A Research Example

The human cardiovascular model upon which RCVSIM is based was originally constructed in order to advance research in the general area of beat-to-beat hemodynamic variability [4,,8]. The RCVSIM software enhances the potential of the original human cardiovascular model in facilitating cardiovascular research by making the model more user friendly and compatible with the open-source software provided by PhysioNet. By further disseminating RCVSIM to the cardiovascular research community through PhysioNet, researchers may conveniently utilize the computational model to complement their studies with the experimental data sets available on PhysioNet. For example, RCVSIM has been previously utilized to develop an algorithm for monitoring systemic arterial resistance from only a peripheral arterial pressure waveforms which was subsequently validated with data from the MIMIC database on PhysioNet [4]. Another research example which illustrates how RCVSIM may be utilized in conjunction with the open-source software and experimental data sets of PhysioNet in order to improve the accuracy of the model, and thus possibly physiologic understanding, is provided below.

The default or nominal parameter values of the human cardiovascular model are set such that the power spectra of the simulated beat-to-beat hemodynamic variability resembles power spectra measured from a group of normal humans in the standing posture [4,5]. The objective of the research example here is to determine a set of parameter values which permit the model to generate a realistic supine posture, heart rate power spectrum. In order to address this objective, it is necessary to obtain experimental data sets to define what is realistic and software to compute the heart rate power spectrum - both of which are available from PhysioNet. The specific steps which were implemented to achieve the research objective are given below.

1. Establish realistic supine posture, heart rate power spectrum.
   1. Visit the following web page:
      http://www.physionet.org/physiobank/database/meditation/data/
      which houses Exaggerated Heart Rate Oscillations During two Meditation Techniques: Data.
   2. Download the data in the metronomic breathing group from the bottom of this web page - M#.hea and M#.qrs, where # ranges from 1 to 14. (These data provide the qrs times of 14 volunteer subjects in the supine posture breathing at a fixed-rate of 0.25 Hz.)
   3. Calculate an instantaneous heart rate tachogram from the qrs times for each subject by executing the following command at the Linux prompt (14 times):
      tach -r M# -a qrs -f $>$ hr#
      (Note that tach is open-source software provided by PhysioNet. Type tach -h at the Linux prompt for help.)
   4. Calculate the maximum entropy power spectrum of the instantaneous heart rate tachogram for each subject by executing the following command at the Linux prompt (14 times):
      memse -f 2 -Z -o 15 hr# $>$ phr#
      (Note that memse is open-source software provided by PhysioNet. Type memse -h at the Linux prompt for help. The generated files phr# are two-column, ASCII format files in which the first column represents frequencies and the second column represents the corresponding power spectral densities.)
   5. Average the power spectra over the 14 subjects and write the averaged spectra to a two-column ASCII file called avephr (by writing a simple program or using any pre-existing software such as MATLAB).
   6. Plot the averaged power spectrum by executing the following command at the Linux prompt:
      plot2d avephr 0 1
      (Note that plot2d, which is a simple program that controls Gnuplot, is open-source software provided by PhysioNet. Type plot2d -h at the Linux prompt for help.)
2. Determine model parameter values which permit the model and averaged, experimental heart rate power spectra to match.
   1. Copy file $DIR/bin/parameters.def to the current directory with the new file name parameters_r.
   2. Open the file parameters_r with any text editor (e.g., emacs).
   3. Re-assign the following parameters: waveform: -1, baro: 3, dncm: 1, breathing: 1, dra: 1, df: 1, Tr: 4, and Qt: 430. (Since accompanying experimental respiratory data is not available, the last parameter is arbitrarily set such that the alveolar ventilation rate is 70 ml/s.)
   4. Save the file parameters_r.
   5. Execute the following commands at the Linux prompt:
      rcvsim parameters_r foor
      tach -r foor -a qrs -f $>$ hrsim
      memse -f 2 -Z -o 15 hrsim $>$ phrsim
      plot2d phrsim 0 1
   6. If this plot matches the experimental plot above, then the research objective has been achieved. Otherwise, re-assign the following parameters: bgain, again, pgain, stdwr, and stdwf, and repeat the steps above beginning with Step (d). (Note that these five parameters have been identified based on a priori knowledge of the physiologic differences between supine and standing postures.)

When the values assigned to the parameters of Step (f) are set as follows: bgain: 0.5, again: 0.5, pgain: 1, stdwr: 0.04, and stdwf: 0.175, the averaged experimental and model supine posture, heart rate power spectra match (see Figure 22). As expected, the parameter changes from the standing posture to supine posture reflected a shift in autonomic balance favoring the parasympathetic nervous system. Interestingly, a further comparison of these parameter values with the nominal values suggests that the posture peak in humans ($\sim$0.1 Hz [10]; present in the model with default parameter values) could be due to both a system resonance which is established by increased sympathetic nervous activity as well as increased fluctuations in local vascular resistance beds which may be due to increased leg muscle activity.

  

Figure 22: Model (red) and experimental (blue) supine posture, heart rate power spectra at fixed-rate breathing of 0.25 Hz. The dark blue line is the average spectrum computed from 14 volunteers, while the two lighter blue lines are the corresponding 95% confidence intervals. See text for additional details.