Evaluation of four tumour growth models to describe the natural history of meningiomas.

BACKGROUND: The incidence of newly diagnosed meningiomas, particularly those diagnosed incidentally, is continually increasing. The indication for treatment is empirical because, despite numerous studies, the natural history of these tumours remains difficult to describe and predict. METHODS: This retrospective single-centre study included 294 consecutive patients with 333 meningiomas who underwent three or more brain imaging scans. Linear, exponential, power, and Gompertz models were constructed to derive volume-time curves, by using a mixed-effect approach. The most accurate model was used to analyse tumour growth and predictors of rapid growth. FINDINGS: The Gompertz model provided the best results. Hierarchical clustering at the time of diagnosis and at the end of follow-up revealed at least three distinct groups, which can be described as pseudoexponential, linear, and slowing growth with respect to their parameters. Younger patients and smaller tumours were more frequent in the pseudo-exponential clusters. We found that the more "aggressive" the cluster, the higher the proportion of patients with grade II meningiomas and who have had a cranial radiotherapy. Over a mean observation period of 56.5 months, 21% of the tumours moved to a cluster with a lower growth rate, consistent with the Gompertz's law. INTERPRETATION: Meningiomas exhibit multiple growth phases, as described by the Gompertz model. The management of meningiomas should be discussed according to the growth phase, comorbidities, tumour location, size, and growth rate. Further research is needed to evaluate the associations between radiomics features and the growth phases of meningiomas. FUNDING: No funding.

Phase-field model of bilipid membrane electroporation.

This paper proposes a new model of membrane electropermeabilisation that combines the water content of the membrane and the transmembrane voltage. Interestingly, thanks to a well defined free-energy of the membrane, we somehow generalise the seminal approach of Chizmadzhev, Weaver and Krassowska, getting rid of the geometrical cylindrical assumption upon which most of the current electroporation models are based. Our approach is physically relevant and we recover a surface diffusion equation of the lipid phase proposed by Leguèbe et al. in a previous phenomenological model. We also perform a fine analysis of the involved nonlocal operators in two simple configurations (a spherical membrane and a flat periodic membrane) that enables us to compare the time constants of the phenomenon in spherical and flat membranes. An accurate splitting scheme combined with Fast Fourier Transforms is developed for efficient computations of the model. Our numerical results enable us to make a link between the molecular dynamics simulations of membrane permeabilisation and the experimental observations on vesicles and cells.

Using a population-based Kalman estimator to model the COVID-19 epidemic in France: estimating associations between disease transmission and non-pharmaceutical interventions.

In response to the COVID-19 pandemic caused by SARS-CoV-2, governments have adopted a wide range of non-pharmaceutical interventions (NPI). These include stringent measures such as strict lockdowns, closing schools, bars and restaurants, curfews, and barrier gestures such as mask-wearing and social distancing. Deciphering the effectiveness of each NPI is critical to responding to future waves and outbreaks. To this end, we first develop a dynamic model of the French COVID-19 epidemics over a one-year period. We rely on a global extended Susceptible-Infectious-Recovered (SIR) mechanistic model of infection that includes a dynamic transmission rate over time. Multilevel data across French regions are integrated using random effects on the parameters of the mechanistic model, boosting statistical power by multiplying integrated observation series. We estimate the parameters using a new population-based statistical approach based on a Kalman filter, used for the first time in analysing real-world data. We then fit the estimated time-varying transmission rate using a regression model that depends on the NPIs while accounting for vaccination coverage, the occurrence of variants of concern (VoC), and seasonal weather conditions. We show that all NPIs considered have an independent significant association with transmission rates. In addition, we show a strong association between weather conditions that reduces transmission in summer, and we also estimate increased transmissibility of VoC.

A Model-Strengthened Imaging Biomarker for Survival Prediction in EGFR-Mutated Non-small-cell Lung Carcinoma Patients Treated with Tyrosine Kinase Inhibitors.

Non-small-cell lung carcinoma is a frequent type of lung cancer with a bad prognosis. Depending on the stage and genomics, several therapeutical approaches are used. Tyrosine Kinase Inhibitors (TKI) may be successful for a time in the treatment of EGFR-mutated non-small cells lung carcinoma. Our objective is here to introduce a survival assessment as their efficacy in the long run is challenging to evaluate. The study includes 17 patients diagnosed with EGFR-mutated non-small cell lung cancer and exposed to an EGFR-targeting TKI with 3 computed tomography (CT) scans of the primary tumor (one before the TKI introduction and two after). An imaging biomarker based on evolution of texture heterogeneity between the first and the third exams is derived and computed from a mathematical model and patient data. Defining the overall survival as the time between the introduction of the TKI treatment and the patient death, we obtain a statistically significant correlation between the overall survival and our imaging marker ([Formula: see text]). Using the ROC curve, the patients are separated into two populations and the comparison of the survival curves is statistically significant ([Formula: see text]). The baseline exam seems to have a significant role in the prediction of response to TKI treatment. More precisely, our imaging biomarker defined using only the CT scan before the TKI introduction allows to determine a first classification of the population which is improved over time using the imaging marker as soon as more CT scans are available. This exploratory study leads us to think that it is possible to obtain a survival assessment using only few CT scans of the primary tumor.

Spatial mechanistic modeling for prediction of the growth of asymptomatic meningiomas.

BACKGROUND AND OBJECTIVE: Mathematical modeling of tumor growth draws interest from the medical community as they have the potential to improve patients' care and the use of public health resources. The main objectives of this work are to model the growth of meningiomas - slow-growing benign tumors requiring extended imaging follow-up - and to predict tumor volume and shape at a later desired time using only two times examinations. METHODS: We develop two variants of a 3D partial differential system of equations (PDE) which yield after a spatial integration systems of ordinary differential equations (ODE) that relate tumor volume with time. Estimation of models parameters is a crucial step to obtain a personalized model for a patient that can be used for descriptive or predictive purposes. As PDE and ODE systems share the same parameters, they are both estimated by fitting the ODE systems to the tumor volumes obtained from MRI examinations acquired at different times. A population approach allows to compensate for sparse sampling times and measurement uncertainties by constraining the variability of the parameters in the population. RESULTS: Description capabilities of the models are investigated in 39 patients with benign asymptomatic meningiomas who had had at least three surveillance MRI examinations. The two models can fit to the data accurately and more realistically than a naive linear regression. Prediction performances are validated for 33 patients using a population approach. Mean relative errors in volume predictions are less than 10% with ODE systems versus 12.5% with the naive linear model using only two times examinations. Concerning the shape, the mean Sørensen-Dice coefficients are 85% with the PDE systems in a subset of 10 representative patients. CONCLUSIONS: Our strategy - based on personalization of mathematical model - provides a good insight on meningioma growth and may help decide whether to extend the follow-up or to treat the tumor.

Numerical simulation of electrocardiograms for full cardiac cycles in healthy and pathological conditions.

This work is dedicated to the simulation of full cycles of the electrical activity of the heart and the corresponding body surface potential. The model is based on a realistic torso and heart anatomy, including ventricles and atria. One of the specificities of our approach is to model the atria as a surface, which is the kind of data typically provided by medical imaging for thin volumes. The bidomain equations are considered in their usual formulation in the ventricles, and in a surface formulation on the atria. Two ionic models are used: the Courtemanche-Ramirez-Nattel model on the atria and the 'minimal model for human ventricular action potentials' by Bueno-Orovio, Cherry, and Fenton in the ventricles. The heart is weakly coupled to the torso by a Robin boundary condition based on a resistor-capacitor transmission condition. Various electrocardiograms (ECGs) are simulated in healthy and pathological conditions (left and right bundle branch blocks, Bachmann's bundle block, and Wolff-Parkinson-White syndrome). To assess the numerical ECGs, we use several qualitative and quantitative criteria found in the medical literature. Our simulator can also be used to generate the signals measured by a vest of electrodes. This capability is illustrated at the end of the article. Copyright © 2015 John Wiley & Sons, Ltd.