# In Vivo Validation of the BIANCA Biophysical Model: Benchmarking against Rat Spinal Cord RBE Data

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## Abstract

**:**

## 1. Introduction

## 2. Results

#### 2.1. RBE-LET Relationship

#### 2.2. Carbon Ions: Dose Dependence

#### 2.3. Carbon Ions: LET Dependence

#### 2.4. Protons

## 3. Discussion

## 4. Materials and Methods

#### 4.1. The BIANCA Model: Assumptions, Parameters and Structure

#### 4.2. Construction of a Radiobiological Database and RBE Prediction

_{ref}is the CL yield used for the reference cell line irradiated with the same radiation quality, whereas (CL⋅Gy

^{−1}⋅cell

^{−1}) and (CL⋅Gy

^{−1}⋅cell

^{−1})

_{ref}are the CL yields (mean number of CLs per unit dose and per cell) used to simulate photon irradiation of the cell line of interest and the reference cell line, respectively. Finally, V

_{ref}and V represent the nucleus volume of the reference cell line and the cell line of interest, respectively. In a previous study, V79 cells have been chosen as a reference, and V79 cell survival curves have been simulated for a wide range of particle types and LET values. Afterwards, the aforementioned formula has been successfully applied to predict the survival of CHO cells irradiated by two opposing fields of C-ions or protons at HIT [18].

_{X}= 0.10 Gy

^{−1}and β

_{X}= 0.05 Gy

^{−2}, leading to a reasonable α

_{X}/β

_{X}ratio of 2 Gy. Nowadays, additional data are available, both for in vitro [37,38] and for in vivo [39] settings. In particular, Henderson and co-workers irradiated chordoma patients (with a tumor volume of about 100 cm

^{3}) with a total dose D = 35 Gy and a fractional dose d = 7 Gy getting a TCP (Tumor Control Probability) of about 60%, and they estimated an α

_{X}/β

_{X}ratio of 2.45 Gy:

_{X}D − β

_{X}Dd)]

^{7}cells/cm

^{3}, as reported in the literature [40,41]. From this calculation, we obtained α

_{X}= 0.159 and β

_{X}= 0.065, which appears to be a reasonable estimation for photon irradiation of chordoma in vivo. Importantly, the α

_{X}/β

_{X}ratio of 2.45 Gy is still consistent with the value α

_{X}/β

_{X}=2 Gy adopted in clinical LEM applications to minimize normal tissue damage.

^{2}) was performed to produce a radiobiological database, i.e., a table of alpha and beta coefficients as a function of particle type and energy.

_{X}and β

_{X}are the photon coefficients, α

_{i}and β

_{i}are the ion coefficients (at a given ion energy, and thus LET), and S is the considered survival level.

#### 4.3. Interface between BIANCA and the FLUKA Monte Carlo Transport Code

_{i}and β

_{i}values from the radiobiological table and calculated the respective values for the mixed beam conditions based on the TDRA (Theory of Dual Radiation Action) [43] as described in [42], i.e.,

_{i}is the absorbed dose (in the considered voxel) due to the i-th particle calculated by FLUKA, α

_{i}and β

_{i}are the corresponding radiobiological parameters provided by BIANCA, and α and β are their values under mixed-beam conditions. The corresponding cell survival fraction, RBE-weighted dose (D

_{RBE}) and RBE were then calculated as follows:

_{X}and β

_{X}are the photon parameters provided by BIANCA.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Relative biological effectiveness–Linear Energy Transfer (RBE-LET) relationship calculated by BIANCA for chordoma cell survival following irradiation with monochromatic carbon beams at 1 Gy (upper curve) or 2 Gy (lower curve) Carbon dose.

**Figure 2.**RBE as a function of carbon ion dose for irradiation of the rat spinal cord in the SOBP (upper line and filled data points) or in the entrance plateau (lower line and open data points). The lines are predictions by BIANCA, the points are experimental data taken from [10].

**Figure 3.**RBE as a function of dose-averaged LET for single-fraction (panel

**a**) or two-fraction (panel

**b**) irradiation of the rat spinal cord at different positions within the carbon-ion Spread-Out Bragg Peak (SOBP). The lines are predictions obtained by BIANCA, the points are experimental data taken from [12,14] (panel

**a**), or [13] (panel

**b**). In panel a, at 99 keV/µm the higher experimental value is from a repetition experiment [14] and is considered as more reliable.

**Figure 4.**RBE as a function of depth for single-fraction (panel

**a**) or two-fraction (panel

**b**) proton irradiation of the rat spinal cord. The lines are predictions by BIANCA, the points are experimental data taken from [15].

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**MDPI and ACS Style**

Carante, M.P.; Aricò, G.; Ferrari, A.; Karger, C.P.; Kozlowska, W.; Mairani, A.; Sala, P.; Ballarini, F.
In Vivo Validation of the BIANCA Biophysical Model: Benchmarking against Rat Spinal Cord RBE Data. *Int. J. Mol. Sci.* **2020**, *21*, 3973.
https://doi.org/10.3390/ijms21113973

**AMA Style**

Carante MP, Aricò G, Ferrari A, Karger CP, Kozlowska W, Mairani A, Sala P, Ballarini F.
In Vivo Validation of the BIANCA Biophysical Model: Benchmarking against Rat Spinal Cord RBE Data. *International Journal of Molecular Sciences*. 2020; 21(11):3973.
https://doi.org/10.3390/ijms21113973

**Chicago/Turabian Style**

Carante, Mario P., Giulia Aricò, Alfredo Ferrari, Christian P. Karger, Wioletta Kozlowska, Andrea Mairani, Paola Sala, and Francesca Ballarini.
2020. "In Vivo Validation of the BIANCA Biophysical Model: Benchmarking against Rat Spinal Cord RBE Data" *International Journal of Molecular Sciences* 21, no. 11: 3973.
https://doi.org/10.3390/ijms21113973