MAKING IT REAL: BRAIN DAMAGE, MATHEMATICAL MODELING AND METAPHOR

by Sam Sober

My research group studies how monkeys recover from damage to a part of the brain that helps them see moving objects. When this part of the brain, which is called area MT, is damaged in humans or monkeys, the victim loses the ability to perceive motion accurately. My research has been to use mathematical models of the brain to study why surviving cells in MT change after brain damage, and how these changes, together with the death of cells, make the monkey incapable of seeing.

Area MT is part of the visual system, which includes all of the parts of the brain that can become active when light enters the eye. Brain cells called neurons communicate with each other by firing electrical impulses. These impulses are passed from neuron to neuron across gaps called synapses. Signals enter the visual system when light falls on the cells that make up the retina at the back of the eve. A specialized class of cells transforms these light signals into electrical signals and passes these electrical signals on to other neurons in the retina. These retinal neurons then pass the signal along to neurons in other areas of the brain.

Neurons in area MT fire only when the retina "sees" certain kinds of things. Specifically, MT cells fire when light from a moving object passes across the retina, Single cells are picky about the kind of visual input to which they will respond. A particular MT cell will fire if an object is moving in a certain direction and at a certain speed. If an object moves at the wrong speed or in the wrong direction, the neuron will fire less or not at all. So MT neurons are said to "prefer" to respond to certain kinds of movement.

Area MT neurons are also picky about the position of a moving object. A neuron in MT will only fire when a moving object passes through a certain part of space in front of the animal's eyes (fig. 1). This part of the visual field is called the neuron's receptive field. Most of the parts of the brain that deal with vision are in a thin, wrinkled sheet of cells called the cortex, which covers most of the outside of the brain. In many parts of the visual system (including area MT), neurons that are next to each other in the brain have receptive fields that are next to each other in space. As a result of this, neurons in area MT are like a kind of map of the visual field -- if you move from neuron to neuron across MT and ask where each cell's receptive field is, you will find that receptive fields move across visual space.

Figure 1---Area NT is a two-dimensional sheet of brain cells. Each brain cell fires when a moving object passes through a certain area of visual space, called the cell's receptive field (RF). RFs are shown here as zones on a TV screen that fill the monkey's visual field. The visual field is mapped across MT. If two cells are adjacent in area MT, then their receptive fields are adjacent or overlapping in visual space.

The most interesting change in receptive field properties that follows brain damage is a "filling-in" effect. Since a cluster of neighboring neurons all have receptive fields in roughly the same part of space, when this cluster of cells is killed, all the receptive fields in this part of space disappear. After brain damage, an area in which the monkey can't see motion correctly appears where the receptive fields of dead cells used to be.

Filling in happens when neurons surrounding the dead cells expand their receptive fields. About 75% of expanding cells expand their fields into the "dead" region (see fig. 2). In an important sense this compensates for the loss of dead cells. If filling in did not happen, then part of the visual world would not be in any MT neuron's receptive field, and area MT would have no information whatsoever about the motion of objects there.

Figure 2 -- Filling In: When a cluster of MT cells are killed, a "hole" appears in the visual world where the receptive fields of the dead cells used to be. In this hole, the monkey's perception of motion is disrupted. "Filling in" happens when cells that survive damage (three are shown here) expand their receptive fields into the hole.

Professors Sonny Yarnasaki and William Lytton, my bosses at the University of Wisconsin, had been talking about collaborating on a project for a few years when they hired me. Dr. Yarnasaki was studying the consequences of damage to area MT in monkeys, and was the first researcher to describe the filling in effect in area MT. He was especially interested in how electrical activity and receptive fields changed as the monkey recovered its vision, a process that is complete two months after damage. Dr. Lytton is a mathematical modeler, and most of my time is spent in his laboratory building a mathematical model of area MT.

The first part of my project was to try to explain why the filling-in effect happened. We first created a model of area MT and then did experiments by simulating damage to it. To make a mathematical model of the brain (or any system that changes over time), one defines a set of variables that describe the states of whatever it is that one is modeling. In the models I worked with, the state of each variable represents the average firing rate of small group of neurons in area MT. Since neurons are connected to each other by synapses, the variables in the model are connected to each other mathematically. With these mathematical connections, the state of one variable, which represents the firing of one group of neurons, can influence that of another. We also added other connections to the model to simulate input from other areas of the brain that transmit information from the retina. We tried to program connections and other parameters to reflect, as accurately as possible, the properties of real neurons.

The initial simulations were fairly successful in that the modeled receptive fields of some surviving neurons did fill in towards the damaged area. This was the result of an extremely simple model of a lesion, in which we assumed that all brain cells are killed in a given area.

When we looked more carefully at the model data, however, we saw that some aspects of the model's output did not agree with the real-world data. One problem was that the model could not explain why some receptive fields shrink after damage. (Although shrinkage was not as common as expansion, it did happen in a significant number of neurons. )

Next, we tried to figure out what was wrong with the initial model. Since we were pretty confident that our model of healthy MT was generally accurate, we focused on the way that we had modeled the lesion. We made very little progress until we revised our assumption that damage to MT had killed cells indiscriminately. At the same time we were working with these models, a collaborator of Dr. Yamasaki's was examining the brain of one of the monkeys used in the initial experiment. She saw a halo-shaped area around the main lesion in which only a specific type of neurons had died.

The brain's billions of cells are divided into hundreds of types based on several criteria. The two most fundamental classes of cells, however, are excitatory neurons, which make their target neurons fire, and inhibitory neurons, which prevent their targets from firing. In the halo-shaped area, only inhibitory cells were reduced in number.

When we incorporated this new information into the model, we found that the filling-in effect still happened, and that the model now predicted RF shrinkage as well. The more complex lesion -- a regular lesion surrounded by a ring in which only inhibitory cells died -- seemed like a better mechanism for the observed receptive field data.

To strengthen our case in favor of the complex lesion, we had to come up with an additional test to show that using the complex lesion model made the difference between achieving a good fit and a bad fit to the experimental data. To do this, we went back to the model data to look for predictions. We wanted to show that in addition to being responsible for RF shrinkage and expansion, the complex lesion also predicted other effects that actually happen in the real-world data.

We found that the complex lesion model predicted that, given the best possible stimulus, cells with expanded receptive fields should fire more following damage, whereas cells with shrunken fields should fire less. Analysis of the physiological data showed this to be the case for nearly all brain cells studied. What was even better was that this prediction was not made by the earlier model of the lesion, which was a second reason to think that the ring of inhibitory cell loss was responsible for the effects we were studying.

The other half of our project, which we began after completing the work described above, investigates the possible ways that changes in the receptive field properties and the neuron number can alter the perception of visible motion. We believe that the complex lesion dramatically changes the range of motion that MT neurons prefer, and that this in turn interferes with the accurate perception of motion. Preliminary work on this model suggests that for small brain injuries, the type of brain cell that is killed (inhibitory vs. excitatory) can be nearly as important as the total number of neurons that die.

The point of a mathematical model is not to replicate a phenomenon, but to investigate it. There are an infinite number of models that can reproduce a phenomenon observed experimentally, and the fact that any given model can do so is not significant. Checking the predictions of different models makes it possible to narrow down the number of potential mechanisms. If a model makes false predictions, it is wrong. If a model makes successful predictions, it is more probably correct. Different theoretical models can be evaluated relative to each other based on their predictions and explanatory scope, but the absolute validation or invalidation of a successful model must come from experimental data.

A model such as ours is useful only in that it allows a separation of variables not possible experimentally. In other words, it was impossible for us to choose to include or exclude the ring of inhibitory cell death in the real lesion, but through modeling we were able to make an argument that the ring determines how receptive fields change after brain damage.

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