The Connectional Organization of the Cortico-thalamic System of the Cat

J.W. Scannell, G.A.P.C. Burns, C.C. Hilgetag, M.A. O'Neil1 and M.P. Young

Neural Systems Group, Psychology Department, Ridley Building, University of Newcastle, Newcastle upon Tyne NE1 7RU and , 1 The Bee Systematics and Biology Unit, Hope Entomological Collections, University Museum, Oxford University, Parks Road, Oxford OX1, UK


    Abstract
 Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
 References
 
Data on connections between the areas of the cerebral cortex and nuclei of the thalamus are too complicated to analyse with naked intuition. Indeed, the complexity of connection data is one of the major challenges facing neuroanatomy. Recently, systematic methods have been developed and applied to the analysis of the connectivity in the cerebral cortex. These approaches have shed light on the gross organization of the cortical network, have made it possible to test systematically theories of cortical organization, and have guided new electrophysiological studies. This paper extends the approach to investigate the organization of the entire corticothalamic network. An extensive collation of connection tracing studies revealed ~1500 extrinsic connections between the cortical areas and thalamic nuclei of the cat cerebral hemisphere. Around 850 connections linked 53 cortical areas with each other, and around 650 connections linked the cortical areas with 42 thalamic nuclei. Non-metric multidimensional scaling, optimal set analysis and non-parametric cluster analysis were used to study global connectivity and the `place' of individual structures within the overall scheme. Thalamic nuclei and cortical areas were in intimate connectional association. Connectivity defined four major thalamocortical systems. These included three broadly hierarchical sensory or sensory/motor systems (visual and auditory systems and a single system containing both somatosensory and motor structures). The highest stations of these sensory/motor systems were associated with a fourth processing system composed of prefrontal, cingulate, insular and parahippocampal cortex and associated thalamic nuclei (the `fronto-limbic system'). The association between fronto-limbic and somato-motor systems was particularly close.


    Introduction
 Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
 References
 
Empirical neuroanatomy has had tremendous success in tracing the connections that link different regions of the brain. However, individual connection tracing studies focus on the connections of a few brain structures in a few individuals. Therefore, each study describes only a small piece of the connectional architecture of the whole brain. Trying to piece together such data for an accurate overview of brain organization is like trying to solve an intricate jigsaw puzzle. There are many complimentary approaches to help put the jigsaw together. High-quality anatomical studies give us the right pieces. Physiological and behavioural data help show how the pieces fit together. We also think that systematic collation and analysis of connection data are valuable tools to help assemble the puzzle and describe the picture (Young, 1992Go; Hilgetag et al., 1996Go; Scannell, 1997Go).

Preliminary attempts to collate neuronal connection data have already been published for the extrinsic connections linking areas in the cerebral cortices of the cat (Scannell and Young, 1993Go; Scannell et al., 1995Go; Scannell, 1997Go) and the macaque (Pandya and Yeterian, 1985Go; Felleman and Van Essen, 1991Go; Young, 1992Go, 1993Go). Systematic analyses of the data show that the cortical networks of cats and macaques contain three sensory systems and a fourth system, termed the `fronto-limbic' system, composed of prefrontal, insular, cingulate, perirhinal, retrosplenial and entorhinal cortex and the hippocampal formation (Scannell and Young, 1993Go; Young, 1993Go; Scannell et al., 1995Go; Young et al., 1995aGo,bGo). The sensory systems all exhibit a degree of hierarchy, both in terms of laminar origin and termination patterns (Felleman and Van Essen, 1991Go; Young, 1992Go; Scannell et al., 1995Go) and because there is a topological progression with some areas being connectionally close to peripheral input and others being distant from peripheral input. Systematic collation and data analysis have also shown that the simple local wiring rules can account for much of the pattern of cortico-cortical connections in the cat and macaque (Young, 1992Go; Cherniak, 1994Go; Scannell et al., 1995Go; Scannell, 1997Go). They have shown that sulci and gyri are arranged in a way that efficiently reduces the volume of the connections in the extrinsic cortico-cortical network (Scannell, 1996Go, 1997Go; Van Essen, 1997Go). In addition, systematic analysis of cortical connectivity has had success in guiding electrophysiological investigations of the cat visual system (Scannell et al., 1996Go), and in providing simple network models that account for classical strychnine neuronographic data (Hilgetag et al., 1997aGo).

It is important to extend the systematic approach to include the thalamus. First, almost all neural signals from the sensory and motor periphery reach the cerebral cortex via the thalamus (e.g. Le Gros Clark, 1932; Jones, 1985). Second, cortical and thalamic processing are closely co-ordinated (e.g. Le Gros Clark, 1942; Kato, 1990; Guillery, 1995; Contreras et al., 1996; Crick and Koch, 1998). Consequently, an undue emphasis on the cortical networks ignores much of the machinery that may be responsible for sensory and motor processing (Guillery, 1995Go). This paper considers the extrinsic connections of both the thalamus and cortex of the cat.

Researchers seeking large-scale principles of neuronal organization face, in addition to the `jigsaw puzzle' problem, sampling bias and random sampling error in the primary neuroanatomical literature. There is a strong bias towards a small number of model structures (e.g. areas 17, 18 and LGN in the case of the cat) for studies on laminar origin and termination patterns, cellular targets, synaptic morphology, physiological function, interindividual variability or development of connections. It is not clear if these structures are representative of the rest of the brain. In contrast, systematic collation, while not free from sampling bias, can yield relatively comprehensive catalogues of the gross cortical connections (Young, 1993; Scannell and Young, 1993; Scannell et al., 1995; Burns, 1997; Scannell et al., 1997, and this paper). Therefore, although lacking much of the richness and detail of the original reports, the approach presented here is unusual in its breadth. We hope that it can compliment the more traditional approaches to neuroanatomy, upon which it is entirely dependent for data.

We are currently extending our collation methods (e.g. http://riposte.usc.edu/NeuroScholar) to emphasize available data on laminar origin and termination patterns, cellular targets, synaptic morphology, physiological function, interindividual variability and development. We intend to apply systematic analysis to these aspects of connectivity as and when data become available for a wider range of connections.

Before systematically analysing connection data, it is necessary to produce an accurate catalogue of connections. This step presents major practical problems. The primary data differ in, for example, individual animals, quality, method, anatomist, parcellation and nomenclature. There is considerable variability in the cortical connectivity of individuals, though less so in thalamic connectivity (MacNeil et al., 1997Go). Parcellation is difficult, especially in brain regions that lack systematic maps of the sensory periphery (Colby and Duhamel, 1991Go). Further more, connection tracing is rarely quantitative, `interesting' parts of the brain have been studied more than `boring' parts, and connections are not all the same. Therefore, it is necessary to exercise considerable judgement at this stage of the study. These problems notwithstanding, systematic collation is the only way to produce an explicit summary of known connectivity. The first part of this paper presents such a collation of the connectional neuroanatomy of the cat thalamo-cortico-cortical network.

The second part of the paper presents the results of three formal analyses that summarize the thalamo-cortical system's connectional architecture in a relatively compact and comprehensible way. The analyses illustrate the `place' of individual structures in the global connectional scheme and show global features of the organization of the system that are not apparent on casual inspection of the primary connection data. We hope that both the collation and the analyses will guide new empirical research and test organizational models of the thalamo-cortical network as they have already done in the cortical network (Scannell et al., 1996Go; Hilgetag et al., 1996Go; Scannell, 1997Go).


    Materials and Methods
 Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
 References
 
Full details of cortical and thalamic parcellation, connections and citations of the original connection and mapping studies are published at http://www.psychology.ncl.ac.uk/jack/cor_thal.html.

Table 1Go gives a list of abbreviations used.


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Table 1 Anatomical abbreviations
 
Cortical Parcellation

The cortical parcellation used in this study was based on Reinoso-Suarez (1984), adapted by Scannell et al. (1995). Parcellation of the prefrontal cortex and cortex on the medial side of the hemisphere (sometimes termed `limbic' cortex) was modified from Scannell et al. (1995) to bring it into line with the schemes of Musil and Olson (1988a,b, 1991), Olson and Jeffers (1988), and Olson and Musil (1992). All prefrontal cortex on the lateral side of the hemisphere has been assigned to the area PFCl. Areas ALG, SSF, SVA, DP, Amyg and 5m of the parcellation of Scannell et al. (1995) have been omitted from this study because of a lack of data on their connections with the thalamus or because of our uncertainty over their identity or existence. Areas 4g and 4 of Scannell et al. (1995) have been retained, but are probably cytoarchitectonic subregions of a single primary motor area. Similarly, areas 3b, 1 and 2 probably constitute a single primary somatosensory area, SI (Felleman et al., 1983Go). The auditory cortical area VP is termed `VPc' to distinguish it from the ventroposterior nucleus of the thalamus.

Thalamic Parcellation

Parcellation of the thalamus was based on the atlas of Berman and Jones (1982). In some thalamic regions (e.g. the lateral posterior complex, the medial geniculate body, the ventrobasal complex) Berman and Jones' terminology and parcellation were modified to conform to more recent anatomical and physiological studies. The scheme used in this paper, and its relation to Berman and Jones (1982) and to other recent studies, is outlined in the Appendix.

The Appendix shows that there is a lack of consistency in the nomenclature and parcellation used in different studies of certain thalamic regions. Similar problems apply in the cortex (Scannell et al., 1995Go). In some cases, this is due to methodological differences. Connection tracing (the bulk of the data used in this study), cytoor chemo-architectonics and electrophysiological mapping do not always yield divisions that map neatly onto one another. These problems made collation particularly difficult for connections of the anterior parts of the lateral posterior complex, the posterior group of nuclei and the suprageniculate region. Difficulties were also encountered in the lateral posterior complex, the medial geniculate complex, the posterior group and the ventroposterior complex, where there is controversy or ambiguity as to the `best' parcellation.

Collation of Connection Data

We produced a database of thalamo-cortico-cortical connections from information in a large number of published studies of connectivity in the adult cat. Only data from the cat were used and no extrapolations were made from structures thought to be homologous in other species. We considered data in the text and figures of papers on cat cortico-cortical, cortico-thalamic and thalamo-cortical connectivity. For each reported instance of a connection, the database gives the origin and target regions, the weight or strength (see below), local origin or termination patterns (where known), and the study from which the data were taken. For some connections, the database has notes on alternative parcellation schemes. Connections that were reported as dense or strong were given a strength weighting of 3; weak or sparse connections were weighted as 1; and connections of intermediate strength, or for which no strength information was available, were weighted as 2. We assumed that descriptions of the density of projections as strong, moderate or weak made in different studies were equivalent.

Translation from Database to Connection Matrix

The areas that we have chosen to include in our connection matrix reflect current connection data. We have balanced the need to avoid `lumping' together structures that are known to be distinct, with the need to have sufficient data for each structure listed in the connection matrix. Where the database contains fine areal or nuclear divisions that have not yet been resolved in a substantial number of connection tracing studies, we have tended to `lump' them together for the analyses. For example, Clasca et al. (1997) present compelling evidence that our cortical areas Ia and Ig both contain a number of distinct cortical fields. However, there are no published cortical connection data for these divisions at present, so we include Clasca et al.'s areas ALd, ALv and PI within our area Ia, and Clasca et al.'s areas AS, DI and GI within our area Ig. We hope that our parcellation will improve as new data become available.

The database was used to produce our best estimate of thalamocortical connectivity, shown in Table 2Go. Where there was any doubt in translation between the database and connection matrix, we checked the original papers and reconsidered both text and figures. The translation process was difficult when the reports in the literature could not be unambiguously assigned to a single one of our areas or nuclei. In these cases, we were careful to balance the need to include as many reported connections as possible, with the need to avoid `extrapolating' connections to areas or nuclei which do not, in fact, possess them. For example, if one study identified a connection from a cortical area to the `lateral posterior nucleus', LP, while other studies identified connections to specific nuclei within LP (e.g. LPl and LPm), then we would to assign the connections to LPl and LPm only.


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Table 2 Matrix of cortico-cortical, thalamo-cortical and cortico-thalamic connections in the cat. Connections weighted `3' are strong, connections weighted `2' are intermediate, connections weighted `1' are weak or sparse, and connections marked `.' have been explicitly reported as absent or are unreported. The upper square of the table shows cortico-cortical connections. Reading horizontally in this part of the table, from a cortical structure, shows afferent connections and reading vertically shows efferent connections. The lower rectangle of the table shows cortico-thalamic and thalamo-cortical connections, which we assume are invariably reciprocal (Raczkowski and Rosenquist, 1983Go; Burton and Kopf, 1984b; Symonds and Rosenquist, 1984Go; Jones, 1985Go). The right margin of the table summarizes the frequency distribution of connection weighted 3, 2 and 1 for each anatomical structure. Afferent and efferent connections have been pooled. Darker shades indicate a greater number of connections. The area to area connection data in this table formed the sole input to the NMDS, optimal set, and non-parametric cluster analyses.

 
Occasionally, given all the information in the database, a connection could still not be assigned unambiguously to one of our areas or nuclei. In these cases, where reasonable, we would assign the connection to our areas included within the larger, ambiguous region. For example, if the only available information showed that Sg projected to areas 35 and/or 36, then we would assign the connection to both 35 and 36. We are aware that this risks one false positive connection. However, the alternative (ignoring Sg's projection to 35 and/or 36) is certain to incur at least one, and may incur two, false negatives. In practice, we applied this reasoning to a relatively small number of connections, which disproportionately affected areas 35 and 36, and nuclei PARA and PARP. Areas 35 and 36 are thin, adjacent strips of cortex that are difficult to inject independently. PARA and PARP are small, adjacent thalamic nuclei that are difficult to distinguish in connection tracing studies. Therefore, there is likely to be some `cross-contamination' in our connection matrix and analyses, between areas 35 and 36, and between thalamic nuclei PARA and PARP.

All measurements in all areas of science are likely to contain a degree of error. This is true for our database and our translation from database to connection matrix. While we have make great efforts to be as accurate as possible, we encourage readers to check the primary literature before uncritically accepting connections presented here.

Missing Connections

In principle, our analyses could distinguish between connections that have been explicitly reported as absent and connections for which there are no explicit reports of presence or absence. For several reasons, we have chosen to analyse `confirmed absent' and `unreported' connections as if they were equivalent. First, most areas or nuclei only connect with a small fraction, 5–25%, of the other structures, so non-connections are the norm. Non-connections are rarely reported explicitly unless they are unexpected, controversial or otherwise of particular interest. Therefore, there are few explicitly confirmed absent connections in the cat. However, a substantial proportion of studies in the cat inspect large regions of the brain (sometimes the entire cortex or thalamus) for labelled cells or terminals. We take the lack of reports of connections in the text or figures of such papers as implicit evidence of absence and think it unlikely that there are many substantial undiscovered connections between well-studied regions of the brain. Of course, this may change with the introduction more sensitive connection tracing methods, or more systematic attention to very small quantities of transported tracer that may currently be dismissed as `background' labelling.

Second, many `missing' connections belong to poorly studied regions of the brain. Therefore, we have chosen to omit some of the less studied areas from the analysis. We also think that `missing' connections are most likely to be projections to regions of the brain that have received few tracer injections. This is because retrograde tracing studies are more common than anterograde tracing studies and projections from the poorly studied brain regions show up when the better studied regions are injected.

Third, it is likely that thalamo-cortical connections show complete reciprocity (e.g. Raczkowski and Rosenquist, 1983; Burton and Kopf, 1984b; Symonds and Rosenquist, 1984; Jones, 1985). Therefore, assuming thalamo-cortical reciprocity should give a more accurate picture than using only connections that have been directly demonstrated. For example, many thalamo-cortical connections, found with cortical injections of retrograde tracers, have not been studied using cortical injections of anterograde tracers, or thalamic injection of retrograde tracers. To avoid ignoring such connections, our analyses assume that all connections between cortex and thalamus are strictly reciprocal.

Fourth, to see if `missing' cortical reciprocal connections in Table 2Go have a major effect on the results of our analyses, we have produced, and analysed with non-metric multi-dimensional scaling (NMDS), alternative matrices that assume cortical connections are also reciprocal. First, a symmetrized matrix, `sym', was produced by reflecting the `raw' matrix (Table 2Go) about its leading diagonal and then adding the reflected matrix to the original. Second, a `winner takes all' matrix, `wta', was produced by reflecting the raw matrix about its leading diagonal and then adding it back to the original in a `winner takes all' fashion, so that the strongest connection at any site was retained. The raw matrix (Table 1Go) and the wta matrix have four ranks of connection strength: 0 (absent or unreported), 1 (weak or sparse), 2 (moderate) and 3 (strong or dense). The sym matrix has seven ranks of connection strength (0–6).

Fifth, Young (1992) and Young et al. (1995) have examined quantitatively the effects of different ways of treating non-connections and found that they have a relatively small effect on the overall solution. Few connections in the cat have been explicitly reported as absent, so adding an extra rank to the connection matrix (Table 2Go) to distinguish the few `confirmed absent' connections from the many `presumed absent' connections would have very little effect. We also note that all our analyses on n structures seek to satisfy (n2n) connectional constraints while each structure contributes only (2n – 1) connectional constraints. Therefore, major changes in the connection patterns of a few poorly studied structures will have a major impact on those structures in any connectional analysis, but will have very little impact on the overall analysis (Scannell et al., 1995Go; Young et al., 1995).

We think that this approach is reasonable and we prefer it to mathematically based missing data estimation methods (Jouve et al., 1998Go). The issue of missing connections can be properly resolved only by further anatomical study.

Analysis Methods

Large connection matrices are too complicated for analysis with unaided intuition. We have used three methods to summarize and represent the connection data in a more transparent way. The first, and most widely used to date (e.g. Young, 1992, 1993; Scannell and Young, 1993; Scannell et al., 1995; Young et al., 1995a,b,c), is NMDS. Simmen et al. (1994) and Goodhill et al. (1995) have criticized the use of NMDS on anatomical connection data. While we think that NMDS can recover structure from anatomical connection data (Young et al., 1994Go, 1995cGo), the comments of Simmen et al. (1994) and Goodhill et al. (1995) have been very useful. They have encouraged us to develop and apply a wide range of analysis methods to help distinguish real connectional features from the peculiarities of individual analysis methods. Therefore, we have analysed connection data with NMDS, with non-parametric cluster analysis and with a novel method, optimal set analysis.

Non-metric Multidimensional Scaling

NMDS is a method that finds a configuration of points (in this case cortical areas and thalamic nuclei) that matches a set of experimentally measured `proximities' (in this case anatomical connections). In a theoretically perfect arrangement, all areas or nuclei that are connected by a connection weighted `3' should be closer to each other than all areas linked by a connection weighted `2', which should in turn be closer than areas linked by a `1', and so on. Such an ideal configuration would perfectly capture the connectional proximities present in the connection data — a process exactly analogous to deriving a map from a mileage chart in a road atlas.

NMDS is a form of data compression in which a large set of ordinal measures (e.g. 95 x 95 connection matrix) is represented as a smaller set of metric measures (e.g. 95 x 3 set of coordinates). This kind of data compression is not without problems. For example, if the proximity matrix is asymmetric (e.g. Table 2Go), the connectional constraints cannot be perfectly satisfied by a spatial arrangement of points. Nevertheless, extensive simulation studies (Young et al., 1994Go, 1995cGo), have shown that this approach performs excellently in recovering metric structure from test data that matches as closely as possible the structure of neuroanatomical connection data. Analyses of test data designed to match the cat thalamo-cortical connection data has found that cat thalamo-cortical connection data behaves like `noisy' test data generated in between four and six dimensions (Scannell et al., 1997; J. W. Scannell, unpublished observations). NMDS configurations derived from such test data in the appropriate number of dimensions (i.e. five dimensions for five dimensional test data) typically account for ~90% of the variability of the original test structure. For practical purposes, we are limited to presenting three-dimensional configurations, which typically account for ~50% of the variability of appropriate five-dimensional test data (J.W. Scannell, unpublished observations).

Young et al. (1995c) have shown that for appropriate test data, some matrix transforms can slightly enhance the ability of NMDS to recover metric structure. Consequently, we have performed the wdsm1 transform (Young et al., 1995cGo) prior to NMDS for all the cortical systems illustrated in this paper. The high degree of congruence between solutions of the wdsm1-transformed matrices and the solutions derived from the other matrices is shown in Table 3Go, and is illustrated in Figures 1 and 2GoGo which show configurations derived with ALSCAL from wdsm1, raw and sym matrices. Configurations derived with the other NMDS approaches and have been inspected using computer animation.


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Table 3 Different NMDS methods yield congruent result
 


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Figure 1.  Connectional relationships in the thalamo-cortical network. The figure is a stereogram showing the two least similar three-dimensional configurations yielded by the variety of NMDS analyses of the different versions of the connection matrix. The first configuration (top) was derived using MDS on the wta wdsm1 matrix with FIT=2, and the second (bottom) was derived using MDS on the raw matrix with FIT=1. The R2, by Procrustes' rotation, between the configurations is 0.778. Anatomical structures within the visual system are coloured blue, auditory structures are green, somato-motor structures are red and fronto-limbic structures are brown. CLN, CMN, PAC, PF and CM are black. The figure was computed using all the connection data but, for clarity, only strong reciprocal connections, with a sum of weights in both directions >4, are drawn. All structures have some connections (see Table 2Go). The different NMDS approaches arrange the points in different volumes of space, but the local organization within systems and the relationships between the systems are broadly similar. The apparent badness of fit (Young et al. 1995aGo) for scaling the wdsm1 matrix was 0. 21, with a distance correlation of 0.94. The apparent badness of fit for scaling the raw matrix was 0.26 with a distance correlation of 0.61. The stereograms in this paper may be free-fused to give three-dimensional images. Divergent viewing may be easier for those used to `magic eye' pictures. To view, hold the figure at arm's length in front of the face, just below the line of sight. Look steadily at a distant object, something outside the window, that is just visible over the top of the page, then switch your view to the page without converging the eyes. It helps if the hands are kept clear of the figures while attempting to fuse them. One may practice by drawing two dots with a felt-tipped pen ~4 cm apart at the very top of piece of paper. Repeat viewing the procedure above. At first, you should see four dots at the top of the paper just below the distant object that you are fixating. If you switch your view from the distant object to the dots, the central two dots should move towards each other and then merge when you have achieved divergent fixation. Practice with dots that are further apart until it is possible to fuse the figure. For practice, see Johnstone (1995).

 


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Figure 2.  Connectional relationships in the thalamo-cortical network. The figure shows the three-dimensional NMDS configuration derived using MDS with `FIT=2' on the raw matrix. Anatomical structures within the visual system are coloured blue, auditory structures are green, somato-motor structures are red and fronto-limbic structures are brown. CLN, CMN, PAC, PF and CM are black. The figure was computed using all the connection data. The top figure illustrates only those connections where the sum of the weights in both directions is >=4. The lower figure shows all connections, and graphically illustrates the great complexity of the network of extrinsic connections between cortical areas and thalamic nuclei. Stronger connections are darker grey and weaker connections are lighter grey. The apparent badness of fit of the configuration (Young et al., 1995) is 0.41 and the distance correlation 0.61.

 
Configurations of points derived from low-level ordinal data vary with NMDS method. Previous studies (e.g. Young, 1992, 1993; Scannell and Young, 1993) have derived two-dimensional configurations with the ALSCAL algorithm (Takane et al., 1977Go; Young et al., 1978Go) in the SPSS statistical environment (Young and Harris, 1990Go). In this paper we present stereograms of three-dimensional configurations as they capture more of the data structure. The configurations were derived using a variety of NMDS methods to see which features of the configurations are robust and consistent properties of the connection data. The methods were `MDS' in the SAS statistical programming environment and `ALSCAL' in the SPSS environment. All connection data (raw, sym, wta and wdsm1) were scaled at the ordinal level of measurement using the secondary approach to ties (Kruskal, 1964aGo,bGo; Young et al., 1995cGo). SAS solutions were produced using options `FIT = 1' (fits the data to distances) and `FIT = 2' (fits the data to squared distances). `FIT = 2' emphasizes the importance of long distances (i.e. non-connections) and produces output similar to ALSCAL.

NMDS solutions can become trapped in local minima. To guard against this, we shuffled the order of areas in each matrix while keeping the connections the same. Shuffling input order had no effect on all solutions produced with MDS in SAS, and on solutions derived from symmetric matrices (sym, wta, wdsm1) with ALSCAL in SPSS. However, shuffling input order did influence the apparent fit of solutions derived from raw matrices with ALSCAL in SPSS. In these cases, we found that a `seeding' method was effective in finding low-dimensional configurations with relatively high apparent fit. Configurations derived from wta or sym matrices were used to provide the initial coordinates for scaling the raw matrix. The resulting raw configurations reached convergence in fewer iterations and had higher apparent fit than configurations derived from random co-ordinates.

NMDS configurations can be compared quantitatively using a regression-like procedure, Procrustes' rotation (Schonemann and Carrol, 1970Go; Gower, 1971Go). Procrustes' rotation, implemented in the GENSTAT statistical programming language, can compare structures in any number of dimensions by rigidly reflecting, rotating and then scaling them to find an optimal fit. After finding the best rigid transform, Procrustes yields a variance explained statistic (R2) that reflects the goodness of fit. The statistical rarity of each comparison may be evaluated using a randomization test (Edgington, 1980Go) in which one of the structures is repeatedly randomly shuffled and the R2 statistic recalculated.

Optimal Set Analysis

Optimal set analysis is an alternative and independent method for analysing global connectional architecture. This approach views a `neural system' as something containing components more connected with each other than with the components of other systems. So, for example, the visual system might be thought of as the collection of cortical areas and thalamic nuclei that are highly interconnected with each other and relatively weakly connected with the other cortical systems. We wanted to identify the systems within the thalamo-cortical network by arranging areas and nuclei into sets with as few as possible connections between the sets and as few as possible non-connections within the sets. We wanted to let the connection data itself decide the number and the composition of the sets of areas and nuclei.

Optimal set analysis presents a formidable computational problem so connection data were analysed using CANTOR, a custom-written software system for statistical optimization. The CANTOR system consists of a database of objects, linked to each other through relational functions. In the present application, the CANTOR objects represented cortical areas and thalamic nuclei, while the relational functions represented their anatomical interconnections. CANTOR arranges the objects by stochastic optimisation to minimize the cost of the relational functions in a way that is chosen by the experimenter. We chose costs that matched our idea of a neural system; a thing containing components more connected with each other than with the components of other systems. Therefore, the cost measured non-connections within sets and connections between sets.

The CANTOR environment provides routines that permit the rearrangement of the objects within the database to minimize costs by evolutionary optimization, a method based on simulated annealing (Van Laarhoven and Aarts, 1987Go). More technical details of the optimization algorithm adapted for connectivity analyses are described by Hilgetag et al. (1996, 1997b, 1998). The software is written in ANSI-C and has been implemented on a wide variety of Unix computer systems. Special memory management ensures that the large quantities of complex data can be analysed on medium-sized workstations. Our computations are run on a DEC Alpha 3000–600 workstation with 256 MB of RAM. The runs typically require several hours to weeks of CPU time, depending on the size of the area-to-area connectivity matrices and the thoroughness of search for optimal solutions.

In this study, CANTOR minimized a two-component integer cost function to find optimal connectional sets within the thalamo-cortical system. The cost consisted two terms. The first was a repulsion term that counted non-existing connections within the potential sets. Optimizing the repulsion component alone breaks larger clusters into smaller clusters. The second cost consisted of an attraction term counting existing connections between sets. Optimizing the attraction term alone will, in the limit case, result in one large cluster containing all the areas and nuclei.

The costs of existing connections between sets were proportional to the connection weights (`1', `2' or `3'). This cost function assumes an arithmetic relationship between connection ranks, in contrast to NMDS which simply assumes a monotonic relationship between connection ranks. Starting from a random assignment of areas to sets, the number and structure of the sets were changed iteratively through relocation of one area to another set or by swapping of two areas belonging to different sets. Thresholds were set to ensure that structures made stepwise improvements. These set manipulations and threshold parameters ensured that the space of candidate arrangements was searched at the smallest possible resolution and that the search did not become trapped in local minima. Hence, the CANTOR system determined automatically the number and composition of sets for the optimal overall arrangement of the areas and nuclei of the thalamo-cortical system.

We changed the number and composition of the optimal sets by varying the strength of attraction and repulsion in the cost function. Repulsion ranged from 30 to 1 (cost of non-connections within clusters), with attraction set to 1. Attraction ranged from 1 to 10 (the attraction term is multiplied by connection weight to compute the cost of connections between clusters), while repulsion was held at 1. Increasing the attraction yields larger sets, or only one in the limit case of overwhelming attraction. Reducing attraction yields more, smaller sets. These manipulations make it possible to explore the cluster structure of the thalamo-cortical network over a range of scales. They emphasize different aspects of the organization of the network. Perhaps the most intuitively obvious, and the one shown in Figures 3 and 4GoGo is the case where attraction and repulsion are both set to 1. Here, the cost of individual connections between clusters equals their connection weight and the cost of non-connections within clusters equals 1. Since CANTOR typically finds many different solutions with the same or similar low cost, the results are summarized in a matrix showing the proportion of the solutions in which two structures occupied the same set.



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Figure 3.  Optimal set analysis at balanced attraction and repulsion. The figure summarizes the 31 solutions whose costs lie within 1% of the single lowest cost solution. Attraction (the factor multiplied by connection weight to compute the cost of connections between sets) was 1 and repulsion (the cost of non-connections within sets) was 1. Cortical areas and thalamic nuclei are listed along the top and left of the table. The frequency with which areas or nuclei co-localized within the same set is given by the colour (scale at top right of table). Darker colours show frequent co-localization, while light colours show rare co-localization. The analysis consistently finds a number of sets. From top to bottom of Figure 3Go, these are: a set of frontolimbic, multimodal and higher-order somato-motor structures (LM-Sg to PFCMil); a set of auditory structures (MGM to MGDd); a set of lower-order somato-motor structures (4g to 3b); two small fronto-limbic sets (Sb to Hipp, and pSb to RS); and a large visual set (LPl to PMLS). Some structures do not have a strong affiliation with any of the large sets, either because of few known connections (e.g. LGLGW) or because of strong connections with more than one set (e.g. 7 and ALLS). The number of sets changes substantially when the attraction and repulsion parameters are at different values.

 


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Figure 4.  Optimal set analysis and NMDS are in excellent agreement. The figure is a stereogram that shows the major sets identified by optimal set analysis (Fig. 3Go) colour-coded and plotted on three-dimensional MDS configurations (Fig. 1Go). The set of fronto-limbic, multimodal, and higher-order somato-motor structures (LM-Sg to PFCMil in Fig. 3Go) is coloured brown; the set of auditory structures (MGM to MGDd in Fig. 3Go) is coloured green; the set of lower order somato-motor structures (4g to 3b in Fig. 3Go) is coloured red; The `hippocampal' set (Sb to Hipp in Fig. 3Go) is coloured purple; the `anterior nuclei' set (LD to RS in Fig. 3Go) is coloured blue/green; and the visual set (LPl to PMLS in Fig. 3Go) is coloured blue. The structures outside these sets are black. The figure was computed using all the connection data but, for clarity, only strong reciprocal connections, with a sum of weights in both directions >4, are drawn. The spatial configurations of points are exactly as in Figure 1Go. The sets identified by optimal set analysis map neatly onto compact regions of space identified by NMDS. Furthermore, the unclassified (black) structures tend to occupy peripheral regions, or are near the borders between the sets. This shows that NMDS and optimal set analysis agree over the major features of the connectional organization of the thalamo-cortical network.

 
We estimated the statistical significance of the results of optimal set analysis by comparing the cost of solutions calculated from connection data with the cost of equivalent solutions calculated from randomized connection matrices. The cost of solutions derived from connection data was comparable with the cost of solutions calculated from four to six-dimensional test data (Scannell et al., 1997; J.W. Scannell, unpublished observations).

Non-parametric Cluster Analysis

Cluster analysis is a statistical method that finds groups within a data set. It has already been used in the analysis of connection data by Musil and Olson (1991) to delineate the areas in the medial frontal cortex of the cat, and by Sherk (1986) to map the suprasylvian region of the cat. Here, the rationale behind our use of cluster analysis was similar to that behind optimal set analysis, i.e. to find groups of connectionally associated areas and nuclei (see Hilgetag et al., 1998).

To see the robust and reliable groupings within the thalamo-cortical network, we performed a variety of cluster analyses on a variety of NMDS configurations. We used the SAS/STAT system to make several five dimensional NMDS configurations from the raw connection matrix, setting the FIT option to 0.5, 1 and 2, with both the primary and secondary approach to ties. NMDS analyses in five dimensions were chosen for two reasons. First, the accuracy of density estimation falls with increased dimensionality (Epanechnikov, 1969Go, Silvermann, 1986Go). Second, studies with test data indicate that NMDS in five dimensions is adequate to reasonably represent the cat thalamo-cortical connection data (J.W. Scannell, unpublished observations). We then analysed the configurations using the MODECLUS non-parametric cluster analysis function in the SAS/STAT system.

Before clustering, MODECLUS calculates the probability density within the NMDS configuration using either fixed or variable radius spherical kernels. With fixed radius kernels, all points have identical kernel radii. The variable radius kernel approach is based on finding the distance to the `kth nearest neighbour'. Once a density function has been estimated for a set of points (in this case, representing cortical areas and thalamic nuclei), MODECLUS detects the local maxima of the density function to define the cluster structure of the data. When fixed radii kernels are used, MODECLUS can then test the significance of clusters by comparing the maximum estimated density at points within the cluster to the maximum estimated density at the cluster's boundary.

Since cluster analysis is adept at finding clusters in data where no real clusters exist (Gordon, 1996Go), we ran ten kinds of MODECLUS analysis paradigm on each of the six NMDS configurations and then pooled the results. We did this to `average out' the spurious clusters. We also ensured that our cluster paradigms used a wide range of kernel radii so that both local and large-scale cluster structure were explored. The first paradigm ran 30 cluster analyses with increasing fixed-radius density estimation and clustering kernels. The radius of this kernel ranged from the minimum interpoint distance in the configuration to the mean interpoint distance in the configuration. The second, third and fourth paradigms used a fixed radius kernel that was calculated from the cluster analysis under the first paradigm. The kernel radius was chosen to produce an initial number of clusters equal to the total number of points in the analysis divided by 2, 4 and 8 respectively. A hierarchical cluster tree was obtained for each scheme by testing the significance of the clusters. This procedure compared the maximum estimated density of points within a cluster to the maximum around the cluster's border (referred to here as the `saddle point') in order to estimate the cluster's significance. On successive iterations, the least significant cluster was dissolved or their members assigned to a neighbouring cluster if it was close enough. The fifth, sixth and seventh paradigms were based on nearest-neighbour kernels with K values set to 2, 3 and 4 (i.e. the density estimation and clustering kernels were set to the value so that the number of neighbours of each point was a minimum of 1, 2 and 3). The eight, ninth and tenth paradigms used a nearest-neighbour clustering method and gave a hierarchically organized cluster scheme. This involved the use of fixed-radius density estimation kernel (with radius set to the value of the configuration's mean distance) and a clustering kernel based on a nearest-neighbour CK value set to 2, 3 and 4.

Since the series of cluster analyses finds many different solutions, the results are summarized in a matrix showing the proportion of the solutions in which two structures occupied the same cluster. The summary matrix (Figure 6Go) was corrected so that each paradigm contributed equally to the cluster-count score. Note that a structure from a cluster that had been dissolved (e.g. paradigms 2, 3 and 4) would not be counted as being in the same cluster as any other structures, including itself. Thus there may be cluster counts along the leading diagonal of Figure 4Go of <100%.



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Figure 6.  Cluster structure of the cat thalamo-cortical network. The figure shows the relative frequency with which cortical areas occupied the same cluster in 10 clustering paradigms applied to each of six alternative five-dimensional NMDS configurations (see Materials and Methods). Pooling results from a wide range of clustering and NMDS methods aimed to average out the peculiarities of individual analysis methods, revealing robust connectional features. Dark squares represent areas that frequently occupied the same cluster, while light squares represent areas that are rarely occupied the same cluster (key on right of figure). The names of anatomical structures are listed down the left margin and across the top of the matrix. To ease comparison with Figure 3Go, the gross order of areas is comparable to that in Figure 3Go, although the order of areas has been changed locally (within the basic `sets' identified in Fig. 3Go) to illustrate additional features.

 

    Results
 Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
 References
 
Parcellation and Connections

Table 2Go summarizes the literature on the extrinsic connectivity of the thalamo-cortical network. It is drawn from the full database (see http://www.psychology.ncl.ac.uk/jack/cor_thal.html), which provides considerably more detailed information. The connection strengths are on an ordinal scale that assumes only that the relationship between the ranks is monotonic; a `3' is stronger than a `2' which is stronger than a `1' which is stronger than a `0'. In quantitative terms, connections weighted `3' may be 2 or 3 orders of magnitude stronger than connections weighted `1' (see e.g. Musil and Olson, 1988a,b). Table 2Go shows 826 cortico-cortical connections. Each cortical area connects with, on average, 15 other areas (SD = 8). This level of connectivity corresponds to 28% of possible cortico-cortical connections. Table 2Go also shows 651 connections between thalamus and cortex, which we assume are wholly reciprocal (Raczkowski and Rosenquist, 1983Go; Burton and Kopf, 1984b; Symonds and Rosenquist, 1984Go; Jones, 1985Go). On average, each thalamic nucleus projects to, and receives projections from, 15 cortical areas (SD = 10). This constitutes 28% of all possible thalamo-cortical connections, were each nucleus to project to each cortical area. There are no direct connections between the thalamic nuclei.

The connection density summary of Table 2Go shows that there is great variability in the numbers of connections and the distribution of connection weights between areas and nuclei. Some structures (e.g. 17, SII) have a small number of dense projections, while others (e.g. CMN, CLN, CGp and AES) have much more widespread connectivity. In general, however, weak connections are much more common than strong connections.

While some cortical areas and thalamic nuclei have received vast amounts of experimental attention (e.g. 17, LG, PMLS), some have been the focus of much less research. Further work is required on parcellation in the posterior complex (POi, POl, POm), the suprageniculate region (Sg, LM-Sg) and the anterior parts of the lateral-posterior complex (LIc, LIo). Data are sparse for cortical connections to the midline and intralaminar nuclei, connections to and from the anterior group of nuclei, and connections to and from the thalamic regions where parcellation is unclear. Therefore, we advise caution in interpreting the database for these structures. Structures with very sparsely documented connectivity can be problematic for our quantitative analyses. Consequently, POm, POl, POi, LIc and LIo occupy peripheral or erratic locations in some of the figures.

NMDS Analyses

NMDS provided reasonable three-dimensional representations of the connection data as the apparent fit of the configurations derived from connection data was much better than the fit from appropriate random test data (typically by 10 or more z-scores, P < 10–12). The apparent fit of configurations derived from connection data were comparable with the fit derived from appropriate four to six-dimensional test data (Scannell et al., 1997; J.W. Scannell, unpublished observations).

Congruence of Different NMDS Approaches

Table 3Go shows that across all input matrices the different NMDS methods yield quantitatively similar structures (R2 varies between 0.78 and 1.00). We have used computer animation to visualize all the structures and the similarity of the qualitative impression is even greater than the quantitative similarity might suggest. In general, MDS with `FIT = 2' and ALSCAL, when using low-level ordinal data (wta, sym and raw), give configurations in which the areas and nuclei lie in a shell around a hollow region. This is because these scaling methods emphasize the non connections, or long distances (Takane et al., 1977Go; Young et al., 1978Go), and the arrangement of points that has the most long inter-point distances is a hollow shell (Fig. 1Go). In contrast, MDS with `FIT = 1' (Fig. 2Go) and all analyses with the wdsm1 matrix (e.g. Fig. 1Go) give configurations with points more evenly distributed within a volume of space. MDS with `FIT = 1' fits the experimental disparities (connection data) to distance, so does not emphasize non-connections. The wdsm1 transform interpolates extra ordinal ranks, converting the low-level connection matrix into a higher-level `similarity of connection' matrix. This removes the large number of identical long distances (non connections) that are present in the raw data.

Figure 1Go shows the two least similar NMDS configurations (wdsm1 wta with `FIT=2' and MDS raw with `FIT=1', which account for 78% of each other's variability by Procrustes' rotation). Despite the fact that they are the most quantitatively dissimilar configurations, they give similar qualitative impressions of the connectional architecture of the thalamo-cortical network.

The qualitative similarity of the NMDS configurations (Table 3Go, Figs 1, 2 and 4GoGoGo) arises because the local relations between the points are relatively conserved despite the fact that the configurations occupy different shaped volumes. For example, Figures 1 and 2GoGo show that the hippocampus is always distant from the sensory periphery, that the four major cortical systems are distinguishable, and that the visual system shows some divergence at higher levels into structures associated with the somato-motor system (AES, area 7) and structures associated with the fronto-limbic system (20b, PS). Some of the midline and intralaminar nuclei (CLN, CMN, PAC, PF, CM) do not appear to be closely allied with any particular system, but project widely to a large number of cortical areas. The remaining midline and intralaminar nuclei (RH, MV-RE, PAT, PARA, PARP) appear to be associated with the fronto-limbic complex.

NMDS Representations of the Thalamo-cortical Network

The next section outlines NMDS analyses of the thalamo-cortical network and focuses on the visual, auditory, somato-motor, fronto-limbic and global systems, and on the midline and intralaminar nuclei. We report only those characteristics of the connectional architecture that appear robust and independent of the details of the NMDS method. The NMDS configurations here can best be regarded as provisional attempts at a systematic map of the thalamo-cortical network. Like any early map, they may provide a useful guide, but will also contain omissions and distortions that may be improved with better analysis methods and anatomical data.

Global Thalamo-cortico-cortical System

Figures 1 and 2GoGo show that the basic connectional plan found in the cortex, of three broadly hierarchical sensory/sensory-motor systems and a fourth fronto-limbic system (Scannell and Young, 1993Go; Young, 1993Go), also provides a good summary description of the thalamo-cortical network. The wdsm1 configuration in Figure 1Go, for example, arranges points representing cortical areas, and thalamic nuclei fall in a region of space that is roughly the shape of a triangular pyramid. Three of the corners correspond to the most topologically peripheral parts of the sensory and sensory/motor systems, while the fourth corner corresponds to the most topologically central parts of the frontolimbic complex; the hippocampus and associated structures. The central region of the pyramid (Fig. 1Go) where the four systems meet contains, as might be expected, those regions of cortex where information from the different sensory modalities converges (e.g. EPp, 7, AES, Ia, Ig, CGp; 36).

Figure 2Go shows all the documented connections of the thalamo-cortical network and gives some indication of the complexity of the thalamo-cortical network even at the crude level of organization presented here. The complexity of Figure 2Go shows why systematic collation and data analysis may prove useful tools in the interpretation of primary neuroanatomical data.

Visual System

Figures 1 and 2GoGo illustrate the connectional architecture of the cat thalamo-cortical visual system (blue). Figures 1 and 2GoGo show that the visual system has a complex, yet broadly hierarchical organization. The periphery of the thalamo-cortical visual system are the components of the lateral geniculate nucleus which are in close connectional association with areas 17 and 18. Higher are areas 19, 21a and 21b, which are connectionally close to LPl. Higher still, there appears to be some divergence in the visual system; PLLS and ALLS lead towards AES, 7 and 5Bl, which are in close connectional association with the somato-motor system. LM-Sg is closely associated with AES and Ig. In contrast, PS, 20a and 20b lead towards 35 and 36, RS and limbic structures. Some of these features are not apparent in Figure 2Go from this particular view, but are clearer at when the configuration is viewed from other directions.

The connectional divergence in higher visual areas is reflected in a functional division into areas concerned with motion and visuo-spatial functions (e.g. 7, AES) and those that are involved in static object vision (e.g. 20a, 20b) (Lomber et al., 1996aGo,bGo; Scannell et al., 1996Go). This arrangement is analogous to the functional (Ungerleider and Mishkin, 1982Go) and connectional (Young, 1992Go) divergence into somewhat distinct object versus motion and visuo-spatial streams found in the macaque visual system. Cats and macaques diverged from a small insectivorous ancestor over 60 million years ago (Savage, 1986Go), so the similarities in visual system organization may well reflect convergent evolution rather than homology. This, in turn, could reflect a wiring efficiency advantage in separating form and motion vision (Jacobs and Jordan, 1992Go).

Auditory System

Figures 1 and 2GoGo illustrate the connectional architecture of the thalamo-cortical auditory system (green). The auditory structures occupy a tight cluster, so the system appears less hierarchical than the visual system and somato-motor systems. MGV, MGDdd and MGDd constitute the periphery of the thalamo-cortical auditory system. These structures are in close connectional association with the tonotopically organized `core' fields VPc, AAF and AI (Brugge and Reale, 1985Go; Morel and Imig, 1987Go). Associated with the higher auditory area, Tem, is MGvl. The highest stations in the auditory system appear to include POl, SG and EPp, which are in close association with Ia, Ig, 35 and 36. MGDds tends to occupy a rather peripheral position, which may be an artefactual consequence of the fact that it has few documented connections.

Somato-motor System

Figures 1 and 2GoGo show that area-to-area connection patterns define a single somato-motor network (red) that contains both sensory and motor structures in close connectional association. In terms of extrinsic thalamo-cortical connection patterns, motor and somatosensory structures form a single unit. The somato-motor system is complex yet relatively hierarchical. VPL and VPM, which are closely associated with the primary somatosensory areas 1, 2, 3b and 3a, form the periphery of the somato-motor network. These areas are very closely associated with the primary motor cortex, area SII and some parts of area 5. VA-VL is `higher' than VPL and VPM and is closely associated with areas 4 and 6. VMP is poised between the somato-motor and fronto-limbic systems. Higher somato-motor areas, in particular 6l and 6m, are very closely associated with fronto-limbic structures such as CGa, CGp, Ia and Ig. 5Bl, the most lateral part of posterior area 5, is closely associated with visuo-motor structures such as AES and 7, suggesting a possible visual role for this region.

Fronto-limbic System

We use the term `fronto-limbic system' to describe a result that we obtain when we analyse connection data with several formal methods, namely the tendency of areas of the prefrontal cortex, `limbic system' and associated thalamic nuclei to group together (Scannell and Young, 1993Go; Young, 1993Go). Systematic and principled analysis of connection data decides that these structures belong together. We simply report the association and give it a name. We are aware that the term `limbic system' is problematic (e.g. Kotter, 1992) so our use of the term `fronto-limbic' does not imply any particular functional interpretation. Fronto-limbic structures include cingulate, insular, prefrontal, perirhinal, entorhinal and retrosplenial cortex, the subiculum, presubiculum, hippocampus, amygdala and associated thalamic nuclei such as MD.

From Figures 1 and 2GoGo it is clear that areas 35, 36, Ia, Ig, CGp and CGa are connectionally interposed between the cortical sensory and sensory-motor systems and the `deeper' parts of the fronto-limbic complex. Most distant from the sensory periphery are ER, SB and Hipp. As would be expected, MD is in close association with prefrontal cortical areas, and MV-RE with the components of the hippocampal formation (Hipp, Sb, pSb). Some of the rostral intralaminar nuclei also appear to have a close association with components of the fronto-limbic complex, in contrast to the caudal intralaminar nuclei (see below).

Midline and Intralaminar Nuclei

Figures 1 and 2GoGo suggest that extrinsic connectivity defines two broad categories of midline and intralaminar nuclei. In black (Figs 1 and 2GoGo) are CLN, CMN and PAC (of the rostral intralaminar group, see Appendix) and PF and CM (of the caudal intralaminar group, Appendix 1). These nuclei connect very widely with most areas of the visual, auditory, somato-motor and the fronto-limbic systems. In brown, the same colour as the fronto-limbic complex, are MV-RE, PAT, PARA and PARP (of the caudal intralaminar group, Appendix 1). These nuclei make few connections outside the fronto-limbic complex. This connectional difference suggests a distinction between CLN, CMN, PAC, CM and PF on the one hand, and RH, MV-RE, PAT, PARA and PARP on the other. CLN, CMN, PAC, CM and PF correspond to the `intralaminar complex' proposed by Berman and Jones (1982). These analyses agree with Berman and Jones' suggestion (1982) that RH, MV-RE, PAT, PARA and PARP do not necessarily constitute a functional group.

Optimal Set Analysis

We can be confident that optimal set analysis found genuine sets within the connection data because the low costs of the solutions when compared with solutions computed from randomly shuffled connection matrices. For example, at balanced attraction and repulsion (Figs 8 and 9) with real connection data, the mean (± SEM) cost of the first 20 generations of the first epoch was 1861  15. The mean of the equivalent cost calculated from five randomly shuffled connection matrices was 2729, with a SD of 42. Therefore, in this case, the cost of sets calculated from connection data was ~20 z-scores less than the mean cost of sets calculated with random data (P < 10–12). In general, the costs of solutions computed from connection data were broadly comparable with the costs of solutions computed from four to six-dimensional test data (Scannell et al., 1997; J.W. Scannell, unpublished observations).

We performed optimal set analysis with attraction weights ranging from 1 to 10, with repulsion at 1, and with repulsion weights ranging from 2 to 30, with attraction at 1. For each of the levels of attraction and repulsion, we ran CANTOR for 50 epochs from 50 different random starting configurations. At any given level of attraction and repulsion, optimal set analysis tends to produce a lot of solutions with similar low costs and there is no principled way of choosing which is `best'.

Figure 3Go shows a summary of the 31 solutions we found with costs within 1% of the single lowest-cost solution at balanced attraction and repulsion. The balanced attraction and repulsion case is the most intuitively obvious. In this condition, the cost of a connection between sets is equal to the weight of the connection (1, 2 or 3) and the cost of a non-connection within sets is equal to 1. The difference between the 31 solutions is small and all agree on several clear and consistent sets (solid dark blocks in Fig. 3Go). From top to bottom of Figure 3Go, these correspond to a set containing higher somato-motor and some multimodal and fronto-limbic structures (LM-Sg to PFCMil); an auditory set (MGM to MGDd); a set of lower somato-motor structures (4g to 3b); two small sets of frontolimbic structures (one consisting of Hipp, Sb and MV-Re, and the other containing pSb, LD, AD, AV and RH); and a large set of visual structures (LPl to PS). Around 17 areas or nuclei have variable positions and do not consistently lie in any of these sets. Some of these structures have few connections, so are `pushed' out of sets by the repulsive effect of many non-connections (e.g. LGLA, LGLC). Other areas and nuclei may have substantial connections with structures in more than one of the major sets (e.g. 7, CMN, 36, Enr, POm, SG), so fit into different sets with very little effect on the overall cost of the configuration.

Optimal set analysis is in excellent agreement with NMDS over the main features of the connectional architecture of the cat thalamo-cortico-cortical network. Figure 4Go plots the major sets illustrated in Figure 3Go on a stereogram showing three dimensional configurations yielded by NMDS. Figure 4Go shows that the sets (Fig. 3Go) map neatly and compactly onto the three-dimensional NMDS configurations with little stretching, fracturing or overlap between the sets. It is clear that most of the unclassified structures lie either at the edge of the NMDS configurations (those with few connections), or else lie near the borders between the sets (those with substantial connections with more than one set). Thus there is excellent agreement between two entirely independent data analysis methods.

Over the full range of attraction and repulsion parameters, high attraction gave fewer, larger, clusters, identifying higher order associations between the major thalamo-cortical systems. High repulsion gave more, smaller, clusters, identifying the most closely associated areas or nuclei. Figure 5Go shows the pooled results from the battery of attraction and repulsion levels. Figures 5 and 3GoGo are in good agreement, but the graded nature of Figure 5Go reveals both the local and the large-scale structure of the thalamo-cortical network and allows one to look across levels of organization. For example, the darkest squares show areas or nuclei that very frequently co-localize across all levels of repulsion so are therefore very strongly associated. The lightest squares show areas or nuclei that very rarely co-localize, even at the highest levels of attraction, so are therefore very connectionally distant.



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Figure 5.  Summary of optimal set analysis with the attraction parameter ranging from 1 to 10 (repulsion set to 1), and repulsion parameter ranging from 2 to 30 (attraction set to 1). Cortical areas and thalamic nuclei are listed along the top and left of the table. The frequency with which areas or nuclei co-localized within the same set is given by the colour (scale at top right of table). Darker colours show frequent co-localization within the same set, while light colours show rare co-localization.

 
In line with the balanced attraction and repulsion case (Figs 3 and 4GoGo), the somato-motor system is closely associated with fronto-limbic multimodal cortical areas. The first large block of structures in Figure 5Go (6l to MV-Re) contains fronto-limbic, somato-motor and multimodal structures. Figure 5Go confirms that the auditory system (MGV to AII) is the most topologically isolated of the thalamo-cortical systems, although MGV and Tem occasionally co-localize with fronto-limbic and visual structures. Within the visual system (LGLA to LGLGW), ALLS and PLLS sometimes co-localize with AES and IG, and LM-Sg. 5Bl is closely associated with many visual structures.

A feature of optimal set analysis applied to this data set is that areas or nuclei with few reported connections often end up in sets on their own (e.g. LIc, Hipp). Some areas or nuclei have few reported connections because they genuinely make few, possibly very strong, connections (e.g. LGLA, LGLC). Others have few reported connections because of lack of study or lack of consensus over their existence or classification (possibly LIc, and PF). These aspects of the analyses would benefit from more experiments on the less studied areas and from quantitative connection data for all areas. Quantitative data, which would provide a more accurate cost function, is provided by some researchers (e.g. Sherk, 1986; Musil and Olson, 1991; Peters et al., 1993, 1994; MacNeil et al., 1997; Van Duffel et al., 1997), but is unavailable for the vast majority of connections reported in the neuroanatomical literature.

Cluster Analysis

Figure 6Go shows the pooled results from the battery of nonparametric cluster analysis methods. The areas in Figure 6Go have been ordered so that the sets are comparable to Figure 3Go. It is clear that the cluster analysis methods are in good agreement with optimal set analysis (Figs 3 and 5GoGo). As Figure 6Go shows pooled results from a range of NMDS methods, and a range of clustering paradigms with a widely differing kernel radii, it has a graded nature that reveals considerable detail about both the local and the large-scale structure of the thalamo-cortical network. Large-scale structure has been identified by analyses using large radii kernels and the local structure has been revealed by the analyses with small radii kernels.

The ability of the analysis to look across different scales means that Figure 6Go contains a wealth of information that cannot all be explored in detail here. However, we outline several example features to help the reader to explore the Figure. First, the region corresponding to the first set from Figure 3Go (containing higher somato-motor and some multimodal and fronto-limbic structures) is clearly not homogenous. The areas of prefrontal cortex are much more closely associated with each other than, for example, with VA-VL, 6m, 6l and 7. Second, VA-VL, 6m, 6l, 7, 5Al and 5Bl have associations with structures that lie within the `low somatomotor' set of Figure 3Go, namely 4g, 4, 5Am, SSAi, SSAo and 5Bm. Third, the region of Figure 6Go corresponding to the visual set of Figure 3Go also shows considerable substructure. For example, there are particularly close connectional associations between 17 and 18, and between DLS, LPm and PLLS. These three structures also have associations outside the visual set, with AES and ALLS.

Figure 6Go shows several distinct and robust small connectional groups that are relatively invariant with NMDS method and clustering paradigm (darkest regions in Fig. 6Go). These groups must contain structures that are in very close connectional association since they are consistently identified in different NMDS configurations even by clustering methods with small kernels. From top to bottom of Figure 6Go, particularly tight subgroups include PFCMil, PFCMd and PFCL; CGa and CGp; 6l and 6m; 5Al, 5Bl and 7; AES, SIV and ALLS; 35 and 36; AAF and AI; Tem and MGvl; a low somato-motor group including 1, 2, 3a, 3b, SII, and VPL and VPM; Sb and MV-Re; areas 17 and 18; and LPm and PLLS.

An alternative and informative reading of Figure 6Go is to concentrate on the very light regions which show those groups of areas that are least likely to occur within the same clusters. The unimodal visual structures (LGLGW to PLLS) are very distant from most auditory structures (MGV to MGDd), and from the early somato-motor structures (4g to SII). The early somatomotor structures (4g to SII) are very distant from the early auditory system (MGV to MGDd). All the early sensory and sensory-motor groups are more distant to each other than they are to the fronto-limbic and higher order sensory-motor regions (e.g. PFCL to 36, and PAT to RS). This is consistent with the notion that, at a gross level of description, the thalamo-cortical network is organized into three distinct sensory or sensory motor systems and a topologically central group of structures. In this analysis, the topologically central group of structures includes fronto-limbic structures, some higher somato-motor (e.g. 6l, 5m) and possibly multimodal sensory structures (e.g. AES, 7).


    Discussion
 Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
 References
 
A New Approach

This paper presents an approach to the analysis of anatomical connection data that is still relatively new and that frequently invites questions. First, can one collate brain connectivity data from many different studies on many different individuals? Second, is it practical to produce simple representations of such complicated data? Third, what are the advantages and disadvantages of the different analysis methods? Fourth, what are the limitations of the `grey box' level of explanation (Douglas and Martin, 1991Go) that considers cortical areas, thalamic nuclei and extrinsic connections as the basic units of organization?

Collation and Variability

There are several reasons to collate anatomical connection data. First, collation may highlight gaps in current knowledge (e.g. cortical connections to the midline and intralaminar nuclei, see Table 2Go and Results section; see also Hilgetag et al., 1996Go). Second, it may direct further empirical study (e.g. Scannell et al., 1996). Third, collation provides the opportunity to test theories of neuroanatomical organization with a degree of quantitative rigor (e.g. Cherniak, 1990; Nicolelis et al., 1990; Musil and Olson, 1991; Young, 1992; Hilgetag et al., 1996; Scannell, 1997). Fourth, primary connection data are distributed across a large and, to the non-specialist, difficult literature. Collation can allow a wide range of researchers to benefit from advances in experimental neuroanatomy.

Despite these advantages, collation is complicated by variability in anatomists' parcellation schemes, connection-tracing methods, and by variability in the results of equivalent tracer deposits in different animals. Variability has been highlighted in recent quantitative studies and is substantial both in anatomical structures (e.g. Rajkowska and Goldman-Rakic, 1995; Andrews et al., 1997), and in the density of connections between them (MacNeil et al., 1997Go). MacNeil et al. (1997) have counted the number of labelled thalamic and cortical neurons following injections in the medial suprasylvian visual area. They found that visual cortico-cortical connection densities vary widely between tracer deposits. At first sight, high variability (whether within or between individuals) seems problematic for much of connectional neuroanatomy, and particularly so for studies such as this one.

MacNeil et al.'s (1997) results have prompted us to examine quantitative data from Musil and Olson (1988), Bowman and Olson (1988), Olson and Jeffers (1987), Olson and Lawler (1987), Olson and Musil (1992), and Musil and Olson (1991), and unpublished quantitative connection data on the lateral suprasylvian areas (S. Grant, personal communication). The data suggest that for a wide range of cortico-cortical and thalamocortical connections, the distribution of connection densities across equivalent experiments in different individuals is highly non-normal. In fact, the distribution is closer to an exponential (R.J. Baddeley and J.W. Scannell, unpublished observations). This has important implications. First, statistical methods based on the assumption of a normal distribution are not appropriate for the analysis of such data. Second, the exponential distribution is extremely variable, so large amounts of data are required for confident estimates of sample statistics. Third, the standard measure of variability (sample SD) can show a relatively strong bias when applied to exponentially distributed data. For small sample sizes, the variability will be systematically underestimated. Table 4Go (R.J. Baddeley and J.W. Scannell, unpublished observations) provides a guide to confidence intervals for estimates of mean and SD connection density. It also provides a guide to correcting the bias in sample SD. By providing confidence intervals, a simple indicator of statistical power, Table 4Go should help researchers to choose appropriate sample sizes in connection tracing experiments.


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Table 4 Guide to sampling in quantitative connection tracing experiments
 
Table 4Go shows that small samples (five or fewer individuals) have very wide confidence intervals, so are likely to suffer from serious random sampling error. The benefits of increasing sample size begin to tail off with sample sizes of 10 or more individuals (Table 4Go). This suggests that studies of the connections to a particular cortical area should aim to inject the area in ~10 individuals if reasonable quantitative (or qualitative) estimates of connection densities are required.

Many primary studies of cortico-cortical and cortico-thalamic connections are based on substantially fewer than 10 cases, so risk serious random sampling error. However, where several primary studies have examined the same connection, collation is likely to reduce the problem of random sampling error in the estimation of connection density. This gives some justification to those who have made serious attempts to distil data from many neuroanatomy papers into a single coherent and analysable form (e.g. Pandya and Yeterian, 1985; Felleman and Van Essen, 1991). However, with high variability, presenting any single connectional scheme as representative becomes difficult. This is because most individuals depart considerably from the `average' pattern of connection densities. Indeed, no single individual can have a pattern of connection densities that is very representative of the others. To reflect this genuine aspect of connection data, the nature of the distribution of connection densities should be quantified (Cherniak, 1990Go), reported and represented in future attempts at collation and modelling (MacNeil, 1997).

Complexity

The second question, that connection data are too complicated to summarize, is serious and plausible, but, our data suggest, untrue. One can imagine a brain in which the pattern of area-to-area connections was so complex that it could be described by nothing simpler than the connection matrix itself. Putting random numbers in Table 2Go would simulate the complexity of connectivity of such a brain. Fortunately, the goodness of fit of the NMDS configurations and the low cost of the CANTOR solutions, when compared with analyses of test data, show that the connectional architecture of the real thalamo-cortical network can be well represented relatively simply. This finding is important. It suggests that, in principle, relatively few sources of variability can account for much of the variability in the gross connection pattern of the thalamo-cortical network. We think this apparent simplicity shows that a small number of simple rules, reflecting genetic and/or developmental economy, have been favoured by evolution in the design of the thalamo-cortical network.

Analysis Methods

Many anatomists have sought to present complex connection data in a compact and comprehensible way. McCulloch (1944) provides an excellent example. However, the complexity of modern data make the problem considerable (Nicolelis et al., 1990Go; Felleman and Van Essen, 1991Go). While our methods make a contribution, none are an ideal solution.

NMDS works with ordinal data to give graphical representations of connectivity. However, there are many possible NMDS algorithms and cost functions and it is not always clear which, if any, is best. We are also limited to presenting configurations in no more than three dimensions. We think this acceptable for the thalamo-cortical data in this paper, but it may not be appropriate for other anatomical data. Data that cannot be represented by a low-dimensional spatial arrangement of points (e.g. data with many one way connections, where the proximity of A to B does not equal the proximity of B to A) are unsuitable for graphical presentation with NMDS.

Optimal set analysis avoids dimensional reduction and allows us to specify particular cost functions; in this case, functions that embody an attractive definition of a neural system. Varying the cost function allows us to look for both local and global features of neural organization. However, the method tends to produce a very large number of optimal solutions that then have to be summarized (e.g. Hilgetag et al., 1996). Sometimes the summaries are simple (e.g. Fig. 3Go), but they may be nearly as complex as the connection matrix itself (e.g. Fig. 5Go). In addition, our cost function assumes a metric relationship between connection densities, which is a disadvantage when compared with NMDS.

Non-parametric cluster analysis compromises between NMDS and optimal set analysis. It balances the need to avoid dimensional reduction with the need to avoid the problems of density estimation in high-dimensional spaces (Silvermann, 1986Go; Burns, 1997Go) by using five-dimensional NMDS configurations as a starting point. The method can look for both local and global organization. However, the method is less transparent than either NMDS or optimal set analysis and we have to perform many different cluster analyses and pool the pool the results, so that spurious clusters (Gordon, 1996Go) are averaged out. This makes the summary data complicated.

Despite the limitations of the different methods, we are encouraged by the fact that they yield largely consistent results. We hope they provide relatively comprehensible working models which can, at best, serve as rough `route planners' to the large-scale organization of the thalamo-cortical network.

Levels of Analysis

The final question relates to the level of analysis presented in this paper. Is it useful to pursue the somewhat abstract level of analysis in which the cortical area, thalamic nucleus and extrinsic connection are the basic units?

Our choice of level of analysis has been pragmatic and utilitarian, seeking the greatest number of connections for the greatest number of structures. We have tried to reflect the cortical areas and thalamic nuclei of the cat that have been established by other authors and for which there are connection data. However, the distinctions we have drawn are not necessarily the most principled. For example, we have subdivided the LGN into several subnuclei on the basis of morphological, connectional and physiological differences between neuronal populations, but have treated area 17 as a single unit. However, each layer of area 17 has different extrinsic connections, physiological properties and morphology. It may also be the case that cortical areas and thalamic nuclei are not an appropriate level of organization for our kind of analysis of connectivity. For example, in the early visual system, parts of different areas representing similar regions of retinotopic space may be much more functionally and connectionally associated than parts of the same area representing different regions of space.

We see no easy answer to these questions. However, in the long term, quantitative data on connectivity, morphology and physiology are necessary to determine the most natural parcellation schemes and levels of analysis.

Indeterminate Hierarchies and Directed Loops

Crick and Koch (1998) suggest that directed feed-forward loops should not exist within the extrinsic thalamo-cortico-cortical network, as they would cause runaway excitation (Crick and Koch, 1998Go). They also suggest that by incorporating thalamocortical connections, `indeterminate' hierarchies (Hilgetag et al., 1996Go) might be avoided.

If the direction of connections is only known at the categorical level of measurement (`ascending', descending' or `lateral'), thalamo-cortical connections cannot remove indeterminacy from hierarchical analysis. Cortical hierarchies (e.g. Felleman and Van Essen, 1991) are indeterminate (Hilgetag et al., 1996Go) because connectivity is too sparse to constrain a unique hierarchy, even if the direction of every cortical connection were known. Indeterminacy will not go away if thalamo-cortical connections are included. This is because the cortico-thalamocortical loops that could, in principle, provide additional hierarchical information do, in fact, only link cortical areas that already have direct cortical projections (Scannell et al., 1997Go). The exceptions to this rule are connections to and from the midline or intralaminar nuclei (Scannell et al., 1997Go). The lack of directional thalamic `shortcuts' between areas without direct cortical connections means that thalamic connections cannot provide the additional information necessary remove indeterminacy from sensory-motor hierarchies (cf. Crick and Koch, 1998). Indeterminacy may disappear if it proves possible to obtain metric measures of the direction of cortical connections, as suggested by recent work of Barbas and Rempel-Clower (1997).

Symmonds and Rosenquist (1984) and Scannell et al. (1995) noted that the origin and termination patterns of connections between cat cortical areas frequently do not match the `feed-forward', `feed-back' and `lateral' templates that have been applied in the primate (e.g. Felleman and Van Essen, 1991; Crick and Koch, 1998). For example, cat area 17 sends projections that originate predominantly in the layers II and III (Rosenquist, 1985Go) and terminate predominantly in layers II and III of areas 18 and 19 (Price and Zumbroich, 1989Go). The projection from area 18 to 17 originates in layers II, III and V and terminates in layers I, II, III, IVA, V and superficial layer IV of area 17, while tending to avoiding deep layer VI and layer IVB (Henry et al., 1991Go). At present, the functional implications of the differences in laminar origin and termination patterns in the cat and macaque cortices are unclear. However, the fact that cats are frequently used for studies of cortical microcircuitry, while macaques are favoured for systems neuroscience, means that these differences require further critical evaluation.

Structure–Function Relationships

Connectional neuroanatomy is driven by the idea that there is a close link between brain connectivity and brain function (e.g. Meynert, 1890). Van Duffel et al. (1997) have recently explored this relationship in an ingenious experiment which correlated quantitative measures of anatomic and metabolic connectivity. However, we believe that the efforts of anatomists in finding and describing connections have not been efficiently exploited to explore the structure–function relationship. This is because functional arguments based on extrinsic connectivity have tended to be informal, non-quantitative and/or highly simplistic. Recently, Hilgetag et al. (1997a) have developed more formal network models, whose connectivity is based on the pattern of extrinsic cortical connections collated by Scannell et al. (1995), Young (1993) and others. These models provide excellent quantitative accounts of the spread of electrical activity found in old strychnine neuronographic experiments. It may be possible to extended such methods to explore the functional consequences of cortical lesions. Since the properties of networks may not be intuitively obvious, and since neuronal activity can spread via direct and indirect connections, simple models relying only on the strength of direct connections (e.g. Van Duffel et al., 1997) may not provide a realistic account of functional connectivity within the thalamo-cortical network.

Efficient Wiring

It has been suggested (Cherniak, 1992Go, 1994Go, 1995Go, 1996Go) that the organization of the central nervous system can be explained if `saving wire' is the primary and overriding design constraint. While efficient wiring has long been thought to contribute to some aspects of brain organization (e.g. Cowey, 1984; Mitchison, 1991; Young, 1992; Cherniak, 1994; Scannell et al., 1995; Scannell, 1997; Van Essen, 1997), Young and Scannell (1996) have argued that many other constraints are also important. If saving wire were the overriding design constraint, connectional proximity should map very neatly onto physical proximity. Component placement optimization, therefore, predicts a physical brain organization that resembles Figure 1Go. To `save wire', thalamic nuclei should dissociate from their neighbours, with which they do not connect, and migrate to be close to the cortical areas with which they do connect. However, the thalamic nuclei remain firmly clustered together near the centre of the cerebral hemisphere. This may reflect developmental and evolutionary constraints. The thalamus was well developed in reptiles, long before the origin of neocortex (Masterton, 1976Go). Furthermore, the development of the thalamus and thalamo-cortical projections precedes that of the cortical plate and cortico-cortical projections (O'Leary et al., 1994Go; Payne et al., 1988Go). Therefore, constraints other than the need to save wire may strongly constrain the organization of the central nervous system (Young and Scannell, 1996; Scannell, 1997Go).

Global Architecture

Young (1993), Scannell and Young (1993) and Young et al. (1995a,b) found that the extrinsic connectional architecture of the cortico-cortical network of macaques and cats defined four major systems. There were the visual, auditory and somatomotor systems and a fourth system, termed the `fronto-limbic' system, composed of prefrontal cortex and structures in the medial part of the hemisphere (sometimes termed `limbic' cortex). The sensory-motor systems all showed a degree of hierarchical organization and their highest stations were in close connectional association with the fronto-limbic complex that therefore has access to the most highly processed sensory and motor information. There was more limited cross-talk between the systems outside the fronto-limbic complex, but this differed between the cat and macaque.

Our results show that a similar plan holds for the thalamocortico-cortical network. Different analysis methods consistently detect three groups of areas corresponding to the unimodal components of the visual, auditory and somato-motor systems. The higher stations of these systems are associated with a topologically central group of structures (insular, cingulate and prefrontal cortex, associated nuclei and, depending on analysis method, the higher stations of the somato-motor system and multimodal cortical areas). The analyses also identify a final group of structures (e.g. Hipp, MV-Re, Sb, pSb, AM, AD, Enr), that are at the furthest possible remove from the sensory-motor periphery. This basic plan is a robust and reproducible feature of three independent analyses of a comprehensive body of connection data. Therefore, it should represent a strong constraint on large-scale theories of the organization of the brain.


    Notes
 
This work was supported by the Wellcome Trust.

Address correspondence to J.W. Scannell, Neural Systems Group, Psychology Department, Ridley Building, University of Newcastle, Newcastle upon Tyne NE1 7RU, UK. Email: J.W.Scannell{at}ncl.ac.uk.


    Appendix
 Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
 References
 


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Parcellation of the cat thalamus
 

    References
 Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
 References
 
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