2.2.   Basic Exercises

2.2.1.   Overview

In this section you will learn some of the ways available to specify an input function for the model. You will learn then how to set up the basic parameters required to configure GENTEX. Having these two items in hand, you will be able to run a simulation using GENTEX and will learn how to select results for display.

2.2.2.    Generating an input function

Introduction

In this exercise, you will examine some of the functions that are available from the function generator in GENTEX. A summary of the types available is listed in Table 2.2.3; the types range from simple pulses to a range of probability density functions (PDFs). Another method of generating an input function, deconvolution of the vascular tracer output curve, is discussed in Section 2.5.3.

Three of the input functions provided deserve special consideration. The random walk, gamma variate, and lagged normal density functions have been shown to provide reasonable descriptions of concentration curves obtained from actual indicator dilution experiments in which the indicator remained in the vasculature. Sheppard (1954 ) fit random walk density functions to experimental data obtained from isolated, perfused canine heart, lung (without the heart), and liver experiments. Thompson et al. (1964 ) examined the utility of the gamma variate density function to fit peripheral arterial dye dilution cardiac output curves in patients. In these experiments, injections were made into the right atrium or pulmonary artery, and dye concentrations were measured by continuously sampling peripheral arterial blood through a cuvette densitometer. The lagged normal density function was examined as a model for arterial dilution curves in man by Bassingthwaighte et al. (1966 ). These investigators sampled curves in a peripheral artery following injection of dye into either the superior vena cava or the aorta. All three of these distributions provide good fits to the concentration-time curves of indicator in the arterial system. They can, therefore, be used as an approximation of the form of the input function to the target organ following a bolus injection.

Start GENTEX with parameter file 1input.par of the tutorial database selected:

xsim gentex -p 1input.par

Select Plot Area 1 from the Results pull down menu, then click on the Run button in the main window. The parameters have been set to select a step function that starts at one second and has a four second duration. One result, the value of the input (Cin_v), is plotted in the Plot Area 1 window.

XSIM Note: 

XSIM plots simulation results with open symbols. Thus when a square wave is plotted, you see only the high and low levels with no connection between them. You can direct XSIM to use different colors and symbol sizes by clicking in the desired parameter box and then clicking on a color button or one of the three symbol size buttons.

Summary

Using the function generator is only one method of obtaining an input function for GENTEX. This is the method that will be used for the Basic Exercises, Indicator Dilution Principles Exercises, and most of the Advanced Exercises. Details of generating input functions in GENTEX are given in Section 3.2. You should read that section carefully before using GENTEX for modeling and data analysis, because the number of options is large and some choices of parameter values interact with others.

2.2.3.   Configuring the model

Introduction

In this exercise you will set the parameters that control the basic configuration of the vascular units of GENTEX. These include the mean blood flow, the number of flow paths, the volumes and relative dispersions (RD) of the nonexchanging vessels, and the transport and exchange parameters of the blood--tissue exchange (BTEX) units.

XSIM Note: 

You can load the values from parameter file 2config.par by leaving XSIM, restarting GENTEX, and selecting parameter file 2config.par as the file to be used. If, however, you are already running GENTEX, you can load the values from parameter file 2config.par without leaving the program. Pull down the Par-File menu to select Load..., and click on `No' in the popup window that appears. In the Load Parameter File window that appears, either type 2config.par in the parameter file field and then click on the load button, or double click on 2config.par in the scrolling Files menu.

The mean blood flow

The mean blood flow, F_b , is set in the GENTEX model layout window. Move your cursor over the Fb button to see the current value of mean plasma flow, and note that the value disappears when the cursor moves away from the button. Now double click on the Fb button in order to open the parameter control window for Fb. Note that its units are ml g^-1 min^-1.

The number of flow paths

As shown in Fig. 2.2.3, GENTEX contains a set of parallel flow paths. The number of paths used is also set in the GENTEX model layout window. It must be in the range 1~20.

The nonexchanging vessels

The nonexchanging vessels are the input tubing, artery, arterioles, venules, vein, and output tubing shown in Fig. 2.2.3. Including these vessels allows you to examine the influence of vessels that do not allow exchange with the tissue but do contribute to tracer delay and dispersion. When using these vessels, you must define their volumes (ml/g of organ) and the relative dispersion of the vessel. The windows containing lists of the parameters of all the nonexchanging vessels are also shown in Fig. 2.2.4. Note that the values set for arteriole and venule parameters are used for all flow paths.

If the volume of a nonexchanging vessel is set to zero, that vessel is not included in the modeling. The exercises of this tutorial do not use the nonexchanging vessels, thus all their volumes should be set to zero.

The blood--tissue exchange (BTEX) units

The effects of the BTEX units are controlled by their volumes (V ), membrane conductances (permeability-surface area product, PS ), axial diffusion coefficients (D), tracer consumptions (G), and initial concentrations (C₀). Since GENTEX models three reference tracers (red blood cells, intravascular, and extracellular), and five permeant species including tracers and their nontracer mother substances, there are eight sets of these parameters. Fig. 2.2.6 shows the diagrammatic location of these parameters, and Table 2.2.4 shows the definitions, units, and typical values for the parameters. Note that GENTEX allows nonlinear processes, i.e., the PS's and G's can be functions of nontracer species concentrations. For this exercise the initial concentrations, consumptions and diffusion coefficients will be set to 0.0, and linear symmetric transmembrane transport will be used for all reference tracers and permeant species.

To view the BTEX parameter values, click on the BTEX unit button in the GENTEX model layout window. The vascular unit window will open up. Click on the Extracellular unit button. The second interstitial fluid region is not used in this exercise; thus fV_isf2 and PS_isf are both set to 0.0.

Display the values of the permeant tracer parameters by clicking on the Permeant unit button. The second ISF region is not used for this tracer either. In addition to setting fV_isf2 and PS_isf to zero, PS_pc2 is also set to 0.0.

In addition to the parameters that are specific to each tracer and permeant species, six BTEX parameters are common to all the tracers. Blood flow (F_b), capillary volume (V_cap), hematocrit for large vessles (hctLV), RBC to plasma velocity ratio (rvel) and number of segments (N_seg) determine the internal time step used to evaluate the BTEX units (dtinternal=V_p*60/(F_p*N_seg)). Note that F_p and V_p are the plasma flow and volume, respectively, and are calculated by the model automatically based on the total blood flow, large vessel hematocrit and velocity ratio. For this exercise, hctLV is set to 0 (no RBC's) and rvel is set to 1. Because the time required for solving the model is proportional to the square of N_seg, choosing the number of segments is a compromise between solution time and accuracy. For these exercises, N_seg has been set to 10.   

The final common parameter is the capillary length, l_cap, in centimeters. It is usually set to 0.1, but, since axial diffusion is not used in the tutorial exercises, its value will have no effect.

Running the model

Having set the mean plasma flow, the number of flow paths, and the parameters for the nonexchanging vessels and the BTEX units, you can now run the model by clicking on the run button. The input function that has been selected in this parameter file is a lagged normal density curve (LNDC). You will see it plotted along with outflow concentrations of the vascular (plasma), extracellular, and permeant tracers. (Note that the same input curve is used for each of the three tracers.) Since all of these curves are plotted with small symbols, it helps to know something about the vascular system being modeled to know which is which. In this case, the first curve is, logically, the input curve and the remaining curves are the outflow curves. Which is the vascular tracer outflow curve? Since this tracer is confined to the plasma volume and the others diffuse out into the tissue, you can conclude that it is the outflow curve with the shortest transit time and the highest peak. Since the permeant tracer diffuses into ISF and cells, its curve has the lowest peak and longest transit time; the remaining curve is the extracellular curve.

Summary

In this exercise you have loaded a set of GENTEX parameters, checked the values that govern the behavior of the vascular units, and run the model. A set of results curves were plotted. Knowing what results were plotted, you used some knowledge about the nature of the tracers and the vascular system to associate a specific output curve with the appropriate tracer. The term transit time was introduced; this will be discussed further in an upcoming exercise.

2.2.4.   Selecting results for display

Introduction

GENTEX has several types of results that can be plotted. Of primary interest are the inputs, the outflows, and the tracer contents. In this exercise, you will focus on plotting the outflows and tracer content in the vascular system. To begin, load parameters from parameter file 3plots.par by switching to a new parameter file (Par-File: Load...) or by starting GENTEX with parameter file 3plots.par.

This parameter file has been preset to use a LNDC input for all tracers. Run the model and note that two curves are plotted: the input and the outflow of the intravascular tracer.

XSIM Note: 

There are two methods to specify the plotted curves. Either directly type in a parameter in a `Y Parameters' field, or open the pick control window by right clicking in the `Y Parameters' field, then scroll to and click on the desired parameter in the list. To change the color or style of the curve, click in the `Y Parameters' field of interest, then click on either a color or size button just above the graphing area at the right hand side.

For this exercise, the two curves plotted are the vascular tracer reference input and outflow. (The extracellular tracer reference input and the tracer input of the permeant species #1 in plasma are identical to the vascular tracer reference input.) The size and axis scaling of the plot are under user control. In this data file, values have already been specified.

Table 2.2.5 shows the parameter numbers associated with the input, outflow, and tracer contents curves of the three tracers. Display the permeant outflow by typing Cout_p_trplasma_1 in the third parameter field. Run the model again, and note the additional curve.

Now, add the tracer content for the vascular and permeant tracers (Q_ref_vval and Q_use1_trval) to plot area 1 and run the model again. You should have five curves displayed. The tracer contents curves are near the axis as their scale is quite different than that of the outflow curves. Note that there are two methods to calculate residues: (1) summing up the amount of tracers in the system, and (2) integrating the product of the flow and the difference of input and outflow (Fick's method). For the first method GENTEX allows users to specify a specific volume for the calculation. The control window shown in Fig. 2.2.8 can be launched by selecting Parameters > Model outputs -> Permeant contents by user choice-1.

There are two ways to change the scale used for plotting simulation results. The y-axis scale can be set manually or autoscaling on the largest plotted parameter can be specified. If the maximum values of the curves differ greatly it is usually better to put curves that require a separate scale in another plot area.

Move the content curves to the second plot area by selecting Results: Plot Area 2; then entering Q_ref_vval and Q_use1_trval in the parameter fields. Remove the content curves from the first plot area by clicking on the field containing Q_ref_vval, then clicking on the `Deactivate' button. Do the same for the Q_use1_trval field. Run the model again. Does this scaling make the curves easier to see? Which is the curve for the Vascular tracer? (Remember that the vascular tracer has access to a smaller volume than the permeant tracer, and, thus, leaves the BTEX unit more rapidly.)

XSIM Note: 

There are two ways to change the scale used for plotting simulation results. The y-axis scale can be set manually or autoscaling on the largest plotted parameter can be specified. If the maximum values of the curves differ greatly it is usually better to put curves that require a separate scale in another plot area.

Move the content curves to the second plot area by selecting Results: Plot Area 2; then entering Q_ref_vval and Q_use1_trval in the parameter fields. Remove the content curves from the first plot area by clicking on the field containing Q_ref_vval, then clicking on the `Deactivate' button. Do the same for the Q_use1_trval field. Run the model again. Does this scaling make the curves easier to see? Which is the curve for the Vascular tracer? (Remember that the vascular tracer has access to a smaller volume than the permeant tracer, and, thus, leaves the BTEX unit more rapidly.)

Summary

In this exercise you learned about the XSIM plot parameters, and about adding or deleting graphical output curves. You were also introduced to XSIM plot areas and scaling of simulation output.

2.2.5.   Summary

In these basic exercises, you have learned how to specify an input curve that is generated by the function generator. You have also examined, and perhaps altered the GENTEX parameters. Finally you were introduced to some of the results parameters that are available in GENTEX and learned how to specify which results are plotted. You are now ready to move on to exercises that deal with basic indicator dilution principles using GENTEX.