The use of compressive sensing and peak detection in the reconstruction of microtubules length time series in the process of dynamic instability.

Microtubules (MTs) are intra-cellular cylindrical protein filaments. They exhibit a unique phenomenon of stochastic growth and shrinkage, called dynamic instability. In this paper, we introduce a theoretical framework for applying Compressive Sensing (CS) to the sampled data of the microtubule length in the process of dynamic instability. To reduce data density and reconstruct the original signal with relatively low sampling rates, we have applied CS to experimental MT lament length time series modeled as a Dichotomous Markov Noise (DMN). The results show that using CS along with the wavelet transform significantly reduces the recovery errors comparing in the absence of wavelet transform, especially in the low and the medium sampling rates. In a sampling rate ranging from 0.2 to 0.5, the Root-Mean-Squared Error (RMSE) decreases by approximately 3 times and between 0.5 and 1, RMSE is small. We also apply a peak detection technique to the wavelet coefficients to detect and closely approximate the growth and shrinkage of MTs for computing the essential dynamic instability parameters, i.e., transition frequencies and specially growth and shrinkage rates. The results show that using compressed sensing along with the peak detection technique and wavelet transform in sampling rates reduces the recovery errors for the parameters.

Pharmacokinetic Tumor Heterogeneity as a Prognostic Biomarker for Classifying Breast Cancer Recurrence Risk.

GOAL: Heterogeneity in cancer can affect response to therapy and patient prognosis. Histologic measures have classically been used to measure heterogeneity, although a reliable noninvasive measurement is needed both to establish baseline risk of recurrence and monitor response to treatment. Here, we propose using spatiotemporal wavelet kinetic features from dynamic contrast-enhanced magnetic resonance imaging to quantify intratumor heterogeneity in breast cancer. METHODS: Tumor pixels are first partitioned into homogeneous subregions using pharmacokinetic measures. Heterogeneity wavelet kinetic (HetWave) features are then extracted from these partitions to obtain spatiotemporal patterns of the wavelet coefficients and the contrast agent uptake. The HetWave features are evaluated in terms of their prognostic value using a logistic regression classifier with genetic algorithm wrapper-based feature selection to classify breast cancer recurrence risk as determined by a validated gene expression assay. RESULTS: Receiver operating characteristic analysis and area under the curve (AUC) are computed to assess classifier performance using leave-one-out cross validation. The HetWave features outperform other commonly used features (AUC = 0.88 HetWave versus 0.70 standard features). The combination of HetWave and standard features further increases classifier performance (AUCs 0.94). CONCLUSION: The rate of the spatial frequency pattern over the pharmacokinetic partitions can provide valuable prognostic information. SIGNIFICANCE: HetWave could be a powerful feature extraction approach for characterizing tumor heterogeneity, providing valuable prognostic information.

Heterogeneity wavelet kinetics from DCE-MRI for classifying gene expression based breast cancer recurrence risk.

Breast tumors are heterogeneous lesions. Intra-tumor heterogeneity presents a major challenge for cancer diagnosis and treatment. Few studies have worked on capturing tumor heterogeneity from imaging. Most studies to date consider aggregate measures for tumor characterization. In this work we capture tumor heterogeneity by partitioning tumor pixels into subregions and extracting heterogeneity wavelet kinetic (HetWave) features from breast dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) to obtain the spatiotemporal patterns of the wavelet coefficients and contrast agent uptake from each partition. Using a genetic algorithm for feature selection, and a logistic regression classifier with leave one-out cross validation, we tested our proposed HetWave features for the task of classifying breast cancer recurrence risk. The classifier based on our features gave an ROC AUC of 0.78, outperforming previously proposed kinetic, texture, and spatial enhancement variance features which give AUCs of 0.69, 0.64, and 0.65, respectively.