Dose calculation algorithms are based on the physics of radiation interactions within tissue. Because of the complexity of the physics of these types of interactions, the algorithms usually involve simplifications allowing the calculations to be completed fast enough to be useful to the treatment planner. These simplifications result in approximations to the complicated physics, and therefore the algorithms have inherent uncertainties and generally work well only over a limited range of conditions. Usually, the more complex algorithms handle the physics in more detail, but also require longer calculation times. The extreme example of this is Monte Carlo calculations, which can take hours to days, depending on the mode of treatment and the complexity of the plan, although recent commercial clinical versions for electron beams can be calculated in minutes (47) and photon beams from minutes to hours (48). To be practical, a clinical algorithm should generate dose distributions nearly in real time but usually in seconds. The details of the algorithm implemented on a given commercial TPS are not in the control of the user. The user’s choice of algorithms is limited to what is provided by the different manufacturers and ultimately to the algorithms supplied with the system purchased.

Once a developer of a TPS has determined the nature of the algorithm, the algorithm must be coded into software. This software must include appropriate input–output routines, image display and manipulation routines, options that allow the user to define the treatment technique, and plan optimization and evaluation routines. The development of the software is not under the control of the user. It is the responsibility of the developer of the software to ensure that the algorithms are properly coded.

It is important for the user to have some knowledge of the nature of the dose calculation algorithms, since a knowledge at some level will help understand their capabilities and limitations. Furthermore, a basic knowledge will also help the user diagnose specific TPS problems and can be of some help in developing a QA process. A detailed description of different dose calculation algorithms can be found in Chapters 7 to 10. A broad overview of dose calculation algorithms has also been given by Van Dyk et al. (45) and a detailed report on external beam tissue inhomogeneity corrections for photon beams has been produced by AAPM Task Group 65 (49). In recognizing that the detailed description of algorithms was also beyond the scope of the IAEA TRS-430 (15), the report provides a series of questions that users may want to address either as part of the search process for a new TPS or in attempting to understand the calculation algorithm(s), currently available on their TPS. Thus, it includes 14 tables addressing different issues related to TPSs. To give an idea as to the subjects covered, the titles of these tables are summarized in Table 11.2. Table 11.3 is an example of one of the tables in IAEA TRS-430 (15) and shows questions related to external beam dose calculation algorithms in a water-like medium without any beam modifiers.

For brachytherapy, an interesting review of the evolution of treatment planning has been provided by Rivard et al. (50).

All algorithms, even sophisticated Monte Carlo procedures, require a basic radiation data set as input. For the standard commercial TPS, these data are determined for each energy on each therapy machine in every radiation therapy department. The quality and accuracy of such data depend on the user of the TPS. Such data are always determined over a limited range of conditions. Thus, calculations that extend beyond the range of the original

measured data may be subject to question, depending on the extrapolation procedures used by the calculation algorithms. Furthermore, measured data have their own inherent uncertainties and depend on the type and size of detectors used and the care taken by the experimentalist to generate the data. The accuracy of the measured data also depends on the stability of the radiation therapy machine and its ability to yield the same kind of radiation characteristics from day to day and hour to hour.

The measured data required by TPSs at minimum are relative, in the form of dose ratios, with the denominator being the dose under some reference condition. Any TPS capable of calculating monitor units (MU) or treatment times also requires absolute information in the form of MUs per gray or grays per minute. These data are all part of the input data set required by the TPS. The quality of the input data depends entirely on the therapy machine reproducibility, the quality of the measurement tools, and the expertise of the individual generating the data.

Finally, the clinical use of the TPS requires patient-specific information in the form of patient contours, usually generated with the aid of CT and/or MRI. Appropriate parameters must be entered to determine the treatment configuration. Dose calculations are usually performed for each beam independently, with the summed doses displayed on a video monitor or printed on paper. This clinical application of treatment planning depends entirely on the user and his or her knowledge of the capabilities and limitations of the TPS. Admittedly, the newer inverse planning optimization routines (3) used for IMRT are automated and leave little in the control of the user other than entering the dose-volume constraints as required by the objective function for the optimization.

According to the dictionary, specification is defined as “a detailed, exact statement of particulars, especially a statement prescribing materials, dimensions, and quality of work for something to be built, installed, or manufactured” (51). In the context of treatment planning computers, specifications are required at two levels at least. First, the user needs specifications to determine what type of TPS to purchase. Second, the specifications determine the standards for acceptance testing and QC. Rigorously speaking, purchasers should develop their own specifications and go through a tendering process to determine which system best meets those specifications. Practically, manufacturers of TPSs, as well as other therapy equipment, usually provide specifications that define the capabilities of their equipment. For TPSs, the specifications tend to be much more complex than for other equipment because they have so many components. The computer itself can be considered the heart of the system. Attached to the computer are input and output devices, which usually include network connections, possibly some type of magnetic or optical media for backup storage, laser disks, digitizers, film scanners, video displays, and printers. In addition to the hardware, software provides the major capabilities for calculation and display. Software specifications include detailed descriptions of what the software is capable of doing and how accurate the calculations can be made.

Upon the installation of any new device, the user should assess the device to ensure that it behaves according to its specifications. For a TPS, this takes at least two forms: assessment of the hardware and the software. The latter can also be divided into several components, including assessment of the integrity of the operating system, external beam dose calculations, brachytherapy dose calculations, image transfer, and image display.

Commissioning is the process of putting the system into active clinical service. This process includes the production of a basic radiation database, which is entered into the TPS, after which the user tests the system over a range of clinically relevant conditions. Quality evaluations of the programs’ outputs are then made. Such a process cannot test all the system’s pathways or subroutines; however, it does provide the user with a level of confidence over a wide variety of often-used treatment conditions. In addition, it helps the user understand the degree of uncertainty associated with these specific calculations.

As indicated earlier, QA and QC are closely related. QA is the total process required to ensure that a certain level of quality is maintained for a defined product or service. QC specifically consists of systematic actions necessary to ensure that the product or process performs according to specification. This process contains three components: (a) the measurement of the performance, (b) the comparison of this performance with existing standards or specifications, and (c) the appropriate actions necessary to keep or regain agreement with the standard.

In summary, QA and QC first necessitate defining a series of specifications. Acceptance tests ensure that the system meets the basic requirements as defined by the specifications. Commissioning makes the computer ready for clinical use and provides a series of standards that can
be used for ongoing QC to ensure that the system is maintaining the standards. Ongoing QC must be performed at intervals to confirm that there have been no changes in the basic radiation and machine parameter data files, in the input–output hardware, or in the CT, MRI, or other imaging-related software or hardware.

Patient data can be derived in various ways, including simple methods of external contour determination and various imaging modalities, most commonly CT. The important issue at this stage of planning is to ensure that the patient is positioned identically to the eventual treatment position and that the derived data represent this position (52). It is important that the data be transferred accurately to the TPS. If a digitizer or film scanner is used, the QA process must ensure the accuracy of the input data. Also, any conversions of digitized data, such as the conversion of CT numbers to electron densities, must be handled accurately by the system.

Once the data have been captured by the TPS, the treatment planner can manipulate the information, look at the data on various slices, and allow the system to perform reconstructions of images. With the patient data on the computer, the radiation oncologist is able to outline target volumes on the appropriate slices as well as the critical structures. While it is well recognized that different physicians can produce large variations in target volume definition for the same patient (53,54,55,56), the accuracy of the display of patient data is important for the next step of the planning process, that is, placement of radiation beams.

Beam placement is often performed with the use of a cursor or a mouse, as well as the keyboard to enter some needed parameters such as field size, beam direction, and collimator rotation. At this stage, various options can be used for the definition of the field shape. These include outlining the irregular field shape in its entirety with the mouse, defining the rectangular field and then adding shaped blocks, using the planning target volume and allowing an automatic preset margin, and automated field definition for the multileaf collimator. In each case, the beam edges can be displayed either on a beam’s-eye-view perspective or as perspectives of the beam edges intersecting any specified plane. Associated with the beam edge display, information demonstrating gantry angle, collimator angle, beam energy, and collimator size should also be displayed on the screen.

Once the beam geometry has been determined, the dose distribution can be calculated and displayed. Displays vary from simple colored isodose lines to color washes to individual point doses. The accuracy of the geometric correctness of isodose lines on the display is very difficult to assess, although very specific phantom geometries, whereby one can assess the position of a specific isodose line can help with this process. Doses calculated at individual points can be correlated to the isodose lines as well as measured data.

Dose-calculation output can be provided on a printer, often in color. Screen dumps allow for a quick copy of everything displayed on the screen. The screen hard copies usually are not on a one-to-one scale, even though this is often preferred by the radiation oncologists for assessing the distribution and making necessary changes.

Specifications take various forms. One form is simply a statement of whether the system is capable of doing a particular function or not. Another form is quantitative, for example, speed, number of images it can hold, and so on. A third form is a statement of accuracy. This is

particularly relevant for dose calculations. To assess the accuracy of a system and to define realistic accuracy specifications it is necessary to understand the sources of uncertainties.

The determination of uncertainties in dose calculations is complex because dose calculation algorithms depend on input information, which is usually generated by measurement. Thus, the uncertainty in the calculation output depends on the uncertainties associated with the measurements as well as the limitations of the calculation algorithms. Measurements are of various types, including relative doses in water phantoms, absolute dose calibrations for MU calculations, patient anatomy using imaging techniques or contouring devices, thickness profiles of physical wedges, compensators, or bolus, and distances from x-ray films and optical indicators. Further inaccuracies can be generated by output devices such as printers and screen dumps. Inaccuracies in image display can affect the choice of beam arrangements or field sizes used to cover specified target volumes. Similarly, image distortions can lead to incorrect manual dose optimization procedures.

Criteria of acceptability for dose calculations have been described by various authors (9,11,57,58,59,60). Task Group 53 of the AAPM (14) and IAEA TRS-430 (15) also include discussions on criteria of acceptability and tolerances generally considered achievable. Criteria of acceptability are very dependent on the region of calculation. Greater accuracy can be achieved on the central ray in a homogeneous phantom than in the penumbra region at the beam edge. Generally, four regions can be considered: (a) regions of low dose gradient in the central portion of the beam, (b) regions of large dose gradients such as that occur in the penumbra or in the fall-off region for electron beams, (c) regions of low dose gradients in low-dose areas such as that occur outside the beam or under large shielded areas, and (d) doses in the buildup or build-down regions at the entrance and exit surfaces of the patient. Criteria of acceptability are generally quoted as a percent of the reference dose except in regions of high dose gradients, where a spatial agreement in millimeters is a better descriptor, since the dose uncertainties in such regions can be very large.

Criteria of acceptability should include a statement of confidence. In other words, if we assume that the criterion of acceptability is an accuracy of 2% of the dose calculated on the central ray of the beam for a homogeneous phantom, then the question is whether all the calculated doses on the central ray are within 2%, or does the 2% represent one standard deviation (68% confidence) or two standard deviations (95% confidence)? For one standard deviation, 32% of the results may lie outside the stated criterion of acceptability. This is an important consideration, since ambiguities in these criteria can generate tremendous frustration from the user’s perspective as well as some troublesome legal interactions with manufacturers of TPSs. By way of example, Van Dyk et al. (11) produced some tables of criteria of acceptability clearly outlining the system’s general capabilities. Tables 11.5 and 11.6 are similar to the Van Dyk data, but some adjustments have been made in the numerical values to indicate a slightly tighter range of acceptability reflecting improvements in dose calculation algorithms available with modern TPSs. These criteria of acceptability represent one standard deviation about the mean. Venselaar et al. (60) have used a somewhat more complex, but more rigorous, definition of a “confidence limit” and this has been discussed in IAEA TRS-430 (15). It should also be noted that calculation accuracies depend not only on the input data and the limitations of the algorithms, but also on the user’s performance of the calculation, which includes issues such as the choice of grid spacing. Grid spacing can have a large effect on the accuracy of dose calculations, especially in regions of high dose gradient.