An existing lumped-parameter model of multiple lymphangions (lymphatic vascular segments) in series is adapted for the incorporation of recent physiological measurements of lymphatic vascular properties. The new data show very marked nonlinearity of the passive pressure-diameter relation during distension, relative to comparable blood vessels, and complex valve behaviour. Since lymph is transported as a result of either the active contraction or the passive squeezing of vascular segments situated between two one-way valves, the performance of these valves is of primary importance. The valves display hysteresis (the opening and closing pressure-drop thresholds differ), a bias to staying open (both state changes occur when the trans-valve pressure drop is adverse), and pressure-drop threshold dependence on transmural pressure. These properties, in combination with the strong nonlinearity that valve operation represents, have in turn caused intriguing numerical problems in the model, and we describe numerical stratagems by which we have overcome the problems. The principal problem is also generalised into a relatively simple mathematical example, for which solution detail is provided using two different solvers.

Disease-related phenotype modulation of many cell types has been shown to be closely related to mechanical loading conditions; for example, vascular smooth muscle cell (SMC) phenotype shift from a mature, contractile state to a proliferative, synthetic state contributes to the formation of neointimal tissue during atherosclerosis and restenosis development and is related to SMC mechanical loading in vivo. The majority of past in vitro cell-stretching experiments have employed simplistic (uniform, uniaxial or biaxial) stretching environments to elucidate mechanobiological pathways involved in phenotypic shifts. However, the in vivo mechanics of the vascular wall consists of highly nonuniform stretch. Here we subjected 10T1/2 murine mesenchymal cells (an SMC precursor) to two- and three-dimensional nonuniform stretch environments. After 24 h of stretch, cells on an elastomeric membrane demonstrated varied proliferation [assessed by 5-bromo-2'-deoxyuridine (BrdU) incorporation] depending on location upon the membrane, with maximal proliferation occurring in a region of high, uniaxial stretch. Cells subjected to a nonuniform stretching regimen within three-dimensional polyethylene glycol diacrylate (PEGDA) hydrogel constructs demonstrated marked changes in mRNA expression of several phenotype-related proteins, indicating a sort of "hybrid" phenotype with contractile and synthetic markers being both upregulated and downregulated. Furthermore, expression levels of mRNAs were significantly different between various locations within the stretched gel. With the proliferation results, these data exhibit the capability of nonuniform stretching devices to induce heterogeneous cell responses, potentially indicative of spatial distributions of disease-related behaviors in vivo.