Table 2.
Main characteristics of existing 1-D models
| References | Closed-Loop | Heart Model | Systemic Circulation | Pulmonary Circulation | Coronary Circulation | Cerebral Circulation | Tube Law | Velocity Profile | Convective Acceleration | Distal Vasculature Models | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Streeter et al. | (42) | − | − | − (aorta) | − | − | − | NLE | − P | − | R |
| Schaaf and Abbrecht | (43) | − | − | + | − | − | − | LE | − P | − | R |
| Wemple and Mockros | (44) | − | − | + | − | − | − | NLE | + W | + | 3Wk |
| Raines et al. | (45) | − | − | − (leg) | − | − | − | NLE | − P | − | 3Wk |
| Avolio | (46) | − | − | + | − | − | + | VE | + W | − | R |
| Stettler et al. | (47, 48) | − | − | + | − | + | − | NLE | − P | − | R |
| Kufahl and Clark | (49) | − | − | − (cerebral) | − | − | + | NLE | − p | + | 3Wk |
| Hillen et al. | (50) | − | − | − (cerebral) | − | − | + | LE | − P | − | R |
| Papapanayotou et al. | (51) | − | − | − (cerebral) | − | − | + | LE | − P | − | R |
| Fitchett | (52) | − | +1 C | + | − | − | + | VE | + W | − | R |
| Stergiopulos et al. | (29) | − | − | + | − | − | − | NLE | − P | + | 3Wk |
| Cassot and Zagzoule | (53) | − | − | − (cerebral) | − | − | + | LE | − P | − | R |
| Olufsen | (33) | − | − | + | − | − | − | LE | + BL | − | ST |
| Wan et al. | (54) | − | − | + | − | − | − | LE | − P | + | R |
| Sherwin et al. | (55) | − | − | + | − | − | − | LE | − F | − | R |
| Wang and Parker | (56) | − | − | + | − | − | − | LE | − F | − | R |
| Formaggia et al. | (30) | − | +1 C | + | − | − | − | LE | − P | − | 3Wk |
| Azer and Peskin | (34) | − | − | + | − | − | − | LE | + W | + | ST |
| Bessems et al. | (57) | − | − | − (aorta and coronary) | − | − | − | LE | + BL | + | 3Wk |
| Huo and Kassab | (35) | − | − | − (coronary) | − | + | − | LE | − P | + | ST |
| Liang et al. | (38) | + | +4 C | + | + | − | − | LE | − p | − | Wk+ |
| Reymond et al. | (21) | − | +1 C | + | − | + | + | VE | + W | + | 3Wk |
| Blanco et al. | (26) | − | − | + | − | + | + | VE1 | − P | − | 3Wk |
| Müller and Toro | (31) | + | +4 C | + | − | − | + | LE | − P | − | Wk+ |
| Qureshi et al. | (27) | − | − | − | + | − | − | LE | + BL | − | ST |
| Mynard and Smolich | (39) | + | +4 C | + | + | + | + | VE3 | − p | − | Wk+2 |
| Acosta et al. | (58) | + | +4 C | + | + | − | − | LE | − p | − | Wk+2 |
| Carson et al. | (59) | + | +4 C | + | + | + | − | VE | + BL | − | 3Wk+ |
| Charlton et al. | (28) | − | − | + | − | − | + | VE | − p | − | 3Wk |
| Gallo et al. | (41) | + | +4 C | + | − | − | + | VE | + BL | − | 3Wk+ |
| Westerhof et al. | (60) | − | − | + | − | − | + | VE | − P | − | 3Wk |
Closed-loop: a closed-loop model of the circulation is (+) or not (−) included. Heart model: a heart model is (+) or not (−) coupled to the one-dimensional (1-D) model vessels, with the number of heart chambers (C) indicated. Systemic circulation: the larger systemic arteries are simulated using 1-D modeling (+), as opposed to none or a few arteries as indicated (−). Pulmonary circulation: the larger pulmonary arteries are simulated using 1-D modeling (+), as opposed to none or a few arteries (−). Coronary circulation: the larger coronary arteries are simulated using 1-D modeling (+), as opposed to none or a few arteries (−). Cerebral circulation: the larger cerebral arteries, including the circle of Willis, are simulated using 1-D modeling (+), as opposed to none or a few arteries (−). Tube law: Arterial wall modeled as a linear (LE) or nonlinear (NLE) purely elastic material, or as a viscoelastic (VE) material. Velocity profile: profile calculated (+) using Womersley flow (W) or a boundary layer method (BL), or prescribed (−) using Poiseuille flow (P), a higher-order polynomial (p), a boundary layer method (BL), or a flat profile (F). Convective acceleration: Full term simulated (+) or either simplified by assuming a flat velocity profile or completely neglected (−). Distal vasculature models: single resistance (R), three-element Windkessel (3Wk), Windkessel with more than three elements (Wk+), structured-tree (ST).
Elastin, collagen, smooth muscle contributions accounted for; 2Nonlinear 0-D models, with specific models for the hepatic and coronary beds; 3Nonlinear elastic term using a power law and Voigt-type viscous term.