Blood Flow Model

The blood flow model uses a combination of surface-based fluid cavities and fluid exchanges. See “Surface-based fluid modeling” in the Abaqus Analysis Guide for more information.

The circuit shown in the figure below is a schematic representation of the blood flow model. Resistors represent flow resistances and capacitors represent structural compliances.

Schematic Representation of the Blood Flow Model

The blood flow model uses the approach described in Pilla et al.; however, Pilla et al. use a lumped parameter representation for all components, whereas the Heart Model uses a hybrid approach involving both lumped parameter and 3D representations. In particular, the parameters associated with compliance and contractility of the four heart chambers in Pilla et al. have been replaced by a 3D finite element representation.

The compliance and contractility of the heart within the blood flow model are incorporated into the mechanical simulation through the fluid cavities shown in the table below.

Table 1. Hydrostatic Fluid Cavity Definitions
Abaqus/CAEAbaqus/CAE Feature Name Reference Node Set Name Surface Name
CAV-AORTA Aortic_Arch-1.CAV-RP AORTA-CAV
CAV-LA L_Atrium-1.CAV-RP L_Atrium-1.LA-CAV
CAV-LV LV-RP LV-CAV
CAV-PULMONARY_TRUNK Pulmonary_Trunk-1.CAV-RP Pulmonary_Trunk-1.CAV
CAV-RA R_Atrium-1.CAV-RP R_Atrium-1.RA-CAV
CAV-RV RV-RP RV-CAV
CAV-SVC Superior_Vena_Cava-1.CAV-RP SVC-CAV
CAV-ARTERIAL-COMP Arterial_Compliance-1.RP Arterial_Compliance-1.INNER
CAV-PULMONARY-COMP Pulmonary_Compliance-1.RP Pulmonary_Compliance-1.INNER
CAV-VENOUS-COMP Venous_Compliance-1.RP Venous_Compliance-1.INNER

The last three cavities shown in the table above are defined as cubic volumes and used to model the compliance of the arterial, venous, and pulmonary circulation systems. Initial dimensions of each cavity are chosen to establish a total blood circulation volume of 5 liters. Each cavity is attached to a grounded spring with a stiffness tuned to provide the appropriate pressure-volume response (that is, compliance) for that cavity.

Blood flow between the hydrostatic fluid cavities is modeled using the fluid exchange definitions shown in the table below. Each fluid exchange link possesses a viscous resistance coefficient tuned to obtain atrial and ventricular pressures according to published normal ranges shown in the table in Summary of Simulation Results.

Table 2. Fluid Exchange Link Definitions
3DEXPERIENCE Feature Name Description First Chamber Second Chamber
LINK-ARTERIAL-VENOUS Extra-cardiac resistance CAV-ARTERIAL-COMP CAV-VENOUS-COMP
LINK-VENOUS-RA Venous resistance CAV-VENOUS-COMP CAV-RA
LINK-RA-RV Tricuspid valve resistance CAV-RA CAV-RV
LINK-RV-PULMONARY Pulmonary valve resistance CAV-RV CAV-PULMONARY-COMP
LINK-PULMONARY-LA Pulmonary resistance CAV-PULMONARY-COMP CAV-LA
LINK-LA-LV Mitral valve resistance CAV-LA CAV-LV
LINK-LV-ARTERIAL Aortic valve resistance CAV-LV CAV-ARTERIAL-COMP

Reference values for blood density and bulk modulus are taken from Mourad and Kargl as 1.027 × 10–9 tonne/mm3 and 2.4 MPa, respectively. However, the bulk modulus is reduced by a factor of 1000 to increase the stable time increment and thus reduce run time. The reduced stiffness has a negligible effect on the results as the fluid is still significantly stiffer than the muscle in compression.