Example h5: Simulation of Aortic pressure in the arterial tree

Fig. 1. Pressure Distribution at 0.174 s	Fig. 2. Aortic Pressure variation	Fig. 3. Velocity Distribution at 0.174 s

In this example we simulate the aortic pressure cycle (figure 2) at the proximal end of the ascending aorta in the arterial tree. The arterial tree was created by digitising the visible human data as explained in example_h4. The pressure at the distal ends of the tree is maintained constant at the mean aortic pressure of 12.46 kPa (93.45 mmHg). For the details of the model governing equations and numerical method etc. see example_h2 and example_h3 .

NOTE : As the network consists of 145 elements (1D - Cubic Hermite) and around 4000 grid points after discretisation with a spatial step of 1.00 mm, this example must be run on the HPC.

The comfile run by this example is as follows:

fem define parameter;r;arteries;example      # Declares array dimensions
fem reallocate;
fem define coordinate;r;arteries;example     # Defines the coordinate system
fem define node;r;arteries;example           # Reads in nodal information
fem define base;r;arteries;example           # Defines basis function (02 funcns : 1. 1D cubic hermite 2. 1D linear)
fem define element;r;arteries;example        # Reads in element information
fem define field;r;arteries;example          # Reads in fields. Only first field (unstressed radius at nodes) is necessary for this problem
fem define element;r;arteries;example field  # Defines interpolation of field variables (linear)
fem define grid;r;arteries;example coronary  # Defines grid points with coronary option to discretise the spatial computational domain. 
fem update grid geometry;
fem define equation;r;arteries;example       # Defines equations                          
fem define material;r;arteries;example       # Reads in physical & mechanical properties
fem update material field material 4 no_field 1;
#                                            # Updates unstressed radius (mat 4) from field 1
fem define time;r;aortic;example             # Define boundary conditions. Aortic press. at inlet and mean aortic press.(constant) at distal ends.
fem define initial;r;arteries;example        # Defines initial conditions
fem define solve;r;arteries;example          # Defines solution parameters

$time_initial=0.00;                          # Sets the initial time
$time_final=0.87;                            # Sets the final time
$time_step=0.0001;                           # Sets the time step time
$write_out_period=0.0435;                    # Sets the results write out period

fem export points;$time_initial grid as vessel offset 1000;         
fem export grid;vessel as vessel offset_node 1000 offset_elem 1000 elastic_tube; 

# Results output loop

for ($time=$time_initial;$time<$time_final;$time=$time+$write_out_period)       
{                                                                           
fem solve restart to $write_out_period delta_t $time_step;
fem export points;$time+$write_out_period grid as vessel offset 1000           
}                                                                           

Files used by this example are:

Name             Modified     Size

example_h5.com   09-Oct-2001  2.2k
0.0435.exnode    09-Oct-2001  379k
0.087.exnode     09-Oct-2001  379k
0.1305.exnode    09-Oct-2001  379k
0.174.exnode     09-Oct-2001  379k
0.2175.exnode    09-Oct-2001  379k
0.261.exnode     09-Oct-2001  379k
0.3045.exnode    09-Oct-2001  379k
0.348.exnode     09-Oct-2001  379k
0.3915.exnode    09-Oct-2001  379k
0.435.exnode     09-Oct-2001  379k
0.4785.exnode    09-Oct-2001  379k
0.522.exnode     09-Oct-2001  379k
0.5655.exnode    09-Oct-2001  379k
0.609.exnode     09-Oct-2001  379k
0.6525.exnode    09-Oct-2001  379k
0.696.exnode     09-Oct-2001  379k
0.7395.exnode    09-Oct-2001  379k
0.783.exnode     09-Oct-2001  379k
aortic.iptime    09-Oct-2001  2.1k
arteries.ipbase  09-Oct-2001  2.0k
arteries.ipcoor  09-Oct-2001  570 
arteries.ipelem  09-Oct-2001   50k
arteries.ipelfd  09-Oct-2001   35k
arteries.ipequa  26-May-2003  1.2k
arteries.ipfiel  09-Oct-2001   30k
arteries.ipgrid  27-Nov-2001  216 
arteries.ipinit  26-Aug-2004  567 
arteries.ipmate  09-Oct-2001  6.7k
arteries.ipnode  09-Oct-2001   55k
arteries.ippara  12-Nov-2002  5.9k
arteries.ipsolv  27-Aug-2002  760 
vessel.exelem    09-Oct-2001  491k

Download the entire example:

Name                  Modified     Size

examples_h_h5.tar.gz  19-Aug-2006  1.8M

Html last generated: Sun Mar 6 05:51:37 2016

Input last modified: Tue Jun 13 15:00:59 2006