Comprehensive Analysis of Set-Up Gain of 6-Dimensional Cone-Beam CT Correction Method in Radiotherapy for Head and Neck and Brain Tumors

<div>Workflow for the iterative calculation of effective target error (<span class="nowrap"><svg height="11.9087pt" id="M29" style="vertical-align:-3.2728pt" version="1.1" viewbox="-0.0498162 -8.6359 19.5341 11.9087" width="19.5341pt" 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="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.893,3.132)"><path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.76,3.132)"><path d="M99 437H52L25 408L28 397H99V104C99 38 91 32 32 26V0H246V25C185 32 178 38 178 104V397H365V104C365 38 358 32 303 25V0H526V25C451 32 444 37 444 104V397H555C565 404 568 428 563 437H444V471C443 562 453 609 466 629C476 647 492 661 518 661C551 661 581 639 600 620C609 611 619 612 629 620C637 626 647 636 650 644C654 654 654 666 645 677C627 697 597 710 564 712C521 707 476 686 432 642C412 664 374 688 316 690C269 685 230 668 190 636C139 596 120 551 111 525C104 505 99 477 99 449V437ZM365 437H178V461C178 537 192 580 209 605C223 627 245 648 283 648C336 648 374 615 394 585C384 566 378 550 374 533C369 516 365 488 365 456V437Z"></path></g></svg>).</span> The 6D error dataset and target volume coordinates were the input variables, with <svg height="11.9087pt" id="M30" style="vertical-align:-3.2728pt" version="1.1" viewbox="-0.0498162 -8.6359 19.5341 11.9087" width="19.5341pt" 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="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.893,3.132)"><path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.76,3.132)"><path d="M99 437H52L25 408L28 397H99V104C99 38 91 32 32 26V0H246V25C185 32 178 38 178 104V397H365V104C365 38 358 32 303 25V0H526V25C451 32 444 37 444 104V397H555C565 404 568 428 563 437H444V471C443 562 453 609 466 629C476 647 492 661 518 661C551 661 581 639 600 620C609 611 619 612 629 620C637 626 647 636 650 644C654 654 654 666 645 677C627 697 597 710 564 712C521 707 476 686 432 642C412 664 374 688 316 690C269 685 230 668 190 636C139 596 120 551 111 525C104 505 99 477 99 449V437ZM365 437H178V461C178 537 192 580 209 605C223 627 245 648 283 648C336 648 374 615 394 585C384 566 378 550 374 533C369 516 365 488 365 456V437Z"></path></g></svg> calculated in the Euler rotation matrix equation (Equation (<a href="https://static-preview.hindawi.com/articles/cmmm/volume-2022/2964023/figures/#EEq1">1</a>)).</div>

Computational and Mathematical Methods in Medicine

fig2

Figure 2

Figure 2: Comprehensive Analysis of Set-Up Gain of 6-Dimensional Cone-Beam CT Correction Method in Radiotherapy for Head and Neck and Brain Tumors 