A Computational Model of Acute Focal Cortical Lesions
Background and Purpose Determining how cerebral cortex adapts to sudden focal damage is important for gaining a better understanding of stroke. In this study we used a computational model to examine the hypothesis that cortical map reorganization after a simulated infarct is critically dependent on perilesion excitability and to identify factors that influence the extent of poststroke reorganization.
Methods A previously reported artificial neural network model of primary sensorimotor cortex, controlling a simulated arm, was subjected to acute focal damage. The perilesion excitability and cortical map reorganization were measured over time and compared.
Results Simulated lesions to cortical regions with increased perilesion excitability were associated with a remapping of the lesioned area into the immediate perilesion cortex, where responsiveness increased with time. In contrast, when lesions caused a perilesion zone of decreased activity to appear, this zone enlarged and intensified with time, with loss of the perilesion map. Increasing the assumed extent of intracortical connections produced a wider perilesion zone of inactivity. These effects were independent of lesion size.
Conclusions These simulation results suggest that functional cortical reorganization after an ischemic stroke is a two-phase process in which perilesion excitability plays a critical role.
As computational methods for brain modeling have advanced during the last several years, there has been an increasing interest in adopting such methods to study disorders in neurology, neuropsychology, and psychiatry. For example, models of Alzheimer's disease, epilepsy, aphasia, dyslexia, and schizophrenia have been studied recently to obtain a better understanding of the underlying pathophysiological processes.1
The complexity of events in stroke suggests that computational models can be powerful tools for its investigation, much as they are in the analysis of other complex systems (global climate prediction, geological exploration, etc). Ultimately, one seeks a sufficiently powerful model that can be used to understand better the acute poststroke changes in the ischemic penumbra, to determine which factors lead to worsening or recovery from stroke, and to suggest new pharmacological interventions and rehabilitative actions that could improve stroke outcome. However, the complexity of stroke pathophysiology, and the limitations of current modeling technology and neuroscientific knowledge, make it impractical to create immediately a detailed large-scale model of the brain and all of the effects of a major stroke. Here we consider the more limited yet still challenging objective of creating a computer model of circumscribed regions of cerebral cortex and of small ischemic lesions. We further consider only neuronal activation effects of acute lesions on cortical maps due to disruption of neural elements.
Many past computational models of the cerebral cortex have concentrated on map formation because this is a prevalent organizational aspect of the mammalian brain. Cortical maps represent similar inputs close to one another in the cortex, and they can be divided into topographical and feature maps.2 3 For topographical maps, similarity of input patterns is measured in terms of their geometric proximity. For feature or computational maps, the similarity measure can represent any functional correspondence of the input patterns. For example, in visual cortex, a feature map of stimulus orientation varies systematically over the cortical surface, embedded in a topographical (retinotopic) map.
While both topographical maps and feature maps have been modeled computationally in the past,1 previous studies involving acute focal cortical lesions have focused on topographical somatosensory maps.4 5 6 Conceptually, these latter models simulate the projection of the hand's tactile sensory neurons onto a two-dimensional region of primary somatosensory cortex. Neural activity and synaptic changes are modeled mathematically. Initially, thalamocortical synaptic strengths are random; therefore, a precise cortical map of the hand surface does not exist. The models undergo a developmental training period during which synaptic modifications occur as random stimuli are applied to the hand. Synaptic strengths change over time according to a competitive Hebbian rule: correlated presynaptic and postsynaptic activity leads to strengthening of a synapse, while uncorrelated activity leads to weakening. As a result, the receptive fields of cortical elements in model cortex change with time, and a topographical cortical map appears in which adjacent cortical elements are activated by adjacent stimuli on the hand surface.
After a model is trained as described above, a focal lesion is introduced into the developed topographical map in primary somatosensory cortex. This causes the map to reorganize such that the sensory surface originally represented by the lesioned area spontaneously reappears in adjacent cortical areas, as has been seen experimentally in animal studies.7 Two key hypotheses emerged from this modeling work. First, postlesion map reorganization is a two-phase process, consisting of a rapid phase due to the dynamics of neural activity and a longer phase due to synaptic plasticity. Second, increased perilesion excitability is necessary for useful map reorganization to occur.
These previous simulation studies, as well as others,8 indicate the important role of intracortical interactions in postlesion brain reorganization. Specifically, after a structural lesion that simulates a region of damage and neuronal death, a secondary functional lesion can arise in adjacent cortex because of loss of synaptic connections from the damaged area to surrounding intact cortex. In the following text, we use the term “functional lesion” in this limited sense and not to indicate the ischemic penumbra.
In the work reported in this article, we examined these two map reorganization hypotheses through simulations with a new cortical model. We used a recently developed computational model of primary sensorimotor cortex that controls the positioning of a simulated arm in three-dimensional space.9 This model is substantially more complex than the somatosensory cortex model described above, but neural activation dynamics and synaptic modifications are governed by similar principles and mathematical equations. Starting with initially random synaptic strengths, the model is trained by letting synaptic changes occur while random stimuli are applied to the motor cortex. As a result, maps form in the two cortical regions represented in the model: proprioceptive sensory cortex (PI) and primary motor cortex (MI). Unlike the previous computational models of somatosensory cortex described above that were subjected to simulated focal lesions,4 5 6 the maps involved here are feature maps and involve motor output and sensory input information. In simulations with the model, we examined and compared both perilesion excitability and cortical map reorganization immediately after a lesion and over the long term. The results obtained support the two hypotheses given above. We describe these results, correlate our hypotheses with the findings, and describe how they may influence the fate of the ischemic penumbra in stroke.
Materials and Methods
The computational model used in this study is a recently reported artificial neural network model of primary sensorimotor cortex.9 It consists of two parts: a simulated arm that moves in three-dimensional space and a closed loop of neural elements that controls and senses arm positions. Each neural element in the model represents a population of real neurons, not a single neuron. The structure of the model is illustrated in Fig 1⇓.
The transformation of activity in lower motor neurons to proprioceptive sensory neural activity is generated using a simulated arm (bottom of Fig 1⇑). This model arm is a significant simplification of biological reality.9 10 It consists of upper and lower arm segments, connected at the elbow. It has six generic muscle groups, each of which corresponds to multiple muscles in a real arm. Abductor and adductor muscles move the upper arm up and down through 180°, respectively; flexor and extensor muscles move it forward and backward through 180°, respectively. The lower arm flexes and extends as much as 180°, controlled by lower-arm flexor and extensor muscles. Activation of the lower motor neuron elements place the model arm into a specific spatial position. The simulated arm then generates input signals to the cortex via the proprioceptive neuron elements that indicate the length and tension of each individual muscle group (see Fig 1⇑).
Activation flows in a closed loop through four sets of neural elements: MI, lower motor neurons, proprioceptive neurons, PI, and back to MI (Fig 1⇑). Activity in lower motor neurons sets the arm position, which in turn determines the length and tension of six simulated muscle groups. We use the nonstandard abbreviation PI to designate the region of primary somatosensory cortex receiving proprioceptive input from the upper extremity; this roughly corresponds to Brodmann's area 3a.11 The twelve receptor elements in the proprioceptive input layer are fully connected to PI; they provide six muscle-length and six muscle-tension measures. A length element becomes active when the corresponding muscle is stretched, whereas a tension element activates when the corresponding muscle produces tension through active contraction. Biologically, length (stretch) is measured by the receptors in muscle spindles, and muscle tension is measured by receptors in Golgi tendon organs.12
The PI and MI layers are both two-dimensional arrays of elements with lateral (horizontal) intracortical connections. Each element of these layers represents a cortical column and is connected to its immediate neighboring elements in a hexagonal tessellation. To avoid edge effects, elements on the edges of the cortical sheet are connected with their corresponding neighbor elements on the opposite edges, forming a torus, as is often done in models of this sort. Each element of PI sends synaptic connections to its corresponding element in MI and to surrounding elements in MI within a radius 4, providing a coarse topographical ordering for the connections from PI to MI. This pattern of connectivity is motivated by previous experimental studies that have demonstrated topographical ordering of excitatory connections from primary sensory cortex to MI.13 14 Each MI element is fully connected to the lower motor neurons.
Each neural element i in the model has an associated activation level ai(t), representing the mean firing rate of neurons in that element at time t (see “Appendix”). A “Mexican hat” pattern of cortical activity, ie, a central region of excitation with a surrounding annular region of inhibition such as occurs experimentally,15 16 appears in response to a localized excitatory cortical input. This response is produced by a competitive model of cortical dynamics that has been previously used on multiple occasions for this purpose.4 10 17
Initially, weights on all interlayer connections are randomly assigned; thus the initial cortical maps are poorly organized. During simulations, connection weights representing synaptic strengths are modified using an unsupervised learning rule similar to that used in several previous models of cerebral cortex.1 4 5 10 Only interlayer connections are changed. The learning rule is both correlational (Hebbian) and competitive: the strengths of synapses between simultaneously active neural elements tend to increase (correlational), while those between elements with uncorrelated activities tend to decrease (competitive). Synaptic modifications made in this fashion lead to cortical elements with incoming weights (synaptic strengths) with spatial distribution resembling the input patterns that activate those elements. Because lateral excitatory intracortical connections tend to make nearby cortical elements active simultaneously, neighboring cortical elements develop similar receptive fields, and thus a map appears over time.
Map Formation in the Intact Model
The neural model is initialized with small random weights so that well-formed feature maps are not present in the cortical regions initially. The model is then trained as follows. A patch of external input is repeatedly provided at randomly selected positions in MI (radius 1, intensity 0.3, duration 720 iterations). Two thousand random stimuli to MI, covering the cortical space, are applied to the network during training; further training after these stimuli does not produce qualitative changes in the trained weights or the cortical feature maps that appear.
For examination of the resultant proprioceptive maps in the cortical layers, the two cortical areas are analyzed to determine to which muscle length and tension input each cortical element responds most strongly. Twelve input test patterns are presented, each having only one muscle length or tension element of the proprioceptive input layer activated. Because the proprioceptive input layer elements represent the length and tension of the six muscle groups of the model arm, each test pattern corresponds to the unphysiological situation of having the length or tension of only one muscle group activated (this situation was never present with the training patterns). A cortical element is taken to be “maximally tuned” to an arm input element if the activation corresponding to that input element is largest and above a threshold of 0.4 (the distribution of cortical activations was bimodal, with values mostly between 0.0 and 0.25 or 0.6 and 1.0, thus our results are relatively insensitive to exact choice of threshold). The prelesion feature maps are described in detail elsewhere9 10 and are summarized briefly here.
Fig 2⇓ shows which PI and MI cortical elements are maximally responsive to stretch of specific muscles after training. For example, the element in the upper left corner of Fig 2a⇓ is maximally responsive to stretch of the upper-arm adductor (D). The input map in Fig 2a⇓ is for all six muscle groups for the PI cortical layer; the map in Fig 2c⇓ is the corresponding input map for MI. Before training, elements maximally responsive to the stretch or tension of the same muscle group were irregularly scattered across the map.
Although it is difficult to see in Fig 2a and 2c⇑⇑, the maps form clusters of adjacent elements that respond to the same input. This can be better seen in the maps of Fig 2b and 2d⇑⇑, which show just those elements in Fig 2a and 2c⇑⇑ that are maximally activated by the stretch of the upper-arm extensor (E) and upper-arm flexor (F) in PI and MI, respectively. Fig 2b⇑ illustrates the regular size and spacing of the clusters across the PI layer and that clusters responsive to antagonist muscles tend to be separated (Es and Fs tend to be pushed apart). PI and MI maps of responsiveness to muscle-tension inputs also exhibit uniformity in size and spacing of clusters responsive to the same muscle group. Note that the PI and MI maps of muscle-length sensitivity in Fig 2b and 2d⇑⇑ are not aligned despite the fact that there is a rough topographical ordering in connections between PI and MI. The transformation of the map in MI relative to PI arises because multiple clusters of PI elements are active simultaneously. The divergent connections from such nearby active clusters in PI produce a pattern of activity in MI that is not a copy of that in PI, and the synaptic modification rule captures the correlations between these different activity patterns, leading to nonaligned maps.9 Different maps in the same region of cortex can also have interesting relationships. For example, when the length map for PI is compared with the tension map for that layer, it is found that the length map of a particular muscle matches well with the tension map of its antagonist muscle.9 The maps capture correlated features of input patterns, reflecting the mechanical constraints imposed by the model arm.
In addition to the sensory or input maps in MI, there is simultaneously an MI motor output map. The output map is determined by examining each MI element to see which muscle group(s) it activates most strongly. With training, clusters of elements activating the same muscle group appear in this map as well, resembling the distributed nature of motor output maps observed experimentally in animal studies.18 Further study reveals that the MI input map of the length of a particular muscle matches the MI output map of its antagonist muscle, and the MI input map of a particular muscle's tension matches the MI output map of its corresponding muscle.9 The motor output map in MI (not pictured here) thus resembles the proprioceptive input map in Fig 2d⇑ very closely, except the Es and Fs are reversed.
Lesioning the Model
To examine the effects of sudden focal lesions of various sizes to the cortex (“simulated ischemic strokes”), two sets of simulations were done in which an area of focal damage was suddenly imposed on a previously trained network. The first set involved lesions in PI, the second lesions in MI. In both cases, a focal lesion was simulated by clamping the activation levels of a contiguous set of “lesioned” cortical elements permanently at zero. In addition, connections to and from lesioned cortical elements were severed.
The effect of each lesion on the existing proprioceptive and motor maps in the trained intact cortex was examined twice: immediately after the lesion and after continually training the network with 2000 additional random input stimuli in MI. Random stimuli were used because we were modeling the natural evolution of postlesion changes rather than a specific rehabilitative intervention. An analysis of changes in the position of the model arm after cortical stimuli was also made both immediately after the lesion and after further training. All lesion effects were compared with the prelesion network, as well as with a control network. The control network was an exact copy of the intact prelesion network made immediately before lesioning. Training was continued with this unlesioned control model, with additional random input stimuli, so that any map alterations due to continued training alone could be compared with those due to lesioning plus continued training.
To guard against an interaction between lesion effects and the initial state of the model, simulations were done with several different sets of initial random weights. No significant qualitative difference was identified in the lesion results with any initial set of random weights.
Unlesioned Control Model
In the lesioning experiments described below, we always started with a prelesion model that had been trained so that quasi-stable, well-formed maps were present in both sensory and motor cortical regions. We then induced focal structural damage in these models and allowed interlayer synaptic modifications to continue for 2000 input stimuli. In each case, a corresponding unlesioned model, starting from the same initial state of well-formed maps, was run as a control to examine the effects of the same 2000 input stimuli and synaptic modifications in the absence of a lesion. As expected, little qualitative change was seen in the control cortical maps with this further training beyond the small shifts of cluster positions in the maps expected with this motor loop model.9
As with the cortical maps, the positions assumed by the model arm in response to cortical stimuli did not differ significantly between the trained prelesion model and the control. Fig 3a⇓ shows the model arm in four of six test positions for both the intact prelesion model and the further trained control model, corresponding to “requests” to contract the upper-arm extensor, upper-arm flexor, upper-arm abductor, and upper-arm adductor. As seen in Fig 3a⇓, the four arm positions corresponding to these motor cortex stimuli are in the anticipated directions and are virtually indistinguishable for the trained prelesion model (dotted lines) and the further trained control model (hatched lines). The stability of both cortical maps and arm positioning in response to cortical stimuli in the control model indicate that changes seen in the lesioning simulations described below are caused by the lesions themselves.
Focal Lesions in PI
We examined the effects of structural lesions in PI under a variety of conditions. Changes to the feature maps in PI were observable immediately after a structural lesion occurred in this layer, as the first phase of a two-phase reorganization process. After the primary structural lesion in PI, the activity of surrounding elements was decreased, forming a secondary functional lesion. For example, Fig 4a⇓ shows a perilesion zone of relatively inactive cortical elements (marked by –) seen immediately after an 8×8 focal lesion; these elements do not respond to the stretch of any of the muscles above a threshold of 0.4.
The second phase of reorganization occurred more slowly, with continued synaptic changes during the postlesion period. With time, as the map reorganized in the context of continued proprioceptive input and synaptic changes, the functional lesion gradually enlarged. For example, with an 8×8 structural lesion, there was a 77% increase in perilesion inactivity at distances 1 and 2 from the lesion edge over the long term (compare Fig 4b⇑ with 4a). Similar changes were observed with the proprioceptive map of muscle tension. Over time, clusters of elements responsive to the stretch of a particular muscle also shifted position in the feature map.
The functional lesion effects described above occurred largely independently of structural lesion size in PI. They are representative of the effects observed with lesions that varied incrementally in size from 2×2 to 8×8. The dynamics of these functional lesions can be analyzed further by examining the mean activation level of cortical elements, averaged over all of the test input patterns. There was an essentially uniform prelesion mean activation of the PI elements of roughly 0.12. Immediately after induction of the structural lesion, the mean activation level of cortical elements directly adjacent to the lesion site dropped to 0.08, about 70% of its prelesion value. With additional synaptic modifications after the lesion, these perilesion effects in the PI layer were intensified (about 25% of prelesion value) and shifted outward.
Further examination of the model after lesioning in PI revealed that perilesion cortical elements were activated at essentially the same amount for all input stimuli, in contrast with the prelesion cortex where elements were activated selectively for some specific input stimuli but not others. This uniformity occurred as the result of the loss of excitatory support from cortical elements in the structural lesion via intracortical connections. As the map reorganized after the lesion, the weights to these perilesion cortical elements tended to become uniform.
We attempted to prevent the spread of the perilesion functional deficit by providing a small uniform external input to elements at a distance 1 from the lesion during the postlesion period of continued synaptic modifications. We did this to confirm that it is the low activation levels in the perilesion elements that lead to the spread of the functional deficit. This change arrested the spread of the perilesion functional deficit: there was significantly more reorganization in the map at distance 2 from the lesion. However, when synaptic modifications were subsequently allowed to continue even further without the increased external input, all gains made in arresting the spread of the functional deficit were lost.
Immediately after the onset of larger structural lesions (5×5 and larger) in PI, an irregularly shaped area of inactive motor cortex elements appeared in the center of the sensory maps of the MI layer and did not resolve with further training. Given the coarsely topographical projections from PI to MI (projections from PI to MI elements within a radius 4), the observed inactive zone in the center of the motor cortex sensory map is expected and can be viewed as an example of diaschisis. In addition to these effects on the sensory maps of the MI layer, larger PI lesions produced a central region in the motor output map that did not activate any muscle groups in the lower motor neuron layer. This was due to the loss of excitatory input to this region from the corresponding lesioned area in PI. The percentage of MI elements activating one or more muscle group(s) in the motor output maps was 77% before lesioning. This decreased with larger PI lesions (5×5 and larger); with an 8×8 PI lesion, the percentage dropped to 68% over time.
The decrease in motor output map responsiveness with lesions of increasing size led to “weakness” of the model arm after a lesion in PI. Fig 3b⇑ shows the arm position for the same four test inputs to MI as in Fig 3a⇑ for an 8×8 focal lesion in PI. Immediately after the lesion, a measurable shift was observed in arm positions away from their prelesion position and toward the neutral resting position of the arm. For example, the elbow position immediately after the lesion for the upper-arm flexor test was 20° away from its prelesion position, revealing a weakened flexor response. Similar weakened responses were seen with the contraction tests of the abductor, adductor, and lower-arm flexor immediately after the lesion. This occurred because of functional loss of MI elements that activated each muscle group. However, over time, with continued cortical plasticity, the arm positions for all test inputs realigned with their prelesion positions, representing essentially complete “recovery.” With larger PI lesions (eg, 16×16), such recovery was incomplete.
Focal Lesions in MI
A separate set of simulations was performed to study reorganization of the MI cortical maps after focal structural lesions of various sizes in MI (2×2 to 8×8). For sufficiently large lesions, reorganization after a structural lesion in MI was seen in both the MI sensory and motor output maps. Immediately after the onset of such large focal lesions to MI, both the stretch and tension sensory maps for MI adjusted so that there was an increase in the number of responsive elements in normal cortex near the lesion edge. In contrast to PI lesions, no perilesion zone of decreased activation was present. This reorganization can be seen by comparing the MI sensory map for muscle stretch in Fig 5a⇓ with the corresponding map in Fig 2c⇑. At distances 1 and 2 from the lesion edge, there was an increase in the number of responsive elements over prelesion levels from 91% before lesion to 96% immediately after this 8×8 lesion. Although the change in absolute numbers of responsive elements is small, it accurately reflects a substantial increase in mean activation levels of all elements averaged over all inputs in this perilesion zone (from 0.14 before lesion to 0.21 after). Over time, the responsiveness at distance 1 and 2 stabilized at 99%, as is seen in Fig 5b⇓. Overall rates of responsiveness for the MI sensory maps increased slightly immediately after the onset of the lesion but then dropped back to prelesion levels with continued postlesion synaptic modifications.
This postlesion reorganization result is similar to results of prior studies of structural lesions to cortical layers with topographically ordered somatosensory inputs.5 In this context, it is important to note that the topographically ordered connections between PI and MI in this present model are similar to those between thalamus and sensory cortex in the earlier model (projections from PI to corresponding MI elements are made within a radius 4).
Like the MI sensory maps described above, the MI output map in residual intact cortex demonstrated an increase in relative activity. The number of MI elements activating one or more muscle group(s) increased after an MI lesion of sufficient size (4×4 and larger). For an 8×8 lesion, the percentage of remaining MI elements activating one or more muscle group(s) increased from 77% to 86% of intact elements. This also affected the positioning of the model arm when tested with six external inputs to MI. As seen in Fig 3c⇑, with a 16×16 focal lesion in MI, the arm position revealed a weakened response immediately after the lesion. For example, the elbow position immediately after the lesion for the upper-arm flexor test was 15° away from its prelesion position, roughly in the direction of the resting position. Further postlesion synaptic modifications in the presence of the MI lesion did not produce a complete realignment of the arm positions with their prelesion location, although complete recovery did occur with smaller MI lesions (eg, 8×8).
The lack of any significant postlesion reorganization with small MI lesions (2×2 and 3×3) can be attributed to the coarseness of the topographical projections from PI to MI. Each MI element receives input from 61 PI elements; with such small MI lesions, the distribution of output from PI elements was only minimally perturbed, and perilesion elements continued to experience a distribution of input patterns similar to that before lesioning. As a result, their receptive fields and thus the MI map remained largely unchanged because of the correlational nature of the synaptic modification rule.
Examination of the feature maps for PI (both after a lesion and with further training) did not reveal any qualitative reorganization after MI lesions beyond the small shifts of cluster positions expected with this model.9 Although motor output was weakened with larger MI lesions, it did not appear to affect feature map organization in PI.
It is currently not well understood how the neural circuits of the cerebral cortex adjust to the sudden structural damage occurring with an ischemic stroke. In this study, we induced acute focal lesions in a computational model of primary sensorimotor cortex to examine the resultant functional deficits in surrounding cortex. Although such a neural model is a substantial simplification of reality, it is based on generally accepted concepts of cortical structure, activity dynamics, and synaptic plasticity. It demonstrates interesting postlesion effects concerning cortical map reorganization, along with some insight into why these secondary effects arise. Such effects represent testable predictions of the model.
In our simulations, it was observed that focal lesions resulted in a two-phase map reorganization process in the intact perilesion cortical region. The first very rapid phase was due to changes in activation dynamics, while the second slow phase was due to synaptic plasticity. Thus, the model makes the prediction that biological perilesion map changes will be demonstrable within a few minutes of a cortical lesion. To our knowledge, although there are a few experimental animal studies that have examined postlesion cortical map reorganization (see below), none of these have measured maps immediately after the lesion. Recent experimental studies in animals have repeatedly shown map reorganization within minutes after focal deafferentation of cortex19 20 ; our model predicts that such reorganization will occur after cortical lesions as well and provides some details about their nature.
The second prediction of our model is that increased perilesion excitability is necessary for effective map reorganization in cortex surrounding an acute focal lesion. When increased perilesion excitability was present during the first phase of map reorganization, the cortex surrounding the lesion consistently participated in the map reorganization process, even achieving a higher-density feature map than in the prelesion cortex. Presumably, such effective utilization of surrounding intact cortex after a lesion could contribute to behavioral recovery from an ischemic stroke. On the other hand, when there was decreased excitation in perilesion cortex, this intact cortex consistently did not participate in map reorganization, and the perilesion cortex that “dropped out” of the map actually expanded with time because of the normal modifications of synaptic strengths. These very different results, observed here for pure feature maps (PI) and for feature maps involving topographically arranged inputs (to MI from PI), are consistent with similar results obtained in our earlier study involving pure topographical maps.4 5
The notion that perilesion excitability is an important factor may prove useful in interpreting animal studies of postlesion map reorganization. Under some conditions in these studies, functions originally represented in the infarct zone of sensorimotor cortex reappeared or expanded in nearby intact cortex,7 21 22 whereas under other conditions they did not.23 Our model suggests that assessing perilesion excitability under these differing conditions may shed light on why the different results occur.
The dependence of map reorganization on perilesion excitability in the model can be explained by examining the synaptic modification rule that produces map formation originally (Equation 3 in “Appendix”). Informally, this rule causes changes to the receptive field of a cortical element (1) at a rate proportional to how active that element is and (2) such that the receptive field shifts to become more like the pattern of input elements that activate that cortical element. Thus, when the activation of a perilesion element is low, its receptive field changes very slowly, and little reorganization occurs. When perilesion activity is high, the receptive field will change quickly, and substantial reorganization will occur. In this context, the differences in the input connections to PI and MI account for differences in how these two regions reorganize. In PI, the diffuse afferent inputs have little influence on, and therefore little correlation with, the perilesion elements after a lesion. Thus, intact cortical elements adjacent to the original postlesion functional deficit lose correlated activity from neighbors, become less correlated with specific input patterns, and tend to drop out of the map. In contrast, the coarsely topographical connections from PI to MI that originally supply the outer region of lesioned cortex have an increased influence on, and become more correlated with, perilesion elements, causing the latter's receptive fields to shift and thus substantial map reorganization to occur.
In the context of these modeling results, it is interesting to note that direct experimental evidence does exist for increased excitability in intact cortex after a small focal lesion.24 Such increased excitability has generally been viewed as detrimental, although this is controversial.25 Our computational model suggests that, in addition, increased excitability may play an important and previously unrecognized role in recovery from stroke. At the very least, the model indicates that further experimental investigation of this issue is warranted and will be useful in obtaining a better understanding of recovery after stroke. In our model, the primary factors determining whether perilesion activity increased or decreased were the extent of divergence of afferents to the cortical region and the ratio of intracortical lateral excitation to inhibition. In other words, in both PI and MI the cortex immediately around the lesion lost excitatory input from the lesioned region. However, the widely divergent inputs to PI were insufficiently powerful to compensate for this loss of perilesion excitation from lateral connections arising in the lesion area, while the much more focused afferents to MI were.
Finally, the results of this study raise more global issues about the role of computational models in stroke research in general. Computational modeling represents a truly novel approach to studying stroke that complements traditional methods and may provide useful guidance for future empirical studies. The results reported here, as well as the related recent modeling results described earlier, provide the first demonstration that nontrivial computational models of ischemic stroke are possible. Of course, these models are substantial simplifications of biological reality. We are currently extending our models to encompass some of the biochemical and metabolic alterations occurring in the ischemic penumbra, with an emphasis on ischemic depolarizations resembling cortical spreading depression. Initial results in modeling cortical spreading depression in normal cortex have been encouraging.26 Ultimately, the utility of such computational models may prove to be their heuristic value in suggesting novel experimental investigations and new approaches to therapeutic and rehabilitative intervention.
We produced a “Mexican hat” pattern of lateral interactions using a competitive model of cortical dynamics.5 10 17 The activation level ak(t) of element k at time t is\frac|<|\mathit|<|da_|<|k|>||>|(\mathit|<|t|>|)|>||<|\mathit|<|dt|>||>||<|=|>|\mathit|<|c_|<|s|>|a_|<|k|>||>|(\mathit|<|t|>|)|<|+|>||<|[|>|\mathit|<|M|<|-|>|a_|<|k|>||>|(\mathit|<|t|>|)|<|]|>||<|[|>|\mathit|<|in_|<|k|>||>|(\mathit|<|t|>|)|<|+|>|\mathit|<|ext_|<|k|>||>|(\mathit|<|t|>|)|<|]|>|where cs <0 is the decay rate, M is the maximum activation, ink is the activation received by element k from other elements, and extk is the external input applied to element k. Omitting t for brevity, the input to element k is\mathit|<|in_|<|k|>||>||<|=|>||<|\sum_|<|\mathit|<|j|>||>||>|\mathit|<|c_|<|p|>||>|\frac|<|(\mathit|<|a_|<|k|>|^|<|p|>||<|+|>|q|>|)\mathit|<|w_|<|kj|>||>||>||<||<|\sum|>|_|<|\mathit|<|l|>||>|(\mathit|<|a_|<|l|>|^|<|p|>||<|+|>|q|>|)\mathit|<|w_|<|lj|>||>||>|\mathit|<|a_|<|j|>||>|.where wkj is the synaptic strength from element j to element k. Constant cp >0 is the output gain, and parameters p and q influence the degree of peristimulus inhibition. Synaptic weights wkj are altered according to an unsupervised Hebb-like learning rule (competitive learning):|<|\Delta|>|\mathit|<|w_|<|kj|>||>||<|=|>||<|\eta|>||<|[|>|\mathit|<|a_|<|j|>||<|-|>|w_|<|kj|>||>||<|]|>|\mathit|<|a_|<|k|>||>|where η is a small learning constant. Only the weights of the three sets of interlayer connections are changed; cortico-cortical connections remain constant. Parameter values used here are the same as in Reference 9, with the exception of cs=–0.75 in the MI layer and a smaller step size δ=0.05. A detailed description of the training procedure used, the relative insensitivity of results to parameter variations, and the procedures used to assess map formation are given in Reference 9.
This work was supported by National Institute of Neurological Disorders and Stroke awards NS-29414 and NS-16332. The authors thank Michael Sloan, Steve Kittner, and the anonymous reviewers for helpful comments on this work.
- Received June 24, 1996.
- Revision received August 12, 1996.
- Accepted August 27, 1996.
- Copyright © 1997 by American Heart Association
Reggia J, Ruppin E, Berndt R, eds. Neural Modeling of Brain and Cognitive Disorders. London, UK: World Scientific; 1996.
Sutton G, Reggia J, Armentrout S, D'Autrechy C. Map reorganization as a competitive process. Neural Comput.. 1994;6:1-13.
King J, Gerstein G. Networks with lateral connectivity. J Neurophysiol.. 1996;75:184-232.
Jenkins W, Merzenich M. Reorganization of neocortical representations after brain injury. In: Sell F, Herbert E, Carlson B, eds. Prog Brain Res. Amsterdam, Netherlands: Elsevier; 1987;71:249-266.
Wise S, Tanji J. Neuronal responses in sensorimotor cortex to ramp displacements. J Neurophysiol.. 1981;45:482-500.
Gordon J, Ghez C. Muscle receptors and spinal reflexes. In: Kandel E, Schwartz J, Jessell T, eds. Principles of Neural Science. New York, NY: Elsevier Science Publishing Co; 1991:564-580.
Hess R, Negishi K, Creutzfeldt O. The horizontal spread of intracortical inhibition in the visual cortex. Exp Brain Res.. 1975;22:415-419.
Reggia J, D'Autrechy C, Sutton G, Weinrich M. A competitive distribution theory of neocortical dynamics. Neural Comput.. 1992;4:287-317.
Nudo R, Milliken G. Reorganization of movement representations in primary motor cortex following focal ischemic infarcts in adult squirrel monkeys. J Neurophysiol. 1996;75:2144-2149.
Nudo RJ, Wise BM, SiFuentes F, Milliken GW. Neural substrates for the effects of rehabilitative training on motor recovery after ischemic infarct. Science.. 1996;272:1791-1794.