First published online August 31, 2006
British Journal of Radiology (2007) 80, 32-37
© 2007 British Institute of Radiology
doi: 10.1259/bjr/15764945
On the possible increase in local tumour control probability for gliomas exhibiting low dose hyper-radiosensitivity using a pulsed schedule
W A Tomé, PhD and
S P Howard, MD, PhD
University of Wisconsin, School of Medicine and Public Health, Department of Human Oncology, K4/344 CSC, 600 Highland Ave., Madison, WI 53792, USA
Correspondence: Professor Wolfgang A Tomé, Human Oncology and Medical Physics, University of Wisconsin, CSC K4/344, 600 Highland Avenue, Madison, WI 53792, USA. E-mail: tome{at}humonc.wisc.edu
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Abstract
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Using modelling, we have developed a treatment strategy for gliomas exhibiting low dose hyper-radiosensitivity (HRS) that employs both a reduced dose-rate and pulsed treatment dose delivery. The model exploits the low dose hypersensitivity observed in some glioma cell lines at low radiation doses. We show, based on in vitro data, that a pulsed delivery of external beam radiation therapy could yield significant increases in local control. We therefore propose a pulsed delivery scheme for the treatment of gliomas in which the daily treatment fraction is delivered using 0.20 Gy pulses, separated by three minutes for a time-averaged dose-rate of 0.0667 Gy/min. The dose per pulse of 0.2 Gy is near or below the transition dose observed in vitro for four of the five glioma cell lines we have studied. Using five established glioma cell lines our modelling demonstrates that our pulsed delivery scheme yields a substantial increase in tumour control probability (TCP).
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Introduction
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Malignant gliomas continue to be a significant medical problem. The treatment approach is usually of a multi-modality nature. Depending upon grade and histopathology, surgery and/or radiation is utilized with or without cytotoxic chemotherapy. For the higher-grade tumours (anaplastic astrocytoma and glioblastoma multiforme), combined modality approaches have had only a modest impact upon survival; median survival ranges from 6 to 12 months for patients with glioblastoma multiforme (GBM) and most patients die within two years [1]. The prognosis of patients with malignant gliomas treated by surgical resection alone remains dismal with a median survival of 4–6 months [2]. This reflects the unique infiltrative growth characteristics of malignant gliomas, which make true "total resection" impossible without causing unacceptable neurologic damage to the patient. Historically, radiotherapy has proven to be the most effective treatment for malignant gliomas, extending median survival to 8–9 months. Recently, Stupp et al [3] demonstrated that radiotherapy plus concomitant temozolomide followed by adjuvant temozolomide treatment significantly improves survival, representing the most important advancement in the clinical management of GBM in the past 30 years. However, the overall survival is still poor and most patients will ultimately succumb to this malignancy. An improvement in local control would be particularly relevant in the management of this disease, as 90% of these patients will ultimately develop recurrences within the radiation treatment field [4, 5]. Once patients have tumour progression, conventional chemotherapy has not been shown to significantly prolong survival [6]. Biological differences between normal neural tissue and glial neoplasms in terms of repair of radiation damage and the induction of radiation-induced lethal lesions could potentially be exploited to minimize normal tissue toxicity while maximizing tumour control probability (TCP). Low dose rate interstitial brachytherapy has been used for the treatment of recurrent glioma with an improved median survival reported by some institutions [7]. The radiobiolological properties of low dose-rate radiation have been long established. Reduced dose-rate radiation effect can be tumour/tissue sparing, but there is growing theoretical and experimental data that lower dose-rates can also provide more efficient radiation damage. Because of the increased repair that can occur over a prolonged treatment time, the actually delivered biologically effective dose (BED) may be lower than expected. Currently, a superior dose distribution is felt to be the reason for the efficacy and tolerance observed with brachytherapy as a treatment for malignant glioma. However, an increasing body of both experimental evidence and empiric clinical observations has suggested that reduced dose-rate irradiation may be a biologically different and distinct process compared to acute high dose rate fractionated irradiation.
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Methods and materials
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Shultz and colleagues [8] evaluated the effects of dose-rate on radiosensitivity in two human glioblastoma cell lines. Cells were treated at dose rates ranging from 0.2 Gy/h to 5.4 Gy/h and an inverse dose rate effect was demonstrated at approximately 0.4 Gy/h [8]. The inverse dose-rate effect is defined as a paradoxical increase in cell killing within a narrow range of decreasing dose-rate and is thought to be a consequence of the accumulation of cycling cells in the G2M phase of the cell cycle. During continuous low dose-rate irradiation, the G2M blocked cells are preferentially killed as they are relatively more radiosensitive than cells in G1 and S phase. Validating this hypothesis, cell cycle analysis revealed maximal accumulation of cells in G2M at a dose rate of 0.4 Gy/h [9, 10]. Based on these experimental observations, it appears logical to expect actively proliferating glial tumours to be selectively more radioresensitive to continuously delivered low dose-rate irradiation than the quiescent surrounding normal brain tissue.
In 1970, Pierquin pioneered the concept of reduced dose-rate external beam radiotherapy, treating patients with locally advanced squamous carcinoma of the head and neck with reduced dose rates characteristic of interstitial implants [11]. Patients were treated continuously for 8 to 10 hours a day, for one to two weeks. A subsequent non-randomized trial comparing this approach to conventional radiotherapy demonstrated highly significant differences in local control in favour of the reduced dose-rate treatment arm [11, 12]. This therapeutic rationale has been extended to other disease sites using reduced dose-rates ranging from 1.0–1.5 Gy/h for the palliative treatment of advanced breast cancer [13], bone and soft tissue metastasis [14], pancreas [15], and recurrent pelvic tumours [16].
Perhaps the most intriguing low dose/low dose-rate phenomenon is that of low dose hyper-radiosensitivity (HRS) [17]. Some cells, although not all, treated with low doses of radiation (< 0.5 Gy) demonstrate a level of survival that is considerably lower to that predicted from extrapolation of the survival observed at higher doses. Low dose hypersensitivity may be a consequence of inefficient cell cycle arrest of irradiated cells as a result of the inverse dose effect [18]. Short et al [19] have advanced the hypothesis that low-dose hypersensitivity can be thought of as the constitutive response of cells without the enabling of repair mechanisms triggered by higher doses. It is known that when the dose rate is slowed to a point where cells can proceed through the cell cycle, they can accumulate in a G2-blockade. Because of the exquisite radiosensitivity of cells in the G2-phase, these cells become hypersensitive to radiation. The initial 
slope at this low dose is on average seven times steeper than would be predicted by the linear quadratic model. In order to describe the phenomena of HRS, Short and colleagues [20] have developed the incomplete repair model:
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In Equation (1) SF(d) denotes the surviving fraction of cells after dose d has been delivered, s denotes the low-dose value of the radiation sensitivity derived from the response of cells at very low doses, r denotes the value of the radiation sensitivity extrapolated from the conventional high dose response and dc denotes the "transition" dose at which the change from low dose hypersensitivity to increased radiation sensitivity occurs. In Equation (1) the radiation sensitivity has become a function of dose smoothly varying between s and r. To make the dependence of the radiation sensitivity, , on dose more explicit we define:
Substituting Equation (2) into Equation (1), we can write the surviving fraction in its more conventional form:
Now let us use Equation (3) to study the effect of breaking up the therapy dose per fraction into m sub-fractions of dose 
that are separated by a fixed time interval T. The effective dose rate is then given by 
. Hence by breaking up the dose per fraction d into m subfractions of dose each, separated by fixed time intervals T, one can achieve an effective reduced dose-rate of 
. If = 0.2 Gy and T = 3 min then the effective reduced dose rate is 
. The surviving fraction after a pulse is delivered is given by:
From this we find the surviving fraction corresponding to the delivery of m pulses straightforwardly as:
Depending on the value of the surviving fraction 
may be larger or smaller than the surviving fraction 
. More explicitly, we have that:
Hence, subdividing the dose per fraction into pulses separated by fixed time intervals is only beneficial if the tumour treated exhibits HRS. Now using the fact that d = m we can rewrite Equation (5) as follows:
In Table 1
we have collected published data for five glioma cell lines that have been studied by Short et al [20]. Equation (7) that predicts the expected cell kill due to multiple small fractions contains an term and a 
term to describe cell killing due to a number of small fractions separated by a fixed time interval. For low doses there is effectively no cell kill due to repair. Using our proposed schedule with = 0.2 Gy and m = 10 we find that the -term in Equation (7) becomes indeed small when compared to the -term of cell kill and can effectively be ignored (see last two columns of Table 2).
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Table 1. Parameters used in the calculation of SF2 when treatment is delivered in a pulsed versus conventional fashion
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Using the data presented in Table 1
as input parameters, we have calculated the surviving fraction, if one delivers the dose per fraction of 2 Gy as a single fraction at a dose rate of 4–6 Gy/min or in a pulsed fashion in which the dose is divided into ten pulses of 0.2 Gy, separated by three minutes each. Note that the dose per pulse of 0.2 Gy is near or below the transition dose for four of the five glioma cell lines studied by Short et al [20]. The results of these calculations are collected in the second and third column of Table 3. In what follows, we employ a TCP model that uses the surviving fraction at 2 Gy, SF2, the dose D50 at which 50% of tumours are controlled and the relative slope 
50 of the TCP curve as input parameters. We have described this model in detail in references [21, 22]. We have chosen for our calculations a shallow 50-slope of 1.0 for the TCP curve and have estimated D50 for each cell line, using the SF2 corresponding to a single fraction delivery mode, such that the resulting tumours have an approximately equal number of clonogens, Nc. Hence, we are comparing tumours with a similar number of clonogens, but with a different HRS response. The results of our calculations are collected in columns 4 through 6 in Table 3. In order to estimate the possible gains in tumour control when using a pulsed dose delivery schema at a reduced rate if a glial tumour exhibits HRS, we have calculated the TCP using the values for the surviving fraction after a dose of 2 Gy (see Table 3) for the conventional and pulsed delivery mode. The results of our calculations have been collected in Table 4.
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Table 3. Values for SF2 when treatment is delivered in a pulsed versus conventional fashion and clinical parameters used for TCP calculation
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Table 4. Values for SF2 when treatment is delivered in a pulsed versus unpulsed fashion and clinical parameters used for TCP calculation
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Note that, in the modelling above we have not taken the oxygen effect on HRS into account. Marples and colleagues [23] have studied the effect of oxygen on low-dose hypersensitivity using Chinese hamster fibroblasts (V79-379A) and found that, like aerobic cells, hypoxic cells exhibit a HRS response below a dose of 0.5 Gy (cf. Figure 2 in [23]). Furthermore, even though gliomas are profoundly hypoxic with the majority of cells in the G0 phase of the cell cycle, this is a dynamic and constantly changing microenvironment. Glioblastoma multiforme, the most common and most malignant of human gliomas, exhibits necrotic foci typically surrounded by hypercellular zones referred to as pseudopalisades which are constantly remodelling in response to the magnitude of tissue hypoxia. As a result, cells that are hypoxic and non-cycling at the initiation of treatment may have a change in their oxygenation status and enter the cell cycle during the six weeks of daily treatments. Currently, gliomas are treated with radiotherapy to a dose of 60 Gy delivered using daily 2.0 Gy fractions. Using modern linear accelerators, the daily treatment requires only minutes to deliver. Conversely, delivering daily treatments using a pulsed reduced dose-rate treatment schedule using 0.2 Gy pulses separated by three minute time intervals as we have modelled would require a minimum 30 minutes per treatment to deliver a daily 2.0 Gy fraction over a six week treatment course. When compared to standard fractionated radiotherapy, the overall treatment time would be the same, i.e. six weeks. However, in the case of pulsed reduced dose-rate radiotherapy, tumour exposure time would be considerably more protracted due to the longer time required to deliver daily treatments.
For this approach to be clinically feasible, however, normal tissue should not exhibit HRS, or must have transition doses that are much lower than that of the tumour and the pulse size to be used. Marples and colleagues [24] have found that cells in G1 phase do not exhibit an HRS response. Hence, since white and gray matter do not actively proliferate, they will most likely not exhibit a HRS response. Mu et al [25] have studied the effect of prolongation of fraction delivery time using Chinese hamster fibroblasts (V79-379-A) by subdividing the total dose per fraction into a number of equal sub-fractions separated by fixed time intervals. They found that this approach increased the surviving fraction of Chinese hamster fibroblasts by 6% when compared to the surviving fraction of Chinese hamster fibroblasts when the whole therapeutic dose was administered continuously at 2 Gy/min. In their experimental design, Mu et al [25] have employed a pulsed fractionation schedule and have subdivided each treatment fraction into m subfractions of dose separated by a time interval T, such that the dose per fraction is given by d = m 
and the overall treatment time is given by T = (m–1)T. Since it is assumed that the normal tissue does not exhibit a HRS response, the surviving fraction, due to the protracted delivery of treatment, can be described using an expression that includes a correction factor GT that accounts for repair of sublethal damage taking place during the delivery of a treatment fraction of length T [26].
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Repeating the steps that lead from Equation (4) to Equation (7) (cf. [27] for the complete details) one finds the following
where GT is the correction for repair taking place during a protracted treatment fraction of length T. The following expression for GT has been derived by Dale [26] and Lea and Catcheside [28]:
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where 
is the sublethal repair half time. Now applying Equation (9) to our proposed fractionation schedule using the data in Mu et al [25] for V79-379-A fibroblasts ( = 0.16 Gy–1, = 0.016 Gy–2, and an acute surviving fraction for a fraction of 2 Gy delivered continuously over 1 min of SF2 = 0.68) and using a mono exponential repair model with a sublethal repair half time 
, one obtains a ratio of surviving fractions of pulsed irradiation to the surviving fraction for acute irradiation of 1.067. The use of a mono-exponential rather than a bi-exponential or multi-exponential repair model is justified by the fact that the sublethal repair will be dominated by the repair half time that is of the same order as the treatment delivery time T [26]. This indicates that there may be a protective effect due to the prolonged delivery time of a pulsed schedule for normal tissues that do not exhibit a HRS response.
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Results
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From Table 3 we find that a fraction size of 0.2 Gy delivered in a pulsed fashion over ten sub fractions reduces the resulting surviving fraction for four out of the five cell lines used in the modelling that exhibit HRS in vitro. Analyzing the data in Table 3 we find that the surviving fraction that results from pulsed delivery is 0.369 times that corresponding to conventional dose delivery for the glioma cell line T98G, 0.843 times for the glioma cell line HGL21, 0.751 times for the glioma cell line U87MG, 0.374 times for the glioma cell line A7 and 0.297 times for the glioma cell line U138, respectively. This clearly indicates that, based on in vitro data, potential gains could be made if radiation therapy is delivered in a pulsed temporal fashion and the size of the individual sub-fractions (pulses) is less or equal to the transition dose at which the change from low dose hypersensitivity to increased radiation sensitivity occurs. This is further borne out in our TCP calculations which predict on the one hand complete local control for the cell lines T98G, U87MG, A7 and U138 when a the pulsed delivery of radiotherapy is employed, while on the other hand predict either local failure or significantly reduced local control if conventional dose delivery is employed (see Table 4). For the cell line HGL21, our calculations indicate a significant increase of local control up from 3.9% to 38.55%, which is a 10-fold increase in local control when pulsed delivery instead of conventional high dose delivery is employed. Moreover, the positive 
TCP values in Table 4 clearly indicate that each of these glioma cell lines is predicted to demonstrate an increased response when a pulsed delivery schedule is employed. The actual response that can be achieved, however, has to be demonstrated in in vitro experiments using these cell lines and our pulsed delivery schedule. From Tables 1, 3 and 4 we see that the cell lines that demonstrate the greatest response are those for which the largest reduction in surviving fraction occurred, i.e. those that are very resistant to conventional radiation delivery and whose transition dose is larger than the size of the pulse employed in the pulsed reduced dose rate delivery schema.
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Discussion
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In the modelling above we have shown that if a tumour system exhibits HRS then delivering the treatment in a pulsed fashion (in which each of the pulses delivers a dose that is close to the transition dose) is predicted to yield an increase in TCP. However, as pointed out above, for this approach to be clinically feasible normal tissues cannot exhibit HRS or otherwise have to have transitional doses that are lower than those of tumours, so that one is outside their HRS region. On the one hand, in conventional radiotherapy a dose of 2 Gy is delivered at a dose rate of 4–6 Gy/min, which means that the delivery of this dose takes only a few minutes in most cases. Within this time frame, the initial radiochemical processes, i.e. the generation of free radicals occurs. This time frame however, is too short for most clinically relevant biological repair processes to take place. On the other hand, as one increases the time during which a dose of 2 Gy is delivered (i.e. if one lowers the effective dose-rate in which the radiation is delivered), it becomes possible for repair to occur during irradiation. In addition, this reduction in dose-rate may favourably exploit other differences between normal and malignant cells, such as the greater capacity of normal tissues to repair sublethal damage. Other differences may arise with a lower dose-rate including decreased hypoxia, as a result of ongoing reoxygenation during the protracted irradiation; limited tumour cell proliferation over longer overall treatment times; and cell cycle effects, which may include synchronization of tumour cells into sensitive regions of the cell cycle [29]. In our modelled treatment approach we have chosen to deliver a reduced dose-rate in a pulsed fashion by breaking up a 2 Gy fraction into a number of equal sub-fractions separated by fixed time intervals, such as 3 min, which can be done using a conventional linac and a timer. Our modelling above together with results of Mu and colleagues [25] indicate that there may be a protective effect for normal tissue if one delivers the radiation dose in a pulsed manner. On the other hand, Steel [30] has demonstrated that for different human tumour cell lines the initial slope of the cell survival curve does not change, i.e. unlike normal cells, these human tumour cells do not exhibit an increase in surviving fraction with decreasing dose-rate for doses per fraction of 2 Gy. Therefore, a pulsed approach will theoretically preferentially protect normal tissue, which has a high repair capacity, and have almost the same effect on tumours in terms of tumour cell kill if therapeutic doses of 2 Gy per fraction are used even in the absence of HSR. Hence, for malignancies that exhibit HSR, delivering therapy in a pulsed fashion by dividing the total dose into a number of sub-fractions that are separated by a fixed time interval in which the dose per pulse is below the transition dose could yield an increase in both TCP and normal tissue sparing.
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Conclusion
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Using modelling, we have developed a treatment strategy for gliomas that exhibit HRS employing both a reduced dose-rate and a pulsed treatment dose delivery. The model exploits the increased repair of sublethal damage by normal tissues observed with prolonged treatment times and the low dose hypersensitivity observed in glioma cell lines at low radiation doses. We have shown that pulsed delivery of external beam irradiation may have significant clinical potential in terms of normal tissue sparing while allowing substantial increases in local control. For all five cell lines studied, our modelling shows that a pulsed delivery scheme could yield a substantial increase in TCP. Hence, glioma patients are probably the ideal patient population to evaluate the efficacy of pulsed reduced dose-rate radiotherapy that we have empirically modelled. A growing body of experimental evidence (cf. [31] and references therein) suggests that low-dose hypersensitivity is a common although not universal phenomenon observed in radioresistant human glioma cell lines. However, a mechanistic explanation for this observation has yet to be elucidated. Given the complexities of extrapolating in vitro observations to the development of a useful treatment modality, defining a sub-population of patients that would respond favourably to this treatment is difficult. In an attempt to identify glioma patients that would potentially benefit from this treatment strategy, we have initiated a phase II clinical trial of pulsed reduced dose-rate radiotherapy for patients with recurrent gliomas. In this trial, patients receive a total dose of 50 Gy using 2.0 Gy fractions in a pulsed fashion. Each daily 2.0 Gy fraction is delivered using 0.20 Gy pulses every three minutes, for a time-averaged dose-rate of 0.0667 Gy/min. Although the population of glioma patients is heterogeneous, many of the subgroups within it have well characterized molecular phenotypes that potentially predispose them for a favourable response to this treatment strategy.
Received for publication April 3, 2006.
Revision received July 11, 2006.
Accepted for publication July 14, 2006.
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Abstract
Introduction
