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Spatial mechanistic modeling for prediction of the growth of asymptomatic meningiomas
Computer Methods and Programs in Biomedicine ( IF 6.1 ) Pub Date : 2020-11-07 , DOI: 10.1016/j.cmpb.2020.105829
Annabelle Collin , Cédrick Copol , Vivien Pianet , Thierry Colin , Julien Engelhardt , Guy Kantor , Hugues Loiseau , Olivier Saut , Benjamin Taton

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.



中文翻译:

空间力学模型,用于预测无症状脑膜瘤的生长

背景与目的

肿瘤生长的数学模型吸引了医学界的兴趣,因为它们具有改善患者护理和公共卫生资源利用的潜力。这项工作的主要目的是为脑膜瘤的生长建模(缓慢生长的良性肿瘤,需要延长影像学随访时间),并仅使用两次检查即可在以后的期望时间预测肿瘤的大小和形状。

方法

我们开发了3D偏微分方程组(PDE)的两个变体,它们在将肿瘤体积与时间相关的普通微分方程(ODE)的空间积分系统之后产生。模型参数的估计是获得可用于描述或预测目的的患者个性化模型的关键步骤。由于PDE和ODE系统共享相同的参数,因此都可以通过将ODE系统与从在不同时间获取的MRI检查中获得的肿瘤体积拟合来进行估计。总体方法可以通过限制总体参数的可变性来补偿稀疏的采样时间和测量不确定性。

结果

该模型的描述能力在39例经过至少3次MRI监测检查的无症状良性脑膜瘤患者中进行了调查。与朴素的线性回归相比,这两个模型可以更准确,更实际地拟合数据。使用总体方法对33位患者的预测表现进行了验证。交易量预测中的平均相对误差小于10与ODE系统相比12.5与天真线性模型只使用两次检查。关于形状,平均Sørensen-Dice系数为85 在10名代表性患者的子集中使用PDE系统。

结论

我们的策略-基于数学模型的个性化-提供了有关脑膜瘤生长的良好见解,并可能有助于决定是否扩大随访范围或治疗肿瘤。

更新日期:2020-12-23
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