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Spatio-temporal patterns of neuronal activity: analysis of optical imaging data using geometric shape matching
Journal of Neuroscience Methods 114 (2002) 17 – 23 www.elsevier.com/locate/jneumeth
Spatio-temporal patterns of neuronal activity: analysis of optical imaging data using geometric shape matching R. Ko¨hling a,*, J. Reinel b, J. Vahrenhold b, K. Hinrichs b, E.-J. Speckmann a a
Institut fu¨r Physiologie, Westfa¨lische Wilhelms Uni6ersita¨t, Robert-Koch-Straße 27a, 48149 Mu¨nster, Germany b Institut fu¨r Informatik, Westfa¨lische Wilhelms Uni6ersita¨t, Mu¨nster, Germany Received 31 August 2001; received in revised form 22 October 2001; accepted 24 October 2001
Abstract Optical imaging of neuronal network activity yields information of spatial dynamics which generally is analyzed visually. The transient appearance of spatial activity patterns is difficult to gauge in a quantifiable manner, or may even altogether escape detection. Here, we employ geometric shape matching using Fre´chet distances or straight skeletons to search for pre-selected patterns in optical imaging data with adjustable degrees of tolerance. Data were sampled from fluorescence changes of a voltage-sensitive dye recorded with a 464-photodiode array. Fluorescence was monitored in a neuronal network in vitro. Neuronal activity prompting fluorescence fluctuations consisted of spontaneous epileptiform discharges in neocortical slices from patients undergoing epilepsy surgery. The experiments show that: (a) spatial activity patterns can be detected in optical imaging data; (b) shapes such as ‘mini-foci’ appear in close correlation to bioelectric discharges monitored with field potential electrodes in a reproducible manner; (c) Fre´chet distances yield more conservative matches regarding rectangular, and less conservative hits with respect to radially symmetric shapes than the straight skeleton approach; and (d) tolerances of 0.03– 0.1 are suited to detect faithful images of pre-selected shapes, whereas values \ 0.8 will report matches with any polygonal pattern. In conclusion, the methods reported here are suited to detect and analyze spatial, geometric dynamics in optical imaging data. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Functional organization; Neocortex; Human brain tissue; Spatial dynamics; Neuronal networks; Shape detection
1. Introduction Spatial mapping of neuronal network activity is the focus of interest of a wide scope of neuroscience research fields, ranging from in vivo studies of orientation preference maps in the visual cortex of mammals (Chapman et al., 1996; Tsodyks et al., 1999; Ohki et al., 2000), odorant representations in the olfactory bulb (Rubin and Katz, 1999; Meister and Bonhoeffer, 2001) and activation patterns in cerebellar cortex (Hanson et al., 2000), to in vitro analyses of neo- or archicortical microcircuitry (Albowitz et al., 1998; Tsau et al., 1998; Demir et al., 1999; Ko¨hling et al., 2000; Kohn et al., 2000). Optical imaging data contain information on spatial characteristics such as pinwheel orientation, or * Corresponding author. Tel.: +49-251-835-5537; fax.: +49-251835-5551. E-mail address: [email protected] (R. Ko¨hling).
dynamic activity patterns with high spatial and temporal resolution (Tsau et al., 1999). The final aim is to link such patterns to the underlying circuitry of the neuronal network —such as ‘minicolumns’ (Kohn et al., 1997), orientation columns (Chapman et al., 1996; Tsodyks et al., 1999) or barrels (Laaris et al., 2000). Temporally dynamic patterns, in particular, arising from sequential activation of neuronal processing structures (Fukunishi et al., 1992) are difficult to analyze visually and may even go undetected in case the underlying functionally coherent structures are small and/or are only emergent during short periods of time. In this article, we propose to employ techniques from the field of computational geometry (Preparata and Shamos, 1988; Sack and Urrutia, 2000) to facilitate detection of spatio-temporal coherent patterns. Researchers in computational geometry, a relatively young yet quickly maturing discipline in computer science, usually establish an abstract geometric description of
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R. Ko¨ hling et al. / Journal of Neuroscience Methods 114 (2002) 17–23
the objects to be dealt with and then formulate the problem in this setting. The geometric nature of both the objects and the problem often allows for concise mathematical analysis and proof of correctness of a problem-solving algorithm. These analyses in turn provide means to measure the complexity of a problem and the efficiency of an algorithm, e.g. in terms of running time. The aim of the present article is twofold: (1) to demonstrate the feasibility of pattern search and recognition in optical imaging data with the above techniques using a program working with ASCII data files in an Windows™ environment; and (2) to determine whether distinct shapes possibly mirroring networks of neuronal processing structures can in fact be detected in activity patterns, using spontaneous epileptiform discharges in chronically epileptic human neocortical tissue as a model.
2.2. Optical imaging and data acquisition SSFP-associated fluorescence changes were detected by a 464-element honeycomb shaped photodiode array at a rate of 785 frames/s via 10× and 20 × objective lenses, yielding total fields of view of 1500 and 750 mm diameter, respectively. Xenon-lamp illumination was allowed for a maximum of 2–3 s per single detection period, and detection periods were separated by at least 5 min each. Only data related to field potential discharges spontaneously occurring \ 200 ms after sampling start were evaluated. Raw data (fluorescence intensities) were converted to 20-bin-pseudocolor images scaled to the center diode using the NEUROPLEX software (Red Shirt Imaging, LLC, Fairfield, CT). The fluorescence change (dI/I) for typical events was 0.05– 0.3% of resting light intensity. For further analysis and geometric shape matching, data were exported from NEUROPLEX as ASCII file, yielding a text matrix corresponding to 464 diodes and 1024–3072 time points.
2. Methods
2.3. Geometric shape matching
2.1. Neocortical slice preparations and bioelectric acti6ity
While most pattern-matching algorithms in medical imaging are pixel based, we propose to view a two-dimensional area not as a collection of unrelated pixels but rather as one single polygonal object, that is, as a connected region described by a piecewise linear boundary. This viewpoint allows us to build upon a variety of results on polygonal shape matching (Alt and Guibas, 2000), most prominently an approximate, i.e. tolerance-based, matching algorithm based on the Fre´ chet distance (Alt and Godau, 1995). The Fre´ chet distance indicates the maximum distance between points on a (data) polygon and a superimposed (query) polygon that occurs while traversing the boundaries of both objects in clockwise orientation minimized over all possible startpoints of the traversals. We also develop a simple shape matching technique based on a uniquely defined characterization of a polygonal object: the straight skeleton (Aichholzer et al., 1995). The straight skeleton is a geometric construction based upon angular bisectors of the polygon and can be interpreted as the trusses of a roof erected over a floor-plan given by a polygonal object. Matching the polygons then corresponds to matching the trusses (or, rather, the vertices of the trusses). Specifically, the spatial location of vertices of data and query polygon is compared; matches result when the vertices overlap (within a given tolerance radius m; see below). The basic principle of each of the two methods is demonstrated in Fig. 1. Finally, we formulated heuristics for scaling, rotating, and mirroring query polygons, so that size, as well as rotational or axis symmetries do not hinder object recognition. Approximate matching (matching tolerances) can be intro-
The methods for neocortical slice preparation have been described in detail elsewhere (Ko¨ hling et al., 1998, 2000). Briefly, human neocortical tissue was a small portion of resectates excised for treatment of pharmacoresistant temporal lobe epilepsy from eight patients. Histopathological analysis showed a mild degree of gliosis and/or dysplasia. The experiments were approved by the local ethics committee, and informed consent was obtained from the patients. From a 1 cm3 block of the inferior temporal gyrus, coronal 450 mm sections were made with a vibratome within 5 min after resection. These were placed in a portable incubation chamber (Ko¨ hling et al., 1996) with oxygenated (95% O2, 5% CO2) and warmed (28 °C) artificial cerebrospinal fluid (aCSF) containing (in mM): NaCl, 124; KCl, 4; CaCl2, 2; NaH2PO4, 1.24; MgSO4, 1.3; NaHCO3, 26; and glucose, 10 (pH 7.35– 7.45). In some cases, the Mg2 + concentration was lowered to simulate epileptogenic conditions by omitting MgSO4. Prior to the experiments, slices were stained with 12.5 mg/ml of the voltage-sensitive dye RH795 (1 h), and washed for 1 h before transferal to a submerged-type recording chamber (32 °C) mounted on an inverse microscope. Field potentials were recorded from layers II/III and V using conventional aCSF-filled glass micropipettes. In the slices investigated here, sharp field potentials (SSFP) and dye-related fluorescence signals arose spontaneously as described previously (Ko¨ hling et al., 1998).
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duced by either specifying an upper bound m on the Fre´ chet distance (where zero distance indicates an exact match) or by specifying the maximum distance o that two vertices of the skeletons are allowed to be apart. To investigate the practical relevance of this approach, we realized a software toolkit based on OpenGL™/Windows™ that analyses data in the NEUROPLEX ASCII output format. A description of the program as well as screenshots can be found on the following webpage: http://wwwmath.uni-muenster.de/cs/GeometricAnalysis/. As in the original recording software, we first convert the data in the ASCII file to 20-bin-pseudocolor images. The scaling required for this conversion can be done with respect to the center diode as well as to either all diodes, a variable set of diodes, or a range given by the user. In a second pre-processing step, the program scans all pseudocolor images to extract the desired polygonal shapes. More specifically, for a given pseudocolor-bin b, all connected polygonal shapes are extracted that cover diodes whose pseudocolor-bin is in the range [b −t, b+ t] (t being an adjustable integer tolerance) and that have a minimum width of at least three diodes. At the recording margins, we add virtual neighboring diodes
that fall into any such bin-range in order to avoid automatic exclusion of borderline polygons. All such polygonal shapes can be visualized frame by frame and bin by bin. After having run one of the matching algorithms, matches are shown frame by frame, in a simple histogram displaying hits along the time line, and by means of an interval histogram to support detection of temporal clustering. The matching algorithms simultaneously process all bin ranges of the kind [b− t, b+t], with the parameter b varying from t to 20− t, so that we can find matches on all levels of fluorescence intensity. Prior to running any matching algorithm, the user interactively defines a polygonal shape by selecting a set of active diodes. For exact pattern matching, this pattern has to be matched without any translation, rotation, or scaling. For detecting approximate matches that also include translations, rotations, or scaling, all extracted polygonal shapes are re-evaluated with respect to their similarity to the user-defined shape. In order to handle scaling issues, all detected polygons are scaled to the size of the user-defined object according to either their longest side or (optionally) their largest diameter. Both objects are then superimposed in a virtual Cartesian diagram with the longest side starting at the origin (side comparison), or with their center of gravity located at the origin (diameter scaling); this heuristic is used to handle translations. The user can also decide to have the polygonal shapes rotated such that the longest side or the diameter of each polygonal shape is aligned with the horizontal axis of the Cartesian diagram. In addition, axial symmetries can be taken into account by adequately rotating and/or mirroring the test polygons. At the moment, the toolkit offers the two algorithms for approximate matching described above: Fre´ chet distance comparison and straight skeleton matching. The tolerance m for object matching is an absolute value in the virtual Cartesian diagram in which the two polygonal shapes are superimposed (hence, the tolerance is related to either the longest side or the diameter of the objects) and is adjustable by the user.
Fig. 1. Diagram illustrating the working principle of geometric shape matching using: (A) Fre´ chet distances; or (B) straight skeleton comparison. (A) With Fre´ chet matching, a user-defined object (solid lines) is compared to a test shape (broken lines) by: (1) scaling both objects with respect to longest diameter (A) or side (B); (2) superposition of objects so that longest side or diameter are on top of each other; (3) constructing vectors (fat gray lines) by connecting the shortest distances between the objects when simultaneously following their circumference. The maximal tolerance m is set by the user related to the length of the longest diameter/side of the user-defined object. (B) With the straight skeleton approach, user-defined (solid lines) and test object (broken lines) are matched by following steps (1) and (2) as in (A), and then constructing skeletons analogous to roof trusses for both objects. The positions of the skeletons’ vertices are compared to see whether each vertex of a skeleton lies within radius m of a vertex belonging to the other skeleton. Again, the parameter m is related to the length of the longest diameter/side of the user-defined object.
3. Results Field potential and optical recordings in human neocortical slices revealed spontaneous activity consisting of sharp field potentials (SSFP) and corresponding diminutions of fluorescence in optical signals (Fig. 2A) in 60% of the cases. This type of spontaneous activity has been described in detail elsewhere (Ko¨ hling et al., 1998, 1999, 2000). Using optical imaging, spatial activity patterns can be detected in association with the appearance of SSFP. An example is shown in Fig. 2B. Constructing spatial activity maps from color-coded optical signals picked up by a 464-photodiode matrix, the neuronal population appeared to be largely and
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Fig. 2.
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Fig. 3. Bar chart showing an interval histogram for the appearance of mini-foci as given in Fig. 2C using Fre´ chet comparisons. Width of bins is 2 ms, and from 10 ms onwards, 5 ms. No clustering of hits is evident.
homogeneously hyper- or normopolarized (Fig. 2B, left upper hexagon) at the beginning of the recording. Concomitant with the peak of the SSFP, single photodiodes signaled maximal depolarizations (red) of subsets of neurons. These seemed rather heterogeneous on visual inspection, arising as single-diode hotspots in the recording field (Fig. 2B, middle upper hexagon, Ko¨ hling et al., 2000), and only in the tail of the SSFP, neuronal activity converged to cover a larger field (Fig. 2B, right upper hexagon). One of the questions we were interested in was whether specific neuronal conglomerates initiate the spontaneous discharges, i.e. whether mini-foci can be observed during the initial phases of the discharge. To test this hypothesis, we searched for such mini-foci using a hexagonal 7-diode shape as template (Fig. 2B, middle lower hexagon, C). Indeed, beneath the heterogeneous patterns of neuronal activity, geometric shapes, presumably corresponding to coherent neuronal clusters, could be detected using geometric shape matching. Thus, mini-foci emerged during the first 10–50 ms (the first 10 – 40 frames) of the signals in the manner depicted in Fig. 2B. They were exclusive in the way that no other polygonal shaped activity patterns were present during this period. The location of these mini-foci was stereotypic not only for the first 10– 40 frames of the individual recording, but also for five consecutive recordings of different signals from one slice, indicating that indeed a distinct local network initiates the events. Only with further develop-
ment of the discharge, the network activity converged to cover larger neuronal aggregates (Fig. 2B, right hexagons). Under the latter conditions, mini-foci were still evident, yet now they were located at variable locations and probably represented projection sites of the now-converged activity of large parts of the neuronal network. Matches for mini-foci started approximately 50 ms before the peak of the SSFP (denoted by the second arrow in Fig. 2C on the line chart) independent of the analysis mode and continued to emerge throughout the remaining recording, in this experiment with a more prominent cluster (confluent lines in Fig. 2C) at 190 ms after the signal’s peak, i.e. long after the SSFP had returned to baseline. Other temporal clustering (such as doublets or triplets interspaced by longer intervals) was not evident, either in this or other recordings, as can be judged from the interval histogram in Fig. 3. Larger patterns such as bars (often horizontally oriented) exclusively appeared at this time only, alongside larger complex polygonal shapes or-rarely-in isolation. Angular patterns such as boomerangs emerged only very rarely (Fig. 2C). A similar situation holds true for SSFP observed under epileptogenic (Mg2 + -free) conditions (n=3). Again, SSFP were preceded and accompanied by the appearance of mini-foci, with convergence of activity to larger shapes in the later phases of SSFP. Furthermore, bar- or column-shaped patterns emerged with fullblown activity. These were much rarer, with an average
Fig. 2. Activity patterns and shape matching with spontaneous sharp field potentials (SSFP) and corresponding fluorescence changes (Opt) in human neocortical slice preparation. (A) Diagram of the recording situation depicting the neocortical slice with underlying white matter (WM), the position of the hexagonal photodiode matrix and of the field potential electrode, respectively. SSFP recorded by the field potential electrode is shown in opposition to an optical recording picked up by one diode in the center of the array. Arrows and lettering indicate time points of optical recordings further analyzed in (B) and (C). (B) Spatial pattern of neuronal activity (upper row) in the optical recording field at 1, 358 and 534 ms after beginning of the recording, corresponding to beginning of the trace, peak and tail of the SSFP. Activity is color-coded: blue, normoand hyperpolarization; red, depolarization (corresponding to changes up to − 0.35 and − 0.55%, respectively). Lower row: shape matches found for solitary mini foci of maximal depolarizations (red, circle in pseudocolor calibration bar) consisting of a hexagon of seven diodes. One such hit appears at SSFP peak (358 ms, b), and another one together with a large polygonal confluence of activity during SSFP tail (534 ms, c). (C) Shape matching for different patterns. Three user-defined shapes are given on the left of the three pairs (simple mini-focus, boomerang, bar) and patterns found to also match on the right. The line histograms list the hits for mini-foci (red bars and numbers) using Fre´ chet distance (upper chart) and straight skeleton (lower chart) algorithms at a tolerance of 0.1 with respect to the duration of the recording. Note that the temporal distribution of hits is virtually independent of the search method. For comparison, hits for boomerangs (blue arrows and numbers) and bars (green arrows and numbers) using Fre´ chet distances and skeleton comparisons are also given, showing that particularly for columnar shapes, the two methods differ. Numbers in brackets list the hits with corresponding skeleton match. Note that skeleton match is highly conservative regarding simple straight polygons, and less conservative than Fre´ chet matching with respect to angular figures.
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of 10 –20% of hits as compared to mini-foci. In contrast to SSFP under control conditions, these bars had in \70% of the cases a clearly columnar orientation, sometimes appearing in parallel configurations as to comprise three columns of roughly 500 mm width (not shown). A comparison of the two analysis modes showed that either mode is differentially sensitive regarding different template shapes (Fig. 4). With tolerances of 0.1, Fre´ chet distance matching yielded very conservative results regarding angular polygonal shapes such as boomerangs, whereas the straight skeleton approach under these conditions reported matches of various shapes, provided their common characteristic was a prolonged backbone truss (possibly branched) with bifurcated ends (Fig. 4). Radially symmetric shapes, on the other hand, which will yield rather complex skeletal lattices, were conservatively analyzed in the straight skeleton approach. By contrast, the Fre´ chet match reported similarities with various rounded shapes even if they missed a part of their sides (Fig. 4). Not surprisingly, a sharpening of the tolerance to 0.03 narrowed down the match analysis to faithful images of the template in either analysis mode. Raising the tolerance to 0.8 and beyond, all polygonal shapes were reported as matches (not shown).
4. Discussion The present study was undertaken to: (1) demonstrate that pattern search and recognition can be per-
formed in optical imaging data using geometric shape matching; and (2) to determine whether specific spatial patterns presumably representing coherently active neuronal processing structures can be detected during spontaneous epilepsy-associated neuronal activity which might point to functional initiation sites. We could show that: (1) spatial activity patterns can be detected in optical imaging data; (2) mini-foci appear in close correlation to bioelectric discharges; (3) Fre´ chet distances yield more conservative matches regarding angular, and less conservative hits with respect to radially symmetric shapes than the straight skeleton approach; and (4) tolerances of 0.03–0.1 are suited to detect faithful images of pre-selected shapes. Several papers dealing with optical imaging analysis of neuronal network activity have reported emergent spatial patterns which were usually analyzed visually (Fukunishi et al., 1992; Cohen and Yarom, 1999; Rubin and Katz, 1999; Kohn et al., 2000). Such patterns were generally linked to underlying functional and/or structurally defined neuronal processing structures which were deemed to reflect, e.g. signal detection specificity in olfactory bulb (Rubin and Katz, 1999; Meister and Bonhoeffer, 2001), as well as input and lamina-specific functional cerebellar (Cohen and Yarom, 1999; Hanson et al., 2000) or neocortical (Fukunishi et al., 1992; Chapman et al., 1996; Kohn et al., 1997, 2000; Laaris et al., 2000) microcircuitry. Spatial patterns are thus thought not to arise arbitrarily, but as a result of a structural and/or functional network, which may be, at least in the latter case, also dynamic. Spatial patterns such as the ones observed in the above-cited literature
Fig. 4. Comparison of Fre´ chet (left) and straight skeleton matching (right) with different tolerances (0.1 or 0.03) and different user-defined shapes (boomerang, A; and mini-focus, B). Figures on the right of the user-defined shapes (shown at the beginning of each row) are shape matches found in different runs of the program with different spontaneous events. The annotation ‘+ margin’ accounts for the fact that on the border of the recording hexagonal matrix, imaginary diodes are counted as matches with respect to intensity of activity (i.e. color-code). Regarding angular figures, the straight skeleton approach yields less conservative, and regarding radially symmetric figures, more conservative matches than Fre´ chet distance comparison.
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were either predicted by the authors in view of cytoarchitectonic tissue properties or functional characteristics, or they were analyzed and taken as fingerprints of, e.g. signal detection specificity to even allow interindividual comparisons. In this context, a method enabling automatic geometric shape matching to look for userdefined or predicted shapes (be it microcolumns, minifoci, or other characteristic patterns) will make it possible to even search for discrete patterns which may at first be hidden beneath seemingly inhomogeneous data. The methods shown here provide such a means for pattern search. Regarding the analysis methods, both Fre´ chet and straight skeleton search modes have their advantages. As can be shown in this study, tolerances of 0.03–0.1 yield very conservative to conservative pattern matches using either method. The accuracy of shape identification can further be influenced by using the appropriate search mode: if round or radially symmetric shapes are in the focus of interest, the straight skeleton approach will generate the most faithful matches, if angular objects are looked for, the Fre´ chet search is more conservative. Regarding the application, one interesting—and novel — finding of the present study is the fact that SSFP in human neocortical tissue, which we first saw as rising from inhomogeneous and scattered neuronal activity (Ko¨ hling et al., 2000), appear to start with distinct mini-foci. These are stationary and highly ‘reproducible’ in successive discharges, and precede the peak of the SSFP by 50 ms. Interestingly, during this time period, the overall participation of the neuronal population observed has not yet risen significantly beyond resting levels (compare Fig. 1 in Ko¨ hling et al., 2000). These mini-foci may thus reflect the coherently functioning neuronal population responsible for the initiation of the spontaneous discharge.
References Aichholzer O, Aurenhammer F, Alberts D, Ga¨ rtner B. A novel type of skeleton for polygons. J Univ Comput Sci 1995;1(12):752 – 61. Albowitz B, Kuhnt U, Ko¨ hling R, Lu¨ cke A, Straub H, Speckmann E-J, et al. Spatio-temporal distribution of epileptiform activity in slices from human neocortex: recordings with voltage sensitive dyes. Epilepsy Res 1998;32:224 –32. Alt H, Godau M. Computing the Fre´ chet distance between two polygonal curves. Int J Comput Geom Appl 1995;5:75 – 91. Alt H, Guibas LJ. Discrete geometric shapes: matching, interpolation, and approximation. In: Sack J-R, Urrutia J, editors. Hand-
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book of computational geometry. Amsterdam: Elsevier, 2000 (chap. 3). Chapman B, Stryker MP, Bonhoeffer T. Development of orientation maps in ferret primary visual cortex. J Neurosci 1996;16(20):6443 – 53. Cohen D, Yarom Y. Optical measurements of synchronized activity in isolated mammalian cerebellum. Neuroscience 1999;94(3):859 – 66. Demir R, Haberly LB, Jackson MB. Sustained and accelerating activity at two discrete sites generate epileptiform discharges in slices of piriform cortex. J Neurosci 1999;19:1294 – 306. Fukunishi K, Murai N, Uno H. Dynamic characteristics of the auditory cortex of guinea pigs observed with multichannel optical recording. Biol Cybern 1992;67(6):501 – 9. Hanson CL, Chen G, Ebner TJ. Role of climbing fibres in determining the spatial patterns of activation in the cerebellar cortex to peripheral stimulation: an optical imaging study. Neuroscience 2000;96(2):317 – 31. Ko¨ hling R, Lu¨ cke A, Straub H, Speckmann E-J. A portable chamber for long-distance transport of surviving human brain slice preparations. J Neurosci Methods 1996:233 – 6. Ko¨ hling R, Lu¨ cke A, Straub H, Speckmann E-J, Tuxhorn I, Wolf P, et al. Spontaneous sharp waves in human neocortical slices excised from epileptic patients. Brain 1998;121:1073 – 87. Ko¨ hling R, Qu¨ M, Zilles K, Speckmann E-J. Current source density profiles associated with sharp waves in human epileptic neocortical slices in vitro. Neuroscience 1999;94(4):1039 – 50. Ko¨ hling R, Ho¨ hling J-M, Straub H, Kuhlmann D, Kuhnt U, Tuxhorn I, et al. Optical monitoring of neuronal activity during spontaneous sharp waves in chronically epileptic human neocortical tissue. J Neurophysiol 2000;84:2161 – 5. Kohn A, Pinheiro A, Tommerdahl MA, Whitsel BL. Optical imaging in vitro provides evidence for the microcolumnar nature of cortical response. Neuroreport 1997;8(16):3513 – 8. Kohn A, Metz C, Quibrera M, Tommerdahl MA, Whitsel BL. Functional neocortical microcircuitry demonstrated with intrinsic signal optical imaging in vitro. Neuroscience 2000;95(1):51 –62. Laaris N, Carlson GC, Keller A. Thalamic-evoked synaptic interactions in barrel cortex revealed by optical imaging. J Neurosci 2000;20(4):1529 – 37. Meister M, Bonhoeffer T. Tuning and topography in an odor map on the rat olfactory bulb. J Neurosci 2001;21(4):1351 – 60. Ohki K, Matsuda Y, Ajima A, Kim D-S, Tanaka S. Arrangements of orientation pinwheel centers around area 17/18 transition zone in cat visual cortex. Cereb Cortex 2000;10:593 – 601. Preparata FP, Shamos MI. Computational geometry: an introduction. Berlin: Springer, 1988. Rubin BD, Katz LC. Optical imaging of odorant representations in the mammalian olfactory bulb. Neuron 1999;23:499 – 511. Sack J-R, Urrutia J. Handbook of computational geometry. Amsterdam: Elsevier, 2000. Tsau Y, Guan L, Wu J-W. Initiation of spontaneous epileptiform activity in the neocortical slice. J Neurophysiol 1998;80:978 –82. Tsau Y, Guan L, Wu J-W. Epileptiform activity can be initiated in various neocortical layers: an optical imaging study. J Neurophysiol 1999;82:1965 – 73. Tsodyks M, Kenet T, Grinvald A, Arieli A. Linking spontaneous activity of single cortical neurons and the underlying functional architecture. Science 1999;286:1943 – 6.
Spatio-temporal patterns of neuronal activity: analysis of optical imaging data using geometric shape matching R. Ko¨hling a,*, J. Reinel b, J. Vahrenhold b, K. Hinrichs b, E.-J. Speckmann a a
Institut fu¨r Physiologie, Westfa¨lische Wilhelms Uni6ersita¨t, Robert-Koch-Straße 27a, 48149 Mu¨nster, Germany b Institut fu¨r Informatik, Westfa¨lische Wilhelms Uni6ersita¨t, Mu¨nster, Germany Received 31 August 2001; received in revised form 22 October 2001; accepted 24 October 2001
Abstract Optical imaging of neuronal network activity yields information of spatial dynamics which generally is analyzed visually. The transient appearance of spatial activity patterns is difficult to gauge in a quantifiable manner, or may even altogether escape detection. Here, we employ geometric shape matching using Fre´chet distances or straight skeletons to search for pre-selected patterns in optical imaging data with adjustable degrees of tolerance. Data were sampled from fluorescence changes of a voltage-sensitive dye recorded with a 464-photodiode array. Fluorescence was monitored in a neuronal network in vitro. Neuronal activity prompting fluorescence fluctuations consisted of spontaneous epileptiform discharges in neocortical slices from patients undergoing epilepsy surgery. The experiments show that: (a) spatial activity patterns can be detected in optical imaging data; (b) shapes such as ‘mini-foci’ appear in close correlation to bioelectric discharges monitored with field potential electrodes in a reproducible manner; (c) Fre´chet distances yield more conservative matches regarding rectangular, and less conservative hits with respect to radially symmetric shapes than the straight skeleton approach; and (d) tolerances of 0.03– 0.1 are suited to detect faithful images of pre-selected shapes, whereas values \ 0.8 will report matches with any polygonal pattern. In conclusion, the methods reported here are suited to detect and analyze spatial, geometric dynamics in optical imaging data. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Functional organization; Neocortex; Human brain tissue; Spatial dynamics; Neuronal networks; Shape detection
1. Introduction Spatial mapping of neuronal network activity is the focus of interest of a wide scope of neuroscience research fields, ranging from in vivo studies of orientation preference maps in the visual cortex of mammals (Chapman et al., 1996; Tsodyks et al., 1999; Ohki et al., 2000), odorant representations in the olfactory bulb (Rubin and Katz, 1999; Meister and Bonhoeffer, 2001) and activation patterns in cerebellar cortex (Hanson et al., 2000), to in vitro analyses of neo- or archicortical microcircuitry (Albowitz et al., 1998; Tsau et al., 1998; Demir et al., 1999; Ko¨hling et al., 2000; Kohn et al., 2000). Optical imaging data contain information on spatial characteristics such as pinwheel orientation, or * Corresponding author. Tel.: +49-251-835-5537; fax.: +49-251835-5551. E-mail address: [email protected] (R. Ko¨hling).
dynamic activity patterns with high spatial and temporal resolution (Tsau et al., 1999). The final aim is to link such patterns to the underlying circuitry of the neuronal network —such as ‘minicolumns’ (Kohn et al., 1997), orientation columns (Chapman et al., 1996; Tsodyks et al., 1999) or barrels (Laaris et al., 2000). Temporally dynamic patterns, in particular, arising from sequential activation of neuronal processing structures (Fukunishi et al., 1992) are difficult to analyze visually and may even go undetected in case the underlying functionally coherent structures are small and/or are only emergent during short periods of time. In this article, we propose to employ techniques from the field of computational geometry (Preparata and Shamos, 1988; Sack and Urrutia, 2000) to facilitate detection of spatio-temporal coherent patterns. Researchers in computational geometry, a relatively young yet quickly maturing discipline in computer science, usually establish an abstract geometric description of
0165-0270/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 5 - 0 2 7 0 ( 0 1 ) 0 0 5 0 4 - 0
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the objects to be dealt with and then formulate the problem in this setting. The geometric nature of both the objects and the problem often allows for concise mathematical analysis and proof of correctness of a problem-solving algorithm. These analyses in turn provide means to measure the complexity of a problem and the efficiency of an algorithm, e.g. in terms of running time. The aim of the present article is twofold: (1) to demonstrate the feasibility of pattern search and recognition in optical imaging data with the above techniques using a program working with ASCII data files in an Windows™ environment; and (2) to determine whether distinct shapes possibly mirroring networks of neuronal processing structures can in fact be detected in activity patterns, using spontaneous epileptiform discharges in chronically epileptic human neocortical tissue as a model.
2.2. Optical imaging and data acquisition SSFP-associated fluorescence changes were detected by a 464-element honeycomb shaped photodiode array at a rate of 785 frames/s via 10× and 20 × objective lenses, yielding total fields of view of 1500 and 750 mm diameter, respectively. Xenon-lamp illumination was allowed for a maximum of 2–3 s per single detection period, and detection periods were separated by at least 5 min each. Only data related to field potential discharges spontaneously occurring \ 200 ms after sampling start were evaluated. Raw data (fluorescence intensities) were converted to 20-bin-pseudocolor images scaled to the center diode using the NEUROPLEX software (Red Shirt Imaging, LLC, Fairfield, CT). The fluorescence change (dI/I) for typical events was 0.05– 0.3% of resting light intensity. For further analysis and geometric shape matching, data were exported from NEUROPLEX as ASCII file, yielding a text matrix corresponding to 464 diodes and 1024–3072 time points.
2. Methods
2.3. Geometric shape matching
2.1. Neocortical slice preparations and bioelectric acti6ity
While most pattern-matching algorithms in medical imaging are pixel based, we propose to view a two-dimensional area not as a collection of unrelated pixels but rather as one single polygonal object, that is, as a connected region described by a piecewise linear boundary. This viewpoint allows us to build upon a variety of results on polygonal shape matching (Alt and Guibas, 2000), most prominently an approximate, i.e. tolerance-based, matching algorithm based on the Fre´ chet distance (Alt and Godau, 1995). The Fre´ chet distance indicates the maximum distance between points on a (data) polygon and a superimposed (query) polygon that occurs while traversing the boundaries of both objects in clockwise orientation minimized over all possible startpoints of the traversals. We also develop a simple shape matching technique based on a uniquely defined characterization of a polygonal object: the straight skeleton (Aichholzer et al., 1995). The straight skeleton is a geometric construction based upon angular bisectors of the polygon and can be interpreted as the trusses of a roof erected over a floor-plan given by a polygonal object. Matching the polygons then corresponds to matching the trusses (or, rather, the vertices of the trusses). Specifically, the spatial location of vertices of data and query polygon is compared; matches result when the vertices overlap (within a given tolerance radius m; see below). The basic principle of each of the two methods is demonstrated in Fig. 1. Finally, we formulated heuristics for scaling, rotating, and mirroring query polygons, so that size, as well as rotational or axis symmetries do not hinder object recognition. Approximate matching (matching tolerances) can be intro-
The methods for neocortical slice preparation have been described in detail elsewhere (Ko¨ hling et al., 1998, 2000). Briefly, human neocortical tissue was a small portion of resectates excised for treatment of pharmacoresistant temporal lobe epilepsy from eight patients. Histopathological analysis showed a mild degree of gliosis and/or dysplasia. The experiments were approved by the local ethics committee, and informed consent was obtained from the patients. From a 1 cm3 block of the inferior temporal gyrus, coronal 450 mm sections were made with a vibratome within 5 min after resection. These were placed in a portable incubation chamber (Ko¨ hling et al., 1996) with oxygenated (95% O2, 5% CO2) and warmed (28 °C) artificial cerebrospinal fluid (aCSF) containing (in mM): NaCl, 124; KCl, 4; CaCl2, 2; NaH2PO4, 1.24; MgSO4, 1.3; NaHCO3, 26; and glucose, 10 (pH 7.35– 7.45). In some cases, the Mg2 + concentration was lowered to simulate epileptogenic conditions by omitting MgSO4. Prior to the experiments, slices were stained with 12.5 mg/ml of the voltage-sensitive dye RH795 (1 h), and washed for 1 h before transferal to a submerged-type recording chamber (32 °C) mounted on an inverse microscope. Field potentials were recorded from layers II/III and V using conventional aCSF-filled glass micropipettes. In the slices investigated here, sharp field potentials (SSFP) and dye-related fluorescence signals arose spontaneously as described previously (Ko¨ hling et al., 1998).
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duced by either specifying an upper bound m on the Fre´ chet distance (where zero distance indicates an exact match) or by specifying the maximum distance o that two vertices of the skeletons are allowed to be apart. To investigate the practical relevance of this approach, we realized a software toolkit based on OpenGL™/Windows™ that analyses data in the NEUROPLEX ASCII output format. A description of the program as well as screenshots can be found on the following webpage: http://wwwmath.uni-muenster.de/cs/GeometricAnalysis/. As in the original recording software, we first convert the data in the ASCII file to 20-bin-pseudocolor images. The scaling required for this conversion can be done with respect to the center diode as well as to either all diodes, a variable set of diodes, or a range given by the user. In a second pre-processing step, the program scans all pseudocolor images to extract the desired polygonal shapes. More specifically, for a given pseudocolor-bin b, all connected polygonal shapes are extracted that cover diodes whose pseudocolor-bin is in the range [b −t, b+ t] (t being an adjustable integer tolerance) and that have a minimum width of at least three diodes. At the recording margins, we add virtual neighboring diodes
that fall into any such bin-range in order to avoid automatic exclusion of borderline polygons. All such polygonal shapes can be visualized frame by frame and bin by bin. After having run one of the matching algorithms, matches are shown frame by frame, in a simple histogram displaying hits along the time line, and by means of an interval histogram to support detection of temporal clustering. The matching algorithms simultaneously process all bin ranges of the kind [b− t, b+t], with the parameter b varying from t to 20− t, so that we can find matches on all levels of fluorescence intensity. Prior to running any matching algorithm, the user interactively defines a polygonal shape by selecting a set of active diodes. For exact pattern matching, this pattern has to be matched without any translation, rotation, or scaling. For detecting approximate matches that also include translations, rotations, or scaling, all extracted polygonal shapes are re-evaluated with respect to their similarity to the user-defined shape. In order to handle scaling issues, all detected polygons are scaled to the size of the user-defined object according to either their longest side or (optionally) their largest diameter. Both objects are then superimposed in a virtual Cartesian diagram with the longest side starting at the origin (side comparison), or with their center of gravity located at the origin (diameter scaling); this heuristic is used to handle translations. The user can also decide to have the polygonal shapes rotated such that the longest side or the diameter of each polygonal shape is aligned with the horizontal axis of the Cartesian diagram. In addition, axial symmetries can be taken into account by adequately rotating and/or mirroring the test polygons. At the moment, the toolkit offers the two algorithms for approximate matching described above: Fre´ chet distance comparison and straight skeleton matching. The tolerance m for object matching is an absolute value in the virtual Cartesian diagram in which the two polygonal shapes are superimposed (hence, the tolerance is related to either the longest side or the diameter of the objects) and is adjustable by the user.
Fig. 1. Diagram illustrating the working principle of geometric shape matching using: (A) Fre´ chet distances; or (B) straight skeleton comparison. (A) With Fre´ chet matching, a user-defined object (solid lines) is compared to a test shape (broken lines) by: (1) scaling both objects with respect to longest diameter (A) or side (B); (2) superposition of objects so that longest side or diameter are on top of each other; (3) constructing vectors (fat gray lines) by connecting the shortest distances between the objects when simultaneously following their circumference. The maximal tolerance m is set by the user related to the length of the longest diameter/side of the user-defined object. (B) With the straight skeleton approach, user-defined (solid lines) and test object (broken lines) are matched by following steps (1) and (2) as in (A), and then constructing skeletons analogous to roof trusses for both objects. The positions of the skeletons’ vertices are compared to see whether each vertex of a skeleton lies within radius m of a vertex belonging to the other skeleton. Again, the parameter m is related to the length of the longest diameter/side of the user-defined object.
3. Results Field potential and optical recordings in human neocortical slices revealed spontaneous activity consisting of sharp field potentials (SSFP) and corresponding diminutions of fluorescence in optical signals (Fig. 2A) in 60% of the cases. This type of spontaneous activity has been described in detail elsewhere (Ko¨ hling et al., 1998, 1999, 2000). Using optical imaging, spatial activity patterns can be detected in association with the appearance of SSFP. An example is shown in Fig. 2B. Constructing spatial activity maps from color-coded optical signals picked up by a 464-photodiode matrix, the neuronal population appeared to be largely and
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Fig. 2.
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Fig. 3. Bar chart showing an interval histogram for the appearance of mini-foci as given in Fig. 2C using Fre´ chet comparisons. Width of bins is 2 ms, and from 10 ms onwards, 5 ms. No clustering of hits is evident.
homogeneously hyper- or normopolarized (Fig. 2B, left upper hexagon) at the beginning of the recording. Concomitant with the peak of the SSFP, single photodiodes signaled maximal depolarizations (red) of subsets of neurons. These seemed rather heterogeneous on visual inspection, arising as single-diode hotspots in the recording field (Fig. 2B, middle upper hexagon, Ko¨ hling et al., 2000), and only in the tail of the SSFP, neuronal activity converged to cover a larger field (Fig. 2B, right upper hexagon). One of the questions we were interested in was whether specific neuronal conglomerates initiate the spontaneous discharges, i.e. whether mini-foci can be observed during the initial phases of the discharge. To test this hypothesis, we searched for such mini-foci using a hexagonal 7-diode shape as template (Fig. 2B, middle lower hexagon, C). Indeed, beneath the heterogeneous patterns of neuronal activity, geometric shapes, presumably corresponding to coherent neuronal clusters, could be detected using geometric shape matching. Thus, mini-foci emerged during the first 10–50 ms (the first 10 – 40 frames) of the signals in the manner depicted in Fig. 2B. They were exclusive in the way that no other polygonal shaped activity patterns were present during this period. The location of these mini-foci was stereotypic not only for the first 10– 40 frames of the individual recording, but also for five consecutive recordings of different signals from one slice, indicating that indeed a distinct local network initiates the events. Only with further develop-
ment of the discharge, the network activity converged to cover larger neuronal aggregates (Fig. 2B, right hexagons). Under the latter conditions, mini-foci were still evident, yet now they were located at variable locations and probably represented projection sites of the now-converged activity of large parts of the neuronal network. Matches for mini-foci started approximately 50 ms before the peak of the SSFP (denoted by the second arrow in Fig. 2C on the line chart) independent of the analysis mode and continued to emerge throughout the remaining recording, in this experiment with a more prominent cluster (confluent lines in Fig. 2C) at 190 ms after the signal’s peak, i.e. long after the SSFP had returned to baseline. Other temporal clustering (such as doublets or triplets interspaced by longer intervals) was not evident, either in this or other recordings, as can be judged from the interval histogram in Fig. 3. Larger patterns such as bars (often horizontally oriented) exclusively appeared at this time only, alongside larger complex polygonal shapes or-rarely-in isolation. Angular patterns such as boomerangs emerged only very rarely (Fig. 2C). A similar situation holds true for SSFP observed under epileptogenic (Mg2 + -free) conditions (n=3). Again, SSFP were preceded and accompanied by the appearance of mini-foci, with convergence of activity to larger shapes in the later phases of SSFP. Furthermore, bar- or column-shaped patterns emerged with fullblown activity. These were much rarer, with an average
Fig. 2. Activity patterns and shape matching with spontaneous sharp field potentials (SSFP) and corresponding fluorescence changes (Opt) in human neocortical slice preparation. (A) Diagram of the recording situation depicting the neocortical slice with underlying white matter (WM), the position of the hexagonal photodiode matrix and of the field potential electrode, respectively. SSFP recorded by the field potential electrode is shown in opposition to an optical recording picked up by one diode in the center of the array. Arrows and lettering indicate time points of optical recordings further analyzed in (B) and (C). (B) Spatial pattern of neuronal activity (upper row) in the optical recording field at 1, 358 and 534 ms after beginning of the recording, corresponding to beginning of the trace, peak and tail of the SSFP. Activity is color-coded: blue, normoand hyperpolarization; red, depolarization (corresponding to changes up to − 0.35 and − 0.55%, respectively). Lower row: shape matches found for solitary mini foci of maximal depolarizations (red, circle in pseudocolor calibration bar) consisting of a hexagon of seven diodes. One such hit appears at SSFP peak (358 ms, b), and another one together with a large polygonal confluence of activity during SSFP tail (534 ms, c). (C) Shape matching for different patterns. Three user-defined shapes are given on the left of the three pairs (simple mini-focus, boomerang, bar) and patterns found to also match on the right. The line histograms list the hits for mini-foci (red bars and numbers) using Fre´ chet distance (upper chart) and straight skeleton (lower chart) algorithms at a tolerance of 0.1 with respect to the duration of the recording. Note that the temporal distribution of hits is virtually independent of the search method. For comparison, hits for boomerangs (blue arrows and numbers) and bars (green arrows and numbers) using Fre´ chet distances and skeleton comparisons are also given, showing that particularly for columnar shapes, the two methods differ. Numbers in brackets list the hits with corresponding skeleton match. Note that skeleton match is highly conservative regarding simple straight polygons, and less conservative than Fre´ chet matching with respect to angular figures.
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of 10 –20% of hits as compared to mini-foci. In contrast to SSFP under control conditions, these bars had in \70% of the cases a clearly columnar orientation, sometimes appearing in parallel configurations as to comprise three columns of roughly 500 mm width (not shown). A comparison of the two analysis modes showed that either mode is differentially sensitive regarding different template shapes (Fig. 4). With tolerances of 0.1, Fre´ chet distance matching yielded very conservative results regarding angular polygonal shapes such as boomerangs, whereas the straight skeleton approach under these conditions reported matches of various shapes, provided their common characteristic was a prolonged backbone truss (possibly branched) with bifurcated ends (Fig. 4). Radially symmetric shapes, on the other hand, which will yield rather complex skeletal lattices, were conservatively analyzed in the straight skeleton approach. By contrast, the Fre´ chet match reported similarities with various rounded shapes even if they missed a part of their sides (Fig. 4). Not surprisingly, a sharpening of the tolerance to 0.03 narrowed down the match analysis to faithful images of the template in either analysis mode. Raising the tolerance to 0.8 and beyond, all polygonal shapes were reported as matches (not shown).
4. Discussion The present study was undertaken to: (1) demonstrate that pattern search and recognition can be per-
formed in optical imaging data using geometric shape matching; and (2) to determine whether specific spatial patterns presumably representing coherently active neuronal processing structures can be detected during spontaneous epilepsy-associated neuronal activity which might point to functional initiation sites. We could show that: (1) spatial activity patterns can be detected in optical imaging data; (2) mini-foci appear in close correlation to bioelectric discharges; (3) Fre´ chet distances yield more conservative matches regarding angular, and less conservative hits with respect to radially symmetric shapes than the straight skeleton approach; and (4) tolerances of 0.03–0.1 are suited to detect faithful images of pre-selected shapes. Several papers dealing with optical imaging analysis of neuronal network activity have reported emergent spatial patterns which were usually analyzed visually (Fukunishi et al., 1992; Cohen and Yarom, 1999; Rubin and Katz, 1999; Kohn et al., 2000). Such patterns were generally linked to underlying functional and/or structurally defined neuronal processing structures which were deemed to reflect, e.g. signal detection specificity in olfactory bulb (Rubin and Katz, 1999; Meister and Bonhoeffer, 2001), as well as input and lamina-specific functional cerebellar (Cohen and Yarom, 1999; Hanson et al., 2000) or neocortical (Fukunishi et al., 1992; Chapman et al., 1996; Kohn et al., 1997, 2000; Laaris et al., 2000) microcircuitry. Spatial patterns are thus thought not to arise arbitrarily, but as a result of a structural and/or functional network, which may be, at least in the latter case, also dynamic. Spatial patterns such as the ones observed in the above-cited literature
Fig. 4. Comparison of Fre´ chet (left) and straight skeleton matching (right) with different tolerances (0.1 or 0.03) and different user-defined shapes (boomerang, A; and mini-focus, B). Figures on the right of the user-defined shapes (shown at the beginning of each row) are shape matches found in different runs of the program with different spontaneous events. The annotation ‘+ margin’ accounts for the fact that on the border of the recording hexagonal matrix, imaginary diodes are counted as matches with respect to intensity of activity (i.e. color-code). Regarding angular figures, the straight skeleton approach yields less conservative, and regarding radially symmetric figures, more conservative matches than Fre´ chet distance comparison.
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were either predicted by the authors in view of cytoarchitectonic tissue properties or functional characteristics, or they were analyzed and taken as fingerprints of, e.g. signal detection specificity to even allow interindividual comparisons. In this context, a method enabling automatic geometric shape matching to look for userdefined or predicted shapes (be it microcolumns, minifoci, or other characteristic patterns) will make it possible to even search for discrete patterns which may at first be hidden beneath seemingly inhomogeneous data. The methods shown here provide such a means for pattern search. Regarding the analysis methods, both Fre´ chet and straight skeleton search modes have their advantages. As can be shown in this study, tolerances of 0.03–0.1 yield very conservative to conservative pattern matches using either method. The accuracy of shape identification can further be influenced by using the appropriate search mode: if round or radially symmetric shapes are in the focus of interest, the straight skeleton approach will generate the most faithful matches, if angular objects are looked for, the Fre´ chet search is more conservative. Regarding the application, one interesting—and novel — finding of the present study is the fact that SSFP in human neocortical tissue, which we first saw as rising from inhomogeneous and scattered neuronal activity (Ko¨ hling et al., 2000), appear to start with distinct mini-foci. These are stationary and highly ‘reproducible’ in successive discharges, and precede the peak of the SSFP by 50 ms. Interestingly, during this time period, the overall participation of the neuronal population observed has not yet risen significantly beyond resting levels (compare Fig. 1 in Ko¨ hling et al., 2000). These mini-foci may thus reflect the coherently functioning neuronal population responsible for the initiation of the spontaneous discharge.
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