Modeling the Generation of Phase-Amplitude Coupling in Cortical Circuits: From Detailed Networks to Neural Mass Models
Identifieur interne : 000933 ( Pmc/Curation ); précédent : 000932; suivant : 000934Modeling the Generation of Phase-Amplitude Coupling in Cortical Circuits: From Detailed Networks to Neural Mass Models
Auteurs : Roberto C. Sotero [Canada]Source :
- BioMed Research International [ 2314-6133 ] ; 2015.
Abstract
Phase-amplitude coupling (PAC), the phenomenon where the amplitude of a high frequency oscillation is modulated by the phase of a lower frequency oscillation, is attracting an increasing interest in the neuroscience community due to its potential relevance for understanding healthy and pathological information processing in the brain. PAC is a diverse phenomenon, having been experimentally detected in at least ten combinations of rhythms: delta-theta, delta-alpha, delta-beta, delta-gamma, theta-alpha, theta-beta, theta-gamma, alpha-beta, alpha-gamma, and beta-gamma. However, a complete understanding of the biophysical mechanisms generating this diversity is lacking. Here we review computational models of PAC generation that range from detailed models of neuronal networks, where each cell is described by Hodgkin-Huxley-type equations, to neural mass models (NMMs) where only the average activities of neuronal populations are considered. We argue that NMMs are an appropriate mathematical framework (due to the small number of parameters and variables involved and the richness of the dynamics they can generate) to study the PAC phenomenon.
Url:
DOI: 10.1155/2015/915606
PubMed: 26539537
PubMed Central: 4620035
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Modeling the Generation of Phase-Amplitude Coupling in Cortical Circuits: From Detailed Networks to Neural Mass Models</title><author><name sortKey="Sotero, Roberto C" sort="Sotero, Roberto C" uniqKey="Sotero R" first="Roberto C." last="Sotero">Roberto C. Sotero</name><affiliation wicri:level="1"><nlm:aff id="I1">Department of Radiology and Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada T3A 2E1</nlm:aff><country>Canada</country><wicri:regionArea>Department of Radiology and Hotchkiss Brain Institute, University of Calgary, Calgary, AB</wicri:regionArea></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">26539537</idno><idno type="pmc">4620035</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4620035</idno><idno type="RBID">PMC:4620035</idno><idno type="doi">10.1155/2015/915606</idno><date when="2015">2015</date><idno type="wicri:Area/Pmc/Corpus">000933</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000933</idno><idno type="wicri:Area/Pmc/Curation">000933</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Curation">000933</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Modeling the Generation of Phase-Amplitude Coupling in Cortical Circuits: From Detailed Networks to Neural Mass Models</title><author><name sortKey="Sotero, Roberto C" sort="Sotero, Roberto C" uniqKey="Sotero R" first="Roberto C." last="Sotero">Roberto C. Sotero</name><affiliation wicri:level="1"><nlm:aff id="I1">Department of Radiology and Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada T3A 2E1</nlm:aff><country>Canada</country><wicri:regionArea>Department of Radiology and Hotchkiss Brain Institute, University of Calgary, Calgary, AB</wicri:regionArea></affiliation></author></analytic><series><title level="j">BioMed Research International</title><idno type="ISSN">2314-6133</idno><idno type="eISSN">2314-6141</idno><imprint><date when="2015">2015</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>Phase-amplitude coupling (PAC), the phenomenon where the amplitude of a high frequency oscillation is modulated by the phase of a lower frequency oscillation, is attracting an increasing interest in the neuroscience community due to its potential relevance for understanding healthy and pathological information processing in the brain. PAC is a diverse phenomenon, having been experimentally detected in at least ten combinations of rhythms: delta-theta, delta-alpha, delta-beta, delta-gamma, theta-alpha, theta-beta, theta-gamma, alpha-beta, alpha-gamma, and beta-gamma. However, a complete understanding of the biophysical mechanisms generating this diversity is lacking. Here we review computational models of PAC generation that range from detailed models of neuronal networks, where each cell is described by Hodgkin-Huxley-type equations, to neural mass models (NMMs) where only the average activities of neuronal populations are considered. We argue that NMMs are an appropriate mathematical framework (due to the small number of parameters and variables involved and the richness of the dynamics they can generate) to study the PAC phenomenon.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Chen, C C" uniqKey="Chen C">C. C. 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<front><journal-meta><journal-id journal-id-type="nlm-ta">Biomed Res Int</journal-id><journal-id journal-id-type="iso-abbrev">Biomed Res Int</journal-id><journal-id journal-id-type="publisher-id">BMRI</journal-id><journal-title-group><journal-title>BioMed Research International</journal-title></journal-title-group><issn pub-type="ppub">2314-6133</issn><issn pub-type="epub">2314-6141</issn><publisher><publisher-name>Hindawi Publishing Corporation</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">26539537</article-id><article-id pub-id-type="pmc">4620035</article-id><article-id pub-id-type="doi">10.1155/2015/915606</article-id><article-categories><subj-group subj-group-type="heading"><subject>Review Article</subject></subj-group></article-categories><title-group><article-title>Modeling the Generation of Phase-Amplitude Coupling in Cortical Circuits: From Detailed Networks to Neural Mass Models</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Sotero</surname><given-names>Roberto C.</given-names></name><xref ref-type="aff" rid="I1"></xref><xref ref-type="corresp" rid="cor1"><sup>*</sup></xref></contrib></contrib-group><aff id="I1">Department of Radiology and Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada T3A 2E1</aff><author-notes><corresp id="cor1">*Roberto C. Sotero: <email>roberto.soterodiaz@ucalgary.ca</email></corresp><fn fn-type="other"><p>Academic Editor: Vincenzo Romei</p></fn></author-notes><pub-date pub-type="ppub"><year>2015</year></pub-date><pub-date pub-type="epub"><day>11</day><month>10</month><year>2015</year></pub-date><volume>2015</volume><elocation-id>915606</elocation-id><history><date date-type="received"><day>27</day><month>3</month><year>2015</year></date><date date-type="rev-recd"><day>28</day><month>7</month><year>2015</year></date><date date-type="accepted"><day>6</day><month>8</month><year>2015</year></date></history><permissions><copyright-statement>Copyright © 2015 Roberto C. Sotero.</copyright-statement><copyright-year>2015</copyright-year><license xlink:href="https://creativecommons.org/licenses/by/3.0/"><license-p>This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p></license></permissions><abstract><p>Phase-amplitude coupling (PAC), the phenomenon where the amplitude of a high frequency oscillation is modulated by the phase of a lower frequency oscillation, is attracting an increasing interest in the neuroscience community due to its potential relevance for understanding healthy and pathological information processing in the brain. PAC is a diverse phenomenon, having been experimentally detected in at least ten combinations of rhythms: delta-theta, delta-alpha, delta-beta, delta-gamma, theta-alpha, theta-beta, theta-gamma, alpha-beta, alpha-gamma, and beta-gamma. However, a complete understanding of the biophysical mechanisms generating this diversity is lacking. Here we review computational models of PAC generation that range from detailed models of neuronal networks, where each cell is described by Hodgkin-Huxley-type equations, to neural mass models (NMMs) where only the average activities of neuronal populations are considered. We argue that NMMs are an appropriate mathematical framework (due to the small number of parameters and variables involved and the richness of the dynamics they can generate) to study the PAC phenomenon.</p></abstract></article-meta></front><floats-group><fig id="fig1" orientation="portrait" position="float"><label>Figure 1</label><caption><p>Neural mass models. (a) Wilson-Cowan model (<xref ref-type="sec" rid="sec5.1">Section 5.1</xref>) of two coupled populations, one excitatory (<italic>E</italic>) and one inhibitory (<italic>I</italic>). External inputs to these populations are <italic>p</italic><sub><italic>E</italic></sub> and <italic>p</italic><sub><italic>I</italic></sub>, and the connectivity parameters are Γ<sub><italic>EI</italic></sub>, Γ<sub><italic>IE</italic></sub>, Γ<sub><italic>EE</italic></sub>, and Γ<sub><italic>II</italic></sub>. (b) Jansen-Rit model (<xref ref-type="sec" rid="sec5.2">Section 5.2</xref>) of a cortical column. Three populations are modeled: pyramidal cells (PY), excitatory interneurons (<italic>EI</italic>), and inhibitory interneurons. The connectivity parameters are Γ<sub>1</sub>, Γ<sub>2</sub>, Γ<sub>3</sub>, and Γ<sub>4</sub>, and the input to the model is <italic>p</italic>. (c) Neural mass model of the cortical column comprising 14 populations (<xref ref-type="sec" rid="sec5.3">Section 5.3</xref>) distributed across 4 layers. The excitatory populations are the intrinsically bursting (IB) and the regulatory spiking (RS). The inhibitory population are the low-threshold spiking (LTS) and fast-spiking (FS). The connections between the populations are depicted in (d). Any of the 14 populations can be subjected to an external input. In the three models ((a), (b), and (c)), excitatory populations and connections are depicted in red and inhibitory ones in blue. (d) Connectivity matrix values used for coupling the 14 populations are modeled in (c). Negative values correspond to inhibitory connections and positive values correspond to excitatory ones.</p></caption><graphic xlink:href="BMRI2015-915606.001"></graphic></fig><fig id="fig2" orientation="portrait" position="float"><label>Figure 2</label><caption><p>Simulated temporal evolution of the variables of three different neural mass models. (a) Wilson-Cowan model. The phase of a theta oscillation (4 Hz) modulates the amplitude of a gamma oscillation (55 Hz). (b) Jansen-Rit model. The phase of a delta oscillation (3 Hz) modulates the amplitude of an alpha oscillation (11 Hz). (c) Cortical column model. The values of the parameters are given in Tables <xref ref-type="table" rid="tab1">1</xref> and <xref ref-type="table" rid="tab2">2</xref>. Multiple PAC combinations are present (see <xref ref-type="fig" rid="fig3">Figure 3</xref>). In all cases, the temporal dynamics of excitatory and inhibitory populations are depicted in red and blue, respectively.</p></caption><graphic xlink:href="BMRI2015-915606.002"></graphic></fig><fig id="fig3" orientation="portrait" position="float"><label>Figure 3</label><caption><p>Phase-amplitude coupling (PAC) corresponding to the simulation presented in <xref ref-type="fig" rid="fig2">Figure 2(c)</xref>. Nonsignificant values were set to zero and are depicted in white. (a) Delta-theta, (b) delta-alpha, (c) delta-beta, (d) delta-gamma, (e) theta-alpha, (f) theta-beta, (g) theta-gamma, (h) alpha-beta, and (i) alpha-gamma.</p></caption><graphic xlink:href="BMRI2015-915606.003"></graphic></fig><table-wrap id="tab1" orientation="portrait" position="float"><label>Table 1</label><caption><p>Values and physiological interpretation of the parameters.</p></caption><table frame="hsides" rules="groups"><thead><tr><th align="left" rowspan="1" colspan="1">Parameter (units)</th><th align="center" rowspan="1" colspan="1">Interpretation</th><th align="center" rowspan="1" colspan="1">Value</th></tr></thead><tbody><tr><td align="left" rowspan="1" colspan="1"><italic>G</italic>(mV)</td><td align="center" rowspan="1" colspan="1">Gain</td><td align="center" rowspan="1" colspan="1"><italic>G</italic><sub>1</sub> = 3.25, <italic>G</italic><sub>2</sub> = 3.25, <italic>G</italic><sub>3</sub> = 30, <italic>G</italic><sub>4</sub> = 10, <italic>G</italic><sub>5</sub> = 3.25, <italic>G</italic><sub>6</sub> = 30, <italic>G</italic><sub>7</sub> = 10, <italic>G</italic><sub>8</sub> = 3.25, <italic>G</italic><sub>9</sub> = 3.25, <italic>G</italic><sub>10</sub> = 30, <italic>G</italic><sub>11</sub> = 10, <italic>G</italic><sub>12</sub> = 3.25, <italic>G</italic><sub>13</sub> = 30, and <italic>G</italic><sub>14</sub> = 10</td></tr><tr><td align="center" colspan="3" rowspan="1"><hr></hr></td></tr><tr><td align="left" rowspan="1" colspan="1"><italic>k</italic> (s<sup>−1</sup>)</td><td align="center" rowspan="1" colspan="1">Reciprocal of time constant</td><td align="center" rowspan="1" colspan="1"><italic>k</italic><sub>1</sub> = 60, <italic>k</italic><sub>2</sub> = 70, <italic>k</italic><sub>3</sub> = 30, <italic>k</italic><sub>4</sub> = 350, <italic>k</italic><sub>5</sub> = 60, <italic>k</italic><sub>6</sub> = 30, <italic>k</italic><sub>7</sub> = 350, <italic>k</italic><sub>8</sub> = 60, <italic>k</italic><sub>9</sub> = 70, <italic>k</italic><sub>10</sub> = 30, <italic>k</italic><sub>11</sub> = 350, <italic>k</italic><sub>12</sub> = 60, <italic>k</italic><sub>13</sub> = 30, and <italic>k</italic><sub>14</sub> = 350</td></tr><tr><td align="center" colspan="3" rowspan="1"><hr></hr></td></tr><tr><td align="left" rowspan="1" colspan="1"><italic>p</italic></td><td align="center" rowspan="1" colspan="1">External input</td><td align="center" rowspan="1" colspan="1"><italic>p</italic><sub><italic>i</italic></sub> = 0 for <italic>i</italic> ≠ {5,7}, <italic>p</italic><sub>5</sub> = 500, and <italic>p</italic><sub>7</sub> = 150</td></tr><tr><td align="center" colspan="3" rowspan="1"><hr></hr></td></tr><tr><td align="left" rowspan="1" colspan="1"><italic>b</italic></td><td align="center" rowspan="1" colspan="1">Damping coefficient</td><td align="center" rowspan="1" colspan="1"><italic>b</italic> = 0.06 for all populations</td></tr><tr><td align="center" colspan="3" rowspan="1"><hr></hr></td></tr><tr><td align="left" rowspan="1" colspan="1"><italic>S</italic><sub>0</sub> (s<sup>−1</sup>)</td><td align="center" rowspan="1" colspan="1">Maximum firing rate</td><td align="center" rowspan="1" colspan="1"><italic>e</italic><sub>0</sub> = 5 for all populations</td></tr><tr><td align="center" colspan="3" rowspan="1"><hr></hr></td></tr><tr><td align="left" rowspan="1" colspan="1"><italic>v</italic><sub>0</sub> (mV)</td><td align="center" rowspan="1" colspan="1">Position of the sigmoid function</td><td align="center" rowspan="1" colspan="1"><italic>v</italic><sub>0</sub> = 6 for all populations</td></tr><tr><td align="center" colspan="3" rowspan="1"><hr></hr></td></tr><tr><td align="left" rowspan="1" colspan="1"><italic>r</italic> (mV<sup>−1</sup>)</td><td align="center" rowspan="1" colspan="1">Steepness of the sigmoid function</td><td align="center" rowspan="1" colspan="1"><italic>r</italic> = 0.56 for all populations</td></tr></tbody></table></table-wrap><table-wrap id="tab2" orientation="portrait" position="float"><label>Table 2</label><caption><p>Standard values of the connectivity matrix Γ<sub><italic>nm</italic></sub>.</p></caption><table frame="hsides" rules="groups"><thead><tr><th align="left" rowspan="2" colspan="1"> </th><th align="center" rowspan="2" colspan="1"> </th><th align="center" colspan="4" rowspan="1">L2/3</th><th align="center" colspan="3" rowspan="1">L4</th><th align="center" colspan="4" rowspan="1">L5</th><th align="center" colspan="3" rowspan="1">L6</th></tr><tr><th align="center" rowspan="1" colspan="1">RS</th><th align="center" rowspan="1" colspan="1">IB</th><th align="center" rowspan="1" colspan="1">LTS</th><th align="center" rowspan="1" colspan="1">FS</th><th align="center" rowspan="1" colspan="1">RS</th><th align="center" rowspan="1" colspan="1">LTS</th><th align="center" rowspan="1" colspan="1">FS</th><th align="center" rowspan="1" colspan="1">RS</th><th align="center" rowspan="1" colspan="1">IB</th><th align="center" rowspan="1" colspan="1">LTS</th><th align="center" rowspan="1" colspan="1">FS</th><th align="center" rowspan="1" colspan="1">RS</th><th align="center" rowspan="1" colspan="1">LTS</th><th align="center" rowspan="1" colspan="1">FS</th></tr></thead><tbody><tr><td align="left" rowspan="4" colspan="1">L2/3</td><td align="center" rowspan="1" colspan="1">RS</td><td align="center" rowspan="1" colspan="1">25</td><td align="center" rowspan="1" colspan="1">10</td><td align="center" rowspan="1" colspan="1">10</td><td align="center" rowspan="1" colspan="1">15</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">25</td><td align="center" rowspan="1" colspan="1">30</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td></tr><tr><td align="center" rowspan="1" colspan="1">IB</td><td align="center" rowspan="1" colspan="1">10</td><td align="center" rowspan="1" colspan="1">25</td><td align="center" rowspan="1" colspan="1">5</td><td align="center" rowspan="1" colspan="1">5</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td></tr><tr><td align="center" rowspan="1" colspan="1">LTS</td><td align="center" rowspan="1" colspan="1">−10</td><td align="center" rowspan="1" colspan="1">−8</td><td align="center" rowspan="1" colspan="1">−15</td><td align="center" rowspan="1" colspan="1">−10</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">−20</td><td align="center" rowspan="1" colspan="1">−25</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td></tr><tr><td align="center" rowspan="1" colspan="1">FS</td><td align="center" rowspan="1" colspan="1">−15</td><td align="center" rowspan="1" colspan="1">−10</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">−15</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">−20</td><td align="center" rowspan="1" colspan="1">−25</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td></tr><tr><td align="center" colspan="16" rowspan="1"><hr></hr></td></tr><tr><td align="left" rowspan="3" colspan="1">L4</td><td align="center" rowspan="1" colspan="1">RS</td><td align="center" rowspan="1" colspan="1">12</td><td align="center" rowspan="1" colspan="1">10</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">15</td><td align="center" rowspan="1" colspan="1">30</td><td align="center" rowspan="1" colspan="1">25</td><td align="center" rowspan="1" colspan="1">8</td><td align="center" rowspan="1" colspan="1">18</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td></tr><tr><td align="center" rowspan="1" colspan="1">LTS</td><td align="center" rowspan="1" colspan="1">−20</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">−20</td><td align="center" rowspan="1" colspan="1">−25</td><td align="center" rowspan="1" colspan="1">−10</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td></tr><tr><td align="center" rowspan="1" colspan="1">FS</td><td align="center" rowspan="1" colspan="1">−42</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">−22</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">25</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td></tr><tr><td align="center" colspan="16" rowspan="1"><hr></hr></td></tr><tr><td align="left" rowspan="4" colspan="1">L5</td><td align="center" rowspan="1" colspan="1">RS</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">12</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">22</td><td align="center" rowspan="1" colspan="1">18</td><td align="center" rowspan="1" colspan="1">25</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td></tr><tr><td align="center" rowspan="1" colspan="1">IB</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">10</td><td align="center" rowspan="1" colspan="1">10</td><td align="center" rowspan="1" colspan="1">22</td><td align="center" rowspan="1" colspan="1">18</td><td align="center" rowspan="1" colspan="1">25</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td></tr><tr><td align="center" rowspan="1" colspan="1">LTS</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">−10</td><td align="center" rowspan="1" colspan="1">−10</td><td align="center" rowspan="1" colspan="1">−10</td><td align="center" rowspan="1" colspan="1">−20</td><td align="center" rowspan="1" colspan="1">−25</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">−30</td></tr><tr><td align="center" rowspan="1" colspan="1">FS</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">−19</td><td align="center" rowspan="1" colspan="1">−19</td><td align="center" rowspan="1" colspan="1">−17</td><td align="center" rowspan="1" colspan="1">−15</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td></tr><tr><td align="center" colspan="16" rowspan="1"><hr></hr></td></tr><tr><td align="left" rowspan="3" colspan="1">L6</td><td align="center" rowspan="1" colspan="1">RS</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">45</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">10</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">15</td><td align="center" rowspan="1" colspan="1">10</td><td align="center" rowspan="1" colspan="1">10</td></tr><tr><td align="center" rowspan="1" colspan="1">LTS</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">−11</td><td align="center" rowspan="1" colspan="1">−10</td><td align="center" rowspan="1" colspan="1">−8</td></tr><tr><td align="center" rowspan="1" colspan="1">FS</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">−20</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">−15</td></tr></tbody></table></table-wrap></floats-group></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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