A one-dimensional finite element method for simulation-based medical planning for cardiovascular disease.
We have previously described a new approach to planning treatments for cardiovascular disease, Simulation-Based Medical Planning, whereby a physician utilizes computational tools to construct and evaluate a combined anatomic/physiologic model to predict the outcome of alternative treatment plans for an individual patient. Current systems for Simulation-Based Medical Planning utilize finite element methods to solve the time-dependent, three-dimensional equations governing blood flow and provide detailed data on blood flow distribution, pressure gradients and locations of flow recirculation, low wall shear stress and high particle residence. However, these methods are computationally expensive and often require hours of time on parallel computers. This level of computation is necessary for obtaining detailed information about blood flow, but likely is unnecessary for obtaining information about mean flow rates and pressure losses. We describe, herein, a space-time finite element method for solving the one-dimensional equations of blood flow. This method is applied to compute flow rate and pressure in a single segment model, a bifurcation, an idealized model of the abdominal aorta, in three alternate treatment plans for a case of aorto-iliac occlusive disease and in a vascular bypass graft. All of these solutions were obtained in less than 5 min of computation time on a personal computer.
Department of Petroleum Engineering, Durand 213, Stanford University, Stanford, CA 94305-3030, USA.
Jing
J
Wan
Brooke
B
Steele
Sean A
SA
Spicer
Sven
S
Strohband
Gonzalo R
GR
Feijóo
Thomas J R
TJ
Hughes
Charles A
CA
Taylor
D000818:Animals; D001012:Aorta, Abdominal / Q000503:physiopathology / Q000601:surgery; D001157:Arterial Occlusive Diseases / Q000503:physiopathology / Q000601:surgery; D001783:Blood Flow Velocity; D001809:Blood Viscosity; D002318:Cardiovascular Diseases / Q000503:physiopathology* / Q000601:surgery*; D017536:Carotid Artery, Common / Q000503:physiopathology / Q000601:surgery; D003198:Computer Simulation; D003251:Constriction, Pathologic / Q000503:physiopathology / Q000601:surgery; D001026:Coronary Artery Bypass; D005263:Femoral Artery / Q000503:physiopathology / Q000601:surgery; D020342:Finite Element Analysis; D005528:Foot / Q000098:blood supply / Q000503:physiopathology; D006439:Hemodynamics; D006801:Humans; D008955:Models, Cardiovascular; D017711:Nonlinear Dynamics; D010347:Patient Care Planning; D010934:Planning Techniques; D011150:Popliteal Artery / Q000503:physiopathology / Q000601:surgery; D011300:Preoperative Care / Q000379:methods; D011312:Pressure; D011673:Pulsatile Flow; D011786:Quality Control; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013552:Swine; D013813:Therapy, Computer-Assisted / Q000379:methods*; D013895:Thoracic Arteries / Q000503:physiopathology / Q000601:surgery; D016896:Treatment Outcome; D014945:Wound Healing / Q000502:physiology