Background
The fundamental underpinnings of radiobiology were established in 1975, when Rodney Withers proposed the four fundamental “R’s” for the response of cells to fractionated radiation therapy: Repair (the ability of the cell to repair damage from the radiation treatment), Reassortment (progression through the cell cycle, which affects sensitivity to radiation treatment), Repopulation (the rate the tumor grows during the overall treatment) and Reoxygenation (the elimination of hypoxia, which affects radiosensitivity, during treatment) [
1]. In 1989, G. Gordon Steele added a fifth “R” – Radiosensitivity (the innate ability of the radiation to damage the tumor cell) [
2]. In this paper, radiosensitivity refers to the cell damage directly caused by the radiation treatment under ideal conditions, and radiation sensitivity refers to the tumor cell kill from a radiation treatment incorporating all 5 “R’s” of Withers and Steele. The overall radiation sensitivity of the tumor to radiation therapy can be indicated by the SF
2, the surviving fraction after giving a single dose of 2 Gy of radiation. It is more completely modeled in different contexts with some form of the Linear-Quadratic model of dose response [
3‐
8].
The sensitivity of an isolated tumor cell to radiation therapy, the innate radiosensitivity, will vary due to differences of the cell’s radiosensitivity in the various parts of the cell cycle. The cells are most sensitive during G2-M phase and least sensitive in late S phase [
9]. The sensitivity of a tumor cell due to its location within a tumor mass, the spatial sensitivity, varies due to processes such as hypoxia and cell-to-cell communication. A complete description of these effects was modeled by Brenner and colleagues [
10]. Clinically, attempts to exploit spatial heterogeneity have been mainly focused on hypoxia-sensitizing agents, such as misonidazole and hyperbaric oxygen [
11]. The variation in innate radiosensitivity has been exploited by using agents that block the tumor cell cycle from progressing into a less radiosensitive phase, such as S phase [
12], or to maintain the cells in mitosis, during which cells have increased radiosensitivity [
13]. In this paper, only the effects of innate radiosensitivity are being modeled. Therefore, the innate radiation sensitivity of the cells and the radiation sensitivity due to all effects, such as hypoxia and other microenvironmental factors, are identical for the purposes of this paper.
Because it can be difficult to fit clinical data to the classical linear-quadratic dose-response equation, more complex models have been developed (reviewed in [
14,
15]). Recently, the “stem cell” model has been proposed to explain the apparent variation of innate radiosensitivity within a tumor [
16]. In this model, the unexpected, increased resistance of a tumor to radiation therapy during fractionated therapy is modeled with two, distinct population of tumor cells. As stated by Pajonk, most if not all cancers contain a small subpopulation of cancer stem cells [
16]. Rich, and others, have stated that stem cells have increased resistance to radiation therapy and may be the cause of local failure after treatment with radiotherapy [
17,
18]. Yu, and others, modeled the effects of a radiation-resistant stem cell on the expected tumor response [
6,
19,
20]. There is also increasing exploration of the inter-tumoral heterogeneity, that is, between patients, in innate radiation response as measured by a molecular signature. For example, Scott and colleagues presented the results of a “gene-adjusted radiation dose” (GARD) [
21]. They used genetic profiling of tumors to predict radiosensitivity of several cancers and therefore their response to radiation therapy treatment. The authors showed wide heterogeneity across cancers, and that clinical outcome correlated with the GARD [
21].
What has not been adequately explored is the effect of innate, intratumoral heterogeneity on tumor radiosensitivity during a standard clinical course of fractionated radiation therapy. Published preclinical data support that there is heterogeneity in the innate radiosensitivity of cancer cells in tumor masses, independent of cell cycle and microenvironmental heterogeneity. For example, Allam and colleagues studied five glioma cell lines in vitro [
22], and after growth in tissue culture, each was divided into three separate specimens. They then measured the SF
2 (surviving fraction of cells after a single 2 Gy treatment with radiation therapy) of each of these subpopulations and found an intratumoral variation in the SF
2 of about 25%. Britten et al. performed a more complex clonal development on punch biopsies from cervical cancer [
23]. They grew out 96 single cell clones from each of three specimens of squamous cervical carcinomas and then measured their radiosensitivities. The variation in the SF
2 values was very similar to Allam’s glioma lines. Within the three original cell lines, the clones’ SF
2 values varied from 0.240 to 0.518, 0.050 to 0.414, and 0.137 to 0.452. Thus, rather than homogeneous innate radiosensitivity in a single tumor, there is likely a range of innate sensitivities within a single tumor. The Brenner model discussed above [
10], which included a term for innate radiosensitivity variation from the effect of the cell cycle, was only used to look at effects between two fractions, and discounted as unimportant any long-term effects due to variation in the innate radiosensitivity.
Therefore, a model was developed to focus on the effect of introducing intratumoral heterogeneity in innate radiosensitivity during fractionated radiation therapy. The magnitude of effects was explored by analyzing existing experimental data within the linear-quadratic equation modified with a heterogeneity factor. This model was then used to determine the effects of varying the various parameters, including the total dose, the fractional dose, number of fractions, and the rate of tumor cell repopulation.
Discussion
Cancers are genetically diverse, not only between patients but also within an individual patient [
35‐
39]. This perhaps obvious fact has not been evaluated in previous models of radiation response. Pre-clinical data, such as that modeled in Figs.
1,
2 and
3, support the model that radiation therapy rapidly selects out the more radiation-resistant clones of tumor over the dominant, more sensitive cells initially present. Along with the experimental results discussed previously, other experiments report similar findings. McDermott and colleagues exposed a prostate cancer cell with 60 Gy of radiation therapy in 30 treatments (RR cells) and compared the radiation sensitivity of the resulting cell line with the untreated wild type cell line (WT) [
40]. They found increased post-radiation survival, decreased baseline apoptotic rates, and increased DNA repair capacity of the RR cells as compared to the WT cells. This was also shown in cell lines from esophageal cancer [
41], and another cervical cancer line [
42]. These results can be successfully modeled within standard linear-quadratic mechanics by assuming a distribution of radiosensitivity within a single tumor. This expansion of the fifth R (Radiosensitivity) with a distribution of innate radiosensitivity provides a basis for the induction of radiation resistance by the treatment with radiation therapy during treatment and for the clinical phenomenon of accelerated repopulation during treatment. This induction of radiosensitivity is due primarily to the shift in α, with β remaining relatively stable. This is congruent with the increased repair capacity found in the experimental studies.
An important focus of radiation research is to predict when and what type of radiation treatments will be effective. For example, one area of current research is using molecular analysis of tumors to predict radiosensitivity. A similar approach was explored in the 1990’s, using measured SF
2 values, but this approach was ultimately abandoned due to a lack of sufficient correlation with clinical outcome [
43]. The results of this heterogeneity model suggest that the local-control-limiting, resistant cells may be a very small population within a large population of sensitive cells. Therefore, measurements made on the pre-treatment tumor may not be able to detect the most important subpopulation. What may be more effective for predicting local response is to determine the distribution of the radiosensitivities in the tumor. Approaches that could overcome this limitation include: making several measurements early in the treatment and monitoring the shift in radiosensitivity, using a technique that detects the small, most radiation-resistant clones in the tumor, or directly measuring the initial width of the distribution of the tumor radiosensitivity.
Clinical radiation therapy has a limited range of variables to change to try to improve the outcome of treatment. The primary variables are the total dose, the daily dose and the length of treatment. This model suggests that increasing the total dose to tumors that are not cured with standard doses of radiation therapy will not be effective because the remaining cells are the most radiation-resistant cells. That is, each subsequent fraction of radiation therapy is increasingly inefficient in curing the cancer because of the increase in radiation resistance with each treatment fraction. The modeling of Fig.
6 shows that increasing the daily dose and decreasing the total time of the treatments result in higher tumor kill without the development of a predominant radiation-resistant clone. The model indicates that hypofractionation will induce less radioresistance for the same calculated BED. This was shown to be true in vitro for two cell lines by Zhang et al. using dose-response curves [
32]. They also showed by using flow cytometry that longer fractionation induced more “stem cells”, which by this model are the more radioresistant cells. The limitation of hypofractionation is the concomitant increase in damage to the normal tissue, and a decreased therapeutic ratio, in as much as larger fractions are also more efficient in killing the normal cells.
The model also offers an explanation of the clinically seen problem of accelerated repopulation during extended treatment (Fig.
7). The experimental results of McDermott, mentioned above [
40], as well as Kuwuhara [
41], Lynam-Lennon [
30] and Skvortsova [
31], all report in vitro data showing that the radiation-induced clones are both more radiation resistant and have a faster growth rate than the original cell line. Thus, as shown in Fig.
7, the selection of the rapidly growing, resistant fraction of the tumor during extended fractionation supplies a simple explanation of the clinically identified phenomenon of accelerated repopulation during treatment of cancers, and the advantage of shorter treatment times. The model also shows that decreasing the time of the treatment minimizes this affect, also as seen in clinical studies.