Evaluation of Analytical Modeling Functions for the Phonation Onset Process

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">VOT<sub>90</sub> (ms)</td><td class="align_center"><span style="width: 21.1218ptpx;"><svg height="14.7729pt" id="M182" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -11.5914 21.1218 14.7729" width="21.1218pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="617" vert-adv-y="617"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.656,3.132)"><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><g transform="matrix(.0091,0,0,-0.0091,11.627,-5.741)"><path d="M247 635C116 635 39 518 39 421C39 315 113 237 221 237C239 237 258 241 281 253L349 289C315 140 204 42 60 19L66 -15C90 -15 153 -5 207 16C344 70 447 199 447 385C447 521 373 635 247 635ZM231 598C329 598 356 478 356 390C356 371 355 347 352 325C330 309 297 297 262 297C179 297 127 369 127 456C127 515 156 598 231 598Z" id="g50-58"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,16.06,-5.741)"><path d="M245 635C92 635 37 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id="g113-81"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="617" vert-adv-y="617"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.656,3.132)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z" id="g50-52"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,11.627,-5.741)"><path d="M247 635C116 635 39 518 39 421C39 315 113 237 221 237C239 237 258 241 281 253L349 289C315 140 204 42 60 19L66 -15C90 -15 153 -5 207 16C344 70 447 199 447 385C447 521 373 635 247 635ZM231 598C329 598 356 478 356 390C356 371 355 347 352 325C330 309 297 297 262 297C179 297 127 369 127 456C127 515 156 598 231 598Z" id="g50-58"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,16.06,-5.741)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg></span></td><td class="align_center"><span style="width: 21.1218ptpx;"><svg height="14.7729pt" id="M184" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -11.5914 21.1218 14.7729" width="21.1218pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="617" vert-adv-y="617"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.656,3.132)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z" id="g50-53"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,11.627,-5.741)"><path d="M247 635C116 635 39 518 39 421C39 315 113 237 221 237C239 237 258 241 281 253L349 289C315 140 204 42 60 19L66 -15C90 -15 153 -5 207 16C344 70 447 199 447 385C447 521 373 635 247 635ZM231 598C329 598 356 478 356 390C356 371 355 347 352 325C330 309 297 297 262 297C179 297 127 369 127 456C127 515 156 598 231 598Z" id="g50-58"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,16.06,-5.741)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg></span></td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_center" colspan="4">Female group</td></tr><tr><td class="align_left"><span style="width: 34.6967ptpx;"><svg height="12.0444pt" id="M185" style="vertical-align:-3.29106pt" version="1.1" viewbox="-0.0498162 -8.75334 34.6967 12.0444" width="34.6967pt" 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="M692 302H438V274C537 267 543 260 543 188V103C543 61 531 48 511 37C489 26 458 20 424 20C231 20 146 188 146 333C146 517 258 630 411 630C507 630 582 597 606 474L634 480C627 546 622 601 619 636C586 643 510 665 426 665C230 665 44 552 44 321C44 122 191 -15 411 -15C491 -15 573 7 635 21C629 49 628 81 628 116V202C628 261 632 266 692 274V302Z" id="g190-72"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="715" vert-adv-y="715"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,9.295,0)"><path d="M673 0V28C608 34 594 43 563 129C499 303 432 494 370 665L339 656L132 132C98 43 84 37 20 28V0H238V28C162 35 154 45 175 108C188 150 203 192 219 237H432C454 176 474 122 487 83S491 36 428 28V0H673ZM418 280H234C265 362 296 450 328 535H330L418 280Z" id="g190-66"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="691" vert-adv-y="691"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,17.012,0)"><path d="M956 650H736V622C814 613 818 602 804 542C789 471 733 275 691 141H689C628 314 570 476 514 641H485C434 478 377 312 323 142H321C277 284 238 419 199 554C184 605 186 613 259 622V650H16V622C77 615 92 606 117 524C172 346 228 170 281 -11H312C363 151 419 312 475 488H477C528 343 597 150 652 -11H683C765 269 826 458 848 522C878 605 887 613 956 622V650Z" id="g190-88"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="971" vert-adv-y="971"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,29.751,3.132)"><path d="M452 282C452 397 389 451 302 451C268 451 227 441 188 422C95 377 24 281 24 154C24 65 70 -12 173 -12C240 -12 297 16 342 52C418 113 452 201 452 282ZM359 282C359 163 308 66 247 39C237 35 225 32 212 32C151 32 114 79 114 157C114 301 180 380 223 398C240 405 250 408 265 408C315 408 359 369 359 282Z" id="g50-112"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="476" vert-adv-y="476"></glyph.data></g></svg></span></td><td class="align_center">116</td><td class="align_center">113</td><td class="align_center">102</td></tr><tr><td class="align_left">SD</td><td class="align_center">59</td><td class="align_center">73</td><td class="align_center">62</td></tr><tr><td class="align_left"><span style="width: 36.2313ptpx;"><svg height="14.2823pt" id="M186" style="vertical-align:-5.52896pt" version="1.1" viewbox="-0.0498162 -8.75334 36.2313 14.2823" width="36.2313pt" 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="M692 302H438V274C537 267 543 260 543 188V103C543 61 531 48 511 37C489 26 458 20 424 20C231 20 146 188 146 333C146 517 258 630 411 630C507 630 582 597 606 474L634 480C627 546 622 601 619 636C586 643 510 665 426 665C230 665 44 552 44 321C44 122 191 -15 411 -15C491 -15 573 7 635 21C629 49 628 81 628 116V202C628 261 632 266 692 274V302Z" id="g190-72"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="715" vert-adv-y="715"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,9.295,0)"><path d="M673 0V28C608 34 594 43 563 129C499 303 432 494 370 665L339 656L132 132C98 43 84 37 20 28V0H238V28C162 35 154 45 175 108C188 150 203 192 219 237H432C454 176 474 122 487 83S491 36 428 28V0H673ZM418 280H234C265 362 296 450 328 535H330L418 280Z" id="g190-66"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="691" vert-adv-y="691"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,17.012,0)"><path d="M956 650H736V622C814 613 818 602 804 542C789 471 733 275 691 141H689C628 314 570 476 514 641H485C434 478 377 312 323 142H321C277 284 238 419 199 554C184 605 186 613 259 622V650H16V622C77 615 92 606 117 524C172 346 228 170 281 -11H312C363 151 419 312 475 488H477C528 343 597 150 652 -11H683C765 269 826 458 848 522C878 605 887 613 956 622V650Z" id="g190-88"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="971" vert-adv-y="971"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,29.751,3.132)"><path d="M620 667C620 684 593 710 552 710C515 710 459 687 409 634C360 582 334 506 320 433H247L215 400L220 388H310L259 80C224 -129 199 -161 185 -174C175 -183 160 -192 141 -192C123 -192 90 -181 75 -165C69 -158 64 -156 54 -164C39 -178 24 -195 24 -208C24 -231 61 -257 94 -257C124 -257 162 -243 209 -194C267 -134 303 -66 343 107C369 220 378 279 393 385L503 397L523 433H404C432 619 464 660 500 660C522 660 542 646 566 621C573 614 583 615 593 621C603 628 620 648 620 667Z" id="g50-103"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="644" vert-adv-y="644"></glyph.data></g></svg></span></td><td class="align_center">110</td><td class="align_center">110</td><td class="align_center">103</td></tr><tr><td class="align_left">SD</td><td class="align_center">57</td><td class="align_center">69</td><td class="align_center">59</td></tr><tr><td class="align_center" colspan="4"><hr/></td></tr><tr><td class="align_center" colspan="4">Male group</td></tr><tr><td class="align_left"><span style="width: 34.6967ptpx;"><svg height="12.0444pt" id="M187" style="vertical-align:-3.29106pt" version="1.1" viewbox="-0.0498162 -8.75334 34.6967 12.0444" width="34.6967pt" 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="M692 302H438V274C537 267 543 260 543 188V103C543 61 531 48 511 37C489 26 458 20 424 20C231 20 146 188 146 333C146 517 258 630 411 630C507 630 582 597 606 474L634 480C627 546 622 601 619 636C586 643 510 665 426 665C230 665 44 552 44 321C44 122 191 -15 411 -15C491 -15 573 7 635 21C629 49 628 81 628 116V202C628 261 632 266 692 274V302Z" id="g190-72"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="715" vert-adv-y="715"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,9.295,0)"><path d="M673 0V28C608 34 594 43 563 129C499 303 432 494 370 665L339 656L132 132C98 43 84 37 20 28V0H238V28C162 35 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39C237 35 225 32 212 32C151 32 114 79 114 157C114 301 180 380 223 398C240 405 250 408 265 408C315 408 359 369 359 282Z" id="g50-112"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="476" vert-adv-y="476"></glyph.data></g></svg></span></td><td class="align_center">103</td><td class="align_center">94</td><td class="align_center">92</td></tr><tr><td class="align_left">SD</td><td class="align_center">59</td><td class="align_center">60</td><td class="align_center">59</td></tr><tr><td class="align_left"><span style="width: 36.2313ptpx;"><svg height="14.2823pt" id="M188" style="vertical-align:-5.52896pt" version="1.1" viewbox="-0.0498162 -8.75334 36.2313 14.2823" width="36.2313pt" 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="M692 302H438V274C537 267 543 260 543 188V103C543 61 531 48 511 37C489 26 458 20 424 20C231 20 146 188 146 333C146 517 258 630 411 630C507 630 582 597 606 474L634 480C627 546 622 601 619 636C586 643 510 665 426 665C230 665 44 552 44 321C44 122 191 -15 411 -15C491 -15 573 7 635 21C629 49 628 81 628 116V202C628 261 632 266 692 274V302Z" id="g190-72"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="715" vert-adv-y="715"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,9.295,0)"><path d="M673 0V28C608 34 594 43 563 129C499 303 432 494 370 665L339 656L132 132C98 43 84 37 20 28V0H238V28C162 35 154 45 175 108C188 150 203 192 219 237H432C454 176 474 122 487 83S491 36 428 28V0H673ZM418 280H234C265 362 296 450 328 535H330L418 280Z" id="g190-66"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="691" vert-adv-y="691"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,17.012,0)"><path d="M956 650H736V622C814 613 818 602 804 542C789 471 733 275 691 141H689C628 314 570 476 514 641H485C434 478 377 312 323 142H321C277 284 238 419 199 554C184 605 186 613 259 622V650H16V622C77 615 92 606 117 524C172 346 228 170 281 -11H312C363 151 419 312 475 488H477C528 343 597 150 652 -11H683C765 269 826 458 848 522C878 605 887 613 956 622V650Z" id="g190-88"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="971" vert-adv-y="971"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,29.751,3.132)"><path d="M620 667C620 684 593 710 552 710C515 710 459 687 409 634C360 582 334 506 320 433H247L215 400L220 388H310L259 80C224 -129 199 -161 185 -174C175 -183 160 -192 141 -192C123 -192 90 -181 75 -165C69 -158 64 -156 54 -164C39 -178 24 -195 24 -208C24 -231 61 -257 94 -257C124 -257 162 -243 209 -194C267 -134 303 -66 343 107C369 220 378 279 393 385L503 397L523 433H404C432 619 464 660 500 660C522 660 542 646 566 621C573 614 583 615 593 621C603 628 620 648 620 667Z" id="g50-103"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="644" vert-adv-y="644"></glyph.data></g></svg></span></td><td class="align_center">96</td><td class="align_center">94</td><td class="align_center">88</td></tr><tr><td class="align_left">SD</td><td class="align_center">56</td><td class="align_center">71</td><td class="align_center">63</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mean values for VOT<sub>90</sub> (ms) and the standard deviation (SD) for <svg height="14.7729pt" id="M179" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -11.5914 21.1218 14.7729" width="21.1218pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="617" vert-adv-y="617"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.656,3.132)"><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 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Computational and Mathematical Methods in Medicine

tab5

Table 5

Table 5: Evaluation of Analytical Modeling Functions for the Phonation Onset Process 