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BiVSlice

Problem Setup

This problem generates a slice bi-ventricular mesh using the carputils.mesh.BiVSlice class. The bi-ventricular slice is tessellated into tetrahedra as shown below:

In all experiment types in this example, the top and bottom surfaces of the slice 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

Several experiments are defined:

• active-free - Run an active contraction simulation without constraints on cavity size or pressure
• active-iso - Run an active contraction simulation with an isovolumetric cavity constraint
• active-pv-loop - Run an active contraction stimulation with pressure/flux constraints imposed by Windkessel or circulatory models coupled to both RV and LV cavity. In this case both left and right ventricular cavities are coupled to a 3-element Windkessel model

Other Arguments

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

• TanhStress - A very simple active stress model based on activation times and constructed with exponential functions which also accounts for length-dependent development of active tension (see TanhStress model for details).

This active stress model is based on

• [1] Niederer et al. (2011). Cardiovascular research, 89(2), 336-343.

The stress model can be modified with the following arguments:

• s_peak - Peak stress in kPa (default: 50 kPa)
• tau_c - Time constant governing rate of rise in active stress model (default: 45 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
  180            `# duration of the
  experiment (default 180 ms)` \

  --s_peak
  50               `# Peak stress
  in kPa (default 50 kPa)` \

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

                             #     in
  active stress model (default 45 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
  180               `# duration of
  the experiment (default 180 ms)` \

  --s_peak
  50                  `# Peak stress
  in kPa (default 50 kPa)` \

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

                                #    in
  active stress model (default 45 ms)` \

  --np
  10                      `# number
  of processes`

for a simple active-pv-loop-experiment.

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 cav.RV.csv --pressure

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.RV.csv     `# RV 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         : 2018-09-13_active-pv-loop_fast_P1-P0_pt_np2/cav.RV.csv

  negative
  flow       : True

  time
  range          : 0.000 - 180.000 ms

  IVC
  begin           : 24.000 ms

  ejection
  begin      : 54.000

  IVR
  begin           : 135.000 ms

  V0                  :
  5.534 ml

  EDV                 :
  7.268 ml  ( at 54.000 ms )

  ESV                 :
  3.503 ml  ( at 134.000 ms )

  SV                  :
  3.765 ml

  EF                  :
  51.802 %

  peak
  flow           : 0.083 ml/ms  ( 83.496 ml/s ) ( 0.083
  L/s )  ( 5.010
  L/min )

  peak
  flow time      : 85.000 ms

  open
  pressure       : 1.849 kPa  ( 13.870 mmHg )

  open
  pressure time  : 54.000 ms

  peak
  pressure       : 3.976 kPa  ( 29.826 mmHg )

  peak
  pressure time  : 92.000 ms

  mean
  pressure       : 3.543 kPa  ( during ejection )

  hm
  peak pressure    : 4.306 kPa  ( 32.296 mmHg )

  work                :
  13.338 kPa/ml  ( 0.013 J )

  estimated
  work      : 11.977 kPa/ml  ( 0.012 J )

  external
  work       : 13.358 kPa/ml  ( 0.013 J )

  contraction
  time    : 68.000 ms  ( peak pressure time - IVC begin )

  Ea                  :
  0.788 kPa/ml

  Ees(E)              : 0.236 kPa/ml

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

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