We simulated the invasion of a proliferating, diffusing tumor within different surrounding tissue conditions using a hybrid mathematical model. The in silico invasion of a tumor was addressed systematically for the first time within the framework of a generalized diffusion theory. Our results reveal that a tumor not only migrates using typical Fickian diffusion, but also migrates more generally using subdiffusion, superdiffusion, and even ballistic diffusion, with increasing mobility of the tumor cell when haptotaxis and chemotaxis toward the host tissue surrounding the proliferative tumor are involved. Five functional terms were included in the hybrid model and their effects on a tumor's invasion were investigated quantitatively: haptotaxis toward the extracellular matrix tissue that is degraded by matrix metalloproteinases; chemotaxis toward nutrients; cell-cell adhesion; the proliferation of the tumor; and the immune response toward the tumor. Haptotaxis and chemotaxis, which are initiated by extracellular matrix and nutrient supply (i.e., glucose) respectively, as well as cell-cell adhesions all drastically affect a tumor's diffusion mode when a tumor invades its surrounding host tissue and proliferates. We verified the in silico invasive behavior of a tumor by analyzing experimental data gathered from the in vitro culturing of different tumor cells and clinical imaging observations that used the same approach as was used to process the simulation data. The different migration modes of a tumor suggested by the simulations generally conform to the results observed in cell cultures and in clinical imaging. Our study not only discloses some migration modes of a tumor that proliferates and invades under different host tissues conditions, but also provides a heuristic method to characterize the invasion of a tumor in clinical medical imaging analysis.
BackgroundTransmitted drug resistance (TDR) is an important public health issue, because TDR-associated mutation may affect the outcome of antiretroviral treatment potentially or directly. Men who have sex with men (MSM) constitute a major risk group for HIV transmission. However, current reports are scarce on HIV TDR-associated mutations and their co-variation among MSM.MethodsBlood samples from 262 newly diagnosed HIV-positive, antiretroviral therapy (ART)-naïve MSM, were collected from January 2011 and December 2013 in Beijing. The polymerase viral genes were sequenced to explore TDR-associated mutations and mutation co-variation.ResultsA total of 223 samples were sequenced and analyzed. Among them, HIV-1 CRF01_AE are accounted for 60.5%, followed by CRF07_BC (27.8%), subtype B (9.9%), and others. Fifty-seven samples had at least one TDR-associated mutation, mainly including L10I/V (6.3%), A71L/T/V (6.3%), V179D/E (5.4%), and V106I (2.7%), with different distributions of TDR-associated mutations by different HIV-1 subtypes and by each year. Moreover, eight significant co-variation pairs were found between TDR-associated mutations (V179D/E) and seven overlapping polymorphisms in subtype CRF01_AE.ConclusionsTo date, this work consists the most comprehensive genetic characterization of HIV-1 TDR-associated mutations prevalent among MSM. It provides important information for understanding TDR and viral evolution among Chinese MSM, a population currently at particularly high risk of HIV transmission.Electronic supplementary materialThe online version of this article (doi:10.1186/s12879-014-0689-7) contains supplementary material, which is available to authorized users.
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