Purpose: The aim of this study was to assess the potential of machine learning with multiparametric magnetic resonance imaging (mpMRI) for the early prediction of pathological complete response (pCR) to neoadjuvant chemotherapy (NAC) and of survival outcomes in breast cancer patients. Materials and Methods: This institutional review board–approved prospective study included 38 women (median age, 46.5 years; range, 25–70 years) with breast cancer who were scheduled for NAC and underwent mpMRI of the breast at 3 T with dynamic contrast-enhanced (DCE), diffusion-weighted imaging (DWI), and T2-weighted imaging before and after 2 cycles of NAC. For each lesion, 23 features were extracted: qualitative T2-weighted and DCE-MRI features according to BI-RADS (Breast Imaging Reporting and Data System), quantitative pharmacokinetic DCE features (mean plasma flow, volume distribution, mean transit time), and DWI apparent diffusion coefficient (ADC) values. To apply machine learning to mpMRI, 8 classifiers including linear support vector machine, linear discriminant analysis, logistic regression, random forests, stochastic gradient descent, decision tree, adaptive boosting, and extreme gradient boosting (XGBoost) were used to rank the features. Histopathologic residual cancer burden (RCB) class (with RCB 0 being a pCR), recurrence-free survival (RFS), and disease-specific survival (DSS) were used as the standards of reference. Classification accuracy with area under the receiving operating characteristic curve (AUC) was assessed using all the extracted qualitative and quantitative features for pCR as defined by RCB class, RFS, and DSS using recursive feature elimination. To overcome overfitting, 4-fold cross-validation was used. Results: Machine learning with mpMRI achieved stable performance as shown by mean classification accuracies for the prediction of RCB class (AUC, 0.86) and DSS (AUC, 0.92) based on XGBoost and the prediction of RFS (AUC, 0.83) with logistic regression. The XGBoost classifier achieved the most stable performance with high accuracies compared with other classifiers. The most relevant features for the prediction of RCB class were as follows: changes in lesion size, complete pattern of shrinkage, and mean transit time on DCE-MRI; minimum ADC on DWI; and peritumoral edema on T2-weighted imaging. The most relevant features for prediction of RFS were as follows: volume distribution, mean plasma flow, and mean transit time; DCE-MRI lesion size; minimum, maximum, and mean ADC with DWI. The most relevant features for prediction of DSS were as follows: lesion size, volume distribution, and mean plasma flow on DCE-MRI, and maximum ADC with DWI. Conclusions: Machine learning with mpMRI of the breast enables early prediction of pCR to NAC as well as survival outcomes in breast cancer patients with high accuracy and thus may provide valuable predictive information to guide treatment decisions.

The dynamics of complex neural networks must include the aspects of long- and short-term memory. The behavior of the network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. The main idea of this paper is to apply a stability analysis method of fixed points of the combined activity and weight dynamics for a special class of competitive neural networks. We present a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables as a global stability method and a modality of detecting the local stability behavior around individual equilibrium points.

The dynamics of cortical cognitive maps developed by self-organization must include the aspects of long and short-term memory. The behavior of such a neural network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. We present a new method of analyzing the dynamics of a biological relevant system with different time scales based on the theory of flow invariance. We are able to show the conditions under which the solutions of such a system are bounded being less restrictive than with the K-monotone theory, singular perturbation theory, or those based on supervised synaptic learning. We prove the existence and the uniqueness of the equilibrium. A strict Lyapunov function for the flow of a competitive neural system with different time scales is given and based on it we are able to prove the global exponential stability of the equilibrium point.