Relative Quality of Tumor Growth Equations Describing Volume and Vascular Evolution Assessed with Ultrasound (original) (raw)

2018 IEEE International Ultrasonics Symposium (IUS), 2018

Abstract

Three ordinary differential equation models were implemented in Matlab to describe tumor growth: the exponential-linear model (EL), the Gompertz model (G) and the dynamic carrying capacity model (DCC). For 11 control (C) and 10 antiangiogenic (AA)-treated mice with ectopic murine colorectal carcinoma (CT26), ultrasonic data were acquired on days 7, 9, 13, 15 and 21 after implantation (therapy started at day 7). The ellipsoidal volume V was estimated from B-mode measurements and used to estimate Relative Growth Rate. Dynamic Contrast-Enhanced Ultrasound data were acquired and regions with no contrast-enhancement were identified to estimate % perfused area (%P). Average contrast intensity vs. time curves in the P zone were fit to a lognormal model. Initial implementation of the models using a fixed (1 mm3) were compared to models adapted for a variable initial tumor size using the Akaike Information Criterion (AIC). 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 C mice. The Time To Peak (TTP), Wish In and Wash Out Rate (WIR, WOR) at mathbftmathbfn\mathbf{t}_{\mathbf{n}}mathbftmathbfn were linked with future RGR between mathbftmathbfn\mathbf{t}_{\mathbf{n}}mathbftmathbfn and mathbftmathbfn+1\mathbf{t}_{\mathbf{n}+1}mathbftmathbfn+1 (RS = −0.51, 0.44 and −0.46 respectively for C (TTP and WIR) or AA (WOR) group, p<0.01, non-parametric Spearman correlation coefficient). This implies that the microvascular function includes additional information related to tumor growth.

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