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Mathematics is often used to model biological systems. In mammary gland development, mathematical modeling has been limited to acinar and branching morphogenesis and breast cancer, without reference to normal duct formation. We present a model of ductal elongation that exploits the geometrically-constrained shape of the terminal end bud (TEB), the growing tip of the duct, and incorporates morphometrics, region-specific proliferation and apoptosis rates. Iterative model refinement and behavior analysis, compared with biological data, indicated that the traditional metric of nipple to the ductal front distance, or percent fat pad filled to evaluate ductal elongation rate can be misleading, as it disregards branching events that can reduce its magnitude. Further, model driven investigations of the fates of specific TEB cell types confirmed migration of cap cells into the body cell layer, but showed their subsequent preferential elimination by apoptosis, thus minimizing their contribution to the luminal lineage and the mature duct.

This book brings together new insight and research on mechanical, mathematical, physical, and biological approaches for simulating the behavior of cells, specifically tumor cells. It illustrates how phenomena occurring at various scales can be modeled and coupled to account for multiscale aspects. The text links subcellular effects to cellular properties, covers the modeling of cell migration and multicellular systems, and examines cell interactions with the environment, such as the rolling motion of leukocytes on a vessel wall and the forces exerted by cells on a rigid substrate.

Many studies stress the crucial importance of the mechanical component in angiogenesis, but still very few models really integrate mechanics. We propose to investigate the importance of mechanical cues for cell migration in this context with a new hybrid continuous-discrete model that describes the individual migration of contracting cells on an elastic matrix of fibres. The matrix is described as a continuum substrate whereas the cells are described as discrete elements.

Discovered at the beginning of the twentieth century, the Abri Casserole (Dordogne, France) was the subject of salvage excavations in the early nineties. The fieldwork revealed a sequence of 13 archaeological levels that document human occupations from the Gravettian to the Magdalenian, including very rare and poorly known assemblages (e.g. Early Badegoulian, Protosolutrean) that afford a particular importance to this sequence. Results of a previous dating program that focused on the Badegoulian levels were obtained in 1994 but were neither extensively published nor discussed. Five AMS 14C ages obtained for the Gravettian and Solutrean assemblages in the early 2010s served to complement the site’s chronology. However, since the beta counting ages for the Badegoulian levels were in conflict with the accepted AMS chronology for the region’s late Pleniglacial archaeological record, a new AMS dating program was implemented to renew the radiometric framework of this specific portion of the sequence. Compared to the previous beta counting measurements, the seven newly obtained AMS ages are about 1000 years older (23.3–20.5 cal ka BP) and congruent with other AMS-dated Badegoulian sequences. These results thereby restore the inter-site chronological coherence of the Solutrean–Badegoulian and Badegoulian–Magdalenian transitions.

Discovered at the beginning of the twentieth century, the Abri Casserole (Dordogne, France) was the subject of salvage excavations in the early nineties. The fieldwork revealed a sequence of 13 archaeological levels that document human occupations from the Gravettian to the Magdalenian, including very rare and poorly known assemblages (e.g. Early Badegoulian, Protosolutrean) that afford a particular importance to this sequence. Results of a previous dating program that focused on the Badegoulian levels were obtained in 1994 but were neither extensively published nor discussed. Five AMS 14 C ages obtained for the Gravettian and Solutrean assemblages in the early 2010s served to complement the site’s chronology. However, since the beta counting ages for the Badegoulian levels were in conflict with the accepted AMS chronology for the region’s late Pleniglacial archaeological record, a new AMS dating program was implemented to renew the radiometric framework of this specific portion of the sequence. Compared to the previous beta counting measurements, the seven newly obtained AMS ages are about 1000 years older (23.3–20.5 cal ka BP) and congruent with other AMS-dated Badegoulian sequences. These results thereby restore the inter-site chronological coherence of the Solutrean–Badegoulian and Badegoulian–Magdalenian transitions.