## Lyman-Kutcher-Burman (LKB) model for normal tissue complication probability

As an example, calculating the NTCP based on the Lyman-Kutcher-Burman (LKB) model for the endpoint of urethra stricture, we use the following parameters TD50 = 116.7 Gy, m = 0.23, n = 0.3, and α/β = 5.0 Gy. (as published by Panitierri et al., and used in the study of Spohn and Sachpazidis et al.).

We are going to use the pyRadiobiology python package for the LKB NTCP response.

## LKB with physical dose

Let’s assume that the 3D physical dose distribution is given. By that I mean either the physical dose of each voxel or the differential dose volume histogram (DDVH). In the following example we have two voxels/sub-volumes of 15 cc that receive 55 Gy each.

from pyradiobiology.primitives import Dose, DoseType, DoseBag

def test_LKB_usage_example_with_physical_dose(self):
lkb_model = LKB(td50=Dose.gy(116.7, dose_type=DoseType.EQD2), m=0.23, n=0.3)
dose_array = DoseBag.create(data=[55, 55], dose_type=DoseType.PHYSICAL_DOSE)
volume_array_in_cc = [15, 15]
ntcp = lkb_model.response_from_pysical_dose(dose_array_in_physical_dose=dose_array,
volume_array=volume_array_in_cc,
ab_ratio=Dose.gy(5.0),
nfx=25)
print(f"NTCP = {ntcp}")
self.assertEqual(0.0125, round(ntcp, 4))


## LKB with dose in EQD2

In this case, we assume that the absorbed dose is in EQD2.

def test_LKB_usage_example_with_eqd2(self):
lkb_model = LKB(td50=Dose.gy(116.7, dose_type=DoseType.EQD2), m=0.23, n=0.3)

dose_array = DoseBag.create(data=[116.7, 116.7], dose_type=DoseType.EQD2)
volume_array_in_cc = [15, 15]

ntcp = lkb_model.response(dose_array_in_eqd2=dose_array, volume_array=volume_array_in_cc)
print(f"NTCP = {ntcp}")
self.assertEqual(0.5, round(ntcp, 2))


 Panettieri V, Rancati T, Onjukka E, Ebert MA, Joseph DJ, Denham JW, et al. External Validation of a Predictive Model of Urethral Strictures for Prostate Patients Treated With HDR Brachytherapy Boost. Front Oncol (2020) 10:910. doi: 10.3389/fonc.2020.00910

 Spohn SKB, Sachpazidis I, Wiehle R, Thomann B, Sigle A, Bronsert P, Ruf J, Benndorf M, Nicolay NH, Sprave T, Grosu AL, Baltas D and Zamboglou C (2021) Influence of Urethra Sparing on Tumor Control Probability and Normal Tissue Complication Probability in Focal Dose Escalated Hypofractionated Radiotherapy: A Planning Study Based on Histopathology Reference. Front. Oncol. 11:652678. doi: 10.3389/fonc.2021.652678 