Influence of Blood Vessels on Temperature during High-Intensity Focused Ultrasound Hyperthermia Based on the Thermal Wave Model of Bioheat Transfer

<div>Geometric configuration of physical model. The tissue containing a large blood vessel, a cylinder with radius of 35<i> mm</i> and length of 50<i> mm</i>, is placed at <span class="nowrap"><svg height="11.5303pt" id="M7" style="vertical-align:-3.18148pt" version="1.1" viewbox="-0.0498162 -8.34882 61.4383 11.5303" width="61.4383pt" 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="M475 445L452 468C423 436 401 426 385 426S352 427 305 436C268 443 216 448 185 448C156 448 128 425 102 382C89 360 77 338 64 304L89 291C117 340 143 380 190 380C214 380 268 376 295 373C320 370 344 371 362 374L70 101C32 65 23 36 23 18C23 5 27 -3 31 -8C36 -8 39 -6 42 -1C52 15 67 31 80 40S110 49 143 33C195 8 257 -20 290 -20C339 -20 382 11 439 129L416 148C366 74 334 55 305 55C278 55 236 68 203 81C169 94 141 100 122 96C205 170 348 308 411 376L475 445Z" id="g113-123"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.149,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 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379 441 355 427C307 400 234 344 162 249H160L180 324C203 409 197 448 170 448C144 448 82 413 23 349L35 321C57 343 96 374 108 374C115 374 117 371 111 341C87 227 57 112 24 -6L32 -12C53 -4 81 4 108 6C119 68 134 128 149 171C177 229 309 383 364 383C387 383 388 355 373 282C354 190 330 92 303 -6L309 -12C332 -4 356 3 386 6C396 63 411 122 424 171C458 236 590 383 642 383C658 383 664 369 652 315L603 91C587 20 593 -12 619 -12C642 -12 708 23 766 88Z" id="g113-110"></path></g><g transform="matrix(.013,0,0,-0.013,50.953,0)"><path d="M766 88L752 113C719 83 690 64 681 64C674 64 672 74 679 103L724 292C758 436 724 448 701 448C680 448 666 442 639 429C594 407 514 350 441 252H439L447 289C476 423 450 448 419 448C398 448 379 441 355 427C307 400 234 344 162 249H160L180 324C203 409 197 448 170 448C144 448 82 413 23 349L35 321C57 343 96 374 108 374C115 374 117 371 111 341C87 227 57 112 24 -6L32 -12C53 -4 81 4 108 6C119 68 134 128 149 171C177 229 309 383 364 383C387 383 388 355 373 282C354 190 330 92 303 -6L309 -12C332 -4 356 3 386 6C396 63 411 122 424 171C458 236 590 383 642 383C658 383 664 369 652 315L603 91C587 20 593 -12 619 -12C642 -12 708 23 766 88Z" id="g113-110"></path></g></svg>.</span> The blood vessel is at the center of the tissue, <svg height="9.25202pt" id="M8" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 9.96544 9.25202" width="9.96544pt" 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="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z" id="g113-115"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.901,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 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id="g113-101"></path></g></svg> is the distance between ultrasonic focus and central axis of blood vessel. The computational domain <svg height="8.68572pt" id="M10" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 9.97754 8.68572" width="9.97754pt" 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="M719 146L691 147C666 77 657 72 612 72H528C572 125 688 224 688 364C688 546 558 665 384 665C212 665 77 541 77 361C77 221 188 124 239 72H150C110 72 97 80 73 147L46 146L63 0H307L314 18C284 71 178 203 178 360C178 529 256 631 383 631C509 631 588 523 588 363C588 197 485 67 453 18L458 0H701L719 146Z" id="g113-153"></path></g></svg> is <svg height="9.46863pt" id="M11" style="vertical-align:-1.11981pt" version="1.1" viewbox="-0.0498162 -8.34882 113.706 9.46863" width="113.706pt" 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="M535 230V280H52V230H535Z" id="g117-33"></path></g><g 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Advances in Condensed Matter Physics

fig1

Figure 1

Figure 1: Influence of Blood Vessels on Temperature during High-Intensity Focused Ultrasound Hyperthermia Based on the Thermal Wave Model of Bioheat Transfer 

Figure 1 | Influence of Blood Vessels on Temperature during High-Intensity Focused Ultrasound Hyperthermia Based on the Thermal Wave Model of Bioheat Transfer 