- Email: [email protected]
One cortex – many maps: An introduction to coordinate-independent mapping by Objective Relational Transformation (ORT)
Neurocomputing 26}27 (1999) 1049}1054
One cortex } many maps: An introduction to coordinate-independent mapping by Objective Relational Transformation (ORT) Klaas E. Stephan *, Rolf KoK tter C.&O. Vogt Institute for Brain Research, Heinrich Heine University, UniversitaK tsstr. 1, D-40225 Du( sseldorf, Germany Institute of Morphological Endocrinology and Histochemistry, Heinrich Heine University, UniversitaK tsstr. 1, D-40225 Du( sseldorf, Germany Accepted 18 December 1998
Abstract Having accumulated vast amounts of data, the neuroscienti"c community is now challenged to integrate and analyze these data on the system level of the brain. To this end, powerful databases of all types of brain data are indispensible. The main obstacle for such databases is the divergence of brain maps used (the `parcellation problema). First databases have been constructed during the last years, but so far none of them has successfully tackled the parcellation problem. We present key features of the "rst mathematical approach to this problem and outline its use in neuroscienti"c databases. 1999 Elsevier Science B.V. All rights reserved. Keywords: Analysis; Connectivity; Cortex; Database; Mathematical method
1. Introduction With the enormous progress of neuroscience during this century, it has become clear that higher-order analyses and functional interpretations on the system level of the brain will remain impossible without integrating the experimental results of the last decades with the aid of databases [4]. First attempts have been made to provide the neuroscienti"c community with connectivity data which are regarded as key
* Corresponding author. Tel./fax: #49-211-8112095. E-mail addresses: [email protected] (K.E. Stephan), [email protected] (R. KoK tter) 0925-2312/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 2 3 1 2 ( 9 9 ) 0 0 1 0 3 - 4
1050
K.E. Stephan, R. Ko( tter / Neurocomputing 26}27 (1999) 1049}1054
information for the analysis of brain systems [1,2,5,8]. These attempts, however, are hampered by the existence of the many divergent brain maps de"ned and used by di!erent authors (the `parcellation problema). Each of the earlier databases tries to cope with this problem by de"ning an a priori &&reference map'' to which the individual "ndings of di!erent publications are mapped according to the subjective criteria of the database collator. These criteria are opinion based, either resulting from self-conducted comparisons of maps or derived from published opinions of other authors. The criteria and opinions on which the transformation process to the reference map was based, however, were in no case fully documented (e.g. Felleman and Van Essen [2] tabulated alternative names for the areas of their reference map but did not state the exact relations). In addition to this lack of operationalization and observer independence, only the transformed data were represented. Thus users of the databases had no choice than to adopt the reference map of the database, irrespective of their own needs. We here present a mathematical approach to the parcellation problem called `Objective Relational Transformationa (ORT), which intends to overcome some methodological drawbacks of the existing connectivity databases. This methodology increases objectivity (by representing data in their original parcellation scheme), #exibility (by letting the user convert data between arbitrary pairs of di!erent maps), reliability (by formal algorithms for the mapping process) and transparency (by fully documenting the criteria and opinions on which the mapping process is based). Furthermore, it is easily applicable to already published data. Due to the restricted length of this article we can only describe some basic features of ORT. An account of an earlier prototypical version of ORT was published recently [6].
2. Method First, we introduce two simple classi"cations: One describes the information about a cortical area (EC"`Extension Codesa), the other describes the logical relation between areas of di!erent brain maps (RC"`Relation Codesa). Any single experimental "nding on cortical properties can be understood as information being valid for a spatially extended part of the cortex. For example, injecting tracer substance into a given part of the cortex will label some areas whereas others will remain unlabeled. Within one speci"c area, this information can be further speci"ed. For example, a labeled area may be completely labeled, it may be partially labeled, or the existence of label may be known but not its extent. Based on these considerations, one can classify brain data according to the extent that their information is valid for a speci"c cortical area A. This classi"cation, the `Extension Codesa (EC), distinguishes "ve cases: EC (A)"N: The information is Not valid for A. EC (A)"P: The information is valid Partially for A, i.e. there are subparts for which it is not valid. EC (A)"C: The information is valid for the Complete extent of A, i.e. for every subpart of A.
K.E. Stephan, R. Ko( tter / Neurocomputing 26}27 (1999) 1049}1054
1051
EC (A)"X: The information eXists for A, i.e. it is valid at least for a part of A, maybe even for its complete extent. EC (A)"U: It is Unknown whether the information is valid for A. Converting data between di!erent brain maps requires knowledge about the relations that their areas have to each other. Authors have repeatedly o!ered comparisons of brain maps, but no formal classi"cation for the relation of two areas A and B in two di!erent maps AH and BH has been presented so far. We suggest the following classi"cation of `Relation Codesa (RC) which covers all possible logical relations that two such areas A and B can have: RC RC RC RC
(A, B)"I: (A, B)"S: (A, B)"L: (A, B)"O:
RC (A, B)"D:
A and B have Identical boundaries. A is a Subarea of B, i.e. A is contained by B. A is Larger than B, i.e. A contains B. A and B Overlap, i.e. A contains some parts of the cortex which are not contained by B and vice versa. A and B are Disjunct, i.e. A and B are not coextensive in any way.
Based on these two classi"cations EC and RC, we can now formulate simple rules to "nd a general answer to the parcellation problem: How can we transform a speci"c piece of information (i.e. one or several ECs) from one map to another, under the condition that we know about the relations (RCs) of the involved areas of both maps? In order to facilitate algorithmic implementation within databases, we need a formal description of a set of general transformation rules operating on our two sets EC and RC. Such a description is called a `heterogeneous algebraa [3]. We refer to this set of rules as the `algebra of transformationa (AT). The general principle of our AT is the following: Imagine we want to convert information based on map AH to a speci"c area B of map BH. First, we have to determine all areas A , 2, A (n51) in map AH which are coextensive in some way L with area B in map BH. We then decide step by step how the information of each of the areas A , 2, A is transferred to area B. At each step, we "rst determine what L we know about the information of B so far (i.e. our previous knowledge about EC(B)) } we will call this result of previous transformations EC (B). Then we look at the currently processed area A (14i4n) of map AH, determine its relation to B (i.e. G RC(A , B)) and its information (i.e. EC(A )) and look up the respective rule (see Table 1) G G for the entire constellation (EC , RC(A , B), EC(A )). The respective transformation G G rule will then deliver a new temporarily resulting EC for B which we call EC (B). This EC (B) will iteratively serve as input (i.e. as EC (B)) for the next step. Having completed the procedure for all areas A , 2, A , we get the "nal EC (B). L There are two more points to make: Initially, we do not know anything about the information contained by area B. For formal reasons, we introduce a further EC called `Ba for `Begina, to mark this special situation. And second, the procedure described above has to be applied only if n'1, i.e. if there is more than one area in map AH which is coextensive with area B of map BH (e.g. several subareas or overlapping areas). Only in this case, we need several steps to compute the resulting EC for area B. Thus, we call the operations involved `multi-step operationsa or `multi-step
K.E. Stephan, R. Ko( tter / Neurocomputing 26}27 (1999) 1049}1054
1052
mappingsa (M ). If, however, there is only one area A in map AH that is larger than or + identical with area B of map BH (RC(A , B)"L or RC(A , B)"I), then the procedure is much simpler. As we can perform the mapping process in one single step, we no longer need to take into account an intermediate result (like our EC above). Instead, all we need to know in this case is the relation between the two areas (i.e. RC(A , B)) and the information of area A (i.e. EC(A )). We call this case the `single-step operationa (M ). 1 With this in mind, we can now specify the transformation algebra more formally: It comprises the sets EC and RC as the basis for the operations M and M . + 1 Multi-step operation M for mapping sub- or overlapping areas: + M : (EC6+B,);+S, O,;ECPEC. + Single-step operation M for mapping identical or larger areas: 1 M : +I, ¸,;ECPEC. 1 The exact speci"cation of these mapping is given by Tables 1 and 2.
(1)
(2)
Table 1 Multi-step operation M + EC (B)
RC(A , B) G
EC(A ) G
EC (B)
EC (B)
RC(A , B) G
EC(A ) G
EC (B)
B
S
N P X C N P X C
N P X C N ; ; C
P
S
N P X C N P X C
P P P P P P P P
N P X C N P X C
N P P P N ; ; P
X
N P X C N P X C
P P X X P X X X
N P X C N P X C
; P X X ; ; ; X
C
N P X C N P X C
P P X C P X X C
O
N
S
O
;
S
O
O
S
O
S
O
K.E. Stephan, R. Ko( tter / Neurocomputing 26}27 (1999) 1049}1054
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Table 2 Single-step operation M 1 RC(A, B)
EC(A)
EC (B)
I
N P X C
N P X C
¸
N P X C
N ; ; C
3. Perspective This short introduction to the main principles of ORT can only give a glimpse of its potential as a transformation and data mining tool within databases of topological brain data. Several additionally incorporated methods from theoretical computer science (e.g. graph theory and "nite automata) make ORT a superior alternative to the former approaches of neuroscienti"c databasing. A complete and formal description of ORT will be given in a forthcoming publication [7]. At the moment, an ORT-based database called CoCoMac (as it represents Corticocortical Connectivity of the Macaque) is constructed which already includes more than 70 di!erent parcellation schemes and several thousand results of anatomical tracing studies.
Acknowledgements We thank Gully Burns, Claus Hilgetag, Jack Scannell, Axel Schleicher, Fritz Sommer, Malcolm Young and Karl Zilles for valuable advice and discussions.
References [1] G.A.P.C. Burns, Neural connectivity of the rat: theory, methods and applications, D.Phil. Thesis, University of Oxford, 1997. [2] D.J. Felleman, D.C. Van Essen, Distributed hierarchical processing in the primate cerebral cortex, Cereb. Cortex 1 (1991) 1}47. [3] R.H. GuK ting, Datenstrukturen und Algorithmen, Teubner, Stuttgart, 1992. [4] M.F. Huerta, S.H. Koslow, A.I. Leshner, The Human Brain Project: an international resource, TINS 16 (1993) 436}438. [5] J.W. Scannell, C. Blakemore, M.P. Young, Analysis of connectivity in the cat cerebral cortex, J. Neurosci. 6 (1995) 3655}3668.
1054
K.E. Stephan, R. Ko( tter / Neurocomputing 26}27 (1999) 1049}1054
[6] K.E. Stephan, R. KoK tter, A formal approach to the translation of cortical maps, in: J. Nicholls, V. Torre (Eds.), Neural Circuits and Networks, Springer, Berlin, 1998, pp. 205}226. [7] K.E. Stephan, K. Zilles, R. KoK tter, Co-ordinate-independent mapping of structural and functional data by Objective Relational Transformation (ORT), submitted. [8] M.P. Young, The organization of neural systems in the primate cerebral cortex, Proc. R. Soc. Lond., B. 252 (1993) 13}18.
Klaas Enno Stephan has been studying Medicine at the Heinrich Heine University DuK sseldorf and Computing Science at the University of Hagen since 1994. His Ph.D. project at the C.&O. Vogt Institute for Brain Research in DuK sseldorf (supervised by Rolf KoK tter and Karl Zilles) deals with computational approaches to the investigation of cortical structure}function relations. He is a scholar of the German National Merit Foundation (Studienstiftung des Deutschen Volkes) and fellow of the Neuroscienti"c Graduate School at the University of DuK sseldorf. Supported by a Wellcome Trust Collaboration Grant, he continuously works in Newcastle as a guest of the `Neural Systems Groupa of Malcolm Young at the Institute of Psychology.
Rolf KoK tter studied medicine at the UniversitaK t Essen, the University of Manchester, and the UniversiteH de Montpellier; Doctoral thesis in the laboratory of Otto-Erich Brodde with a combined pharmacological, biochemical, and physiological characterization of alpha adrenoceptors; advanced studies at the Institute of Neurology, London; introduction to neuroinformatics in the group of GuK nther Palm; research fellow at the Dept. of Anatomy and Structural Biology, University of Otago; Helmholtz scholarship at the C.&O. Vogt Institute for Brain Research chaired by Karl Zilles; specialist in anatomy and faculty member at the Institute of Morphological Endocrinology and Histochemistry. Currently, he is combining morphological, electrophysiological and computational approaches to investigate activity patterns and information processing in the cerebral cortex.
One cortex } many maps: An introduction to coordinate-independent mapping by Objective Relational Transformation (ORT) Klaas E. Stephan *, Rolf KoK tter C.&O. Vogt Institute for Brain Research, Heinrich Heine University, UniversitaK tsstr. 1, D-40225 Du( sseldorf, Germany Institute of Morphological Endocrinology and Histochemistry, Heinrich Heine University, UniversitaK tsstr. 1, D-40225 Du( sseldorf, Germany Accepted 18 December 1998
Abstract Having accumulated vast amounts of data, the neuroscienti"c community is now challenged to integrate and analyze these data on the system level of the brain. To this end, powerful databases of all types of brain data are indispensible. The main obstacle for such databases is the divergence of brain maps used (the `parcellation problema). First databases have been constructed during the last years, but so far none of them has successfully tackled the parcellation problem. We present key features of the "rst mathematical approach to this problem and outline its use in neuroscienti"c databases. 1999 Elsevier Science B.V. All rights reserved. Keywords: Analysis; Connectivity; Cortex; Database; Mathematical method
1. Introduction With the enormous progress of neuroscience during this century, it has become clear that higher-order analyses and functional interpretations on the system level of the brain will remain impossible without integrating the experimental results of the last decades with the aid of databases [4]. First attempts have been made to provide the neuroscienti"c community with connectivity data which are regarded as key
* Corresponding author. Tel./fax: #49-211-8112095. E-mail addresses: [email protected] (K.E. Stephan), [email protected] (R. KoK tter) 0925-2312/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 2 3 1 2 ( 9 9 ) 0 0 1 0 3 - 4
1050
K.E. Stephan, R. Ko( tter / Neurocomputing 26}27 (1999) 1049}1054
information for the analysis of brain systems [1,2,5,8]. These attempts, however, are hampered by the existence of the many divergent brain maps de"ned and used by di!erent authors (the `parcellation problema). Each of the earlier databases tries to cope with this problem by de"ning an a priori &&reference map'' to which the individual "ndings of di!erent publications are mapped according to the subjective criteria of the database collator. These criteria are opinion based, either resulting from self-conducted comparisons of maps or derived from published opinions of other authors. The criteria and opinions on which the transformation process to the reference map was based, however, were in no case fully documented (e.g. Felleman and Van Essen [2] tabulated alternative names for the areas of their reference map but did not state the exact relations). In addition to this lack of operationalization and observer independence, only the transformed data were represented. Thus users of the databases had no choice than to adopt the reference map of the database, irrespective of their own needs. We here present a mathematical approach to the parcellation problem called `Objective Relational Transformationa (ORT), which intends to overcome some methodological drawbacks of the existing connectivity databases. This methodology increases objectivity (by representing data in their original parcellation scheme), #exibility (by letting the user convert data between arbitrary pairs of di!erent maps), reliability (by formal algorithms for the mapping process) and transparency (by fully documenting the criteria and opinions on which the mapping process is based). Furthermore, it is easily applicable to already published data. Due to the restricted length of this article we can only describe some basic features of ORT. An account of an earlier prototypical version of ORT was published recently [6].
2. Method First, we introduce two simple classi"cations: One describes the information about a cortical area (EC"`Extension Codesa), the other describes the logical relation between areas of di!erent brain maps (RC"`Relation Codesa). Any single experimental "nding on cortical properties can be understood as information being valid for a spatially extended part of the cortex. For example, injecting tracer substance into a given part of the cortex will label some areas whereas others will remain unlabeled. Within one speci"c area, this information can be further speci"ed. For example, a labeled area may be completely labeled, it may be partially labeled, or the existence of label may be known but not its extent. Based on these considerations, one can classify brain data according to the extent that their information is valid for a speci"c cortical area A. This classi"cation, the `Extension Codesa (EC), distinguishes "ve cases: EC (A)"N: The information is Not valid for A. EC (A)"P: The information is valid Partially for A, i.e. there are subparts for which it is not valid. EC (A)"C: The information is valid for the Complete extent of A, i.e. for every subpart of A.
K.E. Stephan, R. Ko( tter / Neurocomputing 26}27 (1999) 1049}1054
1051
EC (A)"X: The information eXists for A, i.e. it is valid at least for a part of A, maybe even for its complete extent. EC (A)"U: It is Unknown whether the information is valid for A. Converting data between di!erent brain maps requires knowledge about the relations that their areas have to each other. Authors have repeatedly o!ered comparisons of brain maps, but no formal classi"cation for the relation of two areas A and B in two di!erent maps AH and BH has been presented so far. We suggest the following classi"cation of `Relation Codesa (RC) which covers all possible logical relations that two such areas A and B can have: RC RC RC RC
(A, B)"I: (A, B)"S: (A, B)"L: (A, B)"O:
RC (A, B)"D:
A and B have Identical boundaries. A is a Subarea of B, i.e. A is contained by B. A is Larger than B, i.e. A contains B. A and B Overlap, i.e. A contains some parts of the cortex which are not contained by B and vice versa. A and B are Disjunct, i.e. A and B are not coextensive in any way.
Based on these two classi"cations EC and RC, we can now formulate simple rules to "nd a general answer to the parcellation problem: How can we transform a speci"c piece of information (i.e. one or several ECs) from one map to another, under the condition that we know about the relations (RCs) of the involved areas of both maps? In order to facilitate algorithmic implementation within databases, we need a formal description of a set of general transformation rules operating on our two sets EC and RC. Such a description is called a `heterogeneous algebraa [3]. We refer to this set of rules as the `algebra of transformationa (AT). The general principle of our AT is the following: Imagine we want to convert information based on map AH to a speci"c area B of map BH. First, we have to determine all areas A , 2, A (n51) in map AH which are coextensive in some way L with area B in map BH. We then decide step by step how the information of each of the areas A , 2, A is transferred to area B. At each step, we "rst determine what L we know about the information of B so far (i.e. our previous knowledge about EC(B)) } we will call this result of previous transformations EC (B). Then we look at the currently processed area A (14i4n) of map AH, determine its relation to B (i.e. G RC(A , B)) and its information (i.e. EC(A )) and look up the respective rule (see Table 1) G G for the entire constellation (EC , RC(A , B), EC(A )). The respective transformation G G rule will then deliver a new temporarily resulting EC for B which we call EC (B). This EC (B) will iteratively serve as input (i.e. as EC (B)) for the next step. Having completed the procedure for all areas A , 2, A , we get the "nal EC (B). L There are two more points to make: Initially, we do not know anything about the information contained by area B. For formal reasons, we introduce a further EC called `Ba for `Begina, to mark this special situation. And second, the procedure described above has to be applied only if n'1, i.e. if there is more than one area in map AH which is coextensive with area B of map BH (e.g. several subareas or overlapping areas). Only in this case, we need several steps to compute the resulting EC for area B. Thus, we call the operations involved `multi-step operationsa or `multi-step
K.E. Stephan, R. Ko( tter / Neurocomputing 26}27 (1999) 1049}1054
1052
mappingsa (M ). If, however, there is only one area A in map AH that is larger than or + identical with area B of map BH (RC(A , B)"L or RC(A , B)"I), then the procedure is much simpler. As we can perform the mapping process in one single step, we no longer need to take into account an intermediate result (like our EC above). Instead, all we need to know in this case is the relation between the two areas (i.e. RC(A , B)) and the information of area A (i.e. EC(A )). We call this case the `single-step operationa (M ). 1 With this in mind, we can now specify the transformation algebra more formally: It comprises the sets EC and RC as the basis for the operations M and M . + 1 Multi-step operation M for mapping sub- or overlapping areas: + M : (EC6+B,);+S, O,;ECPEC. + Single-step operation M for mapping identical or larger areas: 1 M : +I, ¸,;ECPEC. 1 The exact speci"cation of these mapping is given by Tables 1 and 2.
(1)
(2)
Table 1 Multi-step operation M + EC (B)
RC(A , B) G
EC(A ) G
EC (B)
EC (B)
RC(A , B) G
EC(A ) G
EC (B)
B
S
N P X C N P X C
N P X C N ; ; C
P
S
N P X C N P X C
P P P P P P P P
N P X C N P X C
N P P P N ; ; P
X
N P X C N P X C
P P X X P X X X
N P X C N P X C
; P X X ; ; ; X
C
N P X C N P X C
P P X C P X X C
O
N
S
O
;
S
O
O
S
O
S
O
K.E. Stephan, R. Ko( tter / Neurocomputing 26}27 (1999) 1049}1054
1053
Table 2 Single-step operation M 1 RC(A, B)
EC(A)
EC (B)
I
N P X C
N P X C
¸
N P X C
N ; ; C
3. Perspective This short introduction to the main principles of ORT can only give a glimpse of its potential as a transformation and data mining tool within databases of topological brain data. Several additionally incorporated methods from theoretical computer science (e.g. graph theory and "nite automata) make ORT a superior alternative to the former approaches of neuroscienti"c databasing. A complete and formal description of ORT will be given in a forthcoming publication [7]. At the moment, an ORT-based database called CoCoMac (as it represents Corticocortical Connectivity of the Macaque) is constructed which already includes more than 70 di!erent parcellation schemes and several thousand results of anatomical tracing studies.
Acknowledgements We thank Gully Burns, Claus Hilgetag, Jack Scannell, Axel Schleicher, Fritz Sommer, Malcolm Young and Karl Zilles for valuable advice and discussions.
References [1] G.A.P.C. Burns, Neural connectivity of the rat: theory, methods and applications, D.Phil. Thesis, University of Oxford, 1997. [2] D.J. Felleman, D.C. Van Essen, Distributed hierarchical processing in the primate cerebral cortex, Cereb. Cortex 1 (1991) 1}47. [3] R.H. GuK ting, Datenstrukturen und Algorithmen, Teubner, Stuttgart, 1992. [4] M.F. Huerta, S.H. Koslow, A.I. Leshner, The Human Brain Project: an international resource, TINS 16 (1993) 436}438. [5] J.W. Scannell, C. Blakemore, M.P. Young, Analysis of connectivity in the cat cerebral cortex, J. Neurosci. 6 (1995) 3655}3668.
1054
K.E. Stephan, R. Ko( tter / Neurocomputing 26}27 (1999) 1049}1054
[6] K.E. Stephan, R. KoK tter, A formal approach to the translation of cortical maps, in: J. Nicholls, V. Torre (Eds.), Neural Circuits and Networks, Springer, Berlin, 1998, pp. 205}226. [7] K.E. Stephan, K. Zilles, R. KoK tter, Co-ordinate-independent mapping of structural and functional data by Objective Relational Transformation (ORT), submitted. [8] M.P. Young, The organization of neural systems in the primate cerebral cortex, Proc. R. Soc. Lond., B. 252 (1993) 13}18.
Klaas Enno Stephan has been studying Medicine at the Heinrich Heine University DuK sseldorf and Computing Science at the University of Hagen since 1994. His Ph.D. project at the C.&O. Vogt Institute for Brain Research in DuK sseldorf (supervised by Rolf KoK tter and Karl Zilles) deals with computational approaches to the investigation of cortical structure}function relations. He is a scholar of the German National Merit Foundation (Studienstiftung des Deutschen Volkes) and fellow of the Neuroscienti"c Graduate School at the University of DuK sseldorf. Supported by a Wellcome Trust Collaboration Grant, he continuously works in Newcastle as a guest of the `Neural Systems Groupa of Malcolm Young at the Institute of Psychology.
Rolf KoK tter studied medicine at the UniversitaK t Essen, the University of Manchester, and the UniversiteH de Montpellier; Doctoral thesis in the laboratory of Otto-Erich Brodde with a combined pharmacological, biochemical, and physiological characterization of alpha adrenoceptors; advanced studies at the Institute of Neurology, London; introduction to neuroinformatics in the group of GuK nther Palm; research fellow at the Dept. of Anatomy and Structural Biology, University of Otago; Helmholtz scholarship at the C.&O. Vogt Institute for Brain Research chaired by Karl Zilles; specialist in anatomy and faculty member at the Institute of Morphological Endocrinology and Histochemistry. Currently, he is combining morphological, electrophysiological and computational approaches to investigate activity patterns and information processing in the cerebral cortex.