Abstract 1942: Volume and vascular evolution assessed with ultrasound in tumor growth: First steps for a future tool of predictive responses of treatment
Authors: Griffon Jerome , Yang Zixin , Guillou-Buffello Delphine Le , Dizeux Alexandre , Lamuraglia Michele , Bridal Lori 
Published: August 2019

Abstract
Background: Mathematical models have been developed to simulate tumor growth, as a goal to predict therapy response. We implemented three models and we investigated their agreement with tumor size assessed by ultrasound. We also investigated the link between microvascular flow parameters and future tumor size evolution.
Methods: Three ordinary differential equation tumor growth models were implemented in Matlab. The exponential-linear model (EL) assumes growth rate tends to linear after initial exponential growth as nutrient support becomes limited. The Gompertz model (G) describes demographic growth with a fixed carrying capacity because growth cannot exceed the capacity of the environment. The dynamic carrying capacity model (DCC) assumes this carrying capacity can change with time, for example, due to angiogenesis or necrosis formation. Experimental data were acquired in 11 control and 10 antiangiogenic (AA) treated mice with ectopic murine colorectal carcinoma (CT26) on Days 7, 9, 13, 15 and 21 after implantation (therapy started at day 7). Ellipsoidal volume (V) was estimated from B-mode measurements of the major transverse and longitudinal axes and used to estimate Relative Growth Rate (RGR): (t{n}) = [V(t_{n}-V(t_{n-1})]/[(t_{n}-t_{n-1}).V(t_{n-1})]. Contrast-Enhanced Ultrasound (CEUS) data were acquired along the longitudinal axis with Sequoia 512, 7-14 MHz probe. Regions with no contrast-enhancement were identified. Average contrast intensity vs. time curves in the perfused zone were fit to a lognormal model to estimate Area Under the Curve (AUC), Peak Enhancement (PE), Time to Peak (TTP), Mean Transit Time (MTT), Wash In Rate (WIR) and Wash Out Rate (WOR). The Akaike Information Criterion (AIC) was used to evaluate the relative quality of the models to describe the tumor size evolution. AIC penalizes models with more parameters to deal with the trade-off between goodness of fit and the model’s simplicity.
Results: Initial implementation of the models using a fixed (1 mm3) and free initial tumor size were compared. In this data set where earliest measured tumor size (day 4) varied from 15 to 39 mm3, the additional free parameter resulted in improved mean AIC (EL: 37 vs. 40 ; G: 37 vs. 41 ; DCC: 43 vs. 45 - free and fixed initial volume respectively). AIC was lowest on average for the G model in control mice. The TTP, WIR and WOR at t_n were linked with future RGR between t_n and t_{n+1} (RS = -0.51, 0.44 and -0.46 respectively for C (TTP and WIR) or AA (WOR) group, p&lt;0.01, non-parametric Spearman correlation coefficient).
Conclusions: The microvascular function includes additional information related to tumor growth. The integration of size and vascularization parameters into the mathematical models is the next step for predictive tumor growth. Such a model based on predictive quantitative ultrasound images has potential application in treatment follow-up.
Citation Format: Jerome Griffon, Zixin Yang, Delphine Le Guillou-Buffello, Alexandre Dizeux, Michele Lamuraglia, Lori Bridal. Volume and vascular evolution assessed with ultrasound in tumor growth: First steps for a future tool of predictive responses of treatment [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 1942.