Dynamic mode decomposition (DMD) represents an effective means for capturing the essential features of numerically or experimentally generated flow fields. In order to achieve a desirable tradeoff between the quality of approximation and the number of modes that are used to approximate the given fields, we develop a sparsity-promoting variant of the standard DMD algorithm. In our method, sparsity is induced by regularizing the least-squares deviation between the matrix of snapshots and the linear combination of DMD modes with an additional term that penalizes the 1-norm of the vector of DMD amplitudes. The globally optimal solution of the resulting regularized convex optimization problem is computed using the alternating direction method of multipliers, an algorithm well-suited for large problems. Several examples of flow fields resulting from numerical simulations and physical experiments are used to illustrate the effectiveness of the developed method. *

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No chemotherapeutic drug can be effective until it is delivered to its target site. Nano-sized drug carriers are designed to transport therapeutic or diagnostic materials from the point of administration to the drug’s site of action. This task requires the nanoparticle carrying the drug to complete a journey from the injection site to the site of action. The journey begins with the injection of the drug carrier into the bloodstream and continues through stages of circulation, extravasation, accumulation, distribution, endocytosis, endosomal escape, intracellular localization and—finally—action. Effective nanoparticle design should consider all of these stages to maximize drug delivery to the entire tumor and effectiveness of the treatment.

Enhanced permeability in tumours is thought to result from malformed vascular walls with leaky cell-to-cell junctions. This assertion is backed by studies using electron microscopy and polymer casts that show incomplete pericyte coverage of tumour vessels and the presence of intercellular gaps. However, this gives the impression that tumour permeability is static amid a chaotic tumour environment. Using intravital confocal laser scanning microscopy we show that the permeability of tumour blood vessels includes a dynamic phenomenon characterized by vascular bursts followed by brief vigorous outward flow of fluid (named 'eruptions') into the tumour interstitial space. We propose that 'dynamic vents' form transient openings and closings at these leaky blood vessels. These stochastic eruptions may explain the enhanced extravasation of nanoparticles from the tumour blood vessels, and offer insights into the underlying distribution patterns of an administered drug.

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