times stiffer than normal tissue. Furthermore, a growing and metastasizing tumor involves the cooperation of many different cell types, like fibroblasts and endothelial cells, that possess different rigidities and could result in local stiffness gradients that guide cell migration. There is increasing evidence that durotaxis plays a role in cancer metastasis. Experiments in mice have demonstrated that tumor cells preferentially invade into the adjacent stroma along stiff collagen fibers. These stiff collagen alignments can be used to identify focal sites of breast tumor cell microinvasion. Pregnancy, which has various links to breast cancer incidence and prognosis, involves postpartum breast involution that relies on collagen remodeling and inflammation that converts these collagen fibers into stiffer counterparts, thus establishing a potential link between pregnancy and metastatic properties. Though some research shows that stiffer tumors are indicative of increased metastasis and decreased survival (which contradicts the concept that durotactic cells should be more attracted to the tumor and metastasize less), this is not counter intuitive because collagen-dependent integrin signaling has a wide range of consequences beyond durotaxis, including inhibition of the tumor suppressor PTEN via upregulation of the miRNA miR-18a. Moreover, there is evidence that increased tumor stiffness does in fact correlate with decreased metastasis, as the principle of durotaxis would suggest. Liver Fibrosis Fibrosis of the liver is the accumulation of ECM proteins, such as collagen, that occurs in many chronic liver diseases. Increased liver stiffness (of existing collagen) has actually been shown to precede fibrosis and to be required for the activation of fibrogenic myofibroblasts. Fibroblasts move towards the stiffer tissue via durotaxis, and upon reaching it, will differentiate into fibrogenic myofibroblasts. This vicious positive feedback loop of durotaxis-dependent fibrosis could potentially be a therapeutic target for the prevention of liver fibrosis. Atherosclerosis The pathology of atherosclerosis is largely dependent on the migration of vascular smooth muscle cells (VSMCs) into the tunica intima layer of the blood vessel, where they can accumulate lipids, undergo necrosis, and elaborate the ECM (fibrosis). The migration of these cells has also been demonstrated to be rigidity-dependent, and matrix stiffness further affects their proliferation in response to growth factors. Mathematical models Several mathematical models have been used to describe durotaxis, including: One 2-dimensional model based on the Langevin equation, modified to include the local mechanical properties of the matrix. One model based on the description of durotaxis as an elastic stability phenomenon where the cytoskeleton is