A Mathematical Model of Regenerative Axon Growing along Glial Scar after Spinal Cord Injury

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Release rate of growth inhibitory factors, <svg height="9.39034pt" id="M137" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 11.1659 9.39034" width="11.1659pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M471 401C471 442 455 448 440 448C421 448 389 439 366 424C314 390 233 331 165 242H163L187 345C193 372 197 393 197 409C197 435 189 448 174 448C146 448 80 408 23 349L40 327C64 351 97 373 107 373C115 373 118 366 111 337L29 -4L36 -12C56 -4 83 3 110 9C123 69 136 126 150 172C227 283 336 381 377 381C392 381 396 370 379 298L326 74C290 -77 273 -172 273 -197C273 -219 316 -261 346 -261L353 -246C348 -227 352 -174 374 -66L457 310C467 352 471 381 471 401Z" id="g113-229"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="494" vert-adv-y="494"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.097,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> (%)</td><td class="align_center">Average drawing speed of axons, <svg height="12.0184pt" id="M138" style="vertical-align:-3.382501pt" version="1.1" viewbox="-0.0498162 -8.6359 28.5245 12.0184" width="28.5245pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 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59 268 59C197 59 123 113 120 245C240 248 367 259 384 262C403 266 407 275 407 296C407 376 338 451 254 451H253C201 451 148 425 105 378C65 334 39 272 39 203C39 88 112 -12 235 -12C266 -12 339 5 402 84L384 109ZM230 411C285 411 319 365 319 313C319 298 313 293 294 293C236 291 180 290 125 290C141 370 185 411 230 411Z" id="g58-99"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="434" vert-adv-y="434"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,25.672,3.132)"><path d="M117 -12C153 -12 178 12 178 50C178 84 153 110 118 110C84 110 59 84 59 50C59 12 84 -12 117 -12Z" id="g50-47"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237"></glyph.data></g></svg> (<i>μ</i>ms<sup>−1</sup>)</td><td class="align_center">The number of axons successfully connected to the target cells</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">3</td><td class="align_center">0.0400</td><td class="align_center">12</td></tr><tr><td class="align_left">4</td><td class="align_center">0.0320</td><td class="align_center">10</td></tr><tr><td class="align_left">5</td><td class="align_center">0.0272</td><td class="align_center">8</td></tr><tr><td class="align_left">6</td><td class="align_center">0.0148</td><td class="align_center">3</td></tr><tr><td class="align_left">7</td><td class="align_center">0.0045</td><td class="align_center">0</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Computational and Mathematical Methods in Medicine

tab1

Table 1

Table 1: A Mathematical Model of Regenerative Axon Growing along Glial Scar after Spinal Cord Injury 