Radiation biology (or radiobiology) is the field of study that examines the effect of radiation on living things. The wikipedia article on the topic provides a nice summary of the field’s history. This page discusses the cellular and biological aspects of the therapeutic use of ionising radiation.
Radiation Induced Damage
There are two processes by which tissue is damaged by ionising radiation: the direct ionisation of DNA and, more prominently (Boyer et al 2002) in traditional therapies, the indirect damage through the creation of free radicals in intracellular material. Direct ionisation is the most effective mechanism for damage, forming radical cations which lead to DNA strand breaks (Purkayastha et al 2006).
The indirect (or diffuse) effect of radiation involves the production of free radicals, predominately hydroxyl, in the intracellular volume (largely comprised of water). Electrons ionise the H2O molecules:
and then hydroxyl (·OH) is subsequently formed:
The hydroxyl radical can cause strand breaks by creating a radiochemical lesion when it diffuses into a DNA molecule. This will only occur when the radical is produced within approximately 10−8 metres of the DNA molecule (Metcalfe et al 2007). Hall and Giaccia (2006) suggest that two thirds of x-ray damage to DNA in mammalian cells is caused by the hydroxyl radical.
The production of these electrons by ionising radiation is discussed on the Radiation Physics page (not yet uploaded), along with ‘dose’, which is synonymous here with ‘absorbed dose’. While absorbed dose is the standard physical measure used to predict the effect of an exposure to radiation, the biological response also depends on the radiation type and the tissue exposed. Radiation with a high linear energy transfer (LET) is more likely to cause direct damage.
Still, it is possible to make generalisations regarding cellular response to external beam photon therapy: the median lethal dose values (level of absorbed dose that would result in 50% of total cells losing reproductive capacity) for malignancies are typically around 2 Gy (Tubiana et al, 1990). According to Mayles et al (2007) a typical tumour (weighing tens or hundreds of grams) might contain 109 clonogenic cells (potentially as few as 1% of the total cells). A simple substitution suggests it would take approximately 30 deliveries of 2 Gy to effectively ‘remove’ clonogenic cells, resulting in a total of 60 Gy absorbed dose (ignoring repopulation and other biological factors). The dose delivered in a clinical treatment will generally fall between 20 to 80 Gy total. Each delivery is referred to as a ‘fraction’, and the multiple fractions are typically delivered daily over the course of a few weeks. Fractionation is motivated by a number of radiobiological variables: it helps spare normal tissue through repair and repopulation, and increases tumour cell death via cell cycle synchronisation and reoxygenation.
The concentration of molecular oxygen in tissue has an effect on the impact of indirect damage. It is suggested by Molls et al (1998) that the free radicals produced by radiation are fixed in the presence of oxygen, which decreases the likelihood of cellular repair. This means that in low oxygen (hypoxic) cells such as in tumours, where the blood supply is poor, the likelihood of indirect damage is decreased. This is one of the reasons a radiotherapy treatment is fractionated: to allow re-oxygenation of the tumour cells between dose deliveries.
Bergonie and Tribondeaus’ Law states that radiation sensitivity is increased when cells are actively proliferating at the time of the exposure. Furthermore, excessive proliferation results in poor cellular differentation, so cancer cells are both more susceptible to damage and less able to repair it. This is another motivation for dose fractionation: to allow healthy cells to repair damage.
Since radiation does not significantly discriminate between healthy and cancerous cells, the potential consequences of exposure need to be considered. Swelling of soft tissue, ulcerations in mucous linings and hair loss may be deemed acceptable side effects. Similar swelling in critical organs might pose serious quality of life concerns or mortality risks. Necrosis can result from excessive levels of radiation in tissue. Long-term concerns can include infertility and the development of radiation induced malignancies. The goal of radiotherapy is to deliver the greatest therapeutic benefit: minimising complications in healthy tissue while maximising the damage, or control, of the tumour. Achieving this requires not only an accurate prediction of dose deposition, but also an understanding of how tissue responds to radiation.
The mean lethal dose is the amount of absorbed energy that results in 50% of the exposed cells being killed. The rate at which cells are killed on subsequent exposures drops off exponentially: an exposure of 2 times the mean lethal dose would kill 75% of the exposed cells. The surviving fraction (SF) of cells following an exposure to dose D can be defined as (Metcalfe et al 2007):
where k is the number of cells left alive, k0 is the inital number of cells and α is a constant of proportionality indicating radiosensitivity. This approach is simplistic: it is derived from “single-target theory” (Metcalfe et al 2007); where the SF is defined as:
where D0 describes the radioresistance of irradiated cells and is called the mean (not median) lethal dose (Niemierko, 1997).
This does not however match experimental cell survival curves because it does not consider cellular repair, the effect of multiple strand breaks, the relation of these two variables to dose rate, the delivery of doses in fractions, the periodicity of these deliveries and so on. This is the motivation for radiobiological modelling: to translate dose to more biologically relevant quantities (Metcalfe et al 2007).
This modelling begins with the linear quadratic model, where, for a single delivery of dose D, the cell survival curve is defined as
where α and β are linear and quadratic coefficients respectively, characteristic for a given type of tissue and often presented as an α/β ratio (Metcalfe et al 2007). These values are obtained via experimentation: cell colonies are seeded, irradiated, allowed to repair and then counted. The α/β ratios for tumours are typically higher than those of normal tissues, due to the faster rate of cell division. Typical ratios are 3 for normal tissue and 10 for tumours (Metcalfe et al 2007), though prostate cancer differs significantly in having a lower α/β ratio, with estimations varying between 1.5 Gy (Brenner and Hall, 1999) and 3.1 to 3.9 Gy (Kal and van Gellekom, 2003). In all cases α exceeds β.
The survival rate for a treatment split into n-fractions of dose D can be most simply expressed as
and so the linear quadratic model becomes, by substitution,
A motivation behind dose fractionation can be observed here: for late-responding normal tissue (which has a low α/β ratio), cell survival drops off more quickly for high doses (as the quadratic term dominates). When dose values are kept smaller, the linear term dominates, and this is generally higher for malignant tissue. The best therapeutic ratio can thus be obtained with small dose fractions. The linear quadratic model can be expanded to predict fractionation effects (Carlone et al 2006):
where T is the overall treatment time and γ is a parameter reflecting repopulation between deliveries, defined as
where Tpot is the potential doubling time, the time required for the number of cells to double.
TCP and NTCP
The linear quadratic model allows us to quantify cellular survival fractions in terms of dose deposition: which is one step closer to quantifying the tumour control probability (TCP) and the normal tissue complication probabilities (NTCP), by using the “critical volume model” (Niemierko and Goitein, 1993). These concepts require an understanding of tissue organisation: tissue can be described as consisting of functional sub-units (FSUs) (Niemierko and Goitein, 1993) which are inactive if all cells within it are killed. For a given organ (or tumour) we can define a complication (or control) as occuring when a given number of FSUs are made inactive.
For a tumour, the presence of an active FSU, which might be the result of a treatment which did not uniformly irradiate the tumour, increases the risk of recurrence (Metcalfe et al 2007), as an FSU is defined here as the volume that one clonogenic cell could repopulate (Niemierko and Goitein, 1993). Tumours are thus referred to as having parallel architecture: the probability of tumour control is strictly dependent on the number of FSUs killed, that is, control of the tumour requires all FSUs to be terminated. The probability of killing an FSU, PFSU, can be defined as (Niemierko and Goitein, 1993):
where k is the number of cells per FSU, which in the case of a tumour would equal the product of ρ, the clonogen density, and V the volume (Webb, 1993). The probability of killing M FSUs of a total N can be derived as (Niemierko and Goitein, 1993):
In the case of a tumour M=N and PN is referred to as the tumour control probability. For normal tissue PM is known as the normal tissue complication probability and M varies depending on `tissue architecture’. In organs with a parallel architecture, such as the kidney, where the inactivation of some nephrons will not necessarily result in a complication, M might be similar to N. In organs with a serial structure, such as the spinal cord, where the death of a small percentage of FSUs might have serious repercussions, M is quite small.
The TCPs and NTCPs discussed give some insight to what magnitude of dose might be desirable when designing a therapeutic strategy: the dose prescribed for the tumour is based on the size and stage of progression (related to the number of clonogenic cells) in order to give the greatest chance of tumour control, while tolerance doses can be defined for the organs at risk based on complication probabilities.
Calculated TCP and NTCP values can be combined in two ways: as an uncomplicated tumour control probability (UTCP), which is equal to
and as a therapeutic ratio, a ratio of doses for which the NTCP and TCP functions are equal (a measure of maximal displacement between the two functions) (Metcalfe et al 2007):
The dose to a volume is generally heterogeneous: so the these prescriptions and tolerances are often specified as dose-to-volume-fractions, for example, that 95% of the tumour needs to receive a dose of 50 Gy. Normal tissue tolerance doses might be more comprehensive, for example, according to Emami et al (1991), a radiation-induced inflammation of the pericardium surrounding the heart has a 5% likelihood of occuring within 5 years if the entire heart receives 40 Gy, if two thirds of the heart receive 45 Gy, or if one third of the heart receives 60 Gy.
Equivalent Uniform Dose
One way to translate the dose to a volume into a single quantity that considers the architecture of the tissue is by using equivalent uniform dose (EUD) (Niemierko, 1997), defined as:
where N is the number of dose points in a region of interest and a is a parameter that represents the organisation of the tissue. The EUD is equal to the mean dose in the structure for a=1, it tends towards the maximum dose for a>1 (which indicates a serial architecture) and tends towards the minimum dose for a<1 (which indicates a parallel architecture). This means that in a tumour, for example, the equivalent uniform dose would represent the smallest dose received by a clonogenic FSU: providing a useful measure of the dose to the tumour that could be compared to a prescribed dose.
Cellular radiation-induced damage is exploited for therapeutic advantage in radiation oncology, but care must be taken to limit the harmful effects of radiation. To this end threshold (or tolerance) doses are prescribed in treatment planning to minimise damage to normal tissue in the patient, and many precautions taken to prevent other parties (clinical staff and the general public) from being exposed to radiation.
Effects can be categorised as either stochastic (where probability of occurrence, but not severity, increases with absorbed dose) or deterministic (where occurrence is reliable beyond a threshold, and severity increases with absorbed dose). Stochastic effects may take a long time to manifest.
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