Proton beam therapy is a form of radiotherapy in which accelerated protons (charged particles found in atomic nuclei, notably comprising the entire nucleus of the hydrogen atom) are directed into tumours to destroy cancerous cells.
The rate of energy deposition from a beam of heavy charged particles into an attenuating medium is described by the Bethe-Bloch formula.  Importantly, the rate at which such particles lose energy to the material increases dramatically as the particles slow (in particular in the region βγ⪝4). This property gives rise to the characteristic energy deposition known as a Bragg curve, shown in figure below. The curve ends in a sudden, large deposition of energy over a very short distance at the end of the path of the beam.  This is known as a Bragg peak, and it is this property of the beam that allows the targeting of cancer cells while minimizing damage to surrounding tissue.
Fig. 1: The doses produced by a proton beam (labelled "native"), multiple proton beams (labelled "modified"), and an x-ray beam (labelled "photon") passing through tissue. The proton dose is an example of a Bragg curve. http://en.wikipedia.org/wiki/Bragg_peak.
For a given charged particle (such that the rest mass of the particle is a fixed parameter), the variables of the Bethe-Bloch formula are the velocity of the particle and properties of the material through which it travels. For a beam of such particles, the range of that beam and location of the corresponding Bragg peak are then fully determined by the energy with which the beam enters the material, if the properties of the material are well known. It is this behaviour that proton beam therapy seeks to harness to improve the outcomes of external radiotherapy for cancer treatment. 
Advantages of Proton Beams for Cancer Therapy
Since the radiation employed in radiotherapy to induce cell death in tumour cells can also induce cell death or carcinogenesis in healthy cells, it is desirable to minimise the dose deposited in healthy tissue. In X-Ray radiotherapy, the dose delivered to tissue decays exponentially with depth, after a short initial build-up. As such, for any single exposure to X-Rays, the tissue near the surface must be more heavily irradiated than the target volume for that target volume to receive a sufficiently high dose for treatment. Furthermore, some dose will necessarily be deposited beyond the targeted volume as the dose continues to decay exponentially beyond the target region.
Some typical ranges for protons in water are given in Proton ranges.
In the case of proton radiotherapy, the energy of the beam can be calibrated such that the Bragg peak lies within the treatment volume. This results in a relatively low dose along the path to the treatment volume (by comparison to the dose received at the treatment volume), with no dose deposited beyond the Bragg peak. Since the tissue volume targeted for treatment is typically larger than a single Bragg peak (which occurs in the last few millimetres of the beam path), many Bragg peaks are usually superposed to construct a region of uniform dose covering the treatment volume. This increases the dose delivered along the path to the target volume. It remains true that the target volume receives a larger total dose with none delivered beyond the target region.  As such, proton beams can deliver radiotherapy to deeper tissues more safely than X-Ray radiotherapy, due to the reduction in unintended exposure along the beam path. Proton beam therapy is also better suited to treating tumours situated in or near more sensitive or critical tissues, as no dose will extend beyond the target volume.
Technical Challenges: Imaging versus Treatment
As stated above, the position of the Bragg peak for a particle travelling in a material is dependent on the energy with which the particle enters the material, and on the properties of the material itself. Hence, the assumption on which the success of proton beam therapy depends is that the material properties of the patient, as relevant to the Bethe-Bloch formula, can be well understood. However, patients' tissues are typically imaged using X-Rays, which interact differently with matter than heavy charged particles do. It then becomes necessary to convert the measurements made using X-Ray imaging to equivalent values for proton therapy. This conversion introduces uncertainty into the calculation of the beam energies needed to target the patient's tumour.
Due to the precise nature of the dose deposition from a proton beam — exactly the feature that makes it desirable for cancer treatment — this uncertainty can make the difference between, for example:
- effectively treating a patient's cancer
- only irradiating a part of the cancer, or worse
- irradiating a highly sensitive tissue near to the targeted tissue volume.
For this reason, it is desirable to develop technologies to more effectively image the patient using protons. By more directly understand the interactions of the proton beam with the patientís tissues it may be possible to eliminate the photon-to-proton conversion step altogether, improving the accuracy of proton-based treatment.
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