Evaluation of breast cancer chemotherapy efficacy with multifractal spectrum analysis of magnetic resonance image.

Multifractal spectrum analysis of dynamic contrast enhanced (DCE) breast MR images was used to establish a new quantitative analysis method for solid tumor blood perfusion and to explore its applicability in evaluating efficacy of breast cancer chemotherapy. Five randomly selected patients suffering from newly diagnosed malignant breast nodule lesions were enrolled in this study, and four of them were treated with neoadjuvant chemotherapy. Their DCE breast MR images were collected before and after treatment. Chemotherapeutic efficacy was analyzed using international response evaluation criteria for solid tumors (RECIST). Sandbox method for statistical number density was employed to measure and calculate multifractal spectra of DCE breast MR images with spatiotemporal characteristics. Multifractal spectral data of malignant lesions before and after chemotherapy were compared. Multifractal spectra of malignant lesions show an asymmetric bell-shape. Chemotherapy efficacy was assessed to be partial remission (PR) for three patients and their multifractal spectral width significantly increased after chemotherapy while to be stable disease (SD) for other patient and of her changed slightly. Multifractal spectral width correlates with blood-supply condition of tumor lesion before and after chemotherapy, providing a potential suitable characteristic parameter for evaluating chemotherapeutic efficacy quantitatively.

Regulation of Turing patterns in a spatially extended chlorine-iodine-malonic-acid system with a local concentration-dependent diffusivity.

A chlorine-iodine-malonic-acid Turing system involving a local concentration-dependent diffusivity (LCDD) has fundamental significance for physical, chemical, and biological systems with inhomogeneous medium. We investigated such a system by both numerical computation and mathematical analysis. Our research reveals that a variable local diffusivity has an evident effect on regulating the Turing patterns for different modes. An intrinsic square-root law is given by λ ∼ (c(1)+c(2)k)(1/2), which relates the pattern wavelength (λ) with the LCDD coefficient (k). This law indicates that the system pattern has the properties of an equivalent Turing pattern. The current study confirms that, for the Turing system with LCDD, the system pattern form retains the basic characteristics of a traditional Turing pattern in a wide range of LCDD coefficients.