Modelling of classified individual tumor lesions in metastatic colorectal cancer (mCRC) patients using delay differential equations.
M.L. Sardu (1), N. Terranova (1), P. Girard (1), A. Munafo (1)
Merck Institute for Pharmacometrics, Merck Serono S.A., Lausanne, Switzerland
Objectives: Standard practice in pharmacometrics applied to oncology since publication of the Claret’s paper  has been to model the relationship between drug exposure and total individual tumor size, which can hide valuable information contained in individual target lesions (iTL) dynamics. In particular, non-identical dynamics of individual lesions, belonging to separate tumor tissues, might explain differences in resistance to anti-tumor drugs . A new method proposed to automatically classify iTL and to measure the degree of similarity in their dynamics showed that iTL can be “desynchronized” . Hence, we propose a model-based approach to assess the applicability of delay differential equations (DDE)  to describe the delayed dynamics of iTL within patients (pts).
Methods: In a recent work based on a non-parametric methodology applied to multiple classified iTL , it was found that the degree of similarity in lesion dynamics increases when accounting for some delay between different tissues. Following this rationale, we propose here a model-based approach to describe the dynamics of classified iTL, accounting for inter-lesion variability  in delays. We first applied the tumor size model proposed by Claret et al [1, 5] to classified iTL and, resorting to DDE, we then introduced delayed terms on the state variables describing either tumor growth or the killing rate. As the model variants (i.e., including the delayed term) are nested to the original Claret one, the comparison was based on the objective function values and the standard model diagnostics.
Data from one phase II study in mCRC pts were analyzed. For each classified tumor tissue, longitudinal measurements of the sum of the product (area) of longest diameters were considered.
The analyses were performed using Monolix 4.3.3.
Results: Data from 902 mCRC pts with 1316 classified iTL  (579 pts with 1 lesion, 245 pts with 2, 67 with 3, 9 with 4, and 2 with 5 lesions) and a total of 3705 observations (measurements), were analyzed. Overall, the three models were able to describe the available data. However, the DDE model with delayed term applied to the killing rate was found the most suitable in describing the classified iTL data.
Conclusions: Given that iTL dynamics might not be synchronized, DDE appears to be a valuable tool in the investigation of the mechanism of potential drug resistance and in the description of the tumor growth dynamics in different tissues.
This work was supported by the DDMoRe project (www.ddmore.eu).
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