Definition of nonstochastic effects: We complete today the discussion of the late effects of radiation on normal tissue that obey dose-response relationships. These non-stochastic effects, as we discussed last week, are the ones for which a threshold dose may be found and for which higher doses produce more pronounced effects within an individual. By contrast, stochastic effects show no explicit dose-response relationship within an individual, but for which the probability of an effect may increase with dose. We will discuss these stochastic effects in the next two chapters.
Vascular damage:
As we discussed last week, one mechanism by which the late non-stochastic effects of radiation arise is damage to the blood vessels feeding a particular tissue system. In circumstances where this mechanism is predominant, we would expect the largest amount of radiosensitivity to occur in tissues that are heavily dependent on oxygen and other nutrients, and for which the vascular system is replenished frequently. The etiology of the damage is reasonably well understood: the endothelial cells lining the capillaries and small artierioles feeding a particular tissue type are damaged either through direct interphase death of the vascular cells, or indirect, i.e. through interference with the renewal of the cells in those small blood vessels. The direct effects might involve apoptosis of vascular cells. The indirect effects involve a multi-step process depicted schematically in fig. 11.1.
Stem-cell damage:Another underlying source
of late non-stochastic effects is damage to stem cells in parenchymal and
stromal tissue systems. If cells in a particular organ turn over relatively
rapidly, then as they die they must be replaced with stem cells that differentiate
to form the matured functional cells. If the stem cells are damaged before
they get a chance to differentiate, the organ will become less useful as
the pool of functional cells becomes depleted.
A system in which this second mechanism appears to predominate is the kidney. The individual nephron is the unit of functionality in the kidney; there the kidney performs its function of filtering out useless and hazardous substances from the blood stream and concentrating them for eventual excretion in the urine. Each nephron is built atop a tubule, and if the epithelial cells that mature into the tubule cells are destroyed, the nephron cannot function
Functional Subunits: Thus it is in the context of the kidney that the notion of a functional subunit;(FSU), i.e. a small element of tissue that can be regenerated from a single surviving cell without loss of functional integrity. The nephron is the functional subunit of the kidney, because if even one tubular epithelial cell survives to repopulate the tubules of a nephron, the nephron will survive damage. In a similar way the alveolus is the FSU of the lung.
Alpen's book describes the effects of radiation on specific systems in
some detail. We have encountered some of this discussion already, in the
accounts in ch. 10 of assay systems involving particular tissues like the
gastrointestinal crypts of the small intestine and the account in the early
part of ch. 11 of the effects on the kidney. Alpen takes us on a slightly
ghoulish tour of the organs of a mammal, outlining radiosensitivities and
mechanism in various organs. Here is a table summarizing Alpen's tour:
| System | Organ | Early Effects | Late Effects | Mechanism | Special Features |
| Gastro- intestinal |
Esophagus | Inflammation (high dose) |
Constriction | vascular | often damaged in radiotherapy |
| Stomach | damage to gastric pits | fibrosis, stenosis | vascular | ||
| Intestines | GI crypt damage | Thickening and atrophy | vascular, connective | blockage possible | |
| Rectum | constriction-> blockage |
as above | often damaged in radiotherapy | ||
| Mucosal Epithelium | Skin | erythema-> swelling | dermal fibrosis | microvascular | useful in dosimetry |
| bladder, oropharynx, ureters, vagina |
various | fibrosis | as with skin | similar to skin | |
| Hepatic | Liver | not much | reduced function; fibrosis |
vascular | sometimes damaged in radiotherapy |
| Renal | Kidney | reduced function | fibrosis and sclerosis |
stem cell; other | complex mechanisms |
| Lung | Lung | not much | inflammation | vascular; stem cells (surfactant) |
emphysema |
| Central Nervous |
Brain | Swelling | Necrosis | vascular | temp. change in blood-brain barrier |
| Spinal Cord | Paralysis | glial depletion; vascular | 2-year lead time | ||
| Visual system |
Eye | Cataracts | Damage in differentiation | hypersensitive to high-LET radiation |
Radiation therapists recognized early on that if they delivered a dose to a tumor there would be a larger therapeutic ratio (ratio of beneficial effects to harmful side-effects) if the dose were split up than if it were delivered all in one sitting. In the 1930's through 1950's studies of this effect were primarily carried out ad hoc in clinical settings, and some important results were derived. Animal models and an awareness of the mechanisms involved have provided a more sophisticated understanding of the effects of fractionation in the last four decades.
The Power Law.Strandqvist found in 1944 that
the dose required in order to produce a given biological effect was related
to the time over which it was delivered by a power law. If the totaldose
was D and the time over which it was delivered was T, Strandqvist's model
stated that, for dose effects on normal tissue, e.g. skin erythema,
D = q T1-p
where the exponent (1-p) appeared to range between 0.2 and 0.3 depending
on the tissue. Ellis showed that the number of treatments, as well as the
time that elapsed between the first and last treatment, mattered too. Ellis
proposed the following model for the "tolerance dose", i.e. the
dose that could be delivered to normal tissue before some form of damage
arose:
D = (NSD) T0.11
N0.24
This equation works reasonably for T measured in days. The "constant"
(NSD) in this equation is different for different tissues, X-ray hardware
and energy, and even methods of dosimetry, and it probably is not really
constant over a very wide range of values of T and N. To model the effects
of fractionation more effectively requires some awareness of what's going
on under the hood. In the 1980's some attempts were made to look under the
hood.
Examine carefully figure 11.3 (p.299) in the text. It shows semilog plots of surviving fraction against dose for various regimens, ranging from no fractionation (the steepest curve) to the condition under which maximum protection is afforded to the cells in question by fractionation (the flattest, and most linear, curve). In the intermediate cases the effect of fractionation is illustrated by the curved segments of the plots, each of which reflects a linear-quadratic response within a single fraction of the dose. As the dose is split up into fractions, some cells (the ones damaged in ways for which no repair mechanism exists) are killed outright, giving rise to the shallower-sloped sections of each plot. In the flattest curve, only this unrepairable damage influences survival, so the overall survival curve is log-linear. In the intermediate cases some damage follows LQ behavior between doses.
Douglas and Fowler developed a model for fractionated damage that reflects an awareness of repair mechanisms. Their model excludes repopulation of the cells in the damaged area through migration from other parts of the body. Alpen provides a rather confusing derivation of their model, which depends only on the following three assumptions:
Presumably for this model to be valid the repair mechanisms themselves should not be subject to radiation damage; otherwise the third of these assumptions might not hold.
Under these conditions we develop a linear-quadratic model for survival.
According to Alpen, it does not strictly depend on whether or not the cell-killing
process itself follows LQ relationships. Within that broad framework we
say that, for n doses each of magnitude D, the survival equation is
ln S = -n (αD + βD2)
Alpen provides a confusing discussion of this subject, but
the result given above is clear enough. The parameter that can
be derived by examining "isoeffect studies", i.e. investigations
of the dose fractionations that give rise to similar biological effects,
is the parameter α / β
i.e., an estimate of the ratio of the linear dose coefficient
to the quadratic coefficient. The larger this ratio is, the weaker the repair
effects are; the smaller it is, the more effective a particular tissue is
in repairing damage. Unfortunately this ratio is not unitless;
α is in units of inverse dose and β
is in units of inverse dose-squared, so the
ratio will be in units of dose. For doses measured in centigray
(rad) the ratio ranges between 5-30 cGy in tumors and tends
to be around 3-5 cGy for late effects and around 10 cGy in normal tissue.
Fractionation will tend to help if the ratio is larger in the tumor
than it is in the surrounding tissue. Some benefit may even be derived from
"microfractionation", i.e., providing several small doses a day over a
several-day period.
Your homework problem explores this possibility using the more naive
Ellis model.