Radiosensitivity of colorectal cancer to ⁹⁰Y and the radiobiological implications for radioembolisation therapy

The success of external beam radiotherapy (EBRT) can partly be attributed to a fundamental understanding of the underlying radiobiology and how this explains the dose response. The evolution of targeted radionuclide therapy (TRT), however, is marked by a recognised deficiency in dose quantification and sound radiobiological understanding. In addition, dosimetry and treatment planning are mostly standardised for EBRT, which is not the situation for TRT (Lassmann et al 2011, Gill et al 2017). In the case of ⁹⁰Y-based selective internal radiation therapy (⁹⁰Y SIRT), a liver-directed treatment for palliative control of inoperable or chemorefractory tumours (van den Hoven et al 2016), doses are usually prescribed using tables or the Body Surface Area method to determine the amount of activity (MBq) to administer (Vauthey et al 2002). Absorbed doses reported in literature can vary from 50 up to 200 Gy (Strigari et al 2010, Cremonesi et al 2014, van den Hoven et al 2016). Consequently, there is a general acknowledgement that patient-specific dosimetry needs to be performed to optimise treatment, especially since a dose effect has been established for ⁹⁰Y SIRT (Strigari et al 2010, Cremonesi et al 2014, van den Hoven et al 2016). Given the recent multicentre phase III trial showing that ⁹⁰Y SIRT provides better tumour control within the liver when used in conjunction with chemotherapy than chemotherapy alone (Wasan et al 2017), this treatment option could be extended if dosimetric and radiobiological considerations are taken into account in treatment planning.

While there has been a concerted effort to integrate dosimetry into the clinic (Giammarile et al 2011), this has not been extended to the incorporation of radiobiological parameters specific for ⁹⁰Y SIRT. Radiobiological modelling based on the linear-quadratic model (LQM) requires detailed knowledge of ⁹⁰Y-specific radiobiological parameters ($\alpha$ and $\beta$) (Cremonesi et al 2008). Yet, radiobiological parameters used for ⁹⁰Y SIRT dosimetry planning are usually taken from EBRT studies (Chiesa et al 2015). These extrapolated parameters might not be representative of ⁹⁰Y SIRT as they do not account for the intrinsic cellular response to ⁹⁰Y β⁻-particles. Furthermore, the protraction of dose delivery for ⁹⁰Y SIRT adds another level of complexity. This effect is encapsulated by the Lea–Catcheside model of sublethal-damage repair (Dale 2018) and has previously been used to describe the in vitro cellular response to protracted photon exposure (Solanki et al 2017). However, studies using ⁹⁰Y are needed to answer fundamental questions regarding differences in the radiobiological response to ⁹⁰Y β⁻-particles and photons of clinically relevant energy.

Recently, Gholami and colleagues (Gholami et al 2018) compared cell-kill responses between ⁹⁰Y and EBRT. Using a colorimetric cell viability assay (MTS), they concluded that ⁹⁰Y is less potent than EBRT, as  ≈56 Gy ⁹⁰Y dose cumulated after 8 d was found to be radiobiologically equivalent to a single fraction of  ≈8 Gy EBRT. It is plausible to consider the cumulated dose after ⁹⁰Y exposure as a large number of infinitesimally small doses delivered per fraction. It is thus possible to relate the biological effect of ⁹⁰Y and EBRT by using the radiobiological measure, biological effective dose (BED), which allows inter-comparison between different fractionation schedules or treatment modalities to achieve a given biological effect (Dale et al 1996). This concept is only valid though for tissue characterised by a specific $\alpha /\beta$ ratio. Thus, to enable the incorporation of radiobiological parameters such as BED into clinical dosimetry planning of ⁹⁰Y SIRT, accurate measurements of the $\alpha$ and $\beta$ parameters are required to establish equivalence to that of EBRT.

In the present study, we determined the radiobiological parameters, $\alpha$ and $\beta$ for colorectal cancer (CRC) cell lines by means of the clonogenic assay. CRC cells were exposed to three radiation sources, namely ⁹⁰Y β⁻-particles (933 keV mean energy and LET range of 0.07–2 keV μm⁻¹), 6 MV x-rays (LET  =  0.2 keV μm⁻¹) delivered via a clinical linear accelerator (LINAC), and ¹³⁷Cs (662 keV γ-ray, LET  =  0.8 keV μm⁻¹). Additionally, we investigated the relationship between EBRT and ⁹⁰Y dose through the concept of BED and establishing equivalent EBRT dose of 2 Gy (${\rm EQD2}$) and 10 Gy (${\rm EQD10}$) fractions.

Cell culture

⁹⁰Y formulations

Clonogenic assays

Colony formation and counting

For all experiments, irradiated cells formed colonies in 6-well plates for 7 d (DLD-1) and 9 d (HT-29). Colonies (⩾50 cells) were then fixed and stained with methylene blue in 50% ethanol and counted using an automated colony counter (GelCount^™, Oxford Optronix Ltd, UK). All experiments were repeated in triplicate.

⁹⁰Y β⁻-particles

Stacks of dishes were constructed as shown in figure 1(A). This geometry, adapted from Howell et al (1991), allowed the simultaneous irradiation of multiple dishes resulting in different cumulative doses at different dishes within a stack. In addition, it circumvented the problem of cellular internalisation of ⁹⁰Y. Cells were plated at 4000–20 000 cells/dish in 1.5 ml medium on the polymer coverslip of ibidi^® low 35 mm μ-dishes so that the cells remained within the central area (diameter of 21 mm) while ⁹⁰Y sources were mixed with phosphate buffered saline (PBS) in 1.5 ml of solution in a Greiner^® 35 mm dish. The use of different dish types for cells and for ⁹⁰Y was to minimise the difference between doses at the centre and the edge of dish thus assuring a near-uniform dose distribution over the irradiated cells (see supplemental figure 2 (stacks.iop.org/PMB/64/135018/mmedia)). Cell stacks were placed inside a custom-made container (figure 1(B)) and exposed for 6 d inside an incubator with 0, 10, 15, and 20 MBq of ⁹⁰Y diluted from stock. After the exposure period, the cells were replated at 3000–5000 cells/well in 1.5 ml of medium in three wells on 6-well plates. The cumulated doses delivered ranged from 0–32 Gy. Radiation dose was delivered at variable average dose rates ranging from 0–0.0037 Gy min⁻¹.

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¹³⁷Cs γ-ray

Cells were plated at 1000–40 000 cells/well in three wells on 6-well plates and irradiated 4 h after plating with a caesium irradiator (IBL637, CIS Bio international, France) at doses ranging from 0–10 Gy. Radiation dose was delivered at 0.77 Gy min⁻¹.

LINAC 6 MV x-rays

The cells were plated at 1000–10 000 cells/well in three wells on 6-well plates 4 h prior to the treatment delivery. A Varian Clinac 2100 series was used to deliver 0–10 Gy at 6.6 Gy min⁻¹ using a 15  ×  15 cm² field size. The gantry was positioned at 180° such that the beam first passed bottom-up through the couch, followed by 1.5 cm of solid water so that the dose maximum was at the cell level, and finally 2 cm of solid water to capture the backscatter dose.

Monte Carlo (MC) modelling

The dose absorbed per ⁹⁰Y disintegration, $S$ (cGy MBq⁻¹ d⁻¹), in a cell monolayer 15 μm in height (water density, ρ  =  1.0 g cm⁻³ was assumed) contiguous with the bottom of each ibidi^® dish placed at different positions above or below the source dish (figure 1(A)) was calculated by the MC method using the PENELOPE code (Salvat et al 2011). The average cell height was measured using confocal microscopy (supplemental table 1). Polystyrene (ρ  =  1.06 g cm⁻³) was assumed for both Greiner^® and ibidi^® dishes and air of 95% humidity at 37 °C and 5% CO₂ (ρ  =  1.276  ×  10⁻³ g cm⁻³) was used for air inside each dish. PBS and ⁹⁰Y solution were assumed as water. The β⁻ spectrum of ⁹⁰Y was taken from medical internal radiation dose (MIRD) tabulation (Eckerman and Endo 2008). A total of 10⁸ primaries were simulated in each run. All primaries and secondaries were followed until their energies reached  <1 keV and their remaining energies were assumed to be deposited locally.

Up to a third of the initial medium volume in each dish was lost by the end of the exposure period due to evaporation. For the source dish and all treatment dishes, two S-values were calculated based on the measured medium volume at the beginning (${{S}_{initial}}$) and conclusion (${{S}_{final}}$) of the exposure period. S-values in between ${{S}_{initial}}$ and ${{S}_{final}}$ were interpolated linearly. As a result, the MIRD formulation (Goddu et al 1997) was modified to account for the evaporation effect in each dish and the final equation used for dose calculation is (see supplemental material for derivation, equations (S1)–(S3)):

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle D\left( T \right)=\frac{{{A}_{0}}}{\lambda }\left[ \frac{{{S}_{final}}-{{S}_{initial}}}{\lambda T}\left( 1-\left( 1+\lambda T \right){{e}^{-\lambda T}} \right)+{{S}_{initial}}\left( 1-{{e}^{-\lambda T}} \right) \right]\nonumber \end{align} \tag{ 1 }$$

where $D\left( T \right)$ is the dose absorbed for cells exposed to ⁹⁰Y for duration $T$ with an initial activity of ${{A}_{0}}$ and $\lambda$ is the physical decay constant of ⁹⁰Y ($\lambda ={\rm ln}2/{{T}_{phys}}$ and physical half-life ${{T}_{phys}}=64.1$ h).

⁹⁰Y dose calibration

A series of calibration experiments was performed to quantify the ⁹⁰Y distribution. Radiochromic films (8.2  ×  9.7 mm; GAFchromic^™ EBT3 film: Ashland Inc., Covington, KY) were exposed to 6 MV x-rays to doses ranging from 0.5–10 Gy in accordance with the AAPM TG-61 protocol (Ma et al 2001). For ⁹⁰Y exposure, the EBT3 films were placed centrally in the treatment dishes (i.e. numbered dishes in figure 1(A)), and exposed for 14–19 h. Exposures were done with the films in situ in dry conditions, due to the solubility of the films, and not submerged in medium to replicate the conditions of cell exposure. Experiments were performed in duplicate for both ⁹⁰Y-DOTATATE and ⁹⁰YCl₃. EBT3 films exposed to 6 MV x-rays and ⁹⁰Y were scanned 24 h after irradiation, using an Epson Expression 10000 XL colour scanner in transmission mode. A calibration curve relating the dose reading to x-ray dose was derived from the 6 MV LINAC data and this was used to inform the dose achieved from the ⁹⁰Y exposure (Technical-Report 2010). A MC simulation (figure 2(B)) emulating the geometry previously described (figure 1(A)) was used to calculate the dose to the EBT3 film. Absolute dose measurements were determined by benchmarking the EBT3 film determined doses across all treatment dishes against the PENELOPE simulation (figure 2(A)). For the MC simulation, the material composition and density of the EBT3 film was based on previously reported values (Fiorini et al 2014). The absolute doses were background-subtracted based on the measured dose for the control dish.

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Radiobiological modelling

We can relate different fractionation schemes in terms of the LQM by using the BED concept (Dale 1996). For a fractionated EBRT treatment of $d$ Gy per fraction (not accounting for repopulation), BED is given by:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm BE}{{{\rm D}}_{{{\left( \alpha /\beta \right)}_{EBRT}}}}=nd\left( 1+\frac{d}{{{\left( \alpha /\beta \right)}_{EBRT}}} \right)\nonumber \end{align} \tag{ 2 }$$

where $n$ is the number of fractions and ${{(\alpha /\beta)}_{EBRT}}$ is an inverse measure of tissue sensitivity to changes in fractionation or dose rate. However, for the protracted dose delivery of ⁹⁰Y SIRT, sublethal damage repair can take place during the irradiation period, making the treatment less effective. Furthermore, radiation of different linear energy transfer (LET) may yield different relative biological effectiveness (RBE). A modified BED equation that accounts for LET and dose-rate effects can be used for ⁹⁰Y radiation (Dale and Jones 1999):

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm BE}{{{\rm D}}_{^{90}{\rm Y},{{\left( \alpha /\beta \right)}_{EBRT}}}}={{D}_{^{90}{\rm Y}}}\left( {\rm RB}{{{\rm E}}_{max}}+\frac{{{G}_{\infty }}{{D}_{^{90}{\rm Y}}}}{{{\left( \alpha /\beta \right)}_{EBRT}}} \right)\nonumber \end{align} \tag{ 3 }$$

where ${{D}_{^{90}{\rm Y}}}$ is the cumulative dose of ⁹⁰Y radiation, ${\rm RB}{{{\rm E}}_{max}}={{\alpha }_{^{90}{\rm Y}}}/{{\alpha }_{EBRT}}$ is the maximum (or intrinsic) RBE at zero dose, and $G$ is the Lea–Catcheside dose-protraction factor. $G$ can be estimated for a fully-decayed radiation source as:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{G}_{\infty }}=\frac{{{T}_{rep}}}{{{T}_{rep}}+{{T}_{phys}}}\nonumber \end{align} \tag{ 4 }$$

where ${{T}_{rep}}$ and ${{T}_{phys}}$ are the sublethal damage repair half-time and radionuclide decay half-life, respectively. For a finite exposure, $G$ can be determined from supplemental equation (S4). This modified BED formalism assumes that the intrinsic quadratic component ($\beta$) remains unchanged between modalities and the dose-rate effect is encapsulated by the $G$ factor resulting in a lower magnitude of the second term of equation (3). To compare relative efficacy of different fractionation schedules and different radiation modalities, it is useful to invoke the concept of equivalent dose in fractionated EBRT (EQD) (Fowler 2009). EQD for ⁹⁰Y physical dose, ${{D}_{^{90}{\rm Y}}}$, absorbed during a SIRT treatment is (see supplemental equation (S5) for derivation):

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm EQ}{{{\rm D}}_{{{\left( \alpha /\beta \right)}_{EBRT}}}}=\frac{{{D}_{^{90}{\rm Y}}}\cdot \left( {\rm RB}{{{\rm E}}_{max}}+\frac{{{G}_{\infty }}{{D}_{^{90}{\rm Y}}}}{{{\left( \alpha /\beta \right)}_{EBRT}}} \right)}{1+\frac{d}{{{\left( \alpha /\beta \right)}_{EBRT}}}}.\nonumber \end{align} \tag{ 5 }$$

Statistics

Dosimetry

PENELOPE simulations were performed for four hypothetical ⁹⁰Y concentration gradients where ⁹⁰Y was assumed to be uniformly distributed in the bottom 25%, 50%, 75%, and 100% of the source solution. EBT3 film measured and MC simulated relative doses were compared (supplemental figure 3). Results show that the dishes were asymmetrically affected by the dose gradient, based on whether the dishes were above or below the source. Furthermore, the  −1 and  −2 dishes were much more sensitive to the dose gradient, whereas relative doses determined from MC simulation and EBT3 film measurements were consistent for the  +1 and  +2 dishes (i.e. all dose points are superimposed on the graph). The comparison suggests that the ⁹⁰Y activity was concentrated at the bottom 75% and 25% of the source solution for ⁹⁰Y-DOTATATE and ⁹⁰YCl₃, respectively. Figure 2 shows that there was good agreement (<10% difference) between the measured absolute dose from calibration experiments compared with MC simulated results when these non-uniform ⁹⁰Y source distributions were assumed. The non-uniformity of the ⁹⁰Y source may be attributed to the chemical interactions between the free ⁹⁰Y³⁺ ions and the PBS used to dilute the ⁹⁰Y activity. This is supported by the fact that free ⁹⁰Y in ⁹⁰YCl₃ exhibited more extreme non-uniformity in distribution than chelated ⁹⁰Y in ⁹⁰Y-DOTATATE and that precipitation was observed visible when cold YCl₃ and PBS were mixed at high concentration. These experimentally determined source distributions were included in the subsequent dose calculations for clonogenic experiments. Table 1 compares the cell monolayer ${{S}_{initial}}$-values calculated for ⁹⁰YCl₃ and ⁹⁰Y-DOTATATE assuming a gradient distribution of ⁹⁰Y in the bottom 25% and 75% of the source dishes, respectively.

Table 1. Comparison of MC calculated ${{S}_{initial}}$-values for the 15 μm-thick cell monolayer in each treatment dish exposed to either ⁹⁰YCl₃ or ⁹⁰Y-DOTATATE.

Dish position	${{S}_{initial}}$-value (cGy MBq−1 d−1)
	90YCl3	90Y-DOTATATE
+2	6.26	8.40
+1	37.9	47.3
−1	31.4	24.3
−2	3.01	2.06

Clonogenic assays

Figure 3 compares the experimental surviving fractions for DLD-1 and HT-29 cells exposed to ⁹⁰Y β⁻-particles, clinical 6 MV x-rays, and ¹³⁷Cs γ-ray. The HT-29 cell line was more radioresistant towards all radiation sources compared with DLD-1 within the dose range considered and this was consistent with previously published results for ¹³⁷Cs γ-ray irradiation (Gao et al 2009). 6 MV x-rays and ¹³⁷Cs γ-ray induced an almost identical radiobiological response from both cell lines but HT-29 was slightly more sensitive to ¹³⁷Cs γ-ray at high doses. Table 2 summarises the fitted $\alpha$, $\beta$ and $\alpha /\beta$ values for the survival curves. For ⁹⁰Y β⁻-particles, the measured $\beta$ parameter encapsulates repair that took place during the 6 d exposure period. The $\alpha$ and $\beta$ parameters for EBRT derived from our methods were consistent with previously reported values (Miura et al 2012, Gholami et al 2018). It is noteworthy that the estimated $\alpha$ parameter for HT-29 exposed to ⁹⁰Y β⁻-particles was slightly higher than other modalities, though the 95% confidence intervals (CIs) for the estimated $\alpha$ for 6 MV x-rays and ¹³⁷Cs γ-ray are overlapped significantly with the 95% CI of the estimated $\alpha$ for ⁹⁰Y β⁻-particles. In contrast, DLD-1 exposed to ⁹⁰Y β⁻-particles exhibited less than half of the linear-term radiosensitivity towards 6 MV x-rays and ¹³⁷Cs γ-ray. $\beta$ values for ⁹⁰Y were very small due to the protracted dose delivery and this led to considerably larger $\alpha /\beta$ ratios.

Table 2. Comparison of $\alpha$, $\beta$, and $\alpha /\beta$-values derived from LQM fitting of the survival curves for DLD-1 and HT-29 cells exposed to either 6 MV x-rays (LINAC), ¹³⁷Cs γ-ray or ⁹⁰Y β⁻-particles. The range shown within brackets represents the 95% CIs of the estimated parameter.

Cell line	Radiation source	α (Gy−1)	$\beta$ (Gy−2)	$\alpha /\beta$ (Gy)
DLD-1	LINAC	0.273	0.0189	14.4
		(0.187–0.359)	(0.009 70–0.0282)	(3.15–25.7)
	137Cs	0.264	0.0153	17.3
		(0.198–0.330)	(0.008 33–0.0222)	(5.37–29.1)
	90Y	0.106	0.00109	97.0
		(0.075–0.137)	(−0.000 122–0.00230)	(36.8–231)
	90Ya	0.129	0	N/A
		(0.114–0.144)
HT-29	LINAC	0.050	0.0276	1.81
		(0.008–0.092)	(0.0230–0.0323)	(0.0247–3.60)
	137Cs	0.056	0.0367	1.54
		(0.003 43–0.109)	(0.0304–0.0429)	(−0.122–3.19)
	90Y	0.090	0.000141	637
		(0.063–0.116)	(−0.000 969–0.00125)	(−4517–5792)
	90Ya	0.0897	0	N/A
		(0.0792–0.100)

^aAdditional fit using only the linear $\alpha$ component since $\beta$ from the standard LQM is consistent with zero.

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Radiobiological parameters, ${\rm RB}{{{\rm E}}_{max}}$ and $G$, used in the derivation of equation (3) for $\alpha /\beta$-ratios provided in table 2, are summarised in table 3. If we adopt the premise that the β parameter for ⁹⁰Y is equal to that of EBRT by incorporating the dose protraction factor G, we can determine ${{G}_{\infty }}$ for a fully-decayed source by solving ${{G}_{T}}={{\beta }_{^{90}{\rm Y}}}/{{\beta }_{EBRT}}$ for ${{T}_{rep}}$ (see ${{G}_{T}}$ in equation S4 in supplemental material) and applying the derived ${{T}_{rep}}$ to equation (4).

Table 3. Comparison of ⁹⁰Y SIRT radiobiological modelling parameters derived for each cell line from LQM fitted parameters in table 2. The repair half-time ${{T}_{rep}}$ was determined using supplemental equation (S4). ${{G}_{\infty }}$ was estimated based on the derived ${{T}_{rep}}$ and equation (4). The last column shows the ${{\left( \alpha /\beta \right)}_{^{90}{\rm Y}}}$ for indefinite exposure. The range shown within brackets represents the 95% CI of the estimated parameter.

Cell line	${\rm RB}{{{\rm E}}_{max}}$ (${{\alpha }_{^{90}{\rm Y}}}/~{{\alpha }_{LINAC}}$)	${{G}_{6}}$ (${{\beta }_{^{90}{\rm Y}}}/{{\beta }_{LINAC}}$)	${{T}_{rep}}$ (h)	${{G}_{\infty }}$	${{\alpha }_{^{{\rm 90}}{\rm Y}}}/{{G}_{\infty }}{{\beta }_{LINAC}}~$ (Gy)
DLD-1	0.388	0.0577	2.51	0.0377	148
	(0.221–0.555)	(−0.0123–0.1277)	(−0.67–5.69)	(−0.0102–0.0856)	(−56.3–353)
HT-29	1.800	0.0051	0.21	0.0033	979
	(0.198–3.402)	(−0.0351–0.0453)	(−1.48–1.90)	(−0.0230–0.0296)	(−6911–8861)

Radiobiological modelling

Figure 4 shows ${\rm EQD}{{{\rm 2}}_{\alpha /{{\beta }_{LINAC}}}}_{~}$(top panel) and ${\rm EQD1}{{0}_{\alpha /{{\beta }_{LINAC}}}}_{~}$ (bottom panel) of ⁹⁰Y physical dose calculated using equation (5) and the radiosensitivity parameters presented in table 2. Physical dose of ⁹⁰Y was extrapolated to 100 Gy assuming an increased initial dose rate is not expected to significantly modify the intrinsic radiosensitivity of DLD-1 and HT-29 towards ⁹⁰Y β⁻ radiation. This assumption is supported by a previous study of DLD-1 and HT-29 that showed the $\alpha$ terms were almost equivalent following exposure to 0.25 and 42 Gy h⁻¹ of ¹³⁷Cs irradiation (Williams et al 2008). The figure shows ⁹⁰Y SIRT would be less effective than EBRT delivered in 2 Gy fractions for treating the DLD-1 cell line because it exhibits a high $\alpha /\beta$ ratio when exposed to LINAC x- or ¹³⁷Cs γ-radiation and a low $\alpha$ value when exposed to ⁹⁰Y β⁻ radiation. Extrapolating from the fit parameters, it requires  ≈100 Gy of ⁹⁰Y dose to achieve the same biological cell-killing effect as an EBRT of 30 fractions of 2 Gy. In contrast, HT-29 would respond to each Gy of ⁹⁰Y similarly to each Gy of EBRT delivered in 2 Gy fractions. However, EBRT delivered in 10 Gy fractions was more potent in treating either cell line than ⁹⁰Y SIRT. It is noteworthy that the accuracy of the predicted EQD is affected by the uncertainties of the estimated radiobiologic parameters (supplemental figure 4).

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With the increased use of TRT such as ⁹⁰Y SIRT for liver cancer, there is a pressing need to incorporate radiobiologic information into the decision-making process to optimise dose given during multiple administrations or to combine ⁹⁰Y SIRT with EBRT, specifically, stereotactic ablative radiotherapy (SABR) for curative intent. Here, the survival of DLD-1 and HT-29 CRC cells after exposure to ⁹⁰Y β⁻-particles, 6 MV x-rays, and ¹³⁷Cs γ-ray were determined by clonogenic assay. Radiosensitivity parameters, $\alpha$ and $\beta ,$ derived from the fitted survival curves were then used to calculate the equivalent dose in fractionated EBRT for ⁹⁰Y SIRT.

The experimental setup shown in figure 1 was designed to simulate the mechanism of dose delivery by ⁹⁰Y SIRT, where ⁹⁰Y-loaded microspheres are permanently trapped at the arteriolar end of the capillary bed and not internalised into cancer cells. This setup physically isolated the ⁹⁰Y from the cells, which contrasts with the recent investigation by Gholami et al (2018), where cells were mixed with ⁹⁰YCl₃ in a 96-well plate. Using the MTS assay, they determined metabolic viability curves for three CRC cell lines (HT-29, HCT-116 and SW-48), exposed to ⁹⁰Y β⁻-particles and 6 MV x-rays. The respective $\alpha$ and $\beta$ parameters of HT-29 derived from the metabolic viability curves were 0.0842 Gy⁻¹ and 0.0239 Gy⁻² for EBRT and 0.0145 Gy⁻¹ and 0.0005 Gy⁻² for ⁹⁰YCl₃. Although the MTS assay measures metabolic viability rather than reproductive cell death, the $\alpha$ and $\beta$ parameters for EBRT agree within the 95% CI of our estimated values. However, results for ⁹⁰Y diverge. Gholami et al found that  ≈56 Gy of ⁹⁰Y dose (cumulated after 8 d) is necessary to decrease metabolic viability to achieve the same cell kill as a single fraction of 8 Gy EBRT. Our results from clonogenic survival suggest a much lower ⁹⁰Y dose (cumulated after 6 d) of 20.7 Gy for DLD-1 and 23.6 Gy for HT-29 is necessary. For indefinite exposure, these values are 22.9 and 23.8 Gy, respectively. This discrepancy could be due to the differences in the two assays or the assumption that ⁹⁰Y did not internalise into the cells and was uniformly distributed throughout the well adopted in Gholami's study. In contrast, our results show that ⁹⁰Y was not uniformly distributed inside a tissue culture-treated dish and this differential distribution of ⁹⁰Y could affect dose calculations if not corrected.

The protracted dose delivery of ⁹⁰Y significantly increased clonogenic survival compared to acute exposure from either LINAC x- or ¹³⁷Cs γ-irradiation. Although the dose rate of the LINAC was nine times higher than that of the ¹³⁷Cs irradiator, the radiobiologic responses of DLD-1 and HT-29 towards these modalities were very similar, as both radiation dose deliveries were completed within minutes before damage repair could reduce cell death (Howard et al 2017). In contrast to the linear component, the experimental ${{\beta }_{^{{\rm 90}}{\rm Y}}}$ was extremely small for ⁹⁰Y β⁻ radiation and was not significantly different from zero by a Wald test (p   >  0.05, DLD-1: 0.001 09 (95% CI, −0.000 122–0.002 30) and HT-29: 0.000 141 (95% CI, −0.000 969–0.001 25)), i.e. not contributing statistically significantly to the fitting of the data within the LQM. The highly suppressed ${{\beta }_{^{{\rm 90}}{\rm Y}}}$ was consistent with the predicted $G$ factor for 6 d exposure (<0.06 for an assumed ${{T}_{rep}}$ of 0–5 h) (Dale 1996). The very small quadratic term of the LQM for a low-dose-rate radiation treatment is a well known issue and a simplified version of BED where $\beta =0$, which neglects dose-rate effects, has been used in the literature (Chiesa et al 2015). As expected, this $\beta =0$ assumption does not appreciably alter the value of $\alpha$ since the CI for ${{\beta }_{^{90}{\rm Y}}}$ in each cell line contains zero (table 2).

Furthermore by adopting the assumptions that ${{\alpha }_{^{90}{\rm Y}}}={\rm RB}{{{\rm E}}_{max }}~\times {{\alpha }_{EBRT}}$ and ${{\beta }_{^{90}{\rm Y}}}=G\times {{\beta }_{EBRT}}$ (Dale and Jones 1999), we are able to perform additional radiobiological modelling (table 3). Using these assumptions, we were able to extract a physiologically meaningful ${{T}_{rep}}$ of 2.5 h for the DLD-1 cell line and an ${\rm RB}{{{\rm E}}_{max}}~$ of 0.4. Interestingly, the HT-29 cell line was seemingly more sensitive to ⁹⁰Y than either LINAC or ¹³⁷Cs, with an ${\rm RB}{{{\rm E}}_{max}}>1$, although the 95% CIs of their $\alpha$-values overlap significantly. Data for HT-29 from Gholami et al (2018) suggest an ${\rm RB}{{{\rm E}}_{max}}~$ of 0.172, but this value is outside the lower CI for HT-29 in the current study. For ${{T}_{rep}}$, the 95% CIs contain negative values for both cell lines and the repair half-time ${{T}_{rep}}$ was only 12 min for HT-29, which was not expected as physiological repair half-times are generally longer. A short ${{T}_{rep}}$ could indicate either the experimental uncertainties are so large that it is not possible to extract a suppressed $\beta$ parameter with high accuracy and thus a physiologically meaningful repair time or the assumption that 'the β-values are equivalent by incorporating the dose protraction factor $G$' is not valid here. If the latter is correct then, for the HT-29 cell line, we cannot assume that there is a relationship between the radiobiological parameters of ⁹⁰Y and EBRT. It is worthwhile to point out that the latter assumes not only that the $\alpha$ values are related through RBE_max but that the $\beta$ values are independent of LET. There are other RBE models that predicted a dependence of the $\beta$ value on LET (Stewart et al 2018). However, these dependencies were seen mainly in proton and heavier ions at LET values exceeding those of the currently used radiation modalities, that is for LET  >4 keV μm⁻¹.

These assumptions need to be tested in other CRC cell lines to determine whether the radiobiology of these cell lines are indeed distinct from that of EBRT. Survival parameters from Gholami et al (2018) suggest ${{T}_{rep}}$ values of 1.04, 1.08, and 1.06 h for HCT-116, SW-48, and HT-29 cell lines, respectively. Although acquired through different methods, these values are consistent with each other and lie within the 95% CI of the parameters extracted from this study. Substituting out ${{G}_{6}}$ with our predicted ${{G}_{\infty }}$, determined from ${{T}_{rep}}$ using equation (4), further supressed the $\beta$s for ⁹⁰Y and results in a very high $\alpha /\beta$ ratio. Unless there is a significant biological effect resulting from the cellular internalisation of ⁹⁰Y, the $\alpha$ and $\beta$ parameters derived in this work would still apply to other targeted radionuclide therapies, such as peptide receptor radionuclide therapy using ⁹⁰Y-DOTATATE.

${\rm EQD2}$ and ${\rm EQD10}$ were derived to quantify the relative effectiveness of ⁹⁰Y SIRT compared to EBRT. In the last decade, SABR has been utilised for treating liver metastases of CRC origin (Comito et al 2015). Figure 4 shows that SABR with 10 Gy fractions could be more effective than both standard EBRT delivered in 2 Gy fractions and ⁹⁰Y SIRT in treating such disease. However, ⁹⁰Y SIRT could be an attractive alternative to standard EBRT as it has comparable efficacy while sparing healthy tissue due to protraction in dose delivery.

In this manuscript, we report a comprehensive study in which the radiosensitivity parameters of two CRC cell lines, DLD-1 and HT-29, to ⁹⁰Y β⁻-particles in comparison to that of EBRT (6 MV x-rays and γ-ray from a ¹³⁷Cs irradiator) were explored. Using statistical regression of the clonogenic survival data within the LQM framework, we conclude that the $\alpha$ values of cells exposed to ⁹⁰Y were significantly different from those exposed to either LINAC or ¹³⁷Cs, whereas the β values were not significantly different from zero. In addition, we provide a framework that relates the physical dose required for ⁹⁰Y to yield an equivalent EBRT biological response based on the concept of BED. Accounting for these differences in radiosensitivity enables researchers and clinicians to calculate equivalent doses (EQD) in a combined therapy (⁹⁰Y SIRT and EBRT) setting.

The authors are grateful to the reviewers who contributed thorough and insightful feedback and to the following collaborators:

John Prentice and Kyle Hallett at the University of Oxford, Department of Oncology, Mechanical Workshop for development of the experimental container. Martin Gill at the University of Oxford, Department of Oncology for microscopy. Pharmacists of the Radiopharmacy at The Churchill Hospital, Oxford, UK for supplying ⁹⁰Y-DOTATATE. Physicists of the Radiotherapy Unit at The Churchill Hospital for helping with the use of LINAC resources.

This work was supported by grants from Cancer Research UK (CRUK, Grant No. C5255/A15935) and the Medical Research Council (MRC, Grant No. MC_PC_12004).