Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis.

Head and neck squamous cell carcinoma (HNSCC) patients have a poor prognosis, with invasion and metastasis as major causes of mortality. The phosphatidylinositol 3-kinase (PI3K) pathway regulates a wide range of cellular processes crucial for tumorigenesis, and PIK3CA amplification and mutation are among the most common genetic alterations in human HNSCC. Compared with the well-documented roles of the PI3K pathway in cell growth and survival, the roles of the PI3K pathway in tumor invasion and metastasis have not been well delineated. We generated a PIK3CA genetically engineered mouse model (PIK3CA-GEMM) in which wild-type PIK3CA is overexpressed in head and neck epithelium. Although PIK3CA overexpression alone was not sufficient to initiate HNSCC formation, it significantly increased tumor susceptibility in an oral carcinogenesis mouse model. PIK3CA overexpression in mouse oral epithelium increased tumor invasiveness and metastasis by increasing epithelial-mesenchymal transition and by enriching a cancer stem cell phenotype in tumor epithelial cells. In addition to these epithelial alterations, we also observed marked inflammation in tumor stroma. AKT is a central signaling mediator of the PI3K pathway. However, molecular analysis suggested that progression of PIK3CA-driven HNSCC is facilitated by 3-phosphoinositide-dependent protein kinase (PDK1) and enhanced transforming growth factor β (TGFβ) signaling rather than by AKT. Examination of human HNSCC clinical samples revealed that both PIK3CA and PDK1 protein levels correlated with tumor progression, highlighting the significance of this pathway. In summary, our results offer significant insight into how PIK3CA overexpression drives HNSCC invasion and metastasis, providing a rationale for targeting PI3K/PDK1 and TGFβ signaling in advanced HNSCC patients with PIK3CA amplification.

We report the measurement of Gamma and Gamma bar yields and inverse slope parameters in d+Au collisions at sqrt sNN = 200 GeV at forward and backward rapidities (y = +-2.75), using data from the STAR forward time projection chambers. The contributions of different processes to baryon transport and particle production are probed exploiting the inherent asymmetry of the d+Au system. Comparisons to model calculations show that baryon transport on the deuteron side is consistent with multiple collisions of the deuteron nucleons with gold participants. On the gold side, HIJING-based models without a hadronic rescattering phase do not describe themeasured particle yields, while models that include target remnants or hadronic rescattering do. The multichain model can provide a good description of the net baryon density in d+Au collisions at energies currently available at the BNL Relativistic Heavy Ion Collider, and the derived parameters of the model agree with those from nuclear collisions at lower energies.

We present the first measurements of the ρ(770)0,K*(892), Δ(1232)++,Σ(1385), and Λ(1520) resonances in d+Au collisions at sNN=200 GeV, reconstructed via their hadronic decay channels using the STAR detector (the solenoidal tracker at the BNL Relativistic Heavy Ion Collider). The masses and widths of these resonances are studied as a function of transverse momentum pT. We observe that the resonance spectra follow a generalized scaling law with the transverse mass mT. The pT of resonances in minimum bias collisions are compared with the pT of π,K, and p̄. The ρ0/π-,K*/K-,Δ++/p,Σ(1385)/Λ, and Λ(1520)/Λ ratios in d+Au collisions are compared with the measurements in minimum bias p+p interactions, where we observe that both measurements are comparable. The nuclear modification factors (RdAu) of the ρ0,K*, and Σ* scale with the number of binary collisions (Nbin) for pT 1.2 GeV/c. © 2008 The American Physical Society.

The QCD phase diagram lies at the heart of what the RHIC Physics Program is all about. While RHIC has been operating very successfully at or close to its maximum energy for almost a decade, it has become clear that this collider can also be operated at lower energies down to 5 GeV without extensive upgrades. An exploration of the full region of beam energies available at the RHIC facility is imperative. The STAR detector, due to its large uniform acceptance and excellent particle identification capabilities, is uniquely positioned to carry out this program in depth and detail. The first exploratory beam energy scan (BES) run at RHIC took place in 2010 (Run 10), since several STAR upgrades, most importantly a full barrel Time of Flight detector, are now completed which add new capabilities important for the interesting physics at BES energies. In this document we discuss current proposed measurements, with estimations of the accuracy of the measurements given an assumed event count at each beam energy.

STAR measurements of dihadron azimuthal correlations (Δφ) are reported in midcentral (20-60%) Au+Au collisions at sNN=200 GeV as a function of the trigger particle's azimuthal angle relative to the event plane, φs=|φt-ψEP|. The elliptic (v2), triangular (v3), and quadratic (v4) flow harmonic backgrounds are subtracted using the zero yield at minimum (ZYAM) method. The results are compared to minimum-bias d+Au collisions. It is found that a finite near-side (|Δφ|<π/2) long-range pseudorapidity correlation (ridge) is present in the in-plane direction (φs∼0). The away-side (|Δφ|>π/2) correlation shows a modification from d+Au data, varying with φs. The modification may be a consequence of path-length-dependent jet quenching and may lead to a better understanding of high-density QCD. © 2014 American Physical Society.