Think of calibration as a single known exchange rate: 1 MU buys 1 cGy, in water, at a fixed distance, at the depth of maximum dose, in a 10 x 10 cm field. Your patient differs from that reference in four ways, and each difference gets one correction factor:

1. Distance from the source to the point. Corrected by the inverse square factor.
2. Depth of tissue the beam crosses before the point. Corrected by PDD or TMR.
3. Field size, which changes how much scattered radiation reaches the point. Corrected by Sc and Sp.
4. Things in the beam such as wedges and block trays. Corrected by their transmission factors.

Every one of these factors sits in the denominator. If a factor is below 1 (deeper point, smaller field, a wedge), dose per MU falls, so you need more MU. If you remember nothing else, remember that direction. It lets you catch most calculation errors without finishing the arithmetic.

An MU is not a dose. It is a count from the ionization chambers in the treatment head, called monitor chambers, which sit in the beam path below the flattening filter (or where it would be, in flattening-filter-free beams). The beam passes through them, they collect charge, and the machine stops when the count reaches the set MU. Physics then tunes the chamber electronics so that, under reference conditions, 1 MU produces 1 cGy.

There are two monitor chambers, a primary and a secondary. If the primary fails, the secondary terminates the beam a few MU later. A backup timer stands behind both. Modern chambers are sealed, so their reading does not drift with room temperature and pressure.

How the machine gets calibrated

Absolute calibration follows the AAPM TG-51 protocol. Physics places a calibrated ion chamber in a water tank at 10 cm depth, 10 x 10 cm field, at either 100 cm SSD or 100 cm SAD, measures charge, and converts it to dose to water using the chamber's calibration coefficient and a beam quality factor, k_Q. Beam quality for photons is specified by %dd(10)_x, the photon-only percent depth dose at 10 cm. The clinic then uses its own depth dose data to carry that measured dose back up to dmax, where the "1 cGy per MU" convention is usually defined.

The convention that changes your arithmetic

Clinics define their reference point in one of two ways. You need to know which, because it decides the inverse square factor in an isocentric calculation.

The photon beam spreads from a nearly point-like source. The same number of photons passes through every cross-section of the beam, but the cross-section's area grows with the square of the distance. Photon fluence, and the dose it produces in air, therefore falls with the square of distance from the source.

Example: a point at 100 cm receives 100 cGy. At 110 cm it receives 100 × (100/110)² = 82.6 cGy. Ten percent farther away costs about 17 percent of the dose.

Inverse square describes the primary beam in air. Inside a patient, attenuation and scatter also act, which is why we need depth dose tables. Inverse square still appears inside every MU equation, but only to account for the change in distance between the calibration point and your point.

Photons do not deposit dose directly. They hand their energy to electrons (mostly by Compton scattering at therapy energies), and those electrons deposit dose along their tracks as they slow down. Megavoltage photons throw electrons mainly forward, and those electrons travel centimetres before stopping.

At the skin, few electrons have been set in motion yet, so dose is low. With each millimetre, electrons generated above add to those generated here. Dose rises until the number of electrons entering a small volume equals the number leaving it. That balance is called charged particle equilibrium, and the depth where dose peaks is d_max. Past d_max, the photon beam is being attenuated, fewer electrons are produced, and dose falls.

Because higher-energy electrons travel farther, d_max moves deeper as beam energy rises. That is the physical basis of skin sparing, and the reason high-energy beams spare skin better.

What raises surface dose

Anything that adds electrons above the skin: larger fields (more electrons scattered from the head and air), a block tray or anything else close to the skin, bolus, and oblique incidence. Surface dose for a 6 MV 10 x 10 field at normal incidence is roughly 15 to 25 percent; it is lower at higher energy.

Percent depth dose (PDD) is the dose at depth d on the central axis divided by the dose at d_max on the central axis, times 100, for one beam at a fixed source-to-surface distance (SSD). The point and the reference point are at different distances from the source. That detail is why PDD depends on SSD and why it is the natural quantity for SSD setups.

The SSD effect is the one residents miss. At 100 cm SSD the d_max point is at 101.5 cm and a 10 cm point at 110 cm, an inverse square ratio of (101.5/110)² = 0.851. At 120 cm SSD the same depths sit at 121.5 and 130 cm, a ratio of 0.874. The deep point loses less to distance, so its PDD is higher. The absolute dose rate is lower at extended SSD, but the shape of the depth dose curve is more penetrating.

Correcting PDD for a different SSD: the Mayneord F factor

PDD tables are measured at one SSD, usually 100 cm. For an extended SSD treatment (large fields, TBI, a patient who does not fit), you scale the table value by the Mayneord F factor, which corrects only the inverse square part of the change.

Modern treatments are isocentric. The machine rotates around a fixed point, the isocenter, 100 cm from the source, and we place the tumor there. From one beam to the next the point stays at 100 cm; what changes is how much tissue lies above it. PDD is clumsy here because it ties depth and distance together. We need a ratio where the point stays at the same distance from the source and only the depth of overlying tissue changes. Three such ratios exist.

TMR depends on energy, depth and field size at the point. It does not depend on SSD, because both doses in the ratio are measured at the same distance from the source, so inverse square cancels. That independence is exactly why it works for isocentric setups.

TMR is always at least as large as PDD at the same depth and field size beyond d_max, because PDD contains an extra inverse square fall-off. At 6 MV, 10 x 10, 10 cm deep: TMR ≈ 0.79 while PDD ≈ 67%.

Open the jaws and two things increase. More of the treatment head (mainly the flattening filter) is visible from the point, so more photons scatter out of the head toward it. And more patient tissue is irradiated, so more photons scatter within the patient toward it. The two are separated because blocking and MLC shaping change them differently.

Rectangles and circles: equivalent square

Tables are indexed by square fields. A rectangular field gives the same central axis scatter as a square field of the same area-to-perimeter ratio (Sterling's rule).

Typical sizes of the effect

For a flattened 6 MV beam, S_c runs roughly from 0.96 at 4 x 4 to about 1.05 at 40 x 40; S_p spans a similar range. A field-size error of a few centimetres therefore moves dose by 1 to 3 percent. Small fields (below about 4 x 4) are a different regime: the source is partly hidden, lateral equilibrium is lost, and output drops steeply. That belongs to the SRS module.

Anything placed in the beam is handled with a transmission factor: dose on the central axis with the device divided by dose without it, same MU. It sits in the denominator with everything else.

Every hand calc on the exam is one of these two equations. Read them as the "one idea" from section 01 with every correction written out.

This runs the equations above on a teaching model of a 6 MV and an 18 MV beam. It shows every factor, so you can change one input and watch which factor moves. Use it to check your own hand calcs from the worked examples; never use it for a patient.

Work each one on paper before opening the solution. Factors are given in the problem, as they are on the exam; the method is what you are practising.

You will not hand-calculate a VMAT plan, but the same physics decides whether a plan's MU look reasonable, whether a setup discrepancy matters, and what to ask when a number looks wrong.

Ballpark numbers to carry in your head

The independent MU check

Every plan gets a second, independent calculation of MU, by hand or with separate software, before first treatment (AAPM TG-114 covers this). For simple geometry the two should agree within a few percent; heterogeneous anatomy, small or highly blocked fields, points far off-axis and oblique surfaces justify wider tolerances, and each clinic sets its own action level. IMRT and VMAT are verified differently, through patient-specific QA measurement or an independent dose recalculation, because a single point calculation cannot describe a modulated field.

When the planning system and the check disagree, the usual reasons are predictable: lung or bone heterogeneity (the hand calc assumes water), a point near a field edge or in a steep gradient, missing tissue or oblique incidence, a wrong field size in S_c or S_p, or a forgotten wedge or tray.

Sources

1. American Board of Radiology. Radiation Oncology Qualifying Exam: Study Guide for Medical Physics for Radiation Oncology (2023 domain ranges).
2. Khan FM, Gibbons JP. The Physics of Radiation Therapy, 5th ed. Chapters on dose distribution, scatter analysis and dose calculation.
3. Ford E. Primer on Radiation Oncology Physics. CRC Press, 2020.
4. Almond PR et al. AAPM TG-51 protocol for clinical reference dosimetry of high-energy photon and electron beams. Med Phys 1999;26:1847.
5. Stern RL et al. Verification of monitor unit calculations for non-IMRT clinical radiotherapy: AAPM TG-114. Med Phys 2011;38:504.
6. Burmeister J et al. ASTRO core physics curriculum for radiation oncology residents. IJROBP 2015.

The interactive explorer and calculator use a simplified beam model fitted to typical published 6 and 18 MV behaviour. They teach direction and magnitude. Clinical numbers come from your machine's commissioning data.