Modular models of brain function
Modular models of the brain aid the understanding of a complex system by decomposing it into structural modules (e.g., brain regions, layers, columns) or functional modules (schemas) and exploring the patterns of competition and cooperation that yield the overall function.
Structural and Functional Modules
Much of computational neuroscience focuses on properties of single neurons and small circuits. However, computational approaches to cognitive neuroscience (e.g., the interaction of perception, action and language) must deal with diverse functions distributed across multiple brain regions. It is argued that a modular approach to modeling is needed to build cognitive models and to compare them as the basis for further model development.
A complex system may be analyzed by being decomposed into a set of interacting subsystems. Such a decomposition succeeds insofar as we can understand the relation between the inputs and outputs of each individual subsystem, and insofar as the interactions between the subsystems can be explained via suitable connections between various of their inputs and outputs, without further analysis of variables internal to the subsystems. Such a decomposition is structural to the extent that the subsystems can be mapped onto physical substructures of a physical structure embodying the overall system.
The work of the nineteenth century neurologists led us to think of the brain in terms of large interacting regions each with a more or less specified function, and this localization was reinforced by the work of the anatomists at the end of the 19th century who were able to subdivide the cerebral cortex on the basis of cytoarchitectonics. It was at this same time that the discoveries of the neuroanatomist Ramon y Cajal and the neurophysiologist Sherrington helped establish the neuron doctrine.
The issue for the brain theorist, then, is to map complex functions upon the interactions of these rather large entities, anatomically defined brain regions, or these very small and numerous components, the neurons. This has led many neuroscientists to look for structures intermediate in size and complexity between brain regions and neurons to provide stepping stones in an analysis of how neural structures subserve various functions. One early example was the Scheibels' suggestion (Scheibel & Scheibel 1958) that the reticular formation could be approximated by a stack of poker chips' each incorporating a large number of neurons receiving roughly the same input and providing roughly the same output to their environments. This modular decomposition of the reticular formation provided the basis for the Kilmer and McCulloch model, RETIC (Kilmer, McCulloch, & Blum 1969). The theoretical ideas of (Pitts & McCulloch 1947) combined with the empirical observations of (Lettvin, Maturana, McCulloch, & Pitts 1959) on the frog visual system to suggest that one model portions of the brain in terms of interacting “horizontal” layers of neurons. (Powell & Mountcastle 1959) working in somatosensory cortex, followed by (Hubel & Wiesel 1962) working in visual cortex, established the notion of the column as a “vertical” aggregate of cells in cerebral cortex, again working on a common set of inputs to provide a well-defined set of outputs.
Integration of Modeling and Experimentation
With this, the concept of a “module” was well established within neuroscience as a structural entity (Mountcastle 1997). However, there is a complementary notion of a module as a functional entity (a schema in the sense of Arbib 1981).
Analysis in neuroscience often goes to the extreme of focusing on one circuit or brain region and trumpeting it as "the" circuit implementing some specific function X. The other extreme is "holism", stressing that X may involve dynamic activity integrating all areas of the brain. Holism may be correct, but seems to be useless as a guide to understanding. The “modular models” approach is a compromise. Any "schema” or function X involves the cooperative computation of many neural circuits. A survey of the literature can focus modeling on a few regions for which good data are available correlating neural activity with the performance of function X.
As time goes by, the model may yield more and more insight into the data on X (some of which may be new data whose collection was prompted by the modeling), whether by conducting new analyses of the model, increasing the granularity of description of certain brain regions, or in extending the model to include representations of more brain regions. Other challenges come from integrating separate models developed to explain distinct functions X, Y, and Z to derive a single model of interacting brain regions able to serve all these functions. As we come to understand more fully the roles of particular brain regions in serving particular functions, we can then turn to more extensive models. However, if we try to model "everything all at once" we will understand nothing, since the map would then be co-extensive with the whole territory (Borges 1975).
Three Views of Modules for Modeling
Modules as Brain Structures
Figure 1 illustrates the modular design of a model. In this case, each module corresponds to some physical structure of the brain – whether a brain region, a smaller brain region or an array of neurons. Other NSL models continue the decomposition to the level of neurons or subcellular structures as objects. But NSL employs two other kinds of module:
Modules as Schemas
In modeling some complex aspect of the brain, one may want to use a detailed structural description for some parts of the model, and functional descriptions for others. For example, in modeling the role of a parietal area in visually directed grasping, one may choose not to burden the model with a detailed representation of the actual brain regions (retina, thalamus, visual cortex, etc.) that process the visual input it receives, but instead combine their functionality in a single abstract schema. In other cases, one may decompose a schema into finer schemas and simulate their interaction, and some but not all of these subschemas will be mapped onto detailed neural structures.
The starting point for schema theory as used here (Arbib, Érdi, & Szentágothai, 1998, Chapter 3) was to describe perceptual structures and distributed motor control in terms of coordinated control programs linking simpler perceptual and motor schemas, but these schemas provide the basis for more abstract schemas which underlie action, perception, thought and language more generally. Thus the modules that constitute a modular model of some aspect of brain function may be designed to represent an actual structure of the brain, or a schema which captures a function which may possibly require interaction of multiple brain structures for its realization.
Modules as Interfaces
The above types of modules represent the component structures and/or functions to be included in a model of some aspect of the brain. Other modules are designed to help the user interact with the model. For example, the key notion of an experimental protocol – which defines a class of experiments by specifying a set of experimental manipulations and observations – is represented by a simulation interface which supports the simulation of experiments using the given protocol.
NSL: A System for Modular Brain Modeling
The Neural Simulation Language (NSL) was developed to support such modular modeling. The environment has been developed to provide an object-oriented approach to brain modeling. This section presents a high-level view of the modular modeling methodology that NSL embraces. (See Weitzenfeld, Arbib, & Alexander, 2002, and http://nsl.usc.edu/nsl/Homepage.php for details and exemplary implementations.) The implication is that this object-oriented methodology is of generic value for computational neuroscience whether or not NSL (which has been developed to run atop C++, Java, or MatLab) is employed for the actual implementation.
The Brain Operation Database BODB
The Brain Operation Database BODB (“Beau D B”) was motivated by the immense diversity of models in cognitive neuroscience, and the sad lack of using benchmarks to compare similar models against each other. BODB was designed to document not only Models but also Brain Operating Principles and Summary Data to aid in finding and comparing related models. Preliminary versions of BODB were developed as Brain Models on the Web (Bischoff-Grethe, Spoelstra, & Arbib 2001) and the Action Recognition Database (ARDB). BODB comprises a major reworking of ARDB and is now fully functional and in its third version (Plangprasopchok, Tinroongroj, Bonaiuto, & Arbib 2006). (Warning: A number of BODB entries are placeholders used to develop and test system functionality so further work is needed to replace these with stable entries.)
A Model in BODB may be (a) an explicitly implemented computational model of the kind described above, or (b) a conceptual model. In general a model is entered in BODB as hierarchically composed of a number of different modules, which themselves may or may not be further decomposable.
Summary Data in BODB can encapsulate any kind of normalized experimental result along with the associated protocol. They can be used both in the design and testing of models. Unfortunately, most models are published in papers in which the data are not systematically classified, and the choice of data is ad hoc rather than systematic. The design of BODB is informed by the view that models will be improved to the extent that they are benchmarked against the data associated with comparable models. To address this, BODB can, given a model of interest, be searched for models linked to similar summary data, and these data can then be used as a basis for model comparison.
Neuroscience is equipped with structural ontologies which allow one to locate neurons within specific brain regions, but almost no work has been done on ontologies for function. A key BODB innovation is the Brain Operating Principle (BOP) to serve as a tool for indexing models and expressing their functional similarities. A BOP is a generalized description of an “operating principle” common to a range of models and empirical data. One example of a BOP is the Winner-Take-All (WTA) Principle. What makes this a BOP rather than a model is that it applies to aspects of the operation of diverse models, such as a model of visual selection in frog tectum (Didday 1976), a model of saccade control in superior colliculus (Dominey & Arbib 1992), a model of attention and visual salience (Itti & Koch 2000), and focusing learning in self-organized formation of feature maps (Kohonen 1988). BOP entries help users of BODB search for Models which share common principles, thus extending the range of neural architectures which can be taken into account in model analysis and design. BOPs also aid model developers by supporting search for implemented submodules of desired functionality.
Models of cognition-related brain networks and functions are large and complex. Thus the direct comparison of such models in toto will be cumbersome. However, it is feasible to compare modules of hierarchically decomposed models against each other and against a range of empirical data. The current version of BODB requires that Summary Data linked to a Model be labeled in one of 5 ways:
- Scene Setting – Background information that is not specifically used in developing or assessing the model.
- Assumptions – Data used to design the model. For example, knowing that there is an inhibitory connection from substantia nigra pars reticulata (SNr) to superior colliculus (SC), a modeler might specify an inhibitory projection from neurons in the module representing SNr to the module representing SC.
- Explanations – These are data that the model explains, in the sense that simulations of the model run using an appropriate simulation interface match the empirical data to a degree that provides insight into the causal relations in the experimental preparation that may be responsible for the observed results.
- Predictions – Simulations with the model may offer predictions for not-yet-conducted experiments.
- Contradictions – Experimental data or simulation results with alternative models may contradict the model. However, the nature of systems models is such that while certain contradictions may lead to wholesale rejection of a model, others may rather point to areas for future research – “this is a good model because it explains A, B and C, but we need to refine it so that it explains D”.
BODB uses the above 5 criteria into a basis for comparison of related models. It provides an automatic “Benchmarking Table” facility. Users are provided with a form which enables them to select which models collated in BODB they wish to compare. BODB then provides a table with one row for each summary datum linked to any of the models, and one column for each model. Each entry in the Table will offer the status of that datum for that model with an active link to information about that status. The finding that two models which address related data succeed in explaining different subsets of the data can then be used to investigate which modules contribute to which explanatory successes. A combination of successful models can then be used as a starting point for further modeling, but in general only as a starting point since modules will need to be modified as a result of this explicit comparison.
The thesis of this article, then, is that modular design of complex models, coupled with tools for comparing simulation results for models and constituent models against summaries of empirical data, supports comparative analysis in a way which is impossible for “spaghetti code” models. Thus Modular Modeling, coupled with appropriate neuroinformatics tools, should help cognitive computational neuroscience enter a new phase where modeling becomes truly cumulative.
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