Studying the regression profiles of cervical tumours during radiotherapy treatment using a patient-specific multiscale model

Apart from offering insight into the biomechanisms involved in cancer, many recent mathematical modeling efforts aspire to the ultimate goal of clinical translation, wherein models are designed to be used in the future as clinical decision support systems in the patient-individualized context. Most significant challenges are the integration of multiscale biodata and the patient-specific model parameterization. A central aim of this study was the design of a clinically-relevant parameterization methodology for a patient-specific computational model of cervical cancer response to radiotherapy treatment with concomitant cisplatin, built around a tumour features-based search of the parameter space. Additionally, a methodological framework for the predictive use of the model was designed, including a scoring method to quantitatively reflect the similarity and bilateral predictive ability of any two tumours in terms of their regression profile. The methodology was applied to the datasets of eight patients. Tumour scenarios in accordance with the available longitudinal data have been determined. Predictive investigations identified three patient cases, anyone of which can be used to predict the volumetric evolution throughout therapy of the tumours of the other two with very good results. Our observations show that the presented approach is promising in quantifiably differentiating tumours with distinct regression profiles.

t is the duration of each pulse, 56 x is the time between pulses without irradiation, 57 μ is the repair rate constant, 58 and T 1/2 is the half time for sub-lethal damage repair. Monoexponential recovery kinetics is assumed. 59 60 In order to simulate within CERONCO, where a time step of one hour is used, the number of cells that 61 are lethally hit by each successive pulse the following consideration has been made: 62 Let P init be the initial tumour cell population. According to the modified LQ model, after N pulses of 63 dose d have been applied the remaining (survived) tumour cell population will be: 64 The number of surviving tumour cells just after each successive pulse in the N-pulse scheme is given Since each pulse acts upon the tumour cell population that remained alive after all previous pulses the 74 following equation applies for every two successive pulses: 75 Where SF i is the survival fraction after the i-th pulse of the N-pulse scheme. 77 The goal is to derive a suitable mathematical formulation of SF i , so that the correct number of lethally 78 hit cells is computed within CERONCO at the appropriate time points, just after each pulse dose. 79  Algorithms and code have been developed in order to transform the imaging data into a form 160 appropriate to be used as an input to CERONCO. For each clinical case the following files are created 161 as an input for CERONCO: 162 1) 3D-reconstructions of the Gross Tumour Volume (GTV) (raw files, tumour or non/tumour per 163 GC) for (up to) 5 time points: Pretherapy (before start of treatment), Midterm (during external 164 beam radiotherapy treatment), BT0 (before brachytherapy treatment), BT1 (start of 1 st 165 brachytherapy fraction), BT2 (start of 2 nd brachytherapy fraction) 166 2) BT1, BT2 spatial dose distribution raw files (dose per GC). 167 These 3D-reconstruction raw files supply the model with the tumour's spatial information and 168 correspond to the region of interest onto which the discretizing mesh of the model is superimposed. 169 Within each raw file each Geometrical Cell (GC) of the mesh is labeled as tumour or non/tumour. The 170 procedure for the creation of these input files is the following: 171   Table 1 of the main article.

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Model parameter or virtual tumour feature

Description Computation
Total Initial total number of tumour cells Computed based on the imaging-based GTV tumour volume, by considering a typical solid tumour cell density (e.g. 10 9 cells/cm 3 ), unless more specific information for a particular tumour is available.

DF (%)
Initial tumour dead fraction (Percentage of dead tumour cells over all tumour cells).
Defined by the user.
In the current study its estimation was based on the provided initial tumour's necrotic diameter.

Dead
Necrosis rate of differentiated cells (fraction of differentiated cells dying through necrosis per hour) Fraction of stem and LIMP cells entering G0 phase after mitosis Necrotic: Initial number of necrotic tumour cells.
Apoptotic: Initial number of apoptotic tumour cells.

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These tumours seem to be incompatible with these specific tumour profiles.