Calculation
Matrix Spacing and Rotation Increment
Two
Dimensional Isodose Control
Three
Dimensional Isodose Control
Compare 1D Dose Profile Relative to a Beam
Difference Dose Volume Histogram
Show RMU
Value and RMU Profile
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The Plans Toolbar |
The plans tool is selected upon selecting Dosimetry Check under the Applications toolbar on the main menu. Options that do not belong to the dosimetry check function but that might otherwise be part of general treatment planning are either grayed out or do not appear. The Dosimetry Check plans are saved under the selected patient directory in a separate subdirectory ckpn.d.
Under the Plan pull down menu are options to create a new plan, to retrieve an existing plan, to edit an existing plan, to copy a plan, or to delete a plan. You must first create or retrieve a plan before you can edit it or delete it. If you have downloaded the plan, the beam’s should be set to the proper location and angles. Otherwise you will have to locate isocenter and type in the gantry, couch, and collimator angle for each beam. The plans and beam parameters are saved as you create and change them. Some beam parameters are saved when you return from the beam’s toolbar. Dose matrices are saved when you return from the plan toolbar.
Note that you may select or create more than one plan, and may selectively display each plan in different frames.
You can compute the dose volume histogram for outlined regions of interest. The dose is that computed by DosimetryCheck, not by the other treatment planning system. Shown below is the volume histogram popup. We will refer you to the RtDosePlan manual for details on the use of this option, under the Plan section. Dose volume histograms are provided here since the function exist and there may be some use in comparing to the planning system. In summary, you can select the same volume for different plans, as well as different volumes. Hitting the compute button will start the computation which you can stop when the plotted curves have settle down.
The dose volume histogram can also be recomputed and displayed from the downloaded 3D dose matrix from the planning system (call the Foreign dose) and shown as a dotted line.
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Dose Volume Histogram |
The “Display Data” button will print the data to a file and then display the contents of the file, which may be suitable to imputing to some other analysis tool, or you can print from there. The statistics button will compute the minimum and maximum dose, the average dose, and the standard deviation of the dose to each volume, for both the reconstructed dose and the plan dose.
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The Plan Toolbar. |
Once you have selected or created a plan, the plan toolbar will be displayed. When the plan is first created you will be required to select the primary stacked image set. This set will specify the skin boundary and the pixel to density conversion curve. Once you have selected the primary image set, you cannot change it. Under those circumstances, you would have to delete the plan and create a new one. The toolbar shows the current plan name in an option menu. You may select different plans with this option menu among the plans that were currently retrieved or created with this run of the program. Next on the toolbar is the name of the primary stacked image set once it is selected, or an option menu to do so if not yet selected.
If you downloaded the plan using the RTOG or Dicom RT protocol, the stacked image set will have been determined. However, neither protocol specifies CT number to density conversion, and so you must select that. Go to the main toolbar to Options under the Stacked Image Set pull down. Then select Density and select a curve. The Dicom RT protocol can specify which ROI volume is the skin boundary, but the RTOG protocol does not. So if the RTOG protocol was used, you will also have to select which ROI volume is the skin boundary. Select Skin on the same Stacked Image Set Options toolbar and select the skin boundary ROI with the option menu provided. If a skin boundary was not downloaded, you can use the automatic skin boundary generation tool on the contouring toolbar. See the System2100 manual, contouring section.
Dosimetry Check will then attempt to find field dose files for each beam that does not have one. The program will look for files that include the beam name in the file name. All such files found for a particular beam will be added together. The directory searched is the FieldDose.d directory in the patient’s directory where program such as ConvertEPIDImages places files after calibration and deconvolution. The plan name and beam name will be shown on each field dose image. The files used to create the field dose will also be shown if there is room. Maximize the frame to see all the text.
The Beams pull down menu has to do with creating and editing beams that belong to the plan. You can create, edit, and delete beams. When you create a new beam it will start out with the isocenter of any prior beam in the same plan if not the first beam. You can also create a new beam that has the same isocenter and angles of a prior existing beam, or create a new beam that is to be parallel opposed to an existing beam. From this pull down you can select a beam to have all the other beams to have the same isocenter location. Each beam is stored in a subdirectory under the plan’s subdirectory.
For the Dosimetry Check program, only x-ray beams may be selected. We presently do not support electron beams with this function. Most electron fields are applied at a fixed distance and the monitor units applied is close to the dose delivered, and so the quality control problem is not so involved as it may be for x-rays.
Under the Display pull down are options pertaining to displaying the plan. Because there may be more than one plan in the run of a program, the plans are not automatically displayed in frames. Rather you must select which frames to display the plans in. You can specify a specific frame on all the frames on the currently displayed screen. However, the program will not allow a plan to be displayed on an image that does not belong to either the primary stacked image set or on an image set not fused to the primary image set. A plan cannot be displayed in a frame in which a plan is all ready displayed. What is displayed are the beams, point doses, and isodose curves if also selected for display.
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Display Plan Control Popup. |
A popup tool is provided to remove a plan from being displayed in a frame. The same controls appear to display a plan but additional controls are provided to remove a plan from a frame or screen.
Controls for turning off and on beam displays is provided. The central ray is drawn as a solid line to isocenter, and then drawn as a dashed line beyond. The beam’s eye view x, y, and z axes are drawn and marked. The z axis is the central ray, positive toward the source of x-rays, and lies coincident with the central ray. With the treatment machine pointed at the floor and the collimator unrotated, the x axis goes from left to right while standing in front of the treatment couch looking toward the gantry. The y axis is parallel to the long axis of the unrotated treatment couch and points toward the gantry. The origin is at isocenter. The Dosimetry Check program has not have the concept of field size since the field is defined by a measured picture of the x-ray field (even though the field collimator positions are defined in the field image data structure).
You can select a default display of transverse, coronal, sagittal, and 3D room perspective view centered on the CT data set, a particular outlined region of interest, a particular point, or the isocenter of a beam. Normally, however, one would pick image planes to correspond to that shown on the planning system. The reformat image option under the Stacked Image Set pull down on the main toolbar would be useful for this purpose.
Items under the evaluate pull down have to do with calculating the dose and displaying the result. Because calculation times may be long, there is control to selectively select which frames the dose is to be displayed in. Each frame is calculated when it is selected here to display the dose. The hot spot in that frame will be displayed and marked with a star asterisk like figure.
Each beam maintains a dose matrix on diverging fan lines, the fan lines covering the area of the beam. A rotating beam would be simulated with multiple dose matrices at increments specified by the plan. The spacing between the fan lines and along the fan lines is also specified by the plan, so that all the beams belonging to a plan use the same parameters. Each beam stores its matrix under its own subdirectory under the plan subdirectory. The matrices are written to disk files when the return button on the plan toolbar is activated.
For any two dimensional plane image displayed in a frame a two dimensional matrix will be generated that covers the entire image. The same spacing parameter specifies the distance between points. When the dose is calculated, the coordinates of each node of the two dimensional matrix is passed to each beam. The beam module will find the diverging box bounded by the fan lines that the point is inside. The eight corners of the box will be referred to when interpolating the dose at the position of the passed in point. Each beam will calculate the dose to each vertex of the diverging box on a need basis. When ever a reference is made to a vertex where the dose has yet to be computed, the dose is computed at that time. After calculating the dose to a plane, all the beams will have a swath through their dose matrices of calculated points. As more planes are computed, more of each beam’s dose matrix is computed. If any change is made to a particular beam, that beam’s matrix is reinitialized.
Likewise when a dose in a 3d perspective room view is computed, a rectangular array (lattice) of points is generated for the patient volume. Each of those points is likewise passed to each beam, so that after a room view display each beam will most likely have calculated the dose to all of the available vertices.
The Calculate All Beam 3D option will force all the beams to compute the dose to all the vertices on their respective dose matrices.
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Calculation Matrix Spacing Control Popup |
A control is available to specify the spacing to use for all the dose matrices and the increment in rotation to simulate beam arcs. Making a change here will force all beams to dump their current dose matrices. The matrices covering planes and the matrix for room views also must be regenerated if a change in spacing is made here. The user will then have to reselect the frame to display the dose in.
The calculation matrix spacing is the distance between points on two dimensional images and between the three dimensional dose matrix. Each beam is queried for a value at these points. Each beam maintains its own divergent matrix within which points are interpolated. The calculation matrix spacing is used in the plane perpendicular to the central ray in the center of the patient. The spacing along the BEV Z axis is the spacing parallel to the central ray. You might want to use a smaller calculation matrix but leave the spacing larger as there is less of a gradient along the diverging rays.
The arc spacing is the increment to use to simulate an arc with fixed beams. This parameter is adjusted somewhat by each beam to fit the arc length of that beam so that the arc is simulated with equally spaced fixed beams.
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2d Isodose Control |
This control provides a tool for the user to specify the isodose value to be displayed. For the Dosimetry Check function, only the dose may be displayed in cG. The dose value desired is to be typed in the text field at the top of the popup. The line width may be changed to make a particular isodose line stand out. The isodose value may be tinted in a single color showing the boundaries and interior (higher doses) of that isodose line. You may use the mouse to select different isodose values to tint on the scrolled list below the text field for the value entry. Note also that the tint may be turned off and the tint color may be changed among the primary colors and additions of any two of the primary colors. Likewise any selected isodose line may be deleted or have its color changed. Colors are initially assigned at random. Note also that each isodose line has tick marks on the down hill side (lower dose) of the isodose line, analogous to topographical maps. The selected isodose lines apply to all 2d frames in which the dose has been selected to be displayed for the plan.
An issue that must be dealt with is what to do when two successive dose vertices span the skin boundary, so that one point is outside the patient and the next point is inside the patient. The plotting of the isodose line simply stops at that point. However, the tinted area necessarily requires a closed contour.
In those regions the tint follows a path between points inside the patient and outside the patient and does not accurately represent the dose.
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3d Isodose Control Popup. |
A three dimensional isodose surface may be shown in 3d perspective room views of the primary stacked image set or any image set fused to it. Only one surface can be shown at a time. The desired value is typed into the text field provided. Under the text field is a control for the transparency of the isodose surface.
Limitations apply here. A transparent surface can only be seen inside a second transparent surface if the inside transparent surface is drawn first. Two transparent surfaces that intersect will present a problem in that if surface A is drawn first and surface B is drawn second, then surface A can be seen inside surface B, but surface B cannot be seen inside surface A. This software will draw the transparent isodose surface before other transparent surfaces. No attempt is make to sort surfaces or part of surfaces. If this becomes a problem you have two options. One, make all the other surfaces opaque or make the isodose surface opaque. You can also use a cutting plane on volumes that are drawn. A second option is to display the isodose surface in wire frame. The wire, solid, off, control is below the transparency scale.
This control controls all frames simultaneously that show 3d room perspective views where the user has chosen to show the dose. The user must first choose to display the plan in the frame.
At this writing, the plan does not have its own list of specific points. Rather, the only list of specific points is maintained by the primary stacked image set. Therefore all plans using the same stacked image set will calculate the dose to the same list of specific points. The controls for the specific points are under the Stacked Image Sets pull down on the main toolbar. Select Options and then Points.
However, we need the ability to specify the coordinates of a point in terms of the beam’s eye view coordinates of a specific beam or the IEC image set coordinates relative to isocenter. Therefore a control is provided here for adding a point where the position is known relative to isocenter. The coordinates are then transformed to the stacked image set coordinates and the point is created and saved. The point is not moved if the beam is later moved. To delete a point use the above controls for points as described under the Stacked Image Sets Options.
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Plan Points Toolbar. |
Under the Evaluate pull down we have a points toolbar. Here the dose to the specific points may be computed, displayed, printed, or saved to a temporary file. We can select the popup to enter new points in beam’s eye view coordinates or IEC couch coordinates relative to isocenter. There is also a mechanism for comparing measured to computed values for testing purposes.
Simply hitting this button will cause the points to be computed and printed. The plan dose will also be printed if the point falls within the 3D dose matrix gotten from the planning system.
Selecting this option, the point’s label and dose value will be written to a file in the temporary file directory where print jobs are also stored. The dose to the points are first computed. An example file follows:
// Test Square 12-Dec-2000-09:19:19(hr:min:sec)
// Label Dose in cGray
<* Example Label *>
1.299286
<* slice 10 row 4
column 7 *> 1.324436
The file is written in our ASCII standard whereby comment lines start with two slashes and are not read. The label for the point is enclosed between the <* and *> symbols. The dose value is simply a number set off by white space. This format will also be referred to below.
This choice will display the dose value computed for each point below the label for the point in all frames where the plan is displayed. The planning system dose, if available, will be interpolated from the foreign 3D dose matrix with the letter P preceding the value displayed.
This will turn off the display of the dose value of the points. Note also that any change to the plan or a beam will also turn of the display of the dose values.
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Locate Points in BEV or IEC Image Set Coordinates Control |
This tool is provided here as a convenience so that a point can be added to the stacked image set in reference to the beam’s eye view coordinates of a beam or the image set relative to isocenter. The control is very much like the one provided by the stacked image set under Options to Points toolbar. However, we have added an option menu to select the beam to define isocenter and two radio buttons to select the coordinate system to use.
Below the option menu are controls for the x, y, and z coordinates of the point. The point may not be located with the mouse here. Do that on the control provided by the stacked image set under the Stacked Image Set pull down on the main toolbar, to Options. The control provided here is for the case when a point must be specified in relationship to isocenter in the coordinate system of a beam or an IEC system relative to isocenter and the image set.
The beam’s eye view coordinate system is described elsewhere as well, where in the unrotated collimator and gantry positions (beam pointed at floor), the x axis goes across the couch left to right when looking into the gantry, the y axis points toward the gantry along the gantry’s axis of rotation, and the z axis points toward the source of x-rays. The x and y axes rotate with the collimator in BEV and the show system rotates with the gantry. The origin is at isocenter.
The IEC image set system is fixed to the patient. The Y+ axis in the image set is always towards the patient’s head. The Z+ axis is always up. The X+ axis is to the patient’s left for a supine patient, right for a prone patient. Here the origin is at the isocenter of the selected beam.
To delete or otherwise edit points, use the other controls provided by the Stacked Image Set Options.
This option was provided for a very narrow purpose. Specifically, we irradiated a Rando Phantom and measured the dose at specific points and wanted to be able to display the measured value with the computed value. The measured values must be written to a file in the same format as the computed points are written to as described above. Selection of this option will prompt you to enter the file name of the measured points. The measured points are associated with the computed points by means of the point’s label. The labels are not directly compared. First each label is converted to lower case and then all spaces are removed and then compared. Care must be taken that the labels will remain unique when the user creates the labels. For a match, the measured value will be displayed below the computed value. An m is also appended to the measured dose value. In our use of the Rando Phantom we labeled the holes according to a scheme. There are 7 rows and 13 columns of holes with the 3 cm matrix drilling. Each hole is known by its slice number, row number, and column number. By labeling the holes consistently, the measured values can be matched up with the computed values and displayed. The specific points are also computed upon selecting this option.
We have also written a program that will compare measured and computed values, CompareRandoPoints. Invoke this program and on the command line provide the name of the file that contains the measured points, the name of the file that contains the computed points, and the name of a file to write the report to. This program assumes that only numbers appear in the label field, consisting of the slice number, row number, and column number separated by spaces and sorts values by those indices.
This labeling scheme could cause some confusion in the above display function in frames as 11 1 1 would be indistinguishable from 1 1 11, for example, after removing spaces. The row number is only in the range of 1 to 7 and the column goes only from 1 to 13. Use leading zeros for the slice number and column number for single digits if there is a possibility of confusion, i.e. 11, 1 01 and 01 1 11.
Several tools are provided for comparing and showing the dose distribution that may have been downloaded from the treatment planning system. These tools can be used for enhancing your understanding of any dose difference. The tools are found under the Evaluate pull down.
You can compare the dose profile between the planning system and reconstructed dose for any line through the patient space. Do you this by selecting any reformatted image through the patient, and then positioning a line on that plane. Shown below is an example. You first must select a current frame. The current frame must be showing a plane through the stacked image set of the plan or one fused. Use the reformat image control to select different planes through the patient (under the Stacked Image Set pull down on the main tool bar). Then use the translate and rotate controls to position the line visually. Hit the “Get Profile” button to see the curve. If you do anything that changes the dose, you must hit the “Get Profile” button again to update the displayed data.

The Show/Write Data to File button will display the data that is plotted and write to an ASCII file.
There is another similar control that will allow you to specify a profile relative to a selected beam in beam’s eye view coordinates (BEV). Here you will select the beam from a cascade on the Evaluate pull down. You will then select the Z BEV coordinate for the profile and an angle of the profile, rotated around the Z axis from the X axis. Isocenter is at Z = 0, and points further away from the source are negative.
Nothing is drawn on images on the main window. In the above example, the profile is shown along the BEV axis for beam “A3 rao” through isocenter (since BEV Z is zero and the rotation angle is 0). The dose is still shown for all beams however. If you want to compare the dose for only one beam, you will have to download a plan for only beam.
You can select to view isodose curves together from the downloaded foreign dose along with the dose computed here. Or show one or the other, or show the difference between the two dose sets. The dose difference is the absolute value between the computed and foreign dose. The foreign dose distribution (and so also the difference) will be limited by the area covered by the read in dose array. Isodose curves will not be plotted outside that area nor outside the patient surface. By necessity the tint must be a closed area and so may have to follow along the skin surface. Where the corresponding isodose curve is not plotted, the tint boundary cannot be taken as accurate but only approximate.

2D compare dose control
Hit the "Display in Current Frame" button to display the dose in a current frame that contains an image from the primary image set or one fused to it. Hit “Display in Current Screen” to display in all the frames on the currently selected screen. This will not engage any particular frame however. If a 3D calculation has not been done, all frames in which the dose can be shown on the screen will be calculated and could take some time. You might want to consider reformatting a stacked image set on the main tool bar for a smaller set of images other than the entire stacked image set.
On the top row you can select which dose you want to see:
Computed: that computed here.
Foreign: that read from the other planning system.
Difference: the difference between the two.
You can select any combination of the above to display.
Below that, you can select the color the isodose curves are displayed in and the tint color. ONLY ONE of the three sets may have a value tinted in, and only a single selected value will be tinted. The tinted area is for the dose or greater. See also the note above about the tint area along the skin boundary. Select a dose value with the mouse to select the value to be tinted. For dose difference, doses smaller then the plan dose (minus) are shown in a different color from doses larger than the plan dose (plus).
Each set of isodose curves is shown in the same color, so that it will be easy to distinguish which curve belongs to which set. The SAME values are displayed for the computed and foreign doses. You can specify a separate value for the dose difference. You can select a dashed line for any of the three sets of isodose lines (Dosimetry Check result, the planning system, or the dose difference) with the corresponding toggle button. The line width sets the width for all three sets of isodose lines. The dash length sets the dash length for any dash that is selected.
Use the delete button to delete any currently selected isodose value. Use the delete all button to delete all the values from the respective list.
Note that the hot spot for each data set will be displayed in the same color as the isodose lines are drawn in. Hot spot is displayed with an ‘*” and can be turned off or on.
This control will disengage from the display if a different frame is selected as the current frame. Hit the "Display in Current Frame" button to reselect the frame or a different one.
Any color changes you make will be saved and also used as the default for new cases.
To engage this control with a current frame, you must first make a 3d room perspective view of the primary image set of the current plan or an image set fused to the primary image set. Use the "Screen Control" button to create a new screen if need be, and select an empty frame by clicking the mouse on the button covering an empty frame. Then go under "Stacked Image Sets" on the main menu to "Display Room View".
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Compare 3d Dose Control |
Select "Foreign Dose" or "Dose Difference", then hit the "Display Foreign Dose in Current Frame" button. This control will disengage from the current frame if you reselect the "Foreign Dose" or "Dose Difference" buttons, or if the frame is no longer current or visible. To reengage, simply hit the "Display Foreign Dose in Current Frame" button again. You may also select a different frame any time, with multiple frames showing the same or different display and dose values.
Selection of "Foreign Dose" will simply show the dose from the other system. "Dose Difference" will show the absolute value of the difference in dose between the other system and that computed here. Positive differences are shown in a different color than negative differences. The default for positive differences is red and for negative is cyan.
Type in the dose or dose different value to display in the provided text field, hitting the Entry key at the end of the number string. You can also change the transparency of the isodose cloud, and select wire frame instead of solid, as well as turn off the cloud display.
Lastly, you can change the color of the cloud for either the foreign dose, or the positive or negative difference.
The gamma method is a method to compare two dose distributions. The following publications are definitive:
“A technique for the quantitative evaluation of dose distributions” by Daniel Low, William Harms, Sasa Multic, and James Purdy, Medical Physics 25(5) May 1998, pp. 656-661. We refer you specifically to equations (4)-(8) on page 658. Another reference is Harms et.al, “A software tool for the quantificative evaluation of 3D dose calculation algorithms”, Medical Physics 25(10) Oct 1998, pp. 1830-1836 and Low et. al, “Evaluation of the gamma dose distribution comparison method”, Medical Physics 30(9) Sept. 2003, pp. 2455-2464.
Two isodose lines might be separated by a large difference, but the dose difference might be small if in a low gradient area. Likewise, there might be a large dose difference at a particular point, but in a high gradient area the distance to the same dose might be small.
The gamma method is a way of comparing two dose distributions taking both dose difference and distance into account.
Here we compute the gamma distribution comparing the dose distribution from the planning system, the reference distribution, to the dose computed here, the evaluation distribution. Given a point rr, the volume around that point is searched to find the minimum gamma value Γ, where gamma is computed according to the equation:

and where rr is at the location of the reference point, Dr(rr) is the dose at the reference point, dm is the distance criteria (0.3 cm for example), Dm is the dose criteria (for example 3% x 200 cGy/100 = 6 cGY). DM would typically be the target dose at isocenter. The user has to specify the value to use.
The search is done for all re in the rest of the volume. This means for every reference point rr for which is known a dose Dr, a search is done for all locations necessitating computing the dose De at each location re. Then finally we take the minimum of all the above gamma values for the value of gamma at rr:
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There are some practical considerations in implementing this calculation. The gamma value is computed for a regularly spaced lattice. The spacing in the lattice is for the same distance set for the dose matrices. Values are interpolated within this lattice for plotting the gamma distributions on planar images. The dose Dr from the planning system is interpolated from the down loaded dose matrix for each of the points in the gamma lattice. The dose De(re) is interpolated from a thee dimensional lattice of doses computed here.
The search is done in steps of 1 mm, re around each reference point rr. This search is limited to a radius not less than three times dm, nor less than 1 cm. For a value of dm = 0.3 cm, the radius will be not less than 1 cm. Searching for a larger radius in 1 mm steps would begin to use an exorbitant amount of computer time since the search volume for each reference point goes by the cube of the search radius.
We note that at a distance r from the point rr, the smallest the gamma value can take would be for the case when De = Dr, resulting in a gamma value of r/dm. Therefore at 1 cm and beyond the gamma value could not be less than 1/0.3 = 3.33. Therefore 3.33 is a lower bound on the gamma value at a radius of 1 cm and beyond. Therefore if at a given search radius of r, if the minimum gamma found within that volume (within that radius) is < r/dm, then there is no reason to search the volume at a larger radius because the gamma value cannot get any smaller. Likewise, by stopping the search at a radius r, minimum gamma values larger then r/dm have a lower bound of r/dm.
In addition, we will assign a sign to the gamma value at a point if the dose computed here at the point is greater (+) or less than (-) the plan dose. The resulting gamma is then shown in different colors where the gamma value is negative or positive.
The gamma method is selected from the Evaluation pull down menu on the plan toolbar. The popup control tool is shown below:

Gamma method control tool.
Using this tool you can display iso-gamma curves on 2D images or an iso-surface in 3D perspective views. The image must contain an image from the stacked image set or one fused to it. You must type in the reference dose in cGy. This reference dose is also used elsewhere in the program to compute dose difference percentage for specifically selected points. Hit the “Display in Current Frame” button to display the gamma distribution in the currently selected frame. The currently selected value is tinted (2D) or is the display value (3D). The hot spot is shown on both 2D and 3D displays. Or hit the “Display in Current Screen” button to display the currently selected values on all frames on a screen.
An example 2D display is shown below:

A volume histogram of the gamma function can be computed.

Gamma volume histogram.
An accumulative distribution or differential distribution may be shown depending upon the choice of a toggle button. The distribution may be shown for any selected outline region of interest. Shown here is an example for the entire patient model volume. Bins are created over the range of gamma value at regularly spaced intervals, here 0.1 in the example, and the points in the gamma distribution lattice is sorted into the appropriate bin. Black above shows the total gamma distribution, red the areas where computed dose was >= plan dose, cyan <= plan dose.
For the differential histogram, the volume at the top of the vertical axis will be the volume with the largest increment. For the accumulative, the volume value shown is computed from that covered by the dose matrix and is not necessarily the volume of the region of interest.
The percent of points less than or equal to a selected gamma value (absolute value) is computed and shown. And the same is shown for the subset of points that is greater than (or equal) to a specified threshold dose, in the example above 1000 cGy is the threshold value.