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Well-posedness of a hydrodynamic phase-field system for functionalized membrane-fluid interaction
A geometric multiscale model for the numerical simulation of blood flow in the human left heart
1. | MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milan, Italy |
2. | Children’s Heart Institute, Hermann Children’s Hospital, University of Texas Health, McGovern Medical School, Houston, TX, USA |
3. | Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Station 8, Av. Piccard, CH-1015 Lausanne, Switzerland (Professor Emeritus) |
We present a new computational model for the numerical simulation of blood flow in the human left heart. To this aim, we use the Navier-Stokes equations in an Arbitrary Lagrangian Eulerian formulation to account for the endocardium motion and we model the cardiac valves by means of the Resistive Immersed Implicit Surface method. To impose a physiological displacement of the domain boundary, we use a 3D cardiac electromechanical model of the left ventricle coupled to a lumped-parameter (0D) closed-loop model of the remaining circulation. We thus obtain a one-way coupled electromechanics-fluid dynamics model in the left ventricle. To extend the left ventricle motion to the endocardium of the left atrium and to that of the ascending aorta, we introduce a preprocessing procedure according to which an harmonic extension of the left ventricle displacement is combined with the motion of the left atrium based on the 0D model. To better match the 3D cardiac fluid flow with the external blood circulation, we couple the 3D Navier-Stokes equations to the 0D circulation model, obtaining a multiscale coupled 3D-0D fluid dynamics model that we solve via a segregated numerical scheme. We carry out numerical simulations for a healthy left heart and we validate our model by showing that meaningful hemodynamic indicators are correctly reproduced.
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[kg/(m |
[mm] | [s] | [s] | |||||||
MV | AV | MV | AV | |||||||
0.6 | 0.6 | 2.0 | 1.0 | |||||||
cells | DOFs ( |
BDF | ||||||||
[mm] | [-] | [-] | [-] | [s] | ||||||
min | avg | max | total | |||||||
0.4 | 1.2 | 4.1 | 1'627'795 | 806'295 | 268'765 | 1'075'060 | 1 |
[kg/(m |
[mm] | [s] | [s] | |||||||
MV | AV | MV | AV | |||||||
0.6 | 0.6 | 2.0 | 1.0 | |||||||
cells | DOFs ( |
BDF | ||||||||
[mm] | [-] | [-] | [-] | [s] | ||||||
min | avg | max | total | |||||||
0.4 | 1.2 | 4.1 | 1'627'795 | 806'295 | 268'765 | 1'075'060 | 1 |
Biomarker | In-silico result | In-vivo measurements | Reference |
LV stroke volume [ml] | 82.6 | [49] | |
LV ejection fraction [%] | 55.8 | [47] | |
Peak AV flowrate [ml/s] | [38] | ||
LV peak pressure [mmHg] | 121.2 | [69] | |
Peak E-wave velocity [m/s] | [77] | ||
Peak A-wave velocity [m/s] | [77] | ||
EA ratio |
[77] |
Biomarker | In-silico result | In-vivo measurements | Reference |
LV stroke volume [ml] | 82.6 | [49] | |
LV ejection fraction [%] | 55.8 | [47] | |
Peak AV flowrate [ml/s] | [38] | ||
LV peak pressure [mmHg] | 121.2 | [69] | |
Peak E-wave velocity [m/s] | [77] | ||
Peak A-wave velocity [m/s] | [77] | ||
EA ratio |
[77] |
Compartment | Parameter | Description | Unit of measure | Value |
Right atrium | Active elastance | [mmHg/ml] | 0.06 | |
Passive elastance | [mmHg/ml] | 0.07 | ||
Duration of contract. | relative w.r.t. |
0.335 | ||
Duration of relax. | relative w.r.t. |
|||
Initial time of contract. | relative w.r.t. |
0.80 | ||
Resting volume | [ml] | 4.00 | ||
Right ventricle | Active elastance | [mmHg/ml] | 0.65 | |
Passive elastance | [mmHg/ml] | 0.05 | ||
Duration of contract. | relative w.r.t. |
0.335 | ||
Duration of relax. | relative w.r.t. |
|||
Initial time of contract. | relative w.r.t. |
0.00 | ||
Resting volume | [ml] | 10.00 | ||
Pulmonary arterial system | Resistance | 0.25 | ||
Capacitance | 5.00 | |||
Inductance | ||||
Pulmonary venous system | Resistance | 0.02 | ||
Capacitance | 100.00 | |||
Inductance | ||||
Systemic arterial system | Resistance | 1.00 | ||
Capacitance | 2.00 | |||
Inductance | ||||
Systemic venous system | Resistance | 0.24 | ||
Capacitance | 60.00 | |||
Inductance | ||||
Tricuspid valve | Minimum resistance | [ |
||
Maximum resistance | [ |
|||
Pulmonary valve | Minimum resistance | [ |
||
Maximum resistance | [ |
Compartment | Parameter | Description | Unit of measure | Value |
Right atrium | Active elastance | [mmHg/ml] | 0.06 | |
Passive elastance | [mmHg/ml] | 0.07 | ||
Duration of contract. | relative w.r.t. |
0.335 | ||
Duration of relax. | relative w.r.t. |
|||
Initial time of contract. | relative w.r.t. |
0.80 | ||
Resting volume | [ml] | 4.00 | ||
Right ventricle | Active elastance | [mmHg/ml] | 0.65 | |
Passive elastance | [mmHg/ml] | 0.05 | ||
Duration of contract. | relative w.r.t. |
0.335 | ||
Duration of relax. | relative w.r.t. |
|||
Initial time of contract. | relative w.r.t. |
0.00 | ||
Resting volume | [ml] | 10.00 | ||
Pulmonary arterial system | Resistance | 0.25 | ||
Capacitance | 5.00 | |||
Inductance | ||||
Pulmonary venous system | Resistance | 0.02 | ||
Capacitance | 100.00 | |||
Inductance | ||||
Systemic arterial system | Resistance | 1.00 | ||
Capacitance | 2.00 | |||
Inductance | ||||
Systemic venous system | Resistance | 0.24 | ||
Capacitance | 60.00 | |||
Inductance | ||||
Tricuspid valve | Minimum resistance | [ |
||
Maximum resistance | [ |
|||
Pulmonary valve | Minimum resistance | [ |
||
Maximum resistance | [ |
Compartment | Parameter | Description | Unit of measure | Value |
Right atrium | Volume | [ml] | 78.95 | |
Right ventricle | Volume | [ml] | 154.00 | |
Pulmonary arterial system | Pressure | [mmHg] | 33.50 | |
Flowrate | [ml/s] | 69.44 | ||
Pulmonary venous system | Pressure | [mmHg] | 16.16 | |
Flowrate | [ml/s] | 0.00 | ||
Systemic arterial system | Pressure | [mmHg] | 91.68 | |
Flowrate | [ml/s] | 63.71 | ||
Systemic venous system | Pressure | [mmHg] | 23.99 | |
Flowrate | [ml/s] | 65.40 |
Compartment | Parameter | Description | Unit of measure | Value |
Right atrium | Volume | [ml] | 78.95 | |
Right ventricle | Volume | [ml] | 154.00 | |
Pulmonary arterial system | Pressure | [mmHg] | 33.50 | |
Flowrate | [ml/s] | 69.44 | ||
Pulmonary venous system | Pressure | [mmHg] | 16.16 | |
Flowrate | [ml/s] | 0.00 | ||
Systemic arterial system | Pressure | [mmHg] | 91.68 | |
Flowrate | [ml/s] | 63.71 | ||
Systemic venous system | Pressure | [mmHg] | 23.99 | |
Flowrate | [ml/s] | 65.40 |
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