Tumor growth curves are classically modeled by means of ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two parameters of the model, which could be used to reduce the dimensionality and improve predictive power. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (population approach). This allowed the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 833 measurements in 94 animals. Candidate models of tumor growth included the exponential, logistic and Gompertz models. The exponential and-more notably-logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The previously reported populationlevel correlation between the Gompertz parameters was further confirmed in our analysis (R 2 > 0.92 in all groups). Combining this structural correlation with rigorous population parameter estimation, we propose a reduced Gompertz function consisting of a single individual parameter (and one population parameter). Leveraging the population approach using Bayesian inference, we estimated times of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using Bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy (prediction error) was 12.2% versus 78% and mean precision (width of the 95% prediction interval) was 15.6 days versus 210 days, for the breast cancer cell line. These results demonstrate the superior predictive power of the reduced Gompertz model, especially when combined with Bayesian estimation. They offer possible clinical perspectives for personalized prediction of

Understanding the dynamics underlying fluid transport in tumour tissues is of fundamental importance to assess processes of drug delivery. Here, we analyse the impact of the tumour microscopic properties on the macroscopic dynamics of vascular and interstitial fluid flow. More precisely, we investigate the impact of the capillary wall permeability and the hydraulic conductivity of the interstitium on the macroscopic model arising from formal asymptotic 2-scale techniques.The homogenization technique allows us to derive two macroscale tissue models of fluid flow that take into account the microscopic structure of the vessels and the interstitial tissue. Different regimes were derived according to the magnitude of the vessel wall permeability and the interstitial hydraulic conductivity. Importantly, we provide an analysis of the properties of the models and show the link between them. Numerical simulations were eventually performed to test the models and to investigate the impact of the microstructure on the fluid transport.Future applications of our models include their calibration with real imaging data to investigate the impact of the tumour microenvironment on drug delivery.

Tumor growth curves are classically modeled by ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two parameters of the model.We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (population approach). This allowed for the simultaneous modeling of tumor dynamics and interanimal variability. Experimental data comprised three animal models of breast and lung cancers, with 843 measurements in 94 animals. Candidate models of tumor growth included the Exponential, Logistic and Gompertz. The Exponential and -more notably -Logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The population-level correlation between the Gompertz parameters was further confirmed in our analysis (R 2 > 0.96 in all groups). Combining this structural correlation with rigorous population parameter estimation, we propose a novel reduced Gompertz function consisting of a single individual parameter. Leveraging the population approach using bayesian inference, we estimated the time of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy was 12.1% versus 74.1% and mean precision was 15.2 days versus 186 days, for the breast cancer cell line.These results offer promising clinical perspectives for the personalized prediction of tumor age from limited data at diagnosis. In turn, such predictions could be helpful for assessing the extent of invisible metastasis at the time of diagnosis. Author summaryMathematical models for tumor growth kinetics have been widely used since several decades but mostly fitted to individual or average growth curves. Here we compared three classical models (Exponential, Logistic and Gompertz) using a population approach, which accounts for inter-animal variability. The Exponential and the Logistic models failed to fit the experimental data while the Gompertz model showed excellent descriptive power. Moreover, the strong correlation between the two parameters of the Gompertz equation motivated a simplification of the model, the reduced Gompertz model, with a single individual parameter and equal descriptive power. Combining the mixed-effects approach with Bayesian inference, we predicted the age of individual tumors with only few late measurements. Thanks to its simplicity, the reduced Gompertz model showed superior predictive power. Although our method remains to be extended to clinical data, these results are promising for the personalized estimation of the age of a tumor from limited measurements at diagnosis. Such predictions could contribute to the development of computational models for metastasis.

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.

Quantitative analysis of tumor growth kinetics has been widely carried out using mathematical models. In the majority of cases, individual or average data were fitted. Here, we analyzed three classical models (exponential, logistic and Gompertz within the statistical framework of nonlinear mixed-effects modelling, which allowed us to account for inter-animal variability within a population group. We used in vivo data of subcutaneously implanted Lewis Lung carcinoma cells. While the exponential and logistic models failed to accurately fit the data, the Gompertz model provided a superior descriptive power. Moreover, we observed a strong correlation between the Gompertz parameters. Combining this observation with rigorous population parameter estimation motivated a simplification of the standard Gompertz model in a reduced Gompertz model, with only one individual parameter. Using Bayesian inference, we further applied the population methodology to predict the individual initiation times of the tumors from only three measurements. Thanks to its simplicity, the reduced Gompertz model exhibited superior predictive power. The method that we propose here remains to be extended to clinical data, but these results are promising for the personalized estimation of the tumor age given limited data at diagnosis.

Combinatorial regimen are a mainstay in oncology. Taxanes and trastuzumab are both gold standards for HER2 positive breast cancer. To what extent they could reshape tumor micro-environment remains to be elucidated. The aim of this study was to compare in breast cancer mice models the antiproliferative efficacy and impact on tumor neo-angiogenesis of trastuzumab stealth immunoliposomes encapsulating docetaxel and stealth liposomal docetaxel associated with free trastuzumab. Nude mice bearing human MDA-MB-231 breast cancer tumors were treated by saline (control), docetaxel liposome (5mg/kg) associated with free trastuzumab (1.9 mg/kg) or trastuzumab immunoliposome (eq. 5 mg/kg docetaxel and 1.9 mg/kg trastuzumab) QW for 4 consecutive weeks. Tumor growth was monitored twice a week by volumetric measurement using a caliper. Blodd vessels density was evaluated in vivo by fluorescence imaging using Angiosense as a vascular probe plus ex-vivo using anti-CD31 antibodies and electronic microscopy at 2, 4 and 6 weeks. A specific algorithm was developed on MatLab for imaging analysis. No treatment-induced toxicities was observed. After 4 weeks of dosing, no difference in efficacy was seen between treatments (p=0.798) and Angiosense imaging did not show differences either (p=0.628). However electronic microscopy showed that both immunoliposomes and liposomes increased tumor vascular density as compared with control. In addition, a difference between treatments was evidenced because a marked increase in vascularization of central tumors VS. peripheral tumors was observed with trastuzumab immunoliposome as compared with standard docetaxel liposome (p=0.00023). A numerical model based on porous medium theory combined with multi-scale approaches has been derived to describe the spatial distribution of the drugs within tissues. Overall our data suggest that trastuzumab stealth immunoliposomes induce a normalization of tumor vessels with an increase in blood vessels density in central tumors. This could pave the way for sequencing combinatorial strategies so as to improve drug delivery into tumors of the associated treatments. Citation Format: Guillaume Sicard, Anne Rodallec, Florian Correard, Cristina Vaghi, Clair Poignard, Joseph Ciccolini, Sébastien Benzekry, Arnauld Sergé, Raphaelle Fanciullino. Turning poorly vascularized tumors into highly vascularized tumors with nanoparticles: Proof of concept and pharmacometric analysis [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 6244.

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We propose in this article a model describing the dynamic of a system of adipocytes, structured by their sizes. This model takes into account the differentiation of a population of mesenchymal cells into preadipocytes and of preadipocytes into adipocytes; the differentiation rates depend on the mean adipocyte radius. The considered equations are therefore ordinary differential equations, coupled with an advection equation, the growth rate of which depends on food availability and on the total surface of adipocytes. Since this velocity is discontinuous, we need to introduce a convenient notion of solutions coming from Filippov theory. We are consequently able to determine the stationary solutions of the system, to prove the existence and uniqueness of solutions and to describe the asymptotic behavior of solutions in some simple cases. Finally, the parameters of the model are fitted thanks to some experimental data and numerical simulations are displayed; a spatial extension of the model is studied numerically.