# Treatment Planning

The radiotherapy process begins with referral – a patient will generally only meet with a radiation oncologist after having been diagnosed and having discussed treatment options (including surgery and/or chemotherapy). Following a consultation with the oncologist, the process of planning a treatment begins.

Dose deposition is not depth-conformal, so it isn’t possible to treat a tumour in isolation: surrounding tissue (upstream and downstream from the tumour) will be irradiated. Radiobiology provides a foundation for the specification of objective doses: prescriptions for tumours and tolerances for normal tissue. The goal of treatment planning is to design the beam delivery so as to minimise the dose to healthy tissue while delivering the prescribed dose to the tumour. Therapeutic strategies are designed on treatment planning systems (TPSs). For conventional external beam radiotherapy (the focus of this summary), the treatment plan is sent to the linear accelerator as a series of machine instructions.

The planning process begins with patient imaging. Contemporary planning systems require the acquisition of computed tomography (CT) data of the patient in their treatment position. This data may be augmented with magnetic resonance imaging (MRI) and/or positron emission tomography (PET) data. The tumour volume and normal tissue, including organs-at-risk (OARS), are contoured within the TPS as “regions of interest” (ROIs), in a process known as delineation. These ROIs can be defined manually or using automated tools such as CT number filters or reference volumes that can be adjusted to match the patient anatomy. A clinical treatment volume (CTV) is then constructed, extending the boundaries of the gross tumour volume (GTV) to account for microscopic spread of the malignancy. A planning treatment volume (PTV) again extends beyond this, to mitigate the effects of any patient movement, set-up errors and delivery uncertainties. The definition of these margins is recommended by the International Commission on Radiation Units and Measurements (ICRU, 1993; ICRU, 1999).

These ROIs have associated prescription and tolerance doses which constitute the clinical objectives of the treatment. An arrangement of beams, with specified energies; gantry, collimator and patient couch angles; and field shapes (Metcalfe et al, 2007), needs to be defined to meet these objectives. For a photon beam the highest dose is delivered within the first few centimeters depth: unfortunately tumours are often located deeper within the patient. As such, treatments are rarely as simple as a single beam incident on the patient. Multiple treatment angles are utilised, providing a relatively high dose concentration at the treatment volume (where the beams superpose) compared to the path of any single beam. This is illustrated in Figure 1 using isodose curves, a common method of visualising dose on a patient CT plane.

Figure 1: View of CT dataset at treatment isocentre overlayed with the following isodose curves: White (8 Gy), Purple (12 Gy), Blue (15 Gy), Aqua (18 Gy), Green (21 Gy), Yellow (24 Gy), Orange (27 Gy) and Red (30 Gy); for a simple 4 beam treatment.

When these beams are collimated to the projection of the tumour in the path of beam this technique is known as 3D conformal radiotherapy. Conventional radiotherapy treatments attempt to produce a uniform beam, but this isn’t necessarily desirable. Intensity modulated radiotherapy (IMRT) allows the variance of fluence over the field, especially useful in cases of concave-shaped tumours surrounding a critical organ.

Figure 2 illustrates how a simplified IMRT treatment is planned and delivered. The dark gray volume represents an organ at risk (the spine as an example), while the light gray volume represents the tumour treatment volume. The individual beams have different intensity profiles, decreasing the dose to the organ at risk, while increasing the dose to the treatment volume.

Figure 2: Intensity modulated radiotherapy treatment

The problem with these highly conformal treatments is the possibility that the treatment volume could shift from the planned position: through patient setup error, change in the patient physiology (a loss of weight during treatment is common) or internal organ movement. These errors can be minimised through the use of image guided radiotherapy: the acquisition of patient anatomy images immediately prior or during treatment.

The selection of beam arrangements is an optimisation process, either peformed manually by the radiation therapist or automatically, of iteratively adjusting parameters until the calculated dose distribution meets clinical objectives. The reliability of these dose calculations is important: any error in the dose calculation will result in a less effective treatment; especially as uncertainties in other aspects of the treatment chain are reduced through the use of treatment techniques such as IMRT and IGRT. Various opinions exist as to what constitutes an acceptable error: 2% to 5% overall (Carrasco et al, 2004; Wyatt et al, 2005) have been suggested in the literature.

### Dose calculation

Note: the definition of dose is defined on the Radiotherapy Physics page here.

The dose calculation algorithms that exist in standard TPSs can be assigned into two categories (Carrasco et al, 2004): correction-based and model (or convolution-superposition) based.

Correction-based systems apply correction factors to existing measured reference dose distribution data. A simple example of this approach is the data-driven Milan and Bentley (1974) system, developed in 1974. A number of measurements were made for the calculations here: 17 equidistant central axis doses and at 5 of these depths 46 off-axis ratios (23 measurements both left and right of central axis, expressed as a ratio of the central value). These 46 measurement locations were spread further apart at larger depths, such that the fan lines connecting the off-axis points met at the source. The off-axis doses at depths other than the 5 measured could be found by interpolation.

Reference measurements like these can be ‘mapped’ to the patient after a number of corrections: in the Milan-Bentley system corrections are applied for patient curvature, source-to-surface distance (SSD) and heterogeneous tissue; more recently effects such as scatter have been considered. An inverse-square law correction is required for patient curvature and treatment SSD: before mapping, each dose is multiplied by

${\left( \frac{\mathrm{SSD} + d}{\mathrm{SSD} + h + d} \right)}^2$

where d is the depth of the measurement point (in the Milan-Bentley system one of the 17 depths along the central axis), and h is the shift accounting for patient curvature (each off-axis fan-line, mentioned earlier, is shifted such that the first CAX dose measurement is located at the conventional depth in the patient). The simplest method to account for heterogeneities is to alter the depth of the corresponding dose according to the tissue density, for example, by treating a given width of lung tissue as a shorter mass-equivalent width of water.

This is representative of all correction-based systems, which calculate primary and scatter dose then apply corrections for inhomogeneities, oblique incidence, SSD, field shape and any present shielding.

Early implementations of density correction algorithms, such as the Batho power law and the TAR methods, weren’t able to accurately calculate doses in lung-equivalent media (Mackie et al, 1984), and while more recent algorithms, such as the modified power law (Thomas, 1991) offer improved agreement, the approach still fails in more complex cases: in relatively simple phantoms with water and lung-equivalent slabs errors of up to 39% (Carrasco et al, 2004) have been found. Dose calculations in the build-up region near the patient surface also tend to be poor, with reports of up to a 47% deviation (Lewis et al, 2000) at 1 mm depth. Effects such as the broadening of the penumbra in low density mediums are not predicted by four of the most prominent algorithms (Batho power law, modified power law, TAR methods and pencil beam approach) (Carrasco et al, 2004).

The weakness of these approaches, generally speaking, are that do not account for electron transport from particle interaction sites. Convolution superposition algorithms are a more complex approach, requiring greater computational power, and are the basis of dose calculations in the current generation of TPSs. This approach aims to determine the dose from first principles (Wyatt et al, 2005): the energy fluence beneath the treatment head is modelled and projected though the patient CT dataset, more specifically, the fluence is attenuated at intervals, using the relevant mass attenuation coefficient (μ/ρ), which are defined in terms of the physical cross section

$\frac{\mu}{\rho} = \frac{N_A}{A} \sigma$

where NA is Avagadro’s number and A is the mass number (Metcalfe et al, 2007). The result of this is the calculation of the total energy released per unit mass, or TERMA (T), for a given volume (the size of which is a parameter of the dose calculation):

$T = \psi \frac{\mu}{\rho}$

where Ψ is the energy incident on the unit mass. The TERMA is convolved with the energy deposition kernels, which indicate the remote deposition of dose from the interaction site, to produce an absorbed dose distribution. This approach allows, for example, the modelling of lateral electron scatter at heterogeneous tissue interfaces In the collapsed cone convolution (CC) algorithm, for example, the distribution of dose from the primary scatter site is characterised using polar angles, such that the deposition kernel function indicates dose within a cone (Metcalfe et al, 2007). These kernels are typically calculated for water and scaled according to tissue density and inhomogeneity (Mayles et al, 2007).

The results of these algorithms are much more accurate than those of correction-based approaches. Carrasco et al (2004) used the Helax-TMS system to calculate doses for heterogeneous slab geometries (with water, lung and cortical bone-equivalent materials) and found all predictions were within 2% of the measurements. A study by Francescon et al (2000) examined Pinnacle dose calculations for breast tissue, and the biggest discrepancy found was 2.5%.

The literature suggests that the results are not as impressive in complex phantoms. An investigation of the Pinnacle system by Wyatt et al (2005) used thermoluminescence dosimeters (TLDs) to measure deposited energy at 37 points in the pelvic region of a RANDO phantom and compared the results with the dose calculations. Nine of the 37 calculations did not meet the 5% standard, and 16 of the 37 were unacceptable under a 2% standard. The largest deviations were seen at points near bone, with a deviation of 35.7% at a TLD positioned on a bone-tissue interface.

Significant deviations in results can exist amongst the various algorithms, in a study by Paelinck et al (2005) involving dose assessment by radiographic film the average difference between calculated doses by Helax-TMS and Pinnacle systems was up to 7.6%. The magnitude of these disagreements depended on the treatment field size and the volume being assessed, it was highest in the lung equivalent region of the phantom used.

The calculation of dose allows the evaluation of a particular beam arrangement, which allows an optimisation. Traditionally the radiation therapist will define an arrangement of beams, and then manually optimise parameters until a calculated dose distribution is obtained that meets the clinical objectives. In IMRT treatments, however, the opposite approach is taken: the radiation oncologist specifies dose prescription and tolerance conditions for each region of interest (ROI), so called “objective functions” along with weights quantifying their importance. Clinical protocols contain requirements reflecting this understanding, for example, the Radiation Therapy Oncology Group (RTOG) studied the adequacy of target coverage for dose prescriptions where:

• at least 95% of the treatment volume receives the prescription dose,
• no more than 20% of the treatment volume receives greater than 110% of the prescription dose,
• and no more than 1% of the treatment volume receives less than 93% of the prescription dose.

Objective functions may also be specified in terms of the EUD. The TPS develops an initial beam arrangement to try and obtain that result. A ‘cost’ is calculated representing the level with which the calculated dose distribution fails to meet the clinical objectives. The beam arrangement is compared with ‘near-by’ arrangements (in which small changes are made), and if lower cost result is available, it is selected. This optimisation process is iteratively applied until a minimal cost is found (this search is not exhaustive). This process is referred to as inverse planning, though the term actually refers to the method of determining the fluence intensity pattern (Kian Ang and Garden, 2002).

The treatment planning system will generally present the calculated dose distributions over the CT data with isodose lines. A common tool for evaluating the dose calculation is the dose volume histogram (DVH), which specifies the percentage of a ROI that receives a defined dose, allowing a simple check, that, for example, 99% of the tumour receives 50 Gy.

Once a treatment strategy has been designed, and the dose resulting from each beam calculated, it needs to be translated into a set of instructions for the linear accelerator. The weight assigned to each beam/field (a measure of its relative contribution to the total dose) in the TPS needs to be converted to a measure of machine output, known as the meterset, a function primarily of the dose rate and the running time. This machine output is measured in monitor units (MU) which generally correspond to the delivery of 1 cGy maximum dose under reference conditions. The number of monitor units for an isocentric treatment can be calculated as (Philips Medical Systems, 2006):

$\mathrm{MU} = \frac{D_\mathrm{presc}}{\mathrm{TPR} \times \mathrm{OAR} \times \mathrm{S}_c \times \mathrm{S}_p \times \mathrm{TTF} \times (D/\mathrm{MU})_\mathrm{cal} \times (\mathrm{SCD}/\mathrm{SAD})^2}$

where Dpresc is the dose at the prescription point (in cGy), TPR is the tissue phantom ratio (a correction for change in SSD between reference conditions and patient treatment), OAR is the off-axis ratio (relating off-axis dose to central axis dose at a given depth), Sc is the collimator scatter factor (a correction in the number of MU due to radiation scatter in the treatment head), Sp is the phantom scatter factor (which quantifies the level of particle scatter in the patient for the given field size, and which is often accurately modelled by the dose calculation algorithm), TTF is the total transmission factor (quantifying the attenuation from any wedges or applicators), D/MU is the calibration dose (generally 1 cGy per MU), and (SCD/SAD)2 is an inverse-square law correction for the difference between the source-to-calibration distance (under reference conditions, often 110 cm) and the source-to-isocentre distance (generally 100 cm).

Many of these variables relate to ‘reference conditions’, the conditions for which linear accelerator commissioning and absolute dose measurements are made. These conditions vary across the various clinical protocols: though they generally involve the measurement of absolute dose in an ion chamber immersed in a water tank. The surface of this water might be located at, for example, 100 cm from the electron target (100 cm SSD), and the calibration measurement D/MU might be made at 10 cm depth (corresponding to an SCD of 110 cm).

### References

• Carrasco P, Jornet N, Duch M A, Weber L, Ginjuame M, Eudaldo T, Jurado D, Ruiz A and Ribas M, 2004. Comparison of dose calculation algorithms in phantoms with lung equivalent heterogeneities under conditions of lateral electronic disequilibrium, Medical Physics 31: 2899-2911.
• Francescon P, Cavedon C, Reccanello S and Cora S, 2000. Photon dose calculation of a three-dimensional treatment planning system compared to the Monte Carlo code BEAM, Medical Physics 27(7): 1579-1587.
• [ICRU] International Commission of Radiation Units and Measurements, 1993. ICRU Report No. 50: Prescribing, Recording, and Reporting Photon Beam Therapy.
• [ICRU] International Commission of Radiation Units and Measurements, 1999. ICRU Report No. 62: Prescribing, Recording, and Reporting Photon Beam Therapy.
• Kian Ang K and Garden A S, 2002. Radiotherapy for Head and Neck Cancers.
• Mackie T R, El-Khatib E, Battista J, Scrimger J, van Dyk J, Cunningham J R, 1984. Lung dose corrections for 6- and 15-MV x-rays, Medical Physics 12: 327-332.
• Mayles P, Nahum A, Rosenwald J-C, 2007. Handbook of Radiotherapy Physics: Theory and Practice.
• Metcalfe P, Kron T and Hoban P, 2007. The Physics of Radiotherapy X-Rays and Electrons.
• Milan J and Bentley R E, 1974. The storage and manipulation of radiation dose data in a small digital computer, British Journal of Radiology 47: 115-121.
• Paelinck L, Reynaert N, Thierens H, De Neve W and De Wagter C, 2005. Experimental verification of lung dose with radiochromic film: comparison with Monte Carlo simulations and commercially available treatment planning systems, Physics in Medicine and Biology 50(9): 2055-2069.
• Philips Medical Systems, 2006. Pinnacle3 Planning: Reference Guide.
• Wyatt M, Corredor C, Tamimi M and Miller L F, 2005. Comparison of treatment planning dose calculations with measurements and Monte Carlo calculations in a rando phantom, Radiation Protection Dosimetry 116: 461-465.