Application of Mathematical Modeling for Simulation and Analysis of Hypoplastic Left Heart Syndrome (HLHS) in Pre- and Postsurgery Conditions

<div>Flow rates in aorta and pulmonary artery. The plots are shown for <svg height="12.4448pt" id="M174" style="vertical-align:-3.446851pt" version="1.1" viewbox="-0.0498162 -8.99795 27.0001 12.4448" width="27.0001pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z" id="g113-83"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="627" vert-adv-y="627"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,8.427,3.264)"><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(.0095,0,0,-0.0095,14.952,3.264)"><path d="M409 504C401 567 396 607 392 642C354 654 312 665 266 665C137 665 60 583 60 487C60 374 161 325 225 290C300 250 355 215 355 141C355 68 311 21 235 21C131 21 86 122 71 183L41 176C48 128 61 42 68 21C78 16 93 8 118 0C142 -7 175 -15 216 -15C349 -15 438 69 438 174C438 287 344 333 265 374C186 414 138 449 138 522C138 576 172 631 249 631C336 631 363 562 380 499L409 504Z" id="g190-84"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="474" vert-adv-y="474"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,19.333,3.264)"><path d="M43 650V622C120 616 128 612 128 526V124C128 39 120 33 34 27V0H270C392 0 492 25 567 83C643 141 690 230 690 350C690 444 655 517 605 565C543 625 450 650 323 650H43ZM213 547C213 587 217 598 226 604C236 612 262 617 304 617C371 617 429 604 474 576C554 529 592 439 592 336C592 176 505 36 319 36C246 36 213 55 213 131V547Z" id="g190-69"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="735" vert-adv-y="735"></glyph.data></g></svg> and <svg height="12.3115pt" id="M175" style="vertical-align:-3.31355pt" version="1.1" viewbox="-0.0498162 -8.99795 27.5998 12.3115" width="27.5998pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z" id="g113-83"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="627" vert-adv-y="627"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,8.427,3.264)"><path d="M46 650V622C120 617 128 613 128 525V125C128 42 120 34 40 28V0H311V28C221 34 212 39 212 124V281L286 262C297 261 316 261 331 263C429 275 526 338 526 468C526 533 501 579 462 609C422 638 364 650 293 650H46ZM212 559C212 588 215 600 223 606C230 613 251 618 279 618C361 618 430 572 430 464C430 337 350 302 285 302C252 302 225 309 212 314V559Z" id="g190-81"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="563" vert-adv-y="563"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,13.719,3.264)"><path d="M43 650V622C120 616 128 612 128 526V124C128 39 120 33 34 27V0H270C392 0 492 25 567 83C643 141 690 230 690 350C690 444 655 517 605 565C543 625 450 650 323 650H43ZM213 547C213 587 217 598 226 604C236 612 262 617 304 617C371 617 429 604 474 576C554 529 592 439 592 336C592 176 505 36 319 36C246 36 213 55 213 131V547Z" id="g190-69"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="735" vert-adv-y="735"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,20.346,3.264)"><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></svg> equal to 1 mmHg·s·mL<sup>−1</sup>. The neonatal situation shown in this figure is dangerous, because most of the flow goes to the pulmonary artery and there is not enough flow going to the vital organs.</div>

BioMed Research International

fig7

Figure 7

Figure 7: Application of Mathematical Modeling for Simulation and Analysis of Hypoplastic Left Heart Syndrome (HLHS) in Pre- and Postsurgery Conditions 

Figure 7 | Application of Mathematical Modeling for Simulation and Analysis of Hypoplastic Left Heart Syndrome (HLHS) in Pre- and Postsurgery Conditions 