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 have been replaced by a 3D finite element representation.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
Part Name 3DX Model Feature Name Reference Point Surfaces
Aortic_Arch A.1 Fluid_Cavity_AA CAV_RP_AA AA_Interior_Face and hole meshes
Left_Atrium A.1 Fluid_Cavity_LA CAV_RP_LA LA_Interior_Face and hole meshes
Ventricles A.1 Fluid_Cavity_LV CAV_RP_LV Ventricles_LV_Interior_Face and hole meshes
Pulmonary_Trunk A.1 Fluid_Cavity_PT CAV_RP_PT AA_Interior_Face and hole meshes
Right_Atrium A.1 Fluid_Cavity_RA CAV_RP_RA RA_Interior_Face and hole meshes
Ventricles A.1 Fluid_Cavity_RV CAV_RP_RV Ventricles_RV_Interior_Face and hole meshes
Superior_Vena_Cava A.1 Fluid_Cavity_SVC CAV_RP_SVC SVC_Interior_Face and hole meshes
Compliance A.1 Fluid_Cavity_AC CAV_RP_C Mechanical_Surface_Mesh_AC (surface mesh)
Compliance A.1 Fluid_Cavity_PC CAV_RP_C Mechanical_Surface_Mesh_PC (surface mesh)
Compliance A.1 Fluid_Cavity_VC CAV_RP_C Mechanical_Surface_Mesh_VC (surface mesh)

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_AC-VC_Body_Resistance Extra-cardiac resistance Fluid_Cavity_AC Fluid_Cavity_VC
LINK_VC-RA_Venous_Resistance Venous resistance Fluid_Cavity_VC Fluid_Cavity_RA
LINK_RA-RV_Tricuspid_Valve Tricuspid valve resistance Fluid_Cavity_RA Fluid_Cavity_RV
LINK_RV_PCPulmonary_Valve Pulmonary valve resistance Fluid_Cavity_RV Fluid_Cavity_PC
LINK_PC-LA_Pulmonary_Resistance Pulmonary resistance Fluid_Cavity_PC Fluid_Cavity_LA
LINK_LA-LV_Mitral_Valve Mitral valve resistance Fluid_Cavity_LA Fluid_Cavity_LV
LINK_LV-AC_Aortic_Valve Aortic valve resistance Fluid_Cavity_VCLV Fluid_Cavity_AC

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.