Solid stress and tissue stiffness affect tumour growth, invasion, metastasis and treatment. Unlike stiffness, which can be precisely mapped in tumours, the measurement of solid stresses is challenging. Here, we show that two-dimensional spatial mappings of solid stress and the resulting elastic energy in excised or in situ tumours with arbitrary shapes and wide size ranges can be obtained via three distinct and quantitative techniques that rely on the measurement of tissue displacement after disruption of the confining structures. Application of these methods in models of primary tumours and metastasis revealed that: (i) solid stress depends on both cancer cells and their microenvironment; (ii) solid stress increases with tumour size; and (iii) mechanical confinement by the surrounding tissue significantly contributes to intratumoural solid stress. Further study of the genesis and consequences of solid stress, facilitated by the engineering principles presented here, may lead to significant discoveries and new therapies.

Delivery of blood-borne molecules and nanoparticles from the vasculature to cells in the tissue differs dramatically between tumor and normal tissues due to differences in their vascular architectures. Here we show that two simple measures of vascular geometry-δ max and λ-readily obtained from vascular images, capture these differences and link vascular structure to delivery in both tissue types. The longest time needed to bring materials to their destination scales with the square of δ max , the maximum distance in the tissue from the nearest blood vessel, whereas λ, a measure of the shape of the spaces between vessels, determines the rate of delivery for shorter times. Our results are useful for evaluating how new therapeutic agents that inhibit or stimulate vascular growth alter the functional efficiency of the vasculature and more broadly for analysis of diffusion in irregularly shaped domains.antiangiogenesis | cancer | fractal dimension | percolation | transport B lood vessels in tumors are highly irregular compared to those in normal tissues (Fig. 1). Unlike normal vessels, tumor vessels lack an orderly branching hierarchy from large vessels into successively smaller vessels that feed a regularly spaced capillary bed. Instead, tumor vessels are dilated, tortuous, and leaky and leave unperfused regions of many sizes (1, 2). Here we address the question of how such differences affect the delivery of bloodborne agents such as nutrients, drugs, and imaging tracersessentially how much material entering the arterial supply reaches a given location in the tissue and how long it takes to get there. Numerous studies of normal tissues have exploited the orderly branching patterns of the arterial network and the highly regular spacing of the capillary bed to devise powerful mathematical relationships linking the typical spacing between blood vessels to their ability to carry out their transport function (3-5). Unfortunately, analogous relationships in tumors have been more elusive due to their more chaotic vascular architectures that lack an obvious length scale, such as the intercapillary spacing, upon which a model can be built. Here we show that despite the differences between tumor and normal vasculature, simple scaling rules can be deduced that relate the number and spacing of blood vessels to the quantity of material transported from arterial supply to cell in a given time.Transport from a feeding artery to a cell in the tissue is a two-step process. First, materials flow near to their destination via blood vessels. Then they cover the remaining distance from the blood vessels to the cells via diffusion and convection. In the case of solid tumors, convection is negligible everywhere except at the tumor margins (6). The time required for diffusion over large distances is often much longer than that needed for flow, because diffusion times grow as the square of distance whereas flow times are proportional to distance. Under normal conditions, blood is distributed to the capillary bed through an orderly tree-like...

No abstract

Advances in immunotherapy have revolutionized the treatment of multiple cancers. Unfortunately, tumors usually have impaired blood perfusion, which limits the delivery of therapeutics and cytotoxic immune cells to tumors and also results in hypoxia-a hallmark of the abnormal tumor microenvironment (TME)-that causes immunosuppression. We proposed that normalization of TME using antiangiogenic drugs and/or mechanotherapeutics can overcome these challenges. Recently, immunotherapy with checkpoint blockers was shown to effectively induce vascular normalization in some types of cancer. Although these therapeutic approaches have been used in combination in preclinical and clinical studies, their combined effects on TME are not fully understood. To identify strategies for improved immunotherapy, we have developed a mathematical framework that incorporates complex interactions among various types of cancer cells, immune cells, stroma, angiogenic molecules, and the vasculature. Model predictions were compared with the data from five previously reported experimental studies. We found that low doses of antiangiogenic treatment improve immunotherapy when the two treatments are administered sequentially, but that high doses are less efficacious because of excessive vessel pruning and hypoxia. Stroma normalization can further increase the efficacy of immunotherapy, and the benefit is additive when combined with vascular normalization. We conclude that vessel functionality dictates the efficacy of immunotherapy, and thus increased tumor perfusion should be investigated as a predictive biomarker of response to immunotherapy.immunotherapy | vascular function | normalization | anti-angiogenic therapy | mechanotherapeutics

No abstract