This latter feature is illustrated by the cartoon in Fig. 4.26, showing an example of a fractionation regime (with dose fractions of d) for two different cell types having dose-response curves characterized by different shoulder regions (curves shown together in the small insert), one with a broad shoulder (small α) and one with a small shoulder (large α). The two dashed lines shown in panel (b) indicate the difference in response for the two cell types. If radiation is given continuously at a dose rate low enough for the cells to complete repair of all sublethal damage at the same rate as they were induced, the β-term of the LQ model will not contribute (all sublethal damage would be repaired before they could cowork to produce potentially lethal damages). This would be equivalent to very many very small doses and the response curve would be a tangent to the initial part of the dose-response curve for acute irradiation. Continuous irradiation at such a low dose rate results in the largest difference obtained for the two cell types.

A and B line graph of surviving fraction versus dose, a decreasing value at an angle d, and the inserted graph of the same.

Fig. 4.26
A cartoon to illustrate the difference in sparing effect of fractionated irradiation versus acute irradiation for two cell types having dose-response curves with a broad (late-responding tissues, panel (a) compared to a small (early-responding tissues, panel (b) shoulder region. The small insert shows the curve shapes after acute irradiation to compare. In conclusion, even if cells characterized by a broad-shouldered dose-response curve are the most sensitive ones to high acute doses, these cells are the most resistant ones to fractionated or low dose rate irradiation


A and B line graph of surviving fraction versus dose, a decreasing value at an angle d, and the inserted graph of the same.


One should notice that the final slopes of the single-dose curves indicate that the cells having the broadest shoulder are in fact more radiosensitive than those having the smallest shoulder at high single doses. Still, with fractionated or low dose rate irradiation it is the other way around. This phenomenon is an important principle, which is the basis for radiotherapeutic practice.


In radiotherapy, it is customary to express this principle in some other words as based on the LQ model. The sparing effect of fractionated or low dose rate irradiation as compared to acute irradiation is most pronounced for cells having a dose-response curve with a small α-parameter.


Cellular radiosensitivity varies with cell cycle stage. At the same time, ongoing low dose rate irradiation may activate cell cycle arrest in the various restriction points in the cell cycle as has been explained by the activation of regulatory cascades related to p53 (at G1k) and the ATM-kinase activated by DNA-DSB. This gives rise to an inverse dose-rate effect (Fig. 4.27), where at very low dose rates cells may see an increase in cellular killing.

A decreasing line graph of surviving fraction versus dose for acute high dose rate 1 gray per minute, lower dose rate 0.37 gray per hour, low dose rate 0.8 grays per hour, threshold dose rate, and the increasing dashed line hormesis.

Fig. 4.27
The effect of dose rate on the cell survival curve. Repair processes are the primary mechanism that adjusts survival curves as the dose rate decreases from an acute level (~1 Gy/min) to a low level (~0.8 Gy/h). An increase in the slope of the cell survival curve (indicating an increase in radiosensitivity, the “inverse dose rate effect”) occurs due to the redistribution of cells throughout the cell cycle when the dose rate further decreases from ~0.8 Gy/h to 0.37 Gy/h. Finally, increased proliferation of cells occurs as the dose rate decreases further towards a threshold or critical dose rate, which varies by cell type. Notice that this cartoon presents a very special case of a cell type having an inverse dose rate effect, which is probably associated with a simultaneous lack of both p53- and pRB-function. The dose rate that can produce a hormetic effect is unclear and not indicated, but is several orders of magnitude lower than the lowest one depicted here (0.37 Gy/h)


A decreasing line graph of surviving fraction versus dose for acute high dose rate 1 gray per minute, lower dose rate 0.37 gray per hour, low dose rate 0.8 grays per hour, threshold dose rate, and the increasing dashed line hormesis.


The standard approach to the explanation of this effect is that cells progress to G2 and undergo a “block” in the G2 phase during ongoing very low-dose irradiation. As cells are radiosensitive during G2, much of the radiation is delivered during a radiosensitive phase of the cell cycle. While the mechanism has some clarity, work by Furre et al. in 1999 [134] and 2003 [135] on the effects of lowering dose rates on the survival of a cervical cancer cell line, NHIK 3025, and a breast cancer line, T47-D, has added a further degree of molecular evidence as to the origin of the effect. Of the two cell lines, only the NHIK3025 had an inverse dose rate effect. Both the NHIK 3025 cells and the T-47D cells lack p53-function, but unlike NHIK 3025 cells, T-47D cells have normal pRB-function. They found that T47-D cells accumulated in G2 during low dose rate irradiation in the same manner as the NHIK 3025 cells, but the T-47D cells still remained resistant during the arrest. The effect of pRB-function here appears to be key. Although pRB is normally not bound to the cell nucleus in G2 (only in G1), the nuclear-bound pRB increased in the arrested cells during radiation-induced prolonged G2 arrest. Although the mechanism for this seeming protection is not clear, there are indications that pRB may have a special protective function under severe cellular stress and that this is not limited to any special cell cycle phase.


Over time, and as radiobiological experience increased regarding the radiation response of cells of different types and from different organs, etc., it was gradually realized how the initial slope of the dose-response curve is of fundamental importance in radiotherapy. This has to do with the observation demonstrated in Fig. 4.28 above, showing the importance of the initial slope of the dose-response curve regarding cellular sensitivity to a fractionated radiation with time for sublethal damage (SLD)-repair between dose fractions. Of equal importance are the two following general observations:
Cells that are mainly proliferating such as cancer cells or some normal stem cells, all seem to have dose-response curves with a large initial slope (i.e., a large α). Such cells are denoted as “early responders” since radiation damage induces cell loss early under ongoing irradiation. Most of these cells enter mitosis within a few days after the start of the radiation treatment. Thus, the cells express a response to the radiation early after the onset of treatment.

Cells which are more prone to stay in the resting phase, like differentiated cells or cells in tissues where growth factor or mitogen stimulation is low, largely seem to have dose-response curves with a small initial slope (i.e., a small α). Such cells are denoted as “late responders” since radiation damage induces cell loss at a late stage after the onset of the treatment. Most of these cells enter mitoses weeks or even months after the start of the treatment. Thus, tissues of such cells express a response to the radiation late; not only late after the onset of the treatment but in many cases long after the end of the treatment.

An error line graph of blood activity versus the total dose of the iso-effect corresponds to a single dose of 16 gray presents at the center. The values are increasing trends.

Fig. 4.28
Mice of age 9–11 weeks were given fractionated irradiation with 240 kV X-rays to the dorsal trunk over a period of 3 weeks (i.e., more than one fraction per day for regimes with 32 and 64 fractions). Chromium-51-ethylene-diamine-tetra-acetate ([51Cr]-EDTA) was injected intraperitoneally (i.p) 26 weeks after completed irradiation and the blood level of radioactivity was measured in blood samples taken 60 min after injection. Increasing blood levels indicate reduced kidney filtration capability and the red line indicates an isoeffect level of reduced kidney function. [Modified from [136] with permission [136], © 2022 Radiation Research Society]


Cells that are mainly proliferating such as cancer cells or some normal stem cells, all seem to have dose-response curves with a large initial slope (i.e., a large α). Such cells are denoted as “early responders” since radiation damage induces cell loss early under ongoing irradiation. Most of these cells enter mitosis within a few days after the start of the radiation treatment. Thus, the cells express a response to the radiation early after the onset of treatment.


Cells which are more prone to stay in the resting phase, like differentiated cells or cells in tissues where growth factor or mitogen stimulation is low, largely seem to have dose-response curves with a small initial slope (i.e., a small α). Such cells are denoted as “late responders” since radiation damage induces cell loss at a late stage after the onset of the treatment. Most of these cells enter mitoses weeks or even months after the start of the treatment. Thus, tissues of such cells express a response to the radiation late; not only late after the onset of the treatment but in many cases long after the end of the treatment.


An error line graph of blood activity versus the total dose of the iso-effect corresponds to a single dose of 16 gray presents at the center. The values are increasing trends.


This difference is central to the whole concept of radiotherapy. Without this difference, radiotherapy of cancer would probably have had little curative success. The reason is that proliferation is an activity that is typical for almost all cancer tumors but only for a few organs of normal tissues. Resting cells, on the other hand, are largely characteristic of most normal tissues and not of cancer tissues.


Thus, while cancer cells largely proliferate and have a large α-parameter, highly differentiated normal cells largely rest and have a small α-parameter. The result of this is that if radiation is given over a prolonged time, (either by repeated dose fractions separated by time for repair or by continuous low dose rate irradiation) there is a much more sparing effect on late-responding normal tissues than on most cancer tissues.


The interesting question is then, How did we obtain the knowledge that late-responding tissues have cells with a small initial slope on their dose-response curves? These cells are largely not proliferating. They are furthermore seated in tissues and do not grow in culture. So, how is it possible to measure the ability of these cells to form a colony after irradiation? The answer is that we cannot do such measurements directly. Still, as mentioned above, we know that these cells have dose-response curves characterized by a small α-parameter. This knowledge stems from the use of the LQ model to measure not α, but the α/β-ratio. The α/β-ratio is actually the dose (D1) where the contribution to cell inactivation by single event killing matches that from multiple event killing, i.e.,


(4.42)or

 (4.43)


These measurements are based on the following idea: The function of a tissue depends on the functionality of the tissue cells. If the radiation inactivates a certain fraction of the cells, the tissue may lose some of its function and the loss of function can be measured. Such measurements as a result of irradiation are usually denoted as measurements of “Functional endpoints.” Two examples of such functional endpoints representing late and early-responding tissues, respectively, are: (a) Kidneys, the clearance of a very small amount of an injected substance from the blood can be measured and (b) Skin, the severity of damage to an irradiated area of skin can be observed and graded (from mild reddening to irreparable wounds and necrosis).


In Fig. 4.28, an example of kidney function damage is shown. As a measure of kidney function, the clearance from blood of the compound ethylene diamine tetra acetate (EDTA) as a function of the total dose given by various fractionation regimes to mice was detected [136]. EDTA was labeled with [51Cr] so that minute amounts in blood could be accurately detected by blood samples taken 1 h after EDTA injection. The red line indicates an isoeffect level and the numbers 1–64 indicate the number of dose fractions given to the animals over a period of 3 weeks. Kidneys are late-responding tissues (the filtration units of kidneys consist of highly differentiated cells) and therefore the clearance was measured late (26 weeks) after the end of irradiation.


Since all fractionation regimes gave the same functional effect along the red line in Fig. 4.30, we assume that cell survival is the same along this red line. For one such fractionation regime with n dose fractions of size d the LQ model predicts the following cell survival as long as time is given for the full repair of SLD between dose fractions:

 (4.44)


We now rearrange to get the following expressions (and we write SD for S(D) and Sd for S(d):

 (4.45)


or

 (4.46)


If we now remember that D = nd this formula can also be rewritten as follows:

 (4.47)


The data from Fig. 4.28 can be plotted according to Eqs. (4.45) (left panel) and Eq. (4.46) (right panel) as shown in Fig. 4.29 [137].

A. line graph of reciprocal total dose versus dose per fraction of the values (1, 0.14), (2, 0.16), (4, 0.2), to (17, 0.66), values are estimated. B. decreasing line graph of the proportion of full effect versus dose per fraction in the gray of alpha beta = 3 grays.

Fig. 4.29
The isoeffect data defined by the red line in Fig. 4.30 are replotted after the two transformations described by Eqs. (4.45) (plotted in panel a) and (4.46) (plotted in panel b). Reprinted with permission from [137]


A. line graph of reciprocal total dose versus dose per fraction of the values (1, 0.14), (2, 0.16), (4, 0.2), to (17, 0.66), values are estimated. B. decreasing line graph of the proportion of full effect versus dose per fraction in the gray of alpha beta = 3 grays.


From Fig. 4.29a, one can see that the data points are well-fitted by a straight line as predicted by the LQ formula (Eq. 4.45). Furthermore, according to Eq. (4.45) we have for 1/D = 0 that

 and thus that d(1/D = 0) =  − α/β.Therefore, since the line crosses the abscissa at d = −3 Gy, the nominal value of the α/β-dose must be 3 Gy.


In Fig. 4.29b, one can see that Eq. (4.46) actually reconstructs the shape of the dose-response curve, but in this case with the survival axis plotted as the fractional effect of a single dose fraction relative to the effect induced by the single-dose acute irradiation of 16 Gy. As indicated in the figure, also this plot results in the α/β-dose being 3 Gy since the contributions at 3 Gy by single and multiple event killing as defined in the LQ model are equal. The importance of the value of the α/β-dose in relation to fractionated radiotherapy is clearly illustrated by the isoeffect tolerance curves plotted in Fig. 4.30 [137].

a and b, scatter plot of the total dose versus the number of fractions of late responding kidney alpha by beta = 3 grays, and early responding skin alpha by beta approximate 12 grays, the scale of dose per fraction present at the bottom.

Fig. 4.30
In (a), the data of Fig. 4.28 on late-responding mouse kidney are replotted as isoeffect tolerance curves with total tolerated dose in a fractionation scheme as a function of the dose per fraction (both axes logarithmic). In (b), similar data are shown for an early-responding normal tissue, namely mouse skin. Notice that the α/β-dose is 3 Gy for the late-responding tissue and 12 Gy for the early-responding tissue. (Reprinted with permission from [137])


a and b, scatter plot of the total dose versus the number of fractions of late responding kidney alpha by beta = 3 grays, and early responding skin alpha by beta approximate 12 grays, the scale of dose per fraction present at the bottom.


These isoeffect curves show which total dose is necessary in order to obtain a certain effect as a function of the dose per fraction (or number of fractions) for two different tissues. Notice that both axes are logarithmic. In (a), the mouse kidney data of Stewart et al. are plotted as an example of a late-responding tissue with α/β = 3 Gy and in (b), data on mouse skin are plotted as an example of an early-responding tissue with α/β ≈ 12 Gy. Thus, while the upper curve represents a dose-limiting normal tissue, the lower curve represents an early-responding tissue such as cancer or some highly proliferative normal tissues. A list of typical values for α/β can be found in Table 4.5.Table 4.5
Ratios of α/β for early and late radiation reactions in normal tissues, determined from laboratory animal and clinical data (Fowler, copyright © 2005 Acta Oncologica Foundation, reprinted by permission of Taylor & Francis Ltd) [138]

Early reactions

 (Gy)

Late reactions

 (Gy)

Skin

9–12

Kidney

2–2.4

Jejunum

6–10

Rectum

2.5–5

Colon

9–11

Lung

2.7–4

Testis

12–13

Bladder

3–7

Mucosa

9–10

CNS: Brain, spinal cord

1.8–2.2


The arrows in Fig. 4.30 show that four large dose fractions of 10 Gy each will represent an advantage to the early-responding tissue (like the tumor), while 64 small dose fractions of 1 Gy each represent an advantage to the late-responding tissue (normal tissue). If tissues are irradiated continuously with a low dose rate, the cells may repair sublethal damage during irradiation and the lower the dose rate, the smaller the probability will be for two or more sublethal damages to combine to create a potentially lethal damage. For the LQ model, this means that reducing the dose rate results in reduced influence by the β-term and more and more dominance by the α-term. The connection between the shape of the dose-response curve and the isoeffect tolerance curves (dashed lines) by continuous irradiation is illustrated in Fig. 4.31. The blue curves represent late-responding tissues (i.e., small α/β-ratio of ≈3 Gy) while the purple curves represent early-responding tissues (i.e., large α/β-ratio of ≈12 Gy). The steep isoeffect tolerance curve at high doses for late-responding tissues indicates good sparing for these tissues by reduced fraction doses and prolonged treatment time. Early-responding tissues will experience much less sparing by prolonged treatment times (Box 4.12).

A multi-line graph of surviving fraction versus dose of late responding tissues, and tumor and early responding tissues. A dashed vertical line for alpha by the beta of late and early on either side.

Fig. 4.31
These cell survival curves illustrate typical differences in the dose-response curves of early- (purple: α/β-ratio of ≈3 Gy) and late- (blue: α/β-ratio of ≈12 Gy) responding tissues. Note that the α/β-dose is the dose where the contributions to the cell kill from the αD-term is the same as for the βD2-term, as indicated with brackets for the late-responding tissues


A multi-line graph of surviving fraction versus dose of late responding tissues, and tumor and early responding tissues. A dashed vertical line for alpha by the beta of late and early on either side.


The linear quadratic model is a mathematical model, which is a good fit for cellular survival data in a median dose range. For low and high dose, the model needs modifications

There have been several biological interpretations of the model

To compare different clinical fractionations regimens, the biologically effective dose can be calculated from the

-value


The linear quadratic model is a mathematical model, which is a good fit for cellular survival data in a median dose range. For low and high dose, the model needs modifications


To compare different clinical fractionations regimens, the biologically effective dose can be calculated from the

-value


From the discussion so far, one might get the impression that most problems with radiotherapy can be resolved by just a further increase of the treatment time, using, for example, larger numbers of smaller dose fractions over a longer time period, or by reducing the dose rate in case of continuous low dose rate irradiation. However, such changes are met with other limitations such as recruitment and proliferation (repopulation). The problem is that if the tissue is given a small dose each day, the induced cell loss will after a while induce increased proliferation (and probably recruitment) in the surviving cells to compensate for the cell loss. The point is that this activity favors the malignant tissue more than most normal tissues. The reason has to do with the very difference between early- and late-responding tissues, which was the basis for the notion of early and late. While early-responding tissues start compensatory proliferation early after the onset of the radiation treatment, late-responding tissues start compensatory proliferation much later, and in humans, long after completed treatment. This is illustrated in Fig. 4.32, which is based on experimental data from rodents using mouse skin as a model for early-responding tissue (cancer included) and rat spinal cord as a model for late-responding tissue. One should keep in mind here that a complete fractionation scheme for radical radiotherapy of a solid tumor with external radiation is typically 6 weeks, i.e., 42 days.

A graph of extra radiation dose in gray for the extra dose required to counteract proliferation. It has a solid curve of early reaction for mouse skin and a dashed curve of late reaction for rat spinal cord.

Fig. 4.32
The curves indicate what extra radiation dose is required to counteract only proliferation during treatment with one daily dose fraction in two different rodent tissues. Human tissues react more slowly than rodent tissues. Thus, the time for increased proliferation therefore would probably start at a later time than indicated in the figure for corresponding human tissues. (Adapted with permission from [139])


A graph of extra radiation dose in gray for the extra dose required to counteract proliferation. It has a solid curve of early reaction for mouse skin and a dashed curve of late reaction for rat spinal cord.


As indicated, the compensatory proliferation starts after the end of the treatment for nerve tissues, while it starts after just 2 weeks of treatment for the cancer-modeling skin tissues. The compensatory proliferation (repopulation) initiated by fractionated irradiation is thus more favorable for early-responding tissues (including cancer) than for late-responding normal tissues. Therefore, one must be careful not to increase the overall treatment time too much. The 6 weeks that are typical for the duration of conventionally fractionated radiation treatment thus is a compromise taking into consideration several different aspects to obtain the maximal probability for a positive effect on the cancer tumor with a minimum of side effects.


We can rewrite Eq. (4.45) to:


is called the Biologically Effective Dose (BED) and describes the dose needed to induce the same effect as if the number of dose fractions was infinitely large and the single dose fractions d approaching zero. This is the equivalent of continuous irradiation with a dose rate sufficiently small for cells to repair sublethal damage at the same rate as they are induced preventing them to cooperate to create lethal damage. BED is a useful parameter to calculate and compare fractionation regimes.


Standard treatment for many cancers is 2 Gy daily fractions (for example, over 7 weeks with five treatment days per week). It is therefore often relevant to compare other fractionation regimes to 2 Gy fractions.


The equivalent total dose D for 2 Gy fractions is called

 (4.49)


We then get

, which can be used to calculate fraction dose d and number of fractions n = Dd/d to get the same BED as 2 Gy fractions to a total dose of EQD2.


While it is relatively straightforward to develop a model relating dose to survival at the cellular level, modeling of dose response at the organ and organism (human) level is far more complex. There remains considerable debate regarding the most appropriate model for use in describing the variation in response to dose in humans [140]. However, each of the models has its basis in radiobiology, and the interaction of ionizing radiation with human tissue at the cellular level [140, 141]. The previous section on target theory provides a basis to begin to define models of human radiation survival. The effects of ionizing radiation on cells may be divided into two types: deterministic and stochastic effects [141]. Deterministic effects result from the substantial injury of cells in affected tissues, and the severity of the effect is a function of the absorbed dose. Stochastic effects are those for which the probability of occurrence of an effect, and not its severity, is a function of dose [141]. Deterministic effects have a well-defined dose threshold in mammalian cells of a particular organ and type, while it is assumed that no threshold exists for stochastic effects [142]. Deterministic effects occur at relatively high doses (0.5 Gy and above depending on the organ system involved), while stochastic effects generally occur at relatively low doses (below 0.5 Gy) [141]. Both sets of effect are modified by the rate at which the dose is administered as well as by the biological damage responses such as DNA repair and immune responses [141]. Stochastic effects usually constitute the mechanisms by which the hereditary (mutagenic) and somatic (carcinogenic) effects of ionizing radiation occur [140]. Carcinogenesis is a multistage process in which radiation may induce one or more of the changes necessary to cause DNA damage, while mutagenesis is usually thought to be the result of single biological changes in germ cells. [140]


From Eq. (4.26), we may simplify and introduce a variable change to obtain a single-hit model of radiation survival in cells where the frequency, f, of cells with one or more hits in a given population of cells is:

 (4.50)where n is the number of critical hits per cell at dose D, and λ is the mean number of critical hits per cell at dose D. For low frequency hits (low doses), the number of critical hits, n, per cell is small and thus Eq. (4.49) reduces to:

 (4.51)


Thus, the dose-response is approximately linear with no threshold. At high hit frequencies, where hit saturation occurs, the equation takes the form of Eq. (4.49), since after the first critical hit in a cell, further hits in it cannot lead to additional effects [140].


Multi-track models may be utilized to describe the effect of the interaction between multiple tracks in a cell. The interaction may either be positive or negative and may result in visible curvature to the dose response [140]. A mathematical description of such a model may be achieved by inserting a general polynomial into Eq. (1.50) as follows [140]:

 (4.52)


which, for low frequency effects (low doses) reduces to:

 (4.53)


In practice, many models have been found to fit the dose response of various bodily organs, depending on the organ in question [143]. The two most common models used are the linear no threshold, LNT (Eq. 4.50), and the linear quadratic (Eq. 4.52) models [143]. At low doses, in a homogeneous cell population, Eq. 4.50 would be the most appropriate dose-response model theoretically, since it is assumed that every cellular hit may be biologically critical and that a single cell is unlikely to be hit more than once [143]. However, for low doses, other mechanisms come into play, such as low dose hypersensitivity, hormesis, and adaptive response mechanisms, as described in Sect. 2.9 and non-targeted effects as described in Sect. 2.10, which will modify the radiation response. In an inhomogeneous cell population, where groups of cells have differing radiosensitivity, the response for single-track events in each subpopulation should follow the form of Eq. (4.52), the overall response should show a decreasing sensitivity with increasing dose, consistent with the LQ model [140].


Historically, the LNT model for radiation risk assessment was introduced after Muller’s discovery of radiation-induced mutations in 1927. After the atomic bombing of Japan in 1945 and the start of the nuclear arms race, ionizing radiation became connected in public mind with nuclear apocalypse. In 1945–1956, there was great controversy and extensive arguments pro and contra LNT. In general, it can be said that among scientists “the data to support the linearity at low dose perspective was generally viewed as lacking but the fear that it may be true was a motivating factor” [144]. In 1956, ICRP officially abandoned the tolerance level concept (that was in use since 1931) and substituted LNT for it. Formally, LNT has been introduced and remains a practical operational model for radiation protection only. De facto however LNT acquired the status of a scientific theory, though supporting evidence is at least inconclusive. Moreover, about 40 years ago, low dose-induced changes in cell signaling with delayed responses were discovered. There is emerging evidence that low doses induce cellular and intercellular changes, which can lead to stress response (adaptive response) metabolic alterations. Adaptive responses against the accumulation of damage—also of non-radiogenic origin—were also discovered [145]. The above evidence suggests that while high-dose ionizing radiation is certainly harmful, low doses may be beneficial for human health; such an effect is called hormesis [146]. At the joint US ANS/HPS conference “Applicability of Radiation-Response Models to Low Dose Protection Standards” in 2018, neither of the three viewpoints—supporting LNT, tolerance level, or hormesis—was marginal [145].


Q1.
Principles of radiation dosimetry?
 Q2.
Radiation microdosimetry(a)
What is lineal energy?
 (b)
How is it related to the LET?

 Q3.
From track structure to early DNA damage(a)
What are the main differences between a general MC code and a track structure (TS) MC code?
 (b)
What are the main sources of uncertainty in the calculation of DNA damage with MCTS code?

 Q4.
Micro-beams and minibeams(a)
Please allocate the research questions mentioned in the following figure to the irradiation pattern, which is best used for investigation, as it is done in the example.

A block diagram of mini beam, single, array to microbeam, dose volume effect, enhanced R B E of high-L E T particle, mechanisms of M R T, bystander effect, cellular response to single ions, and radiosensitivity of subcellular structures.

 Q5.
Target theory and dose-response models

Use the data in the table below (A549 lung cancer cells irradiated with 220 kV X-rays) to:(a)
Find the α/β-value both from a LQ-fitting and by drawing the initial slope and comparing the contributions from each term (see figure provided in Sect. 4.5 above).
 (b)
Calculate the surviving fraction using α and β from your LQ-fitting for 5 fractions of 2 Gy (24 h apart) and compare to a single dose of 10 Gy.
 (c)
How many fractions of 2 Gy should we give to get the same biological effect as for 1 fraction of 10 Gy?

Dose [Gy]

Surviving fraction

Standard error

0

1

0.5

0.88

0.07

1

0.64

0.06

2

0.41

0.04

5

0.07

0.02

10

0.0008

0.0003


Radiation microdosimetry(a)
What is lineal energy?
 (b)
How is it related to the LET?


From track structure to early DNA damage(a)
What are the main differences between a general MC code and a track structure (TS) MC code?
 (b)
What are the main sources of uncertainty in the calculation of DNA damage with MCTS code?


What are the main differences between a general MC code and a track structure (TS) MC code?


What are the main sources of uncertainty in the calculation of DNA damage with MCTS code?


Micro-beams and minibeams(a)
Please allocate the research questions mentioned in the following figure to the irradiation pattern, which is best used for investigation, as it is done in the example.

A block diagram of mini beam, single, array to microbeam, dose volume effect, enhanced R B E of high-L E T particle, mechanisms of M R T, bystander effect, cellular response to single ions, and radiosensitivity of subcellular structures.


Please allocate the research questions mentioned in the following figure to the irradiation pattern, which is best used for investigation, as it is done in the example.

A block diagram of mini beam, single, array to microbeam, dose volume effect, enhanced R B E of high-L E T particle, mechanisms of M R T, bystander effect, cellular response to single ions, and radiosensitivity of subcellular structures.


A block diagram of mini beam, single, array to microbeam, dose volume effect, enhanced R B E of high-L E T particle, mechanisms of M R T, bystander effect, cellular response to single ions, and radiosensitivity of subcellular structures.


Use the data in the table below (A549 lung cancer cells irradiated with 220 kV X-rays) to:(a)
Find the α/β-value both from a LQ-fitting and by drawing the initial slope and comparing the contributions from each term (see figure provided in Sect. 4.5 above).
 (b)
Calculate the surviving fraction using α and β from your LQ-fitting for 5 fractions of 2 Gy (24 h apart) and compare to a single dose of 10 Gy.
 (c)
How many fractions of 2 Gy should we give to get the same biological effect as for 1 fraction of 10 Gy?


Find the α/β-value both from a LQ-fitting and by drawing the initial slope and comparing the contributions from each term (see figure provided in Sect. 4.5 above).


Calculate the surviving fraction using α and β from your LQ-fitting for 5 fractions of 2 Gy (24 h apart) and compare to a single dose of 10 Gy.


How many fractions of 2 Gy should we give to get the same biological effect as for 1 fraction of 10 Gy?


SQ1.
Principles of radiation dosimetry
 SQ2.
Radiation microdosimetry(a)
The lineal energy is the quotient of the total energy imparted to a volume of matter by a single energy deposition event and the mean chord length in that volume.
 (b)
In large-size targets, the number of interactions is large and the distribution of lineal energy converge to an expected value, which is the LET.

 SQ3.
From track structure to early DNA damage1.
Two main characteristics differentiate these two types of MC calculation:(a)
TS MC codes do not use the condensed history approach for electron transport and they discretely simulate all electron interactions (elastic and inelastic)
 (b)
TS MC codes include electron interaction cross sections to explicitly transport the electrons down to very low energies (of the order of 10 eV), which allows to calculate the energy depositions in micrometric and nanometric volumes.

 2.
Cross sections, mainly for liquid water, used by MCTS codes have uncertainties due to the lack of experimental data that could validate them. All the complexity of radiolysis and reactions of radiolytic species with biomolecules is not taken into account. DNA geometrical models require approximations. The conversion of particle interactions or reactions of radiolytic species into damage is a source of interpretation.

 SQ4.
Micro-beams and Minibeams
 (a)

A block diagram illustrates connecting of microbeam, single, array, and mini beam to dose-volume effect, enhanced R B E of high-L E T particles, mechanisms of M R T, bystander effect, cellular response to single ions, and radiosensitivity of subcellular structures,

 SQ5.
Target theory and dose-response models(a)
α/β = 12
 (b)
and 0.001
 (c)
8


Radiation microdosimetry(a)
The lineal energy is the quotient of the total energy imparted to a volume of matter by a single energy deposition event and the mean chord length in that volume.
 (b)
In large-size targets, the number of interactions is large and the distribution of lineal energy converge to an expected value, which is the LET.


The lineal energy is the quotient of the total energy imparted to a volume of matter by a single energy deposition event and the mean chord length in that volume.


In large-size targets, the number of interactions is large and the distribution of lineal energy converge to an expected value, which is the LET.


From track structure to early DNA damage1.
Two main characteristics differentiate these two types of MC calculation:(a)
TS MC codes do not use the condensed history approach for electron transport and they discretely simulate all electron interactions (elastic and inelastic)
 (b)
TS MC codes include electron interaction cross sections to explicitly transport the electrons down to very low energies (of the order of 10 eV), which allows to calculate the energy depositions in micrometric and nanometric volumes.

 2.
Cross sections, mainly for liquid water, used by MCTS codes have uncertainties due to the lack of experimental data that could validate them. All the complexity of radiolysis and reactions of radiolytic species with biomolecules is not taken into account. DNA geometrical models require approximations. The conversion of particle interactions or reactions of radiolytic species into damage is a source of interpretation.


Two main characteristics differentiate these two types of MC calculation:(a)
TS MC codes do not use the condensed history approach for electron transport and they discretely simulate all electron interactions (elastic and inelastic)
 (b)
TS MC codes include electron interaction cross sections to explicitly transport the electrons down to very low energies (of the order of 10 eV), which allows to calculate the energy depositions in micrometric and nanometric volumes.


TS MC codes do not use the condensed history approach for electron transport and they discretely simulate all electron interactions (elastic and inelastic)


TS MC codes include electron interaction cross sections to explicitly transport the electrons down to very low energies (of the order of 10 eV), which allows to calculate the energy depositions in micrometric and nanometric volumes.


Cross sections, mainly for liquid water, used by MCTS codes have uncertainties due to the lack of experimental data that could validate them. All the complexity of radiolysis and reactions of radiolytic species with biomolecules is not taken into account. DNA geometrical models require approximations. The conversion of particle interactions or reactions of radiolytic species into damage is a source of interpretation.


A block diagram illustrates connecting of microbeam, single, array, and mini beam to dose-volume effect, enhanced R B E of high-L E T particles, mechanisms of M R T, bystander effect, cellular response to single ions, and radiosensitivity of subcellular structures,


Target theory and dose-response models(a)
α/β = 12
 (b)
and 0.001
 (c)
8


and 0.001


RT is one of the cornerstones in cancer treatment.

The objective of RT resides in finding an optimal balance between chances of cure and risk of associated toxicity.

Differential effect of RT between tumors and normal tissues depends on multiple factors related to both malignant and healthy tissue radiobiology, but also on beam characteristics and treatment schedule.

Technical advances and sophistication of RT devices improve ballistic accuracy and allows unprecedented changes in treatment schedules, probably changing both malignant and healthy tissue radiobiology.


The objective of RT resides in finding an optimal balance between chances of cure and risk of associated toxicity.


Differential effect of RT between tumors and normal tissues depends on multiple factors related to both malignant and healthy tissue radiobiology, but also on beam characteristics and treatment schedule.


Technical advances and sophistication of RT devices improve ballistic accuracy and allows unprecedented changes in treatment schedules, probably changing both malignant and healthy tissue radiobiology.


Radiation therapy (RT) is a locoregional treatment modality for cancer. Using radiation for therapeutic purposes began only a few months after the discovery of X-rays by Wilhelm Röntgen in 1895. The first “true” RT succeeded in managing a case of lupus erythematosus in 1897 by Eduard Schiff (1899). More than 120 years later, RT is still one of the cornerstones of tumor treatment, with more than half of all cancer patients treated by radiation in the course of their therapeutic management [1] (Box 5.1).


The interesting (but also dangerous) properties of ionizing radiation (IR) reside in its ability to penetrate more or less deeply in biological tissues, depending on its energy, and to react with the environment. These reactions consist in direct energy deposition and the generation of free radicals near and within living cells. The consequence of energy deposition is damage to the DNA structure leading to cell death if unrepairable [2]. Of course, all cells are concerned, tumor cells as well as cells in the healthy tissues, and within the irradiated volume, no difference is made between tumor and healthy cells. Treating a tumor would be easily achievable by the administration of a very high dose if it was not surrounded by the patient. Therefore, several strategies have been developed to ensure both the best tumor control and the least consequences ensuing from healthy tissues exposure, taking advantage of differences between tumor and healthy cells, known as the benefit/risk balance (Fig. 5.1).

The diagram displays the benefit of radiation therapy which is tumor control and the risk is the normal tissue toxicity.

Fig. 5.1
The benefit/risk balance. The objective of RT is to control the tumor while sparing normal tissues, to ensure the patient’s cure without unacceptable side effects


The diagram displays the benefit of radiation therapy which is tumor control and the risk is the normal tissue toxicity.


Some biological processes favor the benefit/risk ratio in RT and the differential effect between tumor and healthy cells. Except for some very radiosensitive or radioresistant tumors, healthy and tumor cells demonstrate quite similar radiation sensitivities. However, DNA damage is less efficiently repaired by tumors than by healthy cells. This is the basis for the dose fractionation principle, demonstrated by Claudius Regaud and applied in the clinic by Henri Coutard in 1934, and which still is used today in modern RT. The total dose necessary to control the tumor is generally delivered in a series of small daily doses. The time lapse between each fraction allows DNA damage to be repaired by healthy cells whereas tumor cells do not repair or do so to a lesser extent. The biological effectiveness (the chances of tumor control but also the risk of damage to normal tissues) is reduced when using fractionated doses due to DNA repair and cell repopulation in both tumors and healthy tissues [3]. Numerous parameters associated with fractionation regimens, such as the total dose, the dose per fraction, and the time between fractions and the total treatment time, will influence both tumor response and normal tissue damage and will be described in more detail below [4]. Another biological factor participating in the differential effect is radiation-induced cell death. In a majority of cases, the initial radiation exposure is not what kills cells but rather unrepaired DNA damage, which condemns them to death as soon as they re-enter in the cell cycle. Rapidly proliferating tumor tissues will suffer significant cell death under these conditions compared to slowly proliferating healthy tissues. However, some healthy tissues such as oral and intestinal mucosa or hematopoietic cells proliferate rapidly and may be susceptible to early mitotic cell deaths if present in the irradiated volume. Finally, tumor control will also depend on other factors such as tumor heterogeneity (the tumor cannot be simply considered as a cluster of tumor cells), oxygenation status before RT and variations during treatment, tumor vascularization, resident and recruited immune cells, and so forth. Considering all these biological factors, the objective of treatment planning in RT is to find the best compromise between chances of cure and risk of associated toxicity [5].


In an ideal world, RT may target only the tumor volume; however, in real life, this is never the case. For healthy tissues, besides dose and fractionation, the volume exposed is of paramount importance in determining the risk of developing toxicity. Technical advances in dose delivery, planning systems and associated imaging devices have helped to achieve ever increasing ballistic accuracy. Advanced technologies, such as volumetric modulated arc therapy (VMAT), image-guided radiotherapy (IGRT), stereotactic body radiotherapy (SBRT), heavy ions [6], or proton therapy have all contributed to progress [7]. Consequently, the use of highly focused beams reduces the volume of normal tissues present within the irradiated volume and can spare very sensitive organs, thus minimizing the risk of toxicity. Reducing the volume also permits changes in fractionation schedules. For example, SBRT uses hypofractionation, delivering ablative doses per fraction between 8 and 20 Gy instead of the conventional 2 Gy/fraction. The gain in biological effectiveness strongly increases tumor control as illustrated in early-stage primary lung cancer. These changes in fractionation schemes may also induce a “new” radiobiology of tumors and healthy tissues in response to very high doses of IR, an area that remains to be explored [8]. Finally, ultra-high dose rate FLASH RT demonstrates a very sharp differential effect between tumor and healthy tissues and is the subject of intense research for future clinical applications [9].


Technical advances have strongly contributed to the chances of cure for numerous cancers and increased patients’ survival. This increased life expectancy following cancer treatment, however, favors the emergence of side effects, especially long-term sequelae. Normal tissues can be divided into “early” and “late” responding tissues. Early-responding tissues (intestinal mucosa, hematopoietic system, skin, gonads) are characterized by the presence of cell proliferation compartments and are mostly implicated in acute radiation-induced toxicity. Late-responding tissues demonstrate no distinct cell proliferation compartment and are mostly implicated in late toxicity. For each normal tissue, dose constraints, which vary depending on the RT technique used, may be applied. These constraints help to minimize the risk of developing severe treatment-associated toxicity [10].


RT still plays a significant role in cancer cures. Its efficiency depends on numerous parameters related to both tumor and normal tissue radiobiology. The objective of cancer therapy, using modern RT often concurrently with other therapeutic strategies (surgery, chemotherapy, immunotherapy, etc.) is for the patients to survive without debilitating sequelae. This goal may be achieved using technological advances in RT, combined with strategic knowledge of both tumor and healthy tissue radiobiology.


Therapeutic window: The difference between tumor control probability (TCP) and normal tissue complication probability (NTCP) at identical irradiation dose.

Therapeutic ratio: The relation between TCP and NTCP or efficacy to toxicity ratio.


Therapeutic window: The difference between tumor control probability (TCP) and normal tissue complication probability (NTCP) at identical irradiation dose.


Therapeutic ratio: The relation between TCP and NTCP or efficacy to toxicity ratio.


RT is one of the most effective treatment modalities in cancer therapy. However, despite modern precision RT, it is generally unavoidable to deposit IR to the tumor volume without risk of radiation injury to the surrounding healthy normal tissues or organs. Hence, the therapeutic effectiveness of radiation is dependent on the balance between tumor control and normal tissue adverse effects. In fact, the tolerance dose of the normal tissues or organs at risk determines the dose which can be safely applied to the tumor volume. For almost all normal tissues and organs, dose-volume constraints are well documented in the literature, for example, the QUANTEC (QUantitative Analysis of Normal Tissue Effects in the Clinic) data, as guidance in the clinical practice (see Sect. 5.13.6) [11]. The so-called therapeutic window is a conceptual window of opportunity between the tumor control probability (TCP) and normal tissue complication probability (NTCP) (Fig. 5.2).

Local tumor control and normal tissue complication probability versus dose plots upward trends for tumor sensitization, hypoxic and non hypoxic modification, biological targeting, tumor microenvironment, D N A repair, Immunotherapy, improved radiation delivery, and normal tissue protection.

Fig. 5.2
Illustration of the therapeutic window. For an identical delivered dose, the curves show the difference between tumor control probability and normal tissue complication probability and methods to widen the window. (Reprinted from Drug radiotherapy combinations: review of previous failures and reasons for future optimism; Figure from Higgins et al. [12], with permission)


Local tumor control and normal tissue complication probability versus dose plots upward trends for tumor sensitization, hypoxic and non hypoxic modification, biological targeting, tumor microenvironment, D N A repair, Immunotherapy, improved radiation delivery, and normal tissue protection.


The ultimate aim of RT in the clinic is accomplished when the therapeutic window is large, with an optimized balance between benefits and risks, hence a treatment that is highly likely to be effective and safe. The shape and position of the dose–response curves for tumor control and toxicity to the normal tissues (Fig. 5.2) determines the probability that enough radiation is delivered to destroy the tumor cells without serious complications. The position of the curves determines the feasibility of the application of RT to the patient. The therapeutic window is large in radiosensitive tumor types like lymphoma, but small for other tumor types such as brain and pancreatic cancer. If the dose–response curve for normal-tissue toxicity is positioned at the left side of the tumor control curve or in case the curves are close together, the aimed tumor response could only be achieved at the cost of a high complication risk. The standard RT treatment is that one with tumor control probability (TCP) ≥0.5 and normal tissue complication probability (NTCP) ≤0.05 [13].


It is worth noting that Fig. 5.2 illustrates an ideal situation. The TCP curve might in particular however deviate for two main reasons. First, tumors are more heterogeneous compared with normal tissue; subsequently, the expression of the TCP curve becomes shallower than that of the NTCP curve. Secondly, not only the region of interest does contain the malignant cells, but there might be metastatic extensions outside the irradiation treatment volume. Hence, it is unlikely that the TCP curve for local control of specific tumors scores 100% [14, 15].


Several treatment parameters influence the therapeutic window. For example, when the overall treatment time is prolonged, the therapeutic window is narrowed (Fig. 5.3) [15, 16]. It is however difficult to practice this strategy because each complication translates the effect of a treatment parameter on the therapeutic window differently.

A line graph represents response versus radiation dose in gray. The dotted curve for split-course treatment, and the solid curve for conventional fractionation treatment have the same upward trend, before slightly declining at the endpoint.

Fig. 5.3
Prolongation of the overall treatment time narrows the therapeutic window. Conventional irradiation course in 6 weeks versus a split-course course in 10 weeks. (Adopted from [16])


A line graph represents response versus radiation dose in gray. The dotted curve for split-course treatment, and the solid curve for conventional fractionation treatment have the same upward trend, before slightly declining at the endpoint.


Several methods can be used to widen the therapeutic window, to increase the probability of complication-free tumor control:
Fractionated RT. See Fig. 5.4. Decrease of the organ or tissue at risk volume using precision RT techniques allowing optimal dose distribution (e.g., stereotactic irradiation/particle irradiation).

Combination therapy with molecular targeting or immune-modulating drugs. Optimally, drugs should be carefully chosen to selectively sensitize tumor and not normal tissue cells, taking the 6R’s or Hallmarks of Radiobiology into account (see Sect. 5.4).

Two line graphs represent probability versus dose in gray. The plotted data in each graph, T C P and N T C P, are in an upward trend, while uncomplicated cures are in a downward trend.

Fig. 5.4
Fractionation as an effective method to widen the therapeutic window. Curves schematically represent the probability of normal tissue side effects (NTCP, red curve), the probability of tumor control (TCP, blue curve) as well as the complication free tumor control curve (green) following single-dose radiation (a) and dose fractionation (b). (Figure from Shrieve and Loeffler [17], with permission from Wolters Kluwer Health, Inc.)


Fractionated RT. See Fig. 5.4. Decrease of the organ or tissue at risk volume using precision RT techniques allowing optimal dose distribution (e.g., stereotactic irradiation/particle irradiation).


Combination therapy with molecular targeting or immune-modulating drugs. Optimally, drugs should be carefully chosen to selectively sensitize tumor and not normal tissue cells, taking the 6R’s or Hallmarks of Radiobiology into account (see Sect. 5.4).


Two line graphs represent probability versus dose in gray. The plotted data in each graph, T C P and N T C P, are in an upward trend, while uncomplicated cures are in a downward trend.


The therapeutic ratio or therapeutic index is an imperative measure used in the treatment planning to ensure that the RT course achieves its goals [18]. The ratio represents the difference between the TCP and NTCP curves for the same delivered dose at a fixed endpoint of NTCP [14]. Therefore, it represents the quantity used in the tumor treatment planning for the purpose of disease cure without complications. The ratio is defined as the relationship between TCP and NTCP, i.e., efficacy/toxicity ratio. Chang et al. stated that a common method used to calculate the therapeutic ratio which is the probability of cure without complications [19] and given by:


As the difference between TCP and NTCP becomes large it means that TR approaches 1 and treatment is fairly effective for tumor control than for causing normal tissue morbidity, but the pattern is reversed when the difference between TCP and NTCP becomes small. That is, TR approaches 0 and the treatment may fail and be relatively more toxic [14]. As explained above, there are many treatment parameters and methods that affect the therapeutic ratio, for example, combination therapy with a radiosensitizing agent or drug. This effect is revealed in practice as increasing tumor cure rate with improved quality of life as a result of a therapeutic gain [13, 16]. In this circumstance, the therapeutic ratio is the ratio of dose-modifying factors (DMFs) of tumor over that for normal tissues.


Finally, the therapeutic ratio differentiates between early and late responding normal tissues in terms of their response to concomitant RT and chemotherapeutics or targeted agents. While the therapeutic ratio of early responding tissue is usually <1, the therapeutic ratio of late responding tissues is >1 which reflects the advantageous consequence of concomitant RT and chemotherapy. This may lead to a high level of early injury, but a neutral level of late damage to late responding tissues. Fortunately, early side effects can be relieved by using either extensive supportive care or adaptation of the standard treatment. The combination of RT and chemotherapy may prove effective if selective radiosensitization of malignancy is obtained and the probability of late-responding normal tissue damage is not increased. However, early toxicities might also be a concern.


Tumor control probability (TCP) is guided by dose, tumor characteristics, and normal tissue radiation sensitivity.

Killing of clonogenic cells within a tumor partly explain TCP during RT, but the effect is also influenced by host factors, for example, immune cell attack.


Tumor control probability (TCP) is guided by dose, tumor characteristics, and normal tissue radiation sensitivity.


Killing of clonogenic cells within a tumor partly explain TCP during RT, but the effect is also influenced by host factors, for example, immune cell attack.


The main objective of curative RT is to successfully achieve local tumor control [16]. The relationship between TCP and radiation dose is shown in Fig. 5.5 which illustrates that there is poor tumor control with low dose, but high tumor control with high dose [20]. The steepness of the curve depends on differences in tumor size, tumor cell radiation sensitivity and repopulation as well as other factors. These factors give rise to variation in TCP of different tumors but also inter-patient variation in clinical practice. Subsequently, this improvement in tumor control is reflected in an increase in the life expectancy of cancer patients. To this end, it is preferable to evaluate RT success based on tumor control.

A schematic diagram of tumor control versus radiation dose. The therapeutic effect and normal tissue are in an upward trend, with the therapeutic index at 50% of tumor control.

Fig. 5.5
Tumor Control Probability (TCP) and radiation dose relationship. The scheme demonstrates the sigmoid relationship of probability of tumor control and normal tissue damage to radiation dose


A schematic diagram of tumor control versus radiation dose. The therapeutic effect and normal tissue are in an upward trend, with the therapeutic index at 50% of tumor control.


Complete tumor control requires that every clonogenic cell is destroyed. Unfortunately, cell killing is randomly distributed within a population of tumor cells, and there are about 109 cells in each gram of tumor. A small fraction of these cells (about 1%), in reality, contains cells with clonogenic-forming ability; so, a human tumor could have billions of clonogenic cells; therefore, eliminating every such cell is a great challenge. The likelihood of obtaining tumor control is related to radiation dose, features of control probability of the tumor and the number of surviving clonogenic tumor cells (Fig. 5.6.).

A graph represents cell kill versus dose in gray. The plotted data, the cell with clonogenic ability has a downward trend.

Fig. 5.6
The response of clonogenic tumor cells at 2 Gy/fraction as a function of the total dose. Assuming that each 2 Gy fraction reduces the clonogenic cell population with 50%, 30 fractions of 2 Gy will reduce 1010 clonogenic tumor cells to ten surviving cells. In order to eliminate each clonogenic tumor cell, additional fractions of 2 Gy are required to reach tumor control


A graph represents cell kill versus dose in gray. The plotted data, the cell with clonogenic ability has a downward trend.


The tumor growth rate can be used to determine how a cancer will respond to RT treatment by predicting or understanding the key features of the tumor tissue response to radiation. The tumor growth rate was developed for examining the capacity of clonogenic-forming cells of a tumor and assumes that the regrowth component is a function of repopulation by the surviving of cells with colony-forming ability [20, 21].


There are considerable differences in growth rate between different tumors due to differences in size and biology. Therefore, the tumor growth curve has exponential and non-exponential parts when plotted on a logarithmic scale. That is, the tumor volume doubling time (VDT), the duration of time required for the tumor to double in size, increases for small tumors because there is a sufficiency in nutrient and oxygen supply resulting in a reduction of cell cycle, a higher proportion of cycling cells or and a lower cell death rate. As a result, the slope of the growth curve, which reflects the doubling time of the cells, has an exponential pattern for small tumors. Conversely, VDT decreases for large tumors because of the limitation of nutrient and oxygen supply. This leads to a prolongation of cell-cycle progression but also a high rate of cell death. As a result, the slope of the growth curve has no exponential patterns for large tumors. The Gompertz equation describes such progressively slowing tumor growth:


(5.1)where V0 is the volume at arbitrary zero time while A and B are parameters that determine the speed of growth [16]. VDTs are remarkably variable in human tumors, both between primary and metastatic lesions and among tumors with different histology (Table 5.1). Please also note that even within one tumor entity (localization, histology, and primary or metastasis similar) there is a range in VDT illustrating the problem of tumor heterogeneity.Table 5.1
Volume Doubling Times (VDTs) for different human tumors (adapted from [16])

Tumor site, histology

Primary vs metastasis

Number of tumors measured

Mean VDT (days) (confidence limits)

Colon-rectum

Primary

19

632
[426–938]

Colon-rectum, adenocarcinoma

Metastasis

55

95
[84–107]

Lung, squamous cell carcinoma

Primary

85

85
[75–95]

Lung, adenocarcinoma

Primary

64

148
[121–181]

Lung, undifferentiated

Primary

55

79
[67–93]

Breast

Primary

17

96
[68–134]

Breast carcinoma

Superficial metastasis

66

19
[16–24]

Breast, adenocarcinoma

Metastasis

44

74
[56–98]

Head and neck, squamous cell carcinoma

Metastasis

27

57
[43–75]

Head and neck, teratoma

Metastasis

80

30
[24–38]

Head and neck, osteosarcoma

Metastasis

34

65
[46–93]

Head and neck, fibrosarcoma

Metastasis

28

69.5
[46–93]

Kidney, adenocarcinoma

Metastasis

14

60
[37–98]

Thyroid, adenocarcinoma

Metastasis

16

67
[44–103]

Uterus, adenocarcinoma

Metastasis

15

78
[55–111]


The growth fraction (GF) refers to the proportion of cycling cells that has highly colony-forming ability and is in the active process of cell cycling (omitting cells in G0 phase), with capacity of DNA duplication and cell division [22]. Similarly, as in normal tissue, some tumor cells are not involved in active proliferation for different reasons, for instance as a result of hypoxia, differentiation, and catabolic insufficiency. Moreover, it is estimated that about 50% of cells in a tumor are not neoplastic cells but are cells making up the tumor stroma. Therefore, it is clear that the cell population in tumors contains quiescent (Q) cells, and since GF is defined as the proportion of cycling cells, it can be calculated as stated by [13, 22]:


(5.2)where p is proliferating cells.


For estimation of the cell-cycle kinetics (TC), three principal methods are used: (1) bromodeoxyuridine (BrdUrd) or thymidine analogues iododeoxyuridine (IdUrd), (2) 3H-thymidine for the synthesis of DNA and (3) positron emission tomography (PET) imaging of the tumors in vivo by radiolabeled 18F-fluoro-3′-deoxy-3′-l-fluorothymidine (FLT) [13, 16].


The first method includes labeling of the cells with BrdUrd or IdUrd. When cells pass through the S-phase, these labels are incorporated into the newly created DNA strand. An antibody against BrdUrd or IdUrd as well as a DNA-specific dye are used to stain a single-cell suspension prepared from a cell culture in vitro or a tumor biopsy, and the duration of the S phase (TS) and fraction of cells in S phase are assessed using flow cytometry.


In the second method, cell-cycle kinetics (TC) is estimated from labeled cells by measuring the duration of the cell cycle by either pulse or continuous labeling with 3H-thymidine. The labeling agent is incorporated into the DNA as cells progress through S-phase and the cell-cycle kinetics (TC) is estimated from the labeled cells [16].


The third principal method applies PET tracers to detect and evaluate tumor proliferation in vivo. In this method, radiolabeled 18F-fluoro-3′-deoxy-3′-l-fluorothymidine (FLT) is used. FLT is phosphorylated by thymidine kinases (TK) and since regulation of TK activity occurs in the S-phase, it means that metabolites of FLT (mono-, di-, and tri-phosphates) are reflecting the number of cells in S-phase and hence replication status. The FLT tracer activity in a tumor is subsequently evaluated by a PET scanner from which the cell-cycle kinetics can be estimated [16].


For estimation of the GF, according to literature the GF is obtained by assessment of two distinct cell subpopulations, one that does not grow and another which grows with a uniform cell-cycle distribution [13, 21]. This method includes the exposure of a growing culture of cells with 3H-thymidine for the synthesis of DNA, and then after the period of at least one complete cell cycle to ensure all cells producing DNA pass through the S-phase and are labeled, an autoradiography of tumor section is taken, and GF is calculated by:


There is also a possibility to take proliferation into account by immunohistochemistry assessment of tumor tissue sections by staining of the nuclear antigen Ki-67, which in tumors has different levels depending on the tumor proliferation. The method includes staining of tumor cell cultures or a tumor biopsy with a Ki-67 specific antibody followed by counting the number of positive tumor cells. The GF growth fraction is estimated from labeled cells by measuring the proportion of proliferating cells using continuous labeling. Although the method is frequently used to assess S-phase cells, recent results have indicated that Ki-67 also has different functions in other cell-cycle phases which may in fact influence proliferation estimations [23].


“The potential doubling time (Tpot) of a tumor is defined as the cell doubling time without any cell loss.” There are two methods used to estimate Tpot. In the first method, DNA is labeled with thymidine analogues and then the cells fraction in S phase (LI) and the duration of the S phase (TS) are estimated by using flow cytometry to calculate Tpot by:


(5.3)where λ is a correction parameter for the non-rectangular age distribution of growing cell populations, in the order of 0.7–1.


Different tumor tissues have different values of LI, but they have similar TS, in the range of 12 h. As a result, Tpot has a spectrum of values ranging from 4 to 34 days, as shown in Table 5.2. Of note, it has been demonstrated that in a clinical RT context, the pre-treatment Tpot does not predict outcome as one also needs to consider the repopulation rate of colony-forming cells [13].Table 5.2
Cell kinetic parameters of human tumors derived from in vivo labeling with iodo-deoxyuridine (IdUrd) or bromo-deoxyuridine (BrdUrd) and monitored by flow cytometry (adapted from [16])

Tumor site

Tumor type

Patients number

Average Tpot (days)

Average LI (%)

Average TS (h)

Skin

Melanoma

24

7.2

4.2

10.7

Hematological

–

106

9.6

13.3

14.6

Head and neck region

–

712

4.5

9.6

11.9

CNS

–

193

34.3

2.6

10.1

Breast

–

159

10.4

3.7

10.4

GIT (upper intestine)

–

183

5.8

10.5

13.5

GIT (colorectal)

–

345

4

13.1

15.3

Kidney

Renal cell carcinoma

2

11.3

4.3

9.5

Bladder

–

19

17.1

2.5

6.2

Prostate

–

5

28

1.4

11.7

Ovarian

–

55

12.5

6.7

14.7

Cervix

–

159

4.8

9.8

12.8


Slow tumor growth is not only explained by the fact that not all cells within a tumor are proliferating but also due to considerable cell loss where multiple parameters regulate these two factors. If there was no cell loss and if every tumor cell was actively proliferating, the tumor doubling time would imitate the cell-cycle kinetics (TC). Therefore, when there is cell loss the TD is long and when there is reduced GF the Tpot of the tumor is longer than the time of cell cycle [14].


The net growth rate, or the VDT, of tumors results from the balance of cell production and cell loss. In clinical settings, the GF and knowledge of the cycle time of the individual cells does not reflect the speed of tumor growth; namely, the cycle time of the individual cells is much faster than the speed of tumor growth. Such discrepancy is attributed to cell loss which can be considered by calculating cell loss factor (CLF). The cell-loss factor refers the ratio of the cell loss rate to the production of new cells, and it can be calculated by:


(5.4)where Tpot is the potential tumor doubling, and VDT is the tumor volume doubling time that is calculated by the essential time for the tumor to double its volume (V) by using:

 (5.5)


When the cell loss factor is high, it means that there is loss of newly produced cells from the GF; thus, tumor growth is slow. Cell loss has been attributed to different parameters [16, 24]: (1) Cells are in the inactive phase of cell cycling (in G0 phase) which is a non-proliferative compartment, (2) There is inadequate nutrition and oxygen levels due to the tumor outgrowth that gives rise to pushing cells into areas at a distance from blood supply, (3) Metastasis, (4) Immune cell killing of the tumor, and (5) Exfoliation (the complete removal of a single epithelial cell or group of cells from a layer of epithelium by spontaneous or induced means). In animal models of tumors, this would not apply but could be a mechanism by which cells lose their integrity in carcinomas of the gastrointestinal tract, for example, where the epithelium is renewed rapidly (Box 5.4).


Tumor volume doubling time (VDT) is influenced by tumor localization site, primary or metastatic status as well as histology but also by intra-tumor heterogeneity factors.

There are differences in growth rates between different tumor types and metastatic lesions tend to grow faster than primary lesions.

A logarithmic scale can be used to judge treatment effectiveness. An estimate of tumor growth rate is determined by cell-cycle kinetics, the growth fraction, the cell loss rate (CL), and the potential doubling time (Tpot). Even among tumors of the same histological type, these parameters differ greatly. Cell kinetics cycle of cells and growth fraction in tumors can be monitored ex vivo using various DNA-labeling strategies and in vivo using PET tracers.

Ki67 immunohistochemistry staining of tumor biopsies is a method for assessing S-phase cell proportion.

The potential doubling time (Tpot) refers to the time it would take for volume to double without loss of cells. Consequently, the potential doubling time and the observed volume doubling time are different because tumors show a high amount of cell loss.

Tumor cell loss also contributes to VDT and may be attributed to limited nutrition and oxygen supply, metastatic propensity, immune cell killing, and tumor cell exfolia.


Tumor volume doubling time (VDT) is influenced by tumor localization site, primary or metastatic status as well as histology but also by intra-tumor heterogeneity factors.


There are differences in growth rates between different tumor types and metastatic lesions tend to grow faster than primary lesions.


A logarithmic scale can be used to judge treatment effectiveness. An estimate of tumor growth rate is determined by cell-cycle kinetics, the growth fraction, the cell loss rate (CL), and the potential doubling time (Tpot). Even among tumors of the same histological type, these parameters differ greatly. Cell kinetics cycle of cells and growth fraction in tumors can be monitored ex vivo using various DNA-labeling strategies and in vivo using PET tracers.


Ki67 immunohistochemistry staining of tumor biopsies is a method for assessing S-phase cell proportion.


The potential doubling time (Tpot) refers to the time it would take for volume to double without loss of cells. Consequently, the potential doubling time and the observed volume doubling time are different because tumors show a high amount of cell loss.


Tumor cell loss also contributes to VDT and may be attributed to limited nutrition and oxygen supply, metastatic propensity, immune cell killing, and tumor cell exfolia.


The Hallmarks of Radiobiology or 6R’s are six typical molecular, cellular, or tissue processes which determine the effects of radiation on both malignant and healthy tissues.

The 6R’s are: Radiosensitivity, Repair, Redistribution, Repopulation, Reoxygenation, Reactivation of the immune response.


The Hallmarks of Radiobiology or 6R’s are six typical molecular, cellular, or tissue processes which determine the effects of radiation on both malignant and healthy tissues.


The 6R’s are: Radiosensitivity, Repair, Redistribution, Repopulation, Reoxygenation, Reactivation of the immune response.


The so-called 6R’s are six biological features which determine the outcome of RT in the clinic: the balance between the complication rate (side effects due to normal tissue injury) and the tumor control rate (palliation or curation due to tumor cell sterilization) (Fig. 5.7). These basic principles or Hallmarks of Radiobiology have been evolved from Withers’ 4R’s—“Recovery/repair, Redistribution, Repopulation and Reoxygenation”—[25] via Steels’ 5R’s—the addition of “intrinsic cellular Radiosensitivity” [26] to 6R’s by including “Reactivation of the immune response” [27] (Box 5.5).

A spoke diagram of the biological effect of ionizing radiation includes repair or recovery, radiosensitivity, reactivation of the immune response, repopulation, redistribution, and reoxygenation.

Fig. 5.7
The Hallmarks of Radiobiology, the 6R’s


A spoke diagram of the biological effect of ionizing radiation includes repair or recovery, radiosensitivity, reactivation of the immune response, repopulation, redistribution, and reoxygenation.


The six Hallmarks of Radiobiology (Fig. 5.7) in brief:
Radiosensitivity: Intrinsic and acquired radioresistance of normal tissue cells and tumor cells to radiation, in particular cancer (stem) cells among the heterogenic tumor cell population.

Repair capacity, efficiency, and mechanisms of sublethal DNA damage repair, and related sensitivity to fractionated irradiation—which is high for most healthy tissues and low for most tumors.

Redistribution of cells in the cell-cycle affects their radioresistance. Cells in mitosis are most sensitive to radiation, while cells in the S-phase are radioresistant. Redistribution following irradiation will push radioresistant S-phase cells towards a radiosensitive cell-cycle phase.

Repopulation: Cell repopulation of—not by radiation eradicated cancer cells—involved in the (accelerated) repopulation of the tumor—which is detrimental—and beneficial repopulation of normal tissue cells recovering from acute injury.

Reoxygenation: Cells in hypoxic niches within the tumor are radioresistant. Reoxygenation between multiple radiation fractions given in a radiation course is an important phenomenon by which originally hypoxic tumor cells will be reoxygenated and hence radiosensitized.

Reactivation of the immune response: Local irradiation induces a systemic immune activation to attack distant tumor cell niches which can be located outside the irradiated volume (abscopal effect).


Radiosensitivity: Intrinsic and acquired radioresistance of normal tissue cells and tumor cells to radiation, in particular cancer (stem) cells among the heterogenic tumor cell population.


Repair capacity, efficiency, and mechanisms of sublethal DNA damage repair, and related sensitivity to fractionated irradiation—which is high for most healthy tissues and low for most tumors.


Redistribution of cells in the cell-cycle affects their radioresistance. Cells in mitosis are most sensitive to radiation, while cells in the S-phase are radioresistant. Redistribution following irradiation will push radioresistant S-phase cells towards a radiosensitive cell-cycle phase.


Repopulation: Cell repopulation of—not by radiation eradicated cancer cells—involved in the (accelerated) repopulation of the tumor—which is detrimental—and beneficial repopulation of normal tissue cells recovering from acute injury.


Reoxygenation: Cells in hypoxic niches within the tumor are radioresistant. Reoxygenation between multiple radiation fractions given in a radiation course is an important phenomenon by which originally hypoxic tumor cells will be reoxygenated and hence radiosensitized.


Reactivation of the immune response: Local irradiation induces a systemic immune activation to attack distant tumor cell niches which can be located outside the irradiated volume (abscopal effect).


Many authors refer to the radiosensitivity as the degree of tumor and normal tissue regression following irradiation. There are many factors that determine the radiosensitivity which are the proportion of cells with clonogenic capacity, growth rate and reproduction rate, mitosis activity, metabolic rate, tissue type, radiation dose, inherent radiosensitivity, and hypoxia. For example, cells with fast growth or high metabolic rate are highly radiosensitive. Essentially, since the reproductive capacity of cancer cells is higher than the reproductive capacity of late responding normal tissue cells, cancer cells are more sensitive to radiation, but this depends on the cancer tissue type.


Tumor and normal cells differ in terms of repair after radiation-induced damage. Unlike normal cells, the repair process and mechanism of tumor cells are defective. While normal tissue cells do repair their radiation-induced DNA damage efficiently, malignant cells often cannot.


There are three types of radiation damage to mammalian cells:1.
Potentially lethal damage (PLD): Cell death depends on the environmental conditions. In a normal situation, damaged cells will not repair and die, but in case of reformed environmental conditions, cells can repair their DNA damage.
 2.
Sublethal damage (SLD): The death of a cell depends on the sublethal damage condition. DNA damage can be repaired if no extra injury is taking place. The recovery kinetics, the repair time, lies in the range of a few hours following DNA double strand break (DNA DSB) induction.
 3.
Lethal damage (LD): Irreparable and irreversible damage leading to cell death.


Potentially lethal damage (PLD): Cell death depends on the environmental conditions. In a normal situation, damaged cells will not repair and die, but in case of reformed environmental conditions, cells can repair their DNA damage.


Sublethal damage (SLD): The death of a cell depends on the sublethal damage condition. DNA damage can be repaired if no extra injury is taking place. The recovery kinetics, the repair time, lies in the range of a few hours following DNA double strand break (DNA DSB) induction.


Lethal damage (LD): Irreparable and irreversible damage leading to cell death.


The main reason for cell death is the production of the asystematic generation of chromosomal aberrations, including rings and di-centric aberrations that result from an interaction between more than one DNA DSB [28]. Details regarding the DNA Damage Response and repair pathways are given in Chap. 3.


Figure 5.8, panel a shows the distribution of eukaryotic cells over the four cell-cycle phases, which include the G1 phase, S-phase (synthesis phase), G2 phase (interphase phase), and M phase (mitosis and cytokinesis). Cells in the different phases of the cell cycle vary in radiation sensitivity. Cells in the S-phase are resistant to radiation (Fig. 5.8, panel a) while cells in the M and G2 phase are sensitive to radiation [14].

A diagram of radiation fraction leads to cell culture then phases sensitivity of cell cycle to radiation. 4 phases are in a falling trend for surviving fraction versus dose in gray. A cancer cell is surrounded by G 1, G 1 per S checkpoint, S, G 2, G 2 per M checkpoint, M, and M per G 1 checkpoint.

Fig. 5.8
The cell-cycle phase and radiation sensitivity. Cell survival curves of V79 Chinese hamster cells irradiated at different phases of the cell cycle on the left side


A diagram of radiation fraction leads to cell culture then phases sensitivity of cell cycle to radiation. 4 phases are in a falling trend for surviving fraction versus dose in gray. A cancer cell is surrounded by G 1, G 1 per S checkpoint, S, G 2, G 2 per M checkpoint, M, and M per G 1 checkpoint.


When cells experience radiation-induced insult, three effects occur:1.
Recruitment: Stem cells of some tumors are in the G0 phase, which is a radioresistant phase; therefore, they may repair their damage and survive. In order to kill these cells efficiently, these cells are recruited into the cell cycle so as to arrive in a radiosensitive phase.
 2.
Cells are blocked in the radiosensitive phase (G2). Cells in G2 are highly likely to be sterilized by the first radiation dose.
 3.
Cells are allowed to re-assort and progress to the radiosensitive phase. Cells in radio-resistant phases survive, yet since they continue to cycle, there is a likelihood that they will arrive at a sensitive phase and be sterilized by a second or later fraction.


Recruitment: Stem cells of some tumors are in the G0 phase, which is a radioresistant phase; therefore, they may repair their damage and survive. In order to kill these cells efficiently, these cells are recruited into the cell cycle so as to arrive in a radiosensitive phase.


Cells are blocked in the radiosensitive phase (G2). Cells in G2 are highly likely to be sterilized by the first radiation dose.


Cells are allowed to re-assort and progress to the radiosensitive phase. Cells in radio-resistant phases survive, yet since they continue to cycle, there is a likelihood that they will arrive at a sensitive phase and be sterilized by a second or later fraction.


The renewal capability of tissue clonogenic cells that follows the reduction of tissue cells, with clonogenic-forming capacity, is referred to as repopulation (regeneration). Following radiation-induced tissue injury, the tissues will react by repopulation of surviving clonogenic cells, i.e., compensation for the lost cells occurs relatively quickly, with decreasing clonogenic doubling times from 9.8 to 3.4 days. This will result in a larger number of tumor cells which is detrimental. For normal tissue injury, repopulation from the stem cell compartment will regenerate the damaged tissue, there with reducing early radiation toxicity [16].


Biologically, there are three reasons for accelerated repopulation. Firstly, when tissue is exposed to radiation, cell kinetics, which may be reminiscent of a normal epithelium is stimulated; thus, this response causes regenerative reaction of clonogenic cells to initiate repopulation by activating growth factors, such as keratinocyte growth factor (KGF). Secondly, reoxygenation will occur during the course of fractionated RT, facilitating tissue regeneration. Finally, signaling such as that via the epithelial growth factor receptor (EGFR) is activated after irradiation; hence, this signal works as the regulated regenerative response [22].


The onset of repopulation in many cases is thought to be about 3 weeks after the start of fractionated RT. Its mechanism and kinetics depend on tissue types and might be dose dependent [29] (see also Chap. 6). From the clinical point of view, the total dose should be delivered over a controlled period of time. Any reduction in overall time is limited by the radiation tolerance of acutely responding normal tissues, but an extended overall treatment time might lead to diminished tumor response due to the increase of cells as a result of repopulation.


The empirical observation that oxygen levels in tumors may be enhanced in the period after irradiation is known as reoxygenation. Reoxygenation of originally hypoxic tumor cells, besides exploiting differences in DNA repair between normal tissue cells and tumor cells, is an important mechanism and reason for fractionated RT. During the fractionation course, lethally damaged cells are removed, and the blood supply increases. Thereby, initially radioresistant hypoxic cells are gradually reoxygenated and become sensitive to radiation (Fig. 5.9).

A diagram of the oxic cell and the hypoxic cell goes through reoxygenation for the overall radiation treatment time in days to weeks.

Fig. 5.9
Simplified illustration of the reoxygenation process. Tumor cell compartments include anoxic, hypoxic, and aerated cells. Most tumors show a heterogeneous pattern of hypoxia with gradients of oxygen pressure decreasing with increasing distance from blood vessels. The oxygen status of the tumor cells is not constant; it is a dynamic, constantly changing phenomenon. Following exposure to irradiation, well-oxygenated cells will be sterilized, but many hypoxic cells will not. During the course of fractionated RT hypoxic cells can be reoxygenated, and therefore become sensitive to radiation and can be sterilized. (Figure was adapted from [13])


A diagram of the oxic cell and the hypoxic cell goes through reoxygenation for the overall radiation treatment time in days to weeks.


The oxygen enhancement ratio and the role of oxygen in the radiation response has been explained in Chap. 2. If reoxygenation is efficient between dose fractions, the presence of hypoxic cells does not have a significant effect on the outcome of a multi-fractionation scheme. In a hypofractionation regimen, the time period to obtain full reoxygenation of hypoxic tumor cells might however be too short (discussed in Chap. 6).


When irradiating a tumor, the tumor microenvironment (TME) will also be exposed. Such exposure of the TME might affect the immune system, both locally and systemically. Activation of an anti-tumor response depends on the treatment regimen, i.e., the fractionation schedule, dose, and timing because these factors disturb the balance between immunosuppressive and immune-stimulatory effects. As a result, a specific radiation treatment protocol can induce an anti-tumor immune reaction. When cells of tissues are exposed to radiation, the immune response to attack tumor cells is generated in a few steps (Fig. 5.10).

A flow diagram of radiation induced systematic immune activation features 5 steps from debris of damaged D N A and T A A released by cell lysis to T A A released from damaged tumor cells cause further amplification of immune signals.

Fig. 5.10
Illustration of the steps of radiation-induced systemic immune activation contributing to attack on distant/metastatic tumor cells


A flow diagram of radiation induced systematic immune activation features 5 steps from debris of damaged D N A and T A A released by cell lysis to T A A released from damaged tumor cells cause further amplification of immune signals.


Different radiation treatment schemes with respect to the total dose and fraction size have been shown to have diverse effects on the immune response, and therewith also on target expression with consequences for combination treatments like with immunotherapy. To obtain optimal modulation of the radiation response, specific immunomodulating or targeted drugs can be selected. The radiation-induced TME effects modulating the immune response requires further research to find the ideal immunotherapy and RT regimen [30].


The 6R’s offer options for modulation of the radiation response. Modulation strategies, such as via combination therapy with immunomodulating agents, should be aimed to widen the therapeutic window (Sect. 5.12) using approaches such as via radioprotection of the normal tissues thus decreasing the NTCP or by tumor radiosensitization by increasing TCP. Options for clinical application of such strategies are highly dependent on the tumor and normal tissue type included in the radiation treatment volume. Finally, to be noted is the close link between the Hallmarks of Radiobiology and the Hallmarks of Cancer [31] and therewith related therapeutic options, which have been discussed in detail elsewhere [32, 33].


Clinically used fractionation schemes are aimed at eradicating malignant tissue while sparing late responding healthy tissue.

The biological rationale of fractionated irradiation is based on the typical radiation response of the dynamic and heterogeneous exposed tissue and cell population.

Dose rates used in clinical RT vary from low dose rate with exposure times in hours-days to ultra-high dose rates with radiation dose delivery in the millisecond range.

The biological effect of radiation decreases with decreasing dose rate to a larger extent for normal tissue with low α/β ratio than for tumors with high α/β ratio.

Experimental data demonstrate that ultra-high dose rate irradiation might better spare late responding normal tissue.

The 6R’s of radiobiology are the biological processes involved in the dose rate effect.


Clinically used fractionation schemes are aimed at eradicating malignant tissue while sparing late responding healthy tissue.


The biological rationale of fractionated irradiation is based on the typical radiation response of the dynamic and heterogeneous exposed tissue and cell population.


Dose rates used in clinical RT vary from low dose rate with exposure times in hours-days to ultra-high dose rates with radiation dose delivery in the millisecond range.


The biological effect of radiation decreases with decreasing dose rate to a larger extent for normal tissue with low α/β ratio than for tumors with high α/β ratio.


Experimental data demonstrate that ultra-high dose rate irradiation might better spare late responding normal tissue.


The 6R’s of radiobiology are the biological processes involved in the dose rate effect.


In the early years of RT, radiation oncologists soon realized that a radiation treatment course delivered in multiple fractions over several weeks resulted in better tumor control than a treatment course delivered in a single fraction and also reduced normal tissue toxicity [21]. The history of RT and fractionation is described in detail in Chap. 2. Generally spoken, a treatment course consisting of 30 daily 2 Gy fractions (total dose 60 Gy) is, at isoeffective normal tissue late response level, more effective in eradication of the tumor than a treatment course consisting of a few high dose fractions. Hence, if the total prescribed dose is divided into multiple small radiation fractions with a time interval between the fractions, tumor control could be enhanced at an acceptable level of associated morbidity, relative to a single large dose fraction [13]. However, modern RT techniques allow to give higher dose per fraction while sparing more efficiently the surrounding normal tissue. This may affect this fractionation concept further in future.


The irradiated cell population comprises the malignant tissue as well as acute and late responding healthy (“normal”) tissues. When an RT dose is delivered in several fractions, there are advantages and disadvantages in terms of tumor cell kill and normal tissue cell sparing, which are discussed in detail in Sect. 5.14.


Acute normal tissue effects of RT depend on both fraction size and the overall treatment time. The intensity of acute reactions depends on weekly applied total dose, i.e., the dose per fraction and number of fractions in a week. After an acute reaction has peaked, further stem cell killing cannot increase the intensity of acute reactions but can prolong the healing time. A persistent early response from severe depletion of regenerating cells is termed a consequential late injury [13]. In contrast, non-consequential late normal tissue effects depend predominantly on fraction size, while the overall treatment time has little influence. Therefore, during hypofractionation, late effects are severe while early effects are matched by appropriate dose adjustment, as discussed in detail in Chap. 6 (Sects. 6.2 and 6.3).


Another important parameter is the inter-fraction interval. Due to the slow repair kinetics of sublethal damage (SLD) in late responding tissues, a minimum of 8 h of inter-fraction interval is recommended for most tissues. The overall treatment time affects both acute effects and tumor control. Prolongation of the overall treatment time (within normal RT range) has a large sparing effect on early responding normal tissues but little sparing effect on late responding normal tissues. However, excessive prolongation of overall treatment time causes the surviving tumor cells to proliferate during treatment. For any prolongation in treatment time, extra dose is required to counteract tumor cell proliferation, due to the phenomenon of accelerated repopulation. For example, in head and neck cancer, after a lag period of 4 weeks during a course of RT, the tumor doubling rate could increase due to triggering of surviving clonogens to divide more rapidly as tumor shrinks after initiation of treatment. A dose of up to 0.6 Gy of each daily dose would be “wasted” due to increased tumor cell load [34]. When the overall treatment time is prolonged, for each extra day, local control would decrease by 1.4% (0.4–2.5%) due to accelerated repopulation.


Differential responses of normal and cancerous tissues when fractionating RT doses can be explained by biological factors that are known as the 6R’s (see Sect. 5.4). During fractionation, tumor cells are redistributed and reoxygenated, causing further tumor damage. Moreover, the fractionation process will spare normal tissues by allowing repair of SLD between dose fractions and by allowing repopulation with new cells to occur over the overall treatment time. Therefore, a prolonged radiation treatment given over several weeks results in a greater therapeutic ratio than one or few short duration sessions because of tumor reoxygenation and early reacting normal tissue regeneration.


Radiation fractionation can lead to biologically optimal RT when the equi-effective total dose is related to the dose per fraction for tumors, early responding tissue, and late responding tissue. This relationship is determined by dose per fraction number, fraction number, tumor type, treatment site, and treatment plan. Using different normal tissues as models, it was found that with decreasing dose per fraction, the isoeffective total dose increases more rapidly than for acute effects or tumor response. This relationship can be described by the linear-quadratic (LQ) model. According to the LQ model, with appropriately chosen α/β values to represent isoeffect dose relationships at least at the 1–6 Gy dose range, a standard fractionation scheme with five small sized fractions per week over a few weeks would be beneficial regarding the tumor cure-normal tissue complication balance. Hence, deviation from standard fractionation affects the Biological Effective Dose (BED), which includes schedules with different fraction size and inter-fraction time as well as overall treatment duration. The BED is the total dose required to produce a particular effect in small dose fractions, used as the quantity to compare different fractionation regimens, see Table 5.3 for models that are used to deal with a deviation from standard fractionation.Table 5.3
Models of biological effective dose (BED) for isoeffect calculations for modified fractionation regiment (adopted from [16])

Model

Formula

Statement

Equivalence dose 2 Gy (EQD2)

D is total dose and d is dose per fraction.

• EQD2 is the 2 Gy dose that carries the same biological effect as a total dose D with a fraction size d Gy.
• The purpose of this model is to compare the effectiveness of schedules containing doses per fraction and different total doses. This is equivalent to converting each schedule into a 2-Gy fraction that has the identical biological effect.

Total effect (TE)

E/β = D[(α/β) + d] = TE
E = isoeffect

• It is used for schedules with different doses per fraction.
• TE and BED are conceptually similar and have been cited in literature, but E is divided by β instead of α.

Extrapolated tolerance dose (ETD)

(

) = D((1 + d(α/β)) = BED

• The ETD refers to levels of effectiveness that imply full tolerance. It is used for schedules with different doses per fraction.

Basic EQD2 formula with incomplete repair factors (Hm).

• Used for tolerance calculations, taking into account the increase in the overall damage caused by interaction of subsequent fractions.

Basic EQD2 formula with Incomplete repair factors (g factors).

• Used for low dose rate exposures.


The dose rate is defined as the ratio of the radiation dose to the duration of the radiation exposure. The term should be used only in the context of short periods of time, for example, dose per second or dose per hour, the SI dose rate unit is Gy/h. Acute exposure refers to a high radiation dose delivered in seconds or minutes, and chronic exposure means that the radiation dose is delivered over a longer period of continuous exposure over hours to days to even months and years. The spectrum of dose rates used in radiation oncology is presented in Table 5.4.Table 5.4
Dose delivery conditions used in the clinic, for internal radiation therapy (brachytherapy) and external beam irradiation, and related dose rates (ICRU 38 definitions and FLASH)

Dose delivery condition

Dose rate (Gy/h)a

Low dose rate (LDR)

<2

Medium dose rate (MDR)

2–12

High dose rate (HDR)

>12

Pulsed dose rate (PDR)

±75% HDR, ±25% MDR and LDR

Ultra-high dose rate (FLASH)

≥144.000

aThe International System of Units (SI) defined dimension for the dose rate is “Gy/h”


Physical aspects of the dose rate are presented in Chap. 2. The application of low dose rate irradiation in brachytherapy in the clinic, is discussed in Chap. 6. FLASH is a novel RT treatment technique using ultra-high dose rates. Using FLASH, multiple studies indicate sparing of healthy tissue acute and late toxicities while maintaining tumor control, hence widening the therapeutic window (Sect. 5.2). FLASH is discussed in detail in Chap. 6. The radiation dose rate has a large biological impact on exposed cells and tissues. Both in vitro and in vivo experimental data revealed that, for a defined biological endpoint, for example, cell survival or a certain late normal tissue reaction like myelitis of the spinal cord, the biological effect decreases with decreasing dose rate. With decreasing dose rate, the total dose to obtain a certain isoeffective biological endpoint—for example, a probability of 50% loss of kidney function or reduction of the cell survival with a fraction of 0.4, is increased. Dose rate sparing is almost absent for acute responding normal tissues and tumors.