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This work aims to theoretically show the development of a nonequilibrium of radiation-induced bystander effect (RIBE) under steep dose gradient regions that typically occur in the field edges of a beam. We applied the kinetics model proposed by (McMahon et al. 2013) for in vivo conditions coupled with a hypothesis called “Layer-limited bystander signaling (LLBS)” to demonstrate 1) an enhancement in TCP (i.e. Enhanced TCP or ETCP) due to bystander signals, 2) the development of nonequilibrium of RIBE under steep dose gradient regions and 3) the reduction in ETCP in the surface of Clinical Target Volume (CTV) due to the non-equilibrium of RIBE. We incorporated the elements of RIBE directly in the existing Poisson LQ model available in Pinnacle3 TPS (Version 9.10.0) to compute the percentage reduction of ETCP in the tumor surface due to nonequilibrium of RIBE. The percentage improvement in TCP obtained in tumor surface by accounting for RIBE is about 46% lower than that obtained in the interior of the tumor. This suggests that relatively more number of cancerous cells might survive in the vicinity of tumor surface. The result obtained from the study is indicative of an additional uncertainty component associated with radiation treatment. Hence, this paper suggests that the radiation treatments employing steep dose gradients could be biophysically different in many ways.

Intensity modulated Radiation Therapy (IMRT) allows for a highly conformal dose distribution to be planned for a target volume, while effectively sparing the surrounding healthy tissues or organs. Clinical trials have shown a promising tumor control and lower normal tissue complications. The reported advantages in IMRT arise from the ability to produce steep dose gradients between tumor surface and surrounding normal tissue.

In IMRT, the desired uniform dose distribution to target volume is achieved by producing an inhomogeneous X-ray dose distribution from multiple directions. Many investigators have suggested methods to account for changes in radiation response of tumour cells when exposed to inhomogeneous dose distributions [

Also the implications of RIBE for modulated X-ray fields have been reported [

In this work, we applied the kinetics model proposed by McMahon et al. for in vivo conditions [

McMahon et al. modelled [

where

In Equation (1), it is considered that a cell receiving dose D will continue to emit signals for a time of

Consider two clusters (Cluster A and B) of equal number of tumor cell populations whose center is separated by a distance

TCP for the cell populations in Cluster A is given by:

where ^{th} cell in Cluster A per fraction.

TCP for the cell populations in Cluster B is given by:

where ^{th} cell in Cluster B per fraction.

In Equations (2) and (3), the parameters α and β represent the linear and quadratic components of the LQ model respectively.

Assuming α/β = 10, and the dose delivered per fraction is 2 Gy, Equations (2) and (3) is reduced to:

where D is the total dose, i.e. D = n ´ d.

If we assume the absorption of signal ρ leads to an overall reduction in surviving fraction, the enhanced tumor control probability (ETCP) for the tumor population in Cluster A can be

where ^{th} cell in Cluster A.

ETCP for the tumor population in Cluster B is given by

^{th} cell in Cluster B. In Equations (6) and (7), a linear increase in α is assumed with respect to the amount of signal above the threshold.

Let us assume that both clusters receive equal amount of dose per fraction at the same time. As mentioned before, the cells receiving dose will continue to emit signals only for a finite amount of time in proportionate to the amount of absorbed dose. Hence, it is apparent that the amount of bystander signal received by both tumor clusters from each other would reach a dynamic equilibrium in time t leading to same overall biological effect, that is,

However, the dynamic equilibrium of the signals received by the tumor clusters from each other will be impaired if the Clusters A and B are exposed to entirely different magnitudes of dose at the same time. Such scenarios usually occur in the field edges of a beam, that is, between tumor and normal tissue surfaces, wherein a steep dose gradient is produced.

In order to prove the reduction of ETCP in tumor surface, we have used a hypothesis called “Layer-limited bystander signaling (LLBS)”. According to LLBS hypothesis, in a 2D geometry, the entire bystander signal received by a given Layer of cells is only from the nearest Layers on both sides, which is illustrated in

Consider five Layers of cells as shown in

According to LLBS hypothesis, the entire bystander signal that Layer Q would get is only from Layers P and R. Likewise, the entire bystander signal that Layer R would get is only from Layers Q and S. It is important to note that the thickness of the Layers is modeled in such a way that one Layer would completely absorb the signals received from its nearest Layer without any further transmission of the signals to other Layers. It was reported that the propagation of RIBE through radicals was found to reach up to 1 mm from the point of origin [

Now let us compute ETCP at Layers Q and R as shown below:

where,

Since Layer S is receiving relatively very low dose, the cells in Layer S will cease to emit signals relatively quickly. Hence the cumulative of signal received by the cells in Layer R from Layer S will be negligible as compared to the amount of signal received from Layer Q over a period of time t, which is much greater than

Also one can say that

Hence,

Therefore,

This theoretical argument indicates a relative reduction in the ETCP of the cells at the tumor surface (i.e. CTV surface) in spite of getting exposed to the same amount of physical dose as received by the cells inside the tumor volume.

We incorporated the elements of RIBE directly in the existing Poisson LQ model available in Pinnacle^{3} TPS (Version 9.10.0) to compute ETCP. We created 2 mm thick Layers in a model water phantom mimicking the illustration given in ^{3} TPS. The volume of each Layer was 1 cc. We assumed α/β = 10 for Layers P, Q and R. We used a fractionation scheme of 2 Gy for 25 fractions, covering at least 95% volume of each Layer. We simulated the exposure of the Layers with a single-field 6-MV photon beam produced with a Varian linear accelerator (Varian Clinac 2100).

The field edge of the beam was set with a margin of 1 mm from the edge of Layer R to the edge of the field (defined only by Jaw). The beam MU was adjusted in such a way that the mean dose obtained in Layers P, Q and R is 50 Gy. Consequently, the Layers P and Q receive a minimum dose of 44 Gy and a maximum dose of 57 Gy in 25 fractions; Layer R receives a minimum dose of 39 Gy, and a maximum dose of 57 Gy in 25 fractions. We used a dose grid setting of 2 mm in X, Y and Z planes and computed the dose using Convolution/Superpo- sition algorithm. In addition, we assumed

With this parameter setting, we computed TCP and ETCP for Layers Q and R. The TCP and ETCP for Layer Q was 0.355 and 0.405 respectively, meaning 14% improvement in TCP due to the impact of bystander signals. The TCP and ETCP for Layer R was 0.328 and 0.353 respectively, meaning 7.6% improvement in TCP due to the impact of bystander signals. This implies that the percentage improvement in TCP obtained in Layer R is 45.7% lower than that obtained in Layer Q.

It was not previously unknown that the cells in tumor surface are prone to get underdosed due to internal organ motion and set-up uncertainty related factors. This is why a planning target volume (PTV) is added to CTV. In this paper, it is argued that even if the CTV surface is given an equal amount of dose as given to the interiors of the CTV, there will be a measurable reduction in ETCP at the surface, when a steep dose gradient is formed right next to the CTV edge. The results indicate that the percentage improvement in ETCP induced by RIBE is 45.7% lower in tumor surface than that in the interior of the tumor. This implies that more number of cancerous cells might survive in the vicinity of tumor surface. We agree that this prediction is not validated by any experimental observations in vivo. But the basis for our work is McMahon’s model [

Current notion of PTV is to mitigate the risk of geometric miss of CTV due to internal motion and set-up uncertainty. The concept of PTV could mitigate the risk of reduction of ETCP in CTV surface to an extent as long as the intended gap between CTV and PTV is maintained. However, during the course of RT (inter and intra fraction), it is possible that CTV margin closely approaches PTV margin, which could increase the risk of causing a reduction of ETCP in CTV surface. This is indicative of an additional uncertainty component associated with radiation treatments. Moreover, the proposed model shows that the degree of reduction in ETCP is directly proportional to the dose gradient produced in the tumor surface. So a huge reduction in ETCP could be expected for treatments employing more intensity modulation such as IMRT and spot scanned proton therapy. In IMRT, the lateral edges of the field are expected to cause the reduction of ETCP, whereas in the case of proton therapy, the distal edge of the beam is expected to cause the reduction.

The assumption of 1% change in α due to the impact of RIBE is based on the theoretical planning study by McMahon et al. [

As far as the extendibility of the proposed model is concerned, inputting a reasonable value for the factor

In this work, we have theoretically demonstrated the development of a nonequilibrium of RIBE under steep dose gradient regions. The results obtained in the study show that the percentage improvement in TCP obtained in tumor surface is about 46% lower than that obtained in the interior of the tumor. This suggests that relatively more number of cancerous cells might survive in the vicinity of tumor surface. Also this is indicative of an additional uncertainty component associated with radiation treatment. Hence, this paper suggests that the radiation treatments employing steep dose gradients could be biophysically different in many ways.

R.Vaitheeswaran,K. J.Maria Das,11, (2015) On the Nonequilibrium of Radiation-Induced Bystander Effects in Tumor Surface and Its Implications in Radiation Therapy. International Journal of Medical Physics, Clinical Engineering and Radiation Oncology,04,208-214. doi: 10.4236/ijmpcero.2015.43025