We seek to better understand brain function and dysfunction. A principal difficulty in this endeavor is that the research entails everything from behavior of molecules, on up to behavior of people. Not only must this information be gathered, it must also be linked together to provide explanation and prediction. Computational neuroscience is developing a set of concepts and techniques to provide these links for findings and ideas arising from disparate types of investigation.    

Marr's Theory of Brain Theory

In his book Vision, David Marr hypothesized that the brain could best be understood using a top-down perspective:

  1. Identify the problem -- what does the brain have to do?

  2. Discover an algorithm -- what is the best way to solve this problem?

  3. Implement in software, hardware, neural tissue or another computational medium.

By way of contrast, much of the field of neuroscience has implicitly hypothesized that that brain will be understood bottom-up: identify all of the molecules, neural types, circuits, activity patterns, etc. and somehow pull it all together just before the neuroscience meeting convenes.  Both approaches are incomplete.

One problem with Marr's problem level is that we cannot guess a priori what the Problems are that the brain, or a particular brain circuit, is designed for.   A good example of this comes from vision, the topic of Marr's book. Subsequent discoveries have shown that the brain solves at least two problems: "what is it?"; "where is it?" and surely many more problems and subproblems as well.

We cannot find the single central problem that the brain solves, because it solves many problems.  An engineer would not a priori imagine that the brain "solves" vision by breaking up the system into 2 or more streams of processing (perhaps as part of designing a workable system, he or she might hack such a system).  Finally, the algorithm that the brain does use, while it surely solves problems, also creates problems. Once you have split up visual information, you need under some circumstances, likely under most non-emergency circumstances, to put the information back together.  This is one part of what is referred to as the binding problem.

Further problems with the problematic Marrian Problem-based approach come when we consider the implementation level.  Neurons are not transistors and they are not neural networks. It remains unclear what kind of device they are and what kind of information processing that they are able to do.  They have a variety of anatomic and dynamic (physiological) features that remain unexplained: What are dendritic spines for?; What are dendrites for? What are spikes for?; What are brain waves (oscillations) for?  …

All of this has led us to adapt Marr's insights by attempting to work the middle path of middle-out:  

with Algorithm in mid-position. Implementation largely determines what algorithms a system is capable of. It is not simply for want of clever algorithms that CMOS (the current technology of computers) cannot achieve adequate control of a bipedal robot or a flying fly.  (CMOS can simulate walking and flight, but cannot do it within the constraints of space, weight, and time required. If it takes 10 minutes to calculate how much to bend the knee, the robot will fall down long before the knee begins to move.)

We can compare this difference in approach to the changes that have taken place in the philosophy, politics and practice of science.  The classic top-down approach would start again with a problem, then hypothesis (cf. Popper), then the gathering of data to attempt to falsify the hypothesis.  More recently, there has been growing appreciation of the usefulness of data gathering, such as the human genome project, as a complementary approach.  One can't generate hypotheses in the absence of data.


Neurological and psychiatric disease

Application projects are aimed at the problems of understanding brain diseases, particularly epilepsy, stroke and schizophrenia. We are trying to extend the notion of rational phamacotherapeutics to permit development of new drug therapies or, in future, genetic interventions, based on predictions of efficacy from simulation results. We hypothesize that both epilepsy and schizophrenia, as well as Parkinson disease (and perhaps to a lesser extent Alzheimer disease and autism) manifest via abnormalities in neurodynamics which can be modeled.   We are also interested in ways that brain disorders can offer insights into brain function that are entirely missed when considering the brain as a logic box, the traditional viewpoint of artificial intelligence and of much philosophical inquiry. Although computers are now able to do remarkably well on tasks as diverse as chess, Jeopardy and facial recognition, it is clear that they do not do these things as humans do them.


Neocortical Models and Neurodynamics

It is often said that a highly developed neocortex distinguishes humans from other animals. Functional magnetic resonance imaging (fMRI) and positron emission tomography (PET) have made marvelous strides in localizing certain functions to specific neocortical areas: specific language, visual, auditory, cognitive functionality. However nothing in this high-level analysis tells us anything about how the neocortex actually goes about processing information or even generating its particular oscillation. This is what we endeavor to better understand through moderately-detailed simulations of neocortex which include wiring of the 6 layers of cortex utilizing highly simplified neurons. That these networks can produce seizures is not surprising -- in neuronal networks, flat-line (dead brain)and seizure are the easiest dynamics to produce. Producing activity similar to that seen in the living, thinking brain is harder. In particular it is difficult to obtain the observed contrast between low firing rates in individual cells (often less than 1 Hz per second for excitatory cells) with the much higher rates of population activity (ranging from 1 Hz up to greater than 100 Hz). Somehow these very slow units are organized in a way that permits them to work together to produce fast frequencies as an emergent property.

Geometrically Layer 2/3 of neocortex seems to be a critical center, based both on the number of cells and on the strength of connections to other areas. Here we show this central position by using an algorithm that shows a layers connective-centrality as centrality of position. Excitatory (E) cells and connections are shown in red and inhibitory in blue.

By arranging the neurons as described above, we have been able to capture these dynamics, although it still is not entirely clear how these dynamics emerge. In the following figure, we compare the oscillatory relations from a real brain (left) with our simulation (right). Both of these show similar cross-frequency peaks, demonstrating prominent coupling between frequencies.


Epilepsy Modeling

Epilepsy has been a major focus of translation computational neuroscience due to the relative simplicity of its neurodynamics. The large amplitude oscillations that characterize the electroencephalogram (EEG) during a seizure represent the coordinated activity of large numbers of neurons that during normal activity would be separately coordinated in multiple independent groups. We have looked at both single cell alterations and network alterations that could produce seizures. Our overall effort is to connect specific abnormalities and specific treatments that operate at the molecular scale of receptors and ion channels with the network scale of generation of concerted activity as seizures. Often we find that relatively small changes are amplified via cellular and network synergies to produce major changes in activity. In the following figure an increase in the duration of the GABAA conductance duration increase (upper left inset) with the drug clonazepam leads to network in a 50-cell network: IPSP changes (below) are associated with changes in spike firing times and patterns (above).


Following brain damage, whether from trauma or stroke, rehabilitation is limited due to the absence of the lost regions of brain. By picking up signals from remaining regions, we can use brain simulation to replace the missing areas. The focus at present is on sensorimotor integration where close coordination is required to permit haptic feedback to modify motor commands for tasks such as grasping and manipulating objects.


Hippocampus and schizophrenia

Above we suggested that human neocortex is special -- human archicortex is also special. The hippocampus (and allied areas - subiculum, entorhinal cortex) are special too. We have remarkable memory for episodes in our lives that are likely unrivaled, even by elephants which proverbially never forget (but alas can never tell us what they have remembered). The hippocampus is a focus of our modeling with a particular emphasis on alterations in dynamics that might lead to schizophrenia. We are looking at alterations in information flow contingent on the dynamical changes identified in schizophrenic patients and in animal models of schizophrenia. One hypothesis is that activity in the psychotic brain might paradoxically be too organized. In the following figure we demonstrate in silico that augmented gamma (a sign of excessive neural coordination) could be associated with reduced information flow-through. 125 separate simulations are done in order to show that similar results can be found despite randomized differences in wiring and driving inputs.


Neural data-mining

We have developed packages for doing high-capacity data-mining of both physiological and simulated signals. Data files from both experimental and modeling techniques can run to tens of gigabytes or more, making it unfeasible to view all of the data directly. Instead algorithms are developed to scan through thousands or millions of recordings to find those of interest or to generate scatter-plots or other graphical devices to view everything at once through some simplifying "lens." Data-mining is also called [i]KDD[/i] which means knowledge discovery and data-mining. The phrase "knowledge discovery" helps to explicate how these procedures differ from traditional methods of data reduction using statistical methods. In statistics, one has a prior hypothesis, sometimes well-founded and sometimes not, regarding the structure of the data. Often, for example, data is assumed to follow a normal distribution and can therefore be described by the Gaussian parameters of mean and standard deviation. By contrast KDD proceeds via explorations with no [i]a priori[/i] assumptions. Instead in KDD, the investigator generates hypotheses quickly on the fly which then can either be supported or discarded through further exploration. KDD is sometimes denigrated as being "fishing" for random facts that are pulled up randomly rather than being tracked and hunted down. Perhaps it is somewhere in between, fishing with one of those new-fangled sonars that allow one to quickly identify the location and approximate composition of a school of fish. The brain is an example of a non-stationary system -- one where the signals occurring now will never be repeated. If one sees the same image 100 times, one doesn't see it each time in quite the same way. If nothing else, ones response to the image is conditioned by the fact that it has been seen before -- it either gets boring so that ones mind (and brain) wanders, or one finds new facets of the image to focus on. Although there will clearly be some common repeated aspects of brain state with repetitive viewing, the most interesting, and revealing, aspects of brain states will be thoese that change. The brain isn't a passive system but instead is always actively correlating and recombining thoughts, memories, and sense perceptions. For these reasons and others, we are generally skeptical about the common practice of averaging brain signals. As above, averaging represents a set of statistical assumptions - one of which is stationarity.