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Cause and effect network models and high-throughput computing

The corpus callosum is the major fiber pathway connecting the left and right hemispheres of the human brain. Its primary function is facilitating communication between the right and left sides, allowing us to coordinate our movements and think about complex information.


Neural pathways. Image courtesy Wayne Patterson.

For children with spina bifida, the rear portion of the corpus callosum may be thin or even missing, which reduces anatomical connectivity between the hemispheres. Researchers at the University of Wisconsin-Madison (UWM), US, were curious if the lack of wiring would show up as a difference in connectivity in the brain. Together with researchers from the University of Texas Health Science Center at Houston, US, they built a simple network model with front and rear regions on the left and right sides.

When looking at the causal interactions of control subjects, the researchers found that their approaches identified more interactions in the rear of the brain than in the front. The opposite was true of spina bifida subjects. This implies that the reduced anatomical connectivity is associated with reduced interaction between the hemispheres and suggests increased connectivity in the front may be a compensatory effect.

These results are welcomed by Barry VanVeen, Lynn H. Matthias professor of electrical and computer engineering at UWM, as he and project collaborators develop signal-processing tools for measuring how parts of the human brain talk to one another.

Connectivity

Anatomical connectivity in the brain can be thought of as the highway or roadmap - essentially what parts are physically connected to other parts. Anatomical connectivity answers the question "is it possible to send traffic or signals from one area of the brain to another?" Just because it is possible, however, doesn't mean that signals actually travel along a particular path during a task.

Interactions between brain areas are often studied using correlation. If activity in one area rises and falls in a pattern, and another area of activity shows a similar pattern, then those areas are viewed as functionally connected. However, a correlation in activities between areas does not imply causation.

"We can better get at the concept of cause and effect using the idea of temporal precedence. If the activity in a first region helps explain later activity in a second region, then we'll say that there is a cause and effect relationship from the first region to the second," says VanVeen.

Signals

Neurons have cell boundaries and ions flow across the boundaries in response to different chemical and other signals. When ions are flowing you have an electric current. Once you have an electric current, the current causes electromagnetic fields to be produced. The basic laws of physics then govern these fields. Since we cannot noninvasively measure directly in the brain, the only ways to observe these messages are through electroencephalography (EEG) and magnetoencephalography (MEG) - imaging techniques that measure brain activity from the scalp. VanVeen likens the process to trying to understand the rules and best strategy for playing chess, but only by observation and from 30,000 feet away.

"By measuring electric fields at the scalp we have limited insight or spatial resolution into where things are actually happening in the brain," VanVeen says. "Biology determines how the currents are flowing, and physics tells us what we are able to measure. We want to put these two things together to draw some conclusions about how different parts of the brain are interacting with one another."

The mathematical model

VanVeen and his collaborators employ a simple network model that represents connectivity in the cortex. He explains that if you have two brain regions (X1 and X2), then activity in these regions varies as a function of time. They model the variations in each region as a weighted combination of its own past and the past of the other region plus an error term. "Our goal is to find the coefficients that relate the past of one region to the present of another. If we can find those coefficients, then we can approximate the nature of interaction from one region to another."

"But since we can't measure the brain signals directly and can only measure electric or magnetic fields at the scalp, we have to estimate these coefficients taking into account the physics of how the underlying brain signals are measured, and this leads to a difficult optimization problem."

VanVeen's group has developed an iterative approach for estimating the coefficients from the scalp measurements. One of the challenges for testing this approach, VanVeen says, is not knowing the true interactions for comparison to the estimated interactions. So indirect evidence of effectiveness, such as showing reduced cause and effect interactions when anatomical connectivity is reduced, is encouraging.

Computational issues

A typical scenario for an EEG or MEG system involves 256 channels recording approximately 100 samples per second for approximately five minutes. Hence, the data set for each subject and condition could result in a matrix with 256 rows and 15-30,000 columns.

It is common to study a number of subjects (20-30), each of which is evaluated under multiple experimental conditions (3-5) producing a dataset for each experimental condition and subject. The optimization problem for estimating the coefficients is solved using multiple (50) initial conditions. This results in thousands of jobs that can be run in parallel.

"The Center for High Throughput Computing (CHTC) at UWM took our MATLAB code and put various wrappers around it; we didn't have to do any coding. It was incredible. They ported everything onto the grid, and gave us a command line interface and a tool for uploading data and downloading our results. They were very supportive - without the help of Bill Taylor, the campus grid, and Open Science Grid, our research would not have been possible," VanVeen says.

The CHTC, led by Miron Livny, serves both Morgridge and the Wisconsin Institute for Discovery, providing the advanced computing tools and infrastructure necessary to facilitate the leading-edge work of scientists like VanVeen.

Looking ahead

The scientific community is eager to analyze networks in the brain. VanVeen's approach involving iterative algorithms and a high level of parallelism has provided some very interesting results thus far.

His team is looking at the difference between imagination and perception. "How do we form mental pictures even though we are not getting input through our eyes? We're looking at regions in the brain known to be associated with imagination and perception and building a network model between them."

"When viewing a movie, the information flowed from the visual sensory region of the brain to higher regions in the brain for interpretation. However, when imagining similar scenes, the information was flowing in the opposite direction, which made complete sense," VanVeen says. "However, such a reversal of information flow had not been ever shown before."

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