward,” he says. “The major treatment for diabetic retinopathy involves injections into the eye with an intrinsic risk,” he says. “The lack of clarity about when or how often to inject lends itself nicely to a computational approach.”
He acknowledges the plan was perhaps a bit ambitious. “So what we’re doing now is chopping it up into bits and running with those,” he says. For example, one of his graduate students is modeling blood flow in the choroid—the remarkably rich vascular bed at the back of the retina. And Vaghefi and his colleagues are using various imaging methods to try to build models that are more anatomically and physiologically correct. “It’s a move from simple equations put down in the ’80s to make the models more precise.”
Meanwhile, Abbas Shirinifard, PhD, a computational modeling scientist at St. Jude Children’s Research Hospital in Memphis, Tennessee, has been building a multiscale model of the outer retina that covers multiple spatial and time scales. He simulates the cascade of events that lead to a common form of age-Simulating Capillaries Invading the Retina. Shirinifard ran many thousands of simulations of capillaries invading the RPE to see how quickly certain changes to the parameters lead to various types of vascular invasion of the choroid in wet macular degeneration. These four snapshots show one such simulation over the course of a year (months 0, 6, 9, and 12) in 3-D as well as in a 2-D vertical slice (upper left) and a 2-D horizontal slice at the level of the sub-RPE space. Vascular cells are shown in red; RPE in green; and the Bruch’s membrane in light blue. Month zero starts with an activated vascular cell (purple) forming a hole in the Bruch’s membrane. At 6 months, blood vessels have spread into part of the sub-RPE space. At 9 months, the sub-RPE space is well infiltrated by blood vessels. And at 12 months, these vessels are now invading sub-retinal space the zone between the RPE and the photoreceptors. Courtesy of: Abbas Shirinifard, based on data presented in Shirinifard A, et al., Adhesion Failures Determine the Pattern of Choroidal Neovascularization in the Eye: A Computer Simulation Study. PLoS Comput Biol 8(5): e1002440. doi:10.1371/journal.pcbi.1002440 (2012).
related macular degeneration—a primary cause of vision loss in older Americans—known as “wet” macular degeneration.
Scientists know that the wet form of macular degeneration begins with blood vessels invading the retina from a blood-rich zone (the choriocapillaris) that normally nourishes the retina rather than destroying it. Researchers have hypothesized that this process is caused either by an increase in a protein called VEGF (vascular endothelial growth factor) in response to inflammation or injury; or by breaks in the Bruch’s membrane—a physical barrier between the capillary layer and the outer cell layer of the retina (the retinal pigment epithelium, or RPE). To explore these possibilities, Shirinifard modeled the cells of the choriocapillaris, the Bruch’s membrane, and the RPE—and included more than 30 parameters related to transport of oxygen, diffusion, and cell behavior.
In the simulations, his team found that increasing VEGF did cause capillaries to invade the retina, but in the wrong way. Normally, in humans, blood vessels invade the space between the RPE and the Bruch’s membrane first, and then sit there for a while before invading the retina. But in the simulation, there was no pause: “The cells jump in to invade the retina without any invasion of that sub-RPE space,” Shirinifard says. “So that was shocking and surprising.” Simulating holes in the Bruch’s membrane produced the same result. “Both hypotheses failed—or my model was wrong,” he says.
In an attempt to improve his model using experimental data, Shirinifard ordered some post-mortem human eyes. When they arrived, some had been crushed in shipping. The damaged eyes had some patches of detached RPE and some patches that were still attached to the Bruch’s membrane. Shirinifard then had an “aha!” moment: Cellular adhesion could be a key factor in macular degeneration.
In his simulation, Shirinifard began perturbing various adhesion properties (there are multiple types of adhesion—with and without mechanical coupling, for example) between different components at the back of the eye. The result: His simulations produced several different patterns of capillary invasion that are actually seen in people.
Validating the simulation is quite complicated, Shirinifard notes. In a clinical setting, there is typically just a snapshot of a moment in time, whereas the simulation shows a snapshot and also the evolution of a 3-D structure. “There’s not much data to compare it with,” he says.
Currently he is turning his attention to the inner retina, where blood vessel changes occur in diabetic retinopathy. “There’s more data and access to lots of parameters for building these kinds of models,” he says. “It’s a unique opportunity.”
All Eyes: A vision for a physiome model of the eye
Peter Hunter, PhD, of the University of Auckland, has long been interested in creating a physiome model of the eye—a complete computational system that would capture all of the eye’s complexity from the molecular and cellular levels up to the tissue and organ levels
Luthert agrees there could be great value in an integrated model. “To some extent it’s okay to have just the pieces of the eye modeled,” he says. “But if you take one step back, it’s clear that things are very interconnected.” For example, although an integrated model of the outer retina is “utterly compelling” and could help us understand macular degeneration, it would benefit from integration with models of IOP and fluid flow through the vitreous. And, he says, “Front-of-the-eye glaucoma stuff generates input for the back-of-the-eye glaucoma stuff.” Thus, models of how pressure became elevated in the first place—which involves aqueous production and retention in the front of the eye (models not discussed here)—could inform models of how the optic nerve head responds to increased IOP. “It’s these truly complex disorders that need a whole eye approach,” he says.
“It’s not a bad idea,” Pinsky says. “The components of the eye have to interact in very intimate ways. Many of us are experts in one area or another. The idea of a more comprehensive understanding is important to me. It would be a sensible scientific goal.”