Stress relaxation behavior of tessellated cartilage from the jaws of blue sharks

AbstractMuch of the skeleton of sharks, skate and rays (Elasmobranchii) is characterized by a tessellated structure, composed of a shell of small, mineralized plates (tesserae) joined by intertesseral ligaments overlaying a soft cartilage core. Although tessellated cartilage is a defining feature of this group of fishes, the significance of this skeletal tissue type – particularly from a mechanical perspective – is unknown. The aim of the present work was to perform stress relaxation experiments with tessellated cartilage samples from the jaws of blue sharks to better understand the time dependent behavior of this skeletal type.In order to facilitate this aim, the resulting relaxation behavior for different loading directions were simulated using the transversely isotropic biphasic model and this model combined with generalized Maxwell elements to represent the tessellated layer. Analysis of the ability of the models to simulate the observed experimental behavior indicates that the transversely isotropic biphasic model can provide good predictions of the relaxation behavior of the hyaline cartilage. However, the incorporation of Maxwell elements into this model can achieve a more accurate simulation of the dynamic behavior of calcified cartilage when the loading is parallel to the tessellated layer. Correlation of experimental data with present combined composite models showed that the equilibrium modulus of the tessellated layer for this loading direction is about 45 times greater than that for uncalcified cartilage. Moreover, tessellation has relatively little effect on the viscoelasticity of shark cartilage under loading that is normal to the tessellated layer

Multispecies model of cell lineages and feedback control in solid tumors.

We develop a multispecies continuum model to simulate the spatiotemporal dynamics of cell lineages in solid tumors. The model accounts for protein signaling factors produced by cells in lineages, and nutrients supplied by the microenvironment. Together, these regulate the rates of proliferation, self-renewal and differentiation of cells within the lineages, and control cell population sizes and distributions. Terminally differentiated cells release proteins (e.g., from the TGFβ superfamily) that feedback upon less differentiated cells in the lineage both to promote differentiation and decrease rates of proliferation (and self-renewal). Stem cells release a short-range factor that promotes self-renewal (e.g., representative of Wnt signaling factors), as well as a long-range inhibitor of this factor (e.g., representative of Wnt inhibitors such as Dkk and SFRPs). We find that the progression of the tumors and their response to treatment is controlled by the spatiotemporal dynamics of the signaling processes. The model predicts the development of spatiotemporal heterogeneous distributions of the feedback factors (Wnt, Dkk and TGFβ) and tumor cell populations with clusters of stem cells appearing at the tumor boundary, consistent with recent experiments. The nonlinear coupling between the heterogeneous expressions of growth factors and the heterogeneous distributions of cell populations at different lineage stages tends to create asymmetry in tumor shape that may sufficiently alter otherwise homeostatic feedback so as to favor escape from growth control. This occurs in a setting of invasive fingering, and enhanced aggressiveness after standard therapeutic interventions. We find, however, that combination therapy involving differentiation promoters and radiotherapy is very effective in eradicating such a tumor

Multispecies model of cell lineages and feedback control in solid tumors.

We develop a multispecies continuum model to simulate the spatiotemporal dynamics of cell lineages in solid tumors. The model accounts for protein signaling factors produced by cells in lineages, and nutrients supplied by the microenvironment. Together, these regulate the rates of proliferation, self-renewal and differentiation of cells within the lineages, and control cell population sizes and distributions. Terminally differentiated cells release proteins (e.g., from the TGFβ superfamily) that feedback upon less differentiated cells in the lineage both to promote differentiation and decrease rates of proliferation (and self-renewal). Stem cells release a short-range factor that promotes self-renewal (e.g., representative of Wnt signaling factors), as well as a long-range inhibitor of this factor (e.g., representative of Wnt inhibitors such as Dkk and SFRPs). We find that the progression of the tumors and their response to treatment is controlled by the spatiotemporal dynamics of the signaling processes. The model predicts the development of spatiotemporal heterogeneous distributions of the feedback factors (Wnt, Dkk and TGFβ) and tumor cell populations with clusters of stem cells appearing at the tumor boundary, consistent with recent experiments. The nonlinear coupling between the heterogeneous expressions of growth factors and the heterogeneous distributions of cell populations at different lineage stages tends to create asymmetry in tumor shape that may sufficiently alter otherwise homeostatic feedback so as to favor escape from growth control. This occurs in a setting of invasive fingering, and enhanced aggressiveness after standard therapeutic interventions. We find, however, that combination therapy involving differentiation promoters and radiotherapy is very effective in eradicating such a tumor

A Multicompartment Mathematical Model of Cancer Stem Cell-Driven Tumor Growth Dynamics

Tumors are appreciated to be an intrinsically heterogeneous population of cells with varying proliferation capacities and tumorigenic potentials. As a central tenet of the so-called cancer stem cell hypothesis, most cancer cells have only a limited lifespan and thus cannot initiate or re-initiate tumors. Longevity and clonogenicity are properties unique to the subpopulation of cancer stem cells. To understand the implications of the population structure suggested by this hypothesis - a hierarchy consisting of cancer stem cells and progeny non-stem cancer cells which experience a reduction in their remaining proliferation capacity per division - we set out to develop a mathematical model for the development of the aggregate population. We show that overall tumor progression rate during the exponential growth phase is identical to the growth rate of the cancer stem cell compartment. Tumors with identical stem cell proportions, however, can have different growth rates, dependent on the proliferation kinetics of all participating cell populations. Analysis of the model revealed that the proliferation potential of non-stem cancer cells is likely to be small to reproduce biologic observations. Furthermore, a single compartment of non-stem cancer cell population may adequately represent population growth dynamics only when the compartment proliferation rate is scaled with the generational hierarchy depth