A Computational Model for Real-Time Calculation of Electric Field due to Transcranial Magnetic Stimulation in Clinics

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left"> </td><td align="center"><svg height="11.8174pt" id="M127" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 28.9944 11.8174" width="28.9944pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="616" vert-adv-y="616"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.132)"><path d="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z" id="g190-78"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="891" vert-adv-y="891"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,16.051,3.132)"><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(.0091,0,0,-0.0091,22.339,3.132)"><path d="M655 0V28C585 35 563 50 517 120C469 193 414 280 360 366C427 469 460 516 481 545C526 604 545 614 619 622V650H391V622C457 614 462 604 438 560C411 511 381 463 339 398C295 466 258 523 225 580C210 606 211 615 272 622V650H26V622C98 614 111 603 154 538C189 482 235 408 288 324C200 188 149 116 124 85C95 47 64 34 7 28V0H236V28C169 36 164 46 188 89C220 148 261 217 310 291C372 193 417 118 442 77C461 44 454 35 392 28V0H655Z" id="g190-89"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="654" vert-adv-y="654"></glyph.data></g></svg> (V/m)</td><td align="center">SC coordinates (cm)</td><td align="center">SMAPE<br/></td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left">Admittance inhomogeneous 1 mm <br/>(10 cells shell)</td><td align="center">310.78 </td><td align="center">(9.35; 11.60; 14.57)</td><td align="center" rowspan="2">
                  6.91%</td></tr><tr><td align="left">SIM4LIFE inhomogeneous 1 mm</td><td align="center">307.21</td><td align="center">(9.30; 11.62; 14.53)</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Maximum <svg height="14.388pt" id="M125" style="vertical-align:-2.150599pt" version="1.1" viewbox="-0.0498162 -12.2374 15.0013 14.388" width="15.0013pt" 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="M162 -163V703H101V-163H162Z" id="g113-9"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="263" vert-adv-y="263"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,11.444,-2.897)"><path d="M-21 591C-45 610 -87 648 -131 700L-155 684L-108 616H-397V566H-108L-155 498L-131 482C-87 534 -45 572 -21 591Z" id="g117-14"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="0" vert-adv-y="0"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,3.419,0)"><path d="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="616" vert-adv-y="616"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,11.457,0)"><path d="M162 -163V703H101V-163H162Z" id="g113-9"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="263" vert-adv-y="263"></glyph.data></g></svg> (<svg height="11.8174pt" id="M126" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 28.9944 11.8174" width="28.9944pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="616" vert-adv-y="616"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.132)"><path d="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z" id="g190-78"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="891" vert-adv-y="891"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,16.051,3.132)"><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(.0091,0,0,-0.0091,22.339,3.132)"><path d="M655 0V28C585 35 563 50 517 120C469 193 414 280 360 366C427 469 460 516 481 545C526 604 545 614 619 622V650H391V622C457 614 462 604 438 560C411 511 381 463 339 398C295 466 258 523 225 580C210 606 211 615 272 622V650H26V622C98 614 111 603 154 538C189 482 235 408 288 324C200 188 149 116 124 85C95 47 64 34 7 28V0H236V28C169 36 164 46 188 89C220 148 261 217 310 291C372 193 417 118 442 77C461 44 454 35 392 28V0H655Z" id="g190-89"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="654" vert-adv-y="654"></glyph.data></g></svg>), stimulation center (SC) coordinates, and SMAPE calculated for the inhomogeneous brain model with 1 mm resolution and a shell of 10 mesh cells and calculated with the commercial code SIM4LIFE for the inhomogeneous brain model with a regular 1 mm mesh size.

International Journal of Antennas and Propagation

tab1

Table 1

Table 1: A Computational Model for Real-Time Calculation of Electric Field due to Transcranial Magnetic Stimulation in Clinics 