Brachytherapy: Applications and Technique, 1st Edition

1. Radiobiologic Concepts for Brachytherapy


Alexandra J Stewart

Bleddyn Jones

Brachytherapy, from its Greek derivation, refers to “short range therapy” and has been described as the first form of conformal radiation therapy.1 The advantage of placement of radiation sources within or very close to the cancer, allowing a high cancer to normal tissue ratio, outweighs any potential disadvantage of steep dose gradients within the cancer. Precise source placement enables small volumes of normal tissue to be irradiated, with extremely high doses (hyperdoses) within the cancer and sufficient dose at the margin between the cancer and normal tissue, to eradicate microscopic tumor foci and provide a high control rate. It follows that cancers with clinically and radiologically well-defined margins, usually those in the low histologic grading categories with a low risk of regional and metastatic spread, are the most suitable for brachytherapy. The selection of an appropriate prescription point, or the isodose surface, is paramount to achieve the best ratio of cancer dose to that of the critical normal tissue.

Brachytherapy was initially developed empirically with prescription doses (expressed as durations of treatment) being crudely adjusted to obtain improved clinical outcomes. The use of radiobiology to guide brachytherapy prescriptions became more necessary with the change from low dose rate (LDR) treatment to high dose rate (HDR), although radiobiologic principles are important in all brachytherapy treatments. Later in this chapter, we will use clinical situations to illustrate some of these practical applications.

Source placement remains the single most important factor in brachytherapy, such that in an implant with relatively poor geometry, and which cannot be improved, changing the controllable radiobiologic factors (dose rate and fractionation) with attention to the different responsiveness of normal and tumor tissues will change the biologic effect and consequently, the clinical outcomes.

In external beam radiotherapy (EBRT), a relatively large volume is treated with a relatively homogeneous distribution of dose such that deviations of dose within the volume typically can range from 95% to 107% of the dose.2 In contrast, brachytherapy treats a smaller volume with an extremely heterogeneous dose distribution. The average dose within the prescribed volume is usually far higher than the prescribed dose at the reference isodose on the periphery of the implant. This is tolerated due to the volume–effect relationship: very small normal tissue volumes (e.g., 1 to 2 cm3) can tolerate very high doses that larger volumes would not tolerate. This is probably due to the three-dimensional arrangement of vascular supply within normal tissues.

Figure 1.1 Survival curve plot for α = 0.15 Gy-1, β = 0.05 Gy-2 for a treatment time of 24 hours at various dose rates. Note that for a treatment that gave 10 Gy at 1.5 per hour (*) to a very small volume and if a larger volume received 0.5 Gy per hour (*) to a dose of 5 Gy, there is a striking difference in the survival fraction.

The main clinical advantages of brachytherapy are consequently based on the sharp reduction of dose with distance; but not only is there a physical dose sparing, there is also a greater degree of radiobiologic dose sparing, because of the reduction of both dose and dose rate with distance. It can be seen from Figure 1.1 that the survival curve becomes progressively less steep with the reductions in dose rate even if the same dose is given. Therefore, a change from a prescription point that receives 10 Gy at 1.5 Gy per hour to a more distant point that receives 5 Gy at 0.5 Gy per hour shows a large increase in surviving fraction (SF), more so than if 5 Gy had been given at 1.5 Gy per hour. Therefore, a fall of dose and dose rate causes a larger reduction in cell kill than a reduced dose or dose rate used in isolation. For HDR applications, the benefits of a reduced dose per fraction with distance have a similar effect; these benefits are the same as those in EBRT.

Dose Rate Definitions

Three categories of brachytherapy were defined in the International Commission on Radiation Units and Measurements 38 report:3

·     Low dose rate (LDR)—a range of 0.4 to 2 Gy per hour. In clinical practice, the usual range is 0.3 to 1 Gy per hour, although in some countries this is extended to 1.9 Gy per hour.

·     Medium dose rate (MDR) a range of 2 to 12 Gy per hour.

·     High dose rate (HDR) over 12 Gy per hour, which must be delivered by automatic afterloading.

Another brachytherapy method has subsequently been developed: Pulsed dose rate (PDR), which uses a large number of small fractions in an effort to simulate the radiobiologic advantages of LDR, but with the obvious advantages of a stepping source and the radioprotection advantages of remote afterloading as in HDR.

Permanent implants deliver a high total dose at a very low dose rate (vLDR), usually at <0.4 Gy per hour.

Radiobiologic Factors

The discussion of radiobiology will follow the conventions of the linear quadratic (LQ) model of radiation effect, where the SF for treatment given in n fractions of dose d at high dose rate is


Take the natural log of each side and multiply throughout by -1, so that the “log cell kill” may be defined as

where D is the total dose and D = nd.

The biologic effective dose (BED) is obtained by dividing the expression for E by α, so that

BED is therefore the product of the total dose and the “relative effect”, the latter being the terms in parentheses. For continuous radiations, assume that this is a single fraction, that is n = 1, and that the dose rate (R) multiplied by treatment time (T) replaces the total dose D, so that

The factor g, which is discussed in more detail later in the text, compensates for incomplete repair during continuous exposures in the β damage component, for T > 12 hour, g can be approximated by 2/(µ T) where µ is the sublethal damage (SLD) repair rate constant, then

And for continuous radiations, we divide eq. 1.4 by α and include the g factor to give the brachytherapy LDR BED as:

It can be seen in Figure 1.2 that the BED is always larger than the physical dose at any distance and that with distance, the normal tissue BED for late tissue complications changes even more than the tumor BED.

Introducing Tissue Sparing

The equations in the preceding text can be modified for the calculation of normal tissue doses that receive doses smaller or larger than those at the prescription point or surface. This can be achieved by introducing a sparing factor x, such that z = xd where d is now the prescribed dose (or dose rate) and z is the dose (or dose rate) at the point or surface of interest. For example, the x factor will be 0.8 when moving from a prescribed dose of 100% to an 80% surface, or 0.6 for a change in prescribed dose of 100% to a 60% surface and so on. Excess dose regions will have x > 1, for example, for a 100% prescription dose an area with 125% predicted dose will have x = 1.25.

Figure 1.2 Plot of physical dose, tumor, and normal tissue biologic effective doses (using generic α/β values of 10 Gy and 3 Gy, respectively) with distance from a radioactive source and with dose rate varying as the square of distance. The assumed sublethal damage repair half-times are given on the graphic.


Figure 1.3 Schematic diagram of threshold effect and linear dose–response relationship assumed for the increase in late complications or tumor control with increasing biologic effective dose for a large heterogenous population of individuals.

Threshold Effects

The BED concept can be used within dose–response relationships with threshold effects. For example, it was seen in carcinoma of the cervix that severe rectal complications occurred after a threshold BED of 125 Gy3 to the rectal reference point and that further increments in complications occurred at an approximate rate of 1% per additional Gy3 of BED.4 Therefore, as an approximation, we can use:

Estimated %effect = m(BED-BEDThr), where BEDThr is the threshold BED and BED is the calculated BED, m being the slope of the increment with BED (See Figure 1.3).

For example, if it is found that there is a 5% incidence of a grade 3 toxicity at a BED of 110 Gy3 and a 32% incidence at a BED of 140 Gy3, then

5 = m(110 - BEDThr) and 30 = m (140 - BEDThr)

From these two equations we find

m = 0.9


BEDThr = 104.4 Gy3.

That is, there is an increase in grade 3 toxicity of 0.9% per Gy3 BED given beyond a threshold of 104.4 Gy3 in this situation.

Total Biologic Effective Doses

The BED takes account of the physical aspects of dose delivery along with the specific radiobiologic parameters characteristic of the irradiated tissue. BEDs are additive for different radiation modalities, so that brachytherapy BED can be added to the external beam BED as in:


Although some papers on radiotherapy techniques have reported the use of total nominal dose this method is unreliable, as it does not account for the effects of dose rate in LDR and of fractionation in HDR treatments.

The “4 Rs” of radiobiology, normally used with reference to fractionation effects, can be examined with reference to brachytherapy. A fifth category, radiosensitivity (already included in the LQ model parameters) and a sixth R, tumor regression, could also be added.


Repair of sublethally damaged DNA can occur if the cell contains the full complement of DNA damage detection proteins and repair enzyme systems, but there must also be sufficient time for these mechanisms to operate. If successful sublethal damage (SLD) repair has not occurred at a particular site before further SLD is deposited in an appropriately near site, then lethal/unrepairable damage will form. In terms of the LQ model the conversion of sublethal to lethal injury is operative in the β component that accounts for the two-hit probability of damage, that is, two potentially repairable DNA lesions (e.g., single strand break or base lesions) will be sufficiently closely situated in time and space to produce a nonrepairable lesion, for example, double strand breaks. This is a simplistic interpretation for understanding the basic processes, although cell lethality is caused by multiple events of this type to cause lethal chromosome breaks.

The lower the dose rate of radiation that a cell is exposed to, the more likely it is that repair will occur, because there will be more time for SLD repair before a second “hit” confers the unrepairable damage. Late reacting normal tissues have a higher capacity for repair than do some tumor cells (probably because the latter possess mutations that affect repair fidelity and cell cycle checkpoint control) so that tumor is preferentially killed when compared with normal tissues. Late reacting normal tissues, particularly the central nervous system (CNS) and lung that have long tissue turnover times, appear to have longer repair kinetics, that is, they may possess both fast and slow components (or even multicomponents) of repair.5 The half-time of repair is of crucial importance. In human tissues the simplest possible approach is to assume a single half-time (T1/2) of 1.5 to 2 hours for normal tissues and 0.5 to 1 hour for rapidly proliferating tumors (e.g., squamous cell cancers). The number of half-times of repair will give an approximate guide as to the completeness of repair. For an implant that delivers a dose of 50 Gy in 100 hours (the dose rate then is 0.5 Gy per hour), after the first hour of exposure there will be 99 tumor half-times of repair (assuming a T1/2 of 1 hour for tumor) and nearly 50 normal tissue half-times of repair (assuming a T1/2 of 2 hours for normal tissues) during the irradiation. Compare this with an 11-hour implant to a dose of 22 Gy (i.e., at 2 Gy per hour). Considering the SLD at the end of the first hour, we obtain in the remaining time 10 tumor half-times of repair (for a T1/2 of 1 hour) and only five normal tissue half-times of repair (for T1/2 of 2 hours). Five half-times of repair would allow approximately 0.55 = 0.03% of the initial SLD to remain unrepaired.

Normal tissue repair could be disadvantaged by the application of HDR unless there is compensation in terms of a reduction in total dose; the situation is similar to fractionation in EBRT. It follows that there would be much larger amounts of unrepaired SLD formed for each subsequent hour, after the first hour. The more unrepaired damage that exists during the continuous irradiation allows further lethal damage to form. Mathematically this becomes quite complex,1,6but for a single repair time assuming exponential (first-order reaction) kinetics, the full equation can be reduced to a fairly simple expression (g as introduced in the preceding text) that can be used to correct the cell kill linked to the β parameter in the LQ model.

The time course of LDR treatment over several days allows for substantial SLD repair. In conditions of radiation where repair takes place during exposure the LQ equation is modified by incorporating a time factor (g), where

where T is the treatment duration and µ is the DNA SLD repair time constant, which is related to the half-time of mono-exponential repair by the relationship µ = 0.693/(T1/2). This factor depends on the half-life for repair and the duration of exposure, as shown in the preceding text. Its value is one for brief exposures and tends toward zero for long exposures. This gives a linear quadratic survival curve for short irradiations that gradually becomes more linear for protracted irradiation, because the α related cell kill will then predominate over the β related kill (i.e., β related kill tends to zero at very LDRs because g tends to zero).

Essentially, for durations longer than 10 to 12 hours the function g is used, where g = 2/(µ T). The short treatment time of HDR brachytherapy prohibits SLD repair during the actual irradiation. However, if an interval between HDR fractions of say, 12 to 24 hours is maintained, substantial SLD repair can occur, although it may remain incomplete for up to 72 hours in some tissues, which exhibit slow forms of repair.5

For HDR to be radiobiologically equivalent to LDR, the dose per fraction should be kept as low as is practically possible, so that the total dose may require to be split into different fractions. For example, when treating carcinoma of the cervix, most centers in the United States use five or six well-separated fractions of HDR brachytherapy and have survival and complication rates similar to LDR. This finding is probably due to the prior use of well-fractionated EBRT and the combined effect of repair half-life and normal tissue sparing. Sorbe et al.7 have shown equivalent locoregional recurrence rates when treating the vaginal cuff with HDR brachytherapy, randomizing to a schedule of 2.5 Gy in six fractions at 0.5 cm from the cylinder surface over 8 days or 5 Gy in six fractions at 0.5 cm from the cylinder surface over 8 days. However, there were much lower rates of late vaginal morbidity in the lower dose per fraction group.

Orton5 has theorized that the repair half-life of late responding normal tissue in cervix radiotherapy is longer than the 1 to 1.5 hour estimates proposed by other investigators.8,9 If the repair T1/2 was 1.5 hours, an HDR dose of 2 to 3 Gy per fraction would be equivalent to LDR at 0.5 Gy per hour. In contrast, if T1/2 was 4 hours, HDR doses of 5 to 12 Gy per fraction would be equivalent. The latter matches the current practice more closely, but these considerations do not include the heterogeneity of physical dose distributions that inevitably occur in a population of patients. The longer repair half-life would reduce the SLD repair estimates of LDR, making HDR superior for preventing late normal tissue complications. These calculations also make no allowance for volume effects.

Repair may not simply be a mono-exponential function of time and may have both fast and slow components or may be represented by multiple processes.10Serious consideration should be given for such approaches for implants in or close to CNS tissue. The repair rate may vary during a treatment course; for example, it has been seen that the repair rate after a challenge dose of γ radiation may be accelerated if a priming dose of radiation is given first.11 Some authorities speculate that the repair rate may be fastest with low doses of radiation and becomes slower with higher doses and dose rates.12

There are important implications for practice. Although HDR and LDR can be equated, for example, we could choose an equivalent dose per fraction of HDR to match a dose rate in LDR. We can only achieve this at one isodose surface within a patient where BEDHDR = BEDLDR. At all other surfaces the BED values will not equate. In general terms, for an equivalence at the prescription surface, BED values are higher at distances closer to the sources than the prescription surface for HDR than for LDR; conversely at distances further away than the prescription point, the LDR BED is higher than the HDR BED.13 The reader can check this easily by doing the relevant calculations.


In squamous cell carcinoma, studies have shown improved tumor control and increased survival when radiotherapy is given in the shortest overall time.14,15,16,17 This is because shorter treatment times allow less time for substantial tumor cell repopulation or for the phenomenon of accelerated repopulation to establish. The continuous administration of LDR probably prevents repopulation during treatment, at least in all normal tissues but cancers that possess mutated cell checkpoint genes may continue to proliferate. An important caveat is that the use of fractionated HDR brachytherapy, if protracted following external radiotherapy, may result in a markedly increased overall treatment time. Okkan et al.18 showed that the average time to complete treatment when HDR was used was 70 days, compared with 57 days when using LDR. This may decrease tumor control by allowing increased repopulation. Those with extensive experience of HDR brachytherapy have delivered the latter at weekly intervals during external beam therapy,19,20 thereby reducing the overall treatment times; a satisfactory compromise would be to give a few brachytherapy treatments after 28 days of external radiotherapy, at weekly intervals, with the remainder at twice or three times per week frequency following cessation of external radiotherapy. This would allow brachytherapy to be deferred until the benefits of tumor shrinkage had occurred (see subsequent text) and minimize the overall treatment time.

Chen et al.21 showed that when treating cervix cancer with HDR brachytherapy, if treatment was prolonged over 63 days there was a significant decrease in disease-free survival from 83% to 65% (p = 0.004) and in local control from 93% to 83% (p = 0.02). However, the limit of 63 days would be felt by many investigators to be too long as most studies have used a maximum of 55 days to assess the effects of prolonged treatment time.14,15 Importantly, no difference in late complications was seen in the under-63 day treatment group, suggesting that there is no morbidity benefit in extending overall treatment time, as may be expected for late effects.

Tumor BED calculations can be adjusted for repopulation effects by subtracting a daily BED equivalent for repopulation. This can be achieved in several ways.6,22,23 The most conventional method for squamous cell cancers is to assume that accelerated repopulation is significant after a time delay (Tdel) of around 21 to 28 days after the initiation of radiotherapy.24 The BED is reduced by K (TXR - Tdel). This is subtracted from the standard tumor BED for cell kill, where TXR is the overall time of all radiotherapy (including EBRT and BT) and K is the daily BED equivalent for repopulation, usually taken as being between 0.5 and 1 Gy per day in squamous cell cancers.24

If new biologic and functional imaging modalities such as magnetic resonance spectroscopy (MRS) and positron emission tomography (PET) could identify zones of aggressive cell repopulation, then these subvolumes could be specifically dose escalated. Gradients of cancer cell proliferation are known to follow microscopic distributions that are incompatible with the resolution achieved by conventional imaging techniques, so it would be unwise to reduce dose to any area within a cancer.


Owing to inappropriate development of intratumoral vasculature there are large proportions of poorly oxygenated cells within tumors. There are two hypoxic cell populations; long term and transient. In squamous cell carcinoma, the effect of hypoxia on tumor control has been well documented with decreased survival in patients with a low initial hemoglobin level.25,26,27 Owing to the length of administration of LDR, time is allowed for transient hypoxia to correct within the tumor during treatment.28 HDR treatments allow time between insertions for tumor shrinkage and reoxygenation to occur. This reduces the distance between capillary vessels in the tumor and increases oxygen delivery to the cells allowing for areas of long-term hypoxia to be reoxygenated.

LDR has a lower oxygen enhancement ratio than HDR,28,29 it may be as low as 1.6 to 1.7 for LDR compared with 2 to 3 for HDR.30 HDR treatments, in principle, could be combined with hypoxic sensitizer use, at least for some of the treatments.31,32,33 More research is indicated, for example, in the use of PET scan and microelectrode studies to select patients for sensitizer drugs in conjunction with brachytherapy exposures.

Reassortment/Cell Cycle

There is a theoretic advantage of an improved effect on cell cycle reassortment using LDR treatment as cells will pass out of the relatively radio-resistant phases of late S and early G2 into the more radio-sensitive phases of G2 and M during the overall treatment time. This has been shown in vitro with certain cell lines,34 but in practice the effect of reassortment has not been shown to give a true advantage. Correlations of outcomes with mutations in cell cycle checkpoint control genes should eventually provide useful information; the capacity and fidelity of repair is linked to cell cycle regulation. The slower forms of repair in normal tissues are highly dependent on cell cycle checkpoint control and are absent in many cancer types.35 Many cancers therefore, have less capacity for repair, that is, not all the damage is repairable, as it is assumed that the slower mechanisms can repair more complex forms of damage. The classical repair equations need to be reassessed in this respect.


Because of the sharp falloff of dose with distance, tumor volume regression effects can influence brachytherapy dose distributions. Extensive modeling research36,37 has shown the following:

1. Fast repopulation rates, as encountered in rapidly growing cancer types such as squamous cell cancers, can effectively oppose the shrinkage benefits. Accelerated repopulation, after an apparent delay time where insignificant repopulation occurs, can allow for initial advantages in terms of shrinkage, but as time proceeds beyond 25 to 30 days, the faster repopulation results in deterioration in tumor control. The rate of loss of control is less per day than with standard external radiotherapy provided centripetal cancer regression continues to occur, with resultant improvement in brachytherapy dose distribution. In stage I and II cervix cancer, the rate of loss of control with time is less than in stage III and IV cancers, which can remain fixed to surrounding anatomic structures. If brachytherapy catheters have to be placed eccentrically relative to a cancer, the shrinkage effect is also reduced, as there is a limit to the benefits of regression. Anatomic factors also operate here, for example, an exophytic cervix cancer even if symmetrically positioned around the cervical os will regress to the limit of the surface of the cervix, but no further. These concepts, along with random sampling/Monte Carlo modeling provide a rationale for brachytherapy to be deferred until around 28 days to gain from tumor shrinkage in terms of brachytherapy dose distributions; further deferral of brachytherapy should be avoided. A considerable amount of dose will be “wasted” by the use of prolonged overall times, although it will contribute to the risk of serious late effects. The measured loss of control at times beyond 50 days is probably artefactual, because loss of control with treatment extension has been found in the case of schedules where the normal overall time is as short as 30 to 40 days.

2. Tumor shrinkage rates follow exponential kinetics, so that the volume at time t(Vt) is related to the initial volume (Vo) as

where s is the volume regression rate coefficient. For changes in tumor linear dimensions with time, the volume coefficient should be reduced by a factor of three.

3. Slow regression can be a clinical problem. For example, occasional cervical cancers may remain sufficiently large after external radiotherapy and weekly chemotherapy, such that the brachytherapy dose distribution might be suboptimal; there is a clinical dilemma as to whether to proceed with brachytherapy or give more external radiotherapy. The latter option can result in enhanced normal tissue toxicity and is associated with a steep increase in complications. A reasonable alternative option is to protract the chemotherapy, using either more platinum-based chemotherapy or other active agents until a few more weeks have elapsed and then use brachytherapy.36 Doing nothing, for example deferral of brachytherapy would only allow a slowly shrinking tumor to repopulate.38,39

Dose Rate

Dose rate is one of the principal factors in determining the biologic effects of brachytherapy. In general the effects of radiotherapy decrease as the dose rate decreases, predominantly due to an increase in repair. The dose needed for 1% survival in vitro following irradiation is 1.5 to 3 times higher at 1 Gy per hour than at 1 Gy per minute. The dose of acute radiation exposure required for the same biologic effect at 1 Gy per hour is increased by up to twofold in tumors. In healthy tissues, it is two times higher in early reacting tissues and two-and-a-half-times higher in late responding tissue. This gives a differential protection of late reacting tissue with LDR but the in vitro data takes no account of factors such as volume effect and so on.40

There was some degree of controversy over the need to vary the total dose of the implant according to the overall time of the implant, with 60 Gy in 7 days taken as the standard implant. On the basis of the Christie Hospital experience, Paterson41 initially suggested that the total dose of LDR prescribed should be corrected for overall time of the implant and a power law system was used to relate dose rate to tissue effects. The relevant equation was the following:

where R is dose rate, T is treatment time (valid between 1 to 10 days) and C is a constant that represents the dose required in an instantaneous treatment.42However, Pierquin found no difference in control or necrosis with a total dose of 70 Gy and a dose rate ranging from 0.5 to 1.67 cGy per minute.43

Initially, the presence of a dose rate effect was not supported by a randomized study in cervix carcinoma that showed no difference in overall survival or local control for a dose rate of 0.4 versus 0.8 Gy per hour.44,45 However, there was a significant increase in late complications in the higher dose rate group, 45% versus 30%. The analysis of Mazeron showed a dose rate effect on local control in breast carcinoma, perhaps at the cost of increased cosmetic complications.46 Mazeron47 also showed an increase in necrosis in tongue cancer from 12% at 0.5 to 0.99 cGy per minute to 29% at 1 to 1.67 cGy per minute for no significant change in tumor control rate at 70 Gy. When the dose was decreased to 60 Gy there was a significant decrease in tumor control at the lower dose rate, 66% versus 91%.47 Therefore, it is felt that the dose rate should be in the range of 0.3 to 1 Gy per hour more due to the effects on late complications than local control. If the dose rate exceeds 1 Gy per hour, a reduction in the total dose should be considered and can be calculated using the BED concept. In HDR, fractionation will compensate for the lack of relative protection of late responding normal tissues.

Dose and Fractionation

In teletherapy, a homogeneous dose distribution ensures a single BED applicable throughout the whole volume. The dose heterogeneity of brachytherapy can be problematic. A BED at a dose reference point can be calculated, but the BED proximal to the source is likely to be much higher, but lower beyond the prescription point. This is beneficial for tumor sterilization but is an important consideration for any normal tissue structure within the treatment volume. Early reacting normal tissue has a lower sensitivity to dose per fraction (due to the higher α/β ratio) than late reacting tissue. The BED increment with increasing dose per fraction is larger for late reacting tissues than for rapidly growing tumors that have significantly higher α/β ratios.7,48 Therefore, a small dose per fraction in HDR may be associated with a lower risk of late complications and a better therapeutic ratio provided the overall treatment time is not overprotracted. These differences may be marginal for tumors that have low α/β ratios (e.g., prostate, breast, and low grade sarcomas).

The conversion of LDR dose to HDR has been widely studied in carcinoma of the cervix. There continues to be wide variations in dose and fractionation as shown in an analysis by Petereit and Pearcy in 199949 where the average BED of doses used to treat carcinoma of the cervix with EBRT and HDR brachytherapy were 96 Gy10 for stage IB and IIB and 100 Gy10 for stage IIIB. They showed no threshold dose for local control or survival and noted that even studies with total cervix BEDs as low as 46 Gy10 showed excellent local control rates. This is not surprising, as point A dose is not necessarily representative of the actual tumor dose in all situations; low BEDs at point A should cure small cancers, whereas larger cancers that have extended beyond the range of point A will require higher BEDs (see Chapter 1 Case Studies).

Orton et al.50 recommend that the HDR dose per fraction for cervix HDR brachytherapy is lower than 7 Gy to attain excellent cure rates with a significant decrease in late toxicity. Chatani et al.51 showed no difference in local control or complication rates when randomizing patients to 7 Gy versus 6.5 Gy per fraction for cervix HDR, but this is perhaps too small a change in dose to show any difference. The relevance of prescription at point A for tumor control is again questionable. It is only to be expected that the use of isodose surface prescription coupled with a greater degree of source placement and optimization of isodose surfaces to tumor geometry will produce better conditions where radiobiologic models may be used to an advantage.

In cervix cancer, Stitt et al.52 showed that the probability of late normal tissue damage increases as the number of fractions decreases. This is also related to the percentage of dose that the normal tissue receives. If the normal tissue were to receive 100% of the dose, 30 fractions would be needed for LDR late complication equivalence. If it received 90%, 12 to 16 fractions would be needed and if it received 80%, 4 to 6 fractions could be used and so on. These figures apply to the use of exclusive brachytherapy. There is consequently little wonder that only two to four fractions may be sufficient if brachytherapy is used as a “boost” after well-fractionated EBRT, particularly if good normal tissue sparing can be achieved in an individual patient. Hama et al.53 showed that there were increased late complications if four fractions or less were used. However, Patel et al.54 used 18 Gy in two fractions and still showed a very low rate of late complications. It is the total BED to normal tissue from both external radiotherapy and brachytherapy that will be important; good fractionation of the former will dilute the effect of large fractions given by the latter.

Pulsed Dose Rate

PDR was developed to mimic the biologic effect of LDR but takes advantage of the stepping source technology and optimization of HDR. It also carries the advantages of an afterloading device and a single source rather than carrying an inventory of sources of different strengths. Generally, the same total dose and same total time as LDR are prescribed but it is given in a large number of small fractions, generally every 1 to 4 hours. If it is given at a pulse width of 10 minutes and a 1-hour pulse interval the dose is equivalent to LDR 60 cGy per hour.1,30 If the dose per pulse is small (≤0.5 Gy) and the repair half-time is over 30 minutes, the differential effect to LDR is <10%. If the dose per pulse is over 2 Gy or the tissue repair half-time is under half an hour this is not the case and the PDR effect becomes biologically closer to a highly fractionated HDR treatment, especially in close proximity to the source.12 In this case, a lower total dose than LDR can be given in the same overall time. There are indications that the toxicity of PDR can be the same as for LDR/HDR in clinical practice.55

Very Low Dose Rate

Permanent brachytherapy implants are usually in this category, frequently using low energy γ-rays, which result in very rapid dose reduction outside the implanted volume, but may carry a higher relative biologic effect (RBE). The dose rate steadily decreases over time until the sources are completely decayed. The decrease in radiation effectiveness may be compensated for by tumor shrinkage decreasing the distance between the sources.1,56 Also, as the dose rate decreases, the RBE can increase, therefore compensating in part for the dose rate reduction. There is greater dose sparing effect with LDR for normal tissue than tumors. In vivo, normal human fibroblasts have shown increased survival after vLDR when compared with fractionated EBRT, probably due to the effects of repair at LDRs.57 The effectiveness of vLDR is dependent on the rate of proliferation of the tumor cells involved and is therefore more effective in slowly proliferating tumors, for example, well-differentiated prostate cancer.

Some Practical Issues

1. Radiobiologic modeling can be used to assess practical problems, for example, if changes are made in source placement.39

2. The decay of sources with time. How is source decay compensated for by an increase in HDR treatment time, as will inevitably occur through a fractionated treatment course?

In general, consider an interval of time t between the first and second fraction and that the source decays according to the relationship

where Rt is the dose at time t and R0 the dose at time zero, with λ being the decay time constant.

To deliver the same dose D, the exposure time of the first fraction (T0) must be increased to be (Tt) at the next fraction such that

R0 T0 = Rt Tt = D



Let z = eλt. A plot of the z value required for different overall times for different half-times is seen in figure 1.4. Normally, physicists compensate for radioactive decay on a daily basis; sometimes this is forgotten and errors of the magnitude shown in Figure 1.4 can then occur (see Chapter 1 Case Studies).

If no compensation has been allowed for, then for up to n fractions separated by a time t between fractions, each successive dose rate will be given by

In the case of HDR therapy, we can substitute dose per fraction for dose rate in this situation.

3. A further and more complex problem is the effect of decay times on individual fractions because of the time exposure elongation: Should extra dose be given to compensate for an overlong treatment time that allows significantly more SLD repair and a higher SF during the exposure? For example, in HDR brachytherapy, the treatment times become progressively longer with the age of the source and in very large implants that take longer time to deliver using a stepping source, the problem can become significant. Essentially, we require a relatively constant treatment BED, so the priority should be:

BED (standard time) = BED (extended time), at least to within 1%, because a 1% change in BED may produce a 1% change in tumor control probability (TCP).

This problem can be addressed by application of dose rate effect equations in terms of an inequality, for example, if the difference in BED between a standard time (e.g., 10 minutes or 0.17 hour) and a longer treatment to the same dose D exceeds 1 Gy10 (used here generically for tumor control), then

it follows that

Where this condition is met, then iterations of sample calculations can provide a reasonable correction in terms of the additional dose required to overcome the extra repair achieved in tumor cells over a longer exposure time. In this way, the BED for a 10-minute exposure can be compared with a slightly higher dose but at a lower dose rate for a longer exposure (see Chapter 1 Case Studies).

Figure 1.4 Plot of correction factor (z) required for exposure duration to maintain the same dose with elapsed time between treatments for variations in half-time of decay for different isotopes in brachytherapy.


Integral Tumor Doses

Dale et al. published integrated tumor dose correction factors that essentially provide an equivalent uniformly distributed BED across a tumor.13 Generally, these factors vary from 1.1 to 1.3 in most situations. This extra BED may play an important part in overcoming radioresistance, for example, due to hypoxia. For routine clinical purposes, the BED at the tumor margin furthest away from the radioactive sources should be the primary consideration but increasing use of integrated BED may correlate better with outcomes and should be increasingly used in the analysis of treatment results.

Permanent Implants

There are important interactions between physics and radiobiology. Modeling studies58 have shown the following:

1. Isotopes with relatively short decay half-times are more appropriate for tumors that contain rapidly repopulating cells.

2. The protracted treatment times to deliver very high doses in the case of isotopes with long half-times of decay are necessary to overcome repopulation over the extended treatment times, even if the actual rates of repopulation are slow.

Some isotopes have RBE values that exceed unity and BED equations can be modified to include the enhanced α-mediated cell kill, which is independent of the dose rate effect. In such cases the relative effect portion of the BED equation can be modified, replacing the unity term with RBEmax, defined as the RBE at near zero dose or the ratio of α values for the higher linear energy transfer (LET) and low LET, respectively.59

The Influence of Cytotoxic Chemotherapy and Other Biologic Therapies

It is possible to modify the BED equations if other treatments approach influence repopulation (e.g., cytostatic drugs) or cause independent cell kill.60 A BED equivalent for chemotherapy is just as feasible as a BED equivalent for repopulation. If the TCP increases by say 1% per Gy10 of BED, then if a 15% increase in tumor control is found in a clinical trial by the addition of chemotherapy to radiotherapy, this implies that the chemotherapy has an equivalent BED of 15 Gy10. In EBRT, the addition of cyclophosphamide, methotrexate, and fluorouracil (CMF) chemotherapy to whole breast radiotherapy provides a late normal tissue complication dose equivalent of approximately 4 Gy.61

Figure 1.5 shows a modeled example of a clinical scenario for the treatment of cervix cancer where an external beam schedule of 45 Gy in 25 fractions is followed by brachytherapy (25 Gy in five HDR fractions). Also included are the estimated TCPs for the addition of chemotherapy on the assumption that 15 Gy10 BED is gained. The variation of control with treatment time can be seen. The net effect of the chemotherapy is to equate with results at shorter treatment times in the absence of chemotherapy. A major research question is whether shorter treatment times plus chemotherapy will actually provide the increased cure rates predicted by the model.

Chapter 1 Case Studies



Case 1

A patient begins an LDR implant for a head and neck squamous cell cancer prescribed to be given 70 Gy in 140 hours at the reference surface, but which has to be removed after a dose of 30 Gy has been delivered due to an acute onset of intercurrent illness. The LDR implant is replaced after a time gap of 7 days. How might the prescription be changed?

Figure 1.5 Modeling example using random sampling techniques to provide estimates of tumor cure probability with time for a combination of 45 Gy in 25 fractions combined with weekly cis-platinum sufficient to give cell kill to an equivalent biologic effective dose of 15 Gy10. Assumptions are given as means with standard deviations in parentheses: α = 0.32 Gy-1 (0.032), α/β = 10 Gy; clonogen doubling × = 7.5 days (1.7), pretreatment clonogen number = 109 (108), onset of accelerated repopulation = 28 days (2).

Assume µ = 1.38 per hour for tumor and 0.46 per hour for normal tissues. The treatment dose rate is 70/140 = 0.5 Gy per hour.

1. For normal tissues

o  Intended NT BED = 70 (1 + 2 × 0.5/(0.46 × 3)) = 120.73 Gy3

o  Given BED = 30 (1 + 2 × 0.5/(0.46 × 3)) = 51.74 Gy3

o  Deficit = 120.73 - 51.74 = 69 Gy3 approximately

To deliver a further 69 Gy3, the total dose D is given in

69 = D (1 + 2 × 0.5/(0.46 × 3))

D is found to be 40 Gy, that is, no extra dose is required for the late effects. This is because most of the repair occurs during continuous treatments.

2. For tumor control

If we assume that the first 30 Gy is delivered in 60 hours, that is, two-and-a-half days and then we restart after a gap of 7 days, the overall time will be 2.5 + 7 + t, where t is the time for the final part of treatment. Accelerated repopulation will not be fully operative now. There are complex ways of dealing with such short treatment times6 but it can be considered as reasonable to assume a much lower value of K without a time-delay factor in these situations. If a value of K = 0.2 Gy per day is used, then with a µ = 1.4 per hour approximately

intended BEDtum = 70 (1 + 2 × 0.5/(1.4 × 10)) - 0.2 × 7 = 73.6 Gy10

To achieve the same BED for tumor control, the following equation provides the solution for the new value of t.

74.3 Gy10 = 30(1 + 2 × 0.5/(1.4 × 10)

73.6 = 30 (1 + 2 × 0.5/(1.4 × 10) + t × 0.5(1 + 2 × 0.5/(1.4 × 10) - 0.2 × (2.5 + 7 + t/24)

from which t = 82.2 hours, which means a total dose of 0.5 × 82.2 = 41.1 Gy.

This will influence the late NT BED, which would then be

30 (1 + 2 × 0.5/(0.46 × 3)) + 41.1(1 + 2 × 0.5/(0.46 × 3)) = 122.62 Gy3

that is slightly larger (by around 2.5 Gy3) than the original intended NT BED of 120.7 Gy3 and could cause an increase of 2.5% in late serious effects if a 1% increase in the latter occurs per unit increase in Gy3 BED.

Case 2

A patient begins an LDR implant prescribed as in case 1. The patient has moderate dementia, becomes very confused and interferes with the treatment. Treatment is stopped after 12 Gy has been given. Instead of continuing with the LDR technique it is decided to complete the therapy by giving eight HDR treatments to a similar dose distribution under sedation in 4 days (with a minimum of 8 hours between treatments). Calculate the dose per treatment, which would give the same late effect BED.

Assume µ = 0.46 per hour for normal tissues, that is, a T1/2 of 2 hours. The mean interfraction interval is 12 hours so that six half-times of repair can occur following treatment; we make no allowance for incomplete repair of SLD

For normal tissues

Intended NT BED = 70 (1 + 2 × 0.5/(0.46 × 3)) = 120.73 Gy3

Given BED = 12 (1 + 2 × 0.5/(0.46 × 3)) = 20.7 Gy3

Deficit = 120.73 - 20.7 = 100 Gy3 approximately

To deliver a further 100 Gy3, the dose per fraction is given by d in 100 = 8 d(1 + d/3)

the solution for d is 4.8 Gy per fraction.

Check this by calculating a combined BED for LDR and HDR

8 × 4.8(1 + 4.8/3) = 99.84 Gy3 for the HDR

12 (1 + 2 × 0.5/(0.46 × 3)) = 20.7 Gy3 for the LDR

The total BED is approximately 120.5 Gy3

Case 3

A patient with a history of diverticular disease has received 18 Gy in 10 fractions of EBRT to the pelvis for a stage IIB carcinoma of the cervix, but develops a severe acute reaction and refuses further EBRT. It was intended to deliver a dose of 45 Gy in 25 fractions followed by 25 Gy in five fractions HDR brachytherapy at point A, assuming that the maximum rectal dose would be <75% of the point A dose. How can we compensate using LDR brachytherapy using Cesium sources with a dose rate capability of 0.8 Gy per hour at point A given in two separate procedures?

The intended maximum rectal BED was the following:

45 (1 + 1.8/3) + 25 × 0.75(1 + 0.75 × 5/3) = 114.2 Gy3

The actual treatment time (t) for each LDR brachytherapy procedure, assuming the same late effects BED is given by t in

18 (1 + 1.8/3) + 2[0.8 × 0.75 × t(1 + 0.8 × 0.75/(0.463))] = 114.2

t = 38.1 hour

Therefore, two procedures of 38 hours each might be recommended. Note that the 0.75 factor was used to determine the dose rate at the anterior rectal wall. Should the dose rate estimates be higher than this, then a reduction in dose would be required.

Case 4

For logistical and medical reasons, it is decided to treat a patient with cervix cancer with a small stage IB cancer (1.5 cm diameter and positioned symmetrically with respect to the cervical os) with HDR brachytherapy given only in five fractions. The vaginal dimensions are narrow and it is found during the first fraction that the average anterior rectal wall dose is 110% over a 3-cm portion of rectum, that is, it exceeds the point A dose by 10%. The original intention was to deliver a dose equivalent to 70 Gy in 35 fractions at point A assuming that it would have 80% of this dose at the anterior rectum. Justify the treatment policy by means of BED equations.

Intended BED at A = 70 (1 + 2/3) = 116.70 Gy3

In five fractions this would be obtained from

5d(1 + d/3) = 116.7

d = 7.0 Gy per fraction at point A

Intended BED at rectum = 70 × 0.8(1 + 2 × 0.8/3) = 85.9 Gy3

In five fractions

5d(1 + d/3) = 85.9

and d is now 5.83 Gy per fraction, at anterior rectum

Now if the rectal dose is 110% of A then for the allowed rectal dose per fraction of 5.83 Gy, the point A dose per fraction would then be 100/110 × 5.83 = 6.43 Gy.

This has involved a reduction in the intended point A dose from 7 Gy per fraction. How might this affect the tumor control?

First, find the BED to the tumor periphery situated 1.5/2 = 0.75 cm from the source train running through the cervical os, that is, the minimum dose to tumor.

Assuming that there is no shrinkage of tumor dimensions during therapy and that the falloff of dose approximates to the reciprocal of distance for a relatively long line source, the minimum tumor dose would be 2/0.75 × point A dose, which leads to a dose per fraction of 17.14 Gy.

The minimum tumor BED, assuming α/β = 10 Gy would then be:

5 × 17.14(1 + 17.14/10) = 232.6 Gy10

The equivalent dose in 2 Gy fractions (EQD2) would be

EQD2 = BED/(1 + 2/10) = 232.6/(1 + 2/10) = 193.83 Gy

This would have a high probability of tumor control for a small squamous cell cancer. The dose reduction advised would retain the recommended level of dose to the rectum although maintaining a high local control.

Case 5

A time decay correction was inadvertently omitted for the second and third fractions of a 25 Gy in five fractions brachytherapy boost. If the treatments are given three full days apart, calculate what the remaining dose per fraction should be if the half-life of isotope decay is 72 days?

If corrected for late effects only:

·     1st Fraction BED = 5 (1 + 5/3) = 13.33 Gy3

·     2nd Fraction dose = 5 Exp[- 0.693/72 × 3] = 4.86 Gy

·     2nd Fraction BED = 4.86(1 + 4.86/3) = 12.73 Gy3

·     3rd Fraction dose = 5 Exp[- 0.693/72 × 6] = 4.72 Gy

·     3rd Fraction BED = 4.72(1 + 4.72/3) = 12.12 Gy3

Therefore by the end of the third fraction the delivered BED will be

13.33 + 12.73 + 12.12 = 38.18 Gy3

The original intention was to deliver 25 (1 + 5/3) = 66.67 Gy3

Therefore, the deficit of 66.67 - 38.13 = 28.54 Gy3 can be made up by giving the remaining two fractions in a dose d given in

2 d (1 + d/3) = 28.54

d = 5.2 Gy per fraction

Does this influence the tumor BED?

This can be checked by calculating an overall tumor BED for α/β =10 Gy

BED = 5(1 + 5/10) + 4.86(1 + 4.86/10) + 4.72(1 + 4.72/10) + 5.2(1 + 5.2/10) + 5.2(1 + 5.2/10) = 37.48 Gy10

This is reasonably close to the intended BED = 25(1 + 5/10)=37.5 Gy10, so that tumor control should be reasonably well maintained.

Case 6

Compare the tumor BED difference between a 12-minute brachytherapy boost procedure and a 45-minute procedure to give an intended dose of 8 Gy assuming a tumor half-time of repair of 0.5 hr and α/β = 10 Gy.

For the 12-minute case (T = 0.2 hr), dose rate (R)= 8/0.2 = 40 Gy/hr and g = 0.91.

BED = 8(1 + gTR/10) = 13.83 Gy10.

For the 45-minute case (T = 0.75 hr), dose rate (R)= 8/0.75 = 11.33 Gy/hr and g=0.728.

BED = 8(1 + gTR/10) =12.95 Gy10.

It can be seen that there is a significant reduction in the tumor BED.

To attempt correction by increasing the total dose if the lower dose rate of 11.33 Gy/hr has to be used, try two different total doses, for example,

1. 8.2 Gy in 46.13 minutes: yields BED = 13.07 Gy10.

2. 8.5 Gy in 47.81 minutes: yields BED = 13.26 Gy10.

The latter appears to be the best option for maintaining tumor control; the reader is invited to calculate the normal tissue BED values.

Case 7

A mistake is made in the first fraction of HDR: 6 Gy is given instead of the prescribed dose of 3 Gy at the reference surface where the intended prescription was 15 Gy in five fractions as a boost implant for breast cancer. How can the remaining fractions be changed to compensate?

The intended BED is 15(1 + 3/3) = 30 Gy3.

The first fraction BED is 6 (1 + 6/3) = 18 Gy3.

The deficit BED is 30 - 18 = 12 Gy3.

In the remaining four fractions this can be given as d in

4d (1 + d/3) = 12, from that

d = 1.85 Gy per fraction.

This has been calculated for isoeffective late normal tissue side effects; the α/β for breast cancer is likely to be between 3 to 5 Gy; assume a value of 4 Gy

Intended BED is 15(1 + 3/4) = 26.25 Gy4

Given BED will be

6 (1 + 6/4) + 4 × 1.85 (1 + 1.85/4) = 25.82 Gy4

The tumor BED has not changed appreciably.

Case 8

Comment on the expected acute normal tissue BEDs for three proposed boost treatments to the vaginal vault following standard external radiotherapy in a clinical trial. The doses to be given at a distance of 0.5 cm distance from the applicator surface are the following:

1. 6 Gy in 1 fraction.

2. 8 Gy in 2 fractions.

3. 9 Gy in 3 fractions.

The respective BEDs are

6(1 + 6/3) = 18 Gy3

8(1 + 4/3) = 18.66 Gy3

9(1 + 3/3) = 18 Gy3

All seem broadly equivalent in terms of the late effect BED; the differences in tumor control BED will be less and are unlikely to be significant unless overall treatment time and repopulation effects are included; for example if the three-fraction schedule was given over 12 days then an equivalent dose loss of as much as 0.8 Gy 12 = 9.6 Gy could occur in squamous cell cancers; this actually exceeds the given dose! This example shows again how that time protraction due to protracted inter-fraction intervals can be important.



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