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- Hermann B. Frieboes, Fang Jin, Yao-Li Chuang, Steven M. Wise, John S. Lowengrub, Vittorio Cristini
- Journal of theoretical biology
- 2010

We extend the diffuse interface model developed in Wise et al. (2008) to study nonlinear tumor growth in 3-D. Extensions include the tracking of multiple viable cell species populations through a continuum diffuse-interface method, onset and aging of discrete tumor vessels through angiogenesis, and incorporation of individual cell movement using a hybrid… (More)

- Steven M. Wise, Andrew J. Sommese, Layne T. Watson
- ACM Trans. Math. Softw.
- 2000

Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be… (More)

- Steven M. Wise, Cheng Wang, John S. Lowengrub
- SIAM J. Numerical Analysis
- 2009

We present an unconditionally energy stable finite-difference scheme for the phase field crystal equation. The method is based on a convex splitting of a discrete energy and is semiimplicit. The equation at the implicit time level is nonlinear but represents the gradient of a strictly convex function and is thus uniquely solvable, regardless of time step… (More)

- Zhengzheng Hu, Steven M. Wise, Cheng Wang, John S. Lowengrub
- J. Comput. Physics
- 2009

- Steven M. Wise, Junseok Kim, John S. Lowengrub
- J. Comput. Physics
- 2007

We present efficient, second-order accurate and adaptive finite-difference methods to solve the regularized, strongly anisotropic Cahn–Hilliard equation in 2D and 3D. When the surface energy anisotropy is sufficiently strong, there are missing orientations in the equilibrium level curves of the diffuse interface solutions, corresponding to those missing… (More)

- Hermann B. Frieboes, John S. Lowengrub, +4 authors Vittorio Cristini
- NeuroImage
- 2007

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and… (More)

- Vittorio Cristini, Xiang-rong Li, John S. Lowengrub, Steven M. Wise
- Journal of mathematical biology
- 2009

We develop a thermodynamically consistent mixture model for avascular solid tumor growth which takes into account the effects of cell-to-cell adhesion, and taxis inducing chemical and molecular species. The mixture model is well-posed and the governing equations are of Cahn-Hilliard type. When there are only two phases, our asymptotic analysis shows that… (More)

- Xiaobing Feng, Steven M. Wise
- SIAM J. Numerical Analysis
- 2012

- Ying Chen, Steven M. Wise, Vivek B. Shenoy, John S. Lowengrub
- International journal for numerical methods in…
- 2014

In this paper, we extend the 3D multispecies diffuse-interface model of the tumor growth, which was derived in Wise et al. (Three-dimensional multispecies nonlinear tumor growth-I: model and numerical method, J. Theor. Biol. 253 (2008) 524-543), and incorporate the effect of a stiff membrane to model tumor growth in a confined microenvironment. We then… (More)

- Elaine L. Bearer, John S. Lowengrub, +6 authors Vittorio Cristini
- Cancer research
- 2009

Clinical outcome prognostication in oncology is a guiding principle in therapeutic choice. A wealth of qualitative empirical evidence links disease progression with tumor morphology, histopathology, invasion, and associated molecular phenomena. However, the quantitative contribution of each of the known parameters in this progression remains elusive.… (More)