# Physical Considerations in

In supervoltage X-ray or "photon" therapy the absorbed dose at a point in a patient depends mainly on two factors - the exponentially-decreasing transmission factor due to depth from the surface, and the inverse square factor due to divergence of the beam. We can estimate the effects of errors in patient positioning upon these factors from readily available data for the therapy fields used. For calculation points far enough from the surface and from beam boundaries due to collimator, blocks, or missing tissue, these estimates are a precise determination of difference from planned doses due to a change in these setup parameters.

At a depth in the patient, well beyond the buildup layer, 1.5 cm for 6 MV and 3.5 cm for 18 MV photon beams, the transmission factor for one cm of tissue can be found from a Tissue-Maximum Ratio table by dividing a TMR value by the corresponding entry one cm less deep, for representative field sizes and depths beyond the buildup region. Here are some examples:

 energy field size depth, d TMR(d) TMR(d-1) transmission,       per cm 6 MV 10x10 cm2 10 cm .792 .821 .9647 6 10x10 11 .763 .792 .9634 6 10x10 20 .537 .559 .9606 6 10x10 21 .517 .537 .9628 6 15x15 10 .813 .839 .9690 6 15x15 11 .786 .813 .9668 6 15x15 20 .568 .590 .9627 6 15x15 21 .548 .568 .9648 18 MV 10x10 cm2 10 cm .904 .922 .9805 18 10x10 11 .883 .904 .9768 18 10x10 20 .712 .730 .9753 18 10x10 21 .695 .712 .9761 18 15x15 10 .904 .922 .9805 18 15x15 11 .883 .904 .9768 18 15x15 20 .724 .740 .9784 18 15x15 21 .706 .724 .9751

So we can see that the change in transmission factor for 6 MV photons is about 3.6% per cm and for 18 MV about 2.3% per cm of depth, regardless of field size and depth, to within the precision of beam data measurements and roundoff errors in the table.

 An error in distance alone results in a change in intensity of the radiation beam which depends inversely on the square of the distance from a point source such as an x-ray target, since the emitted energy spreads over an area proportional to the square of the distance. The relative change in absorbed dose depends on the ratio of distances squared. Examples for 1 cm difference: (101/100)2 = 1.0201 (99/100)2 = .9801 (91/90)2 = 1.0223 (89/90)2 = .9779 (111/110)2 = 1.0183 (109/110)2 = .9819 Thus the difference in absorbed dose is about 2% per cm of displacement for points of clinical interest.

So what is the effect of a 1 cm error in determining the SSD for a single field, on the dose to a point at representative depth?

• The depth to a point in the patient is unchanged, so the 3.6% difference in transmission         for 6 MV does not apply.
• The 2% per cm difference due to distance error would apply.
• Errors in lateral positioning would be most critical, since the dose gradient at beam margins    is so high that dose differences are near 100% for points inside or outside a beam.
• What if we have parallel-opposed fields?  A 1 cm error in SSD setting is exactly balanced by an opposite error in the opposing field, provided we do not reposition the patient between fields but rely on the precision of gantry motion for the second setup.
• Positioning error does not affect depth, so transmission factors are unchanged.
• In a region where opposing fields are near equal weights, within about 10 cm of the midplane,       the effect of a distance error is almost perfectly canceled.
• Lateral positioning is still critical, and if a treatment plan includes opposed pairs of fields at right angles the lateral positioning requirement of the other pair of fields will be more critical than an    SSD setting.
What about an error in measuring the thickness of the patient? In parallel-opposed fields only half the error applies to each field, or else the whole error could be counted in one field that gives half the dose. Either way this error does not cancel.
• The error in absorbed dose is about 1.8% or 1.2% per cm for 6 MV or 18MV respectively.
• Errors due to distance will cancel when opposed fields are treated without repositioning the patient.
• Distance or thickness measurements might still be critical for patient positioning, not because of the few percent difference in absorbed dose but because of their effect in locating the target volume with respect to beam boundaries.
In the 1950's when gantry-mounted therapy machines were developed it was recognized that the center of rotation would be the point of greatest clinical interest, and the isocentric treatment planning system was developed in the 1960's. Tissue-Air Ratio measurements were made with the detector at a fixed location, for various field sizes and depths in a water phantom. This data was tabulated and used to calculate dose distributions at depth in the patient, by including an explicit inverse square factor in the calculation. The same system is used today with depth-dose measurements relative to an absorbed dose calibration at depth in a tissue-equivalent phantom and tabulated as Tissue-Phantom Ratio, Tissue-Maximum Ratio, or Tissue-Output Ratio.

What do we mean by ISOCENTER?

A point in the therapy beam which stays at the same place
during gantry, collimator, and table rotations.
Thus it is the coincidence of the gantry rotation axis (a horizontal line in space), the table rotation axis (a vertical line in space), and the collimator rotation axis (which traces a plane perpendicular to the gantry axis).

Why is it useful?

Because a radiation beam defined by symmetric collimator jaws is centered there.
But it is hiding inside the patient except at 100 cm SSD!!  To make the isocenter useful for patient positioning we use ORTHOGONAL pointer lights that project perpendicular planes, which cross in perpendicular lines that are the axes of gantry rotation (horizontal), table rotation (vertical), and collimator rotation (when set for a horizontal beam). These coordinate axes point toward the isocenter and can be used with skin marks to reproduce the patient position once it is established.

So we see that "ISOCENTRIC" treatment planning has two meanings:

1.
The system of depth-dose data relative to the dose at isocenter in a standard field geometry, as a function of depth of overlying tissue and field size in surrounding irradiated volume.
Treatment planning computer systems use this data format regardless of how depth-dose data was acquired and entered to the program system; accuracy of calculated dose distributions is better near the isocenter. Any plan that we enter to calculate isodose curves is handled this way internally by the program system, regardless of the conceptual system we use to specify treatment ports.
2.
The system of patient positioning so that multiple ports are treated without repositioning the patient because the center of gantry and table rotation, the isocenter, is the same point in the patient for every field.
We rely on the precision of mechanical rotations to achieve the geometry of combined fields that is planned, and errors in patient positioning result in compensating errors in dose distribution relative to the isocenter.

However we must rely on positioning aids to make the planned treatment volume coincide reliably with the anatomical target volume, and avoid geometrical misses which are the most frequent cause of failure in treatments which should have good prognosis.

1. Use isocenter pointer lights to establish ORTHOGONAL skin marks, opposed where possible,    to reproduce the patient position which has been established by fluoroscope, port films, or localization measurements. These points are not the isocenter, but they mark perpendicular axes pointing to the isocenter.
2. Use quantitative measurements to establish isocenter position relative to reproducible landmarks such as table surface, positioning devices, and bony anatomy.
3. Use mechanical motions such as table lateral, lift, and longitudinal displacement corresponding to     x, y, and z orthogonal displacement of the isocenter in the patient.

Finally, let us avoid confusion by using the term ISOCENTRIC TREATMENT PLAN to refer only to multiple-port plans where all the fields are positioned with the gantry isocenter at the same point in the patient anatomy.

When extended distances are required to achieve larger field sizes or because of access restrictions, a multiple port plan with axes crossing at a common point has been called TELECENTRIC.

Let us borrow from the vocabulary of earthquake geology the word EPICENTER to refer to a surface point above the phenomenon of interest. An EPICENTRIC TREATMENT PLAN is a multiple-port plan where various fields are positioned so that orthogonal skin marks are at the gantry isocenter. This was the standard system for cobalt treatments at 80 cm SSD. The target volume is centered at a point on the beam axis that is a different distance from the isocenter for each field, so this is NOT an isocentric plan, and it does not automatically compensate for distance errors because the patient is repositioned for each field.

Let us borrow also the term HYPOCENTER to refer to a focus below the surface. A HYPOCENTRIC therapy field is one where the gantry isocenter is at a depth in the patient but not at the same point for multiple ports in the treatment plan. For example the combination of AP and PA fields positioned for isocenter at the midplane, with lateral or oblique fields using a different location of the gantry isocenter in the patient, can be called a HYPOCENTRIC plan.

There may be good reasons for using such a plan, for example when the target volumes are different for an initial course of therapy and a planned boost, or when blocking or asymmetric collimator settings make the isocenter unusable as a representative point for the nominal dose prescription in some or all of the fields.

In such cases we must recognize the necessity to establish and locate appropriate calculation points so that absorbed doses from different fields to the same anatomical location can be added. Also we must establish different orthogonal skin marks or prescribe table motions to reposition the patient for each HYPOCENTER location.

Why do we use isocentric treatment plans?

Because the therapy machine calibration is measured at isocenter?

No. In a recent survey by the Quality Assurance Review Center, twice as many institutions used fixed-SSD geometry for machine calibration as used isocentric setups.

Because calibration is specified as absorbed dose at isocenter?
No. We have relative depth-dose data to calculate the dose anywhere.

Because our depth-dose data is formatted for calculating dose at any point relative to isocenter?
No, because computer programs are so fast and reliable that the time required to reformat the data is not a problem.

Because the same patient position can be used for several ports?
Yes, but we must get the right position to begin with.

Because distance errors compensate in parallel-opposed ports?
Yes, but lateral errors do not.

Because wedged fields need extra precision in relative location?
Yes, but SSD and depth errors do not compensate except for parallel-opposed ports.

Because we can use optical pointers (laser beams) and skin marks for positioning?
Yes, but this is also a good reason for fixed-SSD plans.

GS23DEC90:RTTEACH\PT_POSIT.DOC V694 ==> PtPosit.htm
Posted 6 August 1998 by  [Glen Sandberg]