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Ring

Problem Setup

This problem generates a simple ring mesh using the carputils.mesh.Ring class. The ring is tessellated into tetrahedra as shown below:

In all experiment types in this example, the top and bottom surfaces of the ring are constrained to lie in the same plane with Dirichlet boundary conditions, and an additional three nodes on the bottom (\(z=0\)) surface are constrained such that free body rotation and translation is prevented. Two nodes on the x axis are prevented from moving in the y direction, and one node on the y axis is prevented from moving in the x direction:

Experiments

Three types of experiments are defined:

• active-free - Run an active contraction simulation without constraints on cavity size or pressure. This corresponds to a Langendorff-setup where the LV cavity is not pressurized.
• active-iso - Run an active contraction simulation with an isovolumetric cavity constraint. The LV cavity volume is kept constant, that is, both inflow and outflow valves are closed.
• active-pv-loop - Run an active contraction simulation with circulatory coupling. In this case the LV ring is coupled with a simple LA model (constant pressure) and a 3-element Windkessel model through inflow and outflow valves to regulate preload and afterload. The inflow valve closes when the LV pressure exceeds a prescribed pressure (approximately the pressure in the LA at end diastole). The outflow valve opens when the LV pressure exceeds the input pressure of the attached Windkessel model and closes when outflow turns negative. A lumped representation of this setup is given in fig-tutorial-ring-pv-lumped.

Other Arguments

Another key argument is the stress model. The available active stress model is:

• TanhStress - A simple stress model based on Niederer et al. (2011). Cardiovascular research, 89(2), 336-343. (see TanhStress model for details).

The stress model can be modified with the following arguments:

• s_peak - Peak stress in kPa (default: 100 kPa)
• tau_c - Time constant governing rate of rise in active stress model (default: 10 ms)
• ld_on - Turn on length dependence (default: off)

Usage

To run a simple active-free-experiment call

./run.py
  \

  --experiment
  active-free  `# experiment to run,
  possible choices: \

                             #     'active-free', 'active-iso'
  or 'active-pv-loop'` \

  --duration
  500            `# duration of the
  experiment (default 500 ms)` \

  --s_peak
  100              `# Peak stress
  in kPa (default 100 kPa)` \

  --tau_c
  10                `# Time constant
  governing rate of rise \

                             #     in
  active stress model (default 10 ms)` \

  --np
  10                   `# number of
  processes`

or call

./run.py
  \

  --experiment
  active-pv-loop  `# possible experiments:
  \

                                #     'active-free', 'active-iso'
  or 'active-pv-loop'` \

  --duration
  500               `# duration of
  the experiment (default 500 ms)` \

  --s_peak
  100                 `# Peak stress
  in kPa (default 100 kPa)` \

  --tau_c
  10                   `# Time constant
  governing rate of rise \

                                #    in
  active stress model (default 10 ms)` \

  --np
  10                      `# number
  of processes`

for a simple active-pv-loop-experiment.

Expected results

Simulation results computed are shown in the following for a full heartbeat.

Post-processing

The active-pv-loop-experiments output a cavity-information file (usually called cav.LV.csv) which contains pressure information, volume information, flow rates and many other additional informations. This cavity-information file can be used for a post-processing analysis using the following tools.

cavplot

The cavplot-tool is a simple tool for plotting the pressure volume relation. Call

cavplot
  cav.LV.csv

to plot the pressure-volume-relation, see figure fig-ring-cavplot. To plot just a single trace use one of the following flags, --pvloop, --volume, --pressure, --flux or --fluxdot. If you want to add the loading phase to your plot use the --loading flag.

cavinfo

The cavinfo-tool is an improved version of the cavplot tool. In addition to plotting pressure-volume data cavinfo performs a detailed analysis, computes various metrics and annotates the pressure-volume plots. Call

cavinfo
  --file cav.LV.csv     `# cavity
  information file` \

          --output
  cavity.info  `# output file name
  (default 'cavity.info')`

to plot the pressure-volume-relation and to determine many other quantities as ESV, EDV, etc., see figure fig-ring-cavinfo. All the information is stored in the output file and printed to the terminal, see output below.

cavity
  file         : cav.LV.csv

  negative
  flow       : True

  time
  range          : 0.000 - 500.000 ms

  IVC
  begin           : 17.000 ms

  ejection
  begin      : 32.000

  IVR
  begin           : 101.000 ms

  V0                  :
  9.792 ml

  EDV                 :
  13.286 ml  ( at 32.000 ms )

  ESV                 :
  6.080 ml  ( at 100.000 ms )

  SV                  :
  7.206 ml

  EF                  :
  54.238 %

  peak
  flow           : 0.268 ml/ms  ( 268.131 ml/s ) ( 0.268
  L/s )  ( 16.088
  L/min )

  peak
  flow time      : 41.000 ms

  open
  pressure       : 8.680 kPa  ( 65.109 mmHg )

  open
  pressure time  : 32.000 ms

  peak
  pressure       : 14.119 kPa  ( 105.902 mmHg )

  peak
  pressure time  : 56.000 ms

  mean
  pressure       : 13.022 kPa  ( during ejection )

  hm
  peak pressure    : 14.219 kPa  ( 106.651 mmHg )

  work                :
  93.837 kPa/ml  ( 0.094 J )

  estimated
  work      : 81.394 kPa/ml  ( 0.081 J )

  external
  work       : 94.149 kPa/ml  ( 0.094 J )

  contraction
  time    : 39.000 ms  ( peak pressure time - IVC begin )

  Ea                  :
  1.480 kPa/ml

  Ees(E)              : 0.164 kPa/ml

To get the total argument list run cavinfo --help.

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07_constitutive_fitting 09_bivslice