GENTEX_Userguide

3.2. Input Functions

3.2.1. General

As shown in Table 3.2.1, four options are available for selecting input functions. Input functions can be taken from the reference data curves stored in TAC (Time-Activity Curve) files; they can be generated by deconvolving a vascular output curve from the reference data. Additionally, a function generator can generate twelve different types of input functions. Regardless of the method used to select an input function, the data need not be at the same time points as those used for the simulation. For all input functions, linear interpolation is used to get the actual values used as inputs to the model.

Table 3.2.1.: Options available for tracer input functions

1.	Use reference data curve
2.	Use deconvolution (Vascular or excellular tracer only)
3.	Use the function generator

3.2.2. Using reference data curves

Data files for XSIM, and thus for GENTEX, are stored in a specialized file format known as TAC (Time-Activity Curves) and will be referred to as "reference data." The format of TAC files is described in the UNIX man page. (Enter "man tac" at the system prompt for details). A TAC file consists of one or more experimental runs. Each run may contain auxiliary data, physiological data, input data, and sample (or output) data. XSIM permits up to 10 input curves and 20 output curves to be loaded from the reference data file. XSIM will allow the user to see a summary of the TAC file structure (Reference: TAC contents), but this feature is currently not fully implemented.

To select a curve from the reference data to be used as the input function for a specified tracer, open the appropriate input window (e.g. Parameters: input functions> Reference tracers -> Vascular ref tracer input), then press the Select button to choose

Reference TAC

. Click with the right mouse button in the TAC field, and select the appropriate input curve from the pop-up window. Entering a positive value in the

Delay

field will shift the curve to the right, and a negative value will shift it to the left.

Example 1

Fig. 3.2.3 shows the vascular (plasma) tracer input taken from reference data curve #1, and the extracellular input from curve #2..


Figure 3.2.3. Reference data used as inputs for two tracers.

3.2.3. Using deconvolution to generate a vascular tracer input curve

Introduction

Deconvolution uses a vascular or a excellular tracer output data curve and the transfer function of the vascular or excellular model (dependent upon the flow heterogeneity, large vessel volumes and dispersions, and vascular BTEX parameters) to calculate a vascular input curve. An example of deconvolution is depicted in Fig. 3.2.4.


Figure 3.2.4. An example of deconvolution.

The deconvolution process is significantly affected by noise in the measured data. The algorithm used for deconvolution attempts to minimize the inaccuracies caused by noise, and several smoothing parameters, discussed below, are under control of the user. Nevertheless, recording the vascular and/or excellular input at the time of the experiment will nearly always be preferable to using deconvolution. In some experiments, however, it may be impossible to record the signal, and deconvolution is required.

Deconvolution applies only to the vascular or excellular tracer input. The scaled results may, however, be used for the other tracers. This is appropriate when all the tracers are injected simultaneously and have the same waveform.

Selecting deconvolution

To calculate an input function by deconvolution, click on the Deconvolution button in the GENTEX model layout window, and set Use deconvolution to `yes'.The deconvolution calculations can take considerable time; thus, when you next run the model, you may notice a significant delay prior to any results being plotted. To save time on subsequent runs, GENTEX stores and, as long as the vascular or excellular model parameters or the deconvolution parameters are not altered, reuses the last deconvolution results. Whenever the vascular or excellular model (time step, volume, flow, flow heterogeneity, diffusion coefficients, etc.), the deconvolution parameters, or the reference data file name are changed, the deconvolution is recalculated.

Selecting the data curve to be deconvoluted

The Reference curve field specifies the data curve to be deconvolved. Right click in the field and a pick-menu will pop up, then choose the curve (the data file must be loaded first). It is important to insure that the curve selected is actually a vascular tracer or an excellular outflow curve and choose the corresponding model. [e.g., using an albumin (vascular tracer) concentration output curve and choose vascular tracer model.]

Selecting the model tused in deconvolution

The model used for deconvolution can be either vascular model or excellular model.

Selecting the stop time and the time step for deconvolution

The default stop time and time step for deconvolution is linked to the XSIM simulation stop time and time step. Users can use different stop time and time step for deconvolution and for simulation runs. For example, use small time step for deconvolution to obtain accurate input curves; and then use larger time step for faster simulation runs because the deconvolved input curve is reused and is sampled at the simulation time step.

Deconvolution control parameters

Four parameters are available to the user to control the deconvolution process.

Deconvolution smoothing factor is an overall smoothing parameter for the deconvolution process, which controls the scaling of regularization matrices. This factor should be set to 1 for noise-free data, and in the range of 10 to 100 for noisy data. Permissible values are
Extracted pic [6] to
Extracted pic [7] . The degree of smoothing increases as the smoothing factor value increases.

Optimize smoothing factor? If this button is set to `yes,' then the deconvolution smoothing factor will be optimized. The optimization minimizes both the coefficient of variation between the output data and the deconvolved output and the excess variation of the estimated input function. If the optimizer returns a smoothing factor of the order of 1000 or more, the data curve may not be suitable for deconvolution with this routine. See the manual page for more information (Type man dcnopt at the system prompt).

Data tail extension, controls smoothing of the tail of the derived vascular tracer input curve. Time to start tail extension specifies the time at which the power law or multi-exponential fit is applied.

Scaling factors are scalars for the other input curves.

Example

An example window configuration to deconvolve the reference data output curve #1 is given in Fig. 3.2.5.


Figure 3.2.5. Configuration to obtain a deconvoluted input from the first reference data output curve.

3.2.4. Using the function generator to generate a tracer input curve

Introduction

The function generator provides a variety of waveforms for creating input functions for all three tracers. The inputs for each of the three tracers may be independent, or they can be scaled to the vascular input by using input function scaling, described in the next section. Detailed information about the function generator subroutine, named cinput, can be found in the online UNIX manual page (man cinput).

Selecting a function generator

To select a function generator, open the desired input window and click on the Select button. In the following example, Parameters: Input functions > Reference tracers > Vacular ref tracer input was used. Next, choose one of the functions by selecting from the Function button menu. In the example Fig. 3.2.6, a pulse input of 1 second duration has been chosen.


Figure 3.2.6. Function generator options with a pulse input function selected.

Example

In the example of Fig. 3.2.7, a lagged normal density curve (LNDC) has been specified for the vascular input. The LNDC has an area of 1.0, a mean of 5 seconds, a relative dispersion of 0.3, and a skewness of 1.2. Linearization of the upslope has been specified.