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Computational Model of Lateralization As Affected by Cortical Asymmetries and Overlapping Inputs |
Cerebral lateralization is defined as the tendency for either hemisphere to be dominant over the other for specific functions, leading to a differential primacy, functional asymmetry, or preference for one side of the body.
Topographic maps are detailed, two-dimensional representations of the environmental stimuli in the cortex. It is observed that in general, similar stimuli activate the same area of the map.
Corpus callosum is a mass of transverse fibers connecting the cerebral hemispheres.
Hemispheric asymmetry is based of the concept that each hemisphere is specialized and dominates the other in certain functions.
The purpose of this study is to model asymmetry and lateralization in somatosensory cortical maps. Recent experimental studies (4, 25) have shown that such maps in mirror image regions of cerebral cortex exhibit a variety of asymmetries, the mechanisms of which are unclear. This research uses neural network models to help clarify these mechanisms.
Self-organizing maps (31, 17) based on competitive distribution of activation (26) were shown to model cortical topographic maps very well (29, 2). The S1 simulator used in this research models topographic map formation in one cortical region receiving input from a thalamus region. The hemispheric regions have spatial organization, while unsupervised (Hebbian) learning is used. Levitan and Reggia (18) developed the first model involving two cortical maps interacting via a simulated corpus callosum. They modified the S1 simulator to model two cortical regions connected by callosal connections and receiving simultaneous identical inputs from one thalamic set. Special metrics were used to map asymmetries and lateralization (1). When callosal strengths were excitatory, absent, or weakly inhibitory, symmetric maps were observed in both hemispheric regions, but if they were strongly inhibitory, maps formed in a complementary fashion. Lateralization due to hemispheric asymmetries occurred.
This study, a generalization of the last research presented, models topographic map formation in two cortical regions receiving independent, identical, or overlapping inputs from two separate thalamic sets. The effects of different overlaps of the training inputs on topographic map formation are studied, where all hemispheric parameters except initial random weights are identical. Then various model asymmetries are introduced and their effects on map organization are systematically studied for various callosal strengths and different overlaps of training inputs. This research provides support for and extends the previous research done using only one thalamic set since the most lateralization and asymmetry have been observed for identical training inputs. It was also observed that lateralization occurred largely in the models with asymmetric excitability and asymmetric cortical sizes. This supports the hypotheses that functional asymmetries may be associated with the size of cortical regions (12) and that multiple factors may be responsible for lateralization.
Past research studies have demonstrated anatomical asymmetries in the two hemispheres of the brain (10). Other studies demonstrated that many of the more specialized functions such as language, handedness, visuo-spatial processing, and emotions are controlled mainly by one hemisphere of the brain (9, 11, 24). This phenomenon is known as lateralization. Since its first description, lateralization has been studied from different perspectives. Currently lateralization is viewed as genetically transmitted (5) and evolutionarily significant (33). It has also been demonstrated function lateralization is not limited to humans (6).
Different studies have reported intrinsic hemispheric differences and the hemispheric connections via the corpus collosum as potential causes of cerebral asymmetries. It is unknown if the dominant influences of the corpus callosum are excitatory or inhibitory (8, 22).
Asymmetries in the size of cortical regions are in general associated with functional lateralization (12). However, cortical asymmetries may be present even in the absence of clear functional asymmetry and vice versa. Understanding the degree of asymmetry in structures that do not show clear functional lateralization is critical in interpreting data gathered from cortical regions that are functionally asymmetric (12).
Different methods have been used to investigate the brain functions and implicitly the cortical symmetry and lateralization (11). The use of these methods has led to a charting of the most specialized regions such as the motor cortex, the somato-sensory cortex, the primary visual area, Wernicke's area, the primary auditory area, the angular gyrus, and Broca's area, among others. The complex charting of the cortex has led to cortical maps. Topographic cortical maps are regions of the cortex that represent some aspect of the environment in a topology preserving fashion (14). Some studies have revealed that maps in primary sensorimotor cortex exhibit numerous patterns of individual lateralization and asymmetry (4, 25). Other studies demonstrated that maps in primary sensory cortex undergo reorganization, called self-organization (29). Biologically, maps undergo reorganization due to de-efferentation (27), deafferentation (23, 14), focal cortical lesions (13), and localized repetitive stimuli. Over the years, neural modeling researchers have developed computational models of topographic cortical map formation based on principles of competitive learning. Some studies demonstrated that both competitive and non-competitive activation mechanisms can be used to generate central-excitation (26, 16).
Recently, maps in mirror-image right and left cortical regions have been simulated for the first time (17). These maps were used to study affects of asymmetries in learning rates, cortical size, and excitability on lateralization. The model used was based on generally accepted concepts of neural connectivity, activation dynamics, and Hebbian synaptic changes. According to this model the hemispheric regions have a spatial structure and there are connections between different regions/areas. Levitan and Reggia demonstrated that the corpus callosum plays mostly an inhibitory role, and that underlying hemispheric asymmetries may cause lateralization.
The present study uses a model consisting of two parts of the sensory cortex connected by the corpus callosum, each receiving inputs from a separate thalamic set. Each thalamic and cortical set is a two dimensional surface made up of individual elements which hexagonally tessellate it. The use of two thalamic sets facilitates the study of the effects of the identical, non-simultaneous inputs and the effects of independent and partially dependant inputs. This research uses modeling devices to study lateralization instead of the traditional experimental methods. This study intends to provide more data in understanding functional lateralization.
A computer program in C, initially developed by D'Authercy, Sutton III, and Armentrout was modified by the researcher to accommodate two thalamic regions and two cortical regions as shown in figure 1. The sets are two-dimensional arrays of individual elements representing cortical columns; each element is connected to its six nearest neighbors in a hexagonal tessellation. Each sensory element in the thalamic set sends outputs to its corresponding element in the cortical set. Each cortical element sends inputs to its neighbors within a specified radius and through the corpus callosum to the corresponding element and its neighbors in the other cortex. Opposite edges on the thalamic and sensory surfaces are connected in order to avoid edge effects.
On the connections from each thalamic element to its corresponding cortex elements, unsupervised competitive learning occurs. For these connections, the researcher initially assigned uniformly random numbers between 0.00001 and 1.0 to the weights. Stimuli were applied on the sensory surface to random elements and neighbors within a radius of 2. The total number of elements stimulated by an input radius of 2 as used in these simulations was 19.
Programs were run with different degrees of overlap of 0, 10, 19, where each number represents the number of stimulated nodes in the two thalamic sets that are mirror images of each other. An overlap of 0 means the two inputs from the thalamic sets are completely independent of each other and rarely occur on the same, or corresponding, nodes. An overlap of 19 corresponds to identical input patterns from both thalamic sets, and is equivalent to the stimuli used in previous experiments which had only one thalamic set (18).
Figure 1: The Cortex Model Receiving Inputs From Two Separate Thalamic Sets
The simulations were divided into four categories based on the asymmetry/symmetry of the cortical regions: symmetric case, asymmetric excitability, asymmetric learning rates, and asymmetric cortical size. For all these cases, simulations were run for corpus callosum values ranging from -3, strongly inhibitory, to +1, excitatory. For each of these K values simulations were run for input pattern overlaps of 0, 10, and 19. Symmetry and lateralization of the resultant maps were studied as functions of callosal connection strength K. The same seed was used for random weight generation. The seed chosen was that which caused the least lateralization in the symmetric case.
The researcher used three basic measures to study the results. The first one was an organization measure that shows the degree of map formation in a single hemispheric region on a 0 to 1 scale. The second measure was a lateralization measure, showing the degree of map formation of the left hemisphere compared to the map formation of the right hemisphere, with values between -1, for complete left dominance, and 1, for complete right dominance. The third measure was a mirror symmetry measure, indicating the degree to which the two maps formed are symmetric, 1, or complementary, -1 (1).
The control version of the model for this experiment used symmetric cortical sizes, excitability, and learning rates. The two hemispheric regions were thus identical, except for the initial random weights. In all simulations this symmetrical model produced practically no lateralization. The first trials run with the symmetric case were with all possible degrees of overlap for an input radius of 2, as shown in figure 2. The results from these initial simulations showed sharp transitions at the input overlap of 10. Because of this, 10 was used as the partial overlap for the rest of the simulations along with 0, or independent inputs, and 19, or identical inputs, for the remaining simulations.
Figure 2: Degrees of Overlap vs. Organization and Mirror Symmetry
For inhibitory, absent, or excitatory corpus callosum values, the organization was close to 1, while for strongly inhibitory callosal values it dropped significantly, as seen in figure 3. The symmetry followed the same basic pattern, with values close to -1, implying complementary maps, for K values between -4 and -1, showing a sharp transition and increase towards 1 for K values greater than -1. The results for symmetry showed no substantial difference between the different degrees of overlap, as seen in figure 4.
Figure 3: Organization for Overlaps of 0, 10, 19.
Figure 4: Mirror Symmetry for Overlaps of 0, 19
Studies have shown that functional lateralization occurs towards the larger hemispheric side. In order to examine this theory, the model was modified to accommodate two hemispheres of differing sizes: one a 12 x 12 matrix of elements, the other a 16 x 16 matrix.
The organization follows the same pattern for overlaps of 0 and 19. The smaller cortex has a smaller organization of about 0.8, but reaches 1 and equals the organization for the larger cortex at a value of K of about -0.5. For an overlap of 10, both cortices start with low organizations of around 0.5 at K = -3, and increase to a value of 1. The smaller cortex always has a lower organization than the larger cortex, reaching a value of 1 at around K = -0.5, as seen in figure 5. Lateralization is evident for corpus callosum values that are strongly inhibitory. Symmetry for all cases follows the same pattern, with a value of -1 for K values less than -1, showing complimentary maps, and with a sharp transition at K= -0.5, with values of symmetry of 1, as seen in figure 6.
Figure 5- Organization for Overlaps 0, 10, 19
Figure 6- Mirror Symmetry for Overlaps 0, 10, 19
Asymmetric cortical excitability is caused by differing levels of neurotransmitter levels and in previous experiments has been found to correlate to functional lateralization (20).
The symmetry values for overlaps of 0 and 19 have values of -1 for K< -1 and increase sharply to a 1 for K= -1.5. This pattern also hold true for the overlap of 10 only that for K<-1, the value of symmetry is -0.5, as seen in figure 8. Lateralization is observed for all degrees of overlap and for values of K<-0.5, as seen in figure 7.
Another possible cause of lateralization is a difference in synaptic plasticity in the two hemispheres (18). The biological existence of such asymmetries is suggested by asymmetric neurotransmitter levels. Simulations were run to study the effect of these asymmetries by keeping everything constant except for the initial random weights and the learning rates, 0.01 for the left hemisphere and 0.001 for the right hemisphere. Initially the hemisphere with a higher learning rates organizes faster, but after sufficient, the difference between the two hemispheres is negligible.
Figure 7: Organization for Overlaps of 0, 10, 19
Figure 8: Mirror Symmetry for Overlaps of 0, 10, 19
Lateralization occurred for an inhibitory corpus callosum towards the hemisphere of greater size, or with greater excitability or faster learning rate. Similar results were observed for all asymmetric cases, for both complete and absent overlaps. Lateralization occurred in a similar manner for inputs which were identical and inputs which were completely independent. For a partial overlap, lateralization was significantly smaller than for independent and identical overlaps. Symmetry was also slightly greater for the partial overlap of 10, and for K values less than -1. These results are caused by a shift in the topographic maps which occurs for overlaps of 10. The maps are organized but are shifted to accommodate this almost perfect organization. The results from simulations run for differing overlaps with a value of K= -2 also show that mirror symmetry and organization follows a similar pattern for all values except for an input stimuli overlap of 10.
The degree to which the two maps were symmetric followed the same pattern for all simulations, including the symmetric case. For a strongly inhibitory corpus callosum, with values less than -1, the maps were complementary, while for K values greater than -1, the maps were symmetric. This illustrates the fact that maps form in a complementary fashion for inhibitory corpus callosum values, even if the two cortexes receive inputs that are overlapping or independent from each other.
There has been much research done to study the brain and lateralization, and a few models of specific parts of the brain have been constructed. However only four of these models have studied hemispheric interactions. This study modeled topographic map formation in two cortical regions receiving independent, identical, or overlapping inputs from two separate thalamic sets.
The results of this study suggest that multiple asymmetries lead to functional lateralization. These asymmetries include asymmetries in synaptic plasticity, cortical size, and excitability. It can be concluded that inhibitory calossal influences lead to lateralization and mirror symmetry. The results showed no significant correlation between the complete or separate overlapping of stimuli and mirror symmetry and organization. For partial overlaps, more research is needed to draw accurate conclusions about the shifting of the topographic maps. There is no clear explanation for these unexpected results, this being the first research of its kind to study partially overlapping inputs to the cortexes.
Furthermore, these results along with those from other modeling projects support the hypothesis that the influence of the corpus callosum is mostly inhibitory. The general implications of this hypothesis are significant in the fields of psychiatry and neurology, where effects of an inhibitory corpus callosum would explain multiple neurological disorders, and brain functioning in general. Successful modeling of brain functioning may eventually lead to better diagnosis and treatment of mental disorders on one hand, and to better computer architectures that mimic the brain, on the other hand.
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