A novel imaging biomarker for survival prediction in EGFR-mutated NSCLC patients treated with TKI

EGFR-mutated non-small cells lung carcinoma are treated with Tyrosine Kinase Inhibitors (TKI). Very often, the disease is only responding for a while before relapsing. TKI efficacy in the long run is therefore challenging to evaluate. Our objective is to derive a new imaging biomarker that could offer better insights on the disease response to treatment. This study includes 17 patients diagnosed as EGFR-mutated non-small cell lung cancer and exposed to an EGFR-targeting TKI. The early response to treatment is evaluated with 3 computed tomography (CT) scans of the primitive tumor (one before the TKI introduction and two after). Using our knowledge of the disease, an imaging biomarker based on the tumor heterogeneity evolution between the first and the third exams is defined and computed using a novel mathematical model calibrated on patient data. Defining the overall survival as the time between the introduction of the TKI treatment and the patient death, we obtain a statistically significant correlation between the overall survival and our imaging marker (p = 0.009). Using the ROC curve, the patients are separated into two populations hence the comparison of the survival curves is statistically significant (p = 0.025). Initial state of the tumor seems to have a role for the prognosis of the response to TKI treatment. More precisely, the imaging marker - defined using only the CT scan before the TKI introduction - allows us to determine a first classification of the population which is refined over time using the imaging marker as more CT scans become available. This exploratory study leads us to think that it is possible to obtain a survival assessment using only few CT scans of the primary tumor.

Introduction 1 Tyrosine Kinase Inhibitors (TKI) were shown to be effective in the treatment of challenging to evaluate. For example, in [3], the authors estimate the relapse median 10 time at 10 months.

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Latest advances in oncology and the discovery of many different sub-types of cancer, 12 partly because of genomic alterations, open the way to a personalized medicine [4]. 13 There is a need of new tools combining different types of available data to help to 14 choose the best treatment for each patient. Medical imaging has an important role to 15 play in this context as these patients are routinely monitored using CT scans. The most 16 current used CT scan evaluation -in particular for lung cancers -is the RECIST 17 (Response Evaluation Criteria In Solid Tumors) which consists in measuring the largest 18 diameters of target lesions [5,6]. Most recent studies have shown the interest of the 19 tumor volume evaluation which is more precise and has a better reproducibility in 20 particular concerning the evaluation of non-small cell lung cancers [7][8][9]. Concerning 21 EGFR-mutated non-small cells lung carcinoma, previous works have studied the 22 correlations between the initial reduction of the primary tumor and the overall survival. 23 One can find contradictory results in the literature: in [10,11], a significant correlation 24 has been established but more recently in [12] this correlation has not be validated 25 using another database. Many recent studies propose to use radiomic approaches which 26 consist in extracting a large number of quantitative features from medical images using 27 data-characterization algorithms. In non-small cell lung cancers, various tumor 28 heterogeneity markers may be computed, see [13] for a proposal for harmonization of 29 methodology. Then, they can be related for example to the distant metastasis 30 probability [14] ; to predict pathological response after neoadjuvant chemoradiation [15] 31 ; to indicate tumor response to radiation therapy [16] ; to advance clinical 32 decision-making by analyzing standard-of-care medical images [17] and to establish 33 independent marker of survival time [18]. In [19], the authors even show that radiomics 34 may help identify a general prognostic phenotype existing in both lung and 35 head-and-neck cancer. These approaches have also been used for EGFR-mutated 36 non-small cell lung cancer. For example, radiomic approaches may predict EGFR 37 mutation status without requiring repeated biopsy acquisitions [20,21] but also identify 38 tumor heterogeneity markers which can be related to early EGFR TKI failure [22]. 39 In this study, instead of testing classical heterogeneity markers, we introduce a novel 40 imaging biomarker that quantifies the evolution of the heterogeneity of the primitive 41 tumor of patients with EGFR-mutated non-small cells lung cancers over time. This 42 criterion is defined using our knowledge of the disease and can be biologically 43 interpreted. The objective of this work is to study the value of this novel marker to 44 predict overall survival in order to help clinicians to detect EGFR TKI treatment failure 45 earlier.

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Patients 48 A monocentric retrospective cohort study has been conducted on patients with a 49 biopsy-proven non-small-cell lung carcinoma -presenting an identified or suspected 50 EGFR (epidermal growth factor receptor) mutation, (established by a TKI clinical 51 benefit of more than 6 months) -which are non-accessible to local treatment (stage IIIB 52 or IV). Patients were included in the study if 3 CT-scans were available: one before the 53 first introduction of TKI treatment and two after. The study was approved by Institut 54 Bergonié and IRB approval was obtained for use of the CT images. Informed consents 55 of data collection were waived for research from each patient, in accordance with the 56 related policy of Institut Bergonié.

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Treatment 58 All patients were exposed to an EGFR-targeting TKI. Two molecules were used: 59 gefitinib (IRESSA®, Astra-Zeneca) and erlotinib (TARCEVA®, Roche). These two 60 therapies were given until progression, unacceptable toxicity, patient refusal to continue 61 treatment or death.

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Imaging and biomarkers 63 Evaluation scans were done every 2 to 6 months. The acquisition was performed after 64 an injection of iodized contrast agent at portal phase on the thorax, the abdomen and 65 the pelvis and then at late-arterial phase on the encephalon. We consider 3 CT-scans 66 (given at times t 0 , t 1 and t 2 ). The first one is acquired immediately before TKI 67 treatment and the second and the third ones are the 2 first ones after the first 68 introduction of TKI treatment. Time t 0 is the baseline. Tumors were delineated using a 69 semi-automatic segmentation library that relies on a deformable model [23]. All the 70 delineations were validated by a junior and a senior radiologists.

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Using these images, we derive various biomarkers. Defining by V (t) the volume of 72 the tumor at time t, we define the following set of biomarkers (computed from the 73 volume): corresponding respectively to the initial slope of volume decreasing (between t 0 and t 1 ), 75 to the slope of volume decreasing (between t 0 and t 2 ), to the initial percentage of 76 volume decreasing (between t 0 and t 1 ) and to the percentage of volume decreasing 77 (between t 0 and t 2 ).

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On CT, high intensities (lighter colors on the image) correspond to high tissue 79 densities and therefore to high cellularity and proliferation while intensities around 0 80 correspond to water and necrosis. We therefore split the set of voxels of the images into 81 two classes. The first class contains the voxels whose values are non-negative while the 82 second class is formed by non-positive intensities voxels. We will refer to the first class 83 (with positive intensities) as being the proliferative one while the second one will be 84 referred as the necrotic one. We denote by P (t) the volume of the set of voxels whose 85 intensities are positive within the tumor on the exam at time t. We then compute the 86 ratio of this proliferative-like compartment with respect to the total volume 87 %P (t) = P (t) V (t) . We define the following set of biomarkers (based on the heterogeneity): corresponding respectively to the area under the curve (AUC) of the quantity %P (t) 89 between t 0 and t 2 , to the AUC of the quantity %P (t) between t 1 and t 2 , and to the 90 initial value of the quantity %P (t).

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Using the first 3 CT-scans, we extract V (t 0 ), V (t 1 ), V (t 2 ), P (t 0 ), P (t 1 ) and P (t 2 ) 92 and approximate the imaging marker t2 t0 %P (t)dt with the trapezoidal rule. However, 93 this strategy has limitations. Indeed, the acquisition times t 0 , t 1 and t 2 and the CT 94 image noise may introduce some instability in the computation, for example if t 1 is too 95 close to t 0 or t 2 .

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We therefore choose another strategy that consists in using a mechanistic model in 97 order to fit the values P (t 0 ), P (t 1 ) and P (t 2 ) continuously on the time interval [t 0 , t 2 ]. proliferative and necrotic compartments. The blue (resp. red, green) curve describes the 107 evolution of the volume (resp. density of proliferative cells, density of necrotic cells) 108 given by the mechanistic model that fits with the data. The purple curve gives the 109 evolution of the ratio of the proliferative compartment with respect to the volume. Whenever appropriate, standard statistics are presented as mean±standard-deviation 113 and number (percentage). We define the overall survival (OS) as the time between the 114 introduction of the TKI treatment and the patient death. Survival curves were 115 computed using the Kaplan-Meier estimator and compared using Log-Rank tests. The 116 association of survival failure with each investigated biomarker was tested using Cox 117 regression. Prediction performances of the biomarkers were assessed using ROC curves. 118 The appropriate statistical tests were performed when required with a significance 119 threshold set to p = 0.05. The mechanistic model was fitted using the Monte Carlo 120 method. All computations were performed using Matlab-R2015a.

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A population of 25 patients has been collected at Institut Bergonié (Bordeaux, France) 123 between 2006 and 2013. We have kept 17 patients among these 25 patients. We have 124 excluded 2 cases for which the CT-scan before the TKI introduction was not available 125 and 6 cases for which it was not possible to delineate the tumor (miliary disease, 126 patients without any discernable lesion e.g. with pleural effusion or atelectasis). Table 1 127 presents the patient cohort: age, sex, smoking information, mutation, stage and if the 128 patient had a treatment before the TKI introduction.

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First of all, there is no significant correlation between each volume-based biomarker 130 and the overall survival (p = 0.48, p = 0.36, p = 0.23 and p = 0.17).

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We will now focus on the heterogeneity-based biomarkers gathered in the vector The values of the first heterogeneity-based biomarkers The ROC curve (AUC = 0.81) is given in Fig. 4 (see blue curve). Using Fig. 4 , we 145 see that a good compromise consists in taking a normalized threshold for the biomarker 146 of 0.4 that is optimal with a sensibility of 0.9 and a specificity of 0.7..

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In this work we have studied the ability of volume-based and heterogeneity-based 164 imaging biomarkers to predict the survival in EGFR-mutated NSCLC patients treated 165 with TKI.

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Our first result is that there is no correlation between volume-based imaging 167 biomarkers and survival. This finding is consistent with the work [12] who noticed a 168 lack of association between tumor shrinkage and long-term survival. This illustrates 169 why the response to TKI treatment is difficult to estimate using only the evolution of 170 tumor volume (or RECIST).

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Our second result is that heterogeneity-based imaging biomarkers may help predict 172 short-term survival. More precisely, we propose an imaging biomarker t2 t0 %P (t)dt that 173 is able to discriminate patients with short-time survival using only 3 successive 174 CT-scans (an imaging monitoring performed as standard of care for such patients). To 175 the best of our knowledge, this is the first study in which a mechanistic model based on 176 June 11, 2019 7/13 disease knowledge has been used to predict the outcome in EGFR-mutated NSCLC 177 patients treated with TKI. This shows that characterizing the content of the tumor and 178 its dynamics using mathematical models might provide valuable information to guide 179 clinical decisions.

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The main strength of this work lies in the fact that the imaging marker is based on a 181 mathematical description of the alleged underlying pathophysiological processes rather 182 than purely empirical observations. As a consequence, the value of the biomarker may 183 be given a phenomenological meaning, an interpretation that would be lacking 184 otherwise. A large value of the biomarker means that the proportion of proliferative 185 cells does not decrease over time (even if the volume of the lesion is decreasing). In the 186 opposite case, a small value of the marker implies a decrease of the proportion of the 187 proliferative compartment, even if the response is modest in terms of whole tumor size. 188 We show that the use of the first image (CT-scan acquired before TKI introduction) 189 is of paramount importance for biomarker to predict the survival. More precisely, the 190 imaging biomarker computed using only this first image provides a first classification of 191 the patient that can be incrementally improved using the imaging marker as more We have shown that the initial volume (or RECIST) evolution under TKI is not 206 sufficient to predict the survival while the tumor heterogeneity before the TKI 207 introduction is a major prognosis factor and provides a first classification of patients.

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Furthermore, this first classification can be incrementally improved using the imaging 209 marker that summarizes the early evolution of the tumor heterogeneity as soon as more 210 CT scans are available. Short term perspectives of this work are about increasing the 211 size of the cohort and improving the segmentation process in order to be able to include 212 patients with non-delineated tumors.
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The evolution of the volume of proliferative cells is supposed to satisfy the following 314 equation: where the quantity J 0 is the growth rate and we assume it constant in order to keep a 316 model with identifiable parameters. The quantity K corresponds to the decreasing rate 317 due to the TKI treatment. We assume that it follows a Gompertz-like law: where δ is an unknown parameter and K 0 the initial decreasing rate of P . We assume 319 that when exposed to the treatment, the proliferative cells die and form the necrotic 320 compartment. The evolution of the density N of this necrotic compartment is supposed 321 to satisfy the following equation: The quantity L is the evacuation rate of the necrotic compartment. We assume that it 323 follows a Gompertz-like law: where η is an unknown parameter and L 0 the initial evacuation rate of N .

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This leads to the following ordinary differential system in which the quantity P can be explicitly determined: δ (e −δt −1)−N0t and the quantity N can be numerically approximated. Figure 7 illustrates this model in 328 the formalism of compartment models.

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Remark 1 Please note that this model may be derived from a spatial PDE model as follows. LetP (resp.N ) be the spatial density of proliferative (resp. necrotic or quiescent) cells and v, the velocity field that describes the evolution of the tumor over time. , the tumor can be described by the evolution in space and time of population ofP andN , where the last equation closes the system using a Darcy law with π the pressure. Using 330 Reynolds theorem, this system of partial differential equation is related to System (1) by 331 where Ω is the tumor domain.

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The model has 5 parameters: K 0 , δ, J 0 , L 0 and η that we want to estimate using (the 334 subscript d is used to design the data):

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• the volumes V d (t 1 ) and V d (t 2 ) (V d (t 0 ) is used for the initial condition),

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• the proliferative parts P d (t 1 ) and P d (t 2 ) (P d (t 0 ) is used for the initial condition). 337 The parametrization is done into two steps. We start by estimating K 0 , J 0 and δ by Two cases are possible:
• Case P d (t 0 ) > P d (t 1 ) and P d (t 1 ) < P d (t 2 ): we search the parameters as: consists in estimating L 0 and η by minimizing As we consider that the TKI treatment is still acting (for all the patients, we have 347 V d (t 0 ) > V d (t 1 ) > V d (t 2 )), the sets of parameters for which V is not strictly decreasing 348 are rejected.

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The evolutions of the densities of proliferative (red) and necrotic (green) cells for the 17 351 patients with the evolution of the volume (in blue) are presented in Fig. 8.