Tumor growth monitoring in breast cancer xenografts: A good technique for a strong ethic

Abstract

Purpose: Although recent regulations improved conditions of laboratory animals, their use remains essential in cancer research to determine treatment efficacy. In most cases, such experiments are performed on xenografted animals for which tumor volume is mostly estimated from caliper measurements. However, many formulas have been employed for this estimation and no standardization is available yet.

Methods: Using previous animal studies, we compared all formulas used by the scientific community in 2019. Data were collected from 93 mice orthotopically xenografted with human breast cancer cells. All formulas were evaluated and ranked based on correlation and lower mean relative error. They were then used in a Gompertz quantitative model of tumor growth.

Results: Seven formulas for tumor volume estimation were identified and a statistically significant difference was observed among them (ANOVA test, p < 2.10-16), with the ellipsoid formula (1/6 π × L × W × (L + W)/2) being the most accurate (mean relative error = 0.272 ± 0.201). This was confirmed by the mathematical modeling analysis where this formula resulted in the smallest estimated residual variability. Interestingly, such result was no longer valid for tumors over 1968 ± 425 mg, for which a cubic formula (L x W x H) should be preferred.

Main findings: When considering that tumor volume remains under 1500mm3, to limit animal stress, improve tumor growth monitoring and go toward mathematic models, the following formula 1/6 π × L × W x (L + W)/2 should be preferred.

Fig 1. Representation of all techniques used in 2019 for tumor growth monitoring on human breast cancer xenografts bearing mice (n = 233).

The bibliographic search was conducted in the PubMed database from January 1^st, 2019 to December 31^st, 2019, using the followings terms in Text Word: Xenograft, breast cancer, tumor growth AND mice. *MR DWI = Diffusion-weighted magnetic resonance; PET CT = positron emission tomography computing tomography; Unknown = information not accessible.

Fig 2

(A) Correlation graphics between real tumor volume (i.e., tumor mass) and estimated tumor volume with Formula 1 (F1), Formula 2 (F2) Formula 3 (F3), Formula 4 (F4), Formula 5 (F5), Formula 6 (F6) or Formula 7 (F7) (n = 83). Dotted line is a representation of y = x and the black dots are our observed data (n = 83). (B) Bar plot of Mean relative error ± SD for all tested volume estimation formulas: F1, F2, F3, F4, F5, F6 and F7 (C) Absolute error sorted by real tumor volume for F1, F2, F3, F4, F5, F6 and F7 (n = 83) (D) Relative error sorted by real tumor volume for F1, F2, F3, F4, F5, F6 and F7 (n = 83). ***: p = 2.10–16 SD = standard deviation.

Fig 3

Correlation graphics between real tumor volume (i.e., tumor mass) and estimated tumor volume with F1, F2, F3, F4, F5, F6 or F7 for the small tumor size population (A) and for the large tumor size population (B). Dotted line is a representation of y = x and the black dots are our observed data (n = 41). Bar plot of Mean relative error ± SD for all tested volume estimation formulas: F1, F2, F3, F4, F5, F6 or F7 for the small tumor size population (C) and for the large tumor size population (D) (n = 41). *SD = standard deviation *** = p < 0.001.

Fig 4. Population analysis of the Gompertz model fitted against data obtained with formula 2.

(A) Prediction distribution of the Gompertz model fitted against the data. P.I. = prediction interval. (B) Observations vs individual predictions (C) Three representative examples of individual fits chosen randomly.

Fig 5. Radar chart displaying volume estimation data for Formula 1 (F1), Formula 2 (F2) Formula 3 (F3), Formula 4 (F4), Formula 5 (F5), Formula 6 (F6) and Formula 7 (F7).

The larger the area, the better the prediction. All raw data used to make this chart are available in supplementary tables (S4 Table). *MRE = mean relative error, MAE = mean absolute error, r² = correlation coefficient of regression line, a = slope of regression line.